13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Figure 4. Initial total reference stress 330MPa (a) , the changing of residual reference stress with total reference stress (b) The relationship between total reference stress relaxation with different . 4. Prediction of crack initiation In this section crack initiation will be examined for two different cases. (1) Relaxation of a residual stress in the absence of any external stress. This represents stress relief cracking situations. (2) Relaxation in the presence of a superimposed applied stress. This simulates crack initiation for combined residual and applied stresses. 4.1 Prediction of crack initiation for residual stress alone By combining Eqs 12 and 17 together with the creep deformation and crack initiation properties listed in Table. 1, the predicted time to crack initiation for a three bar system for state 1 is given by /( 1) 1 1 1 0 0 1 1 ( 1) ( ) 1 it f n Rs n Spec Z n DEt dt C (22) Equation 22 is solved numerically to obtain the initiation time. Predicted creep crack initiation times are shown in Fig 5, for initial residual stresses ranging from 75MPa to 400MPa. Figure 5. The prediction of crack initiation time with different initial reference residual stress, (a) illustrating the mean, upper and lower bound value (b) with different EFU factor with mean value. Z2=10 Time (h) 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 Stress (MPa) 0 50 100 150 200 250 300 350 Total reference stress, Z1=10 Residual reference stress Total reference stress, Z2=3.5 Z2=3.5 Z1=10 Change point (a) (b) Time (h) 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 Normalized total reference stress .2 .4 .6 .8 1.0 Stress relaxation with Z2=3.5 Stress relaxaiton with Z1=10 Initial total reference stress, 330MPa Total Total 0.5, Z change at 0.5 0.25, Z change at 0.75 Total 0.75 Total 0.5 Initial reference residual stress (MPa) 50 100 150 200 250 300 350 400 450 Time for 0.2mm Crack Growth (h) 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 LC test data Fitted line Mean, Z=1 LB, Z=1 UB, Z=1 (a) Initial reference residual stress (MPa) 50 100 150 200 250 300 350 400 450 Time for 0.2mm Crack Growth (h) 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 LC test data Fitted line Mean, Z=1 Mean, Z=3.5 Mean, Z=10 (b)
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