A multiaxial fatigue strain energy density parameter has been formulated which normalizes fatigue data obtained under a variety of mean stress levels and loading combinations. This parameter represents that proportion of the overall strain energy contributed by the stresses and strains on the critical or fracture plane. It is shown that multiaxial fatigue life data may be accurately correlated by applying this parameter to the experimental results of Inconel 718 alloy subjected to a variety of mean normal and shear stress levels, as well as to SAE 1045 steel tested under tension, torsion and simultaneous tension and torsion. NOMENCLATURE k, K = material constants Nf = number of cycles to failure or to the initiation of a 1.0 mm crack n', K' = cyclic strain hardening exponent and strength coefficient respectively R,, = average radius of a thin wall tube t = wall thickness of a thin wall tube W * = multiaxial fatigue strain energy density parameter y* = multiaxial fatigue parameter Sl = amplitude of shear strain component in the critical plane AP = axial load range S, = yield stress AT= torsion moment range AW =elastic strain energy density AWP = plastic strain energy density Ay,, = shear strain range in the critical plane Ae2, = normal strain range in the critical plane Aa,, = shear stress range in the critical plane Aa,, = normal stress range in the critical plane 4 ; = strain components in fixed coordinate system co-axial with the specimen axis E:, = amplitude of normal strain component in the critical plane v , , = effective Poisson's ratio cri. = stress components associated with the critical plane 4 = stress components in fixed coordinate system co-axial with the specimen axis vc, vp = elastic and plastic Poisson's ratios respectively =maximum absolute value of shear stress in the critical plane =maximum value of normal stress in the critical plane e2 = amplitude of normal stress component in the critical plane 6, = amplitude of shear stress component in the critical plane a; = axial cyclic fatigue strength coefficient r; = torsional cyclic fatigue strength coefficient
SUMMARYThe paper presents a solution for calculation of the surface uplift field of a semi-infinite elastic solid embedded with a pressurized elliptical crack oriented at any angle, and at any depth. The results presented are those for a uniform pressure loading on the crack face, simulating a static pressurized hydraulic fracture, but the mathematical technique developed can be extended directly to non-uniform normal loads or general shear loads in the form of a polynomial up to the third order. The result of a special case of the new solution, where the crack is penny shaped and parallel to the free surface, is compared with results from Sun's solution and from experiments which were designed and performed by the authors. The experiments involved pressurization of a penny-shaped crack in a polyurethane material which is linear elastic under low stresses, and measurement of surface deformation by holographic interferometry and Fizeau interferometry. The correspondence between theory and experiment is excellent.
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