Damageability of a material reinforced with unidirectional orthotropic fibers for an exponential function of long-term microstrength

The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law.