Friction Boundary Conditions Research Articles

Transparent sapphire tools

Abstract The friction conditions and stress distributions in metal-shaping operations can be evaluated using sapphire tooling materials that are transparent and exhibit photoelasticity effects. These techniques have been used in metal cutting and forming to quantify the friction and normal stress boundary conditions. The consequences for controlling a manufacturing system are that the basic process (equivalent to the plant in a control loop) is easier to characterize and several appropriate operating parameters can be calculated a priori. For example, the evaluations of the stress boundary conditions in cutting allow choosing the speed-feed combination to minimize the liklihood of brittle fracture of ceramic tools.

Lubricant Modeling and Its Effect on Simulation of Material Forming

Solid cylinder upsetting is analyzed using three different approaches for frictional boundary condition modeling. These are (1) constant shear friction factor, (2) experimentally measured frictional stresses, and (3) analytical models accounting for lubricant entrapment and redistribution. All three approaches are implemented in the CFORM finite element code. The error between the three approaches and actual experimental measurements of the material deformation and interfacial pressures is investigated. It is shown that the constant shear friction factor is more accurate for solid film lubricants than for liquid lubricants. However, the calculations indicate that if accurate prediction of near net shape forming processes is to become a reality, improvements need to be made in the characterization of frictional boundary conditions. New theoretical developments applicable to arbitrary shapes and more accurate than the constant shear friction factor approach are needed.

Rigid-plastic finite element analysis of three-dimensional forging by considering friction on continuous curved dies with initial guess generation

A three-dimensional finite element analysis of forging of blocks with continuous curved dies is carried out on the basis of a rigid-plastic material model. A method of imposing velocity boundary conditions on a three-dimensionally curved surface is proposed using a skew boundary condition. The frictional boundary condition is considered on a continuous curved surface. The initial velocity field is generated by introducing the assumption of linear viscous material. Forging of square blocks with hemispherical punches of various radii is simulated. Experiments are carried out to check the validity of the formulation. The comparison between computation and experiment shows good agreements in forging load as well as in deformed configuration.

Laminated Orthotropic Plates under Subdifferential Boundary Conditions. A Variational‐Hemivariational Inequality Approach

AbstractThis paper deals with an orthotropic laminated plate concerning the delamination problem. A nonmonotone multivalued law simulates the mechanical behaviour of the binding material. This law is written in terms of a generalized gradient (in the sense of F. H. Clarke) of an appropriately defined nonconvex superpotential. Moreover, monotone, e.g. frictional slipallowing boundary conditions of subdifferential type are assumed to hold, which are obtained from a convex superpotential through subdifferentiation. The problem is formulated as a variational‐hemivariational inequality which physically expresses the principle of virtual work in inequality form. The existence and the approximation of the solution of this inequality is discussed by an appropriate combination of compactness, monotonicity and average value arguments.

On the solution of the unilateral contact frictional problem for general static loading conditions

In the present paper the analysis of the unilateral contact frictional problem between elastic bodies, for general static loading conditions is considered. The finite element method is used for the discretization of the problem. The method proposed for the solution of the problem is based on the solution of a series of problems of ‘holonomic’ character. The development of the method is based on a special formulation of the unilateral contact frictional boundary conditions. A detailed investigation of the existence and uniqueness of the solution of the ‘single-node’ problem is carried out. Representative numerical examples demonstrate the applicability and convergence of the method.

Further Analysis of Axisymmetric Upsetting

Analytical modeling of deformation processing methods requires a thorough understanding of the die–billet interfacial conditions, in particular, the nature of frictional boundary conditions. In order to gain insight into the role of friction on the deformation behavior of metals under uniaxial compression, a series of carefully controlled experiments were made with 6061-T6 aluminum cylinder and ring specimens. From measurements of the change in internal diameter and the height of the ring specimens, the average friction coefficient can be found using the calibration method proposed by Male and Cockcroft. Using this friction coefficient, a series of finite element analyses were made to model the deformation of solid aluminum cylinders which were compressed under identical die–billet contact conditions. An updated Lagrangian formulation and the contact surface algorithm of the ADINA finite element code were used in the analysis. Comparison of the experimental findings with those of the finite element analysis shows some discrepancies; possible causes for these differences are identified.

A general matrix operator for linear boundary value problems in slip‐line field theory

AbstractA general matrix operator is established for solving linear boundary value problems in slip‐line field theory. The operator will enable a wider class of problems to be solved than were previously possible with the matrix slip‐line field technique. As an illustration, a range of solutions are generated involving the previously intractable Coulomb friction boundary condition.

Study on the Frictional Boundary Conditions at the Edge of a Tool-Material Interface in Massive Forming : 2nd Report, Confinement of Lubricant and Durability of Lubrication

Study on the Frictional Boundary Conditions at the Edge of a Tool-Material Interface in Massive Forming : 2nd Report, Confinement of Lubricant and Durability of Lubrication

An Analytical Rolling Model Including Through Thickness Shear Stress Distributions

An extension of the slab method of analysis as applied to rolling is presented. The von Mises yield criterion, including shear stresses, is written in terms of the frictional boundary condition at the roll-metal interface. Utilizing simplifying assumptions, an expression results which can then be combined with the equilibrium equations so that analytical expressions for roll force, torque, and extrusion ratio result. Whereas the concept is based on the same physical principles inherent in Orowan’s analysis of rolling, the slab method of analysis used here is less rigorous but has the advantage that analytic expressions are obtainable. Therefore, the equations are applicable for mill control purposes. Furthermore, the analytic expressions can be inverted so that estimates of friction and flow stress may be obtained by roll force and extrusion ratio measurements. In hot rolling, the temperature of the sheet may then be inferred from this value of flow stress, if the material’s flow stress is a known function of temperature and strain rate. Thus, this provides the capability to eventually control sheet temperatures and lubrication conditions by adjusting coolant sprays. Theoretical verification is discussed by comparison with Orowan’s theory and finite element analysis. Accuracy is discussed in terms of hot continuous mill and laboratory reversing mill data.

Study on the Frictional Boundary Conditions at the Edge of a Tool-material Interface in Massive Forming : Prediction of the Deformation Characteristics by Slip-line Field Method and the Friction Testing Apparatus for Plane Strain Forging

The influence of geometrical contact conditions at the edge of a tool-material interface on the frictional shearing stress in massive forming was investigated. The contact conditions were classified into three types : a) the die-surface extends beyond the edge of the workpiece, Edge-EI ; b) the workpiece-surface extends beyond the edge of the die, Edge-EII ; and c) the die and the workpiece surface continuously contact into each other at the edge, Edge-EIII. Based on slip-line or upper-bound analysis of the deformation, characteristics of the deformation and the frictional slip near the edges were shown. A frictional testing apparatus for the plane strain forging which measures the normal and frictional forces operating on a referring frictional plane between edges was made. By using this apparatus, aluminum blanks were forged at slow speed : 1 mm/min. It was shown that the frictional shearing stress was critically affected by the contact conditions.

Study on the Frictional Boundary Conditions at the Edge of Tool-Material Interface in Massive Forming : Prediction of the Deformation Characteristics by Slipe-Line Field Method and the Friction Testing Apparatus for Plane Strain Forging

型と材料の接触界面の幾何学的端末条件を3分類し, その近傍域の変形や摩擦すべりの特徴をすべり線場界を用いて子細に検討する. 次に, その特徴が実際どの程度界面の潤滑条件に影響するかを知る目的で摩擦面に働く垂直力と摩擦力を推測しうる二次元鍛造摩擦試験機を試作し, 二, 三の予備実験を行った. その結果, 接触界面全域に一方向摩擦すべりが生ずる非定常鍛造加工で, 端末条件の影響が顕著に現れ, その定量評価が可能となった.

Determination of stress within ZIRCALOY cladding due to pellet-cladding interaction

A precise calculation of the stress distribution within the Zircaloy cladding of a water-cooled reactor fuel rod subjected to a power increase is a complex problem which, in general, requires a computer code to integrate the behaviour of both the fuel and cladding. This paper develops a simplified model which decouples the clad and fuel pellet analyses, by considering two extremes of fuel pellet mechanical behaviour, which lead to two widely different boundary conditions at the pellet-clad interface. An axisymmetric fuel rod code can be used to give the mean cladding hoop strain imposed by the thermal expansion of the pellet, and when the interfacial friction coefficient is ⩽ 0.5, this information along with the frictional boundary condition can be used to determine the stress distribution within the cladding near a fuel pellet crack. Results from this simplified approach, which does not involve an integrated code, are used to study the growth of stress corrosion cracks within the cladding.

Superpotential flow problems and application to metal forming processes with friction boundary conditions

Superpotential flow problems and application to metal forming processes with friction boundary conditions

A Variational Inequality Approach to the Friction Problem of Structures with Convex Strain Energy Density and Application to the Frictional Unilateral Contact Problem

ABSTRACT The analysis of structures with friction boundary conditions is considered. The stress-strain relations are generally monotone nonlinear allowing for jump, locking, and slacking effects, and are derived from a convex strain energy density by “subdifferentiation.” It is proved that for the considered boundary value problem the principles of virtual and of complementary virtual work hold in an inequality form which constitutes a variational inequality. The theorems of minimum potential and complementary energy are proved to be valid for this type of boundary conditions. These theorems are used to formulate the analysis as a nonlinear programming problem. A numerical example concerning the calculation of a structure having friction boundary conditions combined with unilateral contact boundary conditions illustrates the theory.

A nonlinear programming approach to the unilateral contact-, and friction-boundary value problem in the theory of elasticity

In the present paper the elastic analysis of structures with “unilateral contact” — and “friction” — boundary conditions is considered. It is proved that the considered inequality boundary value problems can be formulated equivalently as variational inequalities, which permit the derivation of the theorems of minimum potential and complementary energy, to account for this type of boundary conditions. These minimum theorems are used to formulate the analysis as a nonlinear programming problem. Numerical examples on structures with coupled unilateral contact- and friction-boundary conditions illustrate the theory.

On the plane-strain compression of a rigid-plastic material, with an entrapped viscous lubricant on the platen face

Results are presented from an analysis of the plane-strain compression of a rigid-plastic non-hardening material between flat platens, with frictional boundary conditions approximating to those in existence when a viscous lubricant is entrapped on the specimen-platen interface. The results are used to show the inadequacy of the mean coefficient of friction, as a boundary condition, in the analysis of fluid-lubricated metalworking processes.

Estimation of dynamic forces in high-speed compression using a free-flight impact forging device

Explicit solutions are obtained for the dynamic die loads generated during high-speed plane strain and axisymmetric compression with a free-flight impact forging device in mind. The influences of both axial and radial inertial forces are included and the die loads are evaluated for zero, full sticking, intermediate and mixed frictional boundary conditions. The manner in which inertial effects operate is exemplified for a range of impact velocities and interface frictional conditions.The onset of appreciable inertial effects can be easily assessed by considering the final dimensionless forging loads, i.e. ωF=1[1+(∞h3f)]for plane strain and ωF=1[1+(∞h3f)]for axial symmetry. A comparison is drawn between three types of impact forming devices on the basis of the effect of inertia on the die loads in a “real” forging operation.

A note on the frictional boundary condition at the earth's surface in relation to a model of the general atmospheric circulation

AbstractIn a paper by Davies and Oakes (1962) concerning the problem of formulating a model of the general atmospheric circulation, the boundary condition used at the surface of the earth involved the assumption that the surface meridional, zonal, and vertical velocities are zero. In this note the effect on the model is evaluated by using as boundary condition at the earth's surface the more realistic assumption that the Reynolds stress is proportional to the first power of the surface wind speed.

Closure to “Discussion of ‘Frictional Boundary Conditions in Plastic Compression’” (1963, ASME J. Eng. Ind., 85, p. 76)

Closure to “Discussion of ‘Frictional Boundary Conditions in Plastic Compression’” (1963, ASME J. Eng. Ind., 85, p. 76)

Frictional Boundary Conditions in Plastic Compression

Distributions of normal stress, shear stress, and coefficient of friction were determined at the interface between a steel tool and a plastically deforming aluminum disk, using two pressure-sensitive pins imbedded in the tool. Comparisons were made with the normal-stress predictions of plasticity analyses, assuming constant shear stress or friction coefficient across the interface. Agreement was improved by considering actual variations in shear stress from lubricant-film deterioration but interesting and unpredicted features were still encountered. The course of liquid-lubricant breakdown was modified significantly by compression with periodic cycles of loading and unloading which resulted in lower friction stress for reactive lubricants, such as fatty acids, and in higher friction stress for inert lubricants, such as mineral oil.