The behavior of screw dislocations dynamically emitted from the tip of a surface crack during loading and unloading
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C. C. Yu Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan, Republic of China
Sanboh Lee Department of Materials Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China (Received 25 January 1994; accepted 15 September 1994)
The behavior of screw dislocations dynamically emitted from the tip of a surface crack during loading and unloading has been investigated using a discrete dislocation model. The critical stress intensity factor at the crack tip for dislocation emission is a function of friction stress, core radius of dislocation, and dislocations near the crack tip. During motion, the velocity of dislocation is assumed to be proportional to the effective shear stress to the third power. The effect of crack length and friction stress on dislocation distributions, plastic zone, and dislocation-free zone during loading and unloading was examined.
I. INTRODUCTION Bilby, Cottrell, and Swinden (BCS)1 proposed that a continuous distribution of dislocations piled up in front of a crack tip. However, Ohr2 observed a dislocationfree zone near a crack tip for some metals. A sequence of modified theories were investigated. For example, the problems of a semi-infinite crack and finite crack in a single crystal were studied by Majumdar and Burns3 and Chang and Ohr4"6 using a model of continuous dislocations. The effect of a grain boundary on the semiinfinite crack and finite crack was analyzed by Li and Li7 and Shiue and Lee8 according to the same model. Dai and Li 9 and Li and Li7 investigated the dislocations piled-up in quasistatic equilibrium near the semi-infinite crack tip of a single crystal and of a polycrystal, respectively, by using the discrete dislocation approach. A similar problem9 was studied by Shiue and Lee, with the sharp surface crack10 and blunt surface crack11 instead of a semi-infinite crack. All workers3"11 found that a dislocation-free zone arises from the critical stress intensity factor for dislocation emission or the energy barrier to create a dislocation from crack tip. They also found that the stress intensity factor at the crack tip depends on the size of the dislocation-free zone and is zero in the limit of no dislocation-free zone. These investigators1'3"11 concentrated on the situation that the emitted dislocations were in static equilibrium. The behavior of dynamic emission of dislocations from a semi-infinite crack tip was studied by Zhao, Dai, and Li.12 Based on these results, Zhao and Li 13 analyzed the behavior of emitted dislocations from a semi-infinite crack during unloading; they12'13 assumed that the critJ. Mater. Res., Vol. 10, No. 1, Jan 1995
ical stress intensity factor for dislocation emission is a material parameter. However, the critical stress intensity factor for dislocation emission was considered a function of dislocation distribution near the crack tip.10'11'14'15 We were thus prompted to study the behavior of dislocations emitted from the tip of a surface crack during loading and unloading. The velocity of dislocation follows
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