Rigid Flat Punch Research Articles

Simulation of capillary pressure hysteresis in drainage and imbibition process

This paper presents the results of a study investigating cutting response of a single worn PDC cutter with special attention on the friction on its wear flat which is badly understood in litterature. So, consider a cutter with horizontal wear flat fixed on a rotating bit with vertical axis. In order to identify frictional forces acting on the wear flat, experiments are conducted on a single worn cutter with a constant applied vertical force on a rotative sample. They show a relationship between imposed vertical load on the cutter and penetration angle α, which is related to the helicoidal movement of the tool. In the same way, the mechanical model is a flat rigid punch sliding parallely to a horizontal surface with the inclination α. The numerical finite element model uses a steady algorithm which allows, in a reference moving with the cutter, to treat the stationary problem on a fixed geometry. The previous relationship was confirmed and it was found too that the frictional mechanism is related to a deformation of elastoplastic type, so, dilatancy and contractancy are discussed using alternative elastoplastic models.

An Analytical Model of the Mechanical Behaviour of Elastic Adhesively Bonded Joints

Abstract Contact and adhesion between two elastic solids bonded by a thin elastic adhesive are considered. The peculiar case of a rigid flat cylindrical punch being adhered to an elastic layer is considered. In order to evaluate the influence of adhesive thickness on the mechanical behaviour of the bonded solids, an approximate solution of the contact problem is derived, using the Ritz method. Comparison of the analytical solution with FE calculations shows a good convergence towards the asymptotic value when the ratio of the punch radius to the layer thickness is greater than 4. Numerical simulation reveals a strong effect of the adhesive compressibility, for a thin adhesive. This effect is assessed quantitatively from a double asymptotic expansion of the analytical solution. Lastly, the rupture stress is evaluated as a function of the adhesive thickness, from the knowledge of the solution of the contact problem: the asymptotic value for a very thin adhesive is determined independently.

The punch problem for shear-index granular materials

Experimental evidence indicates that a wide range of powders and granular materials have shear-index yield conditions of the form (τ/c) n = 1 - (σ/t), where τ and σ denote the shear and normal components of stress and c, t and n are experimentally-determined positive constants that are referred to as the cohesion, tensile strength and shear index respectively. This yield function is also known as the Warren Spring equation and experimentally-determined values of the shear index n indicate that n lies between the values 1 and 2. The value n = 1 corresponds to the well-known Coulomb-Mohr yield function and previous work shows that the special value n = 2 gives the simplest theory amongst those values of n which lie in the range of physical interest. We extend the known Coulomb-Mohr solution for the indentation of a granular material by a flat rigid punch to the case of shear-index materials and we determine an associated velocity field assuming a previously proposed dilatant double-shearing theory. The results obtained are illustrated numerically and it is shown how for general values of n in the range 1 < n < 2 the theories corresponding to n = and n = 2 bound the various quantities arising in the stress and velocity fields. The proposed solution is by no means unique and an alternative solution is noted in an Appendix which although a bonafide solution of the governing equations may not arise physically.

Adhesion of a Rigid Punch to a Thin Elastic Layer

Abstract Adhesion between a rigid flat cylindrical punch and an elastic layer has been investigated. FE analysis was employed to determine the layer stiffness. Linear elastic fracture mechanics was then used to determine the energy release rate, Ga, per unit of bonded area for a circular debond propagating inwards from the edge of the punch. The calculations showed a strong effect of Poisson's ratio for thin layers, small departures from complete incompressibility causing large reductions in stiffness and hence in detachment force. Experiments were performed with an aluminum punch adhered to a rubber layer using a rubber-based adhesive. The ratio of punch radius to layer thickness was varied over the range 0.07 to 3.3. Detachment forces were measured and compared with calculated values. Reasonable agreement was obtained for thick layers but not for thin ones, possibly because of a change in the mode of failure.

Appropriate boundary conditions for FE‐modelled elastic half‐plane

AbstractThe completely adhesive contact between an FE‐modelled orthotropic half‐plane and a vertically loaded rigid flat punch is studied. Interface normal and shear‐stress distributions between the punch and half‐plane are FE‐calculated and compared for some sets of half‐plane boundary conditions frequently used in the literature for contact problems with friction. These results are compared with analytical solutions, and appropriate half‐plane boundary conditions are recommended for frictional contact problems.

Indentation of a power law creeping solid

The aim of this paper is to establish a rigorous theoretical basis for interpreting the results of hardness tests on creeping specimens. We investigate the deformation of a creeping half-space with uniaxial stress-strain behaviour ⋵ = ⋵ 0 (σ/σ 0 ) m , which is indented by a rigid punch. Both axisymmetric and plane indenters are considered. The shape of the punch is described by a general expression which includes most indenter profiles of practical importance. Two methods are used to solve the problem. The main results are found using a transformation method suggested by R. Hill. It is shown that the creep indentation problem may be reduced to a form which is independent of the geometry of the punch, and depends only on the material properties through m . The reduced problem consists of a nonlinear elastic half-space, which is indented to a unit depth by a rigid flat punch of unit radius (in the axisymmetric case), or unit semi-width (in the plane case). Exact solutions are given for m = 1 and m = ∞. For m between these two limits, the reduced problem has been solved using the finite element method. The results enable the load on the indenter and the contact radius to be calculated in terms of the indentation depth and rate of penetration. The stress, strain and displacement fields in the half-space may also be deduced. The accuracy of the solution is demonstrated by comparing the results with full-field finite element calculations. The predictions of the theory are shown to be consistent with experimental observations of hardness tests on creeping materials reported in the literature.

Rigid Punch on Stressed Orthotropic Half-Plane With Partial Slip

An orthotropic half-plane carrying a transverse uniaxial stress and loaded perpendicularly on the free edge by a rigid flat punch is considered. Governing integral equations are stated for the unknown contact stresses between the punch and the half-plane. An analytical solution for contact with complete adhesion and a numerical solution with limiting friction, according to the Coulomb friction law, are presented. Besides distributions of contact stresses the numerical results show relations between vertical load, applied uniform foundation stress, coefficient of Coulomb friction, and size of the slip region.

Three-Dimensional Analysis of Ice Sheet Indentation: Lower-Bound Solutions

The methods of plastic limit analysis are used to determine the indentation pressures of a flat rigid punch on a columnar ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Representative strength parameters of columnar sea ice are used to define anisotropic yield criteria for the ice sheet. The anisotropic yield criteria reflect the variations in mechanical properties caused by the horizontal orientation of the c-axis of sea ice in the columnar zone. Numerical results are obtained by applying the lower-bound theorem of plastic limit analysis. A three-dimensional stress field is optimized for a given ice condition for various indentor sizes. The effects of varying the aspect ratio (defined as the ratio of indentor width to ice thickness) are then addressed. A comparison of results for intermediate aspect ratios to results for extremely high (plane stress) and extremely low (plane strain) aspect ratios is presented. It is found that the transition from plane stress to plane strain is governed by the tensile strength of the ice medium.

Heat Conduction Through a Flat Punch

An elastic half plane is indented by a perfectly conducting rigid flat punch, which is maintained at a different temperature from the half plane. It is found that, depending on the magnitude and direction of the total heat flux, one of the following states occurs: separation at the punch corners, perfect thermal contact throughout the punch face, or an imperfect contact region at the center with adjacent perfect contact regions.

A thermal elastohydrodynamic analysis of flats

A thermal Reynolds equation is developed for a lubricant with an exponential viscosity—temperature variation and for surface contacts with different temperatures. The equation is used to analyse the formation of a lubricant film on a flat rigid punch approaching an elastic plane. The analyses indicate that thermal effects play an important role in controlling the film thickness in such contacts.

The Application of Limit Analysis to Punch-Indentation Problems

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.