Character Change of a Pinned Dislocation during Bowing and Quantitative Evaluation of Particle Dispersion Strengthening

Abstract

Particle dispersion strengthening Δσ is theoretically expressed by the following equation as functions of Taylor factor M, line tension factor of dislocation β, shear modulus G, Burgers vector b, bowing angle θ and the mean free path λ. Δσ= 2MβGb sin θ / λ The β–value is given by the following equation as functions of the radius of elastic stress field of dislocation r, the radius of dislocation core r₀ and the dislocation constant k (= 0.71-1 for bcc iron). β=ln(r/r₀)/4πk During bowing of a pinned dispersion, the r–value becomes smaller with increasing θ due to the interaction between pinned dislocations. In this paper, the r-value is expressed by the following equation as functions of θ, the initial value of elastic stress field r^* and the mean cut-off diameter of particles on a slip plane d^*. r = d^*+ (r^*- d^*) cos θ (r^*> d^*) The r^*–value depends on dislocation density ρ; r^*=(4/π)^1/2/√ρ. Theoretical calculations proved that the maximum value of　Δσ is obtained at θ≒70˚ where cos θ ≒1/3 and sin θ≒0.94. Therefore,　Δσ and β can be rewritten as follows under the condition θ≒70˚. Δσ= 1.88MβGb/λ β= ln{(r^*+2d^*)/3/r₀}/4πk Experimental results agreed well with the calculated values for Δσ, when the r₀–value was put at 2b. It was also confirmed that Δσ is over-estimated by Orowan model and under-estimated by Ashby-Orowan model, because the values of sin θ and r are put as sin θ =1 and r= r^* in Orowan model and also sin θ =0.8 and r= d^* in Ashby-Orowan model. It is concluded that particle dispersion strengthening can be accurately estimated by taking the change of r–value during dislocation bowing into consideration.