13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- and are the initial crack depth, width, net thickness of a CT specimen respectively. The constant given by Eq. 16 is for plane stress and a von-Mises yield criterion with . It can be shown that the change in reference stress with time for the three bar system in state 1 is given by 1/ 1 1 1 1 0 1 1 1 ( 1) n n Rs Rs ref Z AE n t where 0 Rs Rs Rs ref t ref (17) where and are the current and initial reference residual stresses respectively in the CT specimen. For a time much greater than 1 1 0 1 1 ( 1) n Rs ref t Z AE n (18) Equation 17 is approximately independent of the initial reference stress. The influence of the magnitude of initial reference stress is greatest during the early stages of the relaxation process. As an example; take an initial residual reference stress of 200MPa. Using equation 17 together with creep behavior described by equation 13, and the material constants in Table 1, the predicted residual stress relaxation using mean, upper and lower bound creep constants and different elastic follow-up factors are shown in Fig. 3. The results show that the stress relaxation behavior is sensitive to the creep constants and also significantly affected by the elastic follow-up. For Z=1, there is no strain accumulated in the specimen; therefore the total strain across the entire cross-section of specimen remains zero during the relaxation process. This is equivalent to the stress relaxation in a bolt that holds two rigid flanges together. For Z>1, there is slower stress relaxation and extra strain is accumulated in the CT specimen. Figure 3. Prediction of reference residual stress relaxation from an initial value of 200MPa (a) using mean, and upper and lower bound creep constants and Z=1, (b) with mean creep data and different values of Z. 3.2.2 Relaxation of combined residual and applied stress In state 2 the initial total reference stress (equal to residual plus applied stresses), and the elastic Time (h) 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 Referecne Residual Stress (MPa) 60 80 100 120 140 160 180 200 220 Mean, Z=1 Mean, Z=3.5 Mean, Z=10 (b) Time (h) 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 Referecne Residual Stress (MPa) 60 80 100 120 140 160 180 200 220 LB, Z=1 Mean, Z=1 UB, Z=1 (a)
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