fracture lecture of abaqus
DESCRIPTION
FRACTTRANSCRIPT
Basic Concepts of Fracture Mechanics
Lecture 1
L1.2
Modeling Fracture and Failure with Abaqus
Overview
• Introduction
• Fracture Mechanisms
• Linear Elastic Fracture Mechanics
• Small Scale Yielding
• Energy Considerations
• The J-integral
• Nonlinear Fracture Mechanics
• Mixed-Mode Fracture
• Interfacial Fracture
• Creep Fracture
• Fatigue
L1.3
Modeling Fracture and Failure with Abaqus
Overview
• This lecture is optional.
• It aims to introduce the necessary fracture mechanics concepts and
quantities that are relevant to the Abaqus functionality that is presented
in the subsequent lectures.
• If you are already familiar with these concepts, this lecture may be
omitted.
Introduction
L1.5
Modeling Fracture and Failure with Abaqus
Introduction
• Fracture mechanics is the field of solid mechanics that deals with the
behavior of cracked bodies subjected to stresses and strains.
• These can arise from primary applied loads or secondary self-
equilibrating stress fields (e.g., residual stresses).
L1.6
Modeling Fracture and Failure with Abaqus
Introduction
• Objective of fracture mechanics
• The objective of fracture mechanics is to characterize the local
deformation around a crack tip in terms of the asymptotic field around
the crack tip scaled by parameters that are a function of the loading and
global geometry.
Fracture Mechanisms
L1.8
Modeling Fracture and Failure with Abaqus
Fracture Mechanisms
• For engineering materials, such as metals, there are
two primary modes of fracture: brittle and ductile.
• Brittle fracture
• Cracks spread very rapidly with little or no
plastic deformation.
• Cracks that initiate in a brittle material tend to
continue to grow and increase in size provided
the loading will cause crack growth.
• Ductile fracture
• Three stages: void nucleation, growth, and
coalescence.
• The crack moves slowly and is accompanied by
a large amount of plastic deformation.
• The crack typically will not grow unless the
applied load is increased.
L1.9
Modeling Fracture and Failure with Abaqus
Fracture Mechanisms
• Brittle fracture in polycrystalline materials displays either cleavage
(transgranular) or intergranular fracture.
• This depends upon whether the grain boundaries are stronger or
weaker than the grains .
Cleavage fracture
L1.10
Modeling Fracture and Failure with Abaqus
Fracture Mechanisms
• Ductile fracture has a dimpled, cup-and-cone fracture appearance .
• Ductile fracture surfaces have larger necking regions and an
overall rougher appearance than a brittle fracture surface.
L1.11
Modeling Fracture and Failure with Abaqus
Fracture Mechanisms
• Fracture process zone
• The fracture process zone is the region around the crack tip where
dislocation motions, material damage, etc. occur.
• It is a region of nonlinear deformation.
• The fracture process zone size is characterized by
• a number of grain sizes for brittle fracture or
• either inclusion or second phase particle spacings for ductile
fracture.
• Different theories have been advanced to describe the fracture process
in order to develop predictive capabilities
• LEFM
• Cohesive zone models
• EPFM
• Etc.
Linear Elastic Fracture Mechanics
L1.13
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Fracture modes
• Linear Elastic Fracture Mechanics (LEFM)
considers three distinct fracture modes: Modes
I, II, and III
• These encompass all possible ways a crack
tip can deform.
• Mode I:
• The forces are perpendicular to the crack,
pulling the crack open.
• This is referred to as the opening mode.
L1.14
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Mode II:
• The forces are parallel to the crack.
• One force pushes the top half of the
crack back and the other pulls the
bottom half of the crack forward, both
along the same line.
• This creates a shear crack: the
crack slides along itself.
• This is referred to as the in-plane shear
mode.
• The forces do not cause out-of-
plane deformation.
L1.15
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Mode III:
• The forces are transverse to the crack.
• This causes the material to separate
and slide along itself, moving out of
its original plane
• This is referred to as the out-of-plane
shear mode.
• The objective of LEFM is to predict the critical
loads that will cause a crack to grow in a brittle
material.
L1.16
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Stress intensity factor
• For isotropic, linear elastic materials, LEFM characterizes the local
crack-tip stress field in the linear elastic (i.e., brittle) material using a
single parameter called the stress intensity factor K.
• K depends upon the applied stress, the size and placement of the
crack, as well as the geometry of the specimen.
• K is defined from the elastic stresses near the tip of a sharp crack
under remote loading (or residual stresses).
• K is used to predict the stress state ("stress intensity") near the tip
of a crack.
• When this stress state (i.e., K) becomes critical, a small crack
grows ("extends") and the material fails.
• This critical value is denoted KC and is known as the fracture
toughness (it is a material property; discussed further later).
L1.17
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Asymptotic crack tip solutions
• The stress and strain fields in the vicinity of the crack tip are expressed
in terms of asymptotic series of solutions around the crack tip.
• They are valid only is a small region near the crack tip.
• This size of this region is quantified by small scale yielding
assumptions (discussed later).
• The stress intensity factor is the parameter that relates the local
crack-tip fields with the global aspects of the problem.
L1.18
Modeling Fracture and Failure with Abaqus
• The leading-order terms of the asymptotic solution are:
where
r is the distance from the crack tip,
= atan(x2/x1),
KI is the Mode I (opening) stress intensity factor,
KII is the Mode II (in-plane shear) stress intensity factor,
KIII is the Mode III (transverse shear) stress intensity factor, and the
fija define the angular variation of the stress for mode a.
Linear Elastic Fracture Mechanics
( , ) ( ) ( ) ( )2 2 2
I II IIII II IIIij ij ij ij
K K Kr f f f
r r r
,
x1
x2 r
L1.19
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Crack-tip singularity
• The predicted stress state at the crack tip in a linear elastic (brittle)
material possesses a square-root singularity:
• In reality, the crack tip is surrounded by the fracture process zone
where plastic deformation and material damage occur.
• Inside this zone, the LEFM solution is not valid.
• Outside of this zone (i.e., sufficiently "far" from the fracture
process zone), the LEFM is accurate provided the
plastic/damage zone is “small enough.”
• This is called small-scale yielding (discussed further later).
1
r .
L1.20
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Some comments on fracture toughness
• Fracture toughness is strongly dependent on temperature.
• The brittle-ductile transition temperature range depends on the material.
• For many common metals it may lie within the reasonable operating
temperature range for the design, so the temperature dependence
of the fracture toughness must be considered.
Fra
ctu
re t
ou
gh
ness
Temperature
L1.21
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Experimentally, the fracture toughness KC is a function of specimen
thickness.
• Since plane strain gives the practical minimum value of KC …
• The plane strain value is usually the value that is determined
experimentally.
• However, if the application is fracture of thin sheets of material, KC
values somewhere between the plane stress and plane strain values
may be appropriate.
Fra
ctu
re t
ou
gh
ne
ss
Thickness →
KC
L1.22
Modeling Fracture and Failure with Abaqus
• Aside from temperature and thickness, the fracture toughness is also a
function of the crack extension.
• The fracture toughness as a function of crack extension is called the
resistance curve (shown below).
• The resistance curve is used to predict crack growth stability.
Linear Elastic Fracture Mechanics
Variation in fracture toughness
with crack growth is Kr(Da):
Kr(0)= KC
brittle
ductile
L1.23
Modeling Fracture and Failure with Abaqus
Linear Elastic Fracture Mechanics
• Crack growth and stability
• The condition for continued crack growth for a crack length a + Da is
• The condition for stable continued crack growth is
( )applied RK K a D .
applied R
load
K dK
a d a
D.
Small-Scale Yielding
L1.25
Modeling Fracture and Failure with Abaqus
Small-Scale Yielding
• Small-scale yielding (SSY) means the region of inelastic deformation at
the crack tip is contained well within the zone dominated by the LEFM
asymptotic solution.
• For LEFM to be valid, there must be an annular region around the
crack tip in which the asymptotic solution to the linear elasticity
problem gives a good approximation to the complete stress field.
K-dominated zone
Transition zone
Plastic zone
L1.26
Modeling Fracture and Failure with Abaqus
Small-Scale Yielding
• The size of the process zone and the plastic region must be
sufficiently small so that this is true. Typical shapes of plastic zones
follow:
plane strain plane stress
(diffuse)
plane stress
(Dugdale)
L1.27
Modeling Fracture and Failure with Abaqus
Small-Scale Yielding
• We can estimate the plastic zone size, rp, by setting 22 = 0 in the LEFM
asymptotic solution, where 0 is the yield stress. This gives (for Mode I)
• Since the tractions across the boundary of the plastic zone have no net
force or moments (St. Venant’s principle), the effect on the elastic field
surrounding the plastic zone decays rapidly with distance from the
boundary, becoming negligible at ~3rp.
• LEFM predicts infinite stress at the crack tip—obviously this is unrealistic.
• But we can use LEFM results if the region of inelastic deformation near
the crack tip is small enough that there is a finite zone outside this
region where the LEFM asymptotic solution is accurate.
2 2
0 0
1 1
2 6
I Ip
K Kr
.
L1.28
Modeling Fracture and Failure with Abaqus
• If a is a characteristic dimension in the problem, such as remaining ligament
size or thickness or crack length, then, to have a finite zone rK in which the
K-field dominates, we need
or
• This is the limit on specimen size in ASTM Standard E-399 for a valid
KIC test.
• KIC is KC (the fracture toughness) in Mode I.
• The fracture toughness represents the critical value of K required
to initiate crack growth.
2
0
1/5 3
2
ICK p
Ka r r
2
0
2.5 ICKa
.
ASTM Standard for
validity of LEFM
Small-Scale Yielding
L1.29
Modeling Fracture and Failure with Abaqus
Small-Scale Yielding
• For some typical metal materials rp is calculated by matching the yield
stress to the Mises stress of the K field and the minimum characteristic
length is calculated using the ASTM standard limit.
• For materials with high fracture toughness the size of the specimen
for a valid fracture test is very large.
MaterialT
(ºC)
0
(MPa)
KIC
(MN/m3/2)
rp
(mm)
Characteristic
dimension
(mm)
A061-T651 (Al) 20 269 33 5 38
A075-T651 (Al) 20 620 36 0.35 8.4
AISI 4340 (Steel) 0 1500 33 0.05 1.2
A533-B (Steel) 93 620 200 11 260
Energy Considerations
L1.31
Modeling Fracture and Failure with Abaqus
Energy Considerations
• Energy principles play an important role in studying crack problems.
• This is motivated by the fact that crack propagation always involves
dissipation of energy. Sources of energy dissipation include:
• Surface energy, plastic dissipation, etc.
• By considering fracture from an energetic point of view, crack
growth criteria can be postulated in terms of energy release rates.
• This approach offers an alternative to the K-based fracture
criteria discussed earlier and reinforces the connection
between global and local fields in fracture problems.
• The energy release rate is a global parameter while the stress
intensity factor is a local crack-tip parameter.
L1.32
Modeling Fracture and Failure with Abaqus
Energy Considerations
• The energy available to grow a crack
is defined as
where PE is the potential energy and
G is the Energy Release Rate.
• We consider the difference in the
energy for two essentially identical
specimens, one with crack length a,
the other with crack length a + Da.
• The area under the load-
displacement curve gives -PE for
elastic materials.
( )
Loads
PE
a
-
,G
L1.33
Modeling Fracture and Failure with Abaqus
Energy Considerations
• For isotropic linear elastic materials, one can show that
and
• In a three-dimensional body under general loading that contains a crack
with a smoothly changing crack-tip line, the energy release rate
(assuming linear elasticity) per unit crack front length is
• Thus, we see the stress intensity factors are directly related to the
energy release rate associated with infinitesimal crack growth in an
isotropic linear elastic material.
221 v
KE
- for plane strainG
2K
E for plane stress.G
22 2 21 1
( )2
I II III
vK K K
E G
- .G
L1.34
Modeling Fracture and Failure with Abaqus
Energy Considerations
• Initiation of crack growth in SSY
• The necessary condition for crack growth expressed in terms of the
energy release rate is G GC.
• GC is a material property and represents the energy per unit crack
advance going into:
• the formation of new surfaces,
• the fracture process, and
• plastic deformation.
• As noted earlier, for linear elastic materials, G and K are related.
• This leads to an alternative condition for K KC.
• Recall KC is the fracture toughness of the material.
The J-integral
L1.36
Modeling Fracture and Failure with Abaqus
The J-integral
• The J-integral is used in rate-independent quasi-static fracture analysis
to characterize the energy release associated with crack growth.
• It can be related to the stress intensity factor if the material
response is linear.
• As will become apparent in the next section, it also has the
advantage that it provides a method for analyzing fracture in
nonlinear materials.
L1.37
Modeling Fracture and Failure with Abaqus
• J is defined as follows:
• It is path independent when contours are taken around a crack tip.
• The definition of J assumes:
• The material is homogeneous in the crack direction.
• The material is elastic.
• For linear elastic materials, the value of J is equal to the energy
release rate associated with crack advance:
x1
x2
The J-integral
11
iij j
uJ Wn n ds
x
-
J G
L1.38
Modeling Fracture and Failure with Abaqus
The J-integral
• J in small-scale yielding
• Choose , the contour for J, to fall entirely within the annular region in
which the K fields dominate.
• The integrand for J can be evaluated directly in terms of the (known) Kfields. Direct calculation for Mode I in a linear elastic material gives
22
2
1
1
I
I
vJ K
E
J KE
-
for plane strain and
for plane stress.
G
G
3rp
Nonlinear Fracture Mechanics
L1.40
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• LEFM applies when the nonlinear deformation of the material is confined
to a small region near the crack tip.
• For brittle materials, it accurately establishes the criteria for failure.
• However, severe limitations arise when the region of the material
subject to plastic deformation before a crack propagates is not
negligible.
• Nonlinear fracture mechanics attempts to extend LEFM to consider
inelastic effects.
• The theory is sometimes called Elastic-Plastic Fracture Mechanics
(EPFM).
• However, the theory is not based on an elastic-plastic material
model, but rather a nonlinear elastic material.
L1.41
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• Consider a material that has a power-law hardening form,
where 0 is the effective yield stress, e0 = 0 / E is the associated yield
strain, E is Young's modulus, and a and n are chosen to fit the stress-
strain data for the material.
0 0
ne
ae
,
n
L1.42
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• For such a material, Hutchinson, Rice, and Rosengren (extended to mixed
mode loading by Shih) showed that the near-tip fields have the form
• Here is the displacement relative to the displacement of the crack
tip, . These fields are commonly referred to as the HRR crack-tip fields.
ˆi iu u-ˆiu
1
1
00 0
1
00 0
1
00 0
( )
( )
ˆ ( )
n
ij ijn
n
n
ij ijn
n
n
i i in
J
I r
J
I r
Ju u r u
I r
a e
e e e a e
ae a e
-
,
,
.
Loading parameter is J
L1.43
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• Why not elastic-plastic?
• The HRR field assumes a nonlinear
elastic power law material:
• Under monotonic loading, this
nonlinear elastic material can be
matched to the behavior of an
elastic-plastic material whose
hardening behavior is accurately
modeled by a power law.
• Thus, evaluating J allows us to
characterize the strength of the
singularity in the crack-tip region in
an elastic-plastic material subjected
to monotonic loading.
0 0
ne
ae
L1.44
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• In unloading situations, the HRR fields do not describe the state around
the crack tip, and hence J does not characterize the strength of the
stress state ahead of a crack tip for plastic materials. Use caution when:
• The loading is not monotonic and an incremental plasticity material
is used
• Crack growth occurs under monotonic loading (individual material
particles may unload even when the overall structure is being
loaded).
• The HRR solution:
• Gives the leading term in an asymptotic expansion of the
deformation around the crack tip for a power law material; and
• Does not take into account finite-strain effects.
L1.45
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• Some comments on the HRR fields
• The HRR fields, thus, describe the near-tip crack fields in terms of J.
• J gives the strength of the near-tip singularity in any power-law material
(nonlinear elastic or plastic) solid
• Recall that in LEFM K plays this role in linear elastic materials.
• J-based fracture mechanics is applied in much the same way as LEFM.
• Crack growth initiates when J reaches a critical value: J JC .
• To apply the theory, must ensure conditions for J-dominance are
satisfied (discussed next).
L1.46
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• J-dominance
• J-dominance refers to situations when J can be used as a method of
predicting fracture.
• In general, J is an adequate characterization when there exists a state of
high triaxial tension (high triaxiality) ahead of the crack tip.
• High triaxiality ahead of the crack tip leads to low fracture
toughness.
• Examples: states of small-scale and well-contained yielding (where
the plastic zone is surrounded by an elastic zone):
• Deeply notched bend specimen
c «dd
c
L1.47
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• In some situations the crack-tip stress field does not exhibit high triaxiality.
• Example: large-scale yielding (the plastic zone extends to the free
boundaries of the body):
• Fully plastic flow of single-edge cracked specimens under tension
loading
• Shallow cracks under bending
• Center-cracked panel
• A two-parameter approach can be used to extend the fracture
characterization to such cases (discussed next).
L1.48
Modeling Fracture and Failure with Abaqus
Nonlinear Fracture Mechanics
• Two-parameter fracture mechanics
• The Williams’ expansion of the Mode I stress field about a sharp crack in
a linear elastic body with respect to r, the distance from the crack tip, is
• The T-stress thus represents a stress parallel to the crack faces.
• The magnitude of the T-stress affects the size and shape of the
plastic zone and the region of tensile triaxiality ahead of the crack
tip.
• For positive T-stress, J-dominance exists and a single parameter Jcan be used for a fracture criterion.
• For negative T-stress, a two-parameter approach (J, T) is required
to characterize the stress fields.
1/21 1( , ) ( ) ( )
2
Iij ij i j
Kr f T O r
r
.
Mixed-Mode Fracture
L1.50
Modeling Fracture and Failure with Abaqus
Mixed-Mode Fracture
• Under general loading almost all theories for the direction of crack growth
assume or predict that the continued crack growth will be with KII = 0.
• Can assume that macroscopic cracks growing with continuously
turning tangents will advance straight ahead, presumably under Mode
I conditions.
• The crack curvature will evolve in such a way as to maintain this in
response to the loading.
• If the loading changes such that the local crack-tip stress field
experiences a large change in local stress intensities, mixed-mode
fracture will occur.
L1.51
Modeling Fracture and Failure with Abaqus
Mixed-Mode Fracture
• Different criteria for homogeneous,
isotropic linear elastic materials have
been proposed, including:
• The maximum tangential
stress criterion.
• The maximum energy release
rate criterion.
• The KII = 0 criterion.
• Although all three imply that
KII = 0 as the crack extends, they
predict slightly different angles for
crack initiation.
Comparison of predictions of crack
propagation direction for different
ratios of KII / KI
Interfacial Fracture
L1.53
Modeling Fracture and Failure with Abaqus
Interfacial Fracture
• Many engineering applications involve bonded materials.
• Examples:
• adhesive joints;
• protective coatings;
• composite materials;
• etc.
• Engineers must be able to predict the strength of the bond.
• Interfacial fracture mechanics provides a method by which to do this.
• It extends LEFM to predict the behavior of cracks between two
linear elastic materials.
L1.54
Modeling Fracture and Failure with Abaqus
Interfacial Fracture
• Once a crack has started to grow in an
isotropic, homogeneous material, it
generally does so in an opening mode;
that is, in Mode I.
• A crack lying on an interface can
kink off the interface and grow
under Mode I conditions, or it can
grow along the interface under
mixed mode conditions.
• Whether the crack kinks off the
interface or propagates along it is
frequently determined through energy
considerations.
L1.55
Modeling Fracture and Failure with Abaqus
Interfacial Fracture
• If the crack kinks off the interface, the fact that there is an interface is
important only in how it influences the stress and strain fields.
• If the crack grows along the interface, it grows under mixed mode
conditions due to material asymmetry and possibly (though not
necessarily) under mixed remote loading conditions.
• In such situations the conditions for crack growth depend on the
interface properties. It is not sufficient to define crack initiation and
growth criterion based on the conventional fracture toughness, KC.
• Specifically KC = KC ().
• Toughness depends strongly on the mode mixity .
L1.56
Modeling Fracture and Failure with Abaqus
Interfacial Fracture
• Asymptotic fields
• The asymptotic stress field for an interfacial crack between linear elastic
materials is given by
where K* = K1 iK2 is the complex stress intensity factor (i.e., it has real
and imaginary parts) and is a complex function of the angle
and material mismatch parameter e :
*
Re ( , )2
iij ij
Kr
r
e e
1 2 2 1
1 2 2 1
( 1) ( 1)1 1log ,
2 1 ( 1) ( 1)
3
1
3 4
e
- - --
-
-
where , and
for plane stress
for plane strain, axi, 3D
,ij e
L1.57
Modeling Fracture and Failure with Abaqus
Interfacial Fracture
• The complex exponent rie indicates that the stresses will oscillate near
the crack tip:
• Both the stresses and crack opening displacements will oscillate wildly
as the crack tip is approached.
• At some distance ahead of the crack tip, the fields settle down.
• The fracture criterion should be measured at this point. Provided the
location of this point is the same in different specimens, a fracture
criterion is valid.
Creep Fracture
L1.59
Modeling Fracture and Failure with Abaqus
Creep Fracture
• High-temperature fracture
• For temperatures above 0.3M (where M is the melting temperature on
an absolute scale), metals will typically creep.
• In plastics creep can occur even at room temperature.
• There are typically two mechanisms that are active in creep fracture:
• Blunting of the crack tip due to a relaxing stress field.
• This tends to retard crack growth.
• Accumulation of creep damage (microcracks, void growth, and
coalescence).
• This enhances crack growth.
• Steady-state creep crack growth occurs when the two effects balance
one another.
L1.60
Modeling Fracture and Failure with Abaqus
Creep Fracture
• The stress state around a crack tip in a material that can creep is more
complicated than for the corresponding plasticity problem.
• Because of the time-dependent effects there is no one parameter that
can characterize the stress state around the crack tip for all
possibilities.
• This makes measuring the relevant parameters more difficult.
• Hence, creep fracture is not as well established as elastic-plastic
fracture.
Initially, the crack-tip field is the elastic field.
Stationary crack: around the
crack tip (RR field); around this field
(K field).
Growing crack: region develops where
(HR field), which is in turn surrounded by the RR
field. Eventually the HR field envelops the RR
field (which ultimately disappears).
( ) ( )cr elO O e e( ) ( )el crO O e e
( ) ( )el crO O e e
L1.61
Modeling Fracture and Failure with Abaqus
Creep Fracture
• Contour integrals
• The contour integral for creep fracture is called the C(t)-integral.
• It plays an analogous role to the J-integral in the context of time-
dependent creep fracture.
• Its development assumes a power law creep material:
• The C(t)-integral is proportional to the rate of growth of the crack-tip
creep zone for a stationary crack under small-scale creep conditions:
• Under steady-state creep conditions, when creep dominates throughout
the specimen, C(t) becomes path independent and is known as C*.
0
11
( )1r
jij ij i ij
unC t n n ds
n x e
-
.
00
n
el cr
E
e e e e
L1.62
Modeling Fracture and Failure with Abaqus
Creep Fracture
• Asymptotic fields for stationary crack
• The near tip stress and strain fields were obtained by Riedel and Rice in
terms of C(t). They are known as the RR fields and are analogous to the
HRR fields in power law hardening plasticity.
Here In is a function of n and the magnitude of is approximately
1.
1
1
00 0
1
00 0
( )( , )
( )( , )
n
ij ijn
n
ncrij ij
n
C tn
I r
C tn
I r
e
e e e e
( , )ij n
C(t) acts like a time-dependent
loading parameter
Crack tip fields are
similar to those for
an elastic-plastic
material
L1.63
Modeling Fracture and Failure with Abaqus
Creep Fracture
• Small-scale vs. extensive creep
• For the case of no crack growth the
loading parameters that characterize the
crack-tip fields are reasonably well
understood.
• Under small-scale creep conditions
with secondary creep, K is the loading
parameter characterizing the crack-tip
field.
• For extensive secondary creep C* is
a loading parameter characterizing
the crack-tip field upon which a
fracture criterion may be based.
• Suitable criteria for crack extension that
will predict an initiation time for crack
growth for general cases are not yet
available.
( )K
r
creep
zone
Small-scale creep
Extensive creep
Fatigue
L1.65
Modeling Fracture and Failure with Abaqus
Fatigue
• Fatigue is a special kind of failure in which cracks gradually grow under
a prolonged period of subcritical loading.
• It is the single most common cause of failure in metallic structures.
• The Paris Law can be used to predict crack growth as a function of
cycles (or time):
max min
( ) ,ndaC K
dN
K K K
D
D -
where
Damage at the ball grid array
(BGA) in a solder joint after
2700 thermal loading cycles
L1.66
Modeling Fracture and Failure with Abaqus
Fatigue
• Abaqus offers a direct cyclic low-cycle fatigue capability based on the
Paris Law.
• Models progressive damage and failure both in bulk materials and
at material interfaces for a structure subjected to a sub-critical cyclic
loading.
• For more advanced fatigue analysis capabilities, consult www.safetechnology.com.
• fe-safe is a suite of fatigue analysis software that has a direct
interface to Abaqus.
Modeling Cracks
Lecture 2
L2.2
Modeling Fracture and Failure with Abaqus
Overview
• Crack Modeling Overview
• Modeling Sharp Cracks in Two Dimensions
• Modeling Sharp Cracks in Three Dimensions
• Finite-Strain Analysis of Crack Tips
• Limitations Of 3D Swept Meshing For Fracture
• Modeling Cracks with Keyword Options
Crack Modeling Overview
L2.4
Modeling Fracture and Failure with Abaqus
Crack Modeling Overview
• A crack can be modeled as either
• Sharp
• Small-strain analysis
• Singular behavior at the crack tip
• Requires special attention
• In Abaqus, a sharp crack is modeled
using seam geometry
• Blunted
• Finite-strain analysis
• Non-singular behavior at crack tip
• In Abaqus, a blunted crack is modeled
using open geometry
• For example, a notch
L2.5
Modeling Fracture and Failure with Abaqus
Crack Modeling Overview
• Mesh refinement
• Crack tips cause stress concentrations.
• Stress and strain gradients are large as a crack tip is approached.
• The finite element mesh must be refined in the vicinity of the crack
tip to get accurate stresses and strains.
• The J-integral is an energy measure; for LEFM, accurate J values can
generally be obtained with surprisingly coarse meshes, even though the
local stress and strain fields are not very accurate.
• For plasticity or rubber elasticity, the crack-tip region has to be
modeled carefully to give accurate results.
L2.6
Modeling Fracture and Failure with Abaqus
Crack Modeling Overview
• The crack-tip singularity in small-strain analysis
• For mesh convergence in a small-strain analysis, the singularity at the
crack tip must be considered.
• J values are more accurate if some singularity is included in the
mesh at the crack tip than if no singularity is included.
• The stress and strain fields local to the crack tip will be modeled
more accurately if singularities are considered.
• In small-strain analysis, the strain singularity is:
• Linear elasticity r -½
• Perfect plasticity r -1
• Power-law hardening r -n/(n+1)
Modeling Sharp Cracks in Two
Dimensions
L2.8
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• In two dimensions…
• The crack is modeled as an internal edge
partition embedded (partially or wholly) inside
a face.
• This is called a seam crack
• The edge along the seam will have
duplicate nodes such that the elements
on the opposite sides of the edge will not
share nodes.
• Typically, the entire 2D part is filled with a
quad or quad-dominated mesh.
• At the crack tip, a ring of triangles are
inserted along with concentric layers of
structured quads.
• All triangles in the contour domains must
be represented as degenerated quads.
L2.9
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Example: Slanted crack in a plate
• In Abaqus/CAE a seam is defined by
through the Crack option underneath the
Special menu of the Interaction module.
• The seam will generate duplicate
nodes along the edge.
Seam
Create face partition to represent
the seam; assign a seam to the
partition.
L2.10
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• To define the crack, you must specify
• Crack front and the crack-tip
• Normal to the crack plane or the
direction of crack advance
• The crack advance direction is
called the q vector.
The crack extension direction (q vector)
defines the direction in which the crack
would extend if it were growing.
It is used for contour integral
calculations.
Crack tip
same as
crack
front in
this case
Select the vertex at either
end as the crack front.
(Repeat for the other end.)
L2.11
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Other options for defining the crack front and crack tip
Crack front may be:
Vertex/Node
Edges/Element edges
Faces/Elements
Crack tip may be:
Vertex/Node
Geometric
Instances
Orphan
Mesh
Geometric
Instances
Orphan
Mesh
Crack tip for an
orphan mesh
Crack front for a
geometric instance
L2.12
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Example: crack on a symmetry plane
• If the crack is on a symmetry plane, you
do not need to define a seam.
• This feature can be used only for
Mode I fracture.
Crack tip
Crack normal
L2.13
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Modeling the crack-tip singularity with second-order quad elements
• To capture the singularity in an 8-node isoparametric element:
• Collapse one side (e.g., the side made up by nodes a, b, and c) so
that all three nodes have the same geometric location at the crack
tip.
• Move the midside nodes on the sides connected to the crack tip to
the ¼ point nearest the crack tip.
L2.14
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• If nodes a, b, and c are free to move independently, then
everywhere in the collapsed element.
• If nodes a, b, and c are constrained to move together, A = 0:
• The strains and stresses are square-root singular (suitable for
linear elasticity).
• If nodes a, b, and c are free to move independently and the midside
nodes remain at the midsides, B = 0 :
• The singularity in strain is correct for the perfectly plastic case.
• For materials in between linear elastic and perfectly plastic (most metals),
it is better to have a stronger singularity than necessary.
• The numerics will force the coefficient of this singularity to be small.
0A B
rr r
as
L2.15
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Usage:
Quarter-point midside
nodes on the sides
connected to the crack tip
The crack tip nodes are
constrained: r -½ singularity
The crack tip nodes are
independent: r -1 singularity
1,1,2,3
2
13
1,2,3,4
3
1, 24
L2.16
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Aside: Controlling the position of midside nodes for orphan meshes
• Singularity controls cannot be applied to orphan meshes.
• Use the Mesh Edit tools to adjust their position.
L2.17
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• If the side of the element is not collapsed but the midside nodes on the
sides of the element connected to the crack tip are moved to the ¼point:
• The strain is square root singular along the element edges but not in
the interior of the element.
• This is better than no singularity but not as good as the collapsed
element.
nodes moved to ¼ points
L2.18
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Angular resolution
• We need enough elements to resolve the angular dependence of the
strain field around the crack tip.
• Reasonable results are obtained for LEFM if typical elements
around the crack tip subtend angles in the range of 10 (accurate) to
22.5 (moderately accurate).
• Nonlinear material response usually requires finer meshes.
L2.19
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Modeling the crack-tip singularity with first-order quad elements
• Collapsing the side of a first-order quadrilateral element with
independent nodes on the collapsed side gives
0A
rr
as .
L2.20
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Example: Slanted crack in a plate
• To enable the creation of degenerate quads, you must create swept
meshable regions around the crack tips (using partitions) and specify a
quad-dominated mesh.
Quad-dominated mesh + swept
technique for the circular regions
surrounding the crack tips
CPE8R elements; typical nodal
connectivity shows repeated node at crack tip:
8, 8, 583, 588, 8, 1969, 1799, 1970
All crack-tip elements repeat node 8 in
this example (nodes are constrained).
Quadratic element type
assigned to part
Quarter-
point
nodes
24 elements around
crack tip: 15 angles
L2.21
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Example (cont’d):
Alternate meshes
• No degeneracy:
• Degenerate with
duplicate nodes:
With swept meshable region:
CPE6M elements at crack tip —
cannot be used for fracture
studies in Abaqus.
CPE8R elements at crack tip but no
repeated nodes:
1993, 1992, 583, 588, 2016, ...
Coincident nodes
located at crack tip
With arbitrary mesh,
singularity only along edges
connected to crack tip.
L2.22
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Two Dimensions
• Example (cont’d): Deformed shape
Focused mesh; deformation
scale factor = 100
Arbitrary mesh;
deformation scale
factor = 100
Modeling Sharp Cracks in Three
Dimensions
L2.24
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• In three dimensions…
• The seam crack is modeled as a
face partition that is either partially
or totally embedded into a solid
body.
• This can be done by
partitioning or using a cut
(Boolean) operation.
• The face along the seam will have
duplicate nodes such that the
elements on the opposite sides of
the face will not share nodes.
• Wedge elements must be created
along the crack front.
• Generally, this will require
partitioning.
Penny-shaped seam
crack: Full modelQuarter model
Meshed modelWedge elements
L2.25
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Options for defining the crack front and crack line
Crack front may be:
Edges/Element edges
Faces/Element faces
Cells/Elements
Geometric
Instances
Crack line may be:
Edges/Element edges
Orphan
Mesh
Geometric
Instances
Orphan
Mesh
Crack line for an
orphan mesh
Crack front for a
geometric instance
L2.26
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Specifying the crack growth direction in three dimensions
• In 3D you can specify either the
• normal to the crack plane (only when the crack is planar)
or the
• virtual crack extension direction (the q vector).
• Only a single q vector can be defined for geometric instances.
• The implications of this will be discussed shortly.
L2.27
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Modeling the crack-tip singularity in three dimensions
• 20-node and 27-node bricks can be used with a collapsed face to create
singular fields.
C3D20(RH)
2 nodes collapsed to
the same location
crack line
3 nodes collapsed to
the same location
midplane
edge plane
midside nodes
moved to ¼ points
L2.28
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• On an edge plane (orthogonal to the
crack line):
Crack line
Double-edge notch specimen
(symmetry model)
0A B
rr r
as0
Ar
r as
Edge plane nodes
displace together
Edge plane nodes
displace independently
0B
rr
as
L2.29
Modeling Fracture and Failure with Abaqus
• On a midplane for 20-node bricks:
• If the two nodes on the collapsed face at the midplane can displace
independently, r -1 at the midplane (i.e., element interior).
• If on each plane there is only one node along the crack line, no
singularity is represented within the element.
• In either case the interpolation is not the same on the midplane as
on an edge plane.
• This generally causes local oscillations in the J-integral values
along the crack line.
Modeling Sharp Cracks in Three Dimensions
L2.30
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• On a midplane for 27-node bricks with all the extra nodes on the
element faces:
C3D27(RH)
3 nodes collapsed to
same location
midplane
edge plane
3 nodes collapsed to same
location
centroid
crack line
L2.31
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• If all midface nodes and the centroid node are included and moved with
the midside nodes to the ¼ points, the singularity can be made the same
on the edge planes and midplane.
• Abaqus does not allow the centroid node to be moved from the
geometric centroid of the element.
• Therefore, the behavior at the midplane will never be the same as at
the edge planes.
• This usually causes some small oscillation of the crack fields along
the crack line.
• The midface node marked “A” is frequently omitted.
• This creates differences in interpolation between the midplane and
the edge planes and, hence, causes further oscillation in the crack-
tip fields.
• These oscillations are minor in most cases.
L2.32
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Example: Conical crack in a half-
space
• A conical crack in an infinite half-
space is considered.
• Only the aspects related to the
geometric modeling are
considered here.
• The results of this analysis
(J-integral values, etc) will
be considered in the next
lecture.
• The modeling procedure is
outlined next.
L2.33
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
Example (cont’d): Create the basic geometry
• Because of symmetry, only a quarter model is created
Large solid block (300 × 300 ×300)
used to represent the half-space. Conical shell of revolution (revolved 90º);
this will be used to cut the block.
1
a = 15
q = 45º
r = 10
L2.34
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
Example (cont’d): Merge the block and cone
• This will create the edges and surface
necessary to define the seam and the crack.
Instance and merge the
two parts to create a
new part. The instance
must be independent.
2
L2.35
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
Example (cont’d): Define the seam and the crack front/line
Only one q vector can be defined
for geometry. The q vectors will
be adjusted at the end of the
modeling process by editing an
orphan mesh.
3
L2.36
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
Example (cont’d): Partition the block for meshing
A small curved tube is centered
at the crack tip; this region is
meshed with a single layer of
wedge elements. This mesh is
swept along the length of the
tube.
The regions surrounding the
crack front are partitioned to
permit structured meshing.
4
L2.37
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Aside: Why is the small curved tube needed?
The swept meshing technique sweeps a
mesh through a cross section.
For the curved tube, this implies the
sweep direction is along its length. In
order for Abaqus to automatically create
a focused mesh at the crack tip,
however, it would need to sweep around
the circumference.
To overcome this, two concentric tubes
are used; the smaller one is meshed
with a single layer of wedge elements
(which is then swept along the length of
the tube).
If only a single curved tube was created
(shown at right), the mesh around the
crack tip would be arbitrary—not
focused (wedge elements not created).
L2.38
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Aside: What about the seam?
• After all the partitions are created for meshing purposes, the definition of
the seam remains intact.
Mesh seam
L2.39
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
Example (cont’d): Mesh the part
• Specify appropriate edge seeds to create
a focused mesh around the crack front
with minimal mesh distortion.
5
L2.40
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
Example (cont’d): Adjust the q vectors
• As noted earlier, only a single q vector
can be defined for geometry. As seen in
the figure, the vector that was defined is
only accurate at the left end of the crack
line.
• Individual q vectors can be defined on
an orphan mesh, however. Thus,
either…
• Create a mesh part (Mesh module)
or
• Write an input file and import the
model
• This approach has the
advantage that it preserves
attributes (sets, loads, etc).
To take advantage of the input file
approach, define a set that
contains the conical region before
writing the input file. Then you will
be able to easily create a display
group based on this set when
manipulating the orphan mesh.
6
L2.41
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• For the orphan mesh, adjust each
vector individually
To redefine
this particular
vector, select
these nodes
as the start
and end points
of the vector.
L2.42
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• For all elements, the singularities are modeled best if the element edges
are straight.
• In three dimensions the planes of the element perpendicular to the crack
line should be flat.
• If they are not, when the midside nodes are moved to the ¼ points,
the Jacobian of the element at some integration points may be
negative.
• One way to correct this is to move the midside nodes slightly away
from the ¼ points toward the midpoint.
L2.43
Modeling Fracture and Failure with Abaqus
Modeling Sharp Cracks in Three Dimensions
• Example: Conical crack model
Finite-Strain Analysis of Crack Tips
L2.45
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• Finite-strain analyses:
• Singular elements should not be used (normally).
• The mesh must be sufficiently refined to model the very high strain
gradients around the crack tip if details in this region are required.
• Even if only the J-integral is required, the deformation around the
crack tip may dominate the solution and the crack-tip region will
have to be modeled with sufficient detail to avoid numerical
problems.
L2.46
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• Physically, the crack tip is not perfectly sharp, and such modeling makes it
difficult to obtain results.
• Instead, we model the tip as a blunted notch, with a suggested radius
10-3rp.
• Here, rp is the size of the plastic zone (discussed in Lecture 1).
• The notch must be small enough that under the applied loads, the
deformed shape of the notch no longer depends on the original
geometry.
• Typically, the notch must blunt out to more than four times its
original radius for this to be true.
L2.47
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• Geometric modeling of blunt cracks
• In 2D, the geometry of a blunted (or
open) crack is modeled as a cut
having a significant thickness.
• Meshing is done in the usual way.
• A very fine mesh is required at
the crack tip.
• This can be achieved by simply
assigning small element sizes to
the notch.
L2.48
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• 3D open cracks can be created in
Abaqus/CAE in one of two ways:
• Adding a Cut feature in the
Part module.
• Subtracting a flaw from the
original part with a Boolean
operation in the Assembly
module.
• Hex meshing more difficult
due to irregular geometry.
• Creating a fine mesh at the
crack front generally requires
many partitions.
Quarter model Meshed model
Partitions to control mesh Refined mesh
Penny shaped open
crack: Full model
L2.49
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• The size of the elements around the notch must be about 1/10th the
notch-tip radius.
SEN specimen
crack-tip mesh
rnotch
10% of rnotch
Biased edge seeds can
reduce the size of the mesh
by focusing small elements
towards the crack tip.
L2.50
Modeling Fracture and Failure with Abaqus
• For J-integral evaluation, the region on the surface of the blunted notch
should be used to define the crack front.
• For the J- and Ct-integrals to be path independent, the crack surfaces
must be parallel to one another (or parallel to the symmetry plane).
• If this is not the case, Abaqus automatically generates normals on
the crack surface.
• If the notch radius shrinks to zero, all nodes that would be at the crack
tip should be included in the crack-tip node set.
Finite-Strain Analysis of Crack Tips
Crack surface
is detected
automatically
The blunted notch
surface is the crack
front region Symmetry plane
Crack tip
region
q vector
L2.51
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• If the mesh is so coarse that the integration points nearest the crack tip
are far from the tip, most of the details (accurate stresses and strains) of
the finite-strain region around the crack tip will be lost.
• However, accurate J values may still be obtained if cracks are
modeled as sharp.
L2.52
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• Example: SEN specimen
Deformed shape
Undeformed
shape
Moderate blunting
Severe blunting
Contours of PEEQDeformed vs Undeformed Shapes
L2.53
Modeling Fracture and Failure with Abaqus
Finite-Strain Analysis of Crack Tips
• In situations involving finite rotations but small strains, such as the bending of slender structures, a small keyhole around the crack tip should be modeled.
• The region defining the crack front for the contour integral consists of the region on the keyhole.
• The elements should not be singular.
crack-front
region
Limitations Of 3D Swept Meshing For
Fracture
L2.55
Modeling Fracture and Failure with Abaqus
Limitations Of 3D Swept Meshing For Fracture
• For curved regions cannot generate wedges at the center using a hex-
dominated approach and then sweep along the length of the region.
• This was discussed earlier in the context of the conical crack problem.
• To create a focused mesh in this case, embed a small tube within a
larger concentric tube. Mesh the smaller tube with a single layer of
wedge elements; the surrounding regions are meshed with hex
elements.
Sweep direction
L2.56
Modeling Fracture and Failure with Abaqus
Limitations Of 3D Swept Meshing For Fracture
• Partition for a penny-shaped crack
• Illustrates the limitation that the path for the partition must be
perpendicular to its bounding surfaces; thus, cannot properly partition
along the arc of a circle as shown in this example:
Partition by sweeping
circular edge along arc
Cross-sectional
view of block
Tangent direction of arc
arc (not a semi-circle as
in previous example)
L2.57
Modeling Fracture and Failure with Abaqus
Limitations Of 3D Swept Meshing For Fracture
• The workaround is to partition the face with circular arcs, and then
partition the cell using the n-sided patch technique.
n-sided patchFace partition
Note that the cross-sectional area of the swept
region is not constant along its length because
the tangents at the ends are not perpendicular
to the block (generalized sweep meshing)Resulting mesh around
the crack front using
wedge elements
Modeling Cracks with Keyword
Options
L2.59
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Defining a crack with keyword options:
• The *CONTOUR INTEGRAL option is used to define both, the crack itself and the fracture output, in an Abaqus input (.inp) file.
• In this section, we focus solely on the crack-specific parameters of this
option.
• These include:
*CONTOUR INTEGRAL, SYMM, NORMAL
• In the next lecture, we discuss the output-specific parameters of this
option.
• As noted earlier, the main requirements in defining a crack are:
• Defining the crack front
• Defining the crack extension direction
L2.60
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Crack symmetry
*CONTOUR INTEGRAL, SYMM
• The crack lies on a plane of
symmetry and only half the
structure is being modeled
• This feature should only be
used for Mode I problems.
L2.61
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Crack extension
*CONTOUR INTEGRAL, NORMAL
• The NORMAL parameter is used to
define the normal to the crack plane
when the crack is planar.
• Usage:
*contour integral, normal
nx, ny, nz
nodeSet1, nodeSet2, ...
• In this case, give a list of the node
set names defining the crack front
from one end to the other end, in
sequential order, without missing
any points on the crack line.
• In two-dimensional cases,
only one node set is needed.
These sets define the crack front;
the first node in each set defines
the crack tip node for that set.
(An optional CRACK TIP NODES
parameter is available to specify
the crack tip nodes directly).
L2.62
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Example: Penny-shaped crack in an infinite space
*Contour integral, symm, normal, ...
0.0, 1.0, 0.0
Crack-Front-1, Crack-Front-2, Crack-Front-3, ...
Crack-Front-1
L2.63
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• If the NORMAL parameter is omitted, we must give the crack-tip node
set name, and the crack propagation direction q, at each node set
defining the crack front.
• Usage:
*contour integral, ...
nodeSet1, (qx)1, (qy)1, (qz)1nodeSet2, (qx)2, (qy)2, (qz)2
:
• Data must start with the node set at one end and be given for each
node set defining the crack line sequentially until the other end of
the crack is reached.
• The first node in each set is the crack tip node for that set
unless the CRACK TIP NODES parameter is used.
• This format allows nonplanar cracks to be analyzed.
L2.64
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Example: conical crack in an infinite
half-space
*Contour integral, ...
Crack-Front-1, 0.707107, -0.707107, 0.
Crack-Front-2, 0.705994, -0.707107, 0.0396478
Crack-Front-3, 0.702661, -0.707107, 0.0791708
Crack-Front-1
L2.65
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Generating a focused mesh with keyword options
• Example: DEN specimen
• The focused mesh shown in the figure will be generated with the
use of keyword options.
• The options include
*NODE
*NGEN
*NFILL
*ELEMENT
*ELGEN
L2.66
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Node definitions
*node
1, 0.0125, 0.0000
16001, 0.0125, 0.0000
101, 0.0250, 0.0000
4101, 0.0250, 0.0125
12101, 0.0000, 0.0125
16101, 0.0000, 0.0000
*ngen, nset=tip
1, 16001, 1000
*ngen, nset=outer
101, 4101, 1000
4101, 12101, 1000
12101, 16101, 1000
101
410112101
16101
tip
2101
8101
14101
Increment in
node number
Start
nodeEnd node
*NGEN generates nodes
incrementally between any two
previously defined nodes.
In this example, 17 crack-tip nodes are created (contained in the set tip);
the 17 nodes on the outer boundary are contained in set outer.
L2.67
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Quarter-point nodes
*nfill, singular=1
tip, outer, 10, 10
Start set:
first boundEnd set:
second bound
11 21
4021
31
8021
40112021
1021
*NFILL generate nodes for a region of a
mesh by filling in nodes between two
bounds.
In this example, 10 rows of nodes are generated between each tip node and its
corresponding outer node.
Number of
intervals between
bounding nodes
Node
number
increment
This parameter generates quarter-point nodes; the 1 indicates the first
bound represents the crack tip
L2.68
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Element definitions
*element, type=cps8r
1, 1, 21, 2021, 2001, 11, 1021, 2011, 1001
*elgen, elset=plate
1, 5, 20, 10, 8, 2000, 1000
1
11
21
1021
2021
*ELGEN generates elements
incrementally.
In this example, 5 elements form the
first row (extending radially outward
from the tip); a total of 8 rows of
elements (based on the first row) are
created around the crack tip.
1
Nodes 1, 1001,
and 2001 are
coincident
First row of
elementsTotal number of
rows
L2.69
Modeling Fracture and Failure with Abaqus
Modeling Cracks with Keyword Options
• Crack-tip nodes
• If the crack-tip nodes are permitted to behave independently, the
strength of the strain-field singularity is r -1.
• The crack-tip nodes can be constrained using equations, multi-point
constraints, using repeated nodes in the element definition, etc. For
example, to constrain the crack-tip nodes with a multi-point
constraint:
*nset, nset=constrain, generate
1, 15001, 1000
*mpc
tie, constrain, 16001
• Only node 16001 is independent in this case.
• The strain-field singularity is r -½.
Fracture Analysis
Lecture 3
L3.2
Modeling Fracture and Failure with Abaqus
Overview
• Calculation of Contour Integrals
• Examples
• Nodal Normals in Contour Integral Calculations
• J-Integrals at Multiple Crack Tips
• Through Cracks in Shells
• Mixed-Mode Fracture
• Material Discontinuities
• Numerical Calculations with Elastic-Plastic Materials
• Workshop 1
• Workshop 2
Calculation of Contour Integrals
L3.4
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Abaqus offers the evaluation of J-integral values, as well as several
other parameters for fracture mechanics studies. These include:
• The KI, KII, and KIII stress intensity factors, which are used mainly
in linear elastic fracture mechanics to measure the strength of local
crack tip fields;
• The T-stress in linear elastic calculations;
• The crack propagation direction: an angle at which a preexisting
crack will propagate; and
• The Ct-integral, which is used with time-dependent creep behavior.
• Output can be written to the output database (.odb), data (.dat), and
results (.fil) files.
L3.5
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Domain representation of J
• For reasons of accuracy, J is evaluated
using a domain integral.
• The domain integral is evaluated over
an area/volume contained within a
contour surrounding the crack tip/line.
• In two dimensions, Abaqus defines the
domain in terms of rings of elements
surrounding the crack tip.
• In three dimensions, Abaqus defines a
tubular surface around the crack line.
L3.6
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Different contours (domains) are
created automatically by Abaqus.
• The first contour consists of the
crack front and one layer of
elements surrounding it.
• Ring of elements from one
crack surface to the other (or
the symmetry plane).
• The next contour consists of the
ring of elements in contact with the
first contour as well as the
elements in the first contour.
• Each subsequent contour is
defined by adding the next ring of
elements in contact with the
previous contour.
Contour 1 Contour 2
Contour 3 Contour 4
L3.7
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• The J-integral and the Ct-integral at steady-state creep should be
path (domain) independent.
• The value for the first contour is generally ignored.
• Examples of contour domains:
2nd
contour
1st
contour
Crack-tip node crack-front nodes
1st contour2nd contour
Crack-tip node
L3.8
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Usage:
*CONTOUR INTEGRAL, CONTOURS= n,
TYPE={J, C, T STRESS, K FACTORS},
DIRECTION = {MTS, MERR, KII0}
Note: In this lecture, we focus on the output-specific parameters of the *CONTOUR INTEGRAL
option. The crack-specific parameters SYMM and NORMAL were discussed in the previous lecture.
Specifies the number of contours (domains)
on which the contour integral will be
calculated
This is the output
frequency in
increments
L3.9
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Usage (cont’d):
*CONTOUR INTEGRAL, CONTOURS= n,
TYPE={J, C, T STRESS, K FACTORS},
DIRECTION = {MTS, MERR, KII0}
• J for J-integral output,
• C for Ct-integral output.
• T STRESS to output T-stress
calculations
• K FACTORS for stress intensity
factor output
L3.10
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Usage (cont’d):
*CONTOUR INTEGRAL, CONTOURS= n,
TYPE={J, C, T STRESS, K FACTORS},
DIRECTION = {MTS, MERR, KII0}
• Use with TYPE=K FACTORS to specify the criterion to be
used for estimating the crack propagation direction in
homogenous, isotropic, linear elastic materials:
• Maximum tangential stress criterion (MTS)
• Maximum energy release rate criterion (MERR)
• KII = 0 criterion (KII0)
Three criteria to calculate the crack
propagation direction at initiation
L3.11
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Output files
*CONTOUR INTEGRAL, OUTPUT
• Set OUTPUT=FILE to store the
contour integral values in the results (.fil) file.
• Set OUTPUT=BOTH to print
the values in the data and
results files.
• If the parameter is omitted, the
contour integral values will be printed in the data (.dat) file
but not stored in the results (.fil) file.
L3.12
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Loads
• Loads included in contour integral calculations:
• Thermal loads.
• Crack-face pressure and traction loads on continuum elements as well as those applied using user subroutines DLOAD and UTRACLOAD.
• Surface traction and crack-face edge loads on shell elements as well as those applied using user subroutine UTRACLOAD.
• Uniform and nonuniform body forces.
• Centrifugal loads on continuum and shell elements.
• Not all types of distributed loads (e.g., hydrostatic pressure and gravity
loads) are included in the contour integral calculations.
• The presence of these loads will result in a warning message.
L3.13
Modeling Fracture and Failure with Abaqus
Calculation of Contour Integrals
• Other loads not included in contour integral calculations:
• Contributions due to concentrated loads are not included.
• If needed, modify the mesh to include a small element and
apply a distributed load to the element.
• Contributions due to contact forces are not included.
• Initial stresses are not considered in the definition of contour
integrals.
Examples
L3.15
Modeling Fracture and Failure with Abaqus
Examples
• Penny-shaped crack in an infinite space
• Model characteristics
• The mesh is extended far enough
from the crack tip so that the finite
boundaries will not influence the
crack-tip solution.
• The radius of the penny-shaped
crack is 1.
• Two types of loading are
considered:
• Uniform far-field loading
• Nonuniform loading on the
crack face: p = Arn.
L3.16
Modeling Fracture and Failure with Abaqus
Examples
• Different mesh characteristics:
• Axisymmetric or three-dimensional
• Fine or coarse focused meshes
• With or without ¼ point elements
• Various element types used:
• First- and second-order
• With and without reduced integration
Axisymmetric model
20
20
Focused mesh around
crack tip
Crack tip
L3.17
Modeling Fracture and Failure with Abaqus
Examples
• Fine mesh vs. coarse mesh (axisymmetric and 3D models)
~0.08
0.080.0004
The fine mesh is shown to the left;
the coarse mesh above. The length
perpendicular to crack line of the
crack-tip elements are indicated.
L3.18
Modeling Fracture and Failure with Abaqus
Examples
• Axisymmetric model: geometry
Model geometry
Close up of crack tip region for
coarse mesh model (identical for
fine mesh model—only the inner
semicircular region is smaller)
Symmetry planes
L3.19
Modeling Fracture and Failure with Abaqus
Examples
• Axisymmetric model: crack definition
Crack tip with extension direction
Set to 0.5 to use mid-
point rather than ¼ point
elements
L3.20
Modeling Fracture and Failure with Abaqus
Examples
• 3D model: geometry and mesh
• A 90 sector is modeled because
of symmetry.
Additional partition
required for swept
mesh
On planes perpendicular to the crack
front, the mesh is very similar to the
axisymmetric mesh
In the circumferential direction around
the crack line, 12 elements are used.
Partitions used for coarse mesh model
(identical for fine mesh model—only
the inner semicircular region is smaller)
Fine 3D mesh
Symmetry planes
L3.21
Modeling Fracture and Failure with Abaqus
Examples
• Why is the additional partition required?
• Without the additional partition, the region shown below would require
irregular elements at the vertex located on the axis of symmetry.
• This is not supported by Abaqus.
A 7-node element
is an example of an
irregular element.
Irregular elements
required here
because revolving
about a point
L3.22
Modeling Fracture and Failure with Abaqus
Examples
• 3D model: crack definition
• Orphan mesh created to edit q
vectors.
L3.23
Modeling Fracture and Failure with Abaqus
Examples
• Contour integral output requests (axisymmetric and 3D)
Separate output
requests are required
for J, K-factors, and the
T-stress.
L3.24
Modeling Fracture and Failure with Abaqus
Examples
• Loads (axisymmetric and 3D)
The far-field load is suppressed.
L3.25
Modeling Fracture and Failure with Abaqus
Examples
• Results
• MISES stress shown below for
the axisymmetric fine mesh.
Analytical Contour 1 Contour 2 Contour 3 Contour 4 Contour 5
5.796E-02 5.8169E-02 5.8095E-02 5.8121E-02 5.8104E-02 5.8084E-02
Contour 6 Contour 7 Contour 8 Contour 9 Contour 10
5.8064E-02 5.8044E-02 5.8024E-02 5.8005E-02 5.7985E-02
Deformation scale factor = 250
100%analytical numerical
analytical
J J
J
L3.26
Modeling Fracture and Failure with Abaqus
Examples
J values from meshes with ¼ point elements (reduced integration)
• Abaqus values are based on the average of contours 3−5 in each mesh.
LoadingAnalytical
result
3-D Axisymmetric
C3D20R CAX8R
Coarse Fine Coarse Fine
Uniform
far field.0580 .0578 .0580 .0579 .0581
Uniform
crack face.0580 .0578 .0580 .0579 .0581
Nonuniform
crack face (n = 1).0358 .0356 .0357 .0356 .0358
Nonuniform
crack face (n = 2).0258 .0256 .0260 .0256 .0258
Nonuniform
crack face (n = 3).0201 .0199 .0206 .0200 .0202
L3.27
Modeling Fracture and Failure with Abaqus
Examples
J values from meshes with ¼ point elements (full integration)
• Abaqus values are based on the average of contours 3−5 in each mesh.
LoadingAnalytical
result
3-D Axisymmetric
C3D20 CAX8
Coarse Fine Coarse Fine
Uniform
far field.0580 .0577 .0572 .0578 .0580
Uniform
crack face.0580 .0577 .0572 .0578 .0580
Nonuniform
crack face (n = 1).0358 .0355 .0352 .0356 .0358
Nonuniform
crack face (n = 2).0258 .0255 .0253 .0255 .0258
Nonuniform
crack face (n = 3).0201 .0198 .0197 .0199 .0201
L3.28
Modeling Fracture and Failure with Abaqus
Examples
J values from meshes without ¼ point elements (reduced integration)
• Abaqus values are based on the average of contours 3−5 in each mesh.
LoadingAnalytical
result
3-D Axisymmetric
C3D20R C3D8R CAX8R CAX4R
Coarse Fine Coarse Coarse Fine Coarse
Uniform
far field.0580 .0574 .0580 .0563 .0574 .0581 .0562
Uniform
crack face.0580 .0574 .0580 .0563 .0574 .0581 .0562
Nonuniform
crack face (n = 1).0358 .0350 .0357 .0336 .0350 .0358 .0337
Nonuniform
crack face (n = 2).0258 .0250 .0260 .0234 .0250 .0258 .0236
Nonuniform
crack face (n = 3).0201 .0193 .0206 .0177 .0193 .0202 .0179
L3.29
Modeling Fracture and Failure with Abaqus
Examples
J values from meshes without ¼ point elements (full integration)
• Abaqus values are based on the average of contours 3−5 in each mesh.
LoadingAnalytical
result
3-D Axisymmetric
C3D20 C3D8 CAX8 CAX4
Coarse Fine Coarse Coarse Fine Coarse
Uniform
far field.0580 .0573 .0572 .0552 .0574 .0580 .0557
Uniform
crack face.0580 .0573 .0572 .0552 .0574 .0580 .0557
Nonuniform
crack face (n = 1).0358 .0350 .0352 .0329 .0350 .0358 .0333
Nonuniform
crack face (n = 2).0258 .0249 .0253 .0229 .0250 .0258 .0232
Nonuniform
crack face (n = 3).0201 .0193 .0197 .0172 .0193 .0201 .0175
L3.30
Modeling Fracture and Failure with Abaqus
Examples
• Conclusions
• 3D fine meshes with second-order elements are more sensitive to the
choice of integration rule when determining J.
• The results are still very accurate (within 2% of analytical value).
• The inclusion of the singularity helps most in the coarser meshes.
• For mesh convergence in small strain, the singularity must be
included.
L3.31
Modeling Fracture and Failure with Abaqus
Examples
• Conical crack in a half-space
• At each node set along the crack front, the crack propagation direction is
different.
L3.32
Modeling Fracture and Failure with Abaqus
Examples
• Three-dimensional model
• Displaced shape and Mises stress distribution of full three-
dimensional model.
Deformation scale factor = 1.e6
L3.33
Modeling Fracture and Failure with Abaqus
Examples
• J values of three-dimensional mesh
• There is some oscillation between J values evaluated at corner
nodes compared to J values evaluated at midside nodes.
Variation of J with angular position
1.328E-07
1.330E-07
1.332E-07
1.334E-07
1.336E-07
1.338E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l 3D contour 5
3D contour 4
3D contour 3
3D contour 2
L3.34
Modeling Fracture and Failure with Abaqus
Contours 3-5 have
converged
Examples
• Axisymmetric model and results
Axisymmetric results are
used as reference results.
L3.35
Modeling Fracture and Failure with Abaqus
Examples
• Comparison of axisymmetric and 3D results
Variation of J with angular position
Contour 1
1.300E-07
1.320E-07
1.340E-07
1.360E-07
1.380E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l
3D
AXI
Variation of J with angular position
Contour 2
1.329E-07
1.330E-07
1.331E-07
1.332E-07
1.333E-07
1.334E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l
3D
AXI
Variation of J with angular position
Contour 3
1.328E-07
1.330E-07
1.332E-07
1.334E-07
1.336E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l
3D
AXI
Variation of J with angular position
Contour 5
1.328E-07
1.330E-07
1.332E-07
1.334E-07
1.336E-07
1.338E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l
3D
AXI
L3.36
Modeling Fracture and Failure with Abaqus
Examples
• Since the three-dimensional mesh is quite coarse around the axis of
symmetry, these results are considered to be good—the error is less
than 0.5% for all but the first contour.
% difference in J between AXI and 3D results
0.00.51.01.5
2.02.53.03.5
0 45 90
Angle (degrees)
% d
iffe
ren
ce Contour 1
Contour 2
Contour 3
Contour 4
Contour 5
L3.37
Modeling Fracture and Failure with Abaqus
Examples
• Submodeling
• We can use submodeling to create
two meshes that are significantly
smaller than the full three-
dimensional model.
• The top-right figure is the
coarse mesh global model in
the vicinity of the crack.
• The bottom-right figure shows
the refined submodel mesh
overlaid on the global model
mesh.
L3.38
Modeling Fracture and Failure with Abaqus
Examples
• J values of submodel:
• Inaccuracies are introduced
by the coarser mesh used in
the global model.
• Errors in J are less than 1%.
• CPU time was reduced by a
factor of 3.
Variation of J with angular position
1.318E-07
1.320E-07
1.322E-07
1.324E-07
1.326E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l 3D contour 5
3D contour 4
3D contour 3
3D contour 2
Variation of J with angular position
Contour 5
1.315E-07
1.320E-07
1.325E-07
1.330E-07
1.335E-07
0 45 90
Angle (degrees)
J-i
nte
gra
l
3D
AXI
% difference in J between AXI and 3D results
0.00.51.01.52.02.53.03.54.04.5
0 45 90
Angle (degrees)
% d
iffe
ren
ce Contour 1
Contour 2
Contour 3
Contour 4
Contour 5
L3.39
Modeling Fracture and Failure with Abaqus
Examples
• Compact Tension Specimen
• This is one of five standardized specimens defined by the ASTM for the
characterization of fracture initiation and crack growth.
• The ASTM standardized testing apparatus uses a clevis and a pin to
hold the specimen and apply a controlled displacement.
L3.40
Modeling Fracture and Failure with Abaqus
Examples
• Model details
• Plane strain conditions assumed.
• The initial crack length is 5 mm.
• Elastic-plastic material
• Low alloy ferritic steel
Crack seam
q-vector
1/√r singularity modeled in
the crack-tip elements
Prescribed load line displacement
L3.41
Modeling Fracture and Failure with Abaqus
Examples
• Results
Small strain analysis Finite strain analysis
L3.42
Modeling Fracture and Failure with Abaqus
Examples
At small to moderate strain levels,
the small and finite strain models
yield similar results.
Finite strain effects must be
considered to represent this level of
deformation and strain accurately.
Nodal Normals in Contour Integral
Calculations
L3.44
Modeling Fracture and Failure with Abaqus
Nodal Normals in Contour Integral Calculations
• Sharp curved cracks
• For sharp cracks, if the crack faces
are curved, Abaqus automatically
determines the normal directions of
the nodes on the portions of the crack
faces that lie within the contour
integral domains.
• This improves the accuracy of the
contour integral estimation.
• The normal is not used at the
crack-tip node, however.
Normals to top crack
surface nodes
n (normal to
crack plane)
Normals to bottom
crack surface nodes
q
L3.45
Modeling Fracture and Failure with Abaqus
Nodal Normals in Contour Integral Calculations
• Example: sharp curved crack
Contour # 1 2 3 4 5
J without normals 3.363 2.980 2.475 1.888 1.283
J with normals 3.600 3.602 3.605 3.605 3.605
L3.46
Modeling Fracture and Failure with Abaqus
Nodal Normals in Contour Integral Calculations
• Blunt cracks and notches
• All nodes on the notch should be included in the crack-tip node set.
• The J-integral results are more accurate since the q vector is
parallel to the crack surface in this case, as illustrated below.
Crack surfaceCrack surface
Single node in crack-tip node set;
normals calculated on nodes of
blunted surface; q not parallel to
crack surface.
All nodes on blunted surface in
crack-tip node set; q parallel to
crack surface.
Paths for contour
integrals
n
q q
J-Integrals at Multiple Crack Tips
L3.48
Modeling Fracture and Failure with Abaqus
J-Integrals at Multiple Crack Tips
• Abaqus can calculate J (or Ct) at multiple crack tips
• Abaqus/CAE: multiple crack tips and history
output requests
• Input file: repeated use of the *CONTOUR
INTEGRAL option.
• If the domain for one crack tip envelopes the other
crack tip, the J value will go to zero (as it should).
Through Cracks in Shells
L3.50
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Second-order quadrilateral shell elements must be used if contour
integral output is requested.
• Sides of S8R elements should not be collapsed. If a focused mesh is
used, the crack tip must be modeled as a keyhole whose radius is small
compared to the other dimensions measured in the plane of the shell.
Crack-tip mesh for S8R elementsShell mesh
L3.51
Modeling Fracture and Failure with Abaqus
• S8R5 elements can be collapsed and midside nodes moved to the 1/4 points.
• The q vector must lie in the shell surface.
• It should be tangent to the surface.
Through Cracks in Shells
Crack-tip mesh for S8R5 elementsShell mesh
L3.52
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Example: Circumferential through crack under axial load
• Mean radius R = 10.5 in
• Wall thickness t = 0.525 in
• Crack half-angle q = p / 4
• Longitudinal membrane stress = 100 psi
L3.53
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Model details
• Axial load is applied using
a shell edge load
• Symmetry used to reduce
mode size
Edge loads
symmetry
L3.54
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Modeling a crack with a keyhole
Crack tip
Crack front
q vector
L3.55
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Results
Deformed shape—axial loading
J values—axial loading
L3.56
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• In shell element meshes, mechanical loads which act normal to the shell
surface and are applied within the contour integral domain are not taken
into account in the calculation of the contour integral.
• For example, pressure loads are not considered because they act
normal to the shell surface
• Conversely, axial edge loads are considered because they act in
the shell surface.
• Two workarounds exist:
• Run successive shell models with differing crack lengths and
numerically differentiate the potential energy
• Use solid elements (if the response is membrane dominated)
L3.57
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Using numerical differentiation to obtain J:
• The PE values should be obtained from two separate analyses, with
crack lengths differing by Da.
• The values of PE in the Abaqus data (.dat) file are generally not
printed to a sufficient number of figures to be useful for this calculation and must be read from the results (.fil) file.
• A similar technique can be used to get Ct at long times.
Constant Load
Constant Load
( )
a a a
PEJ
a
PE PE
a
D
=
=
D.
Potential energy:
PE = ALLSE ALLWK
L3.58
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Using solid elements:
• If membrane deformation is dominant, the shell can be modeled
with a single layer of 20-node bricks since these solid elements
include loading contributions to contour integrals.
L3.59
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• To obtain accurate values of J through the shell thickness with solid
elements, more than one element should be used in the thickness
direction.
J values will show significant path dependence unless
averaged.
• If only one element is used through the thickness, the values can be
averaged by thinking of J as a force per unit length:
• The average is calculated as if the J values were equivalent
nodal forces:
4
6
A B C
shell
J J JJ
= .
CB
A
L3.60
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Aside: Generating a solid element mesh from a shell mesh.
• A shell mesh can easily be converted to a solid one using the ―Offset
Mesh‖ tool.
• Creates solid layers from a shell mesh.
L3.61
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Example: Circumferential through crack in
an internally pressurized, closed-end pipe
• The same pipe discussed earlier, now
subjected to 10 psi internal pressure +
axial load (which simulates the closed
end).
• Comparison of J values using one layer
of C3D20R elements through the
thickness :
CONTOURJ values 100
1 2 3 4 5
At Node A 2.0965 2.1317 2.1505 2.1557 2.1697
At Node B 3.7396 3.6992 3.7004 3.6968 3.6904
At Node C 5.0226 5.0501 5.0813 5.1471 5.2373
Averaged 3.6796 3.6631 3.6722 3.6817 3.6948
CB
A
L3.62
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Example: Circumferential through crack under axial load revisited
• Now we revisit the problem in which the pipe is subjected to an axial
load.
• Comparison of J values using one layer of C3D20R elements through
the thickness:
CONTOURJ values 100
1 2 3 4 5
At Node A 2.2122 2.2524 2.2700 2.2740 2.2850
At Node B 3.7629 3.7202 3.7212 3.7184 3.7136
At Node C 4.9560 4.9893 5.0175 5.0737 5.1492
Averaged 3.7033 3.6871 3.6954 3.7036 3.7148
Analytical 3.7181
L3.63
Modeling Fracture and Failure with Abaqus
Through Cracks in Shells
• Comparing these results with the
shell element results presented
earlier:
• Errors with respect to the
analytical solution for the 3D
model are less than 1%.
• Much closer agreement because
transverse shear effects are
considered in the 3D model.
• Only in-plane stress and strain
terms are included in the Abaqus
J calculations for shells.
• Transverse shear terms are
neglected.
Mixed-Mode Fracture
L3.65
Modeling Fracture and Failure with Abaqus
Mixed-Mode Fracture
• Abaqus uses interaction integrals to
compute the stress intensity factors.
• This approach accounts for
mixed-mode loading effects.
• Note that the J- or Ct-integrals
do not distinguish between
modes of loading.
• Usage:
*CONTOUR INTEGRAL,
TYPE=K FACTORS
• Stress intensity factors can
only be calculated for linear
elastic materials.
L3.66
Modeling Fracture and Failure with Abaqus
Mixed-Mode Fracture
0K a p=
Element
type
22.5º CPE8 0.185 (2.9%) 0.403 (0.2%)
22.5º CPE8R 0.185 (2.9%) 0.403 (0.2%)
67.5º CPE8 1.052 (3.6%) 0.373 (1.0%)
67.5º CPE8R 1.053 (3.8%) 0.374 (1.3%)
22.5 = 67.5 =
• Example: Center slant cracked plate under tension
*Values enclosed in parentheses are
percentage differences with respect to
the reference solution. See Abaqus
Benchmark Problem 4.7.4 for more
information.
*
Material Discontinuities
L3.68
Modeling Fracture and Failure with Abaqus
Material Discontinuities
• The J-integral will be path independent if the material is homogeneous in
the direction of crack propagation in the domain used for the contour
integral calculation.
• If there is material discontinuity ahead of the crack in this region, the
*NORMAL option can be used to correct the calculation of J so that
it will still be path independent.
• The normal to the material discontinuity line must
be specified for all nodes on the material
discontinuity that will lie in a contour integral domain.
n
L3.69
Modeling Fracture and Failure with Abaqus
Material Discontinuities
• Example: J-integral analysis of a two material plate
• As an example, the figure shows a single-edge
notch specimen made from two materials in
which the material interface runs at an angle to
the sides of the specimen.
• The material containing the crack (left) has a
Young’s modulus of 2 105 MPa and a
Poisson’s ratio of 0.3.
• The uncracked material (right) has Young’s
modulus of 2 104 MPa and a Poisson’s ratio
of 0.1.
• The specimen is stretched by uniform
displacement at its ends.
L3.70
Modeling Fracture and Failure with Abaqus
Material Discontinuities
• J-integral analysis of a two material plate (cont’d)
• Along the material discontinuity, the normal to
the discontinuity is given using the *NORMAL
option.
• The normal needs to be defined on both
sides of the discontinuity.
*NORMAL
LEFT, NORM, 1.0, 0.125, 0.0
RIGHT, NORM, -1.0, -0.125, 0.0
L3.71
Modeling Fracture and Failure with Abaqus
Material Discontinuities
• The calculated J-integral values for 10 contours are as follows:
• The need for the normals on the interface (contours 5–10) is clear.
ContourJ (N/mm)
Without normals With normals
1 55681 55681
2 57085 57085
3 57052 57052
4 57058 57058
5 35188 57116
6 31380 57114
7 27536 57114
8 23512 57113
9 19172 57116
10 14181 57094
Numerical Calculations with
Elastic-Plastic Materials
L3.73
Modeling Fracture and Failure with Abaqus
Numerical Calculations with Elastic-Plastic Materials
• For Mises plasticity the plastic deformation is incompressible.
• The rate of total deformation becomes incompressible (constant
volume) as the plastic deformation starts to dominate the response.
• All Abaqus quadrilateral and brick elements suitable for use in J-integral
calculations can handle this rate incompressibility condition except for
the ―fully‖ integrated quadrilaterals and brick elements without the
―hybrid‖ formulation.
• Do not use CPE8, CAX8, C3D20 elements with these materials.
They will ―lock‖ (become overconstrained) as the material becomes
more incompressible.
L3.74
Modeling Fracture and Failure with Abaqus
Numerical Calculations with Elastic-Plastic Materials
• Second-order elements with reduced integration (CPE8R,
C3D20R, etc.) work best for stress concentration problems in
general and for crack tips in particular.
• If the displaced shape plot shows a regular pattern of deformation,
this state is an indication of mesh locking.
• Locking can be seen in quilt contour plots of hydrostatic
pressure for first-order elements—the pressure shows a
checkerboard pattern.
• Change to reduced integration elements if you are using fully
integrated elements.
• Increase the mesh density if you already using reduced
integration elements.
• If these steps do not help, use hybrid elements.
• Hybrid elements must be used for fully incompressible materials (such
as hyperelasticity, linear elasticity with n = 0.5).
L3.75
Modeling Fracture and Failure with Abaqus
Numerical Calculations with Elastic-Plastic Materials
• Results with elastic-plastic materials (and nonlinear materials in general)
are more sensitive to meshing than for small-strain linear elasticity.
• Meshes adequate for linear elasticity may have to be refined.
• The more complex the solution, the more J values tend to be path
dependent.
• A lack of path dependence can be an indication of a lack of mesh
convergence; however, path independence of J does not prove
mesh convergence.
Workshop 1
L3.77
Modeling Fracture and Failure with Abaqus
Workshop 1
• Crack in a three-point bend specimen
• Two-dimensional geometry
• Mesh sensitivity study
• Focus vs. unfocused mesh
• Quarter-point vs. mid-side nodes
Workshop 2
L3.79
Modeling Fracture and Failure with Abaqus
Workshop 2
• Crack in a helicopter airframe component
• Three-dimensional geometry
• Create mesh and evaluate response for cracks at different locations
Material Failure and Wear
Lecture 4
L4.2
Modeling Fracture and Failure with Abaqus
Overview
• Progressive Damage and Failure
• Damage Initiation for Ductile Metals
• Damage Evolution
• Element Removal
• Damage in Fiber-Reinforced Composite Materials
• Failure in Fasteners
• Material Wear and Ablation
Progressive Damage and Failure
L4.4
Modeling Fracture and Failure with Abaqus
Progressive Damage and Failure
• Abaqus offers a general capability for modeling progressive damage
and failure in engineering structures
• Material failure refers to the complete loss of load carrying capacity that
results from progressive degradation of the material stiffness.
• Stiffness degradation is modeled using damage mechanics.
• Progressive damage and failure can be modeled for:
• Ductile materials
• Continuum constitutive behavior
• Fiber-reinforced composites
• Interface materials
• Cohesive elements with a traction-separation law
• Damage and failure of cohesive elements are discussed in the next
lecture.
L4.5
Modeling Fracture and Failure with Abaqus
Progressive Damage and Failure
• Two distinct types of ductile material
failure can be modeled with Abaqus
• Ductile fracture of metals
• Void nucleation, coalescence, and
growth
• Shear band localization
• Necking instability in sheet-metal
forming
• Forming Limit Diagrams
• Marciniak-Kuczynski (M-K) criterion
• Damage in sheet metals is not
discussed further in this seminar.
L4.6
Modeling Fracture and Failure with Abaqus
Multiple damage definitions are allowed
Keywords
*MATERIAL
*ELASTIC
*PLASTIC
*DAMAGE INITIATION,CRITERION=criterion
*DAMAGE EVOLUTION
*SECTION CONTROLS, ELEMENT DELETION=YES
Progressive Damage and Failure
• Components of material definition
• Undamaged constitutive
behavior (e.g., elastic-plastic
with hardening)
• Damage initiation (point A)
• Damage evolution (path A–B)
• Choice of element removal
(point B)
A
B
Undamaged response
Damaged
response
Typical material response showing
progressive damage
Damage Initiation Criteria for
Ductile Metals
L4.8
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Damage initiation defines the point of initiation of degradation of stiffness
• It is based on user-specified criteria
• Ductile or shear
• It does not actually lead to damage unless damage evolution is also specified
• Output variables associated with each criterion
• Useful for evaluating the severity of current deformation state
• Output
DMICRT
Ductile Shear
Different damage initiation criteria on
an aluminum double-chamber profile
DMICRT > 1 indicates
damage has initiated
L4.9
Modeling Fracture and Failure with Abaqus
• Ductile criterion:
• Appropriate for triggering damage
due to nucleation, growth, and
coalescence of voids
• The model assumes that the
equivalent plastic strain at the onset
of damage is a function of stress
triaxiality and strain rate.
• Stress triaxiality h = - p / q
• The ductile criterion can be used with
the Mises, Johnson-Cook, Hill, and
Drucker-Prager plasticity models,
including equation of state.Ductile criterion for Aluminum Alloy AA7108.50-T6
(Courtesy of BMW)
Pressure stress
Mises stress
Damage Initiation Criteria for Ductile Metals
L4.10
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Usage:
• Specify the equivalent plastic strain at the onset of damage as a
tabular function of
• Stress triaxiality
• Strain rate
*DAMAGE INITIATION,
CRITERION=DUCTILE
• Output:
DUCTCRT (wD)
, , , , pl pliT f h
Temperature and field
variable dependence
optional
Equivalent fracture strain
at damage initiation
The criterion for damage initiation is met when wD = 1.
L4.11
Modeling Fracture and Failure with Abaqus
• Shear criterion:
• Appropriate for triggering damage
due to shear band localization
• The model assumes that the
equivalent plastic strain at the onset
of damage is a function of the shear
stress ratio and strain rate.
• Shear stress ratio defined as:
• The shear criterion can be used with
the Mises, Johnson-Cook, Hill, and
Drucker-Prager plasticity models,
including equation of state.Shear criterion for Aluminum Alloy AA7108.50-T6
(Courtesy of BMW)
ks = 0.3
qs = (q + ks p) /tmax
Damage Initiation Criteria for Ductile Metals
L4.12
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Usage:
• Specify the equivalent plastic strain at the onset of damage as a
tabular function of
• Shear stress ratio
• Strain rate
*DAMAGE INITIATION,
CRITERION=SHEAR, KS=ks
• Output:
SHRCRT (wS)
Temperature and field
variable dependence
optional
, , , , pl pls iT f q
The criterion for damage initiation is met when wS = 1.
Equivalent fracture strain
at damage initiation
ks is a material parameter
L4.13
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Example: Axial crushing of an aluminum
double-chamber profile
Cross
section
Quasi-static buckling mode
L4.14
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Model details
• Steel base:
• C3D8R elements
• Enhanced hourglass control
• Elastic-plastic material
• Aluminum chamber:
• S4R elements
• Stiffness hourglass control
• Rate-dependent plasticity
• Damage initiation
• General contact
• Variable mass scaling Steel base: bottom
is encastred.
Rigid plate
with initial
downward
velocity
Aluminum
chamber
L4.15
Modeling Fracture and Failure with Abaqus
*MATERIAL, NAME=ALUMINUM
*DENSITY
2.70E-09
*ELASTIC
7.00E+04, 0.33
*PLASTIC,HARDENING=ISOTROPIC,RATE=0
:
*DAMAGE INITIATION, CRITERION=DUCTILE
5.7268, 0.000, 0.001
4.0303, 0.067, 0.001
2.8377, 0.133, 0.001
:
4.4098, 0.000, 250
2.5717, 0.067, 250
1.5018, 0.133, 250
:
Damage Initiation Criteria for Ductile Metals
• Material definition : Keywords interface
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6
stress triaxiality
str
ain
at
da
ma
ge
in
itia
tio
n
strain rate=0.001/s
strain rate=250/s
Ductile criteria for Aluminum Alloy AA7108.50-
T6 (Courtesy of BMW)
Equivalent fracture strain at
damage initiation, pl
Strain rate, pl
Stress triaxiality, h
L4.16
Modeling Fracture and Failure with Abaqus
*MATERIAL, NAME=ALUMINUM
:
*DAMAGE INITIATION, CRITERION=DUCTILE
5.7268, 0.000, 0.001
4.0303, 0.067, 0.001
:
*DAMAGE INITIATION, CRITERION=SHEAR, KS=0.3
0.2761, 1.424, 0.001
0.2613, 1.463, 0.001
0.2530, 1.501, 0.001
:
0.2731, 1.424, 250
0.3025, 1.463, 250
0.3323, 1.501, 250
:
Damage Initiation Criteria for Ductile Metals
Equivalent fracture strain at
damage initiation, pl
Strain rate, pl
Shear stress ratio,sq
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.6 1.7 1.8 1.9 2
shear stress ratio
str
ain
at
da
ma
ge
in
itia
tio
n
strain rate=0.001/s
strain rate=250/s
Shear criteria for Aluminum Alloy
AA7108.50-T6 (Courtesy of BMW)
• Material definition : Keywords interface (cont'd)
L4.17
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Material definition :
Abaqus/CAE interface
:
*DAMAGE INITIATION, CRITERION=DUCTILE
5.7268, 0.000, 0.001
4.0303, 0.067, 0.001
2.8377, 0.133, 0.001
:
4.4098, 0.000, 250
2.5717, 0.067, 250
1.5018, 0.133, 250
:
L4.18
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Material definition :
Abaqus/CAE interface (cont'd)
:
*DAMAGE INITIATION,
CRITERION=SHEAR, KS=0.3
0.2761, 1.424, 0.001
0.2613, 1.463, 0.001
0.2530, 1.501, 0.001
:
0.2731, 1.424, 250
0.3025, 1.463, 250
0.3323, 1.501, 250
:
L4.19
Modeling Fracture and Failure with Abaqus
Damage Initiation Criteria for Ductile Metals
• Results (without damage evolution)
DuctileShear
Quasi-static response
Damage Evolution
L4.21
Modeling Fracture and Failure with Abaqus
Damage Evolution
• Damage evolution defines the post damage-initiation material behavior.
• That is, it describes the rate of degradation of the material stiffness
once the initiation criterion is satisfied.
• The formulation is based on scalar damage approach:
• The overall damage variable d captures the combined effect of all
active damage mechanisms.
• When damage variable d = 1, material point has completely failed.
• In other words, fracture occurs when d = 1.
(1 )d= - Stress due to undamaged response
L4.22
Modeling Fracture and Failure with Abaqus
Damage Evolution
• Elastic-plastic materials
• For a elastic-plastic material,
damage manifests in two forms
• Softening of the yield stress
• Degradation of the elasticity
• The strain softening part of the
curve cannot represent a
material property.
• The above argument is
based on
• Fracture mechanics
considerations
• Mesh sensitivitySchematic representation of elastic-plastic
material with progressive damage.
EEd )1( -
d-
0
E
pl
fpl
0
0y)0( =d
softeningDegradation of
elasticity
Undamaged
response
L4.23
Modeling Fracture and Failure with Abaqus
Damage Evolution
• To address the strain softening issue, Hillerborg’s (1976) proposal is
adopted.
• The fracture energy to open a unit area of crack, Gf , is assumed to be a
material property.
• The softening response after damage initiation is characterized by a
stress-displacement response (rather than a stress-strain response)
• This requires the introduction of a characteristic length L associated
with a material point.
L4.24
Modeling Fracture and Failure with Abaqus
Damage Evolution
• The fracture energy is written as
where is the equivalent plastic displacement.
• The characteristic length L is computed automatically by Abaqus based
on element geometry.
• Elements with large aspect ratios should be avoided to minimize mesh
sensitivity.
• The damage evolution law can be specified either in terms of fracture
energy (per unit area) or in terms of the equivalent plastic
displacement.
• Both approaches take into account the characteristic length of the
element.
• The formulation ensures that mesh-sensitivity is minimized.
plu
0
0
pl plf f
pl
upl pl
f y yG L u
= =
L4.25
Modeling Fracture and Failure with Abaqus
Damage Evolution
• Displacement-based damage evolution
*DAMAGE EVOLUTION,TYPE=DISPLACEMENT,
SOFTENING={TABULAR,LINEAR,EXPONENTIAL}
d
plu
1
0
d
plu
1
0pl
fu
d
plu
1
0pl
fu(a) Tabular (b) Linear (c) Exponential
L4.26
Modeling Fracture and Failure with Abaqus
• Procedure for generating d vs
table from tensile test data
Schematic representation of tensile test data
in stress – displacement space for
elastic-plastic materials
0
0y
1. Plot true stress, vs. total
displacement u measured over
the gauge length L
2. For stress values in the
softening branch (i.e. beyond
damage initiation), compute
damage parameter d from the
expression
3. Compute the corresponding
plastic displacement as
shown in the schematic.
4. In the absence of intermediate
data, choose linear softening
and provide value of
(1 )d= -
plu
L
E
L
Ed)1( -
d-
u
L
E
softening
Undamaged
response
pl
fu
plupl
fu
0;0 == upl
d
uupl
f
pl
d == ;1
plu
Damage Evolution
L4.27
Modeling Fracture and Failure with Abaqus
Damage Evolution
• Energy-based damaged evolution
*DAMAGE EVOLUTION,TYPE=ENERGY,
SOFTENING={LINEAR,EXPONENTIAL}
pl
fu
y
0y
plu
fG
y
0y
plu
fG
(a) Linear (b) Exponential
0
2
y
fpl
f
Gu
= NOTE: The response is linear or
exponential only if the undamaged
response is perfectly plastic
L4.28
Modeling Fracture and Failure with Abaqus
Damage Evolution
• Example: Tearing of an X-shaped cross section
Pull and twist this
this end
Fix this endTie constraints
*damage initiation, criterion=fld
0.20,
*damage evolution, type=displacement, softening=tabular
0.0, 0.0
1.0, 0.003damage-plastic displacement data pairs
Failure modeled with different mesh
densities
L4.29
Modeling Fracture and Failure with Abaqus
Damage Evolution
• Comparison of reaction forces and moments confirms mesh insensitivity
of the results.
L4.30
Modeling Fracture and Failure with Abaqus
• Example: Axial crushing of an aluminum double-chamber profile
• Dynamic response with damage evolution
*Material, name=Aluminum
:
*Damage initiation, criterion=Ductile
:
*Damage evolution, type=displacement
0.1,
*Damage initiation, criterion=Shear, ks=0.3
:
*Damage evolution, type=displacement
0.1,
Damage Evolution
L4.31
Modeling Fracture and Failure with Abaqus
Damage Evolution
• With damage evolution, the simulation response is a good approximation
of the physical response.
Simulation without
damage evolutionSimulation with
damage evolutionAluminum double-chamber
after dynamic impact
Element Removal
L4.33
Modeling Fracture and Failure with Abaqus
Element Removal
• Abaqus offers the choice to
remove the element from the
mesh once the material stiffness
is fully degraded (i.e., once the
element has failed).
• An element is said to have
failed when all section
points at any one
integration point have lost
their load carrying capacity.
• By default, failed elements
are deleted from the mesh.
L4.34
Modeling Fracture and Failure with Abaqus
Element Removal
• Removing failed elements before complete degradation
• The material point is assumed to fail when the overall damage variable
D reaches the critical value Dmax.
• You can specify the value for the maximum degradation Dmax.
• The default value of Dmax is 1 if the element is to be removed from
the mesh upon failure.
L4.35
Modeling Fracture and Failure with Abaqus
Element Removal
• Usage:
*SECTION CONTROLS, NAME=Ec-1, ELEMENT DELETION=YES, MAX DEGRADATION=0.9
:
** Refer to the section controls by name on the element section definition.
*SOLID SECTION, ELSET=Elset_1, CONTROLS=Ec-1, MATERIAL=Material_1
:
L4.36
Modeling Fracture and Failure with Abaqus
Element Removal
• Retaining failed elements
• You may choose not to remove failed elements
from the mesh.
*SECTION CONTROLS, ELEMENT DELETION = NO
• In this case the default value of Dmax is
0.99, which ensures that elements will
remain active in the simulation with a
residual stiffness of at least 1% of the
original stiffness.
• Here Dmax represents
• the maximum degradation of the shear stiffness (three-dimensional),
• the total stiffness (plane stress), or
• the uniaxial stiffness (one-dimensional).
• Failed elements that have not been removed from the mesh can
sustain hydrostatic compressive stresses.
L4.37
Modeling Fracture and Failure with Abaqus
Failed elements removed
by default when STAUS
output is available
Element Removal
• Output
• The output variable SDEG
contains the value of D.
• The output variable STATUS
indicates whether or not an
element has failed.
• STATUS=0 for failed elements
• STATUS=1 for active elements
• Abaqus/Viewer will
automatically remove failed
elements when the output database (.odb) file includes
STATUS.
Deactivate status variable to view failed elements
failed
elements
Damage in Fiber-Reinforced Composite
Materials
L4.39
Modeling Fracture and Failure with Abaqus
Common damage types in
composite laminates
Damage in Fiber-Reinforced Composite Materials
• Abaqus offers a general capability for modeling progressive damage
and failure in fiber-reinforced composites.
• Material failure refers to the complete loss of load carrying capacity that
results from progressive degradation of the material stiffness.
• Stiffness degradation is modeled using damage mechanics.
• The model must be used with elements with a plane stress formulation
(plane stress, shell, continuum shell, and membrane elements)
• Four different modes of failure are considered:
• fiber rupture in tension;
• fiber buckling and kinking in
compression;
• matrix cracking under transverse
tension and shearing; and
• matrix crushing under transverse
compression and shearing
L4.40
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• User interface
• Damage Initiation
*DAMAGE INITIATION, CRITERION=HASHIN, ALPHA=<alpha>
XT,XC,YT,YC,SL,ST
L4.41
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Damage Evolution
*DAMAGE EVOLUTION,
TYPE=ENERGY,
SOFTENING=LINEAR
Gft,Gfc ,Gmt,Gmc
• Viscous Regularization
*DAMAGE STABILIZATION
ηft, ηfc, ηmt, ηmc
L4.42
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Output
• Initiation Criteria Variables
• HSNFTCRT – tensile fiber Hashin’s criterion
• HSNFCCRT – compressive fiber Hashin’s criterion
• HSNMTCRT – tensile matrix Hashin’s criterion
• HSNMCCRT – compressive matrix Hashin’s criterion
• Damage Variables
• DAMAGEFT – tensile fiber damage
• DAMAGEFC – compressive fiber damage
• DAMAGEMT – tensile matrix damage
• DAMAGEMC – compressive matrix damage
L4.43
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Output (cont'd)
• Status
• STATUS – element status (1 – present, 0 – removed)
• Energies
• Damage energy (ALLDMD,DMENER,ELDMD,EDMDDEN)
• Viscous regularization (ALLCD, CENER, ELCD, ECDDEN)
L4.44
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Example: Analysis of blunt notched fiber metal laminate
• Fiber metal laminates (FMLs) are composed of:
• laminated thin aluminum layers
• Intermediate glass fiber-reinforced epoxy layers
L4.45
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Geometry of blunt notched fiber metal laminate (Glare 3 3/2–0.3)
• Through-thickness view of the laminate:
Example Problem 1.4.6, "Failure of
blunt notched fiber metal laminates”
1/8 part model Aluminum core
and exterior
glass fiber-reinforced
epoxy layers
a through-thickness hole
L4.46
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Results
damage in matrix and damage in fibers
for one of glass fiber-reinforced epoxy layers Net blunt notch strength (MPa)
Test (De Vries, 2001) 446
Abaqus 453
L4.47
Modeling Fracture and Failure with Abaqus
Damage in Fiber-Reinforced Composite Materials
• Abaqus allows the import of the damage model
for fiber-reinforced composites from
Abaqus/Explicit to Abaqus/Standard.
• Details of the import capability will not be
covered in this lecture (please refer to
―Importing and transferring results,‖ Section
9.2 of the Abaqus Analysis User’s Manual).
• One typical application is the analysis of Barely
Visible Impact Damage (BVID) in composite
structures used in aerospace applications.
• Non-visible damage to composite structures is
a significant concern in the aerospace
industry.
from McGowan, D.M., and Ambur, D.R., NASA TM-110303
Damage-Tolerance Characteristics of Composite Fuselage Sandwich Structures With Thick Facesheets
Damage in Fasteners
L4.49
Modeling Fracture and Failure with Abaqus
Damage in Fasteners
• Connection methodologies—point fasteners
• Fastener (spot weld) compliance and failure are available in Abaqus.
multiple layers
radius of influence
attachment
points
L4.50
Modeling Fracture and Failure with Abaqus
Damage in Fasteners
• Fastener failure
• Model combines plasticity and progressive damage
Plasticity
0
45
90
Schematic representation of the
predicted numerical response
F
plu
– Stages:
• Rigid plasticity with
variable hardening
damage
initiation
boundary
• Damage initiation
Plasticity + Damage
• Progressive damage
evolution using fracture
energy
90N
0S
– Response depends on loading angle (normal/shear)
Spot weld
L4.51
Modeling Fracture and Failure with Abaqus
Damage in Fasteners
• Example
• Spot-welded hat section of three layers of sheet metals subjected to
severe compressive loading
Rigid spot welds Compliant spot welds with damage
Failed fasteners
Deformable fastener
still holding
Material Wear and Ablation
L4.53
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Material wear/erosion in Abaqus/Standard
• Many applications require the modeling
of wear/erosion of material at one or
more surfaces
• Capability enables modeling of material
wear/erosion on the surface of the body
• Idea is to erode material while receding
mesh away from surface (with same
number and topology of elements)
• Involves remeshing, state
mapping—handled through an
Arbitrary Lagrangian-Eulerian (ALE)
technique
• User interface takes advantage of
existing adaptive meshing
framework to define mesh motion
Adaptive mesh domain for modeling
material wear. Wear extent/velocity
applied as mesh constraints
L4.54
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Applications
• Geotechnical
• Well bore sand production
• Plastic strain, fluid velocity
• Aerospace
• Rocket motor ablation
• Pyrolysis, char formation
• Solid propellants
• Automotive
• Tire wear
• Disk brake wear
• Manufacturing
• Machining
Fluid velocity dependent
wear of a well bore
L4.55
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• User interface
*Adaptive mesh, elset=...
*Adaptive mesh constraint, type=[velocity|displacement],
User
*Adaptive mesh controls
• Adaptive mesh constraints define mesh motion (wear extent or velocity)
• Wear criterion
• General descriptions possible through user subroutine UMESHMOTION
• User access to solution variables
• Nodal
• Material
• Contact
• A local surface coordinate system is provided
L4.56
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Example of wear criterion
• Tire wear
• Use of CSLIP, CSHEAR, CPRESS
h E=
Rate of recession
of tread
Rate of frictional
energy dissipation
Proportionality
constant
h
L4.57
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Example: erosion of material
from oil bore hole perforation
tunnel
• Setup consists of bore hole
with perforations, loaded by
weight of material above
• Pore pressure gradient leads
to flow into perforation
• Material wear rate controlled
by fluid flux, transport
concentration, porosity, sand
production coefficient, and the
local plastic deformation
• Optimum design to minimize
wear rate
• Example Problem 1.1.22
Perforation tunnel
Bore hole
Geometry of oil well
Courtesy of Exxon
L4.58
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Analysis steps
• Geostatic
• Model change removal of well bore and casing (drilling operation)
• Apply pore pressure; establish steady state conditions
• Transient soils consolidation (during which the erosion occurs)
• Ablation relation:
V = 10 × (PEEQ - 0.028)
Erosion
velocity
L4.59
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Adaptive mesh constraints
*Adaptive mesh, elset=Adaptive-Zone, Freq=1, Mesh=40
*Adaptive mesh constraint, constraint type=Lagrangian
Lag
*Adaptive mesh constraint, type=velocity, user
Rock-Perf, 1, 1, 1.0
Adaptive-Zone Rock-Perf
Lag: Nodes on back face of
adaptive domain
Cut section of the adaptive mesh
domain showing the perforation tunnel
L4.60
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• User subroutinesubroutine umeshmotion(uref,ulocal,node,nndof,lnodetype,alocal,
$ ndim,time,dtime,pnewdt,kstep,kinc,kmeshsweep,jmatyp,jgvblock,lsmooth)
c
include 'aba_param.inc'
c
parameter (zero=0.d0, ten=10.d0, peeqCrit=0.028d0)
parameter (nelemmax=100)
dimension array(1000)
dimension ulocal(*)
dimension jgvblock(*),jmatyp(*)
dimension alocal(ndim,*)
dimension jelemlist(nelemmax),jelemtype(nelemmax)
locnum = 0
jtyp = 1
peeq = zero
nelems = nelemmax
call getNodeToElemConn(node,nelems,jelemlist,
$ jelemtype,jrcd,jgvblock)
call getVrmAvgAtNode(node, jtyp, 'PE', array, jrcd,
$ jelemlist, nelems, jmatyp, jgvblock)
peeq = array(7)
if (peeq .gt. peeqCrit) then
ulocal(ndim) = ulocal(ndim)- ten*(peeq - peeqCrit)
end if
return
end
When NDIM=3 the 3-direction
is normal to the surface
ulocal passed in as the value determined by
the mesh smoothing algorithm
L4.61
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Results
Material wear at bore hole/perforation junction Total volume lost due to erosion is available
with history output variable VOLC
L4.62
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Mesh smoothing
• Two options
• Original configuration projection
method
• Smoothing performed according
to the original configuration
• Volume-based smoothing
• Either method can include a
geometric-based enhancement
Original-configuration
smoothing
Volumetric
smoothing
L4.63
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Smoothing permitted in conjunction with UMESHMOTION constraints
• Enables UMESHMOTION to describe normal mesh motions, while the
smoothing algorithm handles the tangential mesh motions.
L4.64
Modeling Fracture and Failure with Abaqus
Material Wear and Ablation
• Limitations
• Available for a subset of continuum elements
• Available only for following procedures using geometric nonlinearity
• Static
• Soils
• Coupled Temperature-Displacement
• Tracer particles not supported
Element-based Cohesive Behavior
Lecture 5
L5.2
Modeling Fracture and Failure with Abaqus
Overview
• Introduction
• Element Technology
• Constitutive Response
• Viscous Regularization
• Modeling Techniques
• Examples
• Workshop 3 (Part 1)
• Workshop 4
L5.3
Modeling Fracture and Failure with Abaqus
Overview
• Historical perspective
• The concept of a cohesive zone has been around for some time:
• Dugdale (1960) and Barenblatt (1962) were the first to apply the
concept of a cohesive stress zone to fracture modeling.
• Many extensions since then.
• For example, Needleman (1987) recognized that cohesive
elements are particularly attractive when interface strengths are
relatively weak compared to the adjoining materials.
• Examples: composite laminates and parts bonded with adhesives
Introduction
L5.5
Modeling Fracture and Failure with Abaqus
Introduction
• Cohesive behavior is useful in modeling adhesives, bonded interfaces, and gaskets.
• Models separation between two initially bonded surfaces
• Progressive failure of adhesives
• Delamination in composites
• Idealize complex fracture mechanisms with a macroscopic “cohesive law,” which relates the traction across the interface to the separation.
• The cohesive behavior can be:
• Element-based
• Modeled with cohesive elements
• Surface-based
• Modeled with contact pairs in Abaqus/Standard and general contact in Abaqus/Explicit
Rail crush: Cohesive surfaces
Failed adhesive is red (CSDMG = 1)
T-peel analysis: Cohesive elements are
used for modeling adhesive patches
L5.6
Modeling Fracture and Failure with Abaqus
Introduction
• Element-based cohesive behavior—cohesive elements
• Cohesive elements allow very detailed modeling of adhesive
connections, including
• specification of detailed adhesive material properties, direct control
of the connection mesh, modeling of adhesives of finite thickness,
etc.
• Cohesive elements in Abaqus primarily address two classes of
problems:
• Adhesive joints
• Adhesive layer with finite thickness
• Typically the bulk material properties are known
• Delamination
• Adhesive layer of “zero” thickness
• Typically the bulk material properties are not known
L5.7
Modeling Fracture and Failure with Abaqus
Introduction
• The constitutive modeling depends on the class of problem:
• Based on macroscopic properties (stiffness, strength) for adhesive
joints
• Continuum description: any Abaqus material model can be used
• Modeling technique is relatively straightforward: cohesive layer
has finite thickness; standard material models (including damage).
• The continuum description is not discussed further in this lecture.
• Based on a traction-separation description for delamination
• Linear elasticity with damage
• Modeling technique is less straightforward: typical applications use
zero-thickness cohesive elements; non-standard constitutive law
• This application is the primary focus of this lecture
L5.8
Modeling Fracture and Failure with Abaqus
Introduction
• In addition, the uniaxial response of a laterally unconstrained adhesive
patch can also be modeled
• This represents the behavior of a gasket.
• Limited capability for modeling gaskets with cohesive elements:
• The complexity of the response in the thickness direction is not
as rich as with gasket elements available in Abaqus/Standard.
• Compared to gasket elements, however, cohesive elements:
• are fully nonlinear (can be used with finite strains and
rotations);
• can have mass in a dynamic analysis; and
• are available in both Abaqus/Standard and Abaqus/Explicit.
• The use of cohesive elements for modeling gaskets is not discussed
further in this lecture.
L5.9
Modeling Fracture and Failure with Abaqus
Introduction
• Surface-based cohesive behavior—cohesive surfaces
• This is a simplified and easy way to model cohesive connections, using
the traction-separation interface behavior.
• It offers capabilities that are very similar to cohesive elements
modeled with the traction-separation constitutive response.
• However, it does not require element definitions.
• In addition, cohesive surfaces can bond anytime contact is
established (“sticky” contact)
• It is primarily intended for situations in which interface thickness is
negligibly small.
• It must be defined as a surface interaction property.
• Damage for cohesive surfaces is an interaction property, not a
material property.
• The kinematics of cohesive surfaces is different from that of cohesive
elements.
• By default, the initial stiffness of the interface is computed
automatically.
L5.10
Modeling Fracture and Failure with Abaqus
Introduction
• Cohesive elements are the focus of this lecture.
• Cohesive surfaces are discussed in the next lecture.
• A workshop exercise will allow you to compare and contrast the two
cohesive modeling techniques in the context of a simple problem.
Element Technology
L5.12
Modeling Fracture and Failure with Abaqus
Element Technology
• Element types*
• 3D elements
• COH3D8
• COH3D6
• 2D element
• COH2D4
• Axisymmetric element
• COHAX4
• These elements can be embedded
in a model via
• shared nodes or
• tie constraints.
Bottom face
Top face
*Cohesive pore pressure elements are also available.
L5.13
Modeling Fracture and Failure with Abaqus
Element Technology
• Element and section definition
*ELEMENT, TYPE = COH3D8
*COHESIVE SECTION, ELSET =...,
RESPONSE = {TRACTION SEPARATION, CONTINUUM,
GASKET },
THICKNESS = { SPECIFIED, GEOMETRY},
MATERIAL = ...
Specify thickness in dataline (default is 1.0)
L5.14
Modeling Fracture and Failure with Abaqus
Element Technology
• Default thickness of cohesive elements
• Traction-separation response:
• Unit thickness
• Continuum and gasket response
• Geometric thickness based on nodal coordinates
L5.15
Modeling Fracture and Failure with Abaqus
Element Technology
• Output variables
• Scalar damage (i.e., degradation) variable
• SDEG
• Variables indicating whether damage initiation criteria met or exceeded
• Discussed shortly
• Element status flag
• STATUS
L5.16
Modeling Fracture and Failure with Abaqus
Element Technology
• Import of cohesive elements
• The combination of Abaqus/Standard and Abaqus/Explicit expands the
range of applications for cohesive elements.
• For example, you can simulate the damage in a structure due to an
impact event then study the effect of the damage on the structure's load
carrying capacity.
Constitutive Response
L5.18
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Delamination applications
• Traction separation law
• Typically characterized by peak strength (N) and fracture energy (GTC)
• Mode dependent
• Linear elasticity with damage
• Available in both Abaqus/Standard and Abaqus/Explicit
• Modeling of damage under the general framework introduced earlier
• Damage initiation
• Traction or separation-based criterion
• Damage evolution
• Removal of elements0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
Mode Mix
GT
C
Normal mode
Shear mode
Dependence of fracture toughness
on mode mix
Typical traction-separation response
T
T CG
N
L5.19
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Linear elasticity with damage
• Linear elasticity
• Defines behavior before the
initiation of damage
• Relates nominal stress to nominal
strain
• Nominal traction to separation
with default choice of unit
thickness
• Uncoupled traction behavior:
nominal stress depends only on
corresponding nominal strain
• Coupled traction behavior is more
general*ELASTIC, TYPE = { TRACTION,
COUPLED TRACTION }
L5.20
Modeling Fracture and Failure with Abaqus
Constitutive Response
• The elastic modulus for the traction
separation law should be interpreted as a
penalty stiffness.
• For example, for the opening mode:
Kn = Nmax / ninit
• In Abaqus, nominal stress and strain
quantities are used for the traction
separation law.
• If unit thickness is specified for the
element, then the nominal strain
corresponds to the separation value.
• Elastic response governed by Kn.
• If you specify a non-unit thickness for
the cohesive element, you must scale
your data to obtain the correct
stiffness Kn. Example on next slide.
N
n
maxN
initn fail
n
nK
1
Displacement at damage
initiation in normal
(opening) mode
L5.21
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Example: Peel test model
A
En=Knheff
/ /
n n
n n
n n eff n n eff
N E
K
h K E h
=
=
= =
Abaqus evaluates this…
…which is equivalent to this
Geometric thickness (based
on nodal coordinates) of the
adhesive hgeom = 1e-3
Assume separation at initiation = 1e-3
and Nmax = 6.9e9.
For model A: use geometric thickness
heff = hgeom =1e-3 = /heff = 1;
Nmax = En = 6.9e9 Kn = 6.9e12
For model B: specify unit thickness
heff = 1 = / heff =1e-3;
Nmax = 6.9e9 En = Kn = 6.9e12
initn
initn
initn
initninit
n
B
L5.22
Modeling Fracture and Failure with Abaqus
• Damage initiation
• Mixed mode conditions
• Maximum stress
(or strain) criterion:
• Output:
• MAXSCRT
• MAXECRT
Constitutive Response
max max max
, , 1n t sMAX
N T S
=
0
0 0
n nn
n
=
for
for
* DAMAGE INITIATION, CRITERION = { MAXS, MAXE }
L5.23
Modeling Fracture and Failure with Abaqus
Constitutive Response
• For example, for Mode I (opening mode) the MAXS condition implies
damage initiates when n = Nmax.
N
n
maxN
*Damage initiation,criterion=MAXS
290.0E6, 200.0E6, 200.0E6
Damage initiation point
Nmax Tmax Smax
L5.24
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Quadratic stress (or strain) interaction criterion:
• No damage initiation under
pure compression
• Output:
• QUADSCRT
• QUADECRT
2 2 2
max max max
1n t s
N T S
=
* DAMAGE INITIATION,
CRITERION = { QUADS, QUADE }
L5.25
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Summary of damage initiation criteria
max max max, , 1
n s t
n s t
MAX
=
Maximum nominal strain criterion
*DAMAGE INITIATION, CRITERION=MAXEmax max max, ,n s t
2 2 2
max max max1
n s t
n s t
=
Quadratic nominal stress criterion
*DAMAGE INITIATION, CRITERION=QUADEmax max max, ,n s t
2 2 2
max max max
1n s t
N S T
=
Quadratic nominal stress criterion
*DAMAGE INITIATION, CRITERION=QUADS
max max max, ,N S T
n: nominal stress in the pure normal mode
s: nominal stress in the first shear direction
t: nominal stress in the second shear direction
n: nominal strain in the pure normal mode
s: nominal strain in the first shear direction
t: nominal strain in the second shear direction
*DAMAGE INITIATION, CRITERION=MAXS
max max max, ,N S T
max max max
, , 1n s tMAX
N S T
=
Maximum nominal stress criterion
, ,n s tn s t
o o oT T T
= = =Note : where n, s, and t are components of relative displacement
between the top and bottom of the cohesive element; and To
is the original thickness of the cohesive element.
L5.26
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Damage evolution
• Post damage-initiation response defined by:
• d is the scalar damage variable
d = 0: undamaged
d = 1: fully damaged
d monotonically increases
1 d= -
Typical damaged response
0K
d-
(1 )d-
0K
0(1 )d Κ-
L5.27
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Damage evolution is based on
energy or displacement
• Specify either the total
fracture energy or the post
damage-initiation effective
displacement at failure
• May depend on mode mix
• Mode mix may be defined in
terms of energy or traction
N
n
T CG
Area under the curve
is the fracture energy
maxN
Displacement at failure
in normal (opening) mode
failn
L5.28
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Displacement-based damage evolution
• Damage is a function of an effective
displacement:
• The post damage-initiation softening
response can be either
• Linear
• Exponential
• Tabular
Traction
Linear post-
initiation response
init fail
2 2 2n s t =
L5.29
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Keywords interface for displacement-based damage evolution
• For LINEAR and EXPONENTIAL softening:
• Specify the effective displacement at complete failure fail relative to
the effective displacement at initiation init.
• For TABULAR softening:
• Specify the scalar damage variable d directly as a function of
–init.
• Optionally specify the effective displacement as function of mode mix in tabular form.
• Abaqus assumes that the damage evolution is mode independent otherwise.
*DAMAGE EVOLUTION, TYPE = DISPLACEMENT,
SOFTENING = { LINEAR | EXPONENTIAL | TABULAR },
MIXED MODE BEHAVIOR = TABULAR
L5.30
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Abaqus/CAE interface for displacement-based damage evolution
L5.31
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Energy-based damage evolution
• The fracture energy can be defined as a function of mode mix using
either a tabular form or one of two analytical forms:
• Power law
• BK (Benzeggagh-Kenane)
1I II III
IC IIC IIIC
G G G
G G G
=
For isotropic failure
(GIC = GIIC), the
response is insensitive to
the value of .
shearIC IIC IC TC
T
shear II III
T I shear
GG G G G
G
G G G
G G G
- =
=
=
where
L5.32
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Keywords interface for energy-based damage evolution
• Specify fracture energy as function of mode mix in tabular form, or
• Specify the fracture energy in pure normal and shear deformation modes
and choose either the POWER LAW or the BK mixed mode behavior
*DAMAGE EVOLUTION, TYPE = ENERGY,
SOFTENING = { LINEAR | EXPONENTIAL},
MIXED MODE BEHAVIOR = { TABULAR | POWER LAW | BK },
POWER = value
L5.33
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Abaqus/CAE interface for energy-based damage evolution
L5.34
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Example
• The preceding discussion was very
general in the sense that the full
range of options for modeling the
constitutive response of cohesive
elements was presented.
• In the simplest case, Abaqus requires
that you input the adhesive thickness
heff and 10 material parameters:
*Elastic, type=traction
En, Et, Es
*Damage initiation, criterion =
maxs
Nmax, Tmax, Smax
*Damage evolution, type=energy,
mixed mode behavior=bk, power=
GIC, GIIC , GIIIC
What do you do when you only
have 1 property and the adhesive
thickness is essentially zero?
Diehl, T., "Modeling Surface-Bonded Structures with
ABAQUS Cohesive Elements: Beam-Type Solutions,"
ABAQUS Users' Conference, Stockholm, 2005.
Normal (opening) mode:
maxN
initn fail
n
nK
1Tra
ctio
n
(no
min
al
stre
ss)
Separation
(area under
entire curve)
GIC
Cohesive material law:
Traction, Damage Evolution
nn
eff
EK
h=
L5.35
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Example (cont’d)
• Common case: you know GTC for the surface bond.
• Assume isotropic behavior
GIC = GIIC = GIIIC = GTC
• For MIXED MODE BEHAVIOR = BK, this makes the response
independent of term, so set = any valid input value (e.g.,
1.0)
• Bond thickness is essentially zero
• Specify the cohesive section property thickness heff = 1.0
Nominal strains = separation; elastic moduli = stiffness
• Isotropy also implies the following:
En = Et = Es = Eeff (=Keff since we chose heff = 1.0)
Nmax = Tmax = Smax = Tult
L5.36
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Example (cont’d)
• Introduce concept of damage initiation ratio:
ratio= init /fail, where 0 ratio 1.
• Use GC and equation of a triangle to relate back to Keff and Tult :
• The problem now reduces to two penalty terms: fail and ratio.
• Assume ratio = ½.
• Choose fail as a fraction of the typical cohesive element mesh size.
• For example, use fail = 0.050 typical cohesive element size
as a starting point.
2
2 TCeff
ratio fail
GK
=
2 TCult
fail
GT
=
L5.37
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Example (cont’d)
• Thus, after choosing the two penalty terms, a single (effective)
traction-separation law applies to all modes (normal + shear):
*Cohesive section, thickness=SPECIFIED, ...
1.0,
:
:
*Elastic, type=TRACTION
Keff, Keff, Keff*Damage initiation, criterion = MAXS
Tult, Tult, Tult*Damage evolution, type=ENERGY,
mixed mode behavior=BK, power=1
GTC, GTC , GTC
Effective properties:
ultT
init fail
effK
1Tra
ctio
n
(no
min
al
stre
ss)
Separation
(area under
entire curve)
GTC
Cohesive material law:
Traction, Damage Evolution
effeff
eff
EK
h=
L5.38
Modeling Fracture and Failure with Abaqus
Constitutive Response
• Example (cont’d)
• What if the response is dynamic? What about the density?
• The density of the cohesive layer should also be considered a
penalty quantity.
• For Abaqus/Explicit, the effective density should not adversely affect
the stable time increment. Diehl suggests the following rule:
• The Abaqus Analysis User’s Manual provides additional guidelines
for determining a cohesive element density that minimizes the effect
on the stable time increment in Abaqus/Explicit.
• Dtstable = stable time increment
without cohesive elements in the model
• ft2D = 0.32213 (for cohesive elements
whose original nodal coordinates relate
to zero element thickness)
2
2
stableeff eff
t D eff
tE
f h
D=
Viscous Regularization
L5.40
Modeling Fracture and Failure with Abaqus
Viscous Regularization
• Cohesive elements have the potential to cause numerical difficulties in
the following cases
• Stiff cohesive behavior may lead to reduced maximum stable time
increment in Abaqus/Explicit
• Potentially addressed through selective mass scaling
• Unstable crack propagation may lead to convergence difficulties in
Abaqus/Standard
• Potentially addressed through built-in viscous regularization option
specific to cohesive elements
L5.41
Modeling Fracture and Failure with Abaqus
Viscous Regularization
• Viscous regularization
• Material models with damage often lead to severe convergence
difficulties in Abaqus/Standard
• Viscous regularization helps in such cases
• Helps make the consistent tangent stiffness of softening material
positive for sufficiently small time increments
• Similar approach used in the concrete damaged plasticity model in
Abaqus/Standard
1 vd= -
1
v vd d d
= -
L5.42
Modeling Fracture and Failure with Abaqus
Viscous Regularization
• Consistent material tangent stiffness
K0 is the undamaged elastic stiffness
f is a factor that depends on the details of the damage model
• Viscous regularization ensures that when ,
• “Offending” second term is eliminated when the analysis cuts back
drastically
0t
D
01d
d f
= - -
D K
0(1 )d= -D K
L5.43
Modeling Fracture and Failure with Abaqus
Viscous Regularization
• User interface for viscous regularization
*COHESIVE SECTION, CONTROLS = control1
*SECTION CONTROLS, NAME = control1,
VISCOSITY = factor
• Add-on transverse shear stiffness may
provide additional stability
*COHESIVE SECTION
*TRANSVERSE SHEAR STIFFNESS
• Output
• Energy associated with viscous regularization: ALLCD
L5.44
Modeling Fracture and Failure with Abaqus
Viscous Regularization
• Example: Multiple delamination
problem (Alfano & Crisfield, 2001)
– Industry standard Alfano-
Crisfield nonsymmetric
delamination examples
• Plies are initially bonded with
predefined cracks, then peeled
apart in a complex sequence
• Example done in
Abaqus/Standard and
Abaqus/Explicit
• Effect of viscous regularization
is investigated
10 layers
12 layers2 layers
Interface elementsInitial cracks
a1
a2
a2
L
L5.45
Modeling Fracture and Failure with Abaqus
Viscous Regularization
.e= -1 4
.e= -1 3
= 0
. e= -2 5 4
.e= -5 4
L5.46
Modeling Fracture and Failure with Abaqus
Viscous Regularization
• Effect of viscous regularization on convergence of multiple delamination
problem:
• Significant improvements with small regularization factor
Viscous
regularization
factor
Total number of
increments
0. 375
1.0e-4 171
2.5e-4 153
1.0e-3 164
Modeling Techniques
L5.48
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Model problem: double-cantilever beam
• Alfano and Crisfield (2001)
• Pure Mode I
• Displacement control
• Analyzed using
• 1D (B21),
• 2D (CPE4I), and
• 3D (C3D8I) elements
• Delamination assumed to occur along a straight line
• Beams: Orthotropic material
• Cohesive layer: Traction-separation with damage
Initial crack
u
- u
L5.49
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model
• Use tie constraints between the cohesive layer and the beams
• Require distinct parts for the beam and cohesive zone geometry
• Geometry
L5.50
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model (cont’d)
• Assembly
Create 2 instances of the beam;
one of the cohesive zone
Position the parts to leave gaps
between them; this will later
facilitate picking surfaces
L5.51
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model (cont’d)
• Tie constraints
Define tie constraints between
mating surfaces.
The cohesive side should be the
slave surface (because it is a
softer material)
This approach is required when
quadratic displacement elements
are used.
beam-top
beam-bot
coh-top
coh-bot
L5.52
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model (cont’d)
• Properties: beam
L5.53
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model (cont’d)
• Properties: adhesive
L5.54
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model (cont’d)
• MeshingCohesive elements can only
be assigned to sweep
meshable regions
Sweep path must be aligned
with thickness direction
Assign seeds and mesh
Only one element
through the thickness
1
3
Assign cohesive element
type to the swept region2
L5.55
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• One-dimensional model (cont’d)
• Meshing (cont’d)
Edit the nodal coordinates of each part instance
so that they all have the same 2-coordinate
Toggle this off; otherwise, nodes will
project back to their original positions
Final mesh
4
L5.56
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Two-dimensional model
• All geometry is 2D and planar
• Properties, attributes, etc. treated in a
similar manner to the 1D case presented
earlier
• Modeling options include:
• Shared nodes
• Tie constraints
• Similar to the 1D model
L5.57
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Two-dimensional model (cont’d)
• Shared nodes
Define a finite thickness slit in the beam as shown below
• Use the actual overall thickness of the DCB
• The center region represents the cohesive layer
Mesh the part:
1
2
L5.58
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Two-dimensional model (cont’d)
• Shared nodes (cont’d)
Edit the coordinates of the nodes along the interface3
L5.59
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Two-dimensional model (cont’d)
• Tie constraints
Create two instances of the beams and position them as shown
below.
• Suppress the visibility of the instances to facilitate picking
surfaces, etc.
Create a finite thickness cohesive layer, position it appropriately in
the horizontal direction, define surfaces, etc.
• After meshing, adjust the coordinates of all the nodes in the
cohesive layer so that they lie along the interface between the
two beams.
1
2
L5.60
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Three-dimensional model
• All geometry is 3D
• Solid geometry for beams
• Solid or shell geometry for cohesive layer
• Modeling options include
• Shared nodes
• Tie constraints
L5.61
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Three-dimensional model (cont’d)
• Shared nodes
Partition the geometry and
define a mesh seam
between these two faces
1
L5.62
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Three-dimensional model (cont’d)
• Shared nodes (cont’d)
Mesh the part with solid
(continuum elements).
Create a orphan mesh
Mesh→Create Mesh Part
2
3
L5.63
Modeling Fracture and Failure with Abaqus
Modeling Techniques
Create a single zero-thickness
solid layer by offsetting from the
midplane (selected by angle) of
the orphan mesh created in the
previous step
Tip 2: Use the selection
options tools to facilitate
picking. In particular, select
from interior entities.
Create a set for the new layer so you
can easily assign element type and
section properties.
Tip 1: Remove elements from
top region with display groups
(select by angle)4
L5.64
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Three-dimensional model (cont’d)
• Shared nodes (cont’d)
Assign section properties and
the element type to the set
created in the previous step
5
L5.65
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Three-dimensional model (cont’d)
• Tie constraints
• The cohesive region can be defined
as
• Solid (with finite thickness)
• Edit nodal coordinates of
cohesive elements as in
previous examples
• Shell geometry
• Mesh geometry then create
orphan mesh
• Offset a zero-thickness layer of
solid elements from the orphan
mesh
Define surfaces automatically to
facilitate tie constraints
L5.66
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Three-dimensional model (cont’d)
• Tie constraints (cont’d)
When defining the tie constraints,
query the mesh stack direction to
determine when the “top” and
“bottom” surfaces should be used
Brown = top Purple = bottom
L5.67
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• What if I don't use Abaqus/CAE?
• In this case do the following in the preprocessor of your choice:
1. Generate the mesh for the structure and cohesive layer
(temporarily assigning an arbitrary element type to the cohesive
layer)
2. Position the layer of cohesive elements over the interface
3. Define surfaces on the structure and cohesive layer
4. Write the input file
Surface top-beam
Surface bot-beam
Surface top-coh
Surface bot-coh
L5.68
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Edit the input file:
5. Change the element type assigned to the cohesive layer
6. Assign cohesive section properties
*element, elset=coh, type=coh2d4
*cohesive section, elset=coh, material=cohesive,
response=traction separation, stack direction=2, controls=visco
1.0, 0.02
:
*material, name=cohesive
*elastic, type=traction
5.7e+14, 5.7e+14, 5.7e+14
*damage initiation, criterion=quads
5.7e7, 5.7e7, 5.7e7
*damage evolution, type=energy, mixed mode behavior=bk, power=2.284
280.0, 280.0, 280.0
L5.69
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• The stack direction defines the thickness direction based on the
element isoparametric directions.
• Set STACK DIRECTION = { 1 | 2 | 3 } to define the element
thickness direction along an isoparametric direction.
• 2D example (extends to 3D):
Thickness
direction
Element connectivity: 101, 102, 202, 201
Stack direction = 2
Element connectivity: 102, 202, 201, 101
Stack direction = 1
101
201 202
102
1
2
101
201 202
102
1
2
L5.70
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Edit the input file (cont'd):
7. Define tie constraints between the surfaces
*tie, name=top, adjust=yes, position tolerance=0.002
top-coh, top-beam
*tie, name=bot, adjust=yes, position tolerance=0.002
bot-coh, bot-beam
Setting adjust=yes will force Abaqus to
move the slave (cohesive element) nodes
onto the master surface. By adjusting both
the top and bottom cohesive surfaces in this
way, a zero-thickness cohesive layer is
produced.
The position tolerance should be large
enough to contain the slave nodes when
measured from the master surface. In this
case the overclosure is equal to 0.001 on
either side of the interface so a position
tolerance of 0.002 is sufficient to capture all
slave nodes.
0.001
Cohesive surface
is the slave
L5.71
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Results
L5.72
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Effect of viscous regularization
Viscous
regularization
factor
Total number
of increments
1.e-5 636
2.5e-5 163
5.0e-5 129
1.0e-4 90
L5.73
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Effect of mesh refinement
• Typically, you will need to use
a much finer mesh (for both
the stress/displacement and
cohesive elements) than may
be necessary for a problem
without cohesive elements.
L5.74
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Non-planar geometry
• The technique for embedding a layer of solid elements into an orphan
mesh is not restricted to planar geometry.
• As an example, consider the following fiber-matrix pullout model
Orphan mesh
fiber
matrix
L5.75
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Failure driven by mismatch in CTEs
View cut of the matrix-fiber interface at
100% of the applied load (magnified 5×) Failure levels at 38% of the applied load
L5.76
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Cohesive elements on a symmetry plane
• The traction-separation law is based on
the separation between the top and
bottom faces of the cohesive element.
• On a symmetry plane, however, the
separation that is computed is ½ the
actual value.
• To account for this, specify:
• 2 the cohesive stiffness that would
be used in a full model.
• ½ the fracture toughness that would
be used in a full model.
• Linear equations between the
nodes on the top and bottom faces
in the lateral directions.
N
n
maxN
2
initn
2
failn
2 nK
1
2
CGarea =
22
/ 2
n nn
eff eff
E EK
h h= =
L5.77
Modeling Fracture and Failure with Abaqus
Modeling Techniques
• Symmetry example
Symmetric model
Full model
Symmetric model (top)
overlaid on full model
Constitutive thickness is
same as for the full model so
double the elastic modulus to
double the cohesive stiffness
Constraint on lateral
displacements
Examples
L5.79
Modeling Fracture and Failure with Abaqus
Examples
• Composite components in
aerospace structures
(Courtesy: NASA)
• Stress concentrations
around stiffener
terminations and flanges
• Residual thermal strains at
the interface at room
temperature
• Analysis of the effects of
residual strains on
skin/stiffener debonding
• Delamination initiation and
propagation
Beginning of separation After separation
Abaqus/Standard simulation of skin/stiffener debonding
Example Problem 1.4.5
L5.80
Modeling Fracture and Failure with Abaqus
Examples
Abaqus/Standard simulation of
skin/stiffener debonding
L5.81
Modeling Fracture and Failure with Abaqus
Examples
• Electronic packaging (Courtesy: INTEL)
• Solder to motherboard fracture due to static overload
• Experiments to assess integrity of solder joints under various loading conditions (e.g., board bending)
• Strain in motherboard at which solder joint fails
Ball grid array
L5.82
Modeling Fracture and Failure with Abaqus
Examples
Damage severity in cohesive layer between
motherboard and solder balls
Debonded solder balls
L5.83
Modeling Fracture and Failure with Abaqus
Cohesive layers
Examples
• Delamination of a composite
• This model is a representative of composite
delamination.
• It comprises 3 layers of composite with
adhesive layers applied between
composite layers.
• The composite delaminates under the
impact of a heavy mass displayed in
light greenish shade in the animation.
L5.84
Modeling Fracture and Failure with Abaqus
Examples
• Impact of moving mass with a stationary wall
• Brick wall modeled with adhesives applied
to each face of each brick.
• Simulating damage of the (stationary) wall
from high velocity impact with a heavy
mass
• Analysis performed in Abaqus/Explicit.
• This model is a representative of several
problems that can be modeled using
cohesive elements
• Hydroplaning
• Machining
• Oil Drilling
• Excavation
• Effect of explosion on a building.
Section of the model illustrating
the application of cohesive
layers around the bricks.
L5.85
Modeling Fracture and Failure with Abaqus
Examples
• Deformation sequence
Workshop 3 (Part 1)
L5.87
Modeling Fracture and Failure with Abaqus
Workshop 3 (Part 1)
• Crack growth in a three-point bend specimen using element-based
cohesive behavior
• Generate cohesive element mesh
• Define/assign traction-separation behavior and damage properties
Layer of
cohesive
elements
Workshop 4 (Optional)
L5.89
Modeling Fracture and Failure with Abaqus
Workshop 4 (Optional)
• Crack growth in a helicopter airframe
• Use the mesh offset tool to create a layer of cohesive elements
• Impose symmetry conditions on the cohesive elements using linear
equations
Cohesive element
thickness shrunk to zero
Surface-based Cohesive Behavior
Lecture 6
L6.2
Modeling Fracture and Failure with Abaqus
Overview
• Surface-based Cohesive Behavior
• Element- vs. Surface-based Cohesive Behavior
• Workshop 3 (Part 2)
Surface-based Cohesive Behavior
L6.4
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Surface-based cohesive behavior provides a simplified way to model
cohesive connections with negligibly small interface thicknesses using the
traction-separation constitutive model.
• It can also model “sticky” contact (surfaces can bond after coming into
contact).
• The cohesive surface behavior can be defined for general contact in
Abaqus/Explicit and contact pairs in Abaqus/Standard (with the
exception of the finite-sliding, surface-to-surface formulation).
• Cohesive surface behavior is defined as a surface interaction property.
• To prevent overconstraints in Abaqus/Explicit, a pure master-slave
formulation is enforced for surfaces with cohesive behavior.
L6.5
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• User interface
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR
...
*CONTACT PAIR, INTERACTION=cohesive
surface1, surface2
Abaqus/Standard
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR
...
*CONTACT
*CONTACT PROPERTY ASSIGNMENT
surface1, surface2, cohesive
Abaqus/Explicit
Abaqus/CAE
L6.6
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• The formulae and laws that govern surface-based cohesive behavior are
very similar to those used for cohesive elements with traction-separation
behavior:
• linear elastic traction-separation,
• damage initiation criteria, and
• damage evolution laws.
• However, it is important to recognize that damage in surface-based
cohesive behavior is an interaction property, not a material property.
• Traction and separation are interpreted differently for cohesive elements
and cohesive surfaces:
Relative displacement ()between the top and bottom
of the cohesive layer
Cohesive elements Cohesive surfaces
Nominal strain () = Contact separation ()Initial thickness (To)
Nominal stress () Contact force (F)Contact stress (t) =
Current area (A) at each contact point
separation
traction
traction
separation
GC
L6.7
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Linear elastic traction-separation behavior
• Relates normal and shear stresses to the normal and shear separations
across the interface before the initiation of damage.
• By default, elastic properties are based on underlying element stiffness.
• Can optionally specify the properties.
• Recall this specification is required for cohesive elements.
• The traction-separation behavior can be uncoupled (default) or coupled.
*COHESIVE BEHAVIOR, TYPE= { UNCOUPLED, COUPLED}
Optional data line to specify Knn, Kss, Ktt
L6.8
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Controlling the cohered nodes
• The slave nodes to which cohesive behavior is applied can be controlled
to define a wider range of cohesive interactions: Can include:
• All slave nodes
• Only slave nodes initially in contact
• Initially bonded node set
• Applying cohesive behavior to all slave nodes (default)
• Cohesive constraint forces potentially act on all nodes of the
slave surface.
• Slave nodes that are not initially contacting the master surface
can also experience cohesive forces if they contact the master
surface during the analysis.
*COHESIVE BEHAVIOR,
ELIGIBILITY = CURRENT CONTACTS
1
L6.9
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
Applying cohesive behavior only to slave nodes initially in contact
• Restrict cohesive behavior to only those slave nodes that are in
contact with the master surface at the start of a step.
• Any new contact that occurs during the step will not experience
cohesive constraint forces.
• Only compressive contact is modeled for new contact.
*COHESIVE BEHAVIOR,
ELIGIBILITY = ORIGINAL CONTACTS
2
L6.10
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
Applying cohesive behavior only to an initially bonded node set
(Abaqus/Standard only)
• Restrict cohesive behavior to a subset of slave nodes defined
using *INITIAL CONDITIONS, TYPE=CONTACT.
• All slave nodes outside of this set will experience only
compressive contact forces during the analysis.
• This method is particularly useful for modeling crack
propagation along an existing fault line.
3
*COHESIVE BEHAVIOR,
ELIGIBILITY = SPECIFIED CONTACTS
L6.11
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Example: Double cantilever beam (DCB)
• Analyze debonding of the DCB model using the surface-based cohesive behavior in Abaqus/Standard.
• To model debonding using surface-based cohesive behavior,
• you must define:
• contact pairs and initially bonded crack surfaces;
• the traction-separation behavior;
• the damage initiation criterion; and
• the damage evolution.
• You may also
• specify viscous regularization to facilitate solution convergence in Abaqus/Standard.
• Note: Steps 3, 4, and 5, will be covered later in this lecture.
Initial crack
u
- uCohesive interface
1
2
3
4
5
Note: Only the Keywords interface is illustrated in the example;
the Abaqus/CAE interface is illustrated in the workshop exercise.
L6.12
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Define contact pairs and initially bonded crack surfaces
• The initially bonded portion of the slave surface (i.e., node set bond)
is identified with the *INITIAL CONDITIONS, TYPE=CONTACT
option.
1
Note: Frictionless contact is assumed.
*NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=cohesive
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
slave surface master surface a list of slave nodes
that are initially bonded
BotSurfTopSurf
bond
L6.13
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Define traction-separation behavior
• In this model, the cohesive behavior is only enforced for the node set bond.
• Use the ELIGIBILITY=SPECIFIED CONTACTS
parameter to enforce this behavior.
• Recall the default elastic properties are based
on underlying element stiffness. Here we
specify the properties.
...
*CONTACT PAIR, INTER=cohesive
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR,
ELIGIBILITY=SPECIFIED CONTACTS
5.7e14, 5.7e14, 5.7e14
2
Kn Ks Kt
t
1
Kn (Ks , Kt)
Kn, Ks, and Kt: normal and
tangential stiffness components
Optional
BotSurfTopSurf
bond
L6.14
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
separations at failure
, ,f f fn s t and :
peak values of the contact stress
max max max, ,n s tt t tand :
peak values of the contact separation
max max max, ,n s t and :
max max max,n s tt t t
,f f fn s t
t
max max max,n s t
• Damage modeling for cohesive
surfaces
• Damage of the traction-separation
response for cohesive surfaces is
defined within the same general
framework used for cohesive
elements.
• The difference between the two
approaches is that for cohesive
surfaces damage is specified as
part of the contact interaction
properties.
L6.15
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• User interface
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR
*DAMAGE INITIATION
*DAMAGE EVOLUTION
*CONTACT PAIR, INTERACTION=cohesive
surface1, surface2
Abaqus/Standard
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR
*DAMAGE INITIATION
*DAMAGE EVOLUTION
*CONTACT
*CONTACT PROPERTY ASSIGNMENT
surface1, surface2, cohesive
Abaqus/Explicit
Abaqus/CAE
L6.16
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Damage initiation criteria
max max max, , 1
n s t
n s t
MAX
Maximum separation criterion
*DAMAGE INITIATION, CRITERION=MAXUmax max max, ,n s t
2 2 2
max max max1
n s t
n s t
Quadratic separation criterion
*DAMAGE INITIATION, CRITERION=QUADUmax max max, ,n s t
2 2 2
max max max1
n s t
n s t
t t t
t t t
Quadratic stress criterion
*DAMAGE INITIATION, CRITERION=QUADSmax max max, ,n s tt t t
tn: normal contact stress in the pure normal mode
ts: shear contact stress along the first shear direction
tt: shear contact stress along the second shear direction
n: separation in the pure normal mode
s: separation in the first shear direction
t: separation in the second shear direction
*DAMAGE INITIATION, CRITERION=MAXSmax max max, ,n s tt t t
max max max, , 1
n s t
n s t
t t tMAX
t t t
Maximum stress criterion
Note: Recall the damage initiation criteria for the cohesive elements: if the initial constitutive thickness To = 1,
then = /To = . In this case, the separation measures for both approaches are exactly the same.
L6.17
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Example: Double cantilever beam
• Define the damage initiation criterion
• The quadratic stress criterion is specified for this problem.
3
...
*CONTACT PAIR, INTER=cohesive
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR,
ELIGIBILITY=SPECIFIED CONTACTS
5.7e14, 5.7e14, 5.7e14
*DAMAGE INITIATION, CRITERION=QUADS
5.7e7, 5.7e7, 5.7e7
max max maxn s tt t t
BotSurfTopSurf
bond
L6.18
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Damage evolution
• For surface-based cohesive behavior, damage evolution describes the
degradation of the cohesive stiffness.
• In contrast, for cohesive elements damage evolution describes the
degradation of the material stiffness.
• Damage evolution can be based on energy or separation (same as for
cohesive elements).
• Specify either the total fracture energy (a property of the cohesive
interaction) or the post damage-initiation effective separation at
failure.
• May depend on mode mix
• Mode mix may be defined
in terms of energy or traction
max max max,n s tt t t
,f f fn s t
t
max max max,n s t
GTC
L6.19
Modeling Fracture and Failure with Abaqus
• Separation-based damage evolution
• Damage is a function of an effective
separation:
• As with cohesive elements, the post
damage-initiation softening response can
be either:
• Linear
• Exponential
• Tabular
Surface-based Cohesive Behavior
2 2 2n s t
max max max,n s tt t t
,f f fn s t
t
max max max,n s t
Linear post-
initiation response
L6.20
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Separation-based damage evolution (cont’d)
• Usage:
*DAMAGE EVOLUTION, TYPE = DISPLACEMENT,
SOFTENING = { LINEAR | EXPONENTIAL | TABULAR },
MIXED MODE BEHAVIOR = TABULAR
L6.21
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Energy-based damage evolution
• As with cohesive elements, the energy-based damage evolution criterion
can be defined as a function of mode mix using either a tabular form or
one of two analytical forms:
Power law Benzeggagh-Kenane (BK)
1I II III
IC IIC IIIC
G G G
G G G
shearIC IIC IC TC
T
shear II III
T I shear
GG G G G
G
G G G
G G G
-
where
L6.22
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Energy-based damage evolution (cont’d)
• Usage:
*DAMAGE EVOLUTION, TYPE = ENERGY,
SOFTENING = { LINEAR | EXPONENTIAL},
MIXED MODE BEHAVIOR = { TABULAR | POWER LAW | BK },
POWER = value
L6.23
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Example: Double cantilever beam
• Define damage evolution
• The energy-based damage evolution based on the BK mixed mode
behavior is specified.
4
...
*CONTACT PAIR, INTER=cohesive
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR,
ELIGIBILITY=SPECIFIED CONTACTS
5.7e14, 5.7e14, 5.7e14
*DAMAGE INITIATION, CRITERION=QUADS
5.7e7, 5.7e7, 5.7e7
*DAMAGE EVOLUTION, TYPE=ENERGY,
MIXED MODE BEHAVIOR=BK, POWER=2.284
280.0, 280.0, 280.0
GIC GIIC GIIIC
shearIC IIC IC TC
T
GG G G G
G
-
BotSurfTopSurf
bond
L6.24
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Viscous regularization
• Can be specified to facilitate solution convergence in Abaqus/Standard
for surface-based cohesive behavior when stiffness degradation occurs.
• Output:
• Energy associated with viscous regularization: ALLCD
*DAMAGE STABILIZATION
L6.25
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Example: Double cantilever beam
• Specify a viscosity coefficient for
the cohesive surface behavior
viscosity coefficient,
...
*CONTACT PAIR, INTER=cohesive
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR,
ELIGIBILITY=SPECIFIED CONTACTS
5.7e14, 5.7e14, 5.7e14
*DAMAGE INITIATION, CRITERION=QUADS
5.7e7, 5.7e7, 5.7e7
*DAMAGE EVOLUTION, TYPE=ENERGY,
MIXED MODE BEHAVIOR=BK, POWER=2.284
280.0, 280.0, 280.0
*DAMAGE STABILIZATION
1.e-5
5
BotSurfTopSurf
bond
L6.26
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Example: Double cantilever beam
• Summary of the input for the traction-separation response
*COHESIVE SECTION, MATERIAL=cohesive,
RESPONSE=TRACTION SEPARATION,
ELSET=coh_elems, CONTROLS=visco
, 0.02
*MATERIAL, NAME=cohesive
*ELASTIC, TYPE=TRACTION
5.7e14, 5.7e14, 5.7e14
*DAMAGE INITIATION, CRITERION=QUADS
5.7e7, 5.7e7, 5.7e7
*DAMAGE EVOLUTION, TYPE=ENERGY,
MIXED MODE BEHAVIOR=BK, POWER=2.284
280.0, 280.0, 280.0
*SECTION CONTROLS, NAME=visco,
VISCOSITY=1.e-5
*SURFACE INTERACTION, NAME=cohesive
*COHESIVE BEHAVIOR,
ELIGIBILITY=SPECIFIED CONTACTS
5.7e14, 5.7e14, 5.7e14
*DAMAGE INITIATION, CRITERION=QUADS
5.7e7, 5.7e7, 5.7e7
*DAMAGE EVOLUTION, TYPE=ENERGY,
MIXED MODE BEHAVIOR=BK, POWER=2.284
280.0, 280.0, 280.0
*DAMAGE STABILIZATION
1.e-5
Cohesive elements Cohesive surfaces
L6.27
Modeling Fracture and Failure with Abaqus
Surface-based Cohesive Behavior
• Results
Cohesive elements
Cohesive surfaces
Failed cohesive elements
u2 = 0.006
u2
u2 = 0.006
u2
Element- vs. Surface-based
Cohesive Behavior
L6.29
Modeling Fracture and Failure with Abaqus
Element- vs. Surface-based Cohesive Behavior
Preprocessing
• Cohesive elements
• Gives you direct control over the cohesive element mesh density and stiffness properties.
• Constraints are enforced at the element integration points.
• Refining the cohesive elements relative to the connected structures will likely lead to improved constraint satisfaction and more accurate results.
• Cohesive surfaces
• Are easily defined using contact interactions and cohesive interaction properties.
• A pure master-slave in formulation is used.
• Constraints are enforced at the slave nodes.
• Refining the slave surface relative to the master surface will likely lead
to improved constraint satisfaction and more accurate results.
Integration points on an
8-node cohesive element
L6.30
Modeling Fracture and Failure with Abaqus
Element- vs. Surface-based Cohesive Behavior
Initial configuration:
• Cohesive elements
• Must be bonded at the start of the analysis.
• Once the interface has failed, the surfaces do not re-bond.
• Cohesive surfaces
• Can bond anytime contact is established
(i.e., “sticky” contact behavior).
• Cohesive interface need not be bonded at the start of the
analysis.
• You can control whether debonded surfaces will stick or not stick if
contact occurs again.
• By default, they do not stick.
L6.31
Modeling Fracture and Failure with Abaqus
Element- vs. Surface-based Cohesive Behavior
Constitutive behavior:
• Cohesive elements
• Allow for several constitutive behavior types:
• Traction-separation constitutive model
• Including multiple failure mechanisms
• Continuum-based constitutive model
• For adhesive layers with finite thickness
• Uses conventional material models
• Uniaxial stress-based constitutive model
• Useful in modeling gaskets and/or single adhesive patches
• Cohesive surfaces
• Must use the traction-separation interface behavior.
• Intended for bonded interfaces where the interface thickness is negligibly small.
• Only one failure mechanism is allowed.
L6.32
Modeling Fracture and Failure with Abaqus
Element- vs. Surface-based Cohesive Behavior
Influence on stable time increment (Abaqus/Explicit only):
• Cohesive elements
• Often require a small stable time increment.
• Cohesive elements are generally thin and sometimes quite stiff.
• Consequently, they often have a stable time increment that is
significantly less than that of the other elements in the model.
• Cohesive surfaces
• Cohesive surface behavior with the default cohesive stiffness
properties is formulated to minimally affect the stable time increment.
• Abaqus uses default contact penalties to model the cohesive
stiffness behavior in this case.
• You can specify a non-default cohesive stiffness values.
• However, high stiffnesses may reduce the stable time increment.
e
d
Lt
c
L6.33
Modeling Fracture and Failure with Abaqus
Element- vs. Surface-based Cohesive Behavior
Mass:
• Cohesive elements
• The element material definitions include mass.
• Cohesive surfaces
• Do not add mass to the model.
• Indented for thin adhesive interfaces; thus, neglecting adhesive
mass is appropriate for most applications.
• However, nonstructural mass can be added to the contacting
elements if necessary.
L6.34
Modeling Fracture and Failure with Abaqus
Element- vs. Surface-based Cohesive Behavior
Summary:
• Cohesive elements
• Are recommended for more detailed adhesive connection modeling.
• Additional preprocessing effort (and often increased computational cost) is compensated for by gaining:
• Direct control over the connection mesh
• Additional constitutive response options
• E.g., model adhesives of finite thickness
• Cohesive surfaces
• Provides a quick and easy way to model adhesive connections.
• Negligible interface thicknesses only
• Surfaces can bond anytime contact is established (“sticky” contact)
• Model contact adhesives, Velcro, tape, and other bonding agents that can stick after separation.
Workshop 3 (Part 2)
L6.36
Modeling Fracture and Failure with Abaqus
Workshop 3 (Part 2)
• Crack growth in a three-point bend specimen using surface-based
cohesive behavior
• Repeat the element-based exercise using surface-based behavior
• Use default traction-separation elastic properties
• Compare with element-based results
Virtual Crack Closure Technique
(VCCT)
Lecture 7
L7.2
Modeling Fracture and Failure with Abaqus
Overview
• Introduction
• VCCT Criterion
• Output
• VCCT Plug-in
• Comparison with Cohesive Behavior
• Examples
• Workshop 5
Introduction
L7.4
Modeling Fracture and Failure with Abaqus
Introduction
• Motivation is aircraft composite
structural analysis
• To reduce the cost of laminated
composite structures, large
integrated bonded structures are
being considered.
• In primary structures,
bondlines and interfaces
between plies are required to
carry interlaminar loads.
• Damage tolerance
requirements dictate that
bondlines and interfaces carry
required loads with damage.
Modeling debonding along
skin-stringer interface
L7.5
Modeling Fracture and Failure with Abaqus
Introduction
• Analysis requirements for composite damage
• Apply Linear Elastic Fracture Mechanics (LEFM) to bondlines and
interfaces
• 2D and 3D delaminations
• Propagation
• Mode separation
• Multiple cracks
• Non-linear behavior (e.g., postbuckling)
• Composite structure
• Practical (CPU time, minimum set of models)
L7.6
Modeling Fracture and Failure with Abaqus
Introduction
• VCCT uses LEFM concepts
• Based on computing the
energy release rates for
normal and shear crack-tip
deformation modes.
• Compare energy release
rates to interlaminar fracture
toughness.
• See Rybicki, E. F., and Kanninen,
M. F., "A Finite Element Calculation
of Stress Intensity Factors by a
Modified Crack Closure Integral,"
Engineering Fracture Mechanics,
Vol. 9, pp. 931-938, 1977.
1,6 ,2,5
,2,5
1,6
Nodes 2 and 5 will start to release when:
1
2
where
mode I energy release rate
critical mode I energy release rate
width
vertical force between nodes 2 and 5
vertical
vI IC
I
IC
v
v FG G
bd
G
G
b
F
v
displacement between nodes 1 and 6
Mode II treated
similarly
Node numbers
are shown
Pure Mode IModified VCCT
VCCT Criterion
L7.8
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• The debond capability is used to perform the crack propagation analysis
for initially bonded crack surfaces.
• The crack propagation analysis allows for five types of fracture criteria:
• Critical stress criterion
• Crack opening displacement criterion
• Crack length vs. time criterion
• VCCT criterion
• Low-cycle fatigue criterion
• Defining case 4, “VCCT criterion,” is the subject of this lecture.
• The details of cases 1, 2, and 3 are not discussed here. Please
consult the Abaqus Analysis User’s Manual for more details.
• The details of case 5 will be discussed later in Lecture 8 “Low-cycle
Fatigue.”
1
2
3
4
5
L7.9
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• When using VCCT to model crack propagation,
• you must:
• define contact pairs for potential crack surfaces;
• define initially bonded crack surfaces;
• activate the crack propagation capability; and
• specify the VCCT criterion.
• you also may:
• define spatially varying critical energy release rates;
• use viscous regularization, contact stabilization, and/or automatic
stabilization to overcome convergence difficulties for unstable
propagating cracks;
• use a linear scaling technique to accelerate convergence for VCCT.
1
2
3
4
L7.10
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Defining the VCCT criterion is not currently supported in Abaqus/CAE.
• However, the VCCT plug-in is available and allows you to interactively
define the debond interface(s).
• The details of the VCCT plug-in will be discussed later in this
lecture.
• Downloaded from “VCCT plug-in utility,” SIMULIA Answer 3235.
L7.11
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Example: Double cantilever beam (DCB)
• Analyze debonding of a DCB model using the VCCT criterion.
• Steps required for setting up the model include:
• Define slave (TopSurf) and master (BotSurf) surfaces along the debond
interface.
• Define a set (bond) containing the initially bonded region (part of TopSurf
in this example).
• The Keywords interface is illustrated in this example.
BotSurf
TopSurf
bond
L7.12
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Define contact pairs for potential crack surfaces
• Potential crack surfaces are modeled as slave and master contact
surfaces.
• Any contact formulation except the finite-sliding, surface-to-surface
formulation can be used.
• Cannot be used with self-contact.
1
*NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=...
TopSurf, BotSurf
slave surface master surface
Note: The frictionless interaction property is assumed.
BotSurfTopSurf
bond
L7.13
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Define initially bonded crack surfaces
• The initially bonded contact pair is identified with the *INITIAL
CONDITIONS, TYPE=CONTACT option.
BotSurfTopSurf
bond
*NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=...
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
slave surface master surface a list of slave nodes
that are initially bonded
2
L7.14
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• The unbonded portion of the slave surface will behave as a regular
contact surface.
• If the node set that includes the initially bonded slave nodes is not
specified, the initial contact condition will apply to the entire contact pair.
• In this case, no crack tips can be identified, and the bonded
surfaces cannot separate.
• For the VCCT criterion, the initially bonded nodes are bonded in all
directions.
L7.15
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Activate the crack propagation capability
• The DEBOND option is used to activate crack propagation in a given
step.
• The SLAVE and MASTER parameters identify the surfaces to be
debonded.
BotSurfTopSurf
bond
*NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=...
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf
3
L7.16
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Specify the VCCT criterion
• The BK law model is used in this
example. *NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=...
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf
*FRACTURE CRITERION, TYPE=VCCT,
MIXED MODE BEHAVOIR=BK
280.0, 280.0, 0.0, 2.284
GIC GIIC GIIIC
II IIIequivC IC IIC IC
I II III
G GG G G G
G G G
BotSurfTopSurf
bond
BK law:
4
L7.17
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• The crack-tip node debonds when the fracture criterion, f,
reaches the value 1.0 within a given tolerance, ftol:
where
Gequiv is the equivalent strain energy release rate, and
GequivC is the critical equivalent strain energy release rate calculated
based on the user-specified mode-mix criterion and the bond
strength of the interface.
• For the VCCT criterion, the default value of ftol is 0.2.
• Use following option to control ftol:
,equiv
equivC
Gf
G
*FRACTURE CRITERION, TYPE=VCCT, TOLERANCE=ftol
1 1 .tolf f
L7.18
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• In the DCB model, the tolerance is set to 0.1.
*NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=...
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf
*FRACTURE CRITERION, TYPE=VCCT,
MIXED MODE BEHAVOIR=BK, TOLERANCE=0.1
280.0, 280.0, 0.0, 2.284
BotSurfTopSurf
bond
L7.19
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• In addition to the BK law model, Abaqus/Standard also provides two
other commonly used mode-mix criteria for computing GequivC: the Power
law and the Reeder law models.
• An appropriate model is best selected empirically.
• Power law
• Reeder law
• Applies only to three-dimensional problems
am an ao
equiv I II III
equivC IC IIC IIIC
G G G G
G G G G
*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVIOR=POWER
GIC, GIIC, GIIIC, am, an, ao
*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVIOR=REEDER
GIC, GIIC, GIIIC,
III II IIIequivC IC IIC IC IIIC IIC
II III i
G G GG G G G G G
G G G
L7.20
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Spatially varying critical energy release rates
• The VCCT criterion can be defined with varying energy release rates by
specifying the critical energy release rates at all nodes on the slave
surface.
• In this case, the critical energy release rates should be interpolated
from the critical energy release rates specified at the nodes with the
*NODAL ENERGY RATE option.
• However, the exponents (e.g., ) are still read from the data lines
under the *FRACTURE CRITERION option.
*NODAL ENERGY RATE
node ID1, GIC, GIIC, GIIIC
node ID2, GIC, GIIC, GIIIC
...
*STEP
*STATIC
...
*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVIOR=BK, NODAL ENERGY RATE
GIC, GIIC, GIIIC,
model data
L7.21
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Viscous regularization for VCCT
• Can be used to overcome some
convergence difficulties for
unstable propagating cracks.
• Example: DCB
• Set the value of the viscosity
coefficient to 0.1.
*NSET, NSET=bond, GENERATE
1, 121, 1
*SURFACE, NAME=TopSurf
_TopBeam_S1, S1
*SURFACE, NAME=BotSurf
_BotBeam_S1, S1
*CONTACT PAIR, INTER=...
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf, VISCOSITY=0.1
*FRACTURE CRITERION, TYPE=VCCT, MIXED
MODE BEHAVOIR=BK, TOLERANCE=0.1
280.0, 280.0, 0.0, 2.284
BotSurfTopSurf
bond
L7.22
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• In addition, contact and automatic stabilization that are not specific to
VCCT can be also used to aid convergence.
• They are built into Abaqus/Standard and are compatible with VCCT.
• Note that the crack propagation behavior may be modified by the
damping forces.
• Therefore, monitor the damping energy (ALLVD or ALLSD) and
compare it with the total strain energy in the model (ALLSE) to
ensure that the results are reasonable in the presence of damping.
• ALLVD stores the damping energy generated from viscous
regularization.
• ALLSD stores the damping energy generated from contact
stabilization and automatic stabilization.
L7.23
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Linear scaling to accelerate convergence for VCCT
• Abaqus provides a linear scaling technique to quickly converge to the
critical load state. This reduces the solution time required to reach the
onset of crack growth.
• This technique works best for models in which the deformation is
nearly linear before the onset of crack growth.
• Once the first crack-tip node releases, the linear scaling calculations will
no longer be valid and the time increment will be set to the default value.
• Usage:
*CONTROLS, LINEAR SCALING
where is the coefficient of linear scaling.
• For details of linear scaling to accelerate convergence for VCCT, see
“Crack propagation analysis,” Section 11.4.3 of the Abaqus Analysis
User’s Manual.
L7.24
Modeling Fracture and Failure with Abaqus
VCCT Criterion
• Tips for using the VCCT criterion
• Crack propagation problems using the VCCT criterion are numerically
challenging.
• To help you create a successful model, several tips for using the VCCT
criterion are provided:
• The master debonding surfaces must be continuous.
• The tie MPCs should NOT be used for the slave debonding surface
to avoid overconstraints.
• A small clearance between the debonding surfaces can be specified
to eliminate unnecessary severe discontinuity iterations during
incrementation as the crack begins to progress.
……
• Note: More tips are provided in “Crack propagation analysis,” Section
11.4.3 of the Abaqus Analysis User’s Manual.
Output
L7.26
Modeling Fracture and Failure with Abaqus
Output
• The following output options are
provided to support the VCCT
criterion:
• Abaqus/CAE supports the surface
output requests for VCCT.
*OUTPUT, FIELD, FREQUENCY=freq
*CONTACT OUTPUT, MASTER=master,
SLAVE=slave
*OUTPUT, HISTORY, FREQUENCY=freq
*CONTACT OUTPUT, [(MASTER=master,
SLAVE=slave)|(NSET=nset)]
L7.27
Modeling Fracture and Failure with Abaqus
Output
• The following bond failure quantities can be requested as surface output:
DBT The time when bond failure occurred
DBSF Fraction of stress at bond failure that still remains
DBS Stress in the failed bond that remains
OPENBC Relative displacement behind crack.
CRSTS Critical stress at failure.
ENRRT Strain energy release rate.
EFENRRTR Effective energy release rate ratio.
BDSTAT Bond state (=1.0 if bonded, 0.0 if unbonded)
• All of the above variables can be visualized in Abaqus/Viewer.
• The initial contact status of all of the slave nodes is printed in the data (.dat) file.
L7.28
Modeling Fracture and Failure with Abaqus
Output
• Example: DCB
• Request surface output:
BotSurfTopSurf
bond
...
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf, VISCOSITY=0.1
*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVOIR=BK, TOLERANCE=0.1
280, 280, 280, 2.284
...
*OUTPUT, FIELD, VAR=PRESELECT
*CONTACT OUTPUT, SLAVE=TopSurf, MASTER=BotSurf
DBT, DBS, OPENBC, CRSTS, ENRRT, BDSTAT
*OUTPUT, HISTORY
*CONTACT OUTPUT, SLAVE=TopSurf, MASTER=BotSurf, NSET=bond
DBT, DBS, OPENBC, CRSTS, ENRRT, BDSTAT
*NODE OUTPUT, NSET=tip
U2, RF2
*END STEP
field output
history output
L7.29
Modeling Fracture and Failure with Abaqus
Output
• Results
VCCT
VCCT Plug-in
L7.31
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• VCCT plug-in
• provides an interactive interface to define the debond interface(s).
• supports the following keyword options required for VCCT analysis:
• For details please refer to “VCCT plug-in utility,” SIMULIA Answer 3235.
*INITIAL CONDITIONS, TYPE=CONTACT
*DEBOND, SLAVE=slave, MASTER=master, OUTPUT=[fil|dat|both], VISCOSITY=
*FRACTURE CRITERION, TYPE=VCCT,
MIXED MODE BEHAVIOR=[BK|POWER|REEDER], TOLERANCE=ftol,
NODAL ENERGY RATE
*NODAL ENERGY RATE
*CONTROLS, LINEAR SCALING
L7.32
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• Example: Double Cantilever Beam (DCB)
• The VCCT plug-in is discussed in the context of the Keywords interface
presented earlier.
BotSurf
TopSurf
bond
slave surface
master surface
initially bonded region
L7.33
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• Define contact pairs for potential crack surfaces
• Frictionless contact is assumed.
*SURFACE INTERACTION, NAME=IntProp-1
1.
*FRICTION
0.0
*CONTACT PAIR, INTERACTION=IntProp-1
TopSurf, BotSurf
BotSurfTopSurf
bond
1
L7.34
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• Define the VCCT criterion
• Select the fracture criterion, viscosity
coefficient, and cutback tolerance.
...
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf,
VICOSITY=0.1
*FRACTURE CRITERION, TYPE=VCCT, TOLERANCE=0.2,
MIXED MODE BEHAVOIR=BK
280, 280, 280, 2.284
2
2a
BotSurfTopSurf
bond
L7.35
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• Specify critical strain energy release rates2b
BotSurfTopSurf
bond
...
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf,
VICOSITY=0.1
*FRACTURE CRITERION, TYPE=VCCT, TOLERANCE=0.2,
MIXED MODE BEHAVOIR=BK
280, 280, 280, 2.284
L7.36
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• The VCCT plug-in also supports defining spatially varying critical energy
release rates.
• Click mouse button 3 to manage the table.
*NODAL ENERGY RATE
node ID1, GIC, GIIC, GIIIC
node ID2, GIC, GIIC, GIIIC
...
*STEP
*STATIC
...
*FRACTURE CRITERION, TYPE=VCCT,
MIXED MODE BEHAVIOR=BK, NODAL ENERGY RATE
GIC, GIIC, GIIIC,
L7.37
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• Define the VCCT bonded interface
• Select the initially bonded region,
the crack propagation output file
and frequency, and the debond
initiation step.
• Note: The VCCT plug-in
allows specification of linear
scaling.
3
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NAME=Step-1
*STATIC, NLGEOM
...
*DEBOND, SLAVE=TopSurf, MASTER=BotSurf, VISCOSITY=0.1
*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVOIR=BK
280, 280, 280, 2.284
L7.38
Modeling Fracture and Failure with Abaqus
VCCT Plug-in
• The relevant keywords
will be generated when
Abaqus/CAE writes the
input file.
debond
field output
surface interaction
initial contact conditions
fracture criterion
history output
Comparison with Cohesive Behavior
L7.40
Modeling Fracture and Failure with Abaqus
Comparison with Cohesive Behavior
• VCCT and cohesive behavior are very similar in their application and
formulation.
• Both theories
• are used to model interfacial shearing and delamination crack
propagation and failure,
• use an elastic damage constitutive theory to model the
material's response once damage has initiated, and
• dissipate the same amount of fracture energy between damage
initiation and complete failure.
L7.41
Modeling Fracture and Failure with Abaqus
Comparison with Cohesive Behavior
• The fundamental difference between VCCT and cohesive behavior is in
the way crack propagation is predicted.
• In VCCT an existing flaw is assumed.
• VCCT is appropriate for brittle crack propagation problems.
• However, cohesive behavior can model damage initiation.
• Damage initiation in cohesive behavior is based strictly on the
predefined ultimate (normal and/or shear) stress/strain limit.
• Cohesive behavior can be used for both brittle and ductile crack
propagation problems.
L7.42
Modeling Fracture and Failure with Abaqus
Comparison with Cohesive Behavior
• VCCT may be viewed as more fundamentally based on fracture
mechanics.
• The damage initiation and damage evolution are both based on
fracture energy, whereas cohesive behavior use the fracture energy
only during damage evolution.
• Applicability of VCCT is limited to “self-similar” crack propagation
analyses.
• This implies a steady-state running crack.
• Difficult to reproduce in practice.
L7.43
Modeling Fracture and Failure with Abaqus
Comparison with Cohesive Behavior
• Summary: Complementary techniques for modeling of debonding
• Both are needed to satisfy general fracture requirements
VCCT Cohesive behavior
Use the debond framework (surface based) Interface elements (element based) or
contact (surface based)
Assumes an existing flaw Can model crack initiation
Brittle fracture using LEFM occurring along a
well defined crack front
Ductile fracture occurring over a smeared
crack front modeled with spanning cohesive
elements or cohesive contact
Requires GI, GII, and GIII Requires E, σmax, GI, GII, and GIII
Crack propagates when strain energy release
rate exceeds fracture toughness
Crack initiates when cohesive traction
exceeds critical value and releases critical
strain energy when fully open
Crack surfaces are rigidly bonded when
uncracked.
Crack surfaces are joined elastically when
uncracked.
Available only in Abaqus/Standard Available in Abaqus/Standard and
Abaqus/Explicit
Examples
L7.45
Modeling Fracture and Failure with Abaqus
Examples
• Verification problems
• DCB
• SLB
• ENF
• Alfano-Crisfield
• Alfano, G., and M. A. Crisfield, “Finite Element Interface Models for
the Delamination Analysis of Laminated Composites: Mechanical
and Computational Issues,” International Journal for Numerical
Methods in Engineering, vol. 50, pp. 1701–1736, 2001.
• Also available as Abaqus Benchmark Problem 2.7.1 with cohesive
elements
• NASA Panel
• Reeder, J.R., Song, K., Chunchu, P.B., and Ambur, D.R.,
“Postbuckling and Growth of Delaminations in Composite Plates
Subjected to Axial Compression,” AIAA 2002-1746.
L7.46
Modeling Fracture and Failure with Abaqus
Examples
Euler buckling
0
5000
10000
15000
20000
25000
30000
0 0.01 0.02 0.03 0.04 0.05
Displacement (in)
Lo
ad
(lb
)
FEA
closed form
Multiple crack tips
Buckling driven delaminations
• Compression Buckling/Delamination Single Disbond (Unreinforced)
L7.47
Modeling Fracture and Failure with Abaqus
Examples
L7.48
Modeling Fracture and Failure with Abaqus
Examples
Multiple cracks can also be addressed
• Compression Buckling/Delamination Multiple Disbonds (Unreinforced)
L7.49
Modeling Fracture and Failure with Abaqus
Examples
L7.50
Modeling Fracture and Failure with Abaqus
Examples
• T-Joint Pull–off Model
L7.51
Modeling Fracture and Failure with Abaqus
• Postbuckling Behavior of Skin-Stringer Panels
Examples
• VCCT can be applied to
determine the global
strength and failure mode
for typical aerospace
composite structures like
this skin/stringer panelCourtesy Boeing
L7.52
Modeling Fracture and Failure with Abaqus
Examples
Displacement
imposed at corner nodesContact surfaces defined
for region of fracture
L7.53
Modeling Fracture and Failure with Abaqus
Examples
Initially bonded nodes
Initially debonded nodes
Crack tip
L7.54
Modeling Fracture and Failure with Abaqus
Examples
The Abaqus Tech Brief on skin/stringer bonded joint
analysis can be downloaded from www.simulia.com
L7.55
Modeling Fracture and Failure with Abaqus
Examples
Workshop 5
L7.57
Modeling Fracture and Failure with Abaqus
Workshop 5
• Crack growth in a three-point bend specimen using VCCT
• Repeat the cohesive-based exercises using VCCT and compare results
Low-cycle Fatigue
Lecture 8
L8.2
Modeling Fracture and Failure with Abaqus
Overview
• Introduction
• Low-cycle Fatigue in Bulk Materials
• Low-cycle Fatigue at Material Interfaces
Introduction
L8.4
Modeling Fracture and Failure with Abaqus
Introduction
• Low-cycle fatigue analysis is a quasi-static analysis of a structure
subjected to sub-critical cyclic loading.
• It can be associated with thermal as well as mechanical loading.
• In Abaqus can simulate low-cycle fatigue in:
• bulk ductile materials
• material interfaces
L8.5
Modeling Fracture and Failure with Abaqus
Introduction
• Low-cycle fatigue analysis uses the direct cyclic procedure to directly
obtain the stabilized cyclic response of the structure.
• The direct cyclic procedure combines a Fourier series
approximation with time integration of the nonlinear material
behavior to obtain the stabilized cyclic solution iteratively using a
modified Newton method.
• You can control the number of Fourier terms, the number of
iterations, and the incrementation during the cyclic time period
to improve the accuracy.
• Within each loading cycle, it assumes geometrically linear behavior and
fixed contact conditions.
• Geometric nonlinearity can be included only in any general step
prior to a direct cyclic step
• For more details, please see “Low-cycle fatigue analysis using the direct
cyclic approach,” Section 6.2.7 of the Abaqus Analysis User’s Manual.
L8.6
Modeling Fracture and Failure with Abaqus
Introduction
• Defining low-cycle fatigue analysis
where t0: initial time increment
T: time of a single loading cycle
tmin: minimum time increment allowed
tmax: maximum time increment allowed
n0: initial number of terms in the Fourier series
nmax: maximum number of terms in the Fourier series
n: increment in number of terms in the Fourier series
imax: maximum number of iterations allowed in a step
N: total number of cycles allowed in a step
Nmin: minimum increment in N over which the damage is extrapolated forward
Nmax: maximum increment in N over which the damage is extrapolated forward
Dtol: damage extrapolation tolerance
*DIRECT CYCLIC, FATIGUE, [CETOL=tolerance, DELTMX=max]
t0, T, tmin, tmax, n0, nmax, n, imax
Nmin, Nmax, N, Dtol
controls the incrementation
controls the iteration
controls the Fourier
series representations
controls damage
extrapolation in
the bulk material
Low-cycle Fatigue in Bulk Materials
L8.8
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Abaqus/Standard offers a general capability for modeling the
progressive damage and failure of ductile materials due to stress
reversals and the accumulation of inelastic strain energy when the
material is subjected to sub-critical cyclic loadings.
• Damage in low-cycle fatigue is defined within the same general
framework of modeling progressive damage and failure (continuum
damage approach):
• a constitutive behavior of undamaged ductile materials;
• a damage initiation criterion; and
• a damage evolution response.
• The damage initiation and evolution are characterized by the stabilized
accumulated inelastic hysteresis strain energy per stabilized cycle.
• Note: Damage initiation and evolution for low-cycle fatigue analysis is
currently not supported in Abaqus/CAE.
L8.9
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Example: Thermal cycling failure of solder joint
• Solder joint reliability analysis of automotive electronics under cyclic
thermal loading.
The crack propagates forward
L8.10
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Quarter-symmetry model:
• Solder material (63Sn/37Pb)
• Modeled using temperature-
dependent elasticity and
power-law creep.
• Low-cycle fatigue analysis run for
801 cycles.
• Each thermal cycle is 1920
seconds.
• Define the low-cycle fatigue analysis
step
*STEP, INC=800
*DIRECT CYCLIC, FATIGUE
60., 1920.,,, 29, 29,, 100
50, 100, 801, 1.1
Temperature load in once cycle
Quarter-symmetry model
electronic chip
printed
circuit
board
gullwing
leads
solder joints
L8.11
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Damage initiation criterion for ductile damage in low-cycle fatigue
• The onset of damage in low-cycle fatigue is characterized by the accumulated inelastic hysteresis energy per cycle, w, in a material point when the structure response is stabilized in the cycle.
• The cycle number (N0) in which damage is initiated is given by
where c1 and c2 are material constants.
• Note: c1 depends on the system of units in which you are working;
care is required to modify c1 when converting to a different system units.
• The initiation criterion can be used in conjunction with any ductile material.
• Damage initiation criterion output:
CYCLEINI Number of cycles to initialized the damage
20 1
cN c w
L8.12
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Defining damage initiation criterion
• Example: Thermal cycling failure of solder joint
*MATERIAL, NAME=SOLDERF
*ELASTIC
31976, 0.4, 273
20976, 0.4, 398
*EXPANSION, ZERO=273
21E-6,
*CREEP,LAW=USER
*DAMAGE INITIATION, CRITERION=HYSTERESIS ENERGY
33.3, -1.52
...
*STEP, INC=800
*DIRECT CYCLIC, FATIGUE
60., 1920.,,, 29, 29,, 100
50, 100, 801, 1.1
c1 c2
Quarter-symmetry model
solder joint
bond pad
underneath
solder joint
20 1
cN c w
L8.13
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Damage evolution for ductile damage in low-cycle fatigue
• Once the damage initiation criterion is satisfied at a material point, the damage state is calculated and updated based on the inelastic hysteresis energy for the stabilized cycle.
• The rate of the damage (dD/dN) at a material point per cycle is given by
where c3 and c4 are material constants, L is the characteristic length
associated with the material point, and D is the scalar damage variable.
• The details of choosing characteristic length will be discussed later.
• Note: c3 depends on the system of units in which you are working;
care is required to modify c3 when converting to a different system units.
43
cc wdD
dN L
L8.14
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Defining damage evolution
• Example: Thermal cycling failure of solder joint
Quarter-symmetry model
*MATERIAL, NAME=SOLDERF
*ELASTIC
31976, 0.4, 273
20976, 0.4, 398
*EXPANSION, ZERO=273
21E-6,
*CREEP,LAW=USER
*DAMAGE INITIATION, CRITERION=HYSTERESIS ENERGY
33.3, -1.52
*DAMAGE EVOLUTION, TYPE=HYSTERESIS ENERGY
9.88E-4, 0.98
...
*STEP, INC=800
*DIRECT CYCLIC, FATIGUE
60., 1920.,,, 29, 29,, 100
50, 100, 801, 1.1
c3 c4
43
cc wdD
dN L
L8.15
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Results
Damage initiation at joint toe
Cycle number 199
Damage evolution
Cycle number 749
Damage evolution
Cycle number 801
L8.16
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Characteristic length associated with an integration point
• The characteristic length implemented in the damage evolution model is
based on the element geometry and formulation:
Element type Characteristic length used in
the damage evolution model
first-order element typical length of a line across the element
second-order element half of the typical length of a line across the element
beam and truss characteristic length along the element axis
membrane and shell characteristic length in the reference surface
axisymmetric element characteristic length in the rz plane only
cohesive element the constitutive thickness
L8.17
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• The characteristic length is used because the direction in which fracture
occurs is not known in advance.
• Therefore, elements with large aspect ratios will have rather
different behavior depending on the direction in which the damage
occurs.
• Some mesh sensitivity remains because of this effect, and
elements that are as close to square as possible are
recommended.
• However, since the damage evolution law is energy based,
mesh dependency of the results may be alleviated.
L8.18
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue in Bulk Materials
• Difficulties associated with element removal and LCF
• When elements are removed from the model, their nodes remain in the
model even if they are not attached to any active elements.
• When the solution progresses, these nodes might undergo non-
physical displacements in Abaqus/Standard.
• For example, applying a point load to a node that is not
attached to an active element will cause convergence
difficulties since there is no stiffness to resist the load.
• It is the user’s responsibility to prevent such situations.
Low-cycle Fatigue at
Material Interfaces
L8.20
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Delamination growth in composites due to sub-critical cyclic loadings is a
widespread concern for the aerospace industry.
• The low-cycle fatigue criterion available in Abaqus models progressive
delamination growth at interfaces in laminated composites subjected to
sub-critical cyclic loadings.
• The interface along which the delamination (or crack) propagates
must be indicated in the model.
• The onset and growth of fatigue delamination at the interfaces are
characterized by the relative fracture energy release rate
• The fracture energy release rates at the crack tips in the
interface elements are calculated based on the VCCT
technique.
L8.21
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• The onset and fatigue delamination growth
at the interfaces are characterized by using
the Paris Law, which relates crack growth
rates da/dN to the relative fracture energy
release rate G,
G = Gmax – Gmin
where Gmax and Gmin correspond to the
strain energy release rates when the
structure is loaded up to Pmax and Pmin,
respectively.
• The Paris regime is bounded by Gthresh and
Gpl.
• Below Gthresh, there is no fatigue crack
initiation or growth.
• Above Gpl, the fatigue crack will grow
at an accelerated rate.
a: crack length
N: number of cycles
G: strain energy release rate
Gthresh: strain energy release rate threshold
Gpl: strain energy release rate upper limit
GequivC: critical equivalent strain
energy release rate
L8.22
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• GequivC is calculated based on the
user-specified mode-mix criterion
and the bond strength of the interface.
• This was discussed in Lecture 7
“VCCT.”
• Onset of fatigue delamination
• The fatigue crack growth initiation
criterion is defined as:
where c1 and c2 are material
constants.
• The interface elements at the
crack tips will not be released
unless the above equation is
satisfied and Gmax Gthresh.
21
1.0,c
Nf
c G
a: crack length
N: number of cycles
G: strain energy release rate
Gthresh: strain energy release rate threshold
Gpl: strain energy release rate upper limit
GequivC: critical equivalent strain
energy release rate
L8.23
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Fatigue delamination growth
• Once the delamination growth criterion
is satisfied at the interface, the crack
growth rate da/dN can be calculated
based on G.
• da/dN is given by the Paris Law if
Gthresh< Gmax< Gpl,
where c3 and c4 are material
constants.
43
cdac G
dN
a: crack length
N: number of cycles
G: strain energy release rate
Gthresh: strain energy release rate threshold
Gpl: strain energy release rate upper limit
GequivC: critical equivalent strain
energy release rate
43
cdac G
dN
L8.24
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Fatigue crack growth governed by the Paris Law
• Repeat the above process until the maximum number of cycles is reached or until the ultimate load carrying capability is reached.
Calculate the relative fracture
energy release rate, G, when
the structure is loaded between its
maximum and minimum values.
Crack initiation: 21
coN c G
Crack evolution: 43
cdac G
dN
Damage extrapolation: Calculate
the incremental number of cycles,
N, for each crack tip and find
minimum cycles to fail, Nmin
If N + N > No
N + N
43
cN N Na a Nc G
a: crack length
N: number of cycles
N: incremental number of cycles
c1, c2 , c3, c4: material constants
If Gthresh < Gmax < Gpl
Release the most
critical element
G = Gmax(Pmax) – Gmin(Pmin)
1 2
3
L8.25
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• The syntax used to define the low-cycle fatigue criterion and the
corresponding output requests is similar to those used for the VCCT
criterion except the following:
• For the low-cycle fatigue criterion, set TYPE=FATIGUE on the
*FRACTURE CRITERION option:
• By default, Gthresh/GequivC = 0.01 and Gpl/GequivC = 0.85.
• Note: Defining the low-cycle criterion is not currently supported in
Abaqus/CAE.
*FRACTURE CRITERION, TYPE=FATIGUE, MIXED MODE BEHAVIOR=[BK|REEDER]
c1, c2, c3, c4, Gthresh/GequivC, Gpl/GequivC, GIC, GIIC
GIIIC, , , fv
*FRACTURE CRITERION, TYPE=FATIGUE, MIXED MODE BEHAVIOR=POWER
c1, c2, c3, c4, Gthresh/GequivC, Gpl/GequivC, GIC, GIIC
GIIIC, am, an, ao, , fv
L8.26
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Example: Low-cycle fatigue prediction for the DCB model
• This case consists of the following steps:
• Step 1: VCCT analysis
• This step can be used to check whether the peak loading leads
to static crack propagation.
• Step 2: Low-cycle fatigue analysis
• This step assesses the fatigue life of the DCB model subjected
to sub-critical cyclic loading.
displacement loading in one cycle
0 10.50
=0.001
u2
t
BotSurfTopSurf
bondu2
u2
L8.27
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Partial input:
*STEP, INC=5000
*DIRECT CYCLIC, FATIGUE
0.25,1,,,25,25,,5
,,1000
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf
*FRACTURE CRITERION, TYPE=FATIGUE,
MIXED MODE BEHAVIOR=BK
0.5,-0.1,4.8768E-6,1.15,,,280,280
280,2.284
*OUTPUT, FIELD
*CONTACT OUTPUT
BDSTAT, DBT, DBS, OPENBC, CRSTS,
ENRRT
...
*END STEP
...
*CONTACT PAIR, SMALL SLIDING
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf
*FRACTURE CRITERION, TYPE=VCCT,
MIXED MODE BEHAVIOR=BK
280, 280, 280, 2.284
*OUTPUT, FIELD
*CONTACT OUTPUT, SLAVE=TopSurf,
MASTER=BotSurf
BDSTAT, DBT, DBS, OPENBC, CRSTS,
ENRRT
*END STEP
Step 2:
Fatigue
analysis
Step 1:
VCCT
analysis
Model
data
BotSurfTopSurf
bond
L8.28
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• The procedure to complete the DCB model through the first step (the VCCT analysis) is exactly the same as that discussed in Lecture 7 “VCCT.”
• Define contact pairs for potential crack surfaces
• Define initially bonded crack surfaces
• Activate the crack propagation capability in the first step
• Specify the VCCT criterion in the first step (a static, general step)
• The details of defining the low-cycle fatigue analysis (the second step) will be discussed next.
...
*CONTACT PAIR, SMALL SLIDING
TopSurf, BotSurf
*INITIAL CONDITIONS, TYPE=CONTACT
TopSurf, BotSurf, bond
*STEP, NLGEOM
*STATIC
...
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf
*FRACTURE CRITERION, TYPE=VCCT,
MIXED MODE BEHAVIOR=BK
280, 280, 280, 2.284
*OUTPUT, FIELD
*CONTACT OUTPUT
BDSTAT, DBT, DBS, OPENBC, CRSTS,
ENRRT
...
*END STEP
Step 1:
VCCT
analysis
model
data
BotSurfTopSurf
bond
1
2
3
4
L8.29
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Define the low-cycle fatigue analysis
• The following data are used to define this
low-cycle fatigue analysis:
• Initial time increment: 0.25 sec
• Time of a single loading cycle: 1 sec
• Initial number of terms in the Fourier
series: 25
• Maximum number of terms in the
Fourier series: 25
• Maximum number of iterations
allowed in the step: 5
• Total number of cycles allowed in
the step: 1000
• Default values are used for all other
entries.
...
*STEP, INC=5000
Low-cycle Fatigue Analysis
*DIRECT CYCLIC, FATIGUE
0.25,1,,,25,25,,5
,,1000
BotSurfTopSurf
bond
5
L8.30
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Activate the crack propagation capability
• Similar to the VCCT analysis, the
*DEBOND option is used to activate the
crack propagation in the low-cycle
fatigue analysis step.
• The SLAVE and MASTER
parameters identify the surfaces to
be debonded.
...
*STEP, INC=5000
Low-cycle Fatigue Analysis
*DIRECT CYCLIC, FATIGUE
0.25,1,,,25,25,,5
,,1000
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf
BotSurfTopSurf
bond
6
L8.31
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Specify the low-cycle fatigue criterion
• In this model, the material constants are
assumed to be the following:
• c1 = 0.5,
• c2 = –0.1
• c3 = 4.8768E–6
• c4 = 1.15
• Note: The values of these material
constants should be determined
experimentally.
• The BK model (default) is used.
...
*STEP, INC=5000
Low-cycle Fatigue Analysis
*DIRECT CYCLIC, FATIGUE
0.25,1,,,25,25,,5
,,1000
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf
*FRACTURE CRITERION, TYPE=FATIGUE,
MIXED MODE BEHAVIOR=BK
0.5,-0.1,4.8768E-6,1.15,,,280,280
280,2.284
21
1.0c
Nf
c G
43
cdac G
dN
GIC GIIC
GIIIC
BotSurfTopSurf
bond
7
L8.32
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Request output
• The output options for the low-cycle
fatigue criterion are same as those for
the VCCT criterion.
...
*STEP, INC=5000
Low-cycle Fatigue Analysis
*DIRECT CYCLIC, FATIGUE
0.25,1,,,25,25,,5
,,1000
*DEBOND, SLAVE=TopSurf,
MASTER=BotSurf
*FRACTURE CRITERION, TYPE=FATIGUE,
MIXED MODE BEHAVIOR=BK
0.5,-0.1,4.8768E-6,1.15,,,280,280
280,2.284
*OUTPUT, FIELD
*CONTACT OUTPUT
BDSTAT, DBT, DBS, OPENBC, CRSTS,
ENRRT
BotSurfTopSurf
bond
8
L8.33
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• Results
N=1 N=11
N=21 N=51
initially bonded nodes delamination
N is the number of cycles
L8.34
Modeling Fracture and Failure with Abaqus
Low-cycle Fatigue at Material Interfaces
• More results
delamination growth after 100
loading cycles
crack length vs. cycle
number
Mesh-independent Fracture Modeling (XFEM)
Lecture 9
L9.2
Modeling Fracture and Failure with Abaqus
Overview
• Introduction
• Basic XFEM Concepts
• Damage Modeling
• Creating an XFEM Fracture Model
• Example 1 – Crack Initiation and Propagation
• Example 2 – Propagation of an Existing Crack
• Example 3 – Delamination and Through-thickness Crack Propagation
• Modeling Tips
• Current Limitations
• Workshop 6
• References
Introduction
L9.4
Modeling Fracture and Failure with Abaqus
Introduction
• The fracture modeling methods discussed so far only permit crack
propagation along predefined element boundaries
• This lecture presents a technique for modeling
bulk fracture which permits a crack to be located
in the element interior
• The crack location is independent of the mesh
L9.5
Modeling Fracture and Failure with Abaqus
Introduction
• This modeling technique…
• Can be used in conjunction with the cohesive zone model or the virtual
crack closure technique
• Delamination can be modeled in conjunction with bulk crack
propagation
• Can determine the load carrying capacity of a cracked structure
• What is the maximum allowable flaw size for safe operation?
• Applications of this technique include the modeling of bulk fracture and
the modeling of failure in composites
• Cracks in pressure vessels or engineering structures
• Delamination and through-thickness crack modeling in composite plies
L9.6
Modeling Fracture and Failure with Abaqus
Introduction
• Some advantages of the method:
• Ease of initial crack definition
• Mesh is generated independent of crack
• Partitioning of geometry not needed as when a crack is represented
explicitly
• Nonlinear material and nonlinear geometric analysis
• Arbitrary solution-dependent crack initiation and propagation path
• Crack path does not have to be specified a priori
• Mesh refinement studies are much simpler
• Reduced remeshing effort
• Improved convergence rate for the finite element solution (stationary
crack)
• Due to the use of singular crack tip enrichment
L9.7
Modeling Fracture and Failure with Abaqus
Introduction
• Mesh-independent Crack Modeling – Basic Ingredients
1. Need a way to incorporate discontinuous geometry – the crack – and
the discontinuous solution field into the finite element basis functions
• eXtended Finite Element Method (XFEM)
2. Need to quantify the magnitude of the discontinuity – the displacement
jump across the crack faces
• Cohesive zone model (CZM)
3. Need a method to locate the discontinuity
• Level set method (LSM)
4. Crack initiation and propagation criteria
• At what level of stress or strain does the crack initiate?
• What is the direction of propagation?
• These topics will be discussed in this lecture
Basic XFEM Concepts
L9.9
Modeling Fracture and Failure with Abaqus
Basic XFEM Concepts
• eXtended Finite Element Method (XFEM) Background
• XFEM extends the piecewise polynomial function space of conventional finite
element methods with extra functions
• The solution space is enriched by the extra “enrichment functions”
• Introduced by Belytschko and Black (1999) based on the partition of unity
method of Babuska and Melenk (1997)
• Can be used where conventional FEM fails or is prohibitively expensive
• Appropriate enrichment functions are chosen for a class of problems
• Inclusion of a priori knowledge of partial differential equation behavior into
finite element space (singularities, discontinuities, ...)
• Applications include modeling fracture, void growth, phase change ...
• Enrichment functions for fracture modeling
• Heaviside function to represent displacement jump across crack face
• Crack tip asymptotic function to model singularity
L9.10
Modeling Fracture and Failure with Abaqus
Basic XFEM Concepts
• XFEM Displacement Interpolation
Heaviside enrichment term
H(x) Heaviside distribution
aI Nodal enriched DOF (jump discontinuity)
NG Nodes belonging to elements cut by crack
Crack tip enrichment term
Fa(x) Crack tip asymptotic functions
Nodal DOF (crack tip enrichment)
NG Nodes belonging to elements containing crack tip
b I
a
uI Nodal DOF for conventional shape functions NI
4
1
u (x) (x) u (x (x)b)ah
I I
I
II
I
N
N
I
N
FHN a
aa
G
L9.11
Modeling Fracture and Failure with Abaqus
Basic XFEM Concepts
• The crack tip and Heaviside enrichment functions are multiplied by the
conventional shape functions
• Hence enrichment is local around the crack
• Sparsity of the resulting matrix equations is preserved
• The crack is located using the level set method (discussed shortly)
• Heaviside function
• Accounts for displacement jump across crack
*1 if ( ) 0( )
1 otherwiseH x
x x ns
n
x
x*
Here x is an integration point, x* is the closest point to x on the crack face and n is the unit normal at x*
H(x) = 1 below crack
H(x) = 1 above crack
L9.12
Modeling Fracture and Failure with Abaqus
Basic XFEM Concepts
• Crack Tip Enrichment Functions (Stationary Crack Only)
• Account for crack tip singularity
• Use displacement field basis functions for sharp crack in an isotropic
linear elastic material
]2
cossinr ,2
sinsinr ,2
cosr ,2
sinr[4]-1 ),([
aa xF
Here (r, ) denote coordinate values from a polar coordinate system located at the crack tip
L9.13
Modeling Fracture and Failure with Abaqus
Basic XFEM Concepts
• Phantom Node Approach (Crack Propagation Implementation)
• Implementation of XFEM fitting into the framework of conventional FEM
• Discontinuous element with Heaviside enrichment is treated as a
superposition of two continuous elements with phantom nodes
• Does not include the asymptotic crack tip enrichment functions
• Introduced by Belytschko and coworkers (2006) based on the
superposed element formulation of Hansbo and Hansbo (2004)
L9.14
Modeling Fracture and Failure with Abaqus
Basic XFEM Concepts
• Level Set Method for Locating a Crack
• A level set (also called level surface or isosurface) of a real-valued function
is the set of all points at which the function attains a specified value
• Example: the zero-valued level set of f (x, y) : x2 y2 r2 is a circle of
radius r centered at the origin
• Popular technique for representing surfaces in interface tracking problems
• Two functions F and Y are used to completely describe the crack
• The level set F = 0 represents the crack face
• The intersection of level sets Y = 0 and F = 0 denotes the crack
front
• Functions are defined by nodal values whose spatial variation is
determined by the usual finite element shape functions (example
follows)
• Function values need to be specified only at nodes belonging to
elements cut by the crack
L9.15
Modeling Fracture and Failure with Abaqus
• Calculating F and Y
• The nodal value of the function F is the signed distance of the node from
the crack face
• Positive value on one side of the crack face, negative on the other
• The nodal value of the function Y is the signed distance of the node from
an almost-orthogonal surface passing through the crack front
• The function Y has zero value on this surface and is negative on the
side towards the crack
Basic XFEM Concepts
Y = 0F = 0
1 2
3 4
0.5
1.5
Node F Y
1 0.25 1.5
2 0.25 1.0
3 0.25 1.5
4 0.25 1.0
Damage Modeling
L9.17
Modeling Fracture and Failure with Abaqus
Damage Modeling
• Damage modeling is achieved through the use of a traction-separation
law across the fracture surface
• It follows the general framework introduced in earlier lectures
• Damage initiation
• Damage evolution
• Traction-free crack faces at failure
• Damage properties are specified as part of the bulk material definition
Damage initiation
Failure
L9.18
Modeling Fracture and Failure with Abaqus
Damage Modeling
• Damage Initiation
• Two criteria available at present
• Maximum principal stress criterion (MAXPS)
• Initiation occurs when the maximum principal stress reaches
critical value
• Maximum principal strain criterion (MAXPE)
• Initiation occurs when the maximum principal strain reaches
critical value
• Crack plane is perpendicular to the direction of the maximum principal
stress (or strain)
• Crack initiation occurs at the center of the element
• However, crack propagation is arbitrary through the mesh
• The damage initiation criterion is satisfied when 1.0 ≤ f ≤ 1.0 + ftol
where f is the selected damage criterion and ftol is a user-specified
tolerance value
max
0
max
f
max
0
max
f
L9.19
Modeling Fracture and Failure with Abaqus
Damage Modeling
• Damage Evolution
• Any of the damage evolution models for traction-separation laws
discussed in the earlier lectures can be used
• However, it is not necessary to specify the undamaged traction-
separation response
L9.20
Modeling Fracture and Failure with Abaqus
Damage Modeling
• Damage Stabilization
• Fracture makes the structural response nonlinear and non-smooth
• Numerical methods have difficulty converging to a solution
• As discussed in the earlier lectures, using viscous regularization helps
with the convergence of the Newton method
• The stabilization value must be chosen so that the problem definition
does not change
• A small value regularizes the analysis, helping with convergence
while having a minimal effect on the response
• Perform a parametric study to choose appropriate value for a class
of problems
L9.21
Modeling Fracture and Failure with Abaqus
Damage Modeling
• Damage stabilization can currently be defined in Abaqus/CAE only
through the keyword editor
Creating an XFEM Fracture Model
L9.23
Modeling Fracture and Failure with Abaqus
Creating an XFEM Fracture Model
• Steps
1. Define damage criteria in the material model
2. Define an enrichment region (the associated material model should
include damage)
• Crack type – stationary or propagation
3. Define an initial crack, if present
4. If needed, set analysis controls to aid convergence
• Steps will be illustrated later through examples
• Crack initiation and propagation in a plate with a hole
• Propagation of an existing crack
• Delamination and through-thickness crack propagation in a double
cantilever beam
• The next few slides describe step-dependent enrichment activation
and postprocessing
L9.24
Modeling Fracture and Failure with Abaqus
Creating an XFEM Fracture Model
• Step-dependent Enrichment Activation
• Crack growth can be activated or deactivated in analysis steps
*STEP...
*ENRICHMENT, NAME=Crack-1, ACTIVATE=[ON|OFF]
1
2
L9.25
Modeling Fracture and Failure with Abaqus
Creating an XFEM Fracture Model
• Output Quantities
• Two output variables are especially useful
• PHILSM
• The signed distance function F used to represent the crack
surface
• Needed for visualizing the crack
• STATUSXFEM
• Indicates the status of the element with a value between 0.0
and 1.0
• A value of 1.0 indicates that the element is completely cracked,
with no traction across the crack faces
• Any other output variable available in the static stress analysis
procedure
L9.26
Modeling Fracture and Failure with Abaqus
Creating an XFEM Fracture Model
• Postprocessing
• The crack location is specified by the zero-valued level set of the signed
distance function F
• Abaqus/CAE automatically creates an isosurface view cut named
Crack_PHILSM if an enrichment is used in the analysis
• The crack isosurface is displayed by default
• Contour plots of field quantities should be done with the crack isosurface
displayed
• Ensures that the solution is plotted from the active parts of the
overlaid elements according to the phantom nodes approach
• If the crack isosurface is turned off, only values from the “lower”
element are plotted (corresponding to negative values of F)
• Probing field quantities on an element currently returns values only from
the “lower” element (on the side with negative values of F)
Example 1 – Crack Initiation and
Propagation
L9.28
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
• Model crack initiation and propagation in a plate with a hole
• Crack initiates at the location of maximum stress concentration
• Half model is used taking advantage of symmetry
L9.29
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Define the damage criteria
• Damage initiation
1
Damage initiation tolerance (default 0.05)
*MATERIAL...
*DAMAGE INITIATION, CRITERION=MAXPS, TOL=0.05
L9.30
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Define the damage criteria (cont’d)
• Damage evolution
*DAMAGE INITIATION, CRITERION=MAXPS, TOL=0.05
*DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=POWER LAW, POWER=1.0
2870.0, 2870.0, 2870.0
1
L9.31
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Define the damage criteria (cont’d)
• Damage stabilization
Keyword interface
*DAMAGE STABILIZATION
1.e-5
Coefficient of viscosity m
• Abaqus/CAE interface currently not available
• The keyword editor may be used to add stabilization through
Abaqus/CAE.
1
L9.32
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Define the enriched region
Pick enriched region
Specify contact interaction
(frictionless small-sliding contact only)
Propagating crack
2
L9.33
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Define the enriched region (cont’d)
Keyword interface
No initial crack definition is needed
• Crack will initiate based on specified damage criteria
3
*ENRICHMENT, TYPE=PROPAGATION CRACK, NAME=CRACK-1,
ELSET=SELECTED_ELEMENTS, INTERACTION=CONTACT-1
Frictionless small-sliding contact interaction
2
L9.34
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Set analysis controls to improve convergence behavior
• Set reasonable minimum and maximum increment sizes for step
• Increase the number of increments for step from the default value of
100
*STEP
*STATIC, inc=10000
0.01, 1.0, 1.0e-09, 0.01...
4
L9.35
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Set analysis controls to improve convergence behavior (cont’d)
• Use numerical scheme applicable to discontinuous analysis
*STEP
*STATIC, inc=10000
0.01, 1.0, 1.0e-09, 0.01...
*CONTROLS, ANALYSIS=DISCONTINUOUS
4
L9.36
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
Set analysis controls to improve convergence behavior (cont’d)
• Increase value of maximum number of attempts before abandoning
increment (increased to 20 from the default value of 5)
*STEP
*STATIC, inc=10000
0.01, 1.0, 1.0e-09, 0.01...
*CONTROLS, ANALYSIS=DISCONTINUOUS
*CONTROLS, PARAMETER=TIME INCREMENTATION
, , , , , , , 20
8th field
4
L9.37
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
• Output Requests
• Request PHILSM and STATUSXFEM in addition to the usual output for
static analysis
L9.38
Modeling Fracture and Failure with Abaqus
Example 1 – Crack Initiation and Propagation
• Postprocessing
• Crack isosurface (Crack_PHILSM) created and displayed automatically
• Field and history quantities of interest can be plotted and animated as
usual
Example 2 – Propagation of an Existing
Crack
L9.40
Modeling Fracture and Failure with Abaqus
Example 2 – Propagation of an Existing Crack
• Model with crack subjected to mixed mode loading
• Initial crack needs to be defined
• Crack propagates at an angle dictated by mode mix ratio at crack tip
L9.41
Modeling Fracture and Failure with Abaqus
Example 2 – Propagation of an Existing Crack
Define damage criteria in the material model as described in Example 1
Specify the enriched region as in Example 1
Define the initial crack
• Two methods are available to define initial crack in Abaqus/CAE
1. Create a separate part representing the crack surface or line and
assemble it along with the part representing the structure to be
analyzed
2. Create an internal face or edge representing the crack in the part
• Method 1 is preferred as it takes full advantage of the mesh-
independent crack representation possible using XFEM
• Meshing is easier using this method
• Method 2 will create nodes on the internal crack face
• Element faces/edges are forced to align with the crack
1
2
3
L9.42
Modeling Fracture and Failure with Abaqus
Example 2 – Propagation of an Existing Crack
Define the initial crack (cont’d)3
The crack location can be an edge or a
surface belonging to the same
instance as the enriched region or to a
different instance (preferred)
** Model data
*INITIAL CONDITIONS, TYPE=ENRICHMENT
901, 1, Crack-1, -1.0, -1.5
901, 2, Crack-1, -1.0, -1.4
901, 3, Crack-1, 1.0, -1.4
901, 4, Crack-1, 1.0, -1.5
Element Number
Relative Node Order in Connectivity
Enrichment Name
F Y
L9.43
Modeling Fracture and Failure with Abaqus
Example 2 – Propagation of an Existing Crack
• The other steps are as described in Example 1 and are in line with
those necessary for the usual static analysis procedure
Example 3 – Delamination and
Through-thickness Crack Propagation
L9.45
Modeling Fracture and Failure with Abaqus
Example 3 – Delamination and Through-thickness Crack
• Model through-thickness crack propagation using XFEM and
delamination using surface-based cohesive behavior in a double
cantilever beam specimen
• Interlaminar crack grows initially
• Through-thickness crack forms once interlaminar crack becomes long
enough and the longitudinal stress value builds up due to bending
• The point at which the through-thickness crack forms depends upon the
relative failure stress values of the bulk material and the interface
L9.46
Modeling Fracture and Failure with Abaqus
Example 3 – Delamination and Through-thickness Crack
• This model is the same as the double cantilever beam model presented
in the surface-based cohesive behavior lecture except:
• Enrichment has been added to the top and bottom beams to allow
XFEM crack initiation and propagation
Modeling Tips
L9.48
Modeling Fracture and Failure with Abaqus
Modeling Tips
• General Information
• Averaged quantities are used in an element for determining crack
initiation and the propagation direction
• The integration point principal stress or strain values are averaged
• A new crack always initiates at the center of the element
• Within an enrichment region, a new crack initiation check is performed
only after all existing cracks have completely separated
• This may result in the abrupt appearance of multiple cracks
• Complete separation is indicated by STATUSXFEM=1
• Cracks cannot initiate in neighboring elements
• Crack propagates completely through an element in one increment
• Only the initial crack tip can lie within an element
L9.49
Modeling Fracture and Failure with Abaqus
Modeling Tips
• The enrichment region must not include “hotspots” due to boundary
conditions or other modeling artifacts
• Otherwise, unintended cracks may initiate at such locations
• Damage initiation tolerance
• A larger value may result in multiple cracks initiating in a region
• Small value results in small increment size and convergence difficulty
• Damage stabilization
• As mentioned earlier, judicious use of viscous regularization can aid in
convergence
• Initial crack should bisect elements if possible
• Convergence is more difficult if crack is tangential to element boundaries
• Use displacement control rather than load control
• Crack propagation may be unstable under load control
L9.50
Modeling Fracture and Failure with Abaqus
Modeling Tips
• Limit maximum increment size and start with a good guess for initial
increment size
• In general, this is a good approach for any non-smooth nonlinearity
• Analysis controls
• Can help obtain a converged solution and speed up convergence
• Contour plots of field quantities should be done with the crack
isosurface displayed
• Ensures that the solution is plotted from the active parts of the overlaid
elements according to the phantom nodes approach
• If the crack isosurface is turned off, only values from the “lower” element
are plotted (on the side with negative values of F)
L9.51
Modeling Fracture and Failure with Abaqus
Modeling Tips
• When defining the crack using Abaqus/CAE, extend the external crack
edges beyond base geometry
• This helps avoid incorrect identification of external edges as internal due
to geometric tolerance issues
Defining a through-thickness crack in a cylindrical vessel
Top View
Current Limitations
L9.53
Modeling Fracture and Failure with Abaqus
Current Limitations
• Implemented only for the static stress analysis procedure
• Can use only linear continuum elements
• CPE4, CPS4, C3D4, C3D8 and their reduced integration/incompatible
counterparts
• Element processing is not done in parallel
• On SMP machines, only the solver runs in parallel
• Cannot run in parallel on DMP machines
• Contour integrals for stationary cracks not currently supported
• Cannot model fatigue crack growth
• Intended for single or a few non-interacting cracks in the structure
• Shattering cannot be modeled
• An element cannot be cut by more than one crack
• Crack cannot turn more than 90 degrees in one increment
• Crack cannot branch
L9.54
Modeling Fracture and Failure with Abaqus
Current Limitations
• The first signed distance function F must be non-zero
• If the crack lies along an element boundary, a small positive or negative
value should be used
• This slightly offsets the crack from the element boundary
• Only frictionless small-sliding contact is considered
• The small-sliding assumption will result in nonphysical contact behavior
if the relative sliding between the contacting surfaces is indeed large
• Only enriched regions can have a material model with damage
• If only a portion of the model needs to be enriched define an extra
material model with no damage for the regions not enriched
• Probing field quantities on an element currently returns values only
from the “lower” element (corresponding to negative values of F)
Workshop 6
L9.56
Modeling Fracture and Failure with Abaqus
Workshop 6
• In this workshop, you will
continue with the analysis of a
cracked beam subjected to pure
bending using XFEM
• This workshop demonstrates:
• The ease of meshing and initial
crack definition compared to the
techniques presented in earlier
lectures
• The use of analysis controls
References
L9.58
Modeling Fracture and Failure with Abaqus
References
1. I. Babuska and J. Melenk, Int. J. Numer. Meth. Engng (1997), 40:727-758
2. T. Belytschko and T. Black, Int. J. Numer. Meth. Engng (1999), 45:601-620
3. A. Hansbo and P. Hansbo, Comp. Meth. Appl. Mech. Engng (2004),
193:3523-3540
4. J. H. Song, P. M. A. Areias and T. Belytschko, Int. J. Numer. Meth. Engng
(2006), 67:868-893