Application of Principal Component Analysis (PCA) for the Choice of Parameters of a Micromechanical Model

Abstract

The main objective of this work is to apply the Principal Component Analysis (PCA) to the key parameters of a micromechanical model, namely the shape parameter of inclusion (grain) (ratio =a/b) and γ viscoplastic parameter in view of a better simulation. In this work, the sensitivity of the model to parameters and γ is evaluated on the stabilized global stress during cyclic Tension-Compression (TC) loadings and out-of-phase Tension–Torsion, with a sinusoidal waveform and a phase lag of 90 between the two sinusoidal signals TT90 loadings. Indeed several values ​​of and γ are pulled thanks to these loading, we use later the PCA in order to choose the couple (, γ) adequate to launch our simulation. The model used is expressed as part of the self-consistent approach and time-dependent plasticity. Based on the Eshelby tensor, this model considers that the elastic behavior is compressible. For a polycrystalline structure, the grains are deformed by crystallographic sliding located in the most favorably oriented systems and which support a strong constrained stress . Keywords: PCA, grain shape , viscoplastic parameter γ, Self-consistent model, Non-incremental interaction law, Elasto-inelastic. TC and TT90 loading