620.191.001.57(045) and A. V. Bashta A simulation model for multiple fracture has been developed that reproduces random processes of initiation, growth, and coalescence of dispersed surface cracks. The model is based on the method of statistical simulation (Monte Carlo method) and on the fracture regularities determined experimentally. The main factor responsible for fracture is found to be the coalescence of dispersed cracks, especially at the final stage, which accounts for about 30% of the total life. The ultimate state of a structure is defined by the condition according to which the length of the largest of the available damages is bigger than the calculated value of the maximum crack length.Introduction. The presence of a large number of short cracks scattered over a limited surface area is one of the manifestations of damages in machine parts under cyclic loading. Fracture of materials induced by the processes of initiation, growth, and coalescence of cracks, which are continuous in time, is universal [1], it is called multiple (dispersed or multisite) and is characteristic of many damaging factors, e.g., isothermal and nonisothermal fatigue [2][3][4][5], cyclic creep [6], and corrosion [7].Multiple fracture (MF) is of stochastic nature due to a random process of crack initiation in time, as well as random character of their dispersion on the surface, the rate of their growth and coalescence. During the coalescence of dispersed short cracks, their dimensions increase in a jump-like manner. Under condition of high concentration of defects, this may lead to an unexpected initiation of a critical (inadmissible in size) crack.The amount of experimental data on multiple fracture is rather limited. This is explained by the laboriousness of identification and complexity of monitoring the behavior of a large number of small-size defects on the specimen surface. Yet, the available experimental data make it possible to reveal general manifestation of the multiple fracture and, on this basis, to construct a mathematical model for the process and obtain the required results by means of a numerical experiment. The objective of this work was to develop a simulation model for multiple fracture.The model presented here simulates the processes of random initiation, propagation, and coalescence of surface microcracks occurring simultaneously. The damage evolution is described with allowance for the force interaction of the cracks in close proximity during their coalescence.The ultimate state is characterized by the appearance of a crack of a given critical size or by the formation of a cluster, which penetrates the damaged surface, due to large-scale coalescence of cracks of high concentration.The model is based on the method of statistical simulation (Monte Carlo method). This approach found application in the investigations of multiple surface cracking of materials [5,7,8] and each model is based on individual initial prerequisites depending on the problem to be solved.Initial Prerequisites of the Model. The initial p...
