# A Probable Approach to Reliability Assessment of Reinforced Plates
## 6 Discussion  
Several statistical approaches for the construction of the strength theory do not take into account the defectiveness and heterogeneity of composite materials in an obvious way; that is, their geometric parameters and mechanical properties. The disadvantages of such approaches are the veiled role of the defect in the elementary act of failure, and  
Figure 5: Mean value of failure loading (blue lines for \(\
u=0.1\), red for \(\
u=0.3\)). Figure 6: Dispersion of failure loading (blue lines for \(\
u=0.1\), red for \(\
u=0.3\)). the reduction of the composite element strength. Our proposed approach of explicit introduction into the material model of structural defects with the laws of their geometric parameter's distribution allows for eliminating the specified shortcomings. It opens up the possibility of calculating the statistical characteristics of the structural material's strength and failure based on data on their defect structure and resistance to the initiation and cracks development. In contrast to the previously applicable laws of distribution of cracks random half-length (power-law distribution and beta distribution), in our work we propose an exponential distribution law which simplifies the material model and mathematical calculations, but nevertheless makes it possible to relatively easily obtain several results that adequately reflect reality. Analyzing the constructed curves, we can see that at a given loading level, the probability of composite failure increases with a decrease in the Poisson's ratio of the matrix. On the other hand, an increase in the value \(\
u\) leads to an increase in the loading, which corresponds to a fixed probability of failure. Similar regularities were observed in the paper [22] when choosing the probability distribution density of the half-length of inclusions in the form of a power law. With an increase in the number of inclusions, the probability of material failure increases. A certain loading level corresponds to a very low probability of failure, \(P_{f}\). There exists a certain range of plate sizes (number of inclusions) when the probability of failure increases rapidly. The nature of this growth is invariant to the Poisson's ratio of the plate material. It is possible to assert a certain scale threshold for the value of \(P_{f}\). With biaxial symmetric compression, we observe a significant increase in the value of failure loading compared to the cases of biaxial symmetric tension and uniaxial tension. This feature can be explained by the presence of compressive stress components. At the same level of loading, for plates with the same dimensions and the value of the coefficient \(\
u\), the value \(P_{f}\) for biaxial symmetric tension compression is greater than for uniaxial tension (Figures 2 and 3). It will be the largest under biaxial symmetrical compression (Figure 4). With the increase in the number of plate inclusions (increase in its size), we observe an increase in the failure probability. It should be noted that their nature is almost independent of the type of loading (from \(\eta\)). The revealed regularities were also observed for stochastically defective isotropic plates [22] and orthotropic composite materials [27]. An increase of the inclusions number leads to a decrease in strength (Figure 5). The lowest strength of the composite is obtained under biaxial symmetric tension. For different types of stress states, we observe that an increase in the value \(\
u\) causes an increase in the mean value of failure loading. The strength dispersion is a decreasing function of the inclusions number in the plate (Figure 6). Within a certain interval of the value \(N\) change, we observe a rapid decrease in the value \(D(p)\). Decreasing nature does not depend on the type of stress state and Poisson's ratio as well. With the change of \(\
u\), the dispersion of the failure loading changes by a value that is almost independent of the applied loading type.