390 Mechanics of Materials 2 §10.1 Stress 04 0 04P 2 b.contact semi- Oxis Tu=Ty P。mox.contact pressure Fig.10.5.Variation of stresses beneath the surface of contacting spheres. For a sphere contacting a flat surface of the same material R2=oo and E=E2=E. Substitution in egns.(10.10)and (10.16)then yields maximum compressive stress 0c=-0.62 PE2 4R子 (10.17) and relative displacement of centres P2 e=1.54 2E2R1 (10.18) For a sphere on a spherical seat of the same material 72 oe=-0.62PE2 R2-R (10.19) RR2 P2 R2-R1 with e=1.54 2E2 (10.20) R1R2」 For other,more general,loading cases the reader is referred to a list of formulae presented by Roark and Young(33). 10.1.5.Design considerations It should be evident from the preceding sections that the maximum Hertzian compressive stress is not,in itself,a valid criteria of failure for contacting members although it can be used as a valid design guide provided that more critical stress states which have a more direct influence on failure can be related directly to it.It has been shown,for example,that alternating shear stresses exist beneath the surface which are probably critical to fatigue life390 Mechanics of Materials 2 Stress $10.1 Fig. 10.5. Variation of stresses beneath the surface of contacting spheres. For a sphere contacting a flat surj-ace of the same material R2 = 00 and El = E2 = E. Substitution in eqns. (10.10) and (10.16) then yields maximum compressive stress U, = -0.62’ - /:; (10.17) and relative displacement of centres For a sphere on a spherical seat of the same material (10.18) ( 10.19) with (10.20) For other, more general, loading cases the reader is referred to a list of formuIae presented by Roark and Young(33). 10.1.5. Design considerations It should be evident from the preceding sections that the maximum Hertzian compressive stress is not, in itself, a valid criteria of failure for contacting members although it can be used as a valid design guide provided that more critical stress states which have a more direct influence on failure can be related directly to it. It has been shown, for example, that alternating shear stresses exist beneath the surface which are probably critical to fatigue life