Flaw size values

The decreasing value of K with decreasing flaw size for fracture of IG-11 graphite suggests that the near crack tip failure criterion would be better expressed by combining the near crack tip stress intensification estimated by K with the far field applied stress, Sfraa(Eq. 28). Using simple superposition of the stress perpendicular... 

The second approach to fracture is different in that it treats the material as a continuum rather than as an assembly of molecules. In this case it is recognised that failure initiates at microscopic defects and the strength predictions are then made on the basis of the stress system and the energy release processes around developing cracks. From the measured strength values it is possible to estimate the size of the inherent flaws which would have caused failure at this stress level. In some cases the flaw size prediction is unrealistically large but in many cases the predicted value agrees well with the size of the defects observed, or suspected to exist in the material. 

Example 2.22 A certain grade of acrylic has a Kc value of 1.6 MN and the fatigue crack growth data as shown in Fig. 2.77. If a moulding in this material is subjected to a stress cycle which varies from 0 to 15 MN/m, estimate the maximum internal flaw size which can be tolerated if the fatigue endurance is to be at least 1(P cycles. 

The relationship critical load (Pc)-ball size is less marked in the region of a large flaw. The same applies to flaw size. In fact, the value Cf has no direct bearing on Pc in equation (6.2.3). 

In (1) E is the Young s modulus, cr is the yield stress or some weighted-average value of the yield and ultimate stresses and c is the relevant flaw size. 

Plots of Gc as a function of the nominal prarticle/substrate contact area f are show in Fig. 3(a) for several values of relative humidity. TTie data were initially modeled the data with a two parameter curve fit (gc A ") for each value of relative humidity. Each fit yielded n = 0.5 to within the uncertainty of the curve fitting procedure (typically 0.1). For simplicity the curve fits in Fig. 3(a) represent one parameter least squares fits with n = 0.5, i.e., Gc A-. Since we expect Gc this dep>endence suggests that the initial flaw size is p)ropx)rtional to p>article area (c A). Interfricial flaws are exp)ected to serve as starter cracks, and may be respionsible for the particle size dependence of the shear stress required for detachment. 

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... 

As can be seen in Fig. 10 [29], the fracture toughness in poly crystalline tetragonal zirconia (TZP) and partially-stabilized zirconia (PSZ) appears to reach a maximum. This indicates a transition from flaw-size control of strength to transformation-limited strength. Ranges of fracture toughness values for zirconia composites are given by Richerson [38]. 

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