Computational modeling of viscoplastic polymeric material response during micro-indentation tests

Abstract

The computational modeling of instrumented indentation tests used to characterize material properties is challenging. It is mainly due to the computational techniques demanded to couple the complex physical mechanisms involved, such as, for example, the time-dependent inelastic material response to loads during contact. Therefore, this work aims to simulate the mechanical response of the poly vinylidene fluoride (PVDF) during a micro-indentation test considering a viscoplastic material model, and a prescribed load approach, using the finite element method. Further, model validation is performed based on experimental data measured during the contact between the indenter and the PVDF. Numerical analyses were performed using COMSOL Multiphysics finite element software considering the loading scheme of the experimental tests of 800 mN/ min rate during loading and unloading, and a 400 mN constant load, held by 30 s. Finally, a viscoplastic Chaboche constitutive model is presented considering two cases: (1) a perfectly plastic behavior, and (2) a nonlinear isotropic hardening behavior based on Voce and Hockett-Sherby exponential laws. While the latter models exhibit some discrepancy in capturing the experimental behavior, the former one has shown excellent agreement with the load-depth curves obtained experimentally, achieving the best fitting for the set of Chaboche parameters: A = 1 s −1 , n = 4.62 and ref = 132 MPa. Moreover, several phenomenological features of viscoplastic behavior such as rate dependence, plastic flow (or creep) and stress relaxation were accurately provided by the Chaboche model when describing the behavior of the PVDF material. Keywords Viscoplasticity • Polymers • Microindentation • Finite elements Nomenclature E Young's modulus F y Yield function h max Maximum indentation depth h r Residual or final indentation depth h m , r m PVDF sample thickness and radius J 2 Second deviatoric stress invariant P Applied load P max Maximum applied load Q p Plastic potential r i Indenter radius S Deviatoric stress tensor t h Holding load time vpe Effective viscoplastic strain vp Viscoplastic strain tensor Cauchy's stress tensor Mises Effective von Mises stres ys Yield Stress ys0 Initial yield stress sat , Voce model parameters Technical Editor: João Marciano Laredo dos Reis.

The Study Influence Analysis of the Mathematical Model Choice for Describing Polymer Behavior

“…In addition, if, in the first type there, is a trace of plastic deformations, the second type will have insignificant plastic deformations. Studies aimed at analyzing both the viscoelastic-plastic behavior of materials [24][25][26][27] and viscoelastic behavior of materials [28][29][30] are gaining momentum. The paper considers a mathematical model of only viscoelastic behavior for the first stage of the study.…”

An elasto‐viscoplastic constitutive model for the rate‐dependent behavior of polyvinylidene fluoride

“…Both models however, describe the response up to the yield stress as linear elastic, resulting in a loss of information in the nonlinear preyield response of the material. O'Connor et al 11 used a 3D viscoplastic constitutive model to describe the response of PVDF in microindentation tests, where they also adopted linear elastic behavior up to the yield point. Furthermore, the onset of plastic deformation is based on the Von-Mises yield criterion, which means that no pressure sensitivity is taken into account.…”