Limiting configuration in dislocation glide through a random array of point obstacles

Abstract

We consider a dislocation in glide through a random array of point obstacles. Several important phenomena, including the critical resolved shear stress at zero temperature and the velocity of thermally activated glide at low temperature or at stress near the critical resolved shear stress, are known to be strongly influenced by the properties of the most stable obstacle configuration encountered by the dislocatton during glide. We devise a limiting technique to estimate the mechanical strength, the distribution of forces, and the mean dislocation segment length in this configuration. The estimates are in good agreement with results

Scaling of Dislocation Strengthening by Multiple Obstacle Types

“…Most studies of interactions with a field of obstacles have been performed using a line-tension model and the point-obstacle model. [15][16][17][18][19][20][21] In this framework, the analytic Friedel model is appropriate [22] and is in good agreement with numerical simulations. [18] The strengthening associated with simultaneous operation of multiple obstacle types is less clear.…”

On dislocation–defect interactions and patterning: stochastic discrete dislocation dynamics (SDD)

“…(1) is derived for a simple equidistant two-segment configuration, which is used as a typical dislocation-obstacle configuration. The same functional forms have also been derived by other researchers using statistical approaches [2][3][4][5][6]. Although some computational analyses [7] confirmed Eq.…”

“…We follow the notations and assumptions made by Hanson and Morris [2,3] and Labusch [5] for dislocation segment arrays that form on a glide plane. For simplicity, we normalize the segment length l (between successive obstacles), stress r, and dislocation force f by 2C, s o , and L 0 , respectively, and re-write Eqs.…”

Process model to predict yield strength of AA6063 alloy

“…Several attempts have been made by earlier researchers [46,47] to assess the modulus strengthening in alloys. The widely accepted theory to quantify the modulus strengthening with small particle, as suggested by Hanson and Morris [46] can be expressed as:…”

“…The widely accepted theory to quantify the modulus strengthening with small particle, as suggested by Hanson and Morris [46] can be expressed as:…”