13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- follow-up factor change during total stress relaxation. The relaxation of the total reference stress for combinations of residual and applied loading is similar to Eq. 17, where 1/ 1 1 2 1 0 1 1 1 ( 1) n n Total Total ref Z AE n t where 0 Total Total Total ref t ref (19) 0 0 Rs Total ref ref 0 0 0 Total Rs Applied ref ref ref 0 0 ( ) Rs Rs Total Total ref t ref ref ref t (20) where is the normalized total reference stress, is the ratio of the initial residual to the total stress in the CT specimen. , , and are the reference total stress and residual stresses at time and 0 respectively. From Eqs. 7 to 10, the change from Z1 to Z2 occurs when . This corresponds to when the residual stress is relaxed to zero. Therefore 1 1 1 1 1 0 1 (1 ) , Z=Z ; 1 ( 1) (1 ) n n Total n ref t Z AE n (21a) 1 2 1 1 1 0 1 (1 ) , Z=Z 1 ( 1) (1 ) n n Total n ref t Z AE n (21b) Now consider a three bar structure system with properties so that the relative stiffness ratios are From Eqs 9 and 10 and . Assume an initial residual reference stress of 200MPa and subject the CT specimen to additional applied stress to give a total reference stress equal to 330MPa. For this case . The relaxation of the total and residual stresses is shown in Figure 4, again using the creep law given by Eqn 11 with creep constants given in Table 1. The change from Z1 to Z2 occurs when the total stresses relaxes to . This corresponds to a time where the residual stress relaxes to zero as shown in Figure 4a. Also Figure 4a shows that the residual stress decreases significantly due to the presence of the applied load. Now consider the case when the total reference stress is 330MPa and residual stress is such that the ratio . The stress relaxation behaviour for these two different values of is shown in Figure 4b. The solid line represents the stress relaxation path for and the dashed line represents the stress relaxation for . When the residual stress accounts for 100% of total stress and stress relaxation corresponds to . When this represents the case when there is no residual stress and the applied stress accounts for 100% of the total stress. Stress relaxation corresponds to .
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