This is really a 'mechanics' question. For any shot-peened surface there is a residual stress system that has several components. The 'normal' stresses are those that are usually considered. There must always, however, be a shear stress system that is related to the magnitude and direction of the normal stresses.
For carburized and quenched gears another important factor is the effect of peening on the retained austenite content. Peening reduces high retained austenite levels - by transformation to martensite - which usually produces improved service performance.
