CONSIDERING THE INCREASE IN ELASTIC ANISOTROPY OF TRICLINIC ELASTIC-PLASTIC MATERIAL

The task of deformation of elastic anisotropy in a specific nonlinear elastic-plastic model is considered. According to a given criterion, the excessive growth of anisotropy causes the unexpectably early appearance of macrocracks due to plastic deformation. The elastic properties of material are described by the generalized Murnaghan law of elasticity. Initially, the material is assumed to be isotropic, and the values of anisotropy parameters are zero. The defining equation for the potential energy density of elastic deformation (stress potential) is written in the general form of anisotropy – triclinic. Possible restrictions for transversely isotropic, orthotropic and monoclinic materials were under search. For triclinic material, all seventy seven parameters can be nonzero. For monoclinic material, forty five parameters can be nonzero, and for other types of anisotropy – twenty nine. For transversely isotropic material, the restrictions in the form of homogeneous linear equations are found. Also, the restrictions on cubic-isotropic materials are found, which can be used only in the theory of elasticity, as this anisotropy is nondeformation. The second defining equation in finite form for the Cauchy stress tensor is written. An active elastic-plastic process takes place through an alternate alternation of plastic and elastic material states. The growth of anisotropy occurs in the plastic state (in flow). We introduce three differential equations in flow: for voltage potential, stress tensor and anisotropy parameters. The nonnegative parameter of the anisotropy growth is determined. The system of equations yields the measure speed of elastic distortions and the growth parameter to implement the minimization procedure. The suitability of the last equation to describe the derived constraints is checked. It is found that all of them are performed, but for the part of restrictions for transversely isotropic material. Therefore, for uniaxial loadings this equation should be complemented by twelve homogeneous linear equations.

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