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A method of analysis for finding optimum $hot peening specifications for given parts and loading conditions 1s expi~ineu. T,,c ~ e r h o d IS applied to a part with fillets ioaded in rotating bend~ng. The computed oprlmum inte7-sity 1s 9 C. Fatigue tests are reported which compare thi$ Intensity to the conventionally specified 7A. The higher intensity proved clearly superior. The great improvement in fatigue strength that can be obtained by prestress treatments such as shot peening has been known for about 50 years [ I ]. When production quantities were large enough to justiig the expense of repeated fatisue tests the treatments have been opxmized empirically. For other applications certain rules have been established that recommend or prescribe the treatment, for instance, the specification for shot peening Military Specification for Shot Peening of Metal Parts (MIL-S-13165). This paper shows a m e ~ h o d for finding optimum treaments analytically and reports tests that validated the method by comparing conventional peening to optimized peening, which was four times as heavy as the conventional treatment. Criteria and Assumptions Failures start on the surface in parts that are free of self-equilibrating stresses (called self stresses or residual stresses) and of internal defects. The surface is weaker than the interior because it is exposed to corrosion, it has some roughness, and its particles are not supported by as many neighboring particles as those on the interior. Also, and more importantly, there usually is a stress gradient, with stresses decreasing going from the surface inwards. We neglect the surface weakness and consider only the effects of the stress gradients because shot peening is not very effective in improving fatigue strength in pure axial loading, but is more effective in providing this improvement under the bending and torsion of smooth parts, and surprisingly effective for notches that have high stress gradients. Producing compressive self stresses in the skin is the main effect of mechanical prestress treatments. We neglect other effects such as changes in structure produced by peening. The compressive stresses in the skin are balanced by tensile stresses in the core. The compressive stresses increase fatigue resistance; the tensile stresses decrease it. Greater peening intensity decreases the risk of fatigue failures that start from the surface and increases the risk of fatigue 'Professor, Mechanical Engineering Department, Stanford University, Stanford, CA 94305.

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