applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 89In the case of ductile materials, the length of the work hardening zone H affects an0increasingly greater area of the material as the crack propagates, but the self-similar limit0 0 0H L l is still valid.Figure 6. J-R curves calculated in function of the projected crack length L0 with different ruler lengthsl0 0.0001,0.001,0.01,0.1 and 1.0mm , for a fracture of unit thickness, fractal dimension D 1.32and 2 e 10 KJ / m .However, in the case of brittle materials (ceramics), after the initial stage of hardening, thecrack maintains this state in a region of length H0, very short if compared to the cracklength L0, generating a self-similar fractal structure only when the crack length L0is small,in the order of l 0, i.e., H0 L0 l0. When the crack length L0becomes much larger than theinitial size of the hardening region H0present at the onset of crack growth, the self-similarlimit is not valid, and the self-affine (or global) limit of fracture becomes valid.6.3.2. Case – 2. Brittle self-affine limitIt is easy verify that in stable crack growth, where J 0 R 0, using equations (59) and (79),one has dL / dL0 1 when L . The global self-affine limit of J 0can be calculatedapplying the condition when the observation scale corresponds to a rather small amplitudeof the crack, similar in size to the crack increment, i.e., when H0 l0 L0in equation (79),resulting the linear elastic expressionwhere J0 G0andJ (99)02 effG 2 .(100)Ro e p