numerical implementation and application for life prediction of rocket combustors Tel: +49 (0)

Transcription

1 2nd Workshop on Structural Analsysis of Lightweight Structures. 30 th May 2012, Natters, Austria Continuum damage mechanics with ANSYS USERMAT: numerical implementation and application for life prediction of rocket combustors Waldemar Schwarz EADS Astrium Space Transportation, Munich Tel: +49 (0)

2 Background: thermal loads in a cryogenic rocket combustor liquid oxygen T<100 K Ariane 5 regenerative hydrogen cooling system oxygen-hydrogen combustion T 3600 K combustion chamber liquid pressurized hydrogen T< 40 K The hot wall of a combustion chamber separates the hot gases of ca K from the hydrogen coolant of less than 100K. The resulting thermal gradients lead to severe thermo-mechanical loading conditions page: 2

3 Background: failure mode of the hot wall of cryogenic combustors 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 page: 3

4 Problem: life prediction of the combustion chamber hot wall Conventional process for life prediction 1: structural analysis perform FEM computation obtain stress and strain fields 2: damage analysis choose critical locations evaluate fatigue, creep and ductile damage extrapolate damage until failure B A Problem: the conventional approach is not able to predict the observed failure mode and necessitates high empirical correction factors Discrepancy between observed and simulated deformation hot wall after end of life predicted deformation page: 4

5 Solution: continuum damage mechanics Thermo-mechanical simulation including material damage Predicted vs. observed deformation How to implement in ANSYS? page: 5

6 Development scheme of the continuum damage model material model damage evolution model coupled material-damage model implementation algorithm in ANSYS USERMAT page: 6

7 Development scheme of the continuum damage model Chaboche-type material model Nonlinear hardening Strain-rate sensitivity Relaxation and creep Continuum damage model fatigue failure ductile rupture Coupled material-damage equations Effective stress concept Crack closure effects 2 nd order tensorial damage representation Discretization and implementation into ANSYS USERMAT page: 7

8 Validated chaboche-type visco-plastic material model: a) b) 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 page: 8

9 Development scheme of the continuum damage model Chaboche-type material model Nonlinear hardening Strain-rate sensitivity Relaxation and creep Continuum damage model fatigue failure ductile rupture Coupled material-damage equations Effective stress concept Crack closure effects 2 nd order tensorial damage representation Discretization and implementation into ANSYS USERMAT page: 9

10 Continuum damage model The point of departure is a Coffin-Manson relation based on the total strain range: log(c) Assuming a linear damage accumulation, the damage per 1 cycle is expressed as page: 10

11 Continuum damage model (2) To obtain a damage evolution equation, D cyc is formally derived with respect to time: and Note, that the strain range ε is treated as a state variable. Its rate equals the total strain rate as long as ε>0 and is 0 otherwise page: 11

12 Development scheme of the continuum damage model Chaboche-type material model Nonlinear hardening Strain-rate sensitivity Relaxation and creep Continuum damage model fatigue failure ductile rupture Coupled material-damage equations Effective stress concept Crack closure effects 2 nd order tensorial damage representation Discretization and implementation into ANSYS USERMAT page: 12

13 Coupled material-damage equations The coupling between the damage model and the material equations is performed basing on the effective stress concept. S D : surface of cumulated micro-defects S: remaining undamaged surface σ : σ : effective stress observable stress All constitutive relations are evaluated in the effective undamaged configuration. Once the effective stress is computed, the observable stress is obtained from page: 13

14 Coupled material-damage equations: generalization for the 3D state In the 3D continuum, the damage variable is a symmetrical second order tensor D ij =D ji. 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: 2. Rotate the damage D ij and the inner strain range ε ij in to the eigenframe of the strain increment dε ij 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 page: 14

15 Coupled material-damage equations: crack closure effects Damage acts only on the tensile part of the effective stress tensor: Tensile and compressive part of the stress tensor: page: 15

16 Development scheme of the continuum damage model Chaboche-type material model Nonlinear hardening Strain-rate sensitivity Relaxation and creep Continuum damage model fatigue failure ductile rupture Coupled material-damage equations Effective stress concept Crack closure effects 2 nd order tensorial damage representation Discretization and implementation into ANSYS USERMAT page: 16

17 Algorithm for USERMAT implementation Input material state USTATEV effective stress, σ ij inelastic strain, ε p ij kinematic hardening, X ij isotropic hardening, R inner strain range, ε ij damage, D ij increments from global Newton-Raphson scheme time increment t total strain increment ε ij temperature increment T Material law implicit Euler solution in the effective configuration effective stress, σ ij (t+ t) inelastic strain, ε p ij(t+ t) kinematic hardening, X ij (t+ t) isotropic hardening, R(t+ t) Damage evolution implicit Euler update inner strain range, ε ij (t+ t) damage, D ij (t+ t) Coupling module observable stress algorithmic tangent of the observable stress E ijkl =dσ ij /dε kl Output updated effective state effective stress, σ ij (t+ t) inelastic strain, ε p ij(t+ t) kinematic hardening, X ij (t+ t) isotropic hardening, R(t+ t) updated damage state inner strain range, ε ij (t+ t) damage, D ij (t+ t) observable stress observable stiffness USTATEV STRESS DSDEPL page: 17

18 Continuum damage model: parameter identification Parameter C Under tensile loads a damage of D=1 is reached when ε=c, for any γ. Parameter γ After C is fixed, γ is identified from best fit to low cycle fatigue experiments. C equal to the strain at rupture ε R page: 18

19 Model validation: monotone tensile test Simulation of a tensile test including damage damage contour inside specimen Variate parameter C to fit experiment data of tensile tests page: 19

20 Model validation: low cycle fatigue tests Fix C and variate parameter γ to fit fatigue data page: 20

21 Application: life prediction of a combustion chamber hot wall Finite element model and boundary conditions Workflow thermal transient analysis transient thermal loads coupled structural-damage analysis page: 21

22 Application: life prediction of a combustion chamber hot wall (2) Predicted deformation and damage of a cooling channel after n hot runs n=n R -2 N R -1 N R +1 N R N R = number of cycles to reach end of life, predicted by the coupled material damage model Predicted deformation without continuum damage mechanics after n hot runs n=0.5n R N R 2N R page: 22

23 Application: comparison to conventional life prediction and to experiment data Predicted vs. observed number of cycles Predicted vs. observed deformation page: 23

24 Summary 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. Outlook 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 page: 24