A theoretical development based on a simple physical model is proposed to help the designer predict high strain multi-axial fatigue behaviour. This approach hypothesises that the maximum shear strain y*, on planes driving the crack through the thickness, controls the fatigue crack propagation rate and hence the life. The direct strain E.* acting normal to the plane of y* can exert a secondary modifying influence. Experimental results from several research laboratories have been analysed in this manner with some success. NomenclatureSurface principal strain ratio ; smallerflarger Principal direct strains Principal direct stresses Poisson's ratio Equivalent Poisson's ratios Shear strain Octahedral shear strain Maximum shear strain Direct strain normal to plane of ymax Max. shear strain on plane 45" to surface; larger of y,, and yo, Direct strain normal to plane of y* Ratio applied shear strain/applied tensile strain

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The punch and bulge test provides a technique for the determination of material properties from small specimens. Although the test has been in use for a number of years, the behaviour of the specimen is not fully understood. A finite element analysis of the test has thus been undertaken and validated by comparison with results from experiments, giving good agreement for the punch force for two differing specimen materials. The finite element analysis has enabled punch force±displacement curves, von Mises stresses, equivalent plastic strains and vertical deflections for the upper and lower surfaces of the disc to be obtained.The finite element model has also been used to determine the relationship between the specimen yield stress and the punch force for elastic±perfectly plastic specimens. It is shown that a linear law applies over a 6:1 range of yield stresses and thus the punch and bulge test represents an effective method of yield stress measurement from small specimens.The effect of experimental artefacts on the punch force has been investigated through finite element analysis and physical experiment. The punch force is shown to be effectively insensitive to small uncertainties in the test fixture and experimental conditions. Yield stress results are thus not significantly influenced by experimental uncertainties.

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A test facility has been developed in which a thin walled tube can be subjected to fully reversed fatigue cycles for all biaxial stress or strain ratios. Twin loop servo-control allied to high resolution gauge length extensometry, load and pressure transducers permits stress or strain controlled testing. The rig is unique in that cyclic stress-strain hysteresis loops can be obtained for both axial and circumferential directions during a test.Results from a strain controlled series of low cycle fatigue tests on a ferritic 1Cr-Mo-V steel obeyed the Manson-Coffin relationship with the exponent being sensibly constant for all strain ratios. For a given maximum principal biaxial strain, the damaging effect increased as the strain ratio 4 increased from -1 to + 1. By comparing results from solid and hollow cylindrical specimens, geometry effects on fatigue life were revealed. Data on shakedown and cyclic softening under biaxial strain conditions were also obtained.