magnetic bead manipulation applicable for sensing and diagnostics
TRANSCRIPT
Magnetic Bead Manipulation applicable for Sensing and Diagnostics on a ChipR.J.S. Derks (1) , I. Petousis (1) , F.G.A. Homburg (1) , M.W.J. Prins (2) , A. Dietzel (1)
Dept. of Mechanical Engineering (1) / Applied Physics (2)
Eindhoven University of TechnologyPO Box 513, 5600 MB Eindhoven
+31 (0) 40 - 2473647 [email protected] [email protected]
Molecular diagnostics demand for portable solutions that can operate outside a professional environment and require only small fluidic samples. Therefore, we investigate new fluid manipulation techniques based on magnetic beads.
1 Introduction
A bead, composed out of small iron oxide grains embedded in a polymer, exhibits a superparamagnetic behavior: a strong magnetizability without remanence. The velocity of a single bead, immersed in fluid and actuated with external magnetic fields, is:
2 Magnetic Beads
3 Experimental SetupBeads in a closed fluid volume (~10 µl) are actuated by an external magnetic field. The 4 flux guides concentrate the magnetic flux within the fluid and the 4 coils allow for multiple field shapes and for dynamic field rotation.
Beads that aggregate in chains increase their velocity, expressed as vc = VEF • vb. The VEF reflects the chain shape influence on the total magnetic moment and the hydrodynamic drag force [1].
4 Motion of Chains
[1] R.J.S. Derks, A. Dietzel, R. Wimberger-Friedl, M.W.J. Prins, Magnetic Bead Manipulation in
a Sub-Microliter Fluid Volume applicable for Biosensing, Microfluidics and Nanofluidics, 2006
Rotating bead chains can be used to enhance mixing. Experiments have shown that the shape and length of the rotating chain can be controlled by the strength and rotational frequency of the applied magnetic field.
5 Rotation of Chains
Magnetic beads can be used as miniaturized fluid drivers in micro channels. Moving beads induce translational flow and local exchange of fluid at the channel walls, as can be taken out of first simulations.
6 Fluid Transport in Microchannels
channel wall
channel wall
Magnetic beads can have different applications in microfluidics. Future work will focus on fluid transport, mixing and analyte up-concentration for lab-on-a-chip devices.
7 Outlook
Design of a smart mount for vibrationisolation in precision equipment
G.W. van der Poel, J. van Dijk, J.B. Jonkerand H.M.J.R. Soemers
Institute of Mechanics, Processes and Control TwenteUniversity of Twente, Laboratory of Mechanical Automation
P.O. Box 217, 7500 AE Enschede, The Netherlands+31-(0)53-489 2434, [email protected]
IntroductionDisturbances are becoming increasingly importantin high-precision machinery, in which the requiredaccuracy level is reaching (sub-)nanometer levels. Inmost existing vibration isolation systems, a designtrade-off is made between isolating a machinefrom floor vibrations and reducing the effects ofdisturbances which act directly on the machine.However, this approach only results in satisfactoryperformance if one type of disturbance is insignificant.
ObjectiveThe objective of this research project is to designmachine mounts which offer satisfactory vibrationisolation from both direct disturbances and floorvibrations.
Figure 1 : Schematic drawing of a machine withan internal resonance mode, supported by an activemount. The machine is subjected to a directdisturbance force and floor vibrations.
MethodsMechanical design The machine mounts aredesigned to be stiff, which results in a low complianceto direct disturbances.Control strategy The control system serves twopurposes:• to add artificial damping to the resonance modes
by means of feedback control (FB);• to improve the floor vibration isolation perfor-
mance by using adaptive feedforward control(FF) [1];
Figure 1 shows a schematic drawing of a machinesupported by a mount with an active vibrationisolation system.
ResultsThe control strategy was implemented on a testsetup with a single direction of motion, which closelyresembles the schematic system shown in figure 1. Ashaker was used to excite the ’floor’. Figure 2 showsthe amplitude frequency response of x1 to the shakerforce, for FB only and for FB combined with FF basedon the shaker force.
1 10 100 1000−60
−40
−20
0
20
Frequency (Hz)
Mag
nitu
de (d
B re
1 m
s−2/N
) uncontrolledFB onlyFB + FF
Figure 2 : Amplitude frequency responses of payloadacceleration x1 to shaker force
DiscussionThe combination of feedforward and feedback controlresults in an improved floor vibration transmissibilitywhile maintaining a stiff connection to the floorand thus low compliance to direct disturbances.Further research will focus on 3D mount design andimprovement of the control system.
References1. Elliott, S.J. (2001), Signal processing for active control,
Academic Press.This research project is supported by theIOP Precision Technology program.
Computational Modelling of Fibre ReinforcedCementitious Composites
F.K.F. Radtke, A. Simone and L.J. Sluys
Delft University of TechnologyFaculty of Civil Engineering and Geosciences
P.O. Box 5048, 2600 GA Delftphone +31 15 278 3752, email: [email protected]
IntroductionDaring projects in civil engineering have motivatedthe development of innovative high performance ma-terials. Among them are different fibre reinforced ce-mentitious composites (FRCC).
ObjectiveThese new high performance materials have to bespecifically tailored to meet the needs of modernstructures. To design materials in an efficient way,new computational tools are needed. They have toestablish the link between the physical material prop-erties and the mechanical behaviour.
MaterialFRCC show a number of distinguishing mechanicalproperties. They exhibit a ductile response undertension with a state of multiple cracking. This char-acteristic behaviour originates from the different con-stituents of the material, their distribution and interac-tion. An analysis of the structure of FRCC reveals astrong multiscale character (see Figure 1).
LevelMacro
LevelMeso
LevelMicro
1 µm ≤ lE < 1 mm
Fibres Meso Matrix ITZs
Meso Cracks/Pores Aggregates
Fibre Surface
Micro Cracks/Pores Aggregate Surface Aggregate Matrix
Micro MatrixITZsFibre Matrix
FRCC
Micro Particles
lE ≥ 1 m
1 mm ≤ lE < 1 m
Figure 1 : Multiscale representation of FRCC
ApproachesFull approach A geometrical model of the materialon the meso level including matrix, particles and fi-bres is set up, discretised and solved. Figures 2 and3 show an example of a specimen under tension. The
disadvantage of this approach is the enormous com-putational cost. For this reason, this approach is lim-ited to very small systems.
ParticleFibre 380 969675
SX
590 775683
SX_SectionPlane
Figure 2 : Geometry Figure 3 : Stresses
Reduced approach To overcome the difficulties ofthe full approach a reduced approach is developed.Instead of representing all constituents of FRCC inone model, two processes are identified that domi-nate the material behaviour. One is the developmentof matrix cracks growing from initial cracks. The sec-ond one is the fibre-matrix interaction characterisedby the fibre pull-out behaviour. Both phenomena aremodelled on different levels as shown in Figure 4.
�� �� �� ��
�� ��
���� ��
��
��
����
�� ��
MicroLevel
MesoLevel
Crack
ITZ Matrix
P
Fibre
Matrix
F F
Fibre Position
Figure 4 : Mechanical system of the reduced approach
Acknowledgments
Financial support from the Netherlands Technology Foundation(STW) is gratefully acknowledged.
Finite element implementation ofKoiter’s initial postbuckling theory
T. Rahman and E.L. Jansen
Delft University of TechnologyFaculty of Aerospace EngineeringP.O. Box 5058, NL 2600 GB Delft
phone +31-(0)15-2785386, email [email protected]
Introduction and objectiveThe current simulation methods (Finite Element computermodels) for nonlinear structural analysis calculations re-quire a lot of effort and expertise from the user, and needa long computer run time. Therefore there is a strong needfirstly for methods that help in providing a systematic ap-proach to achieve reliable results, and secondly for fastercomputational methods. The main objective of the presentresearch framework is the availability of fast, Finite Ele-ment (FE) based tools for the nonlinear static and dynamicanalysis of slender and thin-walled structures, that are suit-able for design. As a first step towards this objective, Koi-ter’s initial post-buckling theory has been implemented inthe general purpose FE code DIANA. The current imple-mentation is largely based on the already existing DIANAimplementation of Koiter’s theory [1] and Tiso’s formulation[2].
MethodsKoiter’s initial postbuckling theory is a perturbation tech-nique that describes the static initial postbuckling path byan asymptotic expansion of the displacement field aroundthe bifurcation point. For M buckling modes the displace-ment field can be written as,
u = λu0 +uiξi +ui jξiξ j + . . . i, j = 1, ...,M (1)
where, u0 is the linear pre-buckling displacement field; ui
and ui j are the first order modes (buckling modes) andsecond order modes; ξi are the modal amplitudes. Per-turbation analysis based on Equation (1) leads to a set ofM nonlinear equations (2) for the computation of the am-plitudes ξi,
(1−λ/λI)ξI +aI jkξ jξk +bI jklξ jξkξl
= (λ/λI)ξI I = 1, ...,M(2)
where, λI is the buckling load associated to the bucklingmode uI ; the coefficients aI jk and bI jkl correspond to thepostbuckling slope and curvature respectively. The righthand side term is an additional term that accounts for smallimperfections in the shape of buckling mode uI .
Therefore, instead of a large set of nonlinear equationsin full model analysis we have to deal with only M non-linear equations. This approach has been implementedbased on an existing class of curved shell elements in thegeneral purpose FE code DIANA.
Results and discussionImperfection-sensitive structures such as cylindrical shellshave been analyzed. Cylindrical shells with different lengthto radius ratio (L/R) have been considered. The cylindersare simply supported at two ends and loaded under exter-nal pressure. One of the buckling modes and the resultingsecond order modes of the cylinder (L/R = 0.5) are shownin Figure 1. The resulting negative b-coefficients indicatetheir unstable postbuckling nature and imperfection sensi-tivity. For larger shells lengths, there is a fair agreementin the obtained b-coefficients between DIANA and semi-analytical approach described in [3]. The discrepancy ob-served for the smaller shell length (L/R = 0.5) is presentlyunder investigation.
Figure 1 : First order (left) and second order (right) modes ofthe cylinder (L/R = 0.5)
Analysis case b (DIANA) b (semi-analytical)L/R = 0.5 −1.1086×10−1 −1.8088×10−1
L/R = 1 −1.207×10−2 −1.1981×10−2
L/R = 2 −9.5311×10−4 −9.0219×10−4
Further verification of the implementation for more com-plicated structures and its extension for an even widerclass of elements will be done in the near future.
References1. C. M. Menken, G. M. A. Schreppers, W. J. Groot, and R. Petterson
(1997). Analyzing buckling mode interactions in elastic structuresusing an asymptotic approach; Theory and experiments. Computers& Structures, 64(1-4):473-480.
2. P. Tiso, M. M. Abdalla, E. L. Jansen (2006). Koiter’s post-bucklinganalysis of general shell structures using the finite element method.Conference proceedings, ICAS 2006, Hamburg, Germany.
3. J. Arbocz and J. M. A. M. Hol (1990). Koiter’s stability theory in com-puter aided engineering (CAE) environment. Int. J. Solids Struc-tures, 26(9/10):945-975.
Constitutive Behaviour in Strain PathSensitive Sheet Metal
M. van Riel, A.H. van den Boogaard, J. Huetink
University of Twente/ NIMRP.O. Box 217, 7500 AE Enschede, The Netherlands
phone +31-(0)53-4893605, email [email protected]
IntroductionIn deep drawing processes a material pointexperiences different deformation modes insuccession. Current constitutive models do not fullyrepresent the change in deformation mode. Higherdemands on economic and environmental concernsmeans that this needs to be improved.
Figure 1 : Different stages in the deep drawing process.
Adding strain path sensitivity to the constitutive lawswill result in improved predictions of mechanicalresponses and in more accurate FE simulations.
MethodsThe current work is focussing on two parts;developing a strain path dependent model andcollecting mechanical responses during strain pathchanges in experiments.Modelling A general applicable return mappingalgorithm is developed to create a basis for differenthardening models, independent of the chosen yieldcriterion. The evolution of the isotropic and kinematichardening are separately defined, see Figure 2.
n
n
nσσσσααααεεεε
isotropichardening
incrementn
Return MappingAlgorithm
yieldcriterion
kinematichardening
σσσσααααεεεε n+1
n+1
n+1
incrementn+1
Figure 2 : General applicable return mapping algorithm.
Arbitrarily combinations of isotropic and kinematichardening and even interacting combinations arepossible. A consistent stiffness is determined andboth the return mapping algorithm and the stressiterations converge quadratically.
Experimental A testing device that loads a specimenon plane strain followed by simple shear deformationis used to investigate strain path changes.
ResultsExperimental results from orthogonal tests aredepicted in Figure 3. A momentary strain pathchange is obtained by suddenly freezing the tensilestrain, while a slowdown release of tensile strain givesa gradual strain path change.
0 0.1 0.2 0.3 0.4
0
50
100
150
200
250
300
350
εeq p (−)
σ (N
/mm
2 )
simple shear curvegradual strain path changesudden strain path change
Figure 3 : Results of orthogonal tests. Solid lines: shearstress; dashed lines: tensile stress.
Intermediate strain path changes give shear curvesthat are in between these two shear curves.
Conclusion & Future researchIt is shown that classical isotropic and kinematichardening is not sufficient to describe theexperimental results. Future work will focus ondeveloping a hardening model that is able to describethese phenomena.
Uniqueness of the boundary value problem of linear elastostatics in the circular domain
A. Rohe, F. Molenkamp Delft University of Technology
Faculty of Civil Engineering and Geosciences Section Geo-engineering, P.O. Box 5048, 2600 GA Delft
phone +31-(0)15-2784009, e-mail [email protected]
Introduction Numerical solution procedures are used for the determination of the stress and strain field in a continuum. Their finite element descriptions suffer from instabilities or divergence in certain material parameter ranges for different reasons. Objective The purpose of this study is to give a clarification of the parameter field for which the underlying boundary value problem is uniquely solvable and the solution is stable, in first instance for equivalent linear elasticity for circular elements. Methods Based on the equations of motion, the system of partial differential equations in terms of displacements is derived using an equivalent linear elastic material model for small strains. The boundary conditions are of Dirichlet-type (displacements). Only for the hourglass eigenmode (see figure 1) non-unique solutions can occur. Figure 1: Illustration of hourglass eigenmode for the rectangular and circular element.
An extended method of the separation of variables is used to derive the complete closed form analytical solution of the boundary value problem. Herewith a necessary and sufficient condition of uniqueness can be derived. Results The unique part of the solution for the radial and tangential displacements reads
for Poisson’s ratio ν≠0.5,0.75,1.0 ( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( )
2 2
2 2
1 4 1 13 4 22 3 4
4 5 1 13 4 22 3 4
, sin sin3
, cos cos3
r rr R R
r rR R
u r e e
u r e e
ννν
νθ νν
θ θ θ
θ θ θ
−−−
−−−
= + +
= + +
Herewith stress and strain field and energy distribution are calculated (see figure 2). Non-unique solutions exist if and only if the shear modulus G=0 or ν=0.5,0.75,1.0. The solution is stable for all ν≠0.75. Figure 2: For ν=0.74: (a) Displacements; (b) strain field; (c) stress field (red=tension, blue=com-pression); (d) strain energy distribution (red=positive, blue=negative). Conclusion For the circular element the closed form analytical solution of the displacement field is derived. A necessary and sufficient condition of uniqueness is given. In ongoing research elasto-plastic material models and various elements (rectangular, triangular) will be studied. An implemen- tation in numerical codes will then give better results for exceptional material parameter configurations in geomechanics.
Geo-engineering
−1 −0.5 0 0.5 1
−1
−0.5
0
0.5
1
Principal strains ε*(R/e)
ν=0.74
red = tensionblue = compression
εmax
*(R/e)=50ε
min*(R/e)=−50
x/Ry/
R
−1 −0.5 0 0.5 1
−1
−0.5
0
0.5
1
Principal stresses σ/2G*(R/e)
ν=0.74
red = tensionblue = compression
σmax
/2G*(R/e)=76σ
min/2G*(R/e)=−76
x/R
y/R
−1 −0.5 0 0.5 1
−1
−0.5
0
0.5
1
Total displacements u/e
ν=0.74
(scal
umax
ucent
unode
x/R
y/R
−1 −0.5 0 0.5 1
−1
−0.5
0
0.5
1
Total strain energy W/2G*(R/e)2
ν=0.74
Wmax
/2G*(R/e)2=576W
min/2G*(R/e)2=−524
x/R
y/R
−500
−400
−300
−200
−100
0
100
200
300
400
500
(a) (b)
(c) (d)
Does discreteness matter in plasticity? A. Roy , R.H.J. Peerlings, M.G.D. Geers
Eindhoven University of Technology
Faculty of Mechanical EngineeringP.O.Box 513, NL 5600MB Eindhoven
phone +31-(0)40-2473048, email [email protected]
Introduction
Continuum plasticity theories are incapable of
predicting the formation of pile-ups at hard
obstacles which a Discrete dislocation analysis
can predict with relative ease. The question
then arises: How important is the underlying
discreteness at larger scales? Is there a
directional dependence of this discreteness?
Do we need to incorporate discreteness in a
continuum setting, and if so how?
Fully Discrete Analysis
For illustration, we evaluate infinite walls of
dislocations piling up in an infinite medium
(Figure 1). Discrete dislocation analysis is
performed as a benchmark for comparison with
continuum approximations. Non-linear
equations are solved numerically to evaluate
the equilibrium position of the walls under a
constant, externally applied shear stress
(Figure 2).
Figure 1. Discrete dislocation representation of
a pile-up in an infinite medium. Slip plane
separation is “h”. The red circles represent the
immobile wall at x=a.
.
Conclusion
� Discreteness cannot be ignored in the
direction perpendicular to the slip direction.
� “Smudging” of dislocations is allowed in the
slip direction.
Discrete in y and Continuous in x
Here, the dislocation wall distribution in the slip
plane direction is represented by a continuous
function with the wall discreteness in the y -
direction maintained as before. A converged
solution on the density profile is obtained which
matches exactly with the fully discrete analysis
performed before (Figure 2).
Figure 2. Comparison of dislocation density distribution for positive Screw dislocation
infinite walls .
Continuous in y and Discrete in x
Analytically, if the internal discreteness (in the
y direction) of a single infinite wall is replaced
by a continuous function of infinitesimal
dislocations the stress fields lose all variation in
the slip plane direction and in most cases
reduce identically to zero (Figure 3). Formation
of pile-ups is not observed when multiple walls
are considered.
Figure 3. Shear stress profile of an edge dislocation wall. Stress variation along the y-
axis and consequence of averaging.
Future Work
Formulating techniques to characterize this
unique directional dependence on discreteness
using gradient terms in a continuum plasticity
framework.
-2 -1.5 -1 -0.5 00
500
1000
x/h
f(x
) h
Discrete analysis
Semi-continuum analysis
−∞
∞
2h
h
2h−
h−
0
x a=
y
x
-2 -1 1 2
yÅÅÅÅÅh
-0.002
-0.001
0.001
0.002
sxyÅÅÅÅÅÅÅÅÅÅÅK
xÅÅÅÅÅh
yÅÅÅÅÅh
sxyÅÅÅÅÅÅÅÅÅÅÅ
K
-2 -1 1 2
yÅÅÅÅÅh
-0.002
-0.001
0.001
0.002
sxyÅÅÅÅÅÅÅÅÅÅÅK
average
A method of multiple reflections for modellingsoil vibration induced by a train in tunnel
M. Shamalta and A.V. MetrikineDelft University of Technology
Faculty of Civil Engineering and GeosciencesP.O. Box 5048, 2600 GA Delft
phone: +31 15 278 4167, email: [email protected]
MotivationA high level of ground vibrations induced by under-ground high-speed trains leads to serious problemsrelated to noise and vibration pollution, especially indensely populated urban areas. Therefore it is of im-portance to develop a reliable prediction model forground vibrations caused by underground railways.The main objective of this study is to get a physicalinsight in the vibration transfer from the tunnel to thesurface.
ModelIn this study a basic three-dimensional model of atunnel-in-ground system is considered, Figure 1. Thismodel is composed of an infinitely long elastic cylin-drical shell in a visco-elastic homogenous half-space.The elastic shell represents the tunnel structure andthe visco-elastic half-space models the ground. Thetrain loading is modelled as a harmonic force whichmoves along the tunnel with a constant speed.
Figure 1: Infinitly long cylindrical tunnel in half-space
Steady state solutionThe steady-state solution of the problem is con-structed as the superposition of two components.The first is a wave field generated by the tunnel inthe corresponding visco-elastic full space, Figure 2left. The second is a wave field generated by a mo-tion of the surface of the half-space without the tun-nel, Figure 2 right. These components of the solutiondescribe the vibration transfer from the tunnel to the
surface (the first component) and back (the secondcomponent). Superposing them a sufficient numberof times an accurate prediction of the ground vibra-tion can be accomplished.
Figure 2: Infinitly long cylindrical tunnel in full-space andhalfspace without tunnel
ResultsVibration of the tunnel-ground system can be soughtof as a superposition of waves radiated and thenreflected by the tunnel and waves reflected by theground surface. The number of reflections neededfor the accurate description of the system dynamicsis the larger the longer the waves (the smaller the fre-quencies), the closer the tunnel to the surface, andthe lower the velocity.
Figure 3: Change of stresses on imaginary plane in thefrequency-wavenumber domain as function of the depth of the
tunnel (left), and the load velocity (right)
The competition between solid-state phasetransformations and plastic deformation:
discrete interfaces and discrete dislocationsJingyi Shi
Technology University of DelftFaculty of Aerospace Engineering
tel: +31-(0)15-2781829, email: [email protected]
IntroductionSteels assisted by transformation induced plasticity(TRIP) are a class of high strength-high ductiltiy mate-rials. During mechanical loading, TRIP steels gain ad-ditional strength due to a martensitic transformation.This phenomenon is strongly coupled to plastic defor-mations in the austenitic matrix. In order to optimizethe mechanical properties of these materials, it is im-portant to understand the coupling of the transforma-tion and plasticity.
MethodologyThe martensitic transformation and the plastic defor-mation are modelled explicitly using martensitic platesand discrete dislocations embedded in an austeniticgrain. Superposition is used to obtain the solutionin terms of (i) the nonelastic flows, which arise fromthe collective motion of dislocations and the formationof martensitic plates, and (ii) a complementary solu-tion used to satisfy the actual boundary conditions, asshown in figure 1.
Figure 1 : Schematical illustration of the method
In the volume V of the grain, the actual stress andstrain fields of the problem can be described as
σ = σm + σ
d + σc (1)
ǫ = ǫm + ǫ
d + ǫc (2)
where m,d and c represent the transformation, dislo-cation and complementary elastic field, respectively.The stress and strain fields for the martensitic platesare obtained analytically using Eshelby’s inclusion
theory [1]. The fields associated to plastic deforma-tions are implemented using the discrete dislocationmethod [2]. The complementary field is solved nu-merically using FEM.
SimulationsBased on the framework mentioned above, uniaxialtension cases were simulated. In the calculations, dis-location and transformation sources were evenly dis-tributed. Initially, the specimen deforms elastically andthen plastically. Subsequently, in places where thestress field is high, martensitic plates nucleate andgrow, as shown in figure 2. Due to the stress-free vol-ume expansion of the transformation, the local stressdecreases. However, transformation hardening even-tually occurs since the newly-formed plates act as bar-riers for the dislocations, as shown in figure 3.
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SXX0.030.0250.020.0150.010.0050
-0.005-0.01-0.015-0.02
Figure 2 : Contour plot of stress σxx when ǫ = 0.33%
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------
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-
-
-- -
-
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-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
SXX0.030.0250.020.0150.010.0050
-0.005-0.01-0.015-0.02
Figure 3 : Contour plot of stress σxx when ǫ = 0.43%
References1. Mura, T., (1987) Micromechanics of Defects in Solids.2. Van der Giessen, E., Needleman, A., (1995) Modelling Simul. Mater.
Sci. Eng., 3: 689-735.
Compact Balancing Devices based on Piezoelectric Ultrasonic Motors
P.J. Sloetjes, A. de Boer
Institute of Mechanics, Processes and Control - Twente Chair of Structural Dynamics and Acoustics, University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands phone +31-(0)53-4893405, email [email protected]
Introduction
Time-varying unbalance due to e.g. tool changes or
temperature gradients is increasingly complicating
performance enhancement of production machines.
High speed shafts are already often equipped with
balancer rings (Fig.1a,b), but active balancing
devices that compensate unbalance during machine
operation are getting more and more common. The
conventional electromagnetic balancer device might
be improved and miniaturized by utilizing
piezoelectric ultrasonic motors (PUM's) (Fig.1c,d,e)
for actuation. PUM’s have a simple mechanical
structure and a low response time and they are
easily combined with non-contact power supplies.
Fig.1. (a) Balancer rings with (b) working principle.
(c) Shinsei rotary PUM with (d,e) working principle.
Objective
The present research aims to quantify the
performance of an active balancing device which is
based on two rotary piezoelectric ultrasonic motors.
Methods
A flexible shaft with a heavy disk is selected as test
case. (This enables a comparison between
piezoelectric mass actuators and the force actuators
which were considered in previous research).
Vibration at the bearings and motion of the shaft are
measured with accelerometers and eddy current
sensors, respectively. Two balancer rings separated
by a teflon disk are mounted on the shaft between
two PUM stators (Fig.2a,b,c). The PUM electrodes
are connected to coils which are powered contact-
less by stationary coils. The relative orientations of
the shaft and balancer rings are obtained from key
phasor signals measured with optical sensors. Fig.2. (a) Ring balancer device on a flexible shaft with
disk (drawing). (b) Two facing PUM's (drawing).
(c) Stator of a Shinsei PUM on a flexible shaft (photo). Adaptive unbalance compensation algorithms are
developed which take into account 1) stiffness and
mass asymmetry of the shaft and supports, 2)
transient effects which result from the varying rotor
speed and motion of the balancer rings and 3)
positioning hysteresis in the piezoelectric ultrasonic
motors. The control algorithms are implemented on
a dSpaceTM system. A schematic representation of
the experimental setup is shown in Fig.3.
Fig.3. Experimental setup: (a) flexible shaft,
(b) PUM's, (c) accelerometer, (d) phase sensors,
(e) control system, (f) powering coils.
Results
In previous research, a flexible shaft with surface-
mounted piezoelectric force actuators was
effectively stabilized and unbalance induced
vibration was reduced by 98%.
a)
a) b) c)
b)
c) d) e)
a) b)
e)
d)
c)
f)
Superplastic forming of subatomic particledetector foils
C. Snippe
NIKHEF / University of TwenteEngineering Department
P.O. Box 41882, NL 1009 DB Amsterdamphone +31-(0)20-5922105, email [email protected]
IntroductionSuperplasticity is characterised by the ability to show,within a narrow regime of strain rate and temperature,very high plastic strains before failure, in which thegrains stay or become equi-axed. The main mech-anism of superplastic behaviour is Grain BoundarySliding, the grains themselves do not deform plasti-cally. This research studies the simulation and opti-misation of thin shields made by SPF (see Figure 1).These shields are necessary to act primarily as a gasbarrier between detectors and radiation source.
Figure 1 : Top view of a particle detector shield.
ObjectiveThe goal is to simulate the shields’ SPF process, to-gether with an optimisation procedure, in order to re-duce the development time for future shield designs.
MethodsSuperplasticity Superplastic materials show highlystrain rate dependent properties. Mechanically, SPbehaviour can be visualised by means of the Uni-versal Superplastic Curve, see Figure 2 in which thestress is mainly determined by the strain rate.
slope m
1
inflection
point
I IIIII
log ε
log σ
εopt
σopt
Figure 2 : Superplasticity occurs in the region aroundthe highest curve slope, m ≈ 0.5.
This curve can be represented by a serial/parallelcombination of dampers, the governing equation, with
a being a material constant is:
m
mmax= exp
(− a2
(log
ε
εopt
)2)
(1)
Simulation The SPF process involves strain andstrain rate dependencies. In SPF processes, it is ad-visable to increase the gas pressure on the sheetsuch that the maximum strain rate will not exceeda critical value. Above this value, undesired graingrowth makes the material also strain rate historydependent. In a simulation, this can be achievedby monitoring the maximum strain rate during thesimulation, which is used to control the pressure in-crease. Accurate material properties and models(in FE codes) are hardly available, experiments anduser-supplied material models are necessary to sim-ulate this forming process.
Results and future workA typical SPF pressure-time curve as a result fromsimulations and in practice is shown in Figure 3.
Time
Pre
ssu
re
Bending
Stretching
Closing Contact
Figure 3 : Typical shape of the optimal pressure-timecurve in SPF processes.
SPF experiments have to characterise the uniaxialand biaxial behaviour of these materials. Leak ex-periments have to show the barrier ability againstgases, since cavities can start to initiate and interlink,thereby providing a through-thickness channel (leak).
AcknowledgementsThis project is a cooperation of the National Institute of Nuclear
and High-Energy Physics (NIKHEF) in Amsterdam and the Uni-
versity of Twente
Numerical and experimental analysis ofmultiple Chua circuitsR. van der Steen, H. NijmeijerEindhoven University of Technology
Department of Mechanical Engineering, Dynamics and Control GroupP.O. Box 513, 5600 MB Eindhoven, The Netherlandsphone: +31-(0)40-2474092, email: [email protected]
IntroductionComplex systems receives much attention in litera-ture. One of the reasons for this is that complex sys-tems can be found in several fields such as nature,brain dynamics and robotics. Coupled complex sys-tems can lead to synchronization, which has potentialuse in communication and coordination.
ObjectiveThe goal of this study is to achieve more insight in thecomplicated behavior of complex systems includingsynchronization, numerically and experimentally. Toachieve this three aspects have been considered• Analysis of a single complex system.• Development and comparison of numerical and
experimental results.• Synchronization of multiple systems.
SystemThe Chua circuit [1], see figure 1, is given by
C1v1 = 1R(v2 − v1)− f(v1)
C2v2 = 1R(v1 − v2) + i
Li = −v2 −R0i
with f(v1) = Gbv1 + 12(Ga −Gb)(|v1 + Bp| − |v1 −Bp|).
The variables v1 and v2 are the voltages across thecapacitors C1 and C2, i is the current flowing throughthe inductor L, which has an internal resistance R0.Ga and Gb are the conductances of the piecewise-linear characteristic. Bp is voltage of the breakpoint.The variable resistor R is used as bifurcation para-meter.
L
R0
C2 C1
R
Nr
−10 −5 0 5 10−5
0
5
v [V]
i [m
A]
Figure 1 : Chua circuit with characteristic of Nr.
The Chua circuit is capable of generating bifurcationsand chaos. The dynamic behavior has been analyzedby looking at the stability properties of the equilibriaand Poincare maps have been used to explain the bi-furcations.
Experimental setup
−5 0 5−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
v1 [V]
v 2 [V]
SimulationExperiment
Figure 2 : Experimental setup and results.
• Parameters have been identified using measure-ments and a switching nonlinear Kalman filter.
• Experiments qualitatively match numerical re-sults.
SynchronizationMaster-slave synchronization and mutual synchro-nization of networks have been applied. A networkedsystem consists of coupled identical systems thatcannot be decomposed into disconnected smallernetworks. Besides full synchronization of networkedsystems, there can exist a number of stable linear in-variant manifolds, depending on the size and topologyof the network, corresponding to a partial synchro-nized situation [2], shown in figure 3.
K1
K0Coupling strength
Cou
pling
stre
ngth
System 1 = System 46=
System 2 = System 3
System 1 = System 4=
System 2 = System 3
System 1 = System 2=
System 3 = System 4
System 1 6= System 46=
System 2 6= System 3
−10 −5 0 5 10−10
−5
0
5
10
System 1 v1 [V]
Sys
tem
2 v
1 [V]
−10 −5 0 5 10−10
−5
0
5
10
System 2 v1 [V]
Sys
tem
3 v
1 [V]
−10 −5 0 5 10−10
−5
0
5
10
System 3 v1 [V]
Sys
tem
4 v
1 [V]
−10 −5 0 5 10−10
−5
0
5
10
System 4 v1 [V]
Sys
tem
1 v
1 [V]
Figure 3 : Stability diagram and experimental partialsynchronization of four symmetrically coupled circuits.
Future workFuture steps require improvement of the numericalmodel and development of a robust observer to matchexperiments with simulations.
References1. Matsumoto, T. (1984) A chaotic attractor from Chua’s circuit,
IEEE Transactions on Circuits and Systems, 31(12):1055–1058
2. Steen, R.v.d., Nijmeijer, H. (2006) Partial synchronization ofdiffusively coupled Chua systems: An experimental casestudy, 1st IFAC Conference on Analysis and Control ofChaotic Systems, Reims, France
Effect of Resin Formulation on Viscoelastic behavior of Thermosets
John Suman Nakka Faculty of Mechanical, Maritime and Material Engineering
Mechanics of Materials TU Delft, Mekelweg 2, NL 2628 CD Delft
Tel: +31-(0)15-2785737, e-mail: [email protected]
Introduction Thermosetting polymers are used as adhesives or packaging materials in the electronics industry. Good knowledge of the viscoelastic mechanical properties is imperative for a good understanding of the formation and relaxation of residual stresses. The viscoelastic behaviour of these resins depends, however, largely on the composition of the unreacted resin. Understanding of the relation between the chemistry and the viscoelastic properties can be used to tailor made low stress resin materials. Furthermore it can be used to get a first estimate of cure dependency of viscoelastic behaviour.
Objective To find a relation between the initial resin- harderner composition and the resulting viscoelastic behaviour. Methods
In order to determine the viscoelastic behavior of a thermoset system the crosslink density has to be determined. This will be done using the Mackosko & Miller theory which links the number of reacting (monomer) groups with functionality (f), mixing ratio and crosslink density. As a second step then the obtained crosslink density is related to changes in the viscoelastic master curve.
Results As a first model system we used DER332 epoxy (f=2) and EDA, MEDA, DMEDA (f=4, 3, 2) amines and mixed stoichiometrically. a. Optimum cure schedules were determined so that full conversion of epoxy
was achieved. However, in some cases secondary DMA peaks were still observed. b. A global model was proposed which could describe the master curves of most epoxy-amine mixtures
y = 0,035x + 94,419
80
90
100
110
120
130
140
150
0 200 400 600 800 1000 1200Calc. XLD(mol/m^3)
Tg(D
MA)
Figure 1: Change of glass transition temperature for the different epoxy-amine mixtures Discussion The purity and selection of resin systems become an important criterion for our studies as small changes in the chemistry will lead to unexpected variations in product performance. Future work: a. HPLC to find epoxy purity b. FTIR Study to find the ratio of matrix inclusion phases. And to include in the Viscoelastic Model (double peak fit function) c. SEM studies to determine possible phase separation References 1. K.M.B.Jansen, L.J.Ernst et al. 5th. Int. Conf. on Thermal and Mechanical Simulation and Experiments in Micro-electronics and Micro-systems, EuroSimE2004.
2. Mackosko & Miller, Macromolecules, Vol9, No.2, 1976.
Hardness Profile
0
0.5
1
1.5
2
2.5
0 2000 4000 6000 8000 10000 12000 14000 16000
X-Position
Hard
nes
s (
GP
a)
Extrapolated Hardness
Measured Hardness
Damage vs X-Position
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 2000 4000 6000 8000 10000 12000 14000 16000
X-Position
Dam
ag
e
Forming the Limits of Damage Predictions: From Fundamental to Application
C.C. Tasan*, J.P.M. Hoefnagels, M.G.D. Geers*National Institute of Metals Research
Eindhoven University of Technology, Faculty of Mechanical Engineering
PO Box 513 ,WH 4.13, 5600 MB Eindhoven, Tel: +31 40 247 5169, email: [email protected]
Figure 3 Indent locations and hardness profile
ResultsDamage is measured quantitatively by
comparing the hardness of the damaged
material, to the hardness of the undamaged
material, obtained by extrapolation.
Figure 4 Hardness of damage material vs
undamaged material (left) Damage vs x-
position (right)
ConclusionHardness measurements can be used for
local quantitative measurement of ductile
damage. Next step is the evaluation of the
microvoid density in the specimens to check
the validity of the obtained results.
References[1] Marciniak, Z., 1992, The mechanics of Sheet Metal Forming, Arnold, London.
[2] Lemaitre, J., 1996, A Course on Damage Mechanics,
Springer-Verlag, Berlin.
IntroductionIn sheet metal forming processes, failure
occurs generally due to necking, followed by
instability and fracture. However, in some
cases failure can also occur without necking,
especially with the advanced alloys such as
dual phase and trip steels. It is believed that
internal damage is responsible for this
behaviour [1], but the involved mechanisms
are not clearly identified.
ObjectiveThe main goal of this project is to understand
the micro-mechanisms in ductile damage and
explore the correlation between these mecha-
nisms and the material and production para-
meters involved in industrial applications.
MethodThe first step for this purpose is to come up
with a quantitative evaluation method for
ductile damage. Nanoindentation is a good
candidate for this purpose, due to the direct
relationship between hardness and tensile
strength [2].
Figure 1 Uniaxial Tensile Tests & Image
Correlation Measurements for Local Strains
Figure 2 Preparation of the specimens
An augmented Lagrangian decompositionmethod for quasi-separable problems in MDO
S. Tosserams, L.F.P. Etman, J.E. RoodaEindhoven University of Technology
Department of Mechanical EngineeringP.O. Box 513, 5600 MB Eindhoven, NL
{s.tosserams,l.f.p.etman,j.e.rooda}@tue.nl
IntroductionIn multidisciplinary design optimization, bi-leveldecomposition methods aim at allowing distributeddecision-making by decomposing the system designproblem into disciplinary sub-problems and acoordinating master problem (Fig. 1).Unfortunately, many existing decomposition methodsmay not converge to an optimal solution, or sufferfrom numerical difficulties due to non-smooth and/ordegenerate problem formulations.
Fig. 1. Problem decomposition in aircraft design
ObjectiveThe goal of this research [1] is to develop a bi-leveldecomposition method with:
• subproblem decision autonomy• smooth and non-degenerate formulation• proven convergence to local system optimum• efficient coordination algorithm
MethodsThe proposed decomposed formulation is:
where φj(cj) = vTj (cj) + ‖wj ◦ cj‖2
2 is an augmentedLagrangian penalty on the inconsistencies cj = y – yj .
Fig. 2. Coordination algorithm variants
To coordinate the coupling through y and yj , and toset penalty parameters v and w, we use the methodof multipliers in combination with block coordinatedescent, and convergence follows from existingtheory. Three variants are proposed (Fig. 2):
• ENMOM: exact convergence inner loop (left)• INMOM: inexact convergence inner loop (left)• ADMOM: single iteration inner loop (right)
ResultsThe numerical performance of the three variants arecompared on two example problems (Fig. 3). Resultsshow good numerical convergence behavior for allvariants, and overall lowest costs for ADMOM.
two-subsystem problem five-subsystem problem
Fig. 3. Illustration of results
ConclusionA bi-level decomposition method is proposed with:
• smooth and non-degenerate formulation• convergence proof is available• 20-60 iterations for error ≈ 10−3 (ADMOM)
References1. Tosserams, S., Etman, L.F.P., and Rooda, J.E. (2006),
11th MAO conference, Portsmouth, Virginia.
Physical aging in Molding Compounds J. de Vreugd
Faculty of Mechanical, Maritime and Material Engineering Mechanics of Materials
TU Delft, Mekelweg 2, NL 2628 CD Delft Tel: +31-(0)15-2786512, e-mail: [email protected]
Introduction The encapsulation of a chip with Molding Compound results in residual stresses. These stresses often result in failure of the chip. In order to predict more reliable the stresses and strains in the chips, physical aging of the molding compound has to be implemented in the constitutive equations next to the viscoelastic material behavior. The physical aging effect will be seen when a material is cooled at different cooling velocities.
Objective The research objective is to describe the relation between storage time and changing mechanical properties. The obtained model will be implemented in a finite element program, such that it is possible to predict more accurately stresses and strains caused by physical aging.
Mechanism of physical aging From earlier research, it is seen that amorphous solids are not in thermodynamic equilibrium below their glass transition, see fig. 1.
Fig. 1 Origin of aging.
Below the glass transition temperature the material properties changes with time due to a tendency to optimize the packing of the molecules. Physical aging makes samples stiffer and more brittle.
Results Preliminary results show that the creep compliance is decreasing at increasing storage time as expected. See fig. 2.
10-2 10-1 100 101 102 10340
45
50
55
60
65
Time [min]
Cre
ep C
ompl
ianc
e [ µ
m2 /N
]
23 min. 56 min. 122 min. 254 min. 518 min.1046 min.2102 min.4214 min.
Fig. 2 preliminary result of short time aging test. With the obtained result the creep compliance is modeled as a function of storage time. Also long term behavior is predicted from this experiment.
References
1. Struik, L.C.E., Physical aging amorphous polymers and other materials, Elsevier, Amsterdam, 1978
2. Kovacs, A.J., Transition vitreuse dans les polymères amorphes. Fortschr. Hochpolym.-Forsch., (1963) Tg
Temperature
Spe
cific
vol
ume
AGING RANGE
Storage time
Noise Source Localization on PlanesJ.W. Wind, Y.H. Wijnant and A. de Boer
Institute of Mechanics, Processes and ControlChair of Structural Dynamics and Acoustics
University of TwenteP.O. Box 217, 7500 AE Enschede, The Netherlands
phone +31-(0)53-4893605, email [email protected]
IntroductionAcoustic source localization techniques can play avital role in understanding the causes of unwantedsound in technical products. Since these techniquesare used in a measurement environment, stringentdemands are placed on their speed, accuracy andease of use. We present a fast, accurate and simpletechnique for reconstructing sources on a planarsurface and compare results with an existing method.
Model
v1 v2 v3 v4
p1 p2 p3 p4
sensor grid
source velocities
(a) physical model (b) distance: exampleFigure 1: Model
An acoustic source localization problem consists offinding the normal velocity vector on the source (v),based on the pressure vector (p) measured at agrid of points close to the surface (see figure 1(a)).Mathematically, this problem is solved by solving the
system equations p=Hv for v using regularizationtechniques, where H is a known transfer matrix.The existing technique makes use of the Fast Fouriertransform (FFT) to approximate the transfer matrix.Even though this approach is very efficient, inherentproblems such as aliasing and leakage can not beeliminated completely.In a discretized problem, each element of the transfermatrix hij depends only on the distance betweensensor location i and source point j. On anequidistant grid each distance occurs many times(see figure 1(b)), which leads to a highly structuredtransfer matrix. In our approach, we make use ofthis matrix structure to obtain a fast method withoutcompromising accuracy.
Case studyThe two methods are compared for reconstruction ofacoustic sources on a hard disk and laser vibrometermeasurement is used as a reference result. On lowerfrequencies, both methods have a similar accuracybut on the frequency of 10kHz, serious errors occurin the FFT-based method, where the new method isstill accurate (see figure 2).
(a) Reference: laser vibrometer (b) FFT (c) New
Figure 2: Case study
Multi-level Optimization of Composite Materials A.J. de Wit and F. van Keulen
Department of Precision and Microsystem Engineering, Section of Structural Optimization and Computation Mechanics
Mekelweg 2, 2628 CD Delft phone +31-(0)15-2786506, e-mail: [email protected]
Introduction Multi-level design optimization techniques rely on a decomposition of the optimization problem into separate levels or subsystems. Incorporating design variables, objectives and constraints originating from different levels into the design.
Objective The project concentrates on the multi-level optimization of composite structures. Here both the non-linear mechanical behaviour as well as the optimization covers multiple levels.
Fig. 1 Multi-level hierarchy.
Example Various multi-level optimization methods can be found in literature1. To capture their essence, six of the main stream approaches are applied on a two-bar structural example, see Figure 2.
Fig. 2 Two-bar truss problem.
Results The objective function value is plotted against the number of function calls for QSD2 starting from six
different design points, see Figure 3. As well as a response surface plot for the left truss Element. The response is feasible only for positive values of the curve.
Fig. 3. (A) Response surface right element. 3 (B) Convergence plot QSD for six different design points.
Table 1 shows the results for three different techniques with respect to a classical approach. None of the methods produces a better result compared to the classical AAO approach.
Tb. 1 Results AAO, QSD, CO and ATC.
Conclusions It appears that decomposition of the design problem into independent subsystems introduces changes to the design problem. Due to the decomposition boundaries on the system level optimization become active which has a negative effect on the objective function resulting in inferior designs when compared to a classical all in once approach.
References 1. De Wit et.al., ECCM 2006. 2. Haftka et.al., OE, vol. 6, pp 9-20, 2005. 3. Braun et.al., SIAM, 2003. 4. Kim et.al., JMD, vol. 125, pp. 474-480.
1 x 2 x
x
3 x
2,1 x 2,2 x 2,3 x
2,2 ,1 x 2,2 ,2 x 2,2 ,3 x
1 1 2 21 1 2 1 22
11
, , , , ,max
22
max
11
222
1 21 2 1 2
min
. . 1 0
1 00.9
1 02.0
, , , , , ,
x x x x x xm
u
cr
Euler
rvr
rs t vr
rvr
rvr
x x x x x x x x x
=
= − ≤
= − ≤
⎛ ⎞= − ≤⎜ ⎟⎝ ⎠
≤ ≤
uv
F
1
xx
2
L ix
ix
0 20 40 60 80 100 120 1400
1
2
3
4
5
6
7
8
9
10
Number of function calls
Objective function value
System level convergence curve
1.154
1.154
1.154
1.154
1.154
1.154
CO3 v1
2.242.760.786
2.252.760.785
2.252.760.784
2.252.760.783
2.252.760.782
2.252.760.781
ATC4 v1
QSD2 v1
AAO v1
DesignPoint
BCC Crystal Plasticity for Multi-StageLoading Processes
Tuncay Yalcinkaya, W.A.M. Brekelmans, M.G.D. Geers
Eindhoven University of TechnologyFaculty of Mechanical Engineering (WH 4.115)
P. O. Box 513 , 5600 MB Eindhovenphone +31 40 247 5392, e-mail [email protected]
IntroductionMulti-stage loading is a frequently used process in au-tomotive and packaging industries. After a load pathchange material hardens or softens unexpectedly dueto induced plastic anisotropy. This anisotropy origi-nates from different sources at different length scalesand it has been experimentally observed that disloca-tion sub-structuring has a dominating effect at mod-erate strains.
ObjectiveThe aim of the present work is to develop a constitu-tive model that quantitatively predicts anisotropy pro-duced due to dislocation sub-structuring induced bya strain path change. Figure 1 visualizes the globalmodeling strategy.
(CURRENT STATE)
GRAINS
DISLOCATION CELLS
CONSTITUTIVE MODELING OF DISLOCATION MOVEMENT
DISLOCATION CELL BLOCKS
Figure 1 : Global modeling strategy including thebridges between micro, meso and macro levels.
BCC Crystal PlasticityIn order to model strain path effects within a consti-tutive model, a proper description of the motion ofdislocations is required. A temperature dependent,strain rate sensitive crystal plasticity model at finitestrains has been implemented for this purpose. BCCcrystals have a number of peculiar features that arenot observed in other crystals, which are properly in-corporated within the present approach. State of theart knowledge on the activity of slip planes and non-Schmid effects are also integrated in the model.
Model
The essence of the model is the definition of plasticpart where the thermally activated theory of disloca-tion kinetics is implemented. The slip law:
γα = γα0 exp
−G0
[1−
( |τα+ηα:τ |−sα
sα∗
)p]q
kBT
sign(τα)
includes all the pronounced aspects of BCC crystalssuch as temperature (T ) dependence, thermal andathermal slip resistance (sα, sα∗ ) and the non-Schmidstress terms (ηα : τ ).
Results
The examples in Figure 2 illustrate some intrinsicproperties of BCC crystals (left top & bottom: orienta-tion dependence and tension-compression asymme-try, right top & bottom: temperature dependence andstrain rate sensitivity).
0 1 2 3 4 5 60
50
100
150
St rain rate sensit ivity for [149] oriented Nb single crystal
True strain %
Tru
e S
tre
ss (
MP
a)
1.25x10-4
s-1
2x10-3
s-1
1.2x10-2
s-1
0 2 4 6 8 100
20
40
60
80
100
120
140
160
180Orientataion dependence of three differently oriented α−Fe single crystals
True Strain %
Tru
e S
tres
s (M
pa)
[001] Sim.
[001] Exp.
[011] Sim.
[011] Exp.
[111] Sim.
[111] Exp.
0 1 2 3 4 5 6 7 8 90
20
40
60
80
100
120
140
160Strength differential effect for a [001] oriented α−Fe single crystal
True Strain %
Tru
e S
tres
s (M
Pa)
tensioncompression
0 0.5 1 1.5 2 2.50
5
10
15
20
25
30
35
40
45
50Temperature dependence of [001] oriented Nb single crystals
True strain %
Tru
e S
tres
s (M
Pa)
77K Ex.77K Sim.113K Ex.113K Sim.175K Ex.175K Sim.
Figure 2 : Simulation of the intrinsic properties.
Outlook
The next step is to incorporate the dislocation cell anddislocation cell block forming in the present constitu-tive model.