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The strength and durability of composite materials depend on cohesive bonds (interatomic and intermolecular interaction). and from the defectiveness of their structure. Real strength is formed by the structure of materials and defects of various kinds.

A flat macroelement of a composite material is considered – a homogeneous matrix in which elliptical inclusions of different sizes and orientations from another elastic material are evenly distributed. Inclusions of this form are often found in metals (oxidized layers, graphite inclusions in cast iron, etc.).

The macroelement is located in a flat biaxial field of normal stresses and . The elastic properties of the matrix and inclusions are specified. The modulus of elasticity of the inclusions is small compared to the modulus of elasticity of the matrix. The inclusions are flattened in shape and their defining parameters are length  and angle of orientation relative to the main axis [1]. We consider the case when the failure begins in the inclusions and the cracks dynamically spread along their entire length.

We accept as the criterion for the crack occurrence the condition of a Coulomb friction law with clutch type [2]^

,                                                   (1)

where ,  are the stress in inclusion,  is a clutch coefficient,  is a coefficient of material inclusion internal friction. The stress in inclusion is determined as:

 

where  are the shear modules (),,  are the elastic constants, which are expressed in terms of Poisson's coefficient  [1].

 

Assume that the cracks grow, keeping their straight shape and orientation. Let the law of crack size growth under a given loading over time  have the form

,                                                   (2)

where  is the half-length of the crack at .

 

According to expression (2), it is possible to find the time for the crack to reach the critical size  (the durability of the composite material) in the given stress field. Let this dependence have the form , where  is a random variable.

The durability distribution function of a composite element with one inclusion can be found using the formula

,                   (3)

where  and  are the minimum and maximum value of durability.

Durability of the composite containing  inclusions

.

In this case, the durability distribution function of the composite with  inclusions is determined by the formula

.                                                     (4)

According to expression (4), the mean value, dispersion and other probabilistic characteristics of the composite material durability can be determined.

 

References:

1. Baitsar, R, Kvit, R, Malyar, A. (2019) Statisticalpredictionofthereliability of composite materials with dispersive inclusions. Scientific Journal «ScienceRise»,2-3(55-56), 49–55. doi: 10.15587/2313-8416.2019.160880

2. Cherepanov, G. (1983). Fracture mechanics of composite materials. Nauka, 296.