Characterization of the tip field of a discrete dislocation pileup for the development of physically based micromechanic
- PDF / 345,886 Bytes
- 3 Pages / 594 x 774 pts Page_size
- 93 Downloads / 142 Views
placement, u, between the crack surfaces is related to K. The dislocation density near the tip of a continuous dislocation pileup was obtained by Liu from the following relation :[5] 1
f(r)(,.-,0) - b dr - b dr
7
"trr
Q. GAO and H.W. LIU [1] When a number of dislocations in a slip plane are pushed against a barrier by an applied stress, a dislocation pileup is formed. The stresses and strains at the tip of a pileup and the force on the locked leading dislocation are raised. The high stresses of dislocation pileups are often responsible for the propagation of microslips and the nucleation of micmfractures. This paper will show that a single parameter, such as the force on the leading dislocation or the position of a dislocation in a pileup, is capable of characterizing the entire stress, strain, and displacement fields of a discrete dislocation pileup. Thus, this parameter can be used as a measure of the strength of a barrier resisting the propagation of microslip or the initiation of microfracture. Zener m discussed tlae propagation of microslip and microfracture caused by the stresses at the tip of a pileup or a slipband. His discussion implies the equivalence between blocked slipbands, dislocation pileups, and cracks. Friedel t2] concluded that "a pileup group concentrates the applied stresses in a manner analogous to a plane crack." Keer and Mura taJ studied the strip yielding zone for a plane crack in the anti-plane strain case and the ribbonlike yield zone for a penny-shaped crack. They have shown the equivalence between the method of continuous distribution of dislocations and Dugdale's application of the classical theory of elasticity. Continuous dislocation pileups are equivalent to cracks. The equivalence relations between continuous pileups and cracks were obtained mathematically by Bilby and Eshelby. m The equivalence relation was also obtained earlier by Liu m in a simple but rather rigorous manner from the physical point of view. Both continuous dislocation pileups and cracks are planar defects in elastic solids. The boundary condition of the "stress free" slip plane for a continuous dislocation pileup is identical to the stress free condition on crack surfaces. Both classes of problems are dealt with by the theory of linear elasticity. Thus, the uniqueness theorem demands that continuous dislocation pileups and cracks be equivalent to each other. If continuous pileups are equivalent to cracks, the pileup parameters (F, the force on the leading dislocation, and f, the dislocation density) must be related to the crack parameters (~J, the crack extension force, and K, the stress intensity factor). In a crack-tip region, the relative dis-
Q. GAO, Professor and Director of Engineering Mechanics, is with Southwest Jiaotong University, Sichuan, People's Republic of China. H.W. LIU, Professor of Mechanical Engineering and of Solid State Science and Technology, is with the Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, NY 13244. Manuscript submitted October 4, 1989.
ME
Data Loading...
