13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 1 0 1 1 eff 2 0 1 1 1 eff eff 3 0 1 1 eff (4) The presence of elastic follow-up in the system results in a slower stress relaxation rate when compared to classical stress relaxation. There is also additional strain accumulation in the CT specimen. As an approximation, the creep strains accumulated in the CT specimen are considered to be a scalar factor Z times the creep strain which would be accumulated in the corresponding laboratory relaxation test (at the same initial stress, dwell time and temperature). Z is called the elastic follow-up factor and is given by [5]. inc el el Z where el 1 1 1 Total ref ref E F L K (5) where is the incremental strain accumulation in specimen during creep stress relaxation; and is the change of total reference stress on the CT specimen; is the change in load on the CT specimen and is the reference length of the CT specimen. For state 1 the incremental strain accumulation is given by state-1 inc 1 3 1 2 1 2 F K F K L (6) In state 2, the strain accumulation in specimen has two different solutions. The first solution corresponds to the total reference stress on the CT specimen at any time being greater than the initial residual stress 0 Total Rs ref t ref , and state-2 state-1 inc inc ; (7) The second solution corresponds to when the total reference stress at a given time is less than the initial reference stress from the residual stress, ie: 0 Total Rs ref t ref state-2 inc 1 3 1 2 eff F K K L (8) Combining Eqs. 5-8, the solutions for Z are as follows State 1 : 1 1 1 1 1 1 eff eff Z (9) State 2: 0 Total Rs ref t ref 2 1 Z Z (10a) 0 Total Rs ref t ref 2 1 1 1 Z (10b) Equations 9 and 10 show that Z for states 1 and 2 are the same if the current total reference stresses in the CT specimen is larger than the initial reference residual stress. When the current total reference stress is smaller than the initial reference residual stress, a new solution for Z for state 2 is given by Eq. 10. Those results are based on the assumption that only the CT specimen creeps while the reminder of the structure remains elastic. Z1, Eq. 9, is independent of the initial stress and the creep deformation behavior of the CT specimen, i.e., Z is a constant geometrical value
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