Some numerical slipline field solutions for drawing through circular dies

A method is presented for the generation of slipline fields and their hodographs for the problem of plane strain drawing a rigid, perfectly plastic (rpp) material through frictionless circular dies. An optimization scheme is given, using a readily available multivariable optimization routine, which will reliably adjust the shape of an assumed slipline to ensure hodograph convergence. A number of programme runs using different geometries show some interesting oscillatory variations in the computed stress distributions along the die surface and across the exit slipline.     

Analytical modeling of work hardening of duplex steel alloys in the milling process

Severe plastic deformation in cutting operations such as milling might change mechanical properties (especially the strength and hardness) of the machined surface and its underlying layers. This phenomenon called work hardening and reduces machinability. This study presents an analytical solution to calculate the work hardening of the upper layers of the workpiece in the milling process of 2205 duplex stainless steel. In this regard, the stresses in the cutting regions are calculated to find the stress and temperature fields in the workpiece. Then the strain and strain rate values are calculated for each point of the surface and subsurface layers using the determined stress field. Finally, the Johnson-Cook material model is used to calculate flow stress and work hardening. Experimental results of the different machining conditions have been used to validate the proposed model. However, comparisons of subsurface microhardness and resultant cutting force obtained by an analytical model with experimental tests showed that the model properly predicts the amount of work hardening.

     

Shear deformation of voids with contact modelled by internal pressure

The behaviour of voids in a ductile material subject to simple shear or to a shear-dominated stress state is analyzed numerically. Here the stress triaxiality is so low that instead of void volume growth to coalescence there is void closure leading to micro-cracks that rotate in the shear field. At some stage of the deformation, the void surfaces will come in contact so that sliding with or without friction will start to occur. To avoid problems with strong mesh distortion in the large strain field around the deforming void and with mesh resolution at the tip of the crack, an internal pressure is applied as an approximate representation of void surfaces pressed together in frictionless sliding, and also remeshing is applied. This micromechanical model for a strain hardening elastic–plastic material shows that a maximum overall shear stress is reached, at which localization of plastic flow occurs, leading to final failure in the material.     

A new mechanism of plastic flow

When ductile materials are tested in simple shear, with moderate amounts of compressive stress on the shear plane, what appears to be negative strain hardening occurs at relatively large strains. These results are in apparent contradiction to the commonly held views that metals strain harden without saturation to the highest values of strain and that compressive stress on the shear plane does not influence flow stress.A new mechanism of plastic flow is presented that involves the formation and rewelding or microcracks of limited extent on shear surfaces. Possible applications of the new theory to metal cutting and geological events are briefly discussed.     

An experimental study on influences of material brittleness on chip morphology

Though several material properties such as hardness, thermal conductivity, specific heat, strain hardening, and thermal softening ability have been studied in terms of influencing segmental or serrated chip formation process, rare study about material brittleness affecting the chip formation process has been carried out. In this paper, an orthogonal cutting experiment with four steels with different brittleness was carried out. The effect of workpiece material brittleness on segmental chip formation and consequent chip morphology was investigated. The experimental results show that the material brittleness heavily affects chip formation process and chip shape. A novel chip formation model was developed to explain the mechanism of material brittleness working on the chip formation process. The mechanism is that material brittleness lowers the value of failure strain and thus makes the maximum stress in flow stress curve occur earlier, which leads to the catastrophic shear instability in primary shear zone and consequent segmented chip.     

The use of a shear instability criterion to predict local necking in sheet metal deformation

A shear instability criterion can provide a consistent approach to the onset of local necking in sheet metal forming under biaxial stretching. The neck is anticipated to initiate in the direction of pure shear when the shear stress attains some critical value. The yield function proposed by Hill is employed and the material is assumed to display only normal anisotropy. Empirically it is found that the additional material parameter required by this yield function is simply related to R, the coefficient of normal anisotropy, for a number of materials. This allows the limit strain to be predicted in terms of three well established plastic properties, viz. work hardening coefficient, coefficient of normal anisotropy and initial pre-strain. The influence of these on the limit strain curve is analysed and the coefficient of work hardening shown to play the most important role. Data available in the literature are employed in a comparison of the present theory with that due to Marciniak. In general the predicted limit strains are in reasonable agreement with the trend of experimental results for a wide range of materials. In the case of isotropic materials with work hardening coefficients in the range 0·2-0·6 predictions from the present theory are almost identical with those from that presented by Stören and Rice. The theory presented here exhibits a good correlation with experimental limit strains for materials with high work hardening coefficients, of approx. 0·4 or more. Generally, for low work hardening materials, with coefficients of 0·25 or less, the shear instability theory tends to an underestimate of limit strains and a Marciniak type of analysis may be more appropriate. However, bearing in mind the scatter of the experimental data the present theory constitutes a safe lower bound on limit strains and, in addition, has the advantage of simplicity in the mathematical calculation required.     

Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model

This paper presents an analytical method based on the unequal division shear-zone model to study the machining predictive theory. The proposed model only requires workpiece material properties and cutting conditions to predict the cutting forces during the orthogonal cutting process. In the shear zone, the material constitutive relationship is described by Johnson?CCook model, and the material characteristics such as strain rate sensitivity, strain hardening, and thermal softening are considered. The chip formation is supposed to occur mainly by shearing within the primary shear zone. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of the shear strain rate. The cutting forces are calculated for different machining conditions and flow stress data. Prediction results were compared with the orthogonal cutting test data from the available literature and found in reasonable agreement. In addition, an analysis of the deviation from experimental data for the proposed model is performed, the effects of cutting parameters and tool geometry were investigated.     

Metallic friction under near-seizure conditions

In metal-working theory extreme frictional (perfectly rough) conditions are assumed to apply when the shear stress opposing motion at the tool-work interface is equal to the shear flow stress of the work material. This is normally likened to seizure (sticking) with zero velocity at the actual interface and with plastic flow occurring in the adjacent work material. If the flow stress is assumed constant as in ideal plasticity theory, then this condition can be readily defined. However, if the flow stress is allowed to vary with, for example, strain rate and temperature, it is no longer obvious at what value of flow stress the perfectly rough condition becomes applicable. With the assumption that the velocity changes from zero at the interface to the full rigid body velocity over a narrow plastic zone of intense shear, an analysis is presented in which it is proposed that the thickness of this zone (which must be finite in a strain-rate-sensitive material) and hence the associated strain rate, temperature and flow stress are determined by a minimum work criterion. Recent results in support of this are presented from machining experiments where the flow at the tool-chip interface approximates to perfectly rough conditions. It is suggested that for steady state conditions true seizure cannot occur and a possible mechanism is given for near-seizure conditions in which the velocity at the interface, although very low, is not zero.     

Fluid-Like Properties of Chip Flow in High-Speed Metal Cutting Process

Strain rate in high-speed metal cutting is high, and properties of chip flow under high strain rate conditions are different under low cutting speed conditions. Shear stress and shear strain rate have a linear relationship; hence, the behavior of chip flow during high-speed metal cutting is more similar to fluid than to solid. Therefore, metal cutting should be analyzed by using fluid analytical method. This article investigated the fluid-like properties of chip flow during high-speed metal cutting and determined velocity, pressure, and strain rate distributions on rake face and shear plane. A speed stagnation point is located some distance from the tool tip on the rake face. The location of this point influences the life of the cutting tool and the quality of the finished surface. The pressure peaks, decreases along the rake face, and then reaches zero at some point away from the tool tip. This point represents the separation of the chip from the tool. The total stress on the shear plane is the sum of tensile stress, pressure stress, and shear stress. The strain rate is related to velocity; its value rapidly increases at the tool tip and the free surface corner and then decreases.     

基于弹塑性理论的高速铣削表面粗糙度力学建模

基于分子—机械摩擦理论,提出了已加工表面残留高度的力学模型。并根据热—弹塑性大变形理论,对材料的流动应力方程(非线性)进行了分析,推导出了材料的应变硬化、应变率和温度与切削变形应力增量的关系,研究了不同材料(45钢和3Cr2Mo模具钢)已加工表面残留高度的实验结果,分析了材料物理性能对加工表面粗糙度的影响。     

Stress analysis of the strain rate hardening materials in axially symmetric field

This paper presents an analysis of a circular hollow cylinder composed of strain rate hardening plastic material subjected to a sudden internal pressure loading. Materials satisfying the constitutive relation, and Levy-Mises equation are considered in the analysis. Dynamic and static analyses of axially symmetric material loaded under plane strain condition are described. The paper discusses the effect of strain rate hardening exponent, m, on the dynamic and static plastic response in the axially symmetric medium. A method is presented for the determination of the strain rate hardening exponent by measuring the hoop stress on the outer surface of a thin cylindrical specimen using the static solution.     

Evolution of matt surface topography in aluminium pack rolling. Part II: effect of material properties

A model has been presented in a companion paper [1] to predict the generation of roughness on the matt surface in pack rolling of aluminium foil. The model is based on the finite element method using isotropic plasticity. This model is used in the current paper to investigate the effect of material properties on the generation of surface roughness. There is a large inhomogeneity of strain during deformation, with harder grains generally deforming less than softer ones. It is found that the roughness amplitude is roughly proportional to the standard deviation of the initial grain yield stress distribution, normalised by the initial mean yield stress, so that a wider distribution of the initial yield stress results in greater surface roughness. It is shown that a suitable linear hardening law can be used to approximate the roughening behaviour for real material flow stress curves.     

Plane strain tension of thermo-elasto-viscoplastic blocks

The thermocoupled flow localization of plane strain tension blocks has been investigated. These blocks have a relatively low strain rate sensitivity and comply with an elasto-viscoplastic constitutive equation which has a viscoplastic strain rate noncoaxial with the stress tensor. Attention has been paid to deformations with a strain rate in the range of 0.02–2000/s under isothermal, conductive and adiabatic conditions. A full plane strain finite element analysis of the velocity and temperature fields has partially clarified the effects of the deformation rate, material strain rate sensitivity, thermal conductivity and size of the blocks on flow localization, including the shear band type of flow localization.     

Numerical experiments on the influence of material and other variables on plane strain continuous chip formation in metal machining

Finite element simulations of metal machining chip formation have been carried out with model materials that have been given a range of thermal softening and strain hardening behaviours. For materials that are approximately perfectly plastic, predictions of slip-line field theory regarding the dependence of chip/tool normal contact stress distribution on the combination of shear plane angle, friction angle and tool rake angle are reproduced. But it has not proved possible to generate the full range of non-unique fields predicted by slip-line theory. The introduction of strain hardening causes chips to thicken but with deviations at high hardening rates from the behaviour proposed by Oxley. These observations are generally in agreement with previously published physical test data. A study of the effect of increasing the cutting edge radius confirms the important effect of that, particularly on tool thrust forces. By continually comparing the results to expectations from more simple modelling, and asking the question ‘Is that expected?’, a general problem of creating a friction law applicable to both plastically flowing high stress conditions and to more lightly loaded elastic conditions has been recognised and is the subject of continuing work.     

Axisymmetric deformation of circular elastic-plastic tubes under axial tension and internal pressure

The axisymmetric bifurcation and post-bifurcation behaviour of circular tubes subjected to the combined action of axial tension and internal pressure are investigated numerically using the finite element method. It is assumed that the tubes are made of elastic-plastic strain hardening material with a smooth yield surface and that they deform without shear stress at both ends under the proportional stress path based on the stress values averaged over the cross-section.The bifurcation point and associated mode shape are obtained for each stress path. The initial to medium nonuniform deformation was studied for several specific stress paths and the growth of necking of the tube wall and swelling of the middle plane due to bifurcation are clarified.     

A Finite Element Study of an Elasto-Plastic Disk or Cylindrical Contact Against a Rigid Flat in Plane Stress with Bilinear Hardening

This work presents a finite element study of elasto-plastic cylindrical contact. The geometry could also be described as a vertically aligned disk whose axis of symmetry is parallel to the contact surface. The cylinder is considered to be in the plane stress state. The material of the cylinder is modeled as elasto-plastic with bilinear hardening (also known as linear hardening). Simulations for a range of material properties and deflections typical to engineering applications are carried out. A mesh convergence study has also been performed. By employing symmetry, the cylinder has been modeled as a quarter circle and a straight line is used to model the opposing rigid flat surface. The finite element results for the elastic and fully plastic cylindrical contact cases are compared to other existing models such as Hertz contact and spherical elasto-plastic models. Since the case considered is plane stress, the stress distribution is significantly different from elasto-plastic spherical contacts, which would be closer to a plane strain case. An empirical relationship is fit to the results to allow for prediction of the contact width as a function of displacement and force.     

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlat's 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.     

Hardening laws, surface roughness and biaxial tensile limit strains of sheet aluminium alloys

The roles of hardening laws and surface roughness have been assessed in the prediction of biaxial tensile limit strains of two A1 alloy sheet materials with different strain hardening characteristics namely AA6111-T4 and AA5754-O, utilizing the surface roughness model proposed by Parmar, Mellor and Chakrabarty [6]. In the work of Parmar et al., the predictions of limit strains were based on the Marciniak—Kuczynski inhomogeneity analysis and utilized the commonly used power hardening law (Hollomon equation) to describe the stress—strain behavior of the material. In the present work, (i) the suitability of a Voce hardening law, (ii) the effect of surface roughness parameters and (iii) the effect of grain size parameters on the prediction of biaxial limit strains has been studied. The biaxial limit strains based on Voce equation were obtained by modifying the set of equations of Parmar et al. and utilizing the experimentally measured surface roughness in 3-D, grain size parameters and stress—strain curves from uniaxial tensile and hydraulic bulge tests for the two A1 sheet materials. The predictions from Voce and Hollomon equations have been compared with the experimental forming limits determined by hemispherical punch stretching of gridded blanks. The discrepancy between predictions from Holloman equation and experiments is small for the low strain hardening AA6111-T4 material but is quite significant for the high strain hardening AA5754-O material. Further, the predictions are also strongly dependent upon the measure of surface roughness and the grain size utilized in the calculations. The results indicate good predictions of limit strains for the two alloys when (i) stress—strain data from tensile or hydraulic bulge tests are fitted to a Voce equation and (ii) half of the maximum peaks-to-valley height and grain thickness are utilized as a measure of surface roughness and grain size respectively. The results are discussed in the context of the characteristics of the hardening laws, assumptions of surface roughness model and surface and grain characteristics of the alloys studied.