13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Mean, lower and upper bound creep properties together with Z=1 were assumed for Fig 4a and mean creep properties and different elastic follow-up factors in Fig 4b. The results illustrate that the predictions are sensitive to the creep constants and elastic follow-up factors respectively. However, the initiation times for different constants and different Z tend to converge to similar initiation times for low initial reference stresses. 4.2 Prediction of crack initiation for combined residual and applied stress By combining Eqs. 12 and 19 with the creep properties listed in table 1, the time for crack initiation can be obtained. If the initiation time is less than t1 given by 1 1 1 1 1 0 1 (1 ) 1 ( 1) (1 ) n n Total n ref t Z AE n (23) Then the initiation time is solved from Eqn. 22. If, however, the initiation time is greater than t1 then the initiation time is obtained by solving 1 1 1 /( 1) /( 1) 1 1 1 1 0 2 1 0 1 1 1 ( 1) ( ) 1 ( 1) ( ) 1 i t t f n f n Rs n Rs n Spec Spec t t Z n DEt dt Z n DEt dt C C (24) Solutions obtained by numerically solving equations 22 and 24 are shown in Figure 6. When the system is under load control the initiation time is 91 hours. If the same system is under displacement control (ie the initial stress is entirely residual and Z2 ~1 ) the initiation time is 3132 hours. If was assumed that and therefore and . When the stress (of 330MPa) on the CT specimen arises from applied loading along then Z=3.5 and the initiation time is 659 hours. In contrast if the CT specimen is subjected to a residual stress equal to 330MPa, the Z1 =10. And the initiation time is 248 hours. The influence of different ratios of residual to total stress () are shown in Fig 6b. Applied stress conditions lie to the left hand side while conditions where residual stress conditions dominate lie on the right hand side of the horizontal scale. Figure 6. (a) The crack initiation time for initial total reference stress 330MPa under the displacement control, load control and mixed boundary control (b) the crack initiation time with different and two different reference stresses. Time (h) 1e-1 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 Stress (MPa) 100 150 200 250 300 350 LC DC Z=3.5 Z=10 Initial total referecne stress, 330MPa 91 hrs 248 hrs 659 hrs 3132 hrs , DC , LC , 1 , 0 i i i i t t t t (a) 0.0 .2 .4 .6 .8 1.0 t i (h) 0 200 400 600 800 1000 1200 1400 1600 1800 330MPa 330MPa 225MPa 225MPa 1 10 Z 1 10 Z 2 3.5 Z 2 3.5 Z Fixed parameters =0.25, =0.2 Initial total reference stresses 330MPa and 225MPa
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