Evaluation of an inverse methodology for estimating constitutive parameters in face-centered cubic materials from single crystal indentations

Aritra Chakraborty, Philip Eisenlohr

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Abstract

The feasibility to determine the adjustable parameters of single crystal plasticity constitutive laws by an inverse approach that minimizes the deviation between the measured and simulated indentation response of individual grains (of a polycrystalline sample) is investigated for the case of face-centered cubic (fcc) lattice structure. Optimization uses the Nelder–Mead (NM) simplex algorithm, which was modified to navigate parameter space regions where objective function evaluations fail. A phenomenological power-law is assumed as the constitutive description for crystal plasticity. Simulated cases of indentation with prescribed constitutive parameter values serve as the virtual reference. A sensitivity analysis revealed that the initial and saturation slip resistance τ0 and τsat are the most dominant parameters while the hardening slope h0 has less influence. Reproducibility and robustness are analyzed for different objective functions involving the load–displacement response and residual surface topography for several indentation crystal orientations. Concurrent optimization of load–displacement and topography consistently provided the least scatter in the optimized parameter values from the target solution compared to either one individually and essentially independent of indentation crystal orientation. Deviations in slip activity were typically of the same order of magnitude as the combined deviations of load–displacement and surface topography response. Optimization of more than one crystallographic indentation response at once did not improve the parameter estimation quality but proportionally increases the evaluation effort. It is concluded that for fcc materials one single crystal indentation experiment suffices to closely quantify the two most influential parameters of a phenomenological constitutive plasticity law when the objective function of the modified NM simplex algorithm proposed herein combines the load–displacement response and residual surface topography.

LanguageEnglish (US)
Pages114-124
Number of pages11
JournalEuropean Journal of Mechanics, A/Solids
Volume66
DOIs
StatePublished - Nov 1 2017

Profile

Indentation
Single Crystal
indentation
estimating
Single crystals
Face
methodology
Surface Topography
Methodology
evaluation
single crystals
Evaluation
Surface topography
topography
Plasticity
Crystal Plasticity
plastic properties
Simplex Algorithm
Deviation
Objective function

Keywords

  • Constitutive parameters identification
  • Crystal plasticity
  • Nelder–Mead simplex
  • Reproducibility
  • Robustness
  • Single crystal nanoindentation

ASJC Scopus subject areas

  • Materials Science(all)
  • Mathematical Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

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abstract = "The feasibility to determine the adjustable parameters of single crystal plasticity constitutive laws by an inverse approach that minimizes the deviation between the measured and simulated indentation response of individual grains (of a polycrystalline sample) is investigated for the case of face-centered cubic (fcc) lattice structure. Optimization uses the Nelder–Mead (NM) simplex algorithm, which was modified to navigate parameter space regions where objective function evaluations fail. A phenomenological power-law is assumed as the constitutive description for crystal plasticity. Simulated cases of indentation with prescribed constitutive parameter values serve as the virtual reference. A sensitivity analysis revealed that the initial and saturation slip resistance τ0 and τsat are the most dominant parameters while the hardening slope h0 has less influence. Reproducibility and robustness are analyzed for different objective functions involving the load–displacement response and residual surface topography for several indentation crystal orientations. Concurrent optimization of load–displacement and topography consistently provided the least scatter in the optimized parameter values from the target solution compared to either one individually and essentially independent of indentation crystal orientation. Deviations in slip activity were typically of the same order of magnitude as the combined deviations of load–displacement and surface topography response. Optimization of more than one crystallographic indentation response at once did not improve the parameter estimation quality but proportionally increases the evaluation effort. It is concluded that for fcc materials one single crystal indentation experiment suffices to closely quantify the two most influential parameters of a phenomenological constitutive plasticity law when the objective function of the modified NM simplex algorithm proposed herein combines the load–displacement response and residual surface topography.",
keywords = "Constitutive parameters identification, Crystal plasticity, Nelder–Mead simplex, Reproducibility, Robustness, Single crystal nanoindentation",
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N2 - The feasibility to determine the adjustable parameters of single crystal plasticity constitutive laws by an inverse approach that minimizes the deviation between the measured and simulated indentation response of individual grains (of a polycrystalline sample) is investigated for the case of face-centered cubic (fcc) lattice structure. Optimization uses the Nelder–Mead (NM) simplex algorithm, which was modified to navigate parameter space regions where objective function evaluations fail. A phenomenological power-law is assumed as the constitutive description for crystal plasticity. Simulated cases of indentation with prescribed constitutive parameter values serve as the virtual reference. A sensitivity analysis revealed that the initial and saturation slip resistance τ0 and τsat are the most dominant parameters while the hardening slope h0 has less influence. Reproducibility and robustness are analyzed for different objective functions involving the load–displacement response and residual surface topography for several indentation crystal orientations. Concurrent optimization of load–displacement and topography consistently provided the least scatter in the optimized parameter values from the target solution compared to either one individually and essentially independent of indentation crystal orientation. Deviations in slip activity were typically of the same order of magnitude as the combined deviations of load–displacement and surface topography response. Optimization of more than one crystallographic indentation response at once did not improve the parameter estimation quality but proportionally increases the evaluation effort. It is concluded that for fcc materials one single crystal indentation experiment suffices to closely quantify the two most influential parameters of a phenomenological constitutive plasticity law when the objective function of the modified NM simplex algorithm proposed herein combines the load–displacement response and residual surface topography.

AB - The feasibility to determine the adjustable parameters of single crystal plasticity constitutive laws by an inverse approach that minimizes the deviation between the measured and simulated indentation response of individual grains (of a polycrystalline sample) is investigated for the case of face-centered cubic (fcc) lattice structure. Optimization uses the Nelder–Mead (NM) simplex algorithm, which was modified to navigate parameter space regions where objective function evaluations fail. A phenomenological power-law is assumed as the constitutive description for crystal plasticity. Simulated cases of indentation with prescribed constitutive parameter values serve as the virtual reference. A sensitivity analysis revealed that the initial and saturation slip resistance τ0 and τsat are the most dominant parameters while the hardening slope h0 has less influence. Reproducibility and robustness are analyzed for different objective functions involving the load–displacement response and residual surface topography for several indentation crystal orientations. Concurrent optimization of load–displacement and topography consistently provided the least scatter in the optimized parameter values from the target solution compared to either one individually and essentially independent of indentation crystal orientation. Deviations in slip activity were typically of the same order of magnitude as the combined deviations of load–displacement and surface topography response. Optimization of more than one crystallographic indentation response at once did not improve the parameter estimation quality but proportionally increases the evaluation effort. It is concluded that for fcc materials one single crystal indentation experiment suffices to closely quantify the two most influential parameters of a phenomenological constitutive plasticity law when the objective function of the modified NM simplex algorithm proposed herein combines the load–displacement response and residual surface topography.

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