Identification of viscoplastic material parameters from spherical indentation data: Part I. Neural networks
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In this paper, a new method for the identification of material parameters is presented. Neural networks, which are trained on the basis of finite element simulations, are used to solve the inverse problem. The material parameters to be identified are part of a viscoplasticity model that has been formulated for finite deformations and implemented in the finite element code ABAQUS. A proper multi-creep loading history was developed in a previous paper using a phenomenological model for viscoplastic spherical indentation. Now, this phenomenological model is replaced by a more realistic finite element model, which provides fast computation and numerical solutions of high accuracy at the same time. As a consequence, existing neural networks developed for the phenomenological model have been extended from a power law hardening with two material parameters to an Armstrong–Frederick hardening rule with three parameters. These are the yield stress, the initial slope of work hardening, and maximum hardening stress of the equilibrium response. In addition, elastic deformation is taken into account. The viscous part is based on a Chaboche-like overstress model, consisting of two material parameters determining velocity dependence and overstress as a function of the strain rate. The method has been verified by additional finite element simulations. Its application for various metals will be presented in Part II, [J. Mater. Res. 21, 677 (2006)]. I. INTRODUCTION
The investigation of mechanical properties by indentation experiments has a long tradition of more than a century, starting with conventional hardness testing. Important progress in the experimental technique has been made by the introduction of instrumented indentation devices that read depth and force during loading and unloading of the indenter. This opened up a new field of research, where methods are developed for investigating an increasing variety of mechanical properties. Stress– strain behavior is investigated in Refs. 1–6. Most of the proposed methods for investigation of the stress–strain behavior are based on the work of Tabor7,8 and model the plastic stress–strain behavior using a power law hardening rule. The determination of Young’s modulus9–11 can be attributed to analytical solutions of Hertz, Love, and Sneddon.12–14 These are many relevant examples that show how research is used to develop and improve methods to determine mechanical properties from indentation tests. Another important aspect is to investigate the robustness,
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0076 664
J. Mater. Res., Vol. 21, No. 3, Mar 2006 http://journals.cambridge.org Downloaded: 26 May 2014
suitability, and reliability of these methods for standardization, as has been done for the instrumented indentation test,15 e.g., in Refs. 16 and 17. The EC project indentation into coatings (INDICOAT)18 was an important activity for preparing an additional part 4 on coatings.19 Further development of the international standard
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