Stress intensity factor defined

Plot of log vs. log AKis used to determine the value of from the slope, while C is estimated from the intercept of the Paris equation (extrapolating the value of AR to 10). AK is the range of the linear elastic stress intensity factor defined as and rep-... 

Fracture toughness is the resistance to propagation of cracks through a material and is usually quantified by the stress intensity factor, K, defined as... 

Secondly, Irwin 6) found that the stress field around a sharp crack in a linear elastic material could be uniquely defined by a parameter named the stress-intensity factor, K and stated that fracture occurs when the value of K, exceeds some critical value, K C. Thus, K, is a stress field parameter independent of the material whereas Klc, often referred to as the fracture toughness, is a measure of a material property. Again the subscript I is used to denote the tensile-opening mode. 

The parameter K is the stress intensity factor, whose level defines the stress field around the crack tip. In the case of a mode I loading, it is denoted as Kj. 

Irwin (40) gave an alternative formulation to fracture by considering the distribution or field of stresses around a crack in an elastic material. He proposed that such a distribution could be expressed as a function of a parameter K, known as the stress intensity factor, and he established that the fracture would occur when K exceeds a critical value characteristic of each material. Figure 14.33 shows a sharp crack of length 2a in an infinite lamina subjected to a tensile stress ct. The equations defining the local stresses an, a22 < 12 are (42)... 

The critical stress intensity factor, Kc, obtained at different loading rates and environmental conditions was then reported as a function of fibre orientation. It was expected that the most evident relationship with the considered mechanical property would have been shown by the orientation factor in the applied stress direction (direction 1 in Fig. 2b). Therefore the orientation factor aj, previously measured on the plane 2 -3 was transformed into the orientation factor a, defined with respect to the applied stress direction 1 (Fig. 2 a and b) by a coordinate axis rotation of an angle a. Further details on such data handling can be found in ref [7, 13]. It is worth reminding here that a, and a go opposite when a increases from 0 to 90 degrees a, decreases from 1 to 2ero. 

The mechanics of fracture along bimaterial interfaces have been studied extensively. Excellent reviews have been published [18]. The stress and deformation field near the tip of a crack lying along a bimaterial interface can be uniquely characterized by means of the complex stress intensity factor K = Kl + iK2. K and K2 have the dimension (Pa m112 " ) and are functions of the sample geometry, applied loading and material properties, i = is the imaginary number and is a dimensionless material constant defined below. 

A minimum roughness of the support surface is also required to produce defect-free membrane layers. In the present context, surface roughness is defined as the average perpendicular (to the surface) distance between peaks and dips in the support surface. As discussed in Chapter 6, several other definitions of roughness can be given and used. The roughness of the support may limit the minimum achievable layer thickness. From a fracture mechanics point of view, surface roughness determines the maximum size and sharpness of flaws which can act as crack initiators (via the stress intensity factor). 

Stress intensity factor K determines the nature and intensity of the stress state of a material in the vicinity of the crack tip. The ultimate value of stress intensity factor Kc defines the ability of a material to resist the formation and development of cracks and establishes the level of a material s stress state, the result of which is rapid and uncontrolled growth of cracks. 

In principle then, a fracture toughness parameter has been defined in terms of linear elastic analysis of a cracked body involving the strain energy release rate G, or the stress intensity factor K. For thick sections, the fracture toughness is defined as Gic, and for thinner sections, as Gc or R (referred only to mode 1 loading here). This value is to be measured in the laboratory and applied to design. The validity of... 

By comparing Eqns. (3.34) and (3.28), it is readily seen that the mode I stress intensity factor may be defined by ... 

The lower hmit of integration (at or ai) is usually defined on the basis of nondestructive inspection (NDl) capabilities, or on prior inspection the upper limit is defined by fracture toughness or a predetermined allowable crack size that is consistent with inspection requirements (a/ or 2)- Equations (7.5) and (7.6) may be rewritten in terms of the stress intensity factor K ... 

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