Material Modeling: - A Game for Scientists or an Effective Tool … · Motivation A Simple Example...

Motivation A Simple Example Historical Remarks Creep-Damage Modeling

Material Modeling:A Game for Scientists

or an Effective Tool to Improve Structures

Holm Altenbach

Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät fürMaschinenbau, Otto-von-Guericke-Universität Magdeburg, Germany

15 May 2015 Altenbach Material Modeling 1


Table of Contents

1 Motivation

2 A Simple Example

3 Historical Remarks

4 Creep-Damage Modeling



Outline

1 Motivation

2 A Simple Example





General Statement of European Commission

Research & Innovation > Key Enabling Technologies >Research in Materials > Modelling Materials1

• The future of the European industry is associatedwith a strong materials modelling capacity.

• An efficient modelling approach is needed toshorten the development process ofmaterials-enabled products.

Among the areas

Nanotechnologies

Advanced Materials & Manufacturing

Biotechnology

Coal & Steel1http://ec.europa.eu/research/industrial_technologies/modelling-

materials_en.html15 May 2015 Altenbach Material Modeling 4


Materials Science Approach

Analysis of microstructure

Material productionTesting

Description

Structural analysisManufacturing

Operation time

Failure

Material improvement

Strain

Str

ess

σ = f (ε)RVE

No RVE

Source: O. Prygorniev, PhD Thesis, University of Magdeburg, 2015 (subm.)15 May 2015 Altenbach Material Modeling 5


Outline

1 Motivation

2 A Simple Example





Continuum Mechanics - Basics

V

A

cutting principle (method of sections)

axiom of reciprocal action (Newton’s Third Law)Continuum Mechanics governing equations

geometrical relations, e.g. strain-displacement equationsequilibrium equations, equations of motion



Continuum Mechanics - Non-polar

dA

dF

dF

only force actions

symmetric stress tensor

only translations



Basic Course Engineering Mechanics

Static equilibriumForcesMoments

Equations of motionBalance of momentumBalance of moment of momentum

Dependent or independent relations?2

2Truesdell, C. (1964). Die Entwicklung des Drallsatzes. ZAMM44(4/5):149–158



Continuum Mechanics - Polar

replacements

dA

dFdM

dMdF

force and moments actions

symmetric and nonsymmetric stress tensors

translations and rotations (independent!)



Material Modeling

in both situations we have a statically indeterminate system

establishment of constitutive equations and (maybe)evolution equations for closing the gap between thenumber of equations and the number of unknowns

constitutive equations interlinking in the simplest casestresses and strainsvarious approaches

top - down (from the more general to the simpler cases)bottom - up (stepwise generalization)rheological models



Outline

1 Motivation

2 A Simple Example





First Steps - Archimedes of Syracuse

Born c. 287 BC, Syracuse,Sicily

Died c. 212 BC, Syracuse

Residence Syracuse, Sicily

Fields Mathematics, Physics,Engineering, Astronomy,Invention

Known for Archimedes’Principle, Archimedes’ screw,Hydrostatics, Levers,Infinitesimals



Lever

The earliest remaining writings regarding levers date fromthe 3rd century BC and were provided by Archimedes:Give me a place to stand, and I shall move the earth with alever.This is a remark of Archimedes who formally stated thecorrect mathematical principle of levers (quoted by Pappusof Alexandria).It is assumed that in ancient Egypt, constructors used thelever to move and uplift obelisks weighting more than 100tons.



Leonardo da Vinci

Born April 15, 1452, Vinci, Florence

Died May 2, 1519 Amboise, Touraine

Nationality Italian

Fields Many and diverse fields of arts andsciences

Known for Flying machine



Hooke’s Contributions

ceiiinossssttuv (1676)

Ut tensio, sic vis (1678)

As the extension, so the force.

F

∆l

Hooke’s law (original)

Robert Hooke (18 July 1635 – 3 March 1703)



Hooke’s Contributions

ceiiinossssttuv (1676)

Ut tensio, sic vis (1678)

As the extension, so the force.

σ

ε

Hooke’s law

Robert Hooke (18 July 1635 – 3 March 1703)



Analogy - Elastic Spring

For systems that obeyHooke’s law,

the extension produced isdirectly proportional

to the loadF = −kx

Modern form of the Hooke’s law

σσσ = Eεεε

σ stress, ε strain, E Young’s modulus



Bernoulli’s Contributions

1686postulate of the angularmomentum

Jakob Bernoulli (6 January 1655 - 16 August 1705)



Newton’s Contributions

Newton’s Axioms

ddt

(mv) = 0 (statics)

ddt

(mv) = F (kinetics)

actio = reactio

superposition

Isaac Newton (4 January 1643 - 31 March 1727)



Euler’s Contributions

Euler’s laws of motion

Balance of momentum

Balance of moment ofmomentum

Assumptions

Independence oftranslations and rotations

Force and moment actions

Leonhard Euler (15 April 1707 - 18 September 1783)



Cauchy’s Contributions

Definition of Stress

Stress σ is a measure of the average amount of force F exertedper unit area A . It is a measure of the intensity of the totalinternal forces acting within a body across imaginary internalsurfaces, as a reaction to external applied forces and bodyforces. It was introduced into the theory of elasticity by Cauchyaround 1822.

σ =FA

Augustin Louis Cauchy (21 August 1789 - 23 May 1857)15 May 2015 Altenbach Material Modeling 21


Young’s ContributionRemarkThe concept was developed in 1727 byLeonhard Euler and the first experiments thatused the concept of Young’s modulus in itscurrent form were performed by the Italianscientist Giordano Riccati in 1782 - predatingYoung’s work by 25 years.

Definition

An elastic modulus, or modulus of elasticity, is themathematical description of a material’s tendency to bedeformed elastically (i.e., non-permanently) when a force isapplied to it. The elastic modulus of an object is defined as theslope of its stress-strain curve in the elastic deformation region.

Thomas Young (13 June 1773 - 10 May 1829)15 May 2015 Altenbach Material Modeling 22


Poisson’s Contributions

Isotropic Linear Elastic Behavior (3D)

two or one material parameters

σσσ = α tr(εεε)I + βεεε + γεεεT

σσσ = σσσT ⇒ σσσ = K tr(εεε)I + 2µεεε

K bulk modulus, µ shear modulus

K =E

3(1 − 2ν), µ = G =

E2(1 + ν)

ν - parameter or fixed?

Siméon-Denis Poisson (21 June 1781 - 25 April 1840)15 May 2015 Altenbach Material Modeling 23


Cosserat Brothers

EugéneCosserat

Cosserat Model (1896, 1909)

extended continuum model

balance of forces

balance of angular momentum

no constitutive equations

François Cosserat (26 November 1852 - 22 March 1914),Eugéne Cosserat (4 March 1866 - 31 May 1931)



Hilbert’s Problems

6th Problem (1900)

Axiomatic Formulation ofMechanics

unsolved up to now

David Hilbert (23 January 1862 - 14 Februars 1943)



Noll’s and Truesdell’s Contributions

Contributions to Mathematics and Mechanics

Rational Mechanics

Theory of Simple Materials

Rational Thermodynamics

History of Mechanics

Walter Noll (7 January 1925)Clifford Abmbrose Truesdell III (18 February 1919 - 14 January2000)



Anatolii Isakovich Lurie

Born 19 July 1901 Mogilev,Died 12 February 1980 Leningrad,

Three-dimensional Problems ofthe Theory of Elasticity. Moscow.GITTL, 1955, 492 pp.

Theory of Elasticity. Moscow,Nauka, 1970, 940 pp.(Springer 2005)

Nonlinear Theory of Elasticity.Moscow, Nauka, 1980, 512 pp.(North-Holland Series in AppliedMathematics and Mechanics,Volume 36, 1990)



Maksymilian Tytus Huber

Born 4 January 1872 Kroscienko,Died 9 December 1950 Kraków,Professor at Lwów Polytechnic,Warsaw Polytechnic, Gdansk Poly-technic and Akademia Górniczo-Hutnicza,Solid mechanics,Mechanical engineering,Maxwell (1865) - Huber (1904) -von Mises (1923) - Hencky (1924)criterion



Michał Zyczkowski

Born 12 April 1930 Kraków,Died 24 May 2006 Kraków,Professor at Cracow Polytechnic,Full member of Polish Academy of Sci-ences and Polish Academy of Learning,Foreign Corresponding Member of theAustrian Academy of Sciences,Solid mechanics,Plasticity, Optimization



Representation of Continuum Mechanics

From the previous statement one can conclude:

Differential equations can thus be employed in solvingproblems in continuum mechanics.

Some of these differential equations are specific to thematerials being investigated and are called constitutiveequations, while others capture fundamental physical laws,such as conservation of mass (continuity equation), theconservation of momentum (equations of motion andequilibrium), and energy (first law of thermodynamics).Continuum mechanics deals with physical quantities, which areindependent of any particular coordinate system in which theyare observed. These physical quantities are then representedby tensors, which are mathematical objects that areindependent of coordinate system. These tensors can beexpressed in coordinate systems for computationalconvenience.



Modern Representation

Material independent equations(as usual as integral relations)

Balance of massBalance of momentumBalance of moment of momentumBalance of energyBalance of entropy

Material dependent equationsConstitutive equationsEvolution equations

ConditionsBoundary Conditions

Kinematic conditionsStatic conditionsMixed conditions

Initial ConditionsDisplacementsVelocities



Material Dependent Equations

Specific (individual) response of the given material onarbitrary load.Modeling principles

Inductive approachfrom the simplest to more complex modelsDeductive approachfrom the general frame to special cases

IdentificationExperimental observationsMathematical analysisTheory of symmetry (Curie-Neumann’s principle)



Outline

1 Motivation

2 A Simple Example





Aim (I)

Development of phenomenological constitutive equationsthat describe inelastic behavior at elevated temperature,

To characterize hardening, recovery, and softeningprocesses a composite (fraction) model with creep-hardand creep-soft constituents is introduced,

In the case of heat resistent steels the volume fraction ofthe creep-hard constituent is assumed to decreasetowards a saturation value,

Such an approach describes well the primary creep as aresult of stress redistribution between constituents andtertiary creep as a result of softening (decrease of thevolume fraction)



Aim (II)

To describe the whole creep curve a damage parameter inthe sense of continuum damage mechanics is introduced,

The material parameters and the response functions in themodel are calibrated against published experimentalcurves for X20CrMoV12-1 steel,

To verify the model predictions with experimental creepcurve under stress change conditions and the stress-straincurve under constant strain rate are compared,

The consideration of both softening and damageprocesses is necessary to characterize the long termstrength in a wide stress range,

The model can be generalized to the case of multi-axialstress state,



References

K. Naumenko, H. Altenbach & A. Kutschke: A combinedmodel for hardening, softening, and damage processes inadvanced heat resistant steels at elevated temperature. -Int. J. Damage Mech. 20(2011). - pp. 578-597

K. Naumenko, A. Kutschke, Y. Kostenko & T. Rudolf:Multi-axial thermo-mechanical analysis of power plantcomponents from 9-12% Cr steels at high temperature. -Engng Frac. Mech. 78(2011)8. - pp. 1657-1668



Microstructure of Advanced Chromium Steels

Group of 9% to 12% Cr-steels

Complex microstructure with grains, precipitates, subgrains anddislocations.Source: H. Chilukuru: On the microstructural basis of creep strength andcreep-fatigue interaction in 9-12% Cr steels for application in power plants,PhD-thesis, University Erlangen-Nuremberg, 2007



Basic Idea - Microstructure Observation

M23C6-carbideMX-precipitate

Prior Austenite-grain boundary20 µm

200 nm

Lath-Martensite-grain boundarSubgrain boundary

20 µm

Packet boundary

Block boundary

Gaffard et al. (2004) Masuyama (2001)Polcik et al. (1998) Kimura (2006)



References

V. Gaffard, J. Besson, A.F. Gourgues-Lorenzon: Creep failuremodel of a 9Cr-1MoNbV (P91) steel integrating multipledeformation and damage mechanisms. - ECF 15 (Stockholm)2004. - 8 p.

Polcik, P., Straub, S., Henes, D. and Blum, W.: Simulation of theCreep Behaviour of 9-12% CrMo-V Steels on the Basis ofMicrostructural Data. In: Strang, A., Cawley, J. & Greenwood,G.W. (eds), Microstructural Stability of Creep Resistant Alloys forHigh Temperature Plant Applications, 1998, CambridgeUniversity Press. - pp. 405-429.

F. Masuyama: History of power plants and progress in heatresistant steels. - ISIJ (Iron and Steel Institute of Japan)International 41(2001)6. - pp. 612-625

Kimura, K.: 9Cr-1Mo-V-Nb Steel. In: Martienssen, W. (ed.),Creep Properties of Heat Resistant Steels and Superalloys,2006, Springer. - pp. 126-133



Characteristic Material Behavior

0 0.02 0.04 0.05 0.08 0.1 0.12 0.14

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2 0.25

102

103

104

105

106

ε [-]

σ[M

Pa]

Experimental dataafter Röttger 1997

600◦C

530◦C

500◦C

creep strain

norm

aliz

edcr

eep

rate

|σ| = 150MPa (compression)σ = 150MPa (tension)|σ| = 175MPa (compression)σ = 175MPa (tension)|σ| = 185MPa (compression)σ = 185MPa (tension)|σ| = 196MPa (compression)σ = 196MPa (tension)

Experimental data after STRAUB (1995)

ε [-]

σ [MPa] 1 8151000 1200 1300

stress controlled, symmetric loading cycle,after Bunch and McEvily (1987)

plastic material behavior -hardening and softening

creep behavior - only first andthird creep stage observable

cyclic behavior - width of stressstrain loop increases, stressstrain loop is shifted ratcheting



Basic Idea - Binary Mixture Approach (I)

σs σ σh

F

Stress and Strain Rate Relations for Iso-strain Assumption

σ = (1 − ηh)σs + ηhσh

ηh - volume fraction of the inelastic hard phase

ε = εs = εh



Basic Idea - Binary Mixture Approach (II)

Young’smoduli

nonlinear elementinelastic soft

nonlinear elementinelastic hard

volume fraction

1D Visualization - Iso-strain Approach

kinematic backstress follows for different inelasticproperties, if volume fraction is kept constant it results in abackstress model (Frederick & Armstrong, 2007)

if the volume fraction of the creep hard constituentdecreases towards a saturation value the creep rateincrease after the minimum creep rate is reached



Basic Idea - Binary Mixture Approach (III)

Young’smoduli

nonlinear elementinelastic soft

nonlinear elementinelastic hard

volume fraction

Behavior of the Constituents

soft: εs =σ

E+ f (|σs|)

σs

|σs|

hard: εh =σ

E+

σh − σ

σh∗− σ

|ε|

E - macroscopic Young’s modulus,f - stress response function



Derivation of the Model (I)

The aim is to express the unknowns whether by

known variables,

terms of material model parameters to identify or

internal state variables

1D Equation - Fraction Model

Basic features

because of the iso-strain condition εcr = εs,

for constant stress, as in creep tests, εcr = εs = f (|σs|)σs

|σs|,

σ = ηsσs + ηhσh, σ - applied load,

the sum of the volume fractions is equal to 1, 1 = ηs + ηh,

therefore ηs can be replaced by 1 − ηh,

σ = (1 − ηh)σs + ηhσh



Derivation of the Model (II)

Introducing New Variables

Volume fraction reduces with time: Γ =ηh

ηs

ηs0

ηh0

, 1 ≥ Γ ≥ Γ∗,

ηs0

ηh0

= ch, ch - material model parameter to identify

With Γ the unknown ηh can be expressed as ηh =Γ

Γ + ch,

Therefore one can write σ = (1 −Γ

Γ + ch)σs +

Γ

Γ + chσh

By algebraic manipulations one can obtainσch = σsch + Γ (σh − σ)

By utilizing the overstress concept the variable β can beintroduced chβ = σh − σ

Finally one obtains σs = σ − βΓβΓ can be termed backstress or kinematic stress



Derivation of the Model (III)

Inner State Variables β and Γ

β describes the stress accumulation in the inelastic hardphase, as internal state variable an evolution equation isneeded

one can show by proper algebraic manipulations that fromthe iso-strain condition and by the chosen rate formulationfor the inelastic hard phase a formulation of the

Frederick-Armstrong type follows, β =Ech

εcr(

1 −β

β∗

)

Γ is controlling the volume change of the inelastic hardphase and is motivated by microstructural changes

the idea for the evolution equation is taken from literature:Γ = As(Γ∗ − Γ )εcr

Source: K. Naumenko et al. Engng Frac. Mech. 78(2011)8, 1657-1668



Derivation of the Model (IV)

Summary

εcr = f (σ − βΓ )

β =Ech

εcr(

1 −β

β∗

)

β evolution equation can be integrated and written in termsof εcr:

β = β∗

(

1 − e−E

chβ∗εcr)

Γ = As(Γ∗ − Γ )εcr

Γ evolution equation can be integrated and written in termsof εcr:

Γ = Γ∗ + (1 − Γ∗)(

e−AsΓ∗

εcr)



Derivation of the Model (V)

Required response functions

the stress response function f of the inelastic soft phaseneeds to be defined

a temperature response function that describes thetemperature dependence

β∗ and Γ∗ are stress level dependent and thereforeresponse functions need to be found

Identified Response Functions

viscosity function: f (x) = a0e−αT sinh(Bx)

β∗-hardening saturation β∗(x) = H∗x

Γ∗-softening saturation Γ∗(x) =aΓ

1 + bΓe−x

cΓ



Derivation of the Model (VI)

Continuum Damage Mechanics Approach

evolution equation:

ω = r (ω)h(σ)|εcr|

ε∗(σ)

with:

r (ω) = lωl−1

l ,

ε∗(σ) = εbr +aε

1 + b−

|σ|cε

ε

,

h(σ) =σ + |σ|

2σ



Derivation of the Model (VII)

Identified Response Functions

temperature response function: g(T ) = a0e−αT

stress response function: f (x) = g(T ) sinh(B

E (T )x)

β∗-hardening saturation β∗(x) = H∗x

Γ∗-softening saturation Γ∗(x) =aΓ

1 + bΓe−

xcΓ



Calibration Process (I)

Temperature and Stress Response Function

g(T ) = a0e−αT , f (σ) = g(T ) sinh

[

BE (T )

σ

]

stress, [MPa]

min

imal

cree

pst

rain

rate

,[

1 h

]



Calibration Process (II)

Stress Response Function and Backstress


[

BE (T )

σ

]

β = β∗

(

1 − e−E

chβ∗ε

cr)

creep strain, [-]

cree

pst

rain

rate

,[

1 h

]



Calibration Process (III)

Stress Response Function, Backstress and Softening


[

BE (T )

σ

]

β = β∗

(

1 − e−E

chβ∗ε

cr)

, Γ = Γ∗ + (1 − Γ∗)(

e−AsΓ∗

εcr)

creep strain, [-]

cree

pst

rain

rate

,[

1 h

]



Calibration Process (IV)

Backstress and Softening


[

BE (T )

σ

]

β = β∗

(

1 − e−E

chβ∗ε

cr)

, Γ = Γ∗ + (1 − Γ∗)(

e−AsΓ∗

εcr)

creep strain, [-]

cree

pst

rain

rate

,[

1 h

]



Calibration Process (V)

Backstress and Softening, but ch and As Averaged


[

BE (T )

σ

]

β = β∗

(

1 − e−E

chβ∗ε

cr)

, Γ = Γ∗ + (1 − Γ∗)(

e−AsΓ∗

εcr)

creep strain, [-]

cree

pst

rain

rate

,[

1 h

]



Calibration Process (VI)

β∗ and Γ∗


[

BE (T )

σ

]

β = β∗

(

1 − e−E

chβ∗εcr)

, Γ = Γ∗ + (1 − Γ∗)(

e−AsΓ∗

εcr)

β∗(σ) = H∗σ, Γ∗(σ) =aΓ

1 + bΓe−

σcΓ

σ, [MPa]σ, [MPa]

β∗, [

MP

a]

Γ∗, [

-]



Calibration Process (VII)

Extended Experimental Data

various stress levels (80 MPa to 460 MPa)

various temperature levels (400◦C up to 650C◦)

σ, [MPa]

cree

pst

rain

rate

,[

1 h

]

creep strain, [-]

cree

pst

rain

rate

,[

1 h

]



Calibration Process (VIII)

Introducing a Second Backstress

creep strain, [-]creep strain, [-]

cree

pst

rain

rate

,[

1 h

]

cree

pst

rain

rate

,[

1 h

]

550◦C, 280 MPa - 310 MPa 600◦C, 150 MPa - 230 MPa

600◦C, 235 MPa - 320 MPa550◦C - 650◦C, 230 MPa



Comments Concerning the Calibration Process

Conclusions

The Frederick-Armstrong-type backstress law followsnaturally from the proposed model

The evolution of microstructure is taken into account

The stress accumulation in only one inelastic hard phaseseems to not be sufficient

With the improved backstress formulation all creep curveswere described better

Future Tasks

Modify response functions, e.g. temperature

Simulate the stress strain behavior outside the calibrationrange

Analyze the anomalous ratchetting behavior of 12%-Crsteels



Extension to 3D

Set of Equations (Small Strains, Isotropic Behavior)

creep rate tensor εεεcr =32

f (σvM

1 − ω)

sssσvM

−1

2Gddt

(Γβββ),

sss = sss − Γβββ, σvM =

√

32

tr(sss)2

backstress tensor βββ = Ah(23εεεcr − εvM

βββ

β∗(σvM))

scalar softening Γ = As(Γ∗(σvM) − Γ )εcrvM

scalar damage ω = r (ω)h(σσσ)εcr

vM

ε∗(σvM), h(σσσ) =

12

(σI + |σI |)σI

K. Naumenko, H. Altenbach & A. Kutschke: A Combined Modelfor Hardening, Softening, and Damage Processes in AdvancedHeat Resistant Steels at Elevated Temperature, InternationalJournal of Damage Mechanics, 2011



Verification - Creep Curves

0 0.05 0.1 0.15 0.2 0.25

102

103

104

105

106

creep-strain

norm

aliz

edcr

eep

rate


model-compression

model-tension




Verification - Creep Curves (Continued)

Explanatory Notes

0 0.05 0.1 0.15 0.2 0.25

102

103

104

105

106

creep-strain

norm

aliz

edcr

eep

rate


model-compression

model-tension


The presented creep curvesdo not exhibit a secondarycreep stage with a constantcreep rate.

The difference of the creeprate slope between tensionand compression, above acertain time, is obvious.

The time when the creep rate under tension is changingrapidly is stress level dependent.

The difference between compression and tension isexplained by damage, which is controlled by micro-voids.Under compression micro-voids are not observable.



Verification - Cyclic Creep

0 0.05 0.1 0.15 0.2 0.25

102

103

104

105

106

150

170

196

creep strain

norm

aliz

edcr

eep

rate

|σ| = 150MPa (compression)|σ| = 196MPa (compression)

Exp. data (var. stress)Model (var. stress)


time, h

|σ|,

MP

a



Verification - Cyclic Creep (Continued)

0 0.05 0.1 0.15 0.2 0.25

102

103

104

105

106

150

170

196

|ε|cr

|εcr|/ε 0

|σ| = 150MPa (compression)|σ| = 196MPa (compression)

Exp. data (var. stress)Model (var. stress)

Experimental data after Straub [1995]

|ε|cr

|σ|,

MP

a The creep behavior undercyclic loading is wellreproduced by thedeveloped model.

The experiment shows that the level of the creep responsefor constant stresses 150 MPa and 196 MPa is not thesame level for the periodically constant stresses 150 MPaand 196 MPa, which is reproduced by the model.

The deviation after the changed stress level from 196 MPato 150 MPa will be investigated further.



Verification - Stress Strain Diagramms

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain

100

200

300

400

500

600S

tres

s

500◦C, model simulation530◦C, model simulation600◦C, model simulation500◦C, Experimental data (Straub et al., 1997)530◦C, Experimental data (Straub et al., 1997)600◦C, Experimental data (Straub et al., 1997)



Verification - Stress Strain Diagramms (Continued)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain

100

200

300

400

500

600

Str

ess

500◦C, model simulation530◦C, model simulation600◦C, model simulation500◦C, Experimental data (Straub et al., 1997)530◦C, Experimental data (Straub et al., 1997)600◦C, Experimental data (Straub et al., 1997)

The stress-strain behaviorunder a constantstrain-rate is wellreproduced by thedeveloped model.

As highlighted the transition from the linear to nonlinearbehavior is too strict predicted by the model.

A reason could be the slope of the increasing back-stress,which is maybe overestimated.



Summary (I)

Actual Output

In the range of calibration the models work fine and are able toreproduce the material behavior.

Physical processes on the microstructure level areconsidered, but the model parameters are determined withthe help of macroscopic creep tests.

Complex creep curves, hardening, softening, damage arewell predicted by the models.

The models show some predictive strength if loadingconditions differ from the range of calibration.

Numerical implementations are possible.



Summary (II)

Still Open Questions

Softening is partly overestimated by the model forstress-strain behavior.

For lower temperatures the models predicts too stronghardening.

The transition from linear elastic to nonlinear stress-strainbehavior is too strict.

Next Steps

Extend the database of calibration, replace/modify responsefunctions



ThankYou!!

Further questions:holm.altenba h�ovgu.de


Material Modeling: - A Game for Scientists or an Effective Tool … · Motivation A Simple Example...

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