Force, crack driving

That fraction of the applied work which is not consumed in the elastic-plastic deformation remains to create the new crack surface, i.e., the crack driving force. Therefore, a nonlinear fracture toughness, G, may be defined as follows ... 

Composite structures in service are often subjected to complex 3-D load paths. In general, a delamination will be subjected to a crack driving force with a mode I opening, a mode II forward shear and a mode III anti-plane shear, as illustrated in Fig 3.29. Because delamination is constrained to grow between individual plies, both interlaminar tension and shear stresses are commonly present at the... 

The explanation of the effect of secondary inclusions on the delocalization of shear banding is based on the concept of modification of the local stress fields and achieving favorable distribution of stress concentrations in the matrix due to presence of inclusions. This leads to a reduction in the external load needed to initiate plastic deformation over a large volume of the polymer. As a result, plastically deformed matter is formed at the crack tip effectively reducing the crack driving force. Above approximately 20 vol% of the elastomer inclusions. 

All else being equal, a toughening effect occurs if the crack tilts or twists away from a planar geometry because this reduces the net crack driving force. In homogeneous materials such as glass, cracks tend to propagate in... 

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 Griffith formalism, therefore, requires that the quantity acr /a be a constant. The left-hand side of Eqn. (2.22) represents a crack-driving force, in terms of stress, and the right-hand side represents a material property that governs its resistance to unstable crack growth, or its fracture toughness. From previous consideration of stress concentration, Eqn. (2.12), it may be seen that, as /o 0,... 

Estimation of Crack-Driving Force G from Energy Loss Rate (irwin and Kies [8,9]) 17... 

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. 

Thus, the crack-driving force is identical, irrespective of the loading condition. 

Before closing this chapter, two plasticity-related parameters need to be introduced. The hrst parameter relates to the presence of plastic deformation at the crack tip in technologically important material (i.e., the plastic zone correction factor), and an estimation of its size. The second one relates to the extent of opening of the crack at its tip in the presence of plastic deformation, which is then used as an alternate parameter for characterizing the crack-driving force. 

Figure 4.18 shows the crack growth resistance curve as a function of crack length (i.e., the sum of the starting crack length and the individual crack growth increments) that had been constructed from the data (i.e., the local peaks and valleys in the load-displacement trace) in Fig. 4.17. The increase in crack-driving forces (in terms of G) at two stress levels are shown as dashed line. At the lower stress level, the trend line shows the inadequacy of the driving force to continue crack growth...

According to Landes and Wei [2], the connection between the steady-state creep rate and the crack-driving force (characterized by K) is derived through the use stress-strain results from elastic-plastic analysis by Hutchinson [9] and Rice and Rosengren [10], According to these models, crack-tip stress and strains in the loading direction (y-direction) are given by Eqn. (6.7). 

This fundamental hypothesis reflects the existence of a region (f.e, stage II) in crack growth response over which the growth rate is essentially constant i.e., independent of the mechanical crack-driving force). The existence of this rate-limited region... 

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