Investigation of residual stress relaxation under cyclic load

Abstract

Compressive residual stresses induced by mechanical surface treatment such as shot peening, autofretage, hole expansion, laser shock peening, and low-plasticity burnishing can be highly beneficial to fatigue resistance. Cyclic relaxation of compressive residual stress, however, reduces the benefit. An analytical model is proposed for estimation of residual stress relaxation. Parameters considered by the model include the magnitude and distribution of the residual stress, the degree of cold working required, the applied alternating and mean stresses, and the number of applied loading cycles. An elasto–plastic finite element model was used to demonstrate the model.

Introduction

Fatigue cracking normally initiates at the surface, and can be mitigated by inducing surface compressive residual stresses. The extent of mitigation depends strongly upon the residual stress magnitude and distribution. Any cyclic residual stress relaxation during component operation reduces the achievable benefits. Assessment of the effect of residual stresses and their relaxation on fatigue crack initiation and propagation then becomes an important aspect of component design and life management.

Residual stresses are those stresses existing along a cross-section of a component without applied external forces [1]. In surface treated components, the residual stresses are self-equilibrating and the profiles of the residual stress fields are dominantly dependent on the material and treatment method. Despite considerable research [2], there remains the technical challenge of understanding and accurately quantifying residual stress relaxation and redistribution under cyclic mechanical and thermal load. Mattson and Coleman [3] observed cyclic residual stress relaxation many years ago, Fig. 1. Despite partial relaxation of the compressive residual stress, they still found a beneficial effect on fatigue life. Their fatigue lives were underpredicted if residual stress relaxation wasn't taken into consideration. In practice, however, the difficulties in measuring residual stress relaxation during component operation normally impede the consideration of tracking this relaxation and assessing its effect on remaining fatigue life. Morrow and Sinclair [4] carried out some of the first research on prediction of residual stress relaxation based on mean stress relaxation observed in axial fatigue test. Following the same idea, Jhansale and Topper [5] proposed a logarithm linear relationship between mean stress relaxation against axial strain-controlled cycles. Both models ignored the stress ratio effect with respect to residual stress relaxation because the mean stresses in the axial tests were dictated by the initially applied mean strain which was held constant. Furthermore, neither model had to contend with self-equilibrating residual stress fields. In engineering, the residual stress fields are subject to a different stress ratio depending upon the location in the component. This is not the case in uniaxial mean stress testing. During component operation, the beneficial compressive residual stresses at the surface of the components are often imposed to a cyclic loading with positive mean stress. In this case, it has been found that the rate of residual stress relaxation can be drastic in the early stages of fatigue cycling. In extreme cases [6], residual stress can be relaxed entirely in the first few load cycles.

To clarify the mechanism of residual stress relaxation, Kodama [7] measured residual stress decrease on the surface of shot-peened specimens using X-ray diffraction techniques. The experimental data support the linear logarithmic decrease relationship between residual stress and load cycles only after the first cycle. Obviously, the relationship is not applicable to drastic initial residual stress reductions in the first few load cycles. From his test data (Fig. 2) it is important to note that the compressive residual stress in the first load cycle can be relaxed by more than 50%. It would not be rational to use a model that did not predict this significant relaxation in the first load cycle. Also in the model, the stress ratio effect was not exploded. This relationship was further followed up by Holzapfel et al. [8] to interpolate residual stress relaxation under thermal fatigue loading wherein both cyclic and thermally activated stress relaxation can occur.

The objectives of this study are to investigate the mechanism of residual stress relaxation and to develop an analytical model for its estimation under various applied loading parameters. The analytical stress–strain model uses the Bauschinger effect to account for initial cold work effects on residual stress relaxation. A finite element analysis (FEA) mesh with many very thin surface layers, each specified with different degrees of cold work, was developed to aid in the simulation of residual stress relaxation. The residual stress fields simulated were generated by shot peening (SP), laser shock peening (LSP) and low plasticity burnishing (LPB). The proposed analytical model is validated against the numerical FEA results. The results indicate that the analytical model is able to estimate residual stress relaxation for various applied loading parameters as well as for various surface treatments.