Single crystal hardening under monotonic and cyclic plastic deformation

Constitutive equations that characterize the strain-hardening behavior of crystalline metals are developed within the framework of continuum mechanics. Plastic deformation at low temperature is idealized to be time-independent and assumed to arise from crystallographic slip only. One important goal in this work is to analytically characterize the evolution of the instantaneous hardening moduli consistent with the complex cross-coupling between the work hardening rates and crystallographic slip-rates on all slip systems. In doing so, the variation of work hardening rate with respect to deformation history and current slip-rates is closely examined. Inequality restrictions for the instrantaneous hardening moduli are derived based on some of the well-known phenomena observed in the uniaxial loading test. Latent hardening experiments that utilize a computer data acquisition are conducted to verify these restrictions. Then, an analytical form for the instantaneous hardening moduli is proposed. This new hardening description incorporates the macroscopic slip interaction and the deformation history dependence that are believed to be responsible for many of the strain hardening mechanisms in single crystals. This description not only is consistent with physical observations, but it also leads to a set of plastic constitutive equations that can uniquely predict the stress-strain response for a boundary value problem. Numerical calculations are based upon an extremum principle, which is transformed into and solved as a standard quadratic programming problem. Various aspects of the plastic response of single crystals are studied, e.g., work hardening during uniaxial tensile loading test for different orientations, tensile overshoot, latent hardening and secondary slips. Finally, the hardening description is generalized to include cyclic deformation. A comparison between the dislocation structure in monotonic and cyclic deformation is discussed, and parameters in the hardening law are modified accordingly. Numerical results such as cyclic hysteresis loops with constant plastic strain amplitudes, cyclic hardening curve and cyclic stress-strain curve are presented. The Bauschinger effect and saturation stress are also investigated