A New Mechanism of Asperity Flattening in Sliding Contact The Role of Tool Elastic Microwedge

Transcription

1 Sy-Wei Lo Professor Tung-Sheng Yang Institute of Engineering Science and Technology, National Yunlin University of Science and Technology, Touliu, Yunlin 640, Taiwan New Mechanism of sperity Flattening in Sliding Contact The Role of Tool Elastic Microwedge Based on real-time observation of the workpiece surface in a series of Lo and Tsai s (2002) compression-sliding experiment, it is found that the asperity contact area is much greater than that evaluated by the existing theorems such as the junction-growth theorem. With the aid of finite element analysis, it is verified that the tool sliding motion along with the minute elastic deformation (microwedge) of the tool surface around the asperity peaks increase the asperity contact area significantly even in a frictionless sliding. The microwedge induces a component of force along the sliding direction on the asperity. combination of flattening and smearing effects can therefore aid in expanding the contact area. The greater the wedge angle, the stronger the propellent effect. n incremental model has also been developed to predict the evolution of contact area during sliding. The numerical simulation compares well with the experimental results. The new mechanism not only introduces an important tribological variable to forming processes, but also brings in a new concept of surface quality control for processes having a considerable sliding distance between workpiece and tool such as ironing, forging, and extrusion. New processes performing high relative sliding velocity can therefore be developed to ameliorate the brightness of products. DOI: / Introduction mple investigations and numerous models have been carried out for asperity contact; however, most of them deal with the static equilibrium solution in pure flattening either with or without the friction stress at the interface. In metal forming processes, the roughness of the workpiece may dramatically change at the toolworkpiece interface especially in the presence of relative sliding motion. In the case of a rough tool, the local deformation of the workpiece surface can be modeled by the plowing or abrasive mechanism as a function of the current contact conditions. However, when a smooth tool slides against a relatively rough workpiece, the continuous flattening and the roughening due to substrate strain of the workpiece asperity are path-dependent. That is, the analysis becomes more difficult since all the prior behavior of the asperity deformation must be traced and integrated. ccording to Courtney-Pratt and Eisner s study 1, in addition to the normal force, when the shear force is first applied, tangential motion occurs even while the tangential force is quite low. This motion has the effect of increasing the area of contact, which recreates equilibrium under the joint action of the normal and shear forces, so relative motion of the two surfaces in a normal direction inward ceases 1. If the shear force is continually increased, the increase in real area of contact with increased shear force eventually falls short of that required to maintain static equilibrium and hence sliding motion will occur 2. Such a phenomenon of microscaled expansion of contact area prior to the macroscaled sliding motion has been modeled as the well known junction-growth theory. Recently, Lo and Tsai 3 developed a new system for in situ observation of a sheet metal surface. The workpiece in the system is stationary so that the continuous deformation of a specific group of asperities can be traced and analyzed. Figures 1 and 2 show the typical experimental results of Lo and Tsai 1. In many metal Contributed by the Tribology Division for publication in the SME JOURNL OF TRIBOLOGY. Manuscript received by the Tribology Division ugust 1, 2002; revised manuscript received February 4, ssociate Editor: T. C. Ovaert. forming processes, the sliding distance that a single asperity peak travels frequently exceeds several millimeters, which is long compared with the asperity spacing itself. The contact area continues to grow and eventually approaches to a nearly saturated value at large sliding distance. macroscaled growth of asperity contact area, which is not only much greater than that of indentation pure flattening, but also goes beyond the limit of the junction-grown area is observed. ccording to junction-growth theory, the locus of shear stress and normal pressure on the asperity peak need to follow the elliptical relation, as Kayaba and Kato s 4 observations regarding the transition from static to sliding contact. However the measurements of the shear and pressure in Fig. 1 depict a nearly linear, instead of an elliptical, relationship between shear stress and pressure. ll these findings indicate that the conventional junction-growth theory is not suitable in the present circumstance and a new mechanism for such a post junction-growth behavior is therefore in demand. Our contention in the present paper is that the minute elastic deformation of tool surface the elastic microwedge provokes the continuous growing of asperity contact area under simultaneously decreasing normal pressure and shear stress. The new mechanism will not only introduces an important tribological variable to forming processes, but also brings in a new concept of surface quality control for processes having considerable sliding between workpiece and tool such as ironing, forging, and extrusion. It will be verified by a FEM simulation and a formulation of asperity area evolvement will be proposed. 2 FEM Simulation of Sliding Contact series of FEM simulations using the commercial code DEFORM 2D is carried out to verify the mechanism mentioned above. The roughness of the workpiece surface is modeled with five triangular asperities while the tool is a smooth elastic body, as shown in Fig. 3. It is noteworthy that the terms smooth and rough are described in a sense of relativity. Physically, the resistance of the interfacial microgeometry to the plastic flow of asperity appears as an adhesive force on macroscale. Though a Journal of Tribology Copyright 2003 by SME OCTOBER 2003, Vol. 125 Õ 713

2 Fig. 1 dhesive coefficient versus nondimensional asperity contact pressure for aluminum sheet with transverse roughness 1 perfectly smooth tool is adopted in the FEM analysis, the proposed model is adequate to simulating a realistic tool surface sliding against a relatively rough workpiece. The origin of the coordinate system is located on the left bottom corner of the workpiece in its initial position before compression occurs. The two lateral boundaries of the workpiece are allowed to move vertically normal to the sliding direction of the tool. The width pitch of each triangular asperity is equal to S m, which represents the asperity spacing, and the asperity height can be assigned as the representative roughness, say R q. The contact area ratio is defined as S a /S m (1) where S a is the asperity contact length of the central peak. The asperities are first compressed by a constant normal force to have contact with the stationary tool surface until the status of static equilibrium is reached. Then the tool begins to slide while the normal loading, therefore the mean pressure p, on asperities remains constant. In addition to the case of a rigid tool, the elastic tools with three different values of Young s modulus, E, are also simulated. Three normal loads therefore the mean pressure are tested. The cases of frictionless and frictional sliding with friction coefficients equal to , and 0.3 are considered. The preliminary simulation shows that the sliding speed of the tool is Fig. 2 Contact area ratio versus sliding distance for aluminum sheet with transverse roughness 1 Fig. 3 FEM model of sliding contact irrelevant to the variation of the asperity geometry. On the other hand, the deformation of asperity is a function of the sliding distance, as that found in Lo and Tsai s experiments. Part of the results of the simulation are shown from Fig. 4 6 using the following nondimensional variables: E Y ln E/k (2) P p /k (3) where k is the shear strength of workpiece while E Y and P are the nondimensional Young s modulus and the mean pressure respectively. The logs-definition of E Y is selected based on the fact that the Young s modulus is generally much higher than the shear strength of workpiece. The form of Eq. 2 can give the more feasible values of E Y for the subsequent curve fitting of the numerical results. lso the nondimensional sliding distance S is defined as S s/s m (4) where s is the sliding distance and, S m is the asperity spacing. The DEFORM 2D possesses the function of visualizing the effective stress distribution. The influence of the tool Young s modulus on the effective stress distribution for frictionless sliding is exhibited from Figure 4 a to 4 c. Figure 4 a shows an almost uniform distribution of the effective stress in the case of a rigid tool. The effective stress is slimly less in the middle of the contact plateau. s for the case of an elastic tool in Figures 4 b and c, the low stress region outspreads towards the two edges of the plateau as the Young s modulus gets smaller. The existence of the interfacial adhesion complicates the stress disposition. For the same contact area, say 0.6, Figure 5 indicates that the higher the friction coefficient, the greater the maximum effective stress. Figure 6 depicts the profiles of the deformed asperity during sliding. The valleys ascend with nearly constant surface slopes and move slightly towards the sliding direction. This is concordant with Lo and Tsai s observation. For a rigid tool surface, the contact area ratio of frictionless sliding remains its initial value of pure flattening. However, Figure 7 indicates that even in the frictionless sliding, the contact area will become much greater if the tool is not rigid. Even for a very stiff tool for instance, the tool Young s modulus equals 210 GPa while its counter part is the annealed aluminum strip whose yield strength is lower than 100 MPa, the growth of the contact area is 714 Õ Vol. 125, OCTOBER 2003 Transactions of the SME

3 Fig. 4 Influence of tool Young s modulus on distribution of effective stress a rigid tool, EÄ ; b Young s modulus E Ä210 GPa; and c Young s modulus EÄ83 GPa. Fig. 5 Influence of friction coefficient on distribution of effective stress a frictionless, Ä0; b Ä0.1; and c Ä0.3. substantial. The most significant increase in contact area is in company with the greatest mean pressure and lowest tool stiffness while the mean pressure is the dominating factor. The simulations of the frictional sliding are shown in Figures 8 and 9. Figure 8 depicts the influence of the nondimensional mean pressure while Figure 9 illustrates the effect of the nondimensional Young s modulus in frictional sliding. Both show that the calculated junction-growth area is close to that of the pure flattening case and is much less than that induced by the microwedge. The numerical investigation indicates that the relatively compliant tool under high mean pressure, combined with great friction force, yields the greatest contact area ratio. Furthermore, the influence of the mean Journal of Tribology OCTOBER 2003, Vol. 125 Õ 715

4 Fig. 6 sperity profile for different nondimensional sliding distance pressure is substantial while that of the friction force is comparatively minor. The fact that the frictionless contact still provokes a considerable growth of implies that the conventional theorem of junction-growth does not cover all the mechanisms stimulating the deformation of asperity. On the other hand, the microwedge formed on the asperity peak is responsible for the continuous expansion of the contact plateau. Figure 10 is the schematic representation of the microwedge. Point Q is the center of the asperity prior to flattening. The point Q max has the maximum penetration depth while points Q 1 and Q 2 mark the edges of contact. The bottoms of the valleys are denoted by Q 3 and Q 4, respectively. Figure 11 enlarges the contact profile between Q 1 and Q 2. It is observed that the symmetry of the contact zone is destroyed when the sliding movement commences. The tangential motion of the tool and the friction incline the wedge towards the sliding direction. In addition to the normal load, the microwedge induces a horizontal component of force on the asperity. combination of the flattening and smearing effects can therefore aid in shifting and expanding the contact area albeit there is no relative normal motion between the tool elastic profile and the workpiece profile. In other words, the tool elastic concave embraces the forged asperity peak and deforms together. The greater the wedge angle, the stronger the propellent effect. Fig. 8 Effects of nondimensional mean pressure and friction coefficient on contact area ratio 3 Parametric Study To model the wedge effect, one may calculate the elastic deformation of a semi-infinitive plane loaded by a series of uniform pressure distribution p p, as shown in Fig. 10. Figure 4 a substantiates the availability of such an assumption of uniform pressure distribution. For the sake of simplicity, first, no shear stress and no tool sliding motion are considered and the central point Q is iden- Fig. 9 Effects of nondimensional Young s modulus and friction coefficient on contact area ratio Fig. 7 Evolution of contact area ratio in frictionless sliding Fig. 10 Idealized geometry of flattened asperity 716 Õ Vol. 125, OCTOBER 2003 Transactions of the SME

5 Fig. 12 Function versus tical to the point Q max. The difference in the depth of deformation between point Q max and point Q 1 can be approximated by superimposing the influences from the pressure on the adjacent three asperity peaks while the influences from the remote asperities are neglected based on the theory of elasticity 5 : w S m p p (5) E where is the Poisson s ratio. The function () is written as 2 ln 2 2 ln 2 1 ln ln 2 2 ln 2 (6) The last term of () is associated with the solution of single asperity contact. Equation 5 can be extended to liquid lubrication by replacing p p with p p p v, where p v is the pressure in asperity valley, based on the concept of the effect hardness proposed by Wilson and Sheu 6. The symmetric microwedge determined by Eq. 5 is basically a description of the pure flattening contact and is developed based on the assumption of a uniform pressure distribution. Under such circumstances, the net force along the sliding direction is zero. However, the contact profile is no more symmetric after the sliding starts, as mentioned in the previous section. The wedge angle is therefore estimated by and Fig. 11 Enlarged profile of microwedge w S a / P for S 0 (7) exp E Y w P for S 0 (8) S a exp E Y where P is the nondimensional pressure difference in asperity peaks and valley, i.e., P p p p v /k (9) In the absence of a liquid lubricant, p v is equal to zero and P is therefore equal to P /. Equations 7 and 8 indicate that the wedge angle is a function of, P, E Y, and the Poisson s ratio. Enhancing the pressure difference P or using a compliant tool with low E Y results in a greater wedge angle. It is noteworthy that P or P P) is not only a key factor to forge the tool wedge angle, but also have the vital influence on the asperity deformation. It is therefore reasonable to expect that P or P P) plays double roles in both the tool deformation and asperity deformation. That is, the effect of the mean pressure is more significant than that of the tool Young s modulus E, the latter is merely related to the wedge geometry. Such an inference concurs with the numerical results. From Fig. 12, the variation of () implies that the interference between adjacently distributed pressures reduces the wedge angle when runs up and the increasing rate of is thus decelerated. Neglecting the influences from the remote contact pressures makes () nonzero as approaches one. In the FEM analysis, the wedge angle is similarly estimated by the slope between point Q max and Q 1. The comparisons between the theoretical and numerical wedge angles for the frictionless flattening therefore pure microwedge effect and sliding are exhibited in Figs. 13 and 14, respectively. For pure flattening where S is zero, the analytical solution in Fig. 13 is in good agreement with the calculation. s tracing one specific asperity in sliding, Fig. 14 shows that the wedge angle decreases rapidly in the very beginning and then gradually vanishes. Basically the theoretical result also concurs with the FEM simulation. Though the disturbance in the pressure distribution makes Eq. 8 a little overestimated, the investigation of the frictionless sliding where the adhesion plays no roles validates the considerable influence of tool microwedge on the extension of asperity contact area. nalyzing the plastically deforming behavior of the asperity material beneath the microwedge is a challenging task. However, an alternative semi-analytical approach such as the curve-fitting technique can be carried out based on the FEM simulation. The proposed formulation must be of incremental form for a plastic Fig. 13 Comparison between theoretical and numerical wedge angles in pure flattening Journal of Tribology OCTOBER 2003, Vol. 125 Õ 717

6 Fig. 14 Comparison between theoretical and numerical wedge angles versus nondimensional sliding distance deformation process. It can thereafter be utilized for practical applications where the interfacial pressure between tool and workpiece generally varies during the sliding. Since the change of the contact area is a function of the sliding distance, the derivative of with respect to S is considered, at first sight, as a function of the wedge angle. However, the extremely small value of makes it difficult to be fitted. In stead, Eq. 8 implies that the variable can supersede the role of and the following power-form relationship is suggested: d/ds C m (10) s a modification of Lo and Yang s 7 fitting, the coefficient C and the index m for the frictionless case are fitted as C P/E Y exp P P P E Y P E Y P 2 E Y E Y P E Y E Y 3 (11) m P E Y P E Y E Y P E Y 2 (12) Neglecting the junction growth effect, Eq. 11 reflects the fact of no variation of provided that the pressure distribution is uniform ( P 0) or the tool is rigid with infinitely large E Y. The influence of the Poisson s ratio is also negligible since for most metals the Poisson s ratio is close to 0.3 and its variation is much smaller than that of the other parameters. In the presence of friction, the value of m can keep unchanged, however, the ratio of the C( 0) to the C( 0), say, is given as Fig. 15 Comparison between numerical and experimental results for transverse roughness where is the friction coefficient on the asperity peak. Equation 10 can be integrated to calculate the contact area ratio as tracing the material element at different sliding distance. Figure 15 shows that the numerical results using Eq. 10 are congruous with Lo and Tsai s experiment. To apply Eq. 10 to a manufacturing process, one must compare the calculated contact area with the value computed by the indentation model for instance, Wilson and Sheu s 6. The greater one is chosen since it happens that the indentation effect prevails when the mean pressure varies intensely, or conversely, the microwedge effect dominates where relative sliding is significant. ccording to Lo and Tsai s 1 observation, the evolution of asperity deformation will approach an equilibrium point unless the deterioration of the boundary film leads to a catastrophic galling failure. Lo and Tsai forced the shear stress and the contact pressure p p on the asperity peak to satisfy the relationship of junction-growth theory, that is, p 2 p 2 k 2 (14) where p p is equal to p / in the case of boundary lubrication. Under the circumstances, they found that the corresponding to the equilibrium state is related to the nondimensional mean interface pressure P. With the aid of Eq. 10, similarly we may define the equilibrium condition for which the increasing rate of is equal to a small value : d/ds C m (15) ccordingly the equilibrium contact area ratio is equal to ( /C) 1/m. Since Lo and Tsai s measurement shows that the Coulomb friction model prevails on the asperity peak in most of the cases, the shear can be replaced with p p. Finally from Eq. 14, we have the for equilibrium: P C/ 1/m 2 / 1 P C/ 1/m 2 (16) The comparison between Eq. 16 and Lo and Tsai s results where different roughness pattern, lubricant viscosity, mean pressure, and sliding speed are employed is shown in Fig. 16. The values of E Y and are assigned as 9.0 and 0.1, respectively based on Lo and Tsai s experimental conditions. It is found that the selection of is vital to the determination of, while and E Y have relatively minor influences and, fortunately, the demand of the accurate values of and E Y for computing the is avoided. The appropriate value of is It is noteworthy that the C 0 /C (13) Fig. 16 Theoretical and experimental junction-growth coefficients versus nondimensional mean pressure for various experimental conditions 718 Õ Vol. 125, OCTOBER 2003 Transactions of the SME

7 Coulomb friction model usually fails in the case of high contact pressure and the more serious discrepancy between Eq. 16 and experimental measurement is expected. The forgoing discussion in this section reveals the conceptual impact of the microwedge effect on both understanding and modeling of tribology, as well as on the tool selection for forming process. For instance, without increasing the tool-workpiece interfacial pressure, which is recognized as the key factor to asperity flattening, tool materials posses lower Young s modulus and higher friction coefficient can be employed to enhance the brightness of the product provided that the energy dissipation is controlled within an acceptable range. nother example is to develop a new rolling mill similar to the tribometer designed by Dohda and Wang 8,9. The rolling speed, radius, and surface roughness of the rolls on the opposite sides of the workpiece are different. The rough traction roll is employed to draw the workpiece into the work zone while the function of the smooth roll is to generate a substantial relative sliding velocity with respect to the workpiece. The increase in the relative sliding velocity therefore the distance not only improves the brightness of the workpiece significantly, but also results in a lower friction coefficient, as that found by Doha and Wang 8. It should be kept in mind that the surface topography, for instance, longitudinal, transverse, or isotropic roughness might induce different characteristics of area expansion. In addition, turning back to Figures 7, 8, and 9, the growth of contact area in the case of high interfacial pressure is over estimated by the FEM simulation. When compared with the experimental results of Lo and Tsai, the tendency of area expansion is tempered by unknown factors in the experiment. The plastic flow in the substrate of workpiece also plays an important role in the sliding contact. ll these will be considered in the future work. 4 Conclusions In metal forming processes, the roughness of the workpiece is dramatically changed at the tool-workpiece interface. series of compression-sliding experiments where the hardened glass and annealed aluminum strips are used as the tool and workpiece was therefore conducted under boundary lubrication to investigate the interfacial behavior. Base on the real-time observation of the workpiece surface, it was found that the asperity contact area in the sliding test either arises from that of the pure flattening to a steady value, or soars in a catastrophic mode as the boundary film tends to fail. Even in the former situation, the contact area is much greater than that evaluated by the existing theorems such as the junction-growth theorem. With the aid of finite element analysis, it is verified that the tool sliding motion along with the minute elastic deformation microwedge of the tool surface around the asperity peaks increase the asperity contact area significantly even in a frictionless sliding. The microwedge induces a component of force along the sliding direction on the asperity. combination of the flattening and smearing effects can therefore aid in expanding the contact area. The greater the wedge angle, the stronger the propellent effect. The existence of the shear stress on the asperity peak also encourages the growth of contact area. From elasticity analysis, it is found that the effect of the tool deformation on the variation of contact area is a function of the tool Young s modulus, the shear strength of workpiece, the current contact area, and the difference in the pressures between asperity peak and valley. n incremental model, which is applicable to both the boundary and mixed lubrications, has been developed to predict the evolution of contact area during sliding. The numerical simulation compares well with the experimental results. The new mechanism not only introduces an important tribological variable to the modeling of forming processes, but also brings in a new concept of surface quality control for processes having a considerable sliding distance between workpiece and tool such as ironing, forging, and extrusion. New processes performing high relative sliding velocity can therefore be developed to ameliorate the brightness of products. cknowledgment The authors wish to thank the National Yunlin University of Science and Technology and National Huwei Institute of Technology for the use of their facilities. The support from the National Science Council under grants NSC E is also gratefully acknowledged. Nomenclature fractional contact area, S a /S m C coefficient of increasing rate of asperity contact area ratio E Young s modulus of tool material E Y nondimensional Young s modulus of tool material, E Y ln(e/k) k shear strength of workpiece m index of increasing rate of asperity contact area ratio p p pressure on asperity peak p v lubricant pressure in the valley p mean pressure P p nondimensional pressure on asperity peak, p p /k P v nondimensional lubricant pressure in the valley, p v /k P nondimensional mean pressure, p /k P nondimensional pressure difference, (p p p v )/k s sliding distance S nondimensional sliding distance, s/s m S a asperity contact length S m asperity spacing w height difference in tool deformation junction-growth coefficient small constant for equilibrium state of () function of wedge angle of deformed tool surface ratio of C in frictional case to C in frictionless case friction coefficient on asperity peak Poisson s ratio of tool material References 1 Courtney-Pratt, J. S., and Eisner, E., 1957, The Effect of a Tangential Force on the Contact of Metallic Bodies, Proc. R. Soc. London, Ser., 238, pp Rabinowicz, E., 1995, Friction and Wear of Materials, 2nd ed., John Wiley & Sons, Inc., p Lo, S. W., and Tsai, S. D., 2002, Real-Time Observation of the Evolution of Contact rea Under Boundary Lubrication in Sliding Contact, SME J. Tribol., 124 2, pp Kayaba, T., and Kato, K., 1978, Experimental nalysis of Junction Growth With a Junction Model, Wear, 51, pp Williams, J.., 1996, Engineering Tribology, Oxford University Press Inc., pp Wilson, W. R. D., and Sheu, S., 1988, Real rea of Contact and Boundary Friction in Metal Forming, Int. J. Mech. Sci., 30 7, pp Lo, S. W., and Yang, T. S., 2002, Growth of sperity Contact rea in Sliding Motion, JSME/SME Int. Conf. Materials and Processing 2002, 2, pp Dohda, K., and Wang, Z., 1995, Investigation into Relationship Between Friction Behavior and Plastic Deformation Using a Newly Devised Rolling- Type Tribometer, SME J. Tribol., 117, pp Dohda, K., and Wang, Z., 1998, Effects of verage Lubricant Velocity and Sliding Velocity on Friction Behavior in Mild Steel Sheet Forming, SME J. Tribol., 120, pp Journal of Tribology OCTOBER 2003, Vol. 125 Õ 719