1 / 37

COMING FROM?

COMING FROM?. Polytechnic University of Madrid. Vicente Herrera Solaz 1 Javier Segurado 1,2 Javier Llorca 1,2 1 Politechnic University of Madrid 2 Imdea Materials Institute. IMDEA Materials Institute (GETAFE).

hilel-harrison
Download Presentation

COMING FROM?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. COMING FROM? Polytechnic University of Madrid Vicente Herrera Solaz 1 Javier Segurado 1,2 Javier Llorca1,2 1PolitechnicUniversity of Madrid 2ImdeaMaterialsInstitute IMDEA Materials Institute (GETAFE)

  2. An inverse optimization strategy to determine single crystal mechanics behavior from polycrystaltests: application to Mg alloys WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October)

  3. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 1. Introduction 2. CrystalPlasticityModel 3. OptimizationStrategy 4. Results 5. Conclusions

  4. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 1. Introduction • MagnesiumUsefulfortheindustrydue • High ANISOTROPY • Lowstrength and ductility limitsits use • Anisotropy: very different CRSS(Critical Resolved Shear Stresses) of their slip and twinning systems besides strong initial texture • News alloys and different manufacturing systems are • The influence of the alloyed elements

  5. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) • Macroscopic Properties (E, sy..) Mechanical Tests • Microscopic Properties (grains)  Hard estimation • nº slip and twinning def systems • Micromechanical Tests • Lower scale Models (MD, DD) • Inverse analysis of mechanical tests with FE models

  6. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) • Objetives: • Develop a CP model for HCP materials + twinning • Apply CP in a Polycrystalline homogenization Model • Implement an optimization technique  Inverse analysis

  7. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 2. CrystalPlasticiyModel • Multiplicative decomposition of the deformation gradient is considered • Composite material model: parent and twinphases • ThevelocityGradientLpcontainsthreeterms:

  8. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) With: • Three slip deformation modes (basal, prismatic and pyramidal [c+a]) and tensile twinning (TW) have been considered .

  9. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) • A viscoplastic model is assumed for the shear and twinning rate: depends on the resolved shear stress : • Shear rate • Twinning rate • The evolutionof the CRSR for each slip and twin system follows: • The crystal plasticity model has been programmed using a subroutine (UMAT) in ABAQUS and was resolved on an implicit scheme.

  10. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) • The behavior of the polycristal: •  Numerical Homogenization: Calculation by FE of a boundary problem in a RVE of the microstructure. • Different RVEscan be used: Dream 3D modelwithRealisticmicrostructure (grainsize and shapes) ≈ 200 elements/crystal Voxelsmodelwith 1 element/crystal Voxelsmodelwith 23element/crystal • Uniaxial tension and compression are simulated under periodic boundary conditions • The grain orientations are generated by Montecarloto be statistically representativeof ODF

  11. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 3. Optimizationtechnique Experimental curves Validationnumericalmodel Comparison Micromechanicalproperties (known) Numerical curves Experimental curves Comparison Inverseanalysis Micromechanicalproperties (????) Micromechanicalpropertiesfit Numerical curves

  12. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 3. Optimizationtechnique Subjective Time Trial-error Inverseanalysis Optimizationalgorithm (Levenberg-Marquardt) Objective, AutomaticTime Experimental curves Comparison Inverseanalysis Micromechanicalproperties (????) Micromechanicalpropertiesfit Numerical curves

  13. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 3. Optimizationtechnique IMPLEMENTATION Inverseanalysis Optimizationalgorithm (Levenberg-Marquardt) Objective, Automatic Time Experimental curves Comparison Inverseanalysis Micromechanicalproperties (????) Micromechanicalpropertiesfit Numerical curves

  14. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) • Experimental data: pair of npoints (xi, yi) definingan experimental curve y(x) • Numerical data: pair of npoints (xi, yi*) defining a numerical curve, where: yi*=f(xi,β)=f(β) and β • a set of mparametersonwichour • numericalmodeldepends • Objectivefunction: O(β): • Ifwe do smallincreasesd • in theβparameters , the response • (modifiednumerical curve) • can be written as:

  15. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) • WhereJ istheJacobianMatrix, obtainedherenumerically • Theperturbance of parametersδwhichresults in a minimum of theobjectivefunctionisobtainedwiththefollowing linear system of equations • The new set of βparameterswill be: • The minimization process is iterative, each iteration k is based on the results of the k-1. The loop iteration ends when a goal is reached or it is impossible to minimize the error. • The initial set of parameters is arbitrary • The optimization algorithm has been programmed in python • KEYPOINTS • The procedure is applied hierarchically: From simplistic RVEs to realistic ones → Time saving • Experimental data used have to be representative: Number of curves, load direction → To avoid multiple solutions • The values obtained have to be critically assessed: Predictions of • independent load cases → Validation

  16. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 4. Results • Fitting done onseveral Mg alloys: AZ31, MN10 and MN11 • Validation • Initial and Final textures • Temperatureinfluenceon MN11

  17. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) VALIDATION • To accept the results obtained you need to check the predictive ability of the model in other load cases which are not included in the iterative process. • The independence and representativeness of the initial curves used for the adjustment will influence in the quality of these predictions AZ31 Fitting 1 curves Prediction error= 31 MPa/pt

  18. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) VALIDATION • To accept the results obtained you need to check the predictive ability of the model in other load cases which are not included in the iterative process. • The independence and representativeness of the initial curves used for the adjustment will influence in the quality of these predictions AZ31 Fitting 2 curves Prediction error= 25 MPa/pt

  19. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) VALIDATION • To accept the results obtained you need to check the predictive ability of the model in other load cases which are not included in the iterative process. • The independence and representativeness of the initial curves used for the adjustment will influence in the quality of these predictions AZ31 Fitting 3 curves Prediction error= 11 MPa/pt

  20. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) VALIDATION • To accept the results obtained you need to check the predictive ability of the model in other load cases which are not included in the iterative process. • The independence and representativeness of the initial curves used for the adjustment will influence in the quality of these predictions MN10 Fitting 3 curves Prediction error= 9.5 MPa/pt

  21. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) VALIDATION • To accept the results obtained you need to check the predictive ability of the model in other load cases which are not included in the iterative process. • The independence and representativeness of the initial curves used for the adjustment will influence in the quality of these predictions MN11 Fitting 3 curves Prediction error= 11.3 MPa/pt

  22. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) INITIAL TEXTURES AZ31 MN10 MN11 Experimental Numerical

  23. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) FINAL TEXTURES AZ31 MN10 MN11 Experimental Numerical

  24. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) TEMPERATURE INFLUENCE on MN11 Curves Fit Polar effect (↑Tª)

  25. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) TEMPERATURE INFLUENCE on MN11 • The Polar effect could be attributed to the twinning mechanism but it doesn't appears at high Tª then… • The Inclusion of the non-Schmidt stresses on Pyramidal c+a is the only way to explain it (by modifying Schmidt law) • In other HCP materials (Ti), Pyramidal c+a has this role, but never on Mg. • At high Tª, pyramidal c+a has a great activity due to its low CRSS

  26. WORKSHOP STOCHASTIC AND MULTISCALE INVERSE PROBLEMS PARIS (2-3 October) 5. Conclusions • A CPFE model has been developed for Magnesium. • An optimization algorithm has been implemented Inverse analysis. • Numerical results Precise fit Experimental curves • Experimental curves input (representative)  predictive capacity • Three Mg alloys were analyzed effect of alloyed elements and Tª on the micromechanical parameters • Future work: • Optimization: Texture inclusion as objective function • Others representations of microstructures • Inclusion of grain boundary effects Crack propagation, fatigue crack initiation, grain boundary sliding

  27. Thanksforyourattencion

More Related