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In this study, based on a regression of the crack tip displacements, the stress intensity range in fatigue is quantitatively determined for the shape memory alloy Ni 2 FeGa. The results are compared to the calculated stress intensity ranges with a micro-mechanical analysis accounting for the transformation-induced tractions. The effective stress intensity ranges obtained with both methods are in close agreement. Also, the fatigue crack closure levels were measured as 30 % of the maximum load using virtual extensometers along the crack flanks. This result is also in close agreement with the regression and micromechanical modeling findings. The current work pointed to the importance of elastic moduli changes and the residual transformation strains playing a role in the fatigue crack growth behavior. Additional simulations are conducted for two other important shape memory alloys, NiTi and CuZnAl, where the reductions in stress intensity range were found to be lower than Ni 2 FeGa.

We establish an overall energy expression to determine the twin migration stress in bcc metals. Twin migration succeeds twin nucleation often after a load drop, and a model to establish twin migration stress is of paramount importance. We compute the planar fault energy barriers and determine the elastic energies of twinning dislocations including the role of residual dislocations (br) and twin intersection types such as 1 1 0, 1 1 3 and 2 1 0. The energy expression derived provides the twin migration stress in relation to the twin nucleation stress with a ratio of 0.5-0.8 depending on the resultant residual burgers vector and the intersection types. Utilizing digital image correlation, it was possible to differentiate the twin nucleation and twin advancement events experimentally, and transmission electron microscopy observations provided further support to the modelling efforts. Overall, the methodology developed provides an enhanced understanding of twin progression in bcc metals, and most importantly the proposed model does not rely on empirical constants. We utilize Fe-50at.%Cr in our experiments, and subsequently

We develop an analytical expression for twin nucleation stress in bcc metal and alloys considering generalized planar fault energy and the dislocations bounding the twin nucleus. We minimize the total energy to predict the twinning stress relying only on parameters that are obtained through atomistic calculations, thus excluding the need for any empirical constants. We validate the present approach by means of precise measurements of the onset of twinning in bcc Fe-50at%Cr single crystals showing excellent agreement. The experimental observations of the three activated slip systems of symmetric configuration in relation to the twinning mechanism are demonstrated via transmission electron microscopy techniques along with digital image correlation. We then confirm the validity of the model for Fe, Fe-25at%Ni and Fe-3at%V alloys compared with experiments from the literature to show general applicability.

The development of a twin stress relationship for bcc metals and alloys in agreement with experiments has been both scientifically challenging and technologically vital. A modified approach to Peierls-Nabarro model is formulated that predicts the twinning stress in excellent agreement with experiments. We utilize the first principles energy calculations to extract the energy landscape associated with twinning and obtain the disregistry function to account for the interaction of multiple dislocations comprising the twin. The metals and alloys considered include Fe, V, Nb, Ta, Mo, W, Fe-3at.%V, Fe-35at.%Ni and Fe-3at.%Si. The variation of twinning stress within metals is substantial (90-800 MPa) and depends primarily on the twin boundary migration energy, the shear moduli, the interplanar spacing and the geometrical positions of the fractional dislocations constituting the twin.