The statistical fracture stress distribution of silicon wafers was obtained by biaxial plate bending tests in combination with finite element calculations. For the correct interpretation of these tests it is important that the finite element calculations imply wafer thickness and elastic properties of the multicrystalline silicon wafer, otherwise the resulting stresses will be estimated to high. The Weibull distribution of fracture stresses yields different parameters for each test series of silicon, depending on the surface preparation and wafer manufacturing condition.
This paper is concerned with the implementation of a viscoplastic material model of the Chaboche type in the framework of the finite element method (FEM). The equations of the used constitutive law, that incorporates isotropic hardening, back stress evolution with static recovery terms and drag stress evolution, are introduced. A representation of their numerical integration using the implicit backward Euler method under the assumption of small deformations and an isothermal formulation follows. The use of the backward Euler method leads to a nonlinear algebraic system of three equations, which is solved by a combination of the Pegasus method and a fixed-point iteration. After considering the accuracy of the presented integration algorithm in form of iso-error maps, the derivation of the consistent viscoplastic tangent operator is shown. The integration scheme and the calculation of the consistent viscoplastic tangent operator are implemented in the commercial finite element code ABAQUS, using the possibility of the user-defined material subroutine (UMAT). Finally a numerical example in form of a notched bar under tension is presented.
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