Stress transfer for a SMA fiber pulled out from an elastic matrix and related bridging effect

An analytical model is proposed to examine the stress transfer for a Shape Memory Alloy (SMA) fiber pulled out from an elastic matrix, the transformation characteristic of the SMA fiber and the influence of temperature are considered. The embedded SMA fiber is divided into a full transformation region, a partial transformation region and an intact region. The shear-lag model is utilized to analyze the stress distribution during the pulled-out of the SMA fiber. Compared to an elastic fiber pulled out from an elastic matrix, the transformation induced in the SMA fiber significantly lowers the axial stress, and the lateral contraction due to the transformation increases significantly the radial stress. Temperature has also an important influence on the stress distribution by alternating the transformation characteristic of the SMA material. The obtained results are then applied to analyze the bridging effect due to the SMA fiber, the computed results show that an increase of temperature decreases the stress intensity factor, which is in agreement with experimental observation in the literature. These results are useful for the design of intelligent composite materials.