Flaw size critical

Figure 16.6 shows the general yield and fast fracture loci for a pressure-vessel steel and an aluminium alloy. The critical flaw size in the steel is =9 mm that in the aluminium alloy is =1 mm. It is easy to detect flaws of size 9 mm by ultrasonic testing, and pressure-vessel steels can thus be accurately tested non-destructively for safety -vessels with cracks larger than 9 mm would not be passed for service. Raws of 1 mm size cannot be measured so easily or accurately, and thus aluminium is less safe to use. 

If the critical flaw size for fast fracture is less than the wall thickness (t) of the vessel, then fast fracture can occur with no warning. But suppose the critical size (2a jt) is... 

Solution The first step is to calculate the critical flaw size which will cause brittle failure to occur in one cycle. This may be obtained from equation (2.100) assuming Y =. ... 

Critical flaw size predicted to cause a crack to kink out of the BN interphase, plotted against the ratio of the interfacial fracture resistance to the fracture resistance of Si3N4 (adapted from ref. [30]). 

The preceding reasons for strength reductions are a consequence of microstructural deficiencies, but even perfect microstructures, in which the critical flaw size is the same as for the unreinforced matrix material, can yield smaller strength increases from particle-induced toughening than would... 

It is most unlikely that matrix grain refinement alone can explain the high fracture strengths that have been reported. Using the reported maximum fracture strengths (o = 1100 MPa)12 and the nominal fracture toughness of alumina (A"Ic = 3.5 MPa.m1/2), the critical flaw size, (c), can be estimated from... 

Structural failure may occur when the overall structural cross-section cannot support the applied load or, when the critical flaw size ac is exceeded by preexisting discontinuity or by reaching the critical crack size through fatigue, stress corrosion cracking or creep mechanisms. Using fracture mechanics the stress at a crack tip can be calculated by a stress-intensity parameter K as,... 

The critical stress at which a material fails (q/) is therefore related to the stiffness of the material, its fracture energy or toughness and a critical flaw size q. In a foam structure, Gibson and Ashby have related failure stress of the cell wall to the foam geometry via the equation ... 

Under these circumstances, it has been shown that the apparent critical flaw size a is a linear function of the amine/epoxy ratio, changing from 32 pm to 141 pm (45). 

Whether the critical flaw size corresponds to the aggregates first formed prior to phase inversion or whether it corresponds to the inclusions is, of course, not known. Indeed, the reality of a flaw corresponding to the calculated value of... 

Fig. 2 Diameter of the critical flaw size (d = 2a, ) versus the volume of the specimen (full line) in a double logarithmic plot. The edge length of a cube having the effective volume is also shown (bold, dashed line).

Figure 10.1 Sequence of phenomena that lead to the initiation and propagation of hydrogen-induced cracks and subsequent failure in two materials [A and 6) with different fracture toughness (d = critical flaw size t, = incubation time, t, = time of failure) [2]...

The stress conditions around a cracklike discontinuity can be described by the stress intensity factor (K), which is a function of the applied load, the size of the cracklike flaw, and the material. Fracture occurs when the stress intensity factor reaches a critical level, called the critical stress intensity factor or fracture toughness (Kc). Fracture mechanics relates the applied stress at which a material fractures to the critical stress intensity factor and the critical flaw size of the material ... 

To calculate the critical flaw size (a ) useEq. (E9.13) derived from Eq. (E9.5). 

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 ... 

VI.34. Three different flaw sizes are referred to in this appendix. The reference flaw size is a postulated flaw size used for analysis purposes. The rejection flaw size is a flaw size which, if discovered during pre-service inspection, would fail to meet quality assurance requirements. The critical flaw size is that size which would potentially be unstable under design basis loading conditions. 

Figure 12.13 Bimodal flaw size distribution a narrow peaked flaw population is superposed to a wide population, (a) Relative frequency of flaw sizes (bottom) and density of critical flaw sizes (top) versus the flaw size (b) Weibull plot showing the probability function (through line)...

In a proof test, the component is loaded with a stress Op, which is higher than the design service stress a . The critical flaw size in a proof test is ac(Op) = (1/jt) (Kc/YOp). In a proof test, all components containing equal or larger sized flaws are destroyed in other words, the frequency distribution of flaws is truncated at... 

Ablation of the surface will remove the surface and reduce the diameter of the fibers. This will weaken the individual fiber but it may increase the net strength of the composite because the plasma will preferentially remove small defects in the surface of the fibers. This will increase the critical flaw size of the fibers. 

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