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

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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: \(A=1\,{\mathrm{{s}}}^{-1}, {n}=4.62\) and \(\sigma _\mathrm{{ref}}=132\) 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.

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Notes

  1. $$\begin{aligned}\left\langle x \right\rangle ^{n} = \left\{ \begin{array}{ll} 0\,\, , & \quad x < 0 \\ x ^{n} , & \quad x \ge 0 \end{array} \right. \end{aligned}$$

  2. The value was also checked by computing the reaction force in the PVDF bottom surface.

  3. Being 24 solutions to be analyzed for each Chaboche model set perturbed \(in +/-\,10\%\): Six solutions for each of the two sets of parameters associated with the two experimental compression rates, and for each of the two hardening models, Voce, and H–S. See also Fig. 5.

Abbreviations

E :

Young’s modulus

\(F_{\mathrm{{y}}}\) :

Yield function

\(h_{\mathrm{max}}\) :

Maximum indentation depth

\(h_\mathrm{{r}}\) :

Residual or final indentation depth

\(h_\mathrm{{m}}, r_\mathrm{{m}}\) :

PVDF sample thickness and radius

\(J_{2}\) :

Second deviatoric stress invariant

P :

Applied load

\(P_{\mathrm{{max}}}\) :

Maximum applied load

\(Q_{\mathrm{{p}}}\) :

Plastic potential

\(r_i\) :

Indenter radius

S :

Deviatoric stress tensor

\(t_\mathrm{{h}}\) :

Holding load time

\(\varepsilon\) \(_{\mathrm{{vpe}}}\) :

Effective viscoplastic strain

\({{\varvec{\varepsilon }}}_{\mathrm{{vp}}}\) :

Viscoplastic strain tensor

\({{\varvec{\sigma }}}\) :

Cauchy’s stress tensor

\(\sigma _\mathrm{{Mises}}\) :

Effective von Mises stres

\(\sigma _\mathrm{{ys}}\) :

Yield Stress

\(\sigma _{\mathrm{{ys}}0}\) :

Initial yield stress

\(\sigma _{sat}, \beta\) :

Voce model parameters

\(\sigma _{\infty }, \gamma , m\) :

Hockett-Sherby model parameters

\(\sigma _\mathrm{{ref}}, A, n\) :

Chaboche model parameters

\(\nu\) :

Poisson’s ratio

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Acknowledgements

The authors gratefully acknowledge the financial support provided by the Coordination for the Improvement of Higher Education Personnel (CAPES), the National Program of Post-Doctoral Research (PNPD) under code CAPES-PNPD 31001017030D4, and the National Council for Scientific and Technological Development (CNPq) Grants 304773/2017-4.

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  1. Department of Mechanical Engineering, PEM/COPPE, Federal University of Rio de Janeiro, UFRJ, PO Box 68503, Rio de Janeiro, RJ, 21945-970, Brazil

    Joan O’Connor, Lavinia Borges & Daniel Alves Castello

  2. Metallurgy and Materials Engineering Department, PEMM/COPPE, Federal University of Rio de Janeiro UFRJ, Rio de Janeiro, RJ, 21941-598, Brazil

    Bianca Bastos dos Santos & Marysilvia Ferreira da Costa

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O’Connor, J., Santos, B.B.d., Borges, L. et al. Computational modeling of viscoplastic polymeric material response during micro-indentation tests. J Braz. Soc. Mech. Sci. Eng. 42, 438 (2020). https://doi.org/10.1007/s40430-020-02511-2

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