تجزیه و تحلیل حساسیت پارامتر برای یک مدل دراکر-پراگر بدنبال شبیه سازی های آزمون های دندانه دار
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|26006||2008||8 صفحه PDF||سفارش دهید||3309 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Computational Materials Science, Volume 44, Issue 2, December 2008, Pages 385–391
A parameter sensitivity analysis is carried out from numerical simulations of indention tests. The indented material obeys a simple Drücker–Prager behavior with no hardening rule, involving four material properties. For each of the parameters, the sensitivity is defined as the variation of the error function around a reference indentation curve. It is computed for three loading paths and five indenter shapes: spherical, conical, cylindrical, tetrahedral, and pyramidal. Finally, each of the sensitivities are compared with each other and commented on.
Indentation tests are commonly used to estimate mechanical properties of materials. The special feature of this experimental method is the relative ease of specimen preparation of the studied material. From a modeling viewpoint, dimensional analysis is commonly used to give the general form of the F–δF–δ (force vs. depth) curve, see e.g.  and . To apprehend the complete formulation of F(δ)F(δ), analytic solutions of the displacement field in elasticity and elastoplasticity with power-law hardening has been proposed in  and , and it has been examined in  and  for linear viscoelasticity. Furthermore, many authors use numerical analysis to link the elastoplastic properties of materials with measurable parameters on the F–δF–δ curve, like the slope SS at the beginning of the unloading or the total reversible work WrWr, see , , , , , , , , , ,  and  for power hardening rules,  for linear hardening rule, and ,  and  for gradient plasticity. Other approaches aim to completely solve the indentation problem, i.e. without using dimensional analysis. In this spirit, numerical inverse analysis has been examined in the case of elastoplastic materials by means of several minimization techniques like neural network,  and , simplex method, , Kalman filter,  and , or adjoint state method . Whereas the above approaches aim to determine material properties, a few of them deal with parameters sensitivities. Bocciarelli et al.  and , and Bolzon et al. , studied the sensitivity of the imprint residual vertical displacement with respect to the pre-existing principal stresses inside the material. They also showed that the five parameters of an elastoplastic model with kinematic non-linear hardening can be identified if the imprint geometry is considered, whereas it cannot be done if only indentation curves are used. As a general rule, the computation of parameters sensitivities is of great importance since it can indicate the relevance of the parameters estimation. Indeed, for a set of parameters pipi appearing in the material constitutive equations, it is well established that if one parameter pp is much less sensitive than others, the condition number of the approximate Hessian matrix JT·JJT·J may be high (with JJ the gradient of the error function with respect to the parameters), resulting in a divergence of the iterative algorithm used to minimize the error function (e.g. Levenberg–Marquardt). In this case, one has to set a value to pp, and proceed to the estimation of other properties. So, for a given set of experimental data, some parameters could be precisely identified if their sensitivity is greater than the sensitivity of the other ones. This paper deals with a numerical parameters sensitivities study of a material submitted to indentation tests. The sensitivities of the medium properties shall be computed in the case of a Drücker–Prager elastoplastic model. For the sake of completeness, five shapes of indenters are considered (see Fig. 1 for a schematic representation): • a spherical indenter (also called Brinell indenter), • a conical indenter, • a cylindrical indenter, • a tetrahedral indenter, also known as a Berkovitch indenter, • and finally, a pyramidal indenter, also called Vickers indenter. Full-size image (13 K) Fig. 1. Different shapes of indenters. Figure options Indeed, for each of the indenter shapes, three loading–unloading paths are considered. The aim of the paper is to understand the influence of the loading path on parameters sensitivities, and to discuss the identification of a simple Drücker–Prager model properties. Let us now begin with the presentation of the constitutive equations.