Crack tips plastic zones

Fig. 4. (a) The crack tip plastic zone and (b) the Dugdale plastic zone model. Terms are defined in text. 

In the case of metals, R is mainly plastic energy associated with the formation of a crack tip plastic zone. It is obvious from Eq. 9 that, for plane stress,... 

Use Ae data in Table 2.2 to compare crack tip plastic zone sizes in acrylic, ABS and polypropylene. 

The observation that an increase in temperature or a decrease in rate both result in the same fracture response points toward a viscoelastic influence on thermoset fracture behavior, especially crack initiation. This characteristic behavior of epoxies has been explained qualitatively by consideration of the temperature and strain rate effects on the plasticity of the material at the crack tip . In effect, test conditions which promote the formation of a so-called crack tip plastic zone, or blunt the crack by a ductile process, promote unstable crack propagation. This aspect of unstable fracture is subsequently discussed in more detail. 

Looking at the structure of these crack tip plastic zones in more detail, it is found that the individual crazes are less straight compared to the low temperature crazes (Fig. 21). This indicates a more pronounced influence of the crystalline microstructure on craze formation. Figure 21a and b demonstrate for fine spherulitic, highly isotactic PP the interaction between the crazes and the microstructural features. Most of the... 

BPA Bisphenol-A CTPZ Crack tip plastic zone DCG Discontinuous crack growth FCP Fatigue crack propagation... 

During the DCG process, a single craze forms the crack tip plastic zone (CTPZ). The craze progressively weakens during each successive load cycle, while the... 

The crack-driving force G may be estimated from energy considerations. Consider an arbitrarily shaped body containing a crack, with area A, loaded in tension by a force P applied in a direction perpendicular to the crack plane as illustrated in Fig. 2.6. For simplicity, the body is assumed to be pinned at the opposite end. Under load, the stresses in the body will be elastic, except in a small zone near the crack tip i.e., in the crack-tip plastic zone). If the zone of plastic deformation is small relative to the size of the crack and the dimensions of the body, a linear elastic analysis may be justihed as being a good approximation. The stressed body, then, may be characterized by an elastic strain energy function U that depends on the load P and the crack area A i.e., U = U(P, A)), and the elastic constants of the material. 

In Chapters 2 and 3, the restrictions in the use of linear elastic fracture mechanics (LEFM) were discussed in terms of the dimensions of the crack and the body (specimen, component, or structure) relative to the size of the crack-tip plastic zone. Simple estimates of the plastic zone sizes were given in Section 3.6. A more detailed examination of the role of constraint (plane strain versus plane stress) and the variations in plastic zone size from the surface to the interior of a body would help in understanding fracture behavior and the design of practical specimens for measurements of fracture toughness. Note that the plastic zone size in actual materials... 

In essence, the physical crack size 2ao is being considered in relation to the crack-tip plastic zone size through the following three cases ... 

In this case, the crack size is much larger than the plane strain crack-tip plastic zone size. As such the effective crack length 2a = 2ao + 2rjy would be effectively equal to the initial (or physical) size of the crack 2ao. The load-displacement trace would be essentially hnear up to the point at which the specimen fractures abruptly (see Fig. 4.5a). The plane strain fracture toughness Kic can be computed directly from the maximum load Pmax or stress a ax i e., the load or stress at fracture) and the initial crack size ao using Eqn. (4.7). 

The essence of Krafft s model involves the relationship between the onset of crack growth with that of plastic flow instability in these tensile ligaments ahead of the crack tip. Assuming that the strains within the crack tip plastic zone are constrained by the surrounding elastic material, the strain inside the plastic zone would follow a singularity as dictated by the surrounding elastic stress-strain field namely,... 

Nair and Tien [91] explained the effects of yield strength on Kiscc through hydrogen-induced fracture resulting from the plastic flow on a localized scale in the crack tip plastic zone. The suggested cause of SCC was isolated and unstable local fracture events in the crack plastic zone controlled by the local embrittlement due to adsorbed hydrogen [92]. 

It is commonly assumed that the size of the plastic zone in the crack plane and in the direction perpendicular to crack length is of the same size 1. The size scale I of the crack tip plastic zone relative to specimen dimensions B, D) and crack length (2a) is used to rank failure modes (82) and can be used to describe the displacement of the state of stress from the reference state of plane strain. 

It is clear from Eq. (6.30) that to compare the toughness of two materials of different composition at an equivalent state of stress, the comparison must be done at the same value of the scale factor. It has been shown that the addition of a secondary phase into these polypropylene matrices does not affect the most conservative, plane strain value of Gic, significantly (84). The observed changes in the measured toughness were ascribed to the changes in the scale factor / representing the increase of the crack tip plastic zone size, controlled by a reduction in the material yield strength, Oy. This appears to occur in other filled thermoplastic materials as well (13). 

A key development in fracture mechanics was the analysis of the stress field at a crack tip (45). If Oys is the material s yield strength and Vy the crack-tip plastic zone radius (see Figure 11.23),... 

Crack Tip Plastic Zone EflFect on Fatigue Crack Propagation... 

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