13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- In parallel to a series of laboratory tests [4], an analysis is presented to predict creep crack initiation for different levels of elastic follow-up. We find is that the crack initiation time is sensitive to the assumed creep constants and is significantly different under different loading conditions. The effect of residual stress on the crack initiation time is dependent on ratio of the residual stress to the total stress. Overall, this study provides important insights into the assumptions adopted in structural analysis for creep crack initiation. 2. Response of the three bar system In this analysis, the response of the three bar system will be determined for a system containing an initial misfit, (state 0). The system consists of 2 outer bars (Bar 3) and an inner bar (Bar 2) connected in series to a CT specimen. A long range residual stress is introduced in state 1. State 2 corresponds to the system subjected to external loading as shown in Fig. 1. Figure 1. Parallel bars with an initial misfit subjected to an applied load. In state 1, an initial residual stress field is introduced into system through the introduction of an incompatibility misfit. The displacements in the bars due to the misfit are: 1 0 1 eff 1 2 1 eff eff 3 0 1 1 eff (1) where is the initial misfit, , and are the displacements in the CT specimen, and bars 2 and 3 respectively, , and are the stiffness for the CT specimen, and bars 2 and 3 respectively. Various ratios for the stiffness of the components are given by 2 1 K K 3 1 2K K 3 2 eff eff K K 1 2 1 1 1 eff K K K (2) The structure is then loaded through a rigid block (state 2) such that the displacement for the whole system is given by: 3 2 Sys eff F K K (3) and the displacements in the bars are given by 3K 2K sys F 0 1K State 0: Initial misfit State 1: Force equilibrium State 2: Applied load Bar 3 Bar 3 Bar 2 3K CT specimen
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