Failure Diagram and Chemical Driving Forces for Subcritical Crack Growth
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much greater than c, the latter is generally neglected. However Rice[1] has shown that the above equation can be expressed in an alternate form as
thereby separating the mechanical forces to the lefthand side and the material resistance to the right-hand side, with the requirement that one has to consider the localized deformations that contribute to the crack-tip driving forces. In this formulation, the c term becomes important as environment can reduce the surface energy c, thereby requiring reduced mechanical crack-tip driving forces needed to propagate a crack. In the above equation, the term P, is reinterpreted not as dissipating energy term but as a contributing factor to the net mechanical driving force needed to overcome the material resistance. In addition, it is understood[2] that (a) plastic deformation at lower temperatures takes place via generation of dislocations and their motion, (b) dislocations are conserved (expressed as conservation of Burgers vector, which implies that they are created as loops with every dislocation segment having its balancing negative part in the loop, 180 deg away from it), and (c) the negative parts of the dislocations emitted from the crack tip form ledges that open the crack tip, while the positive parts form the plastic zone ahead of the crack tip. From the point of our discussion, the dislocations contributing to plastic flow are the sources of internal stresses which can either augment or retard the crack-tip driving force because of applied stress. To express Eq. [2] in a more convenient form in terms of dislocation internal stresses, we resort to Irwin’s strain energy release rate[3] expressed in terms of stress intensity factor K, and formally rewrite the above equations, respectively, in terms of K as
G P 2c;
K2 =E0 2c þ P
½3
K2 =E0 P 2c
½4
I.
INTRODUCTION AND BACKGROUND
FOR characterizing the localized material damage in terms of crack initiation and its growth leading to failure of a component, it is important to differentiate the crack-tip driving forces in relation to the material resistance. Damage in terms of crack initiation and growth occurs only if the crack-tip driving forces exceed the material resistance. It is easier to define both material resistance and mechanical crack-tip forces for a limiting case of purely elastic material. In the purely elastic regime, where a simple Griffith-criterion can be applied, the crack-tip driving force is related to the elastic energy release rate that must exceed the material resistance in terms of surface energy, c, to create the new surfaces during separation. The material resistance comes from cohesive forces that bind the material. In the case of the crack-tip plastic relaxation, there is energy dissipation, and Griffith’s condition is modified to include this energy dissipation. Thus, crack-tip driving force, G, expressed as Irwin’s energy release rate should be greater than the total material resistance that includes the surface energy and the energy dissipated as the plastic work term, P. This is ex
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