Withers et al. [2] have pointed out that the comment made by Arsenault and Wu [1] about Pedersen et al. [3] composite model of the Bauschinger effect (BE) is "misconceived". It is our understanding that the comment of Arsenault and Wu [1] was "misconceived". However, before addressing the other specific points raised by Withers et al., let us attempt to clarify our position.
I. We pointed out very clearly that the direction of the initial prestrain is very important, i.e. whether it is tension or compression, in determining the magnitude of the BE. We have been unable to find in the literature any previous reference to this distinction. The large effect which the initial direction of straining has on the BE can be accounted for in terms of the thermal tensile residual stress (TTRS) in the matrix. The TTRS is due to the difference in the coefficients of expansion between the matrix (aluminum) and the reinforcement (SIC). If the test was conducted initially in tension, the magnitude of the TTRS is reduced, thereby giving rise to a small BE: in the terms of Withers et al. this is "transient softening". If the test was started initially in compression, the magnitude of the TTRS would be increased and the net result would be a large BE, i.e. "permanent softening". This will be elaborated on in the following.
The mismatch of the coefficients of expansion gives rise to TTRS in the matrix and thus the stress-strain curve of a composite becomes non-*See ref. 1.