A New Constitutive Model for Work Hardening Based on Gain Boundary Energy Density

Recently, the necessity to grade grain size to ultrafine and nano scale for understanding the mechanical behavior of these materials has been recognized. However, the nature of such classification has remained unclear. As an example, ultrafine (100 nm -1 μm) and nano (<100 nm) grained FCC metals, compared to their coarse grained counterparts, exhibit a grain size strengthening that may deviate from the Hall-Petch relationship. To explain the mechanism of such deviation, previous dislocation theories seem insufficient. To solve this problem, a critical grain size criterion governing the shift of deformation mechanism is proposed in this work. This model employs an energetic approach; it relates the grain boundary energy density to certain critical energy values; and it permits, for the first time, a quantitative grading of grain sizes. Predictions based on this model were evaluated. The prediction on copper polycrystals of various grain sizes showed a very good agreement with experimental results. It is thus wished that the grain size theory on plastic deformation mechanism could be unified with the dislocation theory. In this study, such unification is attempted by using a parameter defined as the defect energy density. The possibility of such generalization is further reasoned upon the fact that the defect energy approach should be a unique but common form applicable for both dislocations and grain boundaries.