The (DD) method was used to model the formation of the plastic zone of the top of the cracks in polycrystalline molybdenum. Special attention was paid to take into account the interaction of dislocations in the plastic zone with grain boundaries. Structural sensitivity of fracture toughness was analyzed under brittle-ductile condition. Simulations were performed for a range of grain sizes from 400 to 100 μm, at which a sudden increase in fracture toughness with a decrease of grain size was experimentally shown. We calculated the value of K1c taking into account the shielding action of dislocations. The position of all dislocations in the plastic zone at fracture moment was calculated. Based on these data, we obtained the dependences of dislocation density on the distance from the crack tip thereby confirming significant influence of the grain boundaries on plastic zone formation. At large grain sizes, when the plastic zone does not touch the boundary, the distribution of dislocations remained unchanged. As grains reduce their size to size of the plastic zone, they start formating a dislocation pile – up near the boundaries. Dislocations on plastic zone move slightly toward the crack tip, but the density of dislocations in the middle of the grain remains unchanged, and fracture toughness remains almost unchanged. Further reduction of the grain size leads to the Frank-Reed source activation on the grain boundary Forming dislocation pile-up of the neighbor grains. Its stress concentration acts on dislocations of the first grain and causes redistribution of plastic zone dislocations. If the reduction in grain size is not enough to form a strong pile-up, density of dislocations on plastic zone increases slightly and crack resistance increases a few percent. Further reduction of grains promotes strong pile-up, dislocations move to crack tip, and its density on plastic zone increases. Crack is shielded and fracture toughness increases sharply. The calculation showed that the fracture toughness jump is observed at grain sizes of 100—150 μm, in good agreement with the experiment. Keywords: dislocation dynamics simulation, molybdenum, fracture toughness, grain size, plastic zone, brittle-ductile transition.
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.
In this paper the effect of lattice friction stress on the process of dislocations annihilation is considered using dislocation dynamics method. It is shown that if dislocations of the opposite sign are located in the area where their own tension is greater than the friction stress, they annihilate. Consideration of this fact allows to connect the microscopic processes of annihilation with evolution of dislocation density in the sample under small external stresses and unloading. The area in which annihilation occurs is calculated to be proportional to the square of the friction stress/shear modulus ratio.It is also shown that the parameter responsible for the rate of dislocation annihilation depends on the cube of the ratio of the friction stress to the shear modulus, because it is inversely proportional to the number of annihilating dislocations and the time in which a dislocation pair annihilates.
The influence of grain size on the physical yield strength of the polycrystal is considered by the method of cellular automata. The physical yield strength of the polycrystal in this model is defined as the stress at which, the plastic deformation covers the entire cross section of the sample from one edge to another. Three mechanisms of plastic deformation are considered. The first one is an initiation of plastic flow from grain to grain by dislocation pile-ups. The second one is plastic flow in different grains independently of each other under the action of external stress and the third one is intergranular slippage. Computer simulations have shown that at large grain sizes (d > 200 nm) deformation propagates from grain to grain by initiating dislocations pile-ups, since in this case pile-ups are quite powerful and have a large effect on neighboring grains. At average values of grain size (20 nm <d <200 nm) plastic deformation occurs in the grains independently of each other, and the external strain give a major influence on plastic deformation. With further reduction of the grain sizes (d <20 nm) the main mechanism of deformation is intergranular slippage. because in grains of this size are quite large image stresses that do not allow large dislocation clusters. In small grains the image forces are quite large to prevent large dislocation pile-ups formation, but the mass and volume of grain are quite small to turn or slip its under the action of external stresses. In accordance with these mechanisms, on the calculated dependence of the physical yield strength vs grain size, there are three areas with different angles of inclination in logarithmic coordinates. Keywords: yield point, grain size, Hall―Petch low.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.