Penny-shaped tensile crack

Based on the micrograph observation in Fig. 7.10, AE wave due to debonding of stainless steel from base metal is simulated. As illustrated in the figure, a penny-shaped tensile crack of 10 pm diameter and 1 pm crack opening is assumed from the observation. Results of detected AE wave... 

Fig. 7.11. (a) Detected AE waveform and (b) synthesized waveform due to a penny-shaped tensile crack of debonding. 

There is considerable literature on material imperfections and their relation to the failure process. Typically, these theories are material dependent flaws are idealized as penny-shaped cracks, spherical pores, or other regular geometries, and their distribution in size, orientation, and spatial extent is specified. The tensile stress at which fracture initiates at a flaw depends on material properties and geometry of the flaw, and scales with the size of the flaw (Carroll and Holt, 1972a, b Curran et al., 1977 Davison et al., 1977). In thermally activated fracture processes, one or more specific mechanisms are considered, and the fracture activation rate at a specified tensile-stress level follows from the stress dependence of the Boltzmann factor (Zlatin and Ioffe, 1973). 

Figure 4.4. Schematic diagram of a circular (penny-shaped) crack inside a large body, snb-jected to nniformly applied, remote tensile stress perpendicnlar to the crack plane.

The median crack is a single, penny-shaped crack nucleated beneath the apex of the plastic zone created by the indentor. The diameter of the median crack is comparable with the indent size, and a median crack is not visible in a polycrystalline, opaque material. The driving force for nucleation of the median crack is the elastic tensile stress developed normal to the indentation direction at the elastic-plastic boundary when the external load is relaxed. Nucleation of a median crack depends on the presence of a suitable flaw. Once nucleated, the median crack will propagate spontaneously to a stable flaw size. The critical flaw size for growth is ... 

Failure criteria of the form of (18) have been considered by others. Indeed, equation (4c) of Ref. 3 is a special case of (18) with Q - l/(l-0.5i ), where v is Poisson s ratio. This failure criterion comes from the assumption that fracture occurs when the local (tensile) stress at some point on the surface of the crack cavity reaches the ultimate strength of the material. Equation (4c) of Ref. 4 derives from results of Paul and Mirandy (Ref. 9) for a penny-shaped crack. 

Fig. 7. Fracture surface in polyacetal resin specimen subjected to tensile fatigue. The penny-shaped crack initiated at a void or other inhomc eniety at its center (25).

In the RBM approach the propagation of a single crack is considered in a matrix reinforced with a system of parallel fibres. The material of the matrix follows linear elasticity, and crack propagation is initiated from an existing intrinsic flaw when stress in the direction perpendicular to that flaw attains the tensile strength cr. If the flaw has the form of a penny-shaped crack of length 2c as it is considered in LEFM (cf. Section 10.1.1), then the critical value of the stress intensity factor is also attained ... 

To verify the DEEM and the SIFs calculation method the following problem is considered. In the infinite media stretched by tensile stress a in the direction y the penny-shaped fracture of radius R is placed. The fracture is inclined around the Oz axis at the angle a as it is shown in Fig. 4. The SIFs on the crack front for this problem were previously determined exactly [9]... 

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