13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- the response of the structure to cyclic loading changes significantly, due to the synergistic interaction of plasticity and creep. A structure subjected to cyclic loading with creep dwell period can present different asymptotic behaviours [2]: 1) no stress relaxation is taking place, as the accumulation of creep strain is determined by the steady-state primary load; 2) with a cyclically enhanced creep during dwell time, the stress relaxation process introduces an additional residual stresses field to enhance the total strain range, causing more significant creep and fatigue damages. In the asymptotic behaviour 2), a closed hysteresis loop could be generated if the creep dwell period is limited and the introducing creep strain could be recovered by the plastic strain during the unloading process. In order to predict lifetime of component under high temperature and creep fatigue conditions, an evaluation of steady state cyclic behaviour of structures under such conditions would be necessary to construct a hysteresis loop. The simplified methods in R5 [1] assessment procedure for the high temperature response of structures are less restrictive than those based on elastic solutions, without requiring the complexity of full inelastic computation. These simplified approaches use reference stress and shakedown concepts and inevitably incorporate conservatism. Another method is to perform incremental step-by-step Finite Element Analysis (FEA). However, to achieving the steady state response of structures subject to cyclic loading, it requires a significantly large number of increments in full step-by-step analysis which becomes computationally expensive. Therefore, direct methods have been developed to assess the stabilised response of structures subject to cyclic loading. The Direct Cyclic Analysis (DCA) [3] has been recently incorporated into Abaqus [4] to evaluate the stabilized cyclic behaviour directly. This method uses a combination of Fourier series and time integration of the nonlinear material behaviour to obtain the stabilized cyclic response of the structure iteratively. Due to the characteristic of DCA and the inevitable numerical error due to the approximation and convergence problem, the DCA may not always be able to provide accurate solutions for complicated engineering problems. In this paper, a novel direct method, the Linear Matching Method (LMM) [5, 6], is adopted for the direct evaluation of steady state cyclic behaviour of structures subjected to high temperature – creep fatigue conditions. The basis of the LMM is through the simple idea of representing histories of stress and inelastic strain as the solution of a linear problem where the linear moduli are allowed to vary both spatially and in time. In this way, the LMM combines both the convenience and efficiency of rule based methods [1] and the accuracy of simulation techniques. The LMM has been implemented into ABAQUS for all stages of life assessment code R5 [1] for the evaluation of high temperature responses of structures, based upon the same fundamental assumptions and materials database as R5 but with significantly greater accuracy. Typical of cyclic problems considered includes shakedown and limit analysis [7], ratchet limit analysis [8], creep rupture analysis [9], creep and fatigue interaction [5, 6]. The LMM ABAQUS user subroutines have been consolidated by the R5 research programme [10] of EDF energy to the commercial standard, and are counted to be the method most amenable to practical engineering applications involving complicated thermomechanical load history. In this paper, the latest extension of the LMM [6] is summarised for directly predicting the steady state cyclic behaviour of component subjected to cyclic thermal and mechanical loads with creep effects. The efficiency and effectiveness of the method was validated in [6] through benchmark examples of Bree problem and a holed plate. In this paper, the developed method is further applied to more practical engineering applications, where two types of weldments subjected to different reverse bending moments with various creep dwell periods are simulated by the proposed method considering a Ramberg-Osgood model for plastic strains under saturated cyclic conditions and a power-law model in “time hardening” form for creep strains during the dwell period. The obtained
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