Crack extension .

The stabihty of crack extension in such materials depends on the rate of change of the appHed driving force to that of the fracture resistance, equation 4. 

Crack extension is often observed to vary significantly at the same nominal value of AK (= Y AOpos Tta) for different values of R-ratio. Elber [26] was the first to explain this observation for metals in terms of the crack closure phenomenon. He determined, by measuring specimen compliance, that fatigue cracks open and close at the crack tip at positive values of stress due to contact between crack surfaces behind the crack tip. For elastic fatigue conditions it is generally found that P p = P, and Kop = K, where P is the applied load. 

The basic assumptions of fracture mechanics are (1) that the material behaves as a linear elastic isotropic continuum and (2) the crack tip inelastic zone size is small with respect to all other dimensions. Here we will consider the limitations of using the term K = YOpos Ttato describe the mechanical driving force for crack extension of small cracks at values of stress that are high with respect to the elastic limit. 

Fracture toughness exhibited a significant dependence on specimen type and specimen size such that fracture toughness appears to increase for larger specimens which require greater crack extension. 

Fig. 5. Diagram of load versus load-point displacement for an elastic-plastic body experiencing stable crack extension [48],...

For an increment of crack extension, A A is represented by a movement from B to D on the load versus deflection curve, the energy consumed may be represented by the area Attjj. Hence the crack growth resistance may be expressed as... 

Fig. 20. The Burchell model, where crack extension occurs by successive fracture of rows of particles, from which the probability of fracture can be evaluated.

Gc is a material property which is referred to as the toughness, critical strain energy release rate or crack extension force. It is effectively the energy required to increase the crack length by unit length in a piece of material of unit width. It has units of J/m. ... 

The acknowledged father of fracture mechanics is A. A. Griffith [6-13]. His principal contribution is an analysis of crack stability based on energy equilibrium. If a crack is in equilibrium, the decrease of strain energy U must be equal to the increase of surface energy S due to crack extension, that is, ... 

Irwin [6-14] extended Griffith s theory to elastic-plastic materials and pointed out the three kinematically admissible crack-extension modes shown in Figure 6-10. These modes, opening, fonward-shear, and parallel-shear, can be summed to obtain any crack. 

The symmetric stress-intensity factor k, is associated ith the opening mode of crack extension in Figure 6-10. The skew/-symmetric stress-intensity factor l<2 is associated ith the fonward-shear mode. These plane-stress-intensity factors must be supplemented by another stress-intensity factor to describe the parallel-shear mode. The stress-intensity factors depend on the applied loads, body geometry, and crack geometry. For plane loads, the stress distribution around the crack tip can always be separated into symmetric and skew-symmetric distributions. 

Fig. 8.4 Mechanisms involving embrittlement of the metal, (a) Crack-tip adsorption, (b) hydrogen adsorption, (c) decohesion by hydrogen influx to dilated lattice and (d) crack extension due to brittle hydride particle forming at crack tip...

The derivative —d(SE)jdc is viewed as the force conjugate to time rate of crack extension and as a measure of elevation of stress near the end of a crack 109. The... 

An alternative to the compliance methods is a direct fracture energy measurement. In this method, the crack extension is related directly to the area, AG,... 

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