The theory of long-term damageability for homogeneous materials is generalized to the case of discrete-fiber composite materials of stochastic structure. The equations of mechanics of micrononuniform media of stochastic structure are put in a basis of the theory. The process of damageability of components of a composite is modeled by the appearance of stochastically located micropores. The criterion of the destruction of an individual microvolume is characterized by its long-term durability determined by dependence of the time of fragile destruction on a degree of closeness of an equivalent stress to its limiting value, describing the short-term durability by the Huber - Mises criterion which is taken as a stochastic function of coordinates. Effective deformative properties and the stress strain state of a discrete-fiber composite with microdamages in components are determined on the basis of the stochastic equations of elasticity of discrete-fiber media with porous components. An algorithm of calculation of dependences of microdamageability of components of a discrete-fiber material and macrostresses or macrodeformations on time are constructed, and the corresponding curves are obtained in the case of an exponential-power function of microdurability.

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