An infinite plane loaded by a rivet of a different material

This paper derives a closed-form solution for the stress distributions in an infinite plane loaded by a rivet of a different material under either plane stress or plane strain condition. A distinctive feature of the present analysis is that the rivet load is modelled by distributed body forces over the section of the rivet, in contrast to the commonly-used assumption of a concentrated load acting at the centre of the rivet. Two body force potentials are introduced to model the cases of conservative, uniform distributed force (Loading Case I) and non-conservative, non-uniform distributed force (Loading Case II), which is similar to those caused by shear force on a circular section. Our results show that the normal contact stress decreases with both the stiffness ratio zeta = mu(2)/mu(1) (mu(1) and mu(2) are the shear moduli for the plane and rivet, respectively) and the frictional coefficient mu between the plane and rivet; conversely, the shear contact stress increases with both mu and zeta. The normal contact stress for Loading Case I is larger than that for Loading Case II, while the opposite conclusion applies to the shear contact stress; their differences are more apparent for larger zeta. Larger values of zeta and mu result in higher maximum hoop stress and the corresponding location of maximum hoop stress deviates farther from the edge of contact zone; and the maximum hoop stress resulted from Loading Case II is larger than that induced by Loading Case I. The hoop stress at the rivet hole agrees well with experimental results by Coker and Filon [Coker, E. G. and Filon, L. N. G. (1931). A Treatise oil Photoelasticity, Cambridge University Press, Cambridge], Frocht [Frocht, M. M. (1949). Photoelasticity, Vol. 1, Wiley, NY], Nisida and Saito [Nisida, M. and Saito, H. (1966). Stress distributions in a semi-infinite plate due to a pin determined by interferometric method. Experimental Mechanics 6, 273-279] and Hyer and Liu [Hyer, M. W. and Liu, D. (1984). Stresses in pin-loaded orthotropic plates using photoelasticity. NASA contractor report, CR-172498, NASA, USA]. In general, a compression zone (pi > \theta\ > theta(1)) and a tension zone (theta(1) > \theta\ > 0) in hoop stress are observed, where theta is measured from the direction of the resultant rivet force and the typical value of theta(1) is about 160 degrees. For the case of a rigid rivet with high friction, a second compressive zone near theta = 0 is observed; this differs from all previous theoretical studies, but agrees with the experimental observation by Frocht [Frocht, M. M. (1949). Photoelasticity, vol. 1: Wiley, NY]. (C) 1997 Elsevier Science Ltd.