Elastic energy crack driving force

This dependence is certainly different from the amplitude of the RR stress and strain-rate fields which is Kjlt. This is an illustration of why the amplitude of the RR-field, C(t), is not necessarily the crack driving force parameter. This is in contrast to the ambient temperature situation wherein the strain energy release rate correlates exactly with either G (= K2/E) or /, both of which also govern the amplitude of the appropriate elastic or elastic-plastic stress fields. 

The use of the concept of equifibrium in this context has been criticized by Sih and others. In more recent discussions of fracture mechanics, therefore, it is preferred to interpret the left-hand side of the equilibrium equation (2.18) as the generalized crack-driving force i.e., the elastic energy per unit area of crack surface made available for an infinitesimal increment of crack extension, and is designated byG ... 

The crack-driving force G may be estimated from energy considerations. Consider an arbitrarily shaped body containing a crack, with area A, loaded in tension by a force P applied in a direction perpendicular to the crack plane as illustrated in Fig. 2.6. For simplicity, the body is assumed to be pinned at the opposite end. Under load, the stresses in the body will be elastic, except in a small zone near the crack tip i.e., in the crack-tip plastic zone). If the zone of plastic deformation is small relative to the size of the crack and the dimensions of the body, a linear elastic analysis may be justihed as being a good approximation. The stressed body, then, may be characterized by an elastic strain energy function U that depends on the load P and the crack area A i.e., U = U(P, A)), and the elastic constants of the material. 

When cracks extend in mode I loading in LEFM they release elastic strain energy in the surrounding stress field. The rate of release of such energy with crack extension can be considered as a generalized crack-driving force and is alternatively a direct representation of the work of fracture when a critical condition Gic for crack extension is reached. 

Griffith used an energy balance approach to predict the crack propagation conditions (see Williams, 1984). The driving force is the elastically stored energy in the notched samples, which can be used to create new surfaces. A parameter Gc, the critical elastic strain energy release rate [GIc in mode I], can be determined and expressed in J m-2. 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

We denote the stress field due to a single Volterra dislocation at position (x, y ) by olp x — x, y — y ). We also note that the original interpretation of the elastic energy release rate offered in section 2.4.4 can be reinterpreted in terms of the driving forces on the various dislocations making up the crack. Now that we have seen how the crack itself may be written in terms of dislocations, we turn to the question of how to think about such a crack when there are other dislocations in its vicinity. 

Linear elastic fracture mechanics (LEFM) has been used successfully for characterization of the toughness of brittle materials. The driving force of the crack advance is described by the parameters such as the stress intensity factor (K) and the strain energy release rate (G). Unstable crack propagates when the energy stored in the sample is larger than the work required for creation of two fracture surfaces. Thus, fracmre occurs when the strain energy release rate exceeds the critical value. Mathematically, it can be written as... 

Fig. 4.14. A hierarchical point of view of interface fracture advance, whereby the complexities of material separation are lumped into a representative phenomenological cohesive rule that is representative of the system its essential features are the work per unit area Fo required for separation of the surfaces and the maximum cohesive traction <7 that arises in the process. The cohesive traction must be imposed by the surrounding film and substrate materials, viewed as elastic-plastic continua. The tendency for significant plastic deformation in either material is determined by the ratio of a to the yield stress of that material. The driving force necessary to effect separation is characterized by an energy release rate Q. To sustain crack growth, its value must be large enough to overcome Fq plus plastic dissipation per unit area Fp. Adapted from Hutchinson and Evans (2000).

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