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Modeling Of Mechanical Properties Of Isotropic Interphase Layers In The Theory Of Continua With Defect Fields

Belov P.A., Kharchenko K.D., Lurie S.A., Lykosova E.D.

#### Abstract:

A model of functional interphase layers is developed on the basis of the general theory of continua with conserved dislocation fields (CCD). It is proven that all known models of gradient media are special cases of the CCD theory. The theorem on the equivalence of deformation of CCD and functionally graded materials is formulated. The variability of the properties of functionally graded materials is defined by the defect fields which are established using nonlocal solutions of the CCD theory. The physical meaning of the variability of the functionally graded materials properties can be connected with the damage of the isotropic material by the defect fields. The proven equivalence theorem provides the effective method for determining of the properties of the damaged continua as an isotropic functionally graded material. Since the defect fields are localized in the neighborhood of stress concentrators or boundaries, then the areas of the variability of properties of functionally graded structures associated with defects are localized. Therefore such structures are conventionally known as “interfacial layers”. The equivalence of the gradient elasticity theory for isotropic materials with constant properties and the classical elasticity theory for functionally graded materials with varying properties is proven. The variability of the properties of functionally graded materials are fully defined by solutions of the nonlocal gradient elasticity theory. The variability of mechanical properties of isotropic interphase layers (functionally graded layers) and the absence of their fixed boundaries is shown on the basis of the proven equivalence. The dependence of the effective properties of interphase layers on the loading conditions is found. The existence of the variable Young modulus of the interphase layer in the compounded bar is presented as an example of the developed theory.

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