Stress state of compound solids of revolution made of damaged orthotropic materials with different tensile and compressive moduli

Abstract

A technique is proposed to allow for damages and different tensile and compressive moduli of orthotropic materials in stress-strain analysis of compound bodies of revolution under nonaxisymmetric loading and heating. The technique combines the semi-analytic finite-element method and the method of successive approximations Keywords: nonaxisymmetric thermostressed state, solid of revolution, orthotropic materials with different tensile and compressive moduli, microdamageIntroduction. Many important engineering problems involve thermostress analysis of various structural members to infer their reliability, performance, and endurance. Efficient methods were developed in [3, 7, 11, etc.] to determine the thermoelastoplastic stress-strain state of bodies of various shapes. The accumulation of damages in viscoplastic isotropic materials is described by introducing a scalar parameter [2, 4, 10, 12, 14, 15, etc.]. This parameter is determined from a kinematic equation that relates its time derivative with some equivalent stress. Such an approach reduces the process of damage to loosening of a microvolume. Another approach to the description of damage is to use a structural model [9, 17, 18, etc.] based on stochastic equations for microinhomogeneous materials. Here, dispersed microdamages are modeled by quasispherical micropores that may be filled with particles of destroyed materials, and the accumulation of microdamages during deformation is modeled as increased porosity. Both approaches assume that all area elements associated with one point are equally damaged. Actually, the distribution of damages over a deformed element under combined stress was experimentally shown to be anisotropic. This can drastically affect the behavior of the material. Therefore, only one measure of damage accumulation may appear insufficient in many cases to correctly identify the onset of failure if for no other reason than different failure mechanisms provided by tangential and normal stresses. In this connection, the papers [5,19] propose to describe damages in orthotropic materials by introducing six damage parameters, one per each area element. These parameters account for changes in the initial structure of a material; nucleation, development, and coalescence of pores; and formation of microdefects during deformation, which decreases the effective area of sections over which the stress components are distributed. Also, these parameters help to explain the nonlinearity of tension, compression, torsion, and shear curves. A literature survey indicates that the numerical analysis of deformational damage in composite materials has received inadequate development.Although the curve of interatomic forces passes through zero smoothly, modern composite materials may have, at the macrolevel, different elastic moduli in tension and compression because of the presence of internal pores, inclusions, and other defects [1, 8, 13, 16, etc.]. In some fibrous and particulate materials, Young's moduli in tension (Å + ) and compression (Å -) may differ by...

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