Modeling of the phenomenon of brittle-plastic transition by the method of dislocation dynamics

Abstract

Computer modeling by the DD method is based on the Rice and Thompson model, according to which the force reliefnear the crack tip is created by three forces: an external load, an image force acting on dislocations from the free surfaces, and a resistance force from the crystal lattice. The interaction between dislocations in the plastic zone is calculated step by step. At each step, the stress is calculated for all dislocations in the ensemble and the velocities and corresponding new positions are calculated. Computer calculations make it possible to predict the impact of dislocation ensemble shielding on the current value of the stress intensity factor. The calculated value of crack resistance was determined under the condition of reaching the critical value of the stress intensity coefficient of the brittle material at the crack head. The effect of temperature and strain rate on the viscous-brittle transition in polycrystalline molybdenum was modeled using the dislocation dynamics method. From the results of the calculations, it follows that when the test temperature changes, the size of the plastic zone increases by more than an order of magnitude. As the loading rate decreases, the abnormal increase in crack resistance shifts to smaller grain sizes. This effect is significantly smaller than the effect of temperature. Changing the parameters of the model does not change the general mechanism of the viscous-brittle transition, which is associated with the peculiarities of the interaction of dislocations in the plastic zone with grain boundaries in polycrystalline molybdenum. Regardless of the speed of loading and the temperature of the tests, three characteristic ranges of grain sizes can be distinguished: With large grains, the fracture toughness remains unchanged because the size of the plastic zone is much smaller than the grain size. With the average grain size, a dislocation cluster is formed near the boundary, grain boundary sources begin to work in the neighboring grain, forming a small number of dislocations there, which contributes to a slight increase in crack resistance. With a small grain size, the fracture toughness begins to increase rapidly, since the plastic zone covers several grains. The dislocation cluster moves to the top of the crack and screens its propagation. Keywords: phenomenon of brittle-plastic transition, dislocation clustering, dislocation dynamics.