Simple Model of Lu¨ders Behaviour in a Novel Compact Tension Specimen for Investigation of Residual Stress Effects

Abstract

Residual stress effects on defects have been investigated by the use of a novel compact tension (CT) specimen. Mild steel CT specimens have been preloaded in compression to generate a plastic zone around the notch prior to precracking. Upon unloading, the specimen contains a residual tensile stress, around the notch tip, into which a defect such as a prefatigue crack can be introduced. The effect of the residual stress on fatigue crack growth and final fracture is then investigated. Here, the uniaxial tensile behaviour of the steel used shows Piobert-Lu¨ders behaviour typical of certain ferritic pressure vessel steels. The mechanical preloading process has been modelled via a finite element (FE) analysis. The plastic deformation behaviour, taken from tensile test data, has been incorporated into the CT specimen model, first ignoring the Lu¨ders behaviour and then including it via a simple plastic model of the phenomenon. The model of Lu¨ders behaviour was tested on a FE model, of an uniaxial tensile test, before it was applied to the CT specimen. The result of this test was the generation of a realistic propagating band of plastic instability along the gauge length of the tensile specimen. Results for FE models of CT specimens, with and without the Lu¨ders behaviour, were then compared to real preloaded CT specimens. The models using only a lower yield point and ignoring Lu¨ders behaviour under predict the deformation of real specimens. The incorporation of plastic data containing an upper yield point predicts with reasonable accuracy the preloading cycle and as a result the shape of the residual stress field generated. Hardness maps have been made, by the use of scanning indentation mechanical microprobe (SIMM), of the free surface, of preloaded specimens. These maps reveal the strain profile of the surface and Lu¨ders bands emanating from the notch region are clearly visible. The FE model of the CT specimen, including Lu¨ders behaviour, shows Von Mises stress contours in a similar pattern to the Lu¨ders bands in the real specimen. Finally, some specimens were precracked, using cyclic compression, and then fractured at lower shelf temperatures (-140°C) to reveal the precrack shape; this matched the predicted shape of the maximum principal stress field responsible for driving crack growth. The lower shelf fracture toughness of preloaded specimens was found to be considerably reduced from reference toughness specimens with no preload. This suggests that the tensile residual stress was dominant over any benefit gained from warm pre-stressing the material.