Lower critical stress intensity

A purely mechanical criterion for the existence of a critical nucleus is that Ki > Kiscc, where Ki is the Mode I loading stress intensity ratio and iscc is the (lower) critical stress intensity ratio for slow (environment-assisted) crack growth (Fig. 38). Because the stress intensity can be defined in terms of crack length (a) and stress a) as (assuming linear elastic fracture mechanics, LEFM)... 

Under conditions of SCC the crack will grow at lower stress intensities than die critical value under non-corrosive conditions, i.e. we have a lower critical stress intensity factor, which we denote by Kiscc. When Equations (7.12) (with Kiscc instead of Kic) are satisfied, Kiscc is a very useful quantity, much more generally relevant than a threshold value of nominal stress. 

The delayed failure curves for precracked specimens of hydrogenated and Cd plated (a) AISI 4340 steel without rare earths, (b) with 0.03% Ce, (c) with 0.09 and 0.17 w/o Ce, (d) with 0.08 and 0.16 w/o La are shown in fig. 18a-d. The Ce and La additions showed a dramatic improvement in the delayed failure of 4340 steel both in fracture times and lower critical stress intensity. The lower critical stress intensity represents a three-fold... 

SPS shows a lower impact strength than APS. The study of the failure and deformation behavior of SPS revealed that the breakage of SPS occurs with a slow and controlled crack growth at a much lower energy level than APS. During the deformation, many craze bands appear in the AI, while no visual evidence of crazing was observed in SPS before the break [12], The critical stress intensity factor, A ic, and the fracture energy, Gu, of SPS are smaller than those of APS. These results show that SPS is more brittle compared with APS. 

Strength also depends on the loading rate. As the loading rate is decreased, strength also decreases. This relation can be explained as follows. As the loading rate is decreased, more time is allowed for the crack to propagate. As crack velocity is decreased, the stress intensity factor is also decreased, as can be obtained from Equation 6.30. That means the critical stress intensity factor (KiJ, at which the fracture takes place, is lowered. This lower Ki, is reached at lower applied stress, which is same as the fracture strength of the material. 

The difference in sorption kinetics is held responsible for the higher critical stress intensity factor and the lower exponent n in PC, relative to PMMA. 

Another aspect to be considered is the difficulty in producing curved structures with the same fibre content as flat laboratory panels. This effect is shown in Figure 16, at the comer the laminate thickness is larger than at the flat section and fibre content is rather lower. This will affect the bending stiffness of the arm and the predicted failure load. This figure also shows the fillet, which is critical to initiation in the specimens without implanted defects. It is well known that fillets can significantly alter the load path in lap shear joints and increase the failure loads (see [1] and Figure 3 for example). If a fracture mechanics approach is to be applied this effect must be considered. Some recent studies on stress intensity factors for such cases may allow this to be addressed [22]. 

To this point, it has been assumed that failure occurs when K =T (or G=R) but, in studies of fracture, it is sometimes found that crack growth can occur at lower values of or G. Thus, kinetic effects must be included in any general formalism. There are several mechanisms that can give rise to sub-critical crack growth, but most attention has been directed to stress corrosion. This behavior has been extensively studied in silicate glasses but it can also occur in many polycrystalline ceramics. Figure 8.72 shows a typical response of ceramics to stress corrosion, with crack velocity v plotted as a function of K (or G). At low values of K, there often appears to be a threshold value of the stress intensity factor below which... 

The question arises whether there is a lower threshold for the stress intensity factor too, below which no craze can develop at all. No crack could then be initiated and stress crack formation would no longer be possible. There are indications in the literature that such a threshold value may be around a tenth of the discussed critical stress concentration factor providing an upper limit for the range of pure stress crack formation. This issue about critical local stresses and critical deformations, which must be exceeded, so that stress crack formation occurs, leads to the third group of... 

At relatively low temperature, i.e. for T < 0.5 Tf, the behavior of materials is mainly elastic and the rapture is brittle in nature. For stresses clearly less than the average breaking stress, the probabihty of destruction is nearly zero. In other words, the growth of flaws is insignificant and the stress intensity factor remains, at any point on the structure, lower than its critical value. If a high deformation speed is imposed (dc/dt > lOs ), we enter into the field of sudden dynamic rapture, which makes it possible, for example in the case of fibers or whiskers, to be free from all enviromnental influences and attain stresses approaching theoretical stress of interatomic decohesion. 

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