Fracture stress field

Linear elastic fracture mechanics (LEFM) is based on a mathematical description of the near crack tip stress field developed by Irwin [23]. Consider a crack in an infinite plate with crack length 2a and a remotely applied tensile stress acting perpendicular to the crack plane (mode I). Irwin expressed the near crack tip stress field as a series solution ... 

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

The decrease in with crack depth for fracture of IG-11 graphite presents an interesting dilemma. The utihty of fracture mechanics is that equivalent values of K should represent an equivalent crack tip mechanical state and a singular critical value of K should define the failure criterion. Recall Eq. 2 where K is defined as the first term of the series solution for the crack tip stress field, Oy, normal to the crack plane. It was noted that this solution must be modified at the crack tip and at the far field. The maximum value of a. should be limited to and that the far... 

Fig. 4. Model of local plastic deformation of lamellae beneath the stress field of the indenter. The mosaic block structure introduces a weakness element allowing faster slip at block boundaries leading to fracture (right)...

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

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. 

Fig. 14.5. An optical micrograph and stress maps in bovine femoral bone near a fracture. The map in (a) was acquired at zero applied stress and in (b) at critical stress for crack propagation. The net stress field was obtained by subtracting (a) from (b) and is shown in (c). Reprinted with permission from [48]...

The first fracture criterion was defined by Griffith, supposing that fracture occurs when sufficient energy is released (from the stress field) by growth of the... 

Most of the time, the three-point bending test (Fig. 12.2c) induces fracture without exhibiting yielding. The stress calculated here is a maximum stress due to the inhomogeneity of the stress field along the thickness ... 

The best approach, however, consists of controlling the defect size and geometry and taking into account the corresponding stress-field inhomogeneity. This is realized in the frame of linear elastic fracture mechanics (LEFM), which was first applied to metals and ceramics and then adapted with success to polymers (Williams, 1984). 

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