Issue 33

A. Winkler et alii, Frattura ed Integrità Strutturale, 33 (2015) 262-288; DOI: 10.3221/IGF-ESIS.33.32 285   1/2    K Y a In here K is the stress intensity factor,  is the applied stress, a is the flaw size, and Y is a geometric function. Assuming 1  Y we obtain   1/2    K a From which we derive, using Kc from [48] 2 2 1 3.6 1 0.00165 1.65 50                    c c K a m mm Here the subscript c denotes “critical”. Throughout the time history, cracks initiating in the material will continue to grow until this critical size has been reached. Bearing in mind the life requirement of 5  10 5 cycles, the following equation [Crawford] can be used to estimate the size of the largest permissible flaw occurring in the volume before cyclic damage commences.         1 1 2 2 2 2 2 2               n n c i f n n a a N YC n Where 2 C is the crack growth rate from the Paris law diagram, n is the slope in a Paris law diagram, i a is the initial crack size, which we are solving for, and c a is the critical flaw size at which fracture occurs. From [48], we choose 2  C 8  10 -5 , n =23.3, and we already found c a =1.65 mm. Rearranging our equation yields         2 1 1 2 2 2 2 2         n n n n c f i YC n a N a And solving for i a (provided n  2)       2 2 1 2 2 2 2 2 1 2                     n n n n n n i c f f a a Y C N n Y C N This function assumes that our geometric function Y does not change as the crack grows. This allows us to calculate 2 i a =90 µm Based on this size we can determine by microscopic inspection, CT or other suitable technique whether or not a component will be able to survive a prescribed number of cycles from a perspective of serial production. A typical spherulite size for high quality processed polyacetal component typically ranges from 25 - 45 µm 14 . The orders of magnitude in the above calculations thus appear realistic, which in turn indicates that a prediction of whether or not the required life can be achieved bears initial plausible merit. The above approach does still not incorporate the thermal influence due to the frequency of loading. However, here factors are working in alternate directions. On the one hand, an increase in temperature will reduce the viscosity and hence the stress. This means that the change in stress intensity factor also decreases. On the other hand it is likely that the Paris parameters will shift as well. Considering the underlying fracture mechanics in play, it is likely that the amount of energy required to fracture will change in a moderate fashion while the temperature rises. Elevated temperatures will facilitate pull out, and thus the fracture energy can be expected to drop. The extent of this effect determines how temperature effects will need to be incorporated into the above approach. Clearly, the geometric function also needs further specification, rather than simply assuming it to be equal to 1. At this stage, it is important to emphasize that Irwin’s idea was intended for materials with moderate plasticity zones. The experiment just conducted is thus promising, but will need some amount of adaptation. The authors are aware of the simplifications being made regarding the behaviour, but we have done so to show the workings of the da/dN idea as a concept. 14 From the authors personal experience.