Abstract
In an attempt to better understand the effect of the difference between the shear moduli of the particle and matrix on the flow stress and the work hardening, a numerical approach based on discrete dislocation simulations is developed in which the image stress caused by a second phase impenetrable particle on dislocations is implemented. Glide of a dislocation line of initially screw type through a channel between two spherical particles of shear modulus G
p is simulated. Shear stress is applied incrementally on the slip plane and the equilibrium position of the dislocation line is calculated for the given applied stress. It is found that the flow stress at which the dislocation bypasses the obstacles by bowing between a pair of particles varies as , where G
m is the shear modulus of the matrix and ΔG is the difference between shear moduli. α is found to be less than 1 and the effect of ΔG is amplified as the radius of the spherical particles increases. The stress increment required to force a dislocation to glide between the particles which have remaining Orowan loops from previous slip becomes higher as the particle gets harder. A relationship giving the hardening stress as a function of the number of loops is proposed. Finally, it is found that dislocations can bypass particles by cross-slip as soon as a certain number of Orowan loops surrounding the particles is reached. The image stress field around the particle induced by a difference between the shear moduli seems to enhance the cross-slip probability.
Notes
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