Thermal stress intensity factors calculation for deepest and surface points of semi-elliptical crack in cylinders under linear gradient thermal load by two dimensional weight function

摘要

In this study the steady state thermal stress problem in a thick-walled cylinder containing aninternal axial semi-elliptical crack is solved. Thermal and mechanical boundary conditions are prescribedon the inner and outer surfaces of the cylinder. Based on analytical thermal stress solutionfor short length cylinders in literatures, hoop stress is analytically derived for a cylinder subjectedto linear varying temperature on inner surface and traction free surfaces, using thermoelastic displacementpotential and biharmonic Love function. The stress intensity factors are extracted fordeepest and surface points of the semi-elliptical crack using the two dimensional Weight Functions.These weight functions can calculate stress intensity factors for any two dimensional mechanicaland thermal loads on the crack face. For the case of cylinder subjected to constant temperatureon inner surface of pressurized cylinder, the comparison between the results obtained from the twodimensional weight function and those available in the literature is presented, indicating a verygood accuracy. In industrial applications, such as an open end cylinder subjected to mechanicaland thermal load, complicated stress fields are applied on crack faces. Because of longitudinalgradient mechanical and thermal load (e.g. exponential or sinusoidal gradient), crack surface issubjected to two dimensional stress field. In fact, a nonlinear two dimensional stress field is appliedon the crack face in short cylinder, cylinder under varying loads, open-end cylinder and weldedcylinder. The two dimensional weight function can be easily used to calculate SIFs for crackedcylinder under two dimensional stress fields.