This paper presents a model for the prediction of the residual stress distribution during and after fatigue. Finite element software is used for incorporating cyclic plasticity into the calculations. A simplified inelastic analysis was applied. Its essential feature consists of the introduction of a group of internal parameters that characterize local inelastic mechanisms and a group of transformed internal parameters that are linearly linked to the previous ones through a symmetrical non-negative matrix. With this approach, the treatment of the local plastic yield conditions can be made easily from simple elastic analysis. This method was applied on two quenched and tempered alloy steels: shot-peened 35NCD16 (nominal 0.32 to 0.39 C, 0.30 to 0.6 Mn, 0.1 to 0.4 Si, 1.0 to 2 Cr, 3.6 to 4.1 Ni, 0.25 to 0.45 Mo) grade steel and ground 42CD4 grade steel (UNS G41420). The influence of different parameters of fatigue testing are studied, including the number of cycles and applied stress. The computed values of relaxed residual stress distributions were compared with experimental results obtained by X-ray diffraction measurements.

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SUMMARYThis paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several kinds of implementation, using various numerical techniques, are proposed. Validations of these implementations and comparisons between them are investigated by means of a set of simple but comprehensive examples.

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