Abstract
Three-dimensional photoelasticity was employed to study a cylinder in contact with a half-space. Both bodies were modeled in epoxy resin. Three loading cases were examined, namely, the cylinder lying on its side subject to a load normal to the plane, the cylinder on its side subject to both normal and tangential loads and the cylinder standing on its end and subject to a normal compressive load, i.e., as a circular punch. The cylinders and the half-space, which was represented by a large block, were stress frozen with a known coefficient of friction and using relatively small loads so that the strain levels were low. After slicing the cylinders, which resulted in lower fringe orders than could be readily analyzed manually, an automated system based on phase stepping was used to record and process the data. Distributions of maximum shear stress and Cartesian shear stress were obtained for a large area of the slice. Stress separation was performed, using the shear difference method, to obtain the Cartesian stress components in the plane of symmetry of the half-space. These results provide confirmation, by experiment, of the theoretical and numerical models of this type of contact obtained by other investigators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a :
-
contact half-width
- c :
-
half-width of the stuck region
- d :
-
distance from center of stuck region to center of contact
- l :
-
lenght of contact
- p(x), q(x) :
-
distribution of the normal and tangential surface tractions within the contact region
- p o :
-
maximum of the normal traction distribution
- r :
-
radius of punch for axisymmetric case
- x :
-
normalized distance,x′/a
- x′ :
-
distance along the contact perpendicular to the axis of the cylinder
- y :
-
normalized distance,y′/a
- y′ :
-
distance perpendicular to the contact plane
- E :
-
Young's modulus
- E * :
-
composite Young's modulus
- P :
-
normal load
- Q :
-
tangential load
- R :
-
radius of curvature of a body
- μ:
-
coefficient of static friction
- σ:
-
direct stress
- τ:
-
shear stress
- τmax :
-
maximum shear stress, (σ1-σ2)/2
- 1,2:
-
principal components
- x,y :
-
Cartesian components
References
Johnson, K.L., Contact Mechanics, Cambridge University Press, Cambridge (1994).
Fessler, H. andOllerton, E., “Contact Stress s in Toroids under Radial Loads,”British J. Appl. Phys.,8,387–393 (1957).
Haines, D.J. andOllerton, E., “Contact Stress Distributions on Elliptical Contact Surfaces Subjected to Radial and Tangential Forces,”Proc. IMechE,177 (4),95–114 (1963).
Leibensperger, R.L. andBrittain, T.M., “Shear Stress below Asperities in Hertzian Contact as Measured by Photoelasticity,”Trans. ASME, J. Lubrication Tech.,93,277–286 (1973).
Shukla, A. andNigam, H., “A Numerical-experimental Analysis of the Contact Stress Problem,”J. Strain Analysis,20 (4),241–245 (1985).
Shih, C.W., Schlein, W.S. andLi, J.C.M., “Photoelastic and Finite Element Analysis of Different Size Spheres in Contact,”J. Mat. Res.,7 (4),1011–1017 (1992).
Haake, S.J., Wang, Z.F. and Patterson, E.A., “3D Separation of Stresses—40 Years On,” Proc. SEM Spring Conf., Grand Rapids, MI, June 12–14, 183–190 (1995).
Fessler, H. andFricker, D.C., “Friction in Femoral Prosthesis and Photoelastic Model Cone Taper Joints,”Proc. IMechE, Part H,203,1–41 (1989).
Fessler, H. andJobson, P.K., “Stresses in a Bottoming Stud Assembly with Chamfers at the Ends of Threads,”J. Strain Analysis,18 (1),1151–1156 (1974).
Carter, F.W., “On the Action of a Locomotive Driving Wheel,”Proc. Royal Soc.,A112,151–157 (1926).
Poritski, H., “Stresses and Deflections of Cylindrical Bodies in Contact with Application to Contact of Gears and of Locomotive Wheels,”Trans. ASME, J. Applied Mech.,72,191–201 (1950).
M'Ewen, E., “Stresses in Elastic Cylinders in Contact along a Generatrix (Including the Effect of Tangential Friction),”Philosophical Magazine,40,454–459 (1949).
Smith, J.O. andLiu, C.K., “Stresses Due to Tangential and Normal Loads on an Elastic Solid with Application to Some Contact Stress Problems,”Trans. ASME, J. Applied Mech.,75,157–166 (1953).
Hills, D.A., Nowell, D. andSackfield, A., Mechanics of Elastic Contacts, Butterworth Heinemann, Oxford (1993).
Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff (1953).
ESDU 85007, “Contact Phenomena III: Calculation of Individual Stress Components in Concentrated Elastic Contacts under Combined Normal and Tangential Loading” (1994).
Khadem, R. andO'Connor, J.J., “Axial Compression of an Elastic Circular Cylinder with Two Identical Elastic Half-spaces,”Int. J. Eng. Sci. 7,785–800 (1969).
Olukoko, O.A., Becker, A.A. andFenner, R.T., “Three Benchmark Examples for Frictional Contact Modelling Using Finite Element and Boundary Element Methods,”J. Strain Analysis,28 (4),293–301 (1993).
Burguete, R.L. andPatterson, E.A., “Photo-mechanical Properties of Some Birefringent Polymers around Their Glass Transition Temperatures,”Experimental Mechanics,36 (4),399–403 (1996).
Kenny, B., “The Casting of a Low Exotherm Epoxy Resin,”J. Sci. Instrum.,42,719–720 (1965).
Carazo-Alvarez, J., Haake, S.J. andPatterson, E.A., “Completely Automated Photoelastic Fringe Analysis,”Opt. Lasers Eng.,21,133–149 (1994).
Frocht, M.M., Photoelasticity, Vol. 1, John Wiley, New York (1941).
Haake, S.J., Wang, Z.F. andPatterson, E.A., “Evaluation of Full Field Automated Photoelastic Analysis Based on Phase Stepping,”Experimental Tech.,17 (6),19–25 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Burguete, R.L., Patterson, E.A. A photoelastic study of contact between a cylinder and a half-space. Experimental Mechanics 37, 314–323 (1997). https://doi.org/10.1007/BF02317424
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02317424