On the accuracy of the Hertz model to describe the normal contact of soft elastic spheres (original) (raw)
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Analytical and Numerical Correlation of Hertz Contact under Elastic and Plastic Regime
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022
The contact of two bodies is found in many engineering applications. Some of the best examples are Hardness Testing, contact between ball bearings in races, Head-Disk interaction in storage devices, Impact of dust and other particles on Fan blades in a gas turbine and in Sports, especially where ball contact is dominant (like Golf, Hockey, Snooker etc.). The major characteristics of the problem are the localized deformation and the variation in the contact area with the contact force. The contact force-displacement relationship is nonlinear and high stresses are often generated. Therefore, plastic deformation is likely to occur for most engineering contact problems. This paper tries to simplify and concise the hertz contact behaviour under both Elastic and Plastic regime, which helps for better understanding in designing various contact parts.
Validation of normal and frictional contact models of spherical bodies by FEM analysis
Contact forces between two spheres are computed, including the contact pressure (normal) and the frictional stress (tangential) using a finite element method (FEM). A CAD model of a part of a sphere was developed. A mesh was created using ANSYS® Solid 186, 20-Noded hexahedral element and analyzed for its sensitivity. ANSYS® Contact 174 and Target 170, 8-Noded surface elements were used. Contact pressure and frictional stress contours were calculated by varying the displacements. Normal and Tangential contact forces were computed by integrating contact pressure and frictional stress over the contact surface. The values obtained for thenormal force were compared with the non-linear spring model as given byHertz [1]. Similarly values of the tangential force were compared with themodel of Mindlin and Deresiewicz (MD) [2]. The FEM results were found tobe in agreement with the models.
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
Journal of Applied Mechanics, 2002
An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences.
Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat
Journal of Tribology, 2006
In this paper we report the experimental investigation to evaluate the published models for the contact of a deformable sphere against a hard flat in the fully plastic contact regime. A new measurement method has been used to measure the contact area. The behavior of the mean contact pressure and the contact area as a function of the contact load are presented. Substantial differences are found between the measurements and the model predictions. A constant value of the mean contact pressure as the load increases is observed, however, the value is lower than the hardness, as often reported. The contact area is found to be a simple truncation of the sphere by a hard flat.
Finite Element based Elastic-Plastic Contact Behaviour of a Sphere against a Rigid Flat – Effect
2014
Abstract—The present study considers an elastic-plastic contact analysis of a deformable sphere with a rigid flat using finite element method. The effect of strain hardening on the contact behaviour of a non-adhesive frictionless elastic-plastic contact is analyzed using commercial finite element software ANSYS. To study the strain hardening effect we have taken different values of tangent modulus. The result of strain hardening effect clearly shows that a generalized solution can not be applicable for all kind of materials as the effect of strain hardening differently influenced the contact parameters. With the increase in the value of hardening parameter this effect also increases. For higher value of hardening parameter the effect of strain hardening is severe on contact parameters. With the increase in strain hardening the resistance to deformation of a material is increased and the material becomes capable of carrying higher amount of load in a smaller contact area. I.
Wear, 2016
The theoretical and experimental analysis described in this paper demonstrate a simple systematic procedure to determine the contact parameters between a spherical impactor and an elastic half space via impact tests. Two main contact parameters were measured at different velocities of impact, that is the time duration of contact and the maximum normal contact force. A general nonlinear contact model based on power law is used to extract the contact stiffness and frequency of contact resonance from these two main contact parameters. Experimental results were obtained and compared for three steel samples with different hardness numbers and impacted by different sphere diameters of 2.0, 2.5 and 3.5 mm to investigate the limits of elastic deformation. Effect of the used sphere diameter on the contact parameters are shown. The test results show that the adopted model using independently measured material data can predict the contact parameters due to hard sphere impact with elastic half space. The general trend shows the increase of contact stiffness with the sphere diameter but the limits of elastic regime decrease.
On the tangential contact behavior at elastic-plastic spherical contact problems
2014
The problem of tangential contact between an elastic-plastic sphere and a rigid plane is studied analytically and numerically with the specific aim to derive force-displacement relations to be used in numerical simulations of granular materials. The simulations are performed for both ideal-plastic and strain hardening materials with different yield stresses and including large deformation effects in order to draw general conclusions. The results are correlated using normalized quantities pertinent to the correlation of indentation testing experiments leading to a general description of the tangential contact problem. Explicit formulas for the normal and tangential forces are presented as a function of the tangential displacement using data that are easily available from axi-symmetric analyses of spherical contact. The proposed model shows very good agreement when compared with the FE-simulations.
Elastic–Plastic Spherical Contact Modeling Including Roughness Effects
Tribology Letters, 2010
The effect of material properties and surface roughness on the contribution of asperities and sphere bulk displacements to the total displacement of a rough spherical contact is investigated. A dimensionless transition load, above which the contribution of the bulk displacement exceeds the contribution of the asperities displacement, is found as a function of the plasticity index and dimensionless critical interference of the sphere bulk. A criterion is proposed for evaluating the importance of surface roughness in calculating the displacement of a rough spherical contact. Some experimental results with a spherical micro-contact are presented to verify the model.