The Energy Dissipation Rate—A New Tool to Interpret Geometry and Size Effects

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Abstract
This presentation is devoted to geometry and size effects on the crack growth resistance of CT specimens. With a simple numerical model, the main influence factors on these effects can be separated. These are the effects of the in-plane and out-of-plane constraint on the deformation behavior and the locally varying fracture toughness properties of the material along the crack front. Crack growth is modeled for different geometries and sizes assuming that the critical values of the crack tip opening displacement, CODi, and the critical crack tip opening angle, CTOAc, remain constant for all geometries and sizes. Crack growth resistance curves are plotted in terms of the J-integral and the energy dissipation rate, D. Two types of materials are considered, a low-strength and a high-strength steel. For smooth specimens having a/W ratios between 0.4 and 0.7, the slopes of the J-Δa curves change due to the varying global out-of-plane constraint. For plane strain conditions, the J-Δa curves remain nearly unaffected by geometry and size (except for the smallest specimens of the high-strength steel). On the contrary, the energy dissipation rate shows a very strong size and geometry effect. It is possible to describe these effects qualitatively and quantitatively. Estimates of D are presented that are valid for bend-type specimens under small-scale yielding and large-scale or general yielding conditions. It is shown that a knowledge of D is essential for instability considerations. The quantitative estimate of D provides a prediction of the onset of unstable fracture. Materials with a low ratio CTOAc/∈y show a strong tendency to instability (∈y is the yield strain). An engineering estimation is given to determine the specimen size for a given material below which instability is impossible. The advantages and disadvantages of the toughness parameters J and D are discussed. It is demonstrated that local (in-plane) constraint parameters, like the Q stress or the local stress triaxiality, are not sufficient to explain the experimentally observed geometry effects.