A carbon steel ball with 25-mm diameter is pressed together with an aluminum ball with a 40-mm diameter by a force of 10 N. Determine the maximum shear stress, and the depth at which it will occur for the aluminum ball. Assume Figure 3–38, which is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. 

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[Ratio of stress to Pmax 0, T 1.0 0.8 0.6 0.4 0.2 x¹ Øy 0.5a 29 1.5a 2a Distance from contact surface Figure 3-38 2.5a 3a