PSI - Issue 33

Evgeny Lomakin et al. / Procedia Structural Integrity 33 (2021) 809–817 Lomakin E.V., Fedulov B.N. / Structural Integrity Procedia 00 (2019) 000–000

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nonhomogeneous; they have cracks, pores, inclusions and other structural imperfections. Usual effect is that these materials, being quite brittle under normal conditions, under high hydrostatic pressure can exhibit plastic properties. The deformation of such materials under shear load can be accompanied by plastic volumetric deformations. This effect is called the dilatancy, that was first experimentally discovered by Reynolds [1] and is most clearly reveals in the deformation of heterogeneous media. These properties of materials, which cannot be characterized using classical approaches, make it necessary to introduce new parameters into the plasticity criteria and constitutive equations, which characterizes the type of stress state in a deformed solid body. One of the most and well-known parameters, which can be treated as stress state type parameter, is the ratio of first stress tensor invariant to the stress intensity or the equivalent von Mises stress: � / � , where � �� /3 , � � � � � �� �� , �� � �� � �� , �� � 0 �� � ��, �� � � . This parameter is also known in literature as triaxiality ratio. 2. Criterion The criterion of plasticity for a dilatant medium can be taken in the following generalized form: �� �� � � � � � � �� (1) The main idea of the proposed criterion is to follow stress intensity or average shear stress, by additional multiplier, which depends on stress state parameter, that gives additional influence to the closeness to the conditions of the initiation of plasticity process. By taking different analytical expressions for the function � � , we can obtain some of the known plasticity conditions used in the mechanics of granular, porous and damaged media. Consider the case of a linear dependence of the function f on the parameter ξ : � � � � � � , (2) with this choice of function of stress state sensitivity � � , the condition (1) coincides with generalized criterion of Mohr-Columb [2]: 0 � � � �� (3) If we use the dependence on triaxiality parameter in such form: � � � �� � � � , (4) we obtain, the well-known Green condition [3]: � 0 2 � � 2 � �� (5) Choice of sensitivity function as a constant � � � � leads to the plasticity criterion by von Mises [4]: 0 � �� (6) Thus, using Equation (1), it turns out that we generalized the well-known criteria. In addition, this result can be considered as a justification for choosing the stress state parameter ξ with given type of generalization for the criteria for dilatation media.