A crack tip driving force model for mode I crack propagation along linear strength gradient: comparison with the sharp strength gradient case

Abstract

In the present work, based on the Dugdale criterion, a closed-form theoretical crack tip driving force model of simple expressions was proposed for static and fatigue crack propagation along a linear yield strength gradient (YSG). Qualitative and quantitative analyses of the YSG effect on the crack tip driving force are given. The crack tip driving force depends on the yield strength at the crack tip, the YSG within the plastic zone and the applied load. A positive (or negative) YSG has a shielding (or amplifying) effect on the crack tip driving force. A difference of material-toughening mechanisms between smooth and sharp strength gradient was revealed both theoretically and numerically. In the linear YSG case, when a fatigue crack propagates along the YSG at a constant applied cyclic crack tip stress intensity factor, the cyclic crack tip opening displacement decreases (or increases) when the crack propagates towards a higher (or lower)-strength region; however, the cyclic crack tip stress intensity factor increases, no matter when the crack propagates towards a higher- or lower-strength region. This abnormal phenomenon causes theoretical and experimental challenges for characterizing the smooth strength gradient effect on the crack tip driving force.