Dynamical Dislocation Theory of Crystal Plasticity. I. The Yield Stress

The derivation is outlined of a general relation connecting the macroscopic plastic strain rate with the configuration and velocity distribution of dislocations in a monocrystal with a single active glide system. This can be simplified for particular cases, the most simple being the case of parallel straight dislocation lines.A new form of the dynamical theory of plasticity is applied to detailed calculations and compared with previous work. The major modification is the use of the equation v=v* exp[−D/τ] to express the quasi‐viscous behavior of dislocation velocities. Here, v=dislocation velocity, v*= terminal velocity, D=characteristic drag stress, and τ=resolved shear stress. Also, a physical relation between dislocation density and plastic strain is derived.The nonlinear differential equation that results from combining the strain‐rate equation with an equation that describes the loading machine is integrated. Approximate analytic solutions, and numerical calculations, are given for the upper yield st...

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