Jung-sun Park*Jung-Sun Park1, Myung-Jun Kim2, Hae-Kyu Hur3, Min-sung Kim3

1 School of Aerospace and Mechanical Engineering, Korea Aerospace University, Koyang, Republic of Korea 2 Graduate School, Korea Aerospace University, Koyang, Republic of Korea 3 Agency for Defense Development, Daejeon, Republic of Korea

Damage Evaluation with Multi-scale Failure Analysis

using Material Degradation Model based on SIFT

1. Introduction

4. Multi-scale Failure Prediction of Composite Plate

6. Conclusions

3. Micro-mechanical Modification

Damage Evaluation with Multi-scale Failure Analysis using Material Degradation Model based on SIFT

2. Strain-based Failure Theory of Composite

5. Damage Evaluation using Property Degradation Model

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1. Introduction

Mechanical Approach for Failure of Composite Materials

Over the years, the macro-mechanicalapproaches have been applied for thefailure of composite materials.

Practical failure mechanism ofcomposite materials cannot bepredicted in the macroscopic level.

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Micro-level of the composite failurecriteria were proposed by Hashin andSun.

In recent years, SIFT is proposed byGosse that a more efficient method topredict the failure of micro-level.

Failure criteria for composite materials are divided into macroscopic and microscopic approach.

Fiber

Failure

Fiber / Matrix

Interaction

Failure Mode

Matrix

Failure

Damage initiation is caused by dilatational and distortional deformations in fiber or matrix phase.

Micro-mechanical approach is required for the failure analysis of composite materials.

In this study, Strain Invariant Failure Theory was applied as the microscopic criterion.

Need of the Micro-mechanical Approach for Composite Failure

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Fiber breakage Fiber pullout Fiber buckling failure

Matrix cracking

Delamination Fiber/Matrix debonding

Failure modes are separated into the fiber failure, matrix failure and fiber/matrix interaction.

Multi-scale failure approach based on SIFT

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Static analysis for composite laminatewith macroscopic loading

Macro-scale

Determination of mesoscopic behavior (σ/ε in each ply )

Loading

Laminate Layer

Micro-mechanical modification by strain amplification factors(Calculating effective strain invariants)

Microscopic failure analysis by strain invariant failure criterion

Micro-scaleRVE

Strain component in each plyMicro-mechanical failure mode

2. Strain-based Failure Theory of Composite

Strain Invariant Failure Theory (SIFT)

Strain Invariant Failure Theory was proposed by Gosse in 2001.

SIFT defines the failure characteristic of each fiber and matrix by using the volumetric strain and the equivalent strain.

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Volumetric strain (sum of strain invariants) Dilatational (volumetric) deformation Equivalent strain (von-Mises strain) Distortional (deviatoric) deformation

Dilatational deformation Distortional deformation

Change of volume

Change of shape

vε eqvε

Volumetric strain

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The strain invariants can be defined as functions of three principal strains from cubic characteristic equation of strain tensor.

3 21 2 3 0J J Jε ε ε− + − =

1 1 2 3J ε ε ε= + +

2 1 2 2 3 3 1J ε ε ε ε ε ε= + +

3 1 2 3J ε ε ε=

1 2 3( , , )f ε ε ε

Cubic characteristic equation

Actually, the volumetric strain is defined by the sum of each strain invariant.

In practice, J1 is considered as significant component of the volumetric strain.

1 2 3 1v J J J Jε = + + ≈

Strain invariants

Most significant component of the volumetric strain

Equivalent strain (von-Mises strain)

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'3 ' ' '2 3 0J Jε ε− − =

( )' 2 2 2 2 2 22

1 1[( ) ( ) ( ) ]

6 4xx yy yy zz zz xx xy yz zxJ ε ε ε ε ε ε ε ε ε= − + − + − − + +

( )2 2 23' ' ' ' ' ' '1

4xx yy zz xy yz zx xx yz yy zx zz xyJ ε ε ε ε ε ε ε ε ε ε ε ε= + − − −

: Cubic characteristic equation of deviatoric strain( )'ε ε ε= −

The equivalent strain (von-Mises strain) is defined as a function of the second invariant of the deviatoric strain tensor.

The deviatoric strain invariants are obtained from cubic characteristic equation of the deviatoric strains tensor.

Deviatoric strain invariants

2 2 21 2 1 3 2 30.5[( ) ( ) ( ) ]ε ε ε ε ε ε= − + − + −'

23vm Jε =

Strain Invariant Failure Criterion

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The effective strain invariants are calculated through the micro-mechanical modification.

- Effective first invariant of strain- Effective equivalent strain (von-Mises strain)

Failure will occur at either the fiber or the matrix phases if any of the effective strain invariants (J1, εvm) exceed the critical value.

1 0 ,J ≥ 1 1criticalJ J≥

1 0 ,J < criticalvm vmε ε≥

For matrix

criticalvm vmε ε≥

Failure criterion in SIFT for matrix and fiber

For fiber

Micromechanical Modification

3. Micromechanical Modification

Concept of Strain Amplification Factor

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Homogenized lamina solution provides an average state of strain representing boththe fiber and matrix phase at the same point in space.

In order to perform the microscopic analysis, a method of the micromechanical modification is required to amplified the average state of strain.

In micro-scale analysis , the mechanical strain amplification factor is very important parameter for connecting the micro-level and macro-level strain tensor.

{ } [ ]{ }ij total ij mechMε ε=( / )

ijij

ij oM

L Lε

=∆

:

:

:

ij

ij

o

local strain

L prescribd unit displacement

L initial length of RVE which is parallel with loading direction

ε

∆

Concept of Strain Amplification Factor

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Strain amplification factor is calculated by finite element analysis for micro-mechanical block model.

The micromechanical block is called the RVE (Representative Volume Element) which is explicit model of fiber and matrix.

The type of RVE is divided by fiber packing arrays, namely square, hexagonal and diamond.

Micromechanical Block Modeling

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In order to obtain the strain amplification factor of IM7/K3B composite materials,finite element model of the RVE was generated by MSC.Patran.

The single cell model of square array type was used to perform the microscopic analysis.

Mechanical Property

Fiber (IM7)

Matrix (K3B)

Composite Lamina

E11 [GPa] 303 3.31 177.075

E22 [GPa] 15.2 3.31 10.403

G12 [GPa] 9.65 1.23 6.105

G23 [GPa] 6.32 1.23 6.105

ν12 0.2 0.35 0.2947

ν23 0.2 0.35 0.2947

RVE (Representative Volume Element) Mechanical properties of IM7/K3B

Vf=60 %

Boundary Condition of Micromechanical block

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RVE is given prescribed unit displacement in three case of normal deformation for one of the faces.

Also, the other five faces are constrained by symmetric condition.

Definition of boundary conditions

Mechanical strain amplification factor Boundary conditions

M11 ε11 = 1, ε22 = ε33 = γ12 = γ13 = γ23 = 0(longitudinal direction)

M22 ε22 = 1, ε11 = ε33 = γ12 = γ13 = γ23 = 0(transverse direction)

M33 ε33 = 1, ε11 = ε22 = γ12 = γ13 = γ23 = 0(transverse direction)

Transverse direction (M33)

Transverse direction (M22)

Longitudinal direction (M11)

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10 points were selected in the single cell for the extraction of local strain values.

- Matrix region : M00 (Interstitial location), M01-M02 (Inter-fiber location), M1-M3 (Fiber/matrix interface)

- Fiber region : F1-F3 (Fiber/matrix interface), F4 (Center of fiber)

Selected points to extract the local strains

Extracting the Strain Amplification Factor

Matrix Phase

Fiber Phase

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M11 for longitudinal direction are all 1.0 at any selected points in fiber and matrix. M22 and M33 are equal due to rotational symmetry for square array.

The result of the strain amplification factor, M22

Extracting the Strain Amplification Factor

Maximum strain amplification factors for each directionRegion Strain invariant M11 M22 M33

Matrix phase Case of J1 1 2.61523 2.61523

Case of εmvm 1 2.72389 2.72389

Fiber phase Case of εfvm 1 0.77291 0.77291

4. Multi-scale Failure Prediction of Composite Plate

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In order to perform the failure analysis, the strain tensor was extracted forcomposite open-hole plate model through the finite element analysis.

- The materials of composite plate is IM7(graphite) / K3B(epoxy).- The stacking sequence is [45°/90°/-45°/0°]s

Static analysis of Composite One-hole Plate Model

Finite element model of composite open-hole plate

FEMmodeling

y-symmetry

x-symm

etry

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Flow chart for multi-scale failure analysis

Multi-scale Failure Analysis based on SIFT

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X Component (Longitudinal direction) Y Component (Transverse direction)

X Component (Longitudinal direction) Y Component (Transverse direction)

Strain distribution of composite plate Layer 1 (45°)

Layer 2 (90°)

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X Component (Longitudinal direction) Y Component (Transverse direction)

X Component (Longitudinal direction) Y Component (Transverse direction)

Strain distribution of composite plate Layer 3 (-45°)

Layer 4 (0°)

Effective Strain invariants

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The strain components were amplified by the strain amplification factors. And then, the effective strain invariants (J1, εvm) were calculated.

Failure analysis of Composite Tensile Plate Model

2 2 211 1 22 2 11 1 33 3 22 2 33 30.5[( ) ( ) ( ) ]vm M M M M M Mε ε ε ε ε ε ε= − + − + −

11 22 331 1 2 3J M M Mε ε ε= + +

Critical strain invariants for graphite/epoxy laminated composite (IM7/K3B) were used experimental data from reference [2].

Critical invariant Value Laminate stacking sequence Failure Mode

J1-crm 0.0274 [90]10 Matrix / Dilatational

εvm-crm 0.103 [10]10 Matrix / Distortional

εvm-crf 0.0182 [0]10 Fiber / Distortional

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Failure indices for each layer [45°/90°/-45°/0°]s

J1 failure is dominant

J1 failure is dominant

J1 failure is dominant

εvmf failure

is dominant

Layer 1 (45°) Layer 2 (90°)

Layer 4 (0°)Layer 3 (-45°)

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Comparing with existing theories (Maximum strain, Tsai-Wu, Hashin, Sun failure criterion)

Similar tendency was confirmed from the distribution of failure index.

Layer 1 (45°) Layer 2 (90°)

Layer 4 (0°)Layer 3 (-45°)

5. Damage Evaluation of Composite Plate using Property Degradation Model

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Micro-mechanical failure modes can be determined with Strain invariant failure criteria.

Micro-mechanical Failure Modes

Constituent Loading Condition Failure Mode Failure Criterion

Fiber

Tensile(Longitudinal)

Fiber fracture

εvmf

Fiber pullout

Compression (Longitudinal)

Fiber kinking

Fiber buckling

MatrixTensile Matrix cracking (J1≥0) J1

Compression Matrix compression failure (J1<0) εvmm

Fiber/Matrix Tensile / Compression Fiber/Matrix shearing (de-bonding) failure εvmm

Matrix cracking(Tens. / Comp.)

Fiber fracture Fiber pullout Fiber/Matrix shearing (de-bonding) failure

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Material degradation models were defined for each failure mode.

- Matrix failure :

- Fiber failure :

- Fiber/matrix shearing :

User-subroutine (USDFLD) in ABAQUS/CAE was used to degrade the material properties.

Material Property Degradation Model

Material State(Failure Mode) Elastic Properties Field variable

#1Field variable

#2Field variable

#3

No failure Ex Ey vxy Gxy 0 0 0Matrix failure Ex 0 0 Gxy 1 0 0Fiber failure 0 Ey 0 Gxy 0 1 0Fiber/matrix shearing failure Ex Ey 0 0 0 0 1Matrix & Fiber failure 0 0 0 Gxy 1 1 0Matrix failure & Fib/mtx shear Ex 0 0 0 1 0 1Fiber failure & Fib/mtx shear 0 Ey 0 0 0 1 1All failure modes 0 0 0 0 1 1 1

1 0 ,J ≥ 1 1m m

crJ J −≥

1 0 ,J < m mvm vm crε ε −≥

f fvm vm crε ε −≥

m mvm vm crε ε −≥

0y xyE ν= =

0x xyE ν= =

0xy xyGν = =

Property

Degradation

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Flow chart for damage evaluation using property degradation models

Damage Evaluation using Property Degradation Model

Displacement loading

X-symmetry

Y-symmetry

Critical Region

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Composite open-hole plate model was generated by ABAQUS/CAE. Static analysis was performed using by property degradation models.

- The materials of composite plate is IM7/K3B.- The stacking sequence is [(-45°/+45°)6]s.

Composite Open-hole Plate Model

L = 2.0 in

W = 0.5 in

d = 0.25 in

t = 0.135 in (total)

Damage for Matrix failure mode>> Strain Invariant : J1 (Tensile) / εvm

m (Compression)

Increment 1 Increment 2 Increment 3 Increment 4 Increment 5

Increment 6 Increment 7 Increment 8

Damage distribution of composite plate

Critical location

Increment 9 Increment 10

Failure regionis extended

Local failure occurs

Increment 1 Increment 2 Increment 3 Increment 4 Increment 5

Increment 6 Increment 7 Increment 8 Increment 9 Increment 10

Damage for Fiber failure mode>> Strain Invariant : εvm

f (Tensile / Compression)

Damage distribution of composite plate

Increment 1 Increment 2 Increment 3 Increment 4 Increment 5

Increment 6 Increment 7 Increment 8 Increment 9 Increment 10

Damage for Fiber/matrix shearing failure mode>> Strain Invariant : εvm

m (Tensile / Compression)

Damage distribution of composite plate

6. Conclusions

The strain amplification factors were obtained from the result of micro-mechanical analysis for RVE model.

Micro-mechanical modification was performed for macroscopic strains of composite plate model.

The strain-based failure analysis was performed by using the SIFT.

The result of failure analysis was verified by comparing with existing theories.

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Damage Evaluation with Multi-scale Failure Analysis using Material Degradation Model based on SIFT

Micro-mechanical progressive damage was evaluated for composite plate using the material property degradation models.

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Q & A