Continuum damage mechanics with ANSYS USERMAT · Continuum damage mechanics with ANSYS USERMAT: numerical implementation and application for life prediction of rocket combustors 2nd

Continuum damage mechanics with ANSYS Continuum damage mechanics with ANSYS USERMAT:USERMAT:numerical implementation and application for life prediction of rocket

combustors

2nd Workshop on Structural Analsysis of Lightweight Structures. 302nd Workshop on Structural Analsysis of Lightweight Structures. 30thth May 2012, Natters, AustriaMay 2012, Natters, Austria

Waldemar SchwarzWaldemar SchwarzEADS Astrium Space Transportation, MunichEADS Astrium Space Transportation, Munich

[email protected]

Tel: +49 (0) 89 607 33486

Background: Background: thermal loads in a cryogenic rocket combustorthermal loads in a cryogenic rocket combustor

Ari

an

e 5

liquid oxygen T<100 K

regenerative hydrogencooling system

oxygen-hydrogen combustion T≈3600 K

22.09.2010 – page: 2

liquid pressurizedhydrogen T< 40 K

� The hot wall of a combustion chamber separates the hot gases

of ca. 3600 K from the hydrogen coolant of less than 100K.

� The resulting thermal gradients lead to severe thermo-mechanical

loading conditions

combustion chamber

Background: Background: failure mode of the hot wall of cryogenic combustorsfailure mode of the hot wall of cryogenic combustors

22.09.2010 – page: 3

� A combination of high temperatures, thermal gradients and pressure loads leads to

excessive inelastic deformations of the cooling channel structure.

� The deformation remains after shut down and accumulates with each operational cycle.

� The initially rectangular cooling channels distort to a roof-like geometry, called doghouse.

Problem:Problem:life prediction of the combustion chamber hot walllife prediction of the combustion chamber hot wall

B

A

2: damage analysis

� choose critical locations

� evaluate fatigue, creep and ductile damage

� extrapolate damage until failure

Conventional process for life prediction

1: structural analysis

� perform FEM computation

� obtain stress and strain fields

22.09.2010 – page: 4

failure

Problem:the conventional approach is not able to predict the observed failure mode and necessitates high empirical correction factors

hot wall afterend of life

predicteddeformation

Discrepancy between observed and simulated deformation

Solution:Solution:continuum damage mechanicscontinuum damage mechanics

Predicted vs. observed deformation

Thermo-mechanical simulation including material damage

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How to implement in ANSYS ?

Development scheme of the continuum damage modelDevelopment scheme of the continuum damage model

material modelmaterial modeldamage evolution modeldamage evolution model

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coupled materialcoupled material--damage modeldamage model

implementation algorithm in ANSYS USERMATimplementation algorithm in ANSYS USERMAT


ChabocheChaboche--typetype

material modelmaterial model

� Nonlinear hardening

� Strain-rate sensitivity

� Relaxation and creep

� fatigue failure

� ductile rupture

Continuum damage modelContinuum damage model

22.09.2010 – page: 7

Coupled materialCoupled material--damage equationsdamage equations

� Effective stress concept

� Crack closure effects

� 2nd order tensorial damage representation

Discretization and implementation into ANSYS USERMATDiscretization and implementation into ANSYS USERMAT

Validated chabocheValidated chaboche--type viscotype visco--plastic material model:plastic material model:

a) b)

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c) d)

a) monotone strain controlled loading

b) strain controlled symmetric cyclic loading

c) stress-relaxation test

d) compression creep test at different stress levels







� fatigue failure

� ductile rupture


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� The point of departure is a Coffin-Manson relation based on the total strain range:

log(C)

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� Assuming a linear damage accumulation, the damage per 1 cycle is expressed as

Continuum damage model (2)Continuum damage model (2)

� To obtain a damage evolution equation, Dcyc is formally derived with respect to time:

and

� Note, that the strain range ∆ε∆ε∆ε∆ε is treated as a state variable. Its rate equals the total strain

rate as long as ∆ε>0 and is 0 otherwise.

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� fatigue failure

� ductile rupture


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� The coupling between the damage model and the material equations is performed

basing on the effective stress concept.

SD: surface of cumulated micro-defects

S: remaining undamaged surface

σ : effective stress

σ : observable stress

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� All constitutive relations are evaluated in the effective undamaged configuration.

� Once the effective stress is computed, the observable stress is obtained from

Coupled materialCoupled material--damage equations:damage equations:generalization for the 3D stategeneralization for the 3D state

� In the 3D continuum, the damage variable is a symmetrical second order tensor Dij=Dji.

� The strain based damage evolution law is computed in the eigen-frame of the strain

increment dε on the basis of the eigenvalues:

1. Diagonalize the strain incement:

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2. Rotate the damage Dij and the inner

strain range ∆εij in to the eigen-frame of the strain increment dεij

3. Actualize the rotated damage and strain range on their diagonals using eigenvalues of the strain increment:

4. Rotate both actualized tensors back to their initial frame

Coupled materialCoupled material--damage equations:damage equations:crack closure effectscrack closure effects

� Damage acts only on the tensile part of the effective stress tensor:

� Tensile and compressive part of the stress tensor:

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� fatigue failure

� ductile rupture


22.09.2010 – page: 16






Algorithm for USERMAT implementationAlgorithm for USERMAT implementation

Coupling module

observable stress

algorithmic tangent of theobservable stress� Eijkl=dσij/dεkl

Material law

implicit Euler solution inthe effective configuration� effective stress, σij(t+∆t)

� inelastic strain, εpij(t+∆t)

� kinematic hardening, Xij(t+∆t)

� isotropic hardening, R(t+∆t)

Damage evolution

Input

material state USTATEV� effective stress, σij

� inelastic strain, εpij

� kinematic hardening, Xij

� isotropic hardening, R

� inner strain range, ∆εij

� damage, Dij

increments from global Newton-Raphson scheme

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Ou

tpu

t

STRESSUSTATEV

updated effective state� effective stress, σij(t+∆t)

� inelastic strain, εpij(t+∆t)

� kinematic hardening, Xij(t+∆t)

� isotropic hardening, R(t+∆t)

updated damage state� inner strain range, ∆εij(t+∆t)

� damage, Dij(t+∆t)

observablestress

DSDEPL

observablestiffness

implicit Euler update� inner strain range, ∆εij(t+∆t)

� damage, Dij(t+∆t)

Newton-Raphson scheme� time increment ∆t

� total strain increment ∆εij

� temperature increment ∆T

Continuum damage model:Continuum damage model:parameter identificationparameter identification

Under tensile loads a damage of

D=1 is reached when ε=C, for any γ.

Parameter C Parameter γγγγ

After C is fixed, γ is identified from best fit to low cycle fatigue experiments.

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�C equal to the strain at rupture εR

Model validation:Model validation:monotone tensile testmonotone tensile test

Simulation of a tensiletest including damage

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damage contourinside specimen

� Variate parameter C to fit experiment data of tensile tests

Model validation: Model validation: low cycle fatigue testslow cycle fatigue tests

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� Fix C and variate parameter γ to fit fatigue data

Application:Application:life prediction of a combustion chamber hot walllife prediction of a combustion chamber hot wall

Finite element model and boundary conditions

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Workflow

thermal transientanalysis

coupled structural-damage analysis

transient thermal loads

Application:Application:life prediction of a combustion chamber hot wall (2)life prediction of a combustion chamber hot wall (2)

NRNR-1n=NR-2 NR+1

NR = number of cycles to reach end of life, predicted by the coupled material damage model

Predicted deformation and damage of a cooling channel after n hot runs

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Predicted deformation without continuum damage mechanics after n hot runs

NRn=0.5NR 2NR

Application:Application:comparison to conventional life prediction and to experiment datacomparison to conventional life prediction and to experiment data

Predicted vs. observed deformation

Predicted vs. observed number of cycles

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Summary and conclusionsSummary and conclusions

� In the case of the hot wall of rocket combustors, conventional life prediction methods considerably overestimate the life of the component.

� In order to improve the life prediction capabilities, a coupled material-damage model was formulated and implemented in ANSYS USERMAT.

� The damage evolution law was formally derived from an empirical fatigue equation and it was shown that a proper choice of parameters enables the model to also predict ductile rupture.

� The model was applied in a thermo-mechanical simulation of a combustion chamber and it was

shown that it considerably improves the life prediction accuracy.

22.09.2010 – page: 24

OutlookOutlook

� The presented damage evolution law was mathematically derived from an empirical model and thus lacks of a sound physical basis.� Developments of micromechanical based damage models are presently running

� The material properties are probabilistic, so should be the model parameters� Sensitivity and statistical studies of the model input-output relations are planned

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Continuum damage mechanics with ANSYS USERMAT · Continuum damage mechanics with ANSYS USERMAT: numerical implementation and application for life prediction of rocket combustors 2nd