Combined Hill-Taylor Theory: Theoretical, Experimental and Finite Element Study

In this study, by combining crystal plasticity notions developed by Taylor and the mathematical expression of Hill’s yield criterion for anisotropic materials, a model is introduced to describe the flow behavior of grains in a grain aggregate. In this model, Hill’s yield criterion coefficients are calculated in terms of Taylor factors for different straining conditions for each grain. The convexity of the proposed model is proved by sign determination of the eigenvalues of the associated Hessian matrix. It is found that the experimental load-displacement curves of specimens showing the size effect are enveloped by the bounds obtained from simulations using the proposed model, which to some extent verifies the applicability of the developed model. Using the developed model, the microforging of miniature rods consisting of 50 and 200 grains in their cross-section are simulated. In agreement with the literature, the results showed that due to the difference in the mechanical behavior of grains, the distribution of strain abruptly changes from one grain to another. Moreover, it is shown that as the number of grains in the cross-section of the specimen increases, the plastic equivalent strain tends toward that predicted by the classical plasticity theories, proving the applicability of the proposed model. Finally, the results suggest that the successful production of microparts by forming processes requires raw materials in microforming to be the products of the severe plastic deformation techniques, where the microstructure is scaled down to the nanometer.