Random Dynamic Fracture And Reliability Analysis Of Functionally Graded Materials And Structures

The random dynamic fracture and reliability analysis were performed for functionally graded materials and structures. An stochastic model is established for anti-plane problem, plane problems and three-dimensional axisymmetric problem in that the material properties of functionally graded materials vary randomly in the thickness direction, and is the spatial non-uniform random field; while the dynamic loadings applied on the crack faces are treated as both stationary and non-stationary stochastic processes of time. In order to obtain the solution, the functionally graded materials is divided into several sub-layers, and the material properties of each layer are reduced to random variables. A fundamental problem is constructed for the solution. By the use of integral transforms and singular integral equations, both stress intensity factor history with its statistics and dynamic reliability (or the first passage time probability) are analytically derived.Numerical calculations were carried out to show the effects of related parameters on the stress intensity factor history and reliability. Based on numerical results, the following conclusions can be made:(1) High accuracy can be achived when the functionally graded materials is divided into more than nine sub-layers.(2) Whether the stochastic loadings are stationary or non-stationary, the dynamic stress intensity factor history is non-stationary stochastic processes of time. The effect of the power spectral density on the mathematical expectation of the dynamic stress intensity factor history is negligible. But the effect of the power spectral density on both the standard deviation of the dynamic stress intensity factor history and the first passage time probability becomes significant.(3) The non-uniform random field has great influence on both the dynamic responses and the reliability. The statistic behaviours of the dynamic stress intensity factor history and the first passage time probability increase with the increasing of material non-uniformity or correlation between two field points. Higher the non-uniformity or the correlation, larger the dynamic responses and response scatters, and higher the probability of crack initiaton.(4) Both the mathematical expectation and the standard deviation of the dynamic stress intensity factor history, as well as the first passage time probability, increase with the loading amplitude and crack geometry.(5) Variation of crack location will lead to the change of both the mathematical expectation and the standard deviation of the dynamic stress intensity factor history, as well as the first passage time probability.