Abstract
The subloading surface model is based on the simple and natural postulate that the plastic strain rate develops as the stress approaches the yield surface. It therefore always describes the continuous variation of the tangent modulus. It requires no incorporation of an algorithm for the judgment of yielding, i.e., a judgment of whether or not the stress reaches the yield surface. Furthermore, the calculation is controlled to fulfill the consistency condition. Consequently, the stress is attracted automatically to the normal-yield surface in the plastic loading process even if it goes out from that surface. The model has been adopted widely to the description of deformation behavior of geomaterials and friction behavior. In this article, it is applied to the formulation of the constitutive equation of metals by modifying the past formulation of this model. This modification enables to avoid the indetermination of the subloading surface, to make the reloading curve recover promptly to the preceding loading curve, and to describe the cyclic stagnation of isotropic hardening. The applicability of the present model to the description of actual metal deformation behavior is verified through comparison with various cyclic loading test data.
Highlights
The conventional elastoplasticity model [9], premised upon the idea that the interior of a yield surface is an elastic region, has contributed to the prediction of the elastoplastic deformation behavior of solids such as metals, geomaterials, and concretes
They are termed the unconventional plasticity model by Drucker [9] and designated as the cyclic plasticity model [32]. They are classified into models based on the concepts of kinematic hardening, i.e., the “translation” ofyield surface enclosing a purely elastic region and the concept of expansion/contraction, i.e., “size-variation” of the loading surface
The multi surface model [36,43], the two surface model [5,40], and the nonlinear kinematic hardening model [1,3,4] belong to the former category, and only the subloading surface model belongs to the latter category
Summary
The conventional elastoplasticity model [9], premised upon the idea that the interior of a yield surface is an elastic region, has contributed to the prediction of the elastoplastic deformation behavior of solids such as metals, geomaterials, and concretes. Various elastoplasticity models aimed at describing cyclic loading behavior have been proposed to date They require a pertinent description of the plastic strain rate induced by the rate of stress inside the yield surface. They are termed the unconventional plasticity model by Drucker [9] and designated as the cyclic plasticity model [32]. Any strain accumulation is not predicted during cyclic loading inside that surface, even if the (sub)yield surface reaches the fully yield (high stress) state. It produces a risky mechanical design because remarkable strain accumulation is induced for real materials in such state. The direct notations AB for Air Br j , A : B for Ars Brs, : A for Γi jrs Ars and A : for Ars Γrsi j are used for arbitrary second-order tensors A, B and fourth-order tensor , where Einstein’s summation convention is applied for a letter of the repeated suffix taking 1, 2, 3
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