| Popis: |
The problem treated in this paper is of interest for the analysis of coatings that consist of one or more elastic or viscoelastic layers bonded together and to a substrate. Each coating-cum-substrate (“cylinder”) is modeled as a twodimensional elastic or viscoelastic half-space consisting of layers with arbitrary thickness whose material constants differ. The cylinders are in rolling contact; friction is modeled by Coulomb's law; partial slip in the contact area is allowed. The analysis is linear. The problem is attacked by an influence function method (Green's functions). The influence functions are the displacement-stress field in the half-space due to a normal and a shearing standard loading moving over the (visco)elastic half-space with rolling velocity. They are determined by means of a complex Fourier transform, which is inverted by a method that warrants a prescribed accuracy. The two influence functions are each convoluted by a weight function. The weight functions are found with the aid of algorithms which have proved their utility in Kalker's programs CONTACT and LAAGROL, and which have been established rigorously by Kalker (1988) in the elastic case. Apart from frictionless and fully sliding contact, loadings due to partial slip in the contact may be determined; the displacement-stress field both on and inside the half-space may be computed. Up to now, an implementation has been made in which the cylinders consist of a single elastic layer bonded to a rigid base, and where only the surface load and displacement distributions are calculated (LAAGROL). The determination of the surface elastic field due to finite creepage resulting in partial slip in the contact area is the main thrust of this program. The method presented is akin to that of Bentall-Johnson (1968), but automated, modernised, and extended. |
