Small scale yielding

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

The length s of the plastic zone for small-scale yielding can be expressed by... 

Lastly, we studied the effect of 7-stress on the effective time to steady state and the corresponding magnitude of the peak hydrogen concentration. We found that a negative T -stress (which is the case for axial pipeline cracks) reduces both the effective time to steady state and the peak hydrogen concentration relative to the case in which the T -stress effect is omitted in a boundary layer formulation under small scale yielding conditions. This reduction is due to the associated decrease of the hydrostatic stress ahead of the crack tip. It should be noted that the presented effective non-dimensional time to steady state r is independent of the hydrogen diffusion coefficient D 9. Therefore, the actual time to steady state is inversely proportional to the diffusion coefficient (r l/ ). 

S. G. Larsson and A. J. Carlsson, Influence of Non-Singular Stress Terms and Specimen Geometry on Small Scale Yielding at Crack Tips in Elastic-Plastic Material, J. Mech. Phys. Solids, 21, 263-278 (1973). 

Analogous to the arguments of small-scale yielding in linear elastic fracture mechanics, small-scale creep conditions (i.e., the situation where the size of the creep zone ahead of the fatigue crack tip is small compared to the characteristic dimensions of the test specimen, including the size of the crack and that of the uncracked liagment) can be assumed to exist when... 

Subsequently, Estevez et al. [22] incorporated a cohesive surface along the crack symmetry plane to permit the development of crazing together with bulk plasticity. They assumed bulk plasticity to remain confined near the crack tip so that the small-scale yielding framework is allowed. A single cohesive surface is used, but the framework allows cohesive surfaces to be embedded throughout the volume as performed in [20,21]. 

Fig. 7 The small-scale yielding problem in which crazing is allowed along the crack symmetry plane with a plastic bulk. The boundary conditions of the coupled thermomechanical problem are reported from [22,57]...

For small scale yielding (i.e. fracture mechanics terms as ... 

The dimensions of the specimen need to meet theoretical and practical size requirements. From a dimensional point of view, the classical size criterion for plain strain and small scale yielding conditions needs to be verified [3] ... 

When this zone is small enough and does not disturb the global elastic behaviour of the structure, the stress intensity factors can be corrected. Among all small-scale yielding corrections, two are particularly famous that of Dugdale-Barenblatt [6] and that of Irwin [7]. In this paper, we will concentrate on the latter. 

In this work, a small-scale yielding model of a stationary crack is assumed, with the remote boundary being subjected to a mode I loading at a constant loading rate f i. The crack initially has a blunt tip with a radius n. Crack growth by crazing is allowed to occur only along the plane of the crack fe = 0). 

More refined mechanical criteria may be defined on the basis of treatments that consider small-scale yielding, and hence an energy integral (e.g., the 7 integral), as the criterion for the nucleation of a crack. Regardless of the mechanical treatment that is employed, Tiscc is essentially an environmentally determined parameter because its value is normally much less than K c, and it may depend on the applied potential and the composition of the environment. For example, for Type 304SS at 288 °C, ic 60 MPa m, whereas Tiscc — 10 MPa m in oxygenated water at the same... 

The crack, semi-infinite in length, is assumed to propagate along the interface of two linearly elastic half spaces with a steady state velocity of a under small-scale yielding conditions, which implies that the region of pullout is small compared with typical specimen dimension. The interfaces are reinforced by chains which obey the pullout laws stated above. The steady state condition implies that all quantities are independent of time with respect to an observer moving with the crack tip. 

A comparison [32] of standard (ASTM and DIN) Charpy notch-impact test results with those of critical strain energy release rates G... obtained in accordance with LEFM criteria under the condition of small-scale yielding, were made for various unfilled polypropylenes. blends of PP with ethylene-propylene random copolymer (EPR) and also with... 

Fig. 12.6 Increasing pervasiveness of the plastic zone (a) small-scale yielding (SSY), (b) contained yielding, and (c) fully developed plasticity (after Williams (1984).

A necessary connection between the traditional impact experiments and more definitive and quantitative methods of fracture mechanics was made by Plati and Williams (1975a, 1975b) for cases of moderate plastic response of small-scale yielding (SSY) and accounted for yielding, whereby the measured impact-fracture work could be related to the size of the fracture area by consideration of the character of the deformation geometry of the bent bar and the crack-tip field. For a standard Izod or Charpy geometry as shown, e.g., for the Izod experiment depicted in Fig. 12.23, Plati and Williams considered the connection for two forms of approach that were based on measurement of the peak resistive force. Pc, or on measurement of the work of fracture W. 

---