Crack stress field

We consider an equilibrium problem for a shell with a crack. The faces of the crack are assumed to satisfy a nonpenetration condition, which is an inequality imposed on the horizontal shell displacements. The properties of the solution are analysed - in particular, the smoothness of the stress field in the vicinity of the crack. The character of the contact between the crack faces is described in terms of a suitable nonnegative measure. The stability of the solution is investigated for small perturbations to the crack geometry. The results presented were obtained in (Khludnev, 1996b). 

Crack Reflection. Crack deflection can result when particles transform ahead of a propagating crack. The crack can be deflected by the locali2ed residual stress field which develops as a result of phase transformation. The force is effectively reduced on the deflected portion of the propagating crack resulting in toughening of the part. 

The use of the single parameter, K, to define the stress field at the crack tip is justified for brittle materials, but its extension to ductile materials is based on the assumption that although some plasticity may occur at the tip the surrounding linear elastic stress field is the controlling parameter. 

Stress in crystalline solids produces small shifts, typically a few wavenumbers, in the Raman lines that sometimes are accompanied by a small amount of line broadening. Measurement of a series of Raman spectra in high-pressure equipment under static or uniaxial pressure allows the line shifts to be calibrated in terms of stress level. This information can be used to characterize built-in stress in thin films, along grain boundaries, and in thermally stressed materials. Microfocus spectra can be obtained from crack tips in ceramic material and by a careful spatial mapping along and across the crack estimates can be obtained of the stress fields around the crack. ... 

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 ... 

K[ is the mode I stress intensity factor which serves as a scalar multiplier of the crack tip stress field. 

Fig. 2. Elastic solution for the crack tip stress field with. small scale yielding [24].

In metals, inelastic deformation occurs at the crack tip, yielding a plastic zone. Smith [34] has argued that the elastic stress intensity factor is adequate to describe the crack tip field condition if the inelastic zone is limited in size compared with the near crack tip field, which is then assumed to dominate the crack tip inelastic response. He suggested that the inelastic zone be 1/5 of the size of the near crack tip elastic field (a/10). This restriction is in accordance with the generally accepted limitation on the maximum size of the plastic zone allowed in a valid fracture toughness test [35,36]. For the case of crack propagation, the minimum crack size for which continuum considerations hold should be at least 50 x (r ,J. 

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... 

The second physical quantity of interest is, r t = 90 pm, the critical crack tip stress field dimension. Irwin s analysis of the crack tip process zone dimension for an elastic-perfectly plastic material began with the perfectly elastic crack tip stress field solution of Eq. 1 and allowed for stress redistribution to account for the fact that the near crack tip field would be limited to Oj . The net result of this analysis is that the crack tip inelastic zone was nearly twice that predicted by Eq. 3, such that... 

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