Crack initiation calculation, cycle number

Fig. 9 Changes in the crack initiation times and crack depths in an epoxy resin as a function of the amplitude of the imposed cyclic displacement, a Number of cycles to the initiation of the primary cracks at the edge of the contact zone, b Measured depths of the primary cracks at various number of cycles and displacement amplitudes. Circles 103 cycles, solid diamonds 5 x 103 cycles, squares 5 x 104 cycles, c Calculated values of the maximum tensile stress at the edge of the contact using Hamilton (gross slip condition) or Mindlin—Cattaneo (partial slip condition) theories. The two curves correspond to calculations using the initial (/x = 1.0) and the steady-state (/x = 1.5) values of the coefficient of friction. PSR Partial slip regime, MR mixed regime, GSR gross slip regime...

As for the epoxy polymers, a quantitative comparison of the contact fatigue behaviour was attempted on the basis of an estimate of the maximum tensile stress at the edge of the contact. The coefficient of friction of the copolymers increased as the tests proceeded, with a variation which was dependent upon the level of the normal loading. As a first approach, the value of //. at crack initiation was taken into account in the calculation of a . The results are reported in a S-N fatigue diagram giving the maximum applied tensile stress as a function of the number of cycles to crack initiation (Fig. 23). These data show a marked increase in the contact fatigue resistance of the GIM copolymers compared with the MIM material. 

This equation corresponds to Archard s law with = l/ crit- The wear coefficient in this case represents the inverse of the critical number of asperity contacts that lead to fracture by fatigue. At each passage of an asperity the subsurface crack grows by an increment until it reaches a critical size at which fracture occurs. The quantity Merit can be associated to the number of cycles leading to fracture in a common fatigue test. Many parameters affect the value of Mj in a wear test and it is not possible to calculate it from first principles. For the model structure shown in Figure 10.19, the critical number of cycles can be brought in relation with the number of inclusions or precipitates that act as crack initiation sites [10]. 

It was assumed that in the weld there is an elliptic surface crack with a ratio of half length to depth (d/C) = 2/3, with C = 0.25, So = 4 mm (So is the thickness of the pipe wall. So = 16 mm), and the crack length 2d = 5.3 mm. The calculations have shown that the initial crack becomes a through crack for do = 0.46 mm after 2 100 cycles of reactor start-up and shutdown. As the expected number of such cycles for BN-800 is < 300, a depressurization of the pressure pipe is... 

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