Approximate SIF of Mode-I Crack Closure in Matrix by Knotted SMA Fiber

Abstract

In this article, a theoretical model is proposed on closure of mode-I crack in matrix embedded with prestrained shape memory alloy (SMA) fiber as an actuator. To overcome fiber de-bonding in matrix, two knots are made on a SMA fiber. By shape memory effect with the rise in temperature, the SMA fiber generates a couple of recovery forces acting on the matrix at the two knots. This couple of recovery forces may restrain opening of the mode-I crack. Based on Tanaka constitutive law on SMA fiber and complex stress function near an elliptic hole under a point load, we have an analytical expression of relation between stress intensity factor (SIF) of mode-I crack closure and temperature in SMA fiber. Simulation results show that SIF of mode-I crack closure decreases obviously with the rise in temperature higher than the austenite start temperature of SMA fiber, and that there is an optimal position for SMA fiber to restrain crack opening, which is behind the crack tip.