An Analysis of the Deformation of Contacting Rough Surfaces : 4th Report. Formulae for Practical Use on Deformation of Plane Joints Making the Directions of Surface Asperities Parallel to Each Other

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Contact of rough surfaces can be replaced by that between a rough surface and a rigid flat one, so that the methods of the 3rd report can be reapplied here. In this report, the factors of surface asperities (for example, slope and height of surface asperities in contact) were synthesized, and formulae for practical use on the elastic and the plastic deformation of rough surfaces in contact when the directions of surface asperities were parallel to each other were suggested. This report revealed that the variance of slope of surface asperities of surface asperities in contact is σ_<θ1>^2+ σ_<θ2>^2, where σ_<θ1>^2, σ_<θ2>^2 are variances of slope of projections respectively. As a result, the relations between the elastic and the plastic deformations δ_E,δ_S yielded by the existence of surface asperities and the normal load are as follows. δ^^-_E=a_e{(P^^-+P^^-_0)^<0.09-P^^-_0^<0.09>}, δ^^-_S={P^^-+P^^-_0)^<0.18>-P^^-_0<0.18>} where, δ^^-_E=δ_E/σ,δ^^-_S=δ_S/σ, σ: standard deviation of surface asperity in contact, P^^-=P/Ap_m, A: nominal contact area, p_m : plastic flow pressure, a_e, a_s, P^^-_0 : constants. These constants were given in this research.
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