Gradient Theory: Application on Dislocation Dynamics and Adiabatic Shear Bands Formed in Metal Cutting

Kyriaki Kalaitzidou | MS | 2002

Abstract:

In this work, the gradient theory of plasticity as proposed by Aifantis in the early 1980’s is further explored in terms of determining the phenomenological gradient coefficient entering in the equation for the flow stress and the evolution equations of dislocation dynamics, as well as in interpreting shear localized chip formation during orthogonal cutting.

In the first part of the thesis, a theoretical analysis is proposed for the estimation of the gradient coefficient. Based on a microscopic argument introduced by Aifantis, the strain gradient dependence of the flow stress is justified when coupling with an internal variable with diffusive transport is considered. The gradient coefficient is estimated for different cases depending on the physical interpretation of the internal variable which can be i) mobile dislocation density, ii) point defect concentration, iii) immobile dislocation density and iv) two different populations: dislocation density is the cell walls and in the cell interiors respectively, when a cellular microstructure is considered. For the case of mobile dislocations, different diffusion mechanisms are considered and an estimation of the gradient coefficient is obtained for each one. Using the same argument the gradient dependence of the dislocation dynamics is justified and estimates of the dislocation diffusivity are obtained.

The second part of this thesis is concerned with the study of the shear bands formed in discontinuous chips during orthogonal cutting. The 1-D gradient model analyzed by Huang for the initiation of localization and the prediction of shear band characteristics in metal cutting chips is employed in this study. Metal cutting experiments are performed using three different materials and the effect of cutting conditions on the shear band characteristics is measured using optical microscopy. The model is experimentally validated by comparing the predicted values of shear band width and spacing with the experimental data. Conclusions from the research findings are given along with recommendations for future work that can be done in this area.

Finally, a third topic related to plastic instabilities due to geometrical softening of materials is briefly discussed in the Appendix. Tensile experiments were conducted in room temperature using two different specimen sizes in order to study size effects in necking and ductile fracture. The material used is a solder of 90% Pb and 10% Sn.

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