The yield stress gradient effect in inhomogeneous materials

In materials with local variations in yield stress, such as functionally graded materials or materials with interfaces or interlayers, the local near-tip crack driving force can become di€erent from the nominally applied far-®eld value. The near-tip crack driving force is enhanced, if the yield stress increases in the crack growth direction, and vice versa. This e€ect is termed as the yield stress gradient e€ect. A model is developed that allows us to derive analytical expressions to quantify the e€ect and to evaluate the e€ective crack driving force for smooth and abrupt variations in yield stress. These expressions can be used to optimize graded materials and interface and interlayer transitions so that the fracture resistance increases. The predictions of the model agree well with the results of previously reported ®nite element computations for cracks near bimaterial interfaces. Available experimental observations of the fatigue crack growth normal to interfaces and interlayers can be qualitatively explained. The yield stress gradient e€ect plays an important role for the fracture behavior in multiphase or composite materials, in functionally graded materials, in materials with special surface treatments like nitrided or case hardened steels, as well as in brazed and welded components