An infinite plane loaded by a rivet of a different material

K. C. Ho, Kam Tim Chau

Research output: Journal article publicationJournal articleAcademic researchpeer-review

25 Citations (Scopus)

Abstract

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 ζ = μ2/μ1(μ1and μ2are the shear moduli for the plane and rivet, respectively) and the frictional coefficient μ between the plane and rivet; conversely, the shear contact stress increases with both μ and ζ. 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 ζ. Larger values of ζ and μ 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 on 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 (π > |θ| > θ1) and a tension zone (θ1> |θ| > 0) in hoop stress are observed, where θ is measured from the direction of the resultant rivet force and the typical value of θ1is about 160°. For the case of a rigid rivet with high friction, a second compressive zone near θ = 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].
Original languageEnglish
Pages (from-to)2477-2496
Number of pages20
JournalInternational Journal of Solids and Structures
Volume34
Issue number19
DOIs
Publication statusPublished - 1 Jan 1997

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this