On a thermomechanical model of shear instability in machining

On a Thermomechanical Model of Shear Instability in Machining Hou Zhen-Bin, Ranga Komanduri (1) Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, USA Received on January 4,1995 ABSTRACT Shear instability was observed experimentally in machining some of the difficult-tomachine materials, such as hardened alloy steels, titanium alloys, and nickelbase superalbys yielding cyclic chips Recht in 1964 developed a classical model of catastrophic shear instability in machining In this investigation, based on the analysis of cyclic chip formation in machining, possible sources of heat (including preheating effects by these heat sources) contributing toward the temperature rise in the shear band were identified The temperature rise was calculated using Jaeger's classical solutions of stationary and moving heat sources Recht's original catastrophic shear instability model for shear localization was extended by predicting analytically the conditions for the onset of shear localization Key Words: machining, cutting, shear "Ioften say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science whatever !he Lord Kelvin matter may be" INTROOUCTlON Machining of conventional metals and their alloys, such as low carbon steels, aluminum alloys, carbon steels in the practical cutting speed range is characterized by a continuous (Type II) chip [l] These materials exhibit high ductility (having a bcc or a fcc crystal structure) and good thermal properties There are, however, other materials, such as titanium alloys, nickelbase superalloys, hardened alloy steels which produce cyclic chips when machined due to shear instability [2-7l For some of these materials, as in the case of hardened alloy steels, a transition from a continuous to a shear localized chip occurs as the cutting speed is increased 61.However, once the transition from a continuous to a s ear localized chip occurs, no further transition or reversal to a continuous chip was observed with further increase in speed For other materials, such as titanium alloys, shear localization seems to occur throughout the cutting speed range, i.e from an extremely low speed to very high speeds Materials that tend to form shear localized chips can be characterized by poor thermal properties and/or limited ductility (as in the case of materials with a hcp crystal structure) Shear localization causes cyclic variation of force (both cutting and thrust) and consequent vibration or chatter in the metal cutting process Consequently, an understanding of the process, the criteria for shear instability, and the conditions leading to shear localization are im rtant considerations in our quest for improving pro uctiviiy, r part quality, and overall efficiency of the cutting operation F, CRITERIA FOR SHEAR INSTABILITY Recht in 1964 [a] developed a classical model of catastrophic shear instability in machining Accordingly, catastrophic shear occurs at a plastically deforming Annals of the ClRP Vol 44/1/1995 region within a material when the slope of the true stresstrue strain curve becomes zero, i.e., the local rate of change of temperature has negative effect on strength which is equal to or greater than the positive effect of strain hardening Assuming an approximate value of the temperature generated in machining, Recht estimated the values of thermo-mechanical properties and calculated the shear strength In this paper, this model was further developed based on the experimental results obtained usin h' h-speed photo raphy, in situ machining inside an #Elf, and a metahrgical analysis of the chips generated in conventional machining tests over a range of cutting speeds Recht's original thermo-mechanical model for shear localization in metal cutting was extended and an attempt was made to predict quantitatively the conditions for the onset of shear localization The temperature raise in the shear band due to the three heat sources as well as the preheating effects by these heat sources on the following segment being generated was calculated A reasonably ood correlation of the experimental work with the aniytical modeling was found Samiatin and Rao (91 developed another model for shear localization which incorporates a heat transfer analysis and materials properties, such as the strainhardening rate, the temperature dependence of the flow stress and the strain rate sensitivity of the flow stress to establish the tendency towards localized flow Using the data available in the literature, they found the non-uniform flow in metal cutting is imminent when the ratio of the normalized flow softening rate to the strain rate sensitivity is equal to or greater than In addition to thermo-plastic instability (strain hardening versus thermal softening) leading to shear localization, there can be other mechanisms where an actual reduction in the shear stren th in the shear band can take place without the therma softening effect For example, the generation of microcracks in the shear band and a reduction in the actual area undergoin stress Walker and Shaw [lo] pro sed this for materia s undergoing large shear and omanduri and Brown [ll] proposed this as a possible mechanism for chip segmentation in machining Recent1 , Shaw and Vyas [12] proposed it for machining an All1 4340 steel at low cutting speeds This concept seems to be valid particularly for the case of cyclic chips generated in machining of titanium alloys at very low speeds These B R" 69 speeds are so low that the heat generated in the shear band could diffuse on either side with the result thermal softening would be rather difficult Instead, the actual shear strength may be lowered by the presence of microcracks Other mechanisms proposed for shear instability include structural transformation, as in the reversion of marten-site to austenite in some steels [13] In this paper, only the first mechanism of shear instability, name1 , thermal softening versus strain hardening is consdered PHYSICAL MODEL OF SHEAR LOCALIZATION IN MACHINING The followin is the sequence of events leading to shear-localized clip formation This model is developed based on the ex erimental results obtained using highs eed photograpiy, in d u machining inside a scanning erectron microscope and metallur ical analysis of the chips obtained in conventional mac ining tests of these materials over a range of cutting speeds There are basically two stages involved in this process One stage involves shear instability and stain localization in a narrow band in the primary zone ahead of the tool The other stage involves u setting of an inclined wed e of work material by the a ancing tool, with negligible eformation, forming a chip segment During upsetting of the segment ahead of the tool in the primary zone, intense shear takes place at approximately 4!5O to the direction of cuttin This occurs not between the chi and the tool face gut between the last segment an the one just formin Thermo-mechanical response of these drfficultto-mac%ine materials under the conditions of cutting tend to localize the heat generated due to strain localization and subsequent shear in a narrow band Thus, thermal softening takes place resulting in the shear stress being lower than that of the bulk material With increase in cutting speed, this intense shear takes place so rapidly that the contact area between any two se ments gradually decrease to a stage when the in8ividual segments of the chip are actually separated Such a phenomenon was observed at higher cuttin speeds (above 1,000 m/min) in the case of hardened al oy steels and nickelbase superalloys Figure I (a) to (c) show various stages of shear localization in machining, Figure (a) shows the inltial stage where chip segment I has just formed and under the essure exerted by the tool face on the weakest plane a Figure (b)], shear S1 commences on the main shear plane This high1 intense, narrow shear zone is designated as ABZD Note that svgment ll.(i.e in the s ment to be deformed) undergoes very little plastic de ormation Figure l b shows an intermediate sta e where the cutting tool has moved a distance T e width of the shear zone has increased from AB [Figure (a)] to AC Figure (b)] Also, the shear zone has rotated due to pastic indentation (or upsetting) and the deformation of segment II takes place by the movement of the cuqing tool This deformation is caused by the shear S2 in the weakest plane b of that part of the chip segment which has its own shear angle @ * and moves forward together with the cutting tool tip Figure (c) shows the final stage where the chip segment I has sheared along the main shear plane to its maximum extent and the weakest lane in segment II has reached its extreme position Aler that, the weakest plane will shift to a' as shown in the figure Thus the next chip segment is formed It asain will begin to shear along the new main shear lane a At this instant the length of the shear zone on t e main shear plane of the former chi segment has its maximum value A'C or ABC [Figure (cf a 8, s B r e.6 I R It may be noted that the chip formation process yielding shear localization is far different from that with a continuous chip In the case of a continuous chip, strain hardening always predominates ove! thermal softening Once shear takes place along the main shear plane a, the stress required for further deformation is higher than before, so the weakest lane will be shifted to the next lane Thus shear will aso be shifted to the next plane his leads to a uniform1 distributed deformation in the chi s on a macroscale !r ut in the case of chip formation wit[ shear localization thermal softening predominates over strain hardening Once shear takes phce along the ? 70 P main shear plane a, the strength there becomes lower than before So, the main shear plane is still the weakest plane and hence the shear continuous on the same ane In other words, shear is localized in a narrow plane # isl results in an inhomogeneous deformation in the chips on a macroscale Figure shows ty ical micrographs of a continuous and a shear localize chip at two different cutting speeds illustrating these features CRITERION FOR THERMO-MECHANICALSHEAR INSTABILITY IN MACHINING In this investigation the criterion for shear instability formulated by Recht in 1964 was further developed by predicting analytically the conditions for the onset of shear localization Based on the analysis of cyclic chip formation in machining described earlier, possible sources of heat (including preheatin effects of these heat sources) in the shear band contrguting towards the temperature rise were identified Using Jaeger's classical solutions for stationary and moving heat sources as bases (141, the temperature rise in the shear band due to various heat sources was calculated Knowing this temperature, the shear stress in the shear band at the shear band tem erature was estimated and compared with the strengtE of the work material at the preheating temperature A thermo-mechanical model was developed wherein if Q' Q, no shear localization takes place but instead strain hardenin occurs If Q ' C 6,then shear localization is imminent The model proposed redicts the onset of shear instability (i.e cutting speed a k v e which shear localization takes place) reasonably well with the experimental results reported in the literature [3.6] THERMO-MECHANICALPROPERTIES OF THE WORK MATERIAL Based on experimental materials property data available in the literature on the strain hardening and thermal softening characteristics, relationships were developed for the calculation of true stress, Q, in terms of true strain, E and temperature, T Only temperature and strain effects were considered here as the strain rate effects could not be considered due to lack of materials properties data Similarly, thermal properties of the work material at different temperatures were obtained from the literature and used in the analysis HEAT TRANSFER MODELING To predict the conditions for the occurrence of shear localization quantitatively, the tem erature rise in the shear band during cutting has to determined Based on an analysis of the cyclic chip formation, the tem erature rise in the shear band is identified as due to the ollowing three heat sources as well as the preheating effects of these sources The three primary heat sources are: The main shear band heat source, a [see Figure is will be the predominant heat source especially (b)l; at igher cutting speeds, (2) the secondary shear band heat source b [see Figures (b) and (c)] This is the heat enerated durin the upsetting stage of cyc!ic chip krmation, and (38 the frictional heat source, c (Figure 1) between the s ment already formed and the rake face of the cutting to? In addition, all the three heat sources also effect the temperature on the new shear band of the next chip segment That is, every new segment, where shear localization begins to takes place, will occur at a temperature higher than the room temperature This is the preheating effect on the main shear band Thus, in this r all the heat sources are identified and used in the !%ulation of shear band temperature-rise It will be shown later that depending on the cutting speed used, the influence of some of these heat sources will be more prominent than others Some can be neglected at higher speeds but becomes more significant at lower speeds Jaeger's classical instantaneous, infinitely long line heat source solution is taken as the startin point for all the three heat sources as well as the t ree preheating sources The temperature rise at any point M and at any instant t due to each of the heat sources is obtained In this investigation, temperatures at 15 locations along the shear band are calculated The mean of these values is taken as the temperature rise The mean temperature rise in the shear band (Ze)caused by the three heat sources and that due to three preheating effects are P $A 7l designated as 6.6,&, Q, 6,and %respectively Due to limitations of space only the final results are given here; details of the analytical modeling are given elsewhere [15] The first heat source is the main shear band heat source a [in Figure l(a)] It is assumed as an infinitely long, stationary, continuous heat source with a variable intensity of heat liberation This heat source includes the heat generated in the shear band (i.e between the segments) and the shear between the segment and the tool face [see Figures (b) and (c) for details] The second heat source is the seconda shear plane heat source b, caused by the upsetting of #e undeformed part of the material ahead of the tool face which begins simultaneously with the be inning of the localized shear in the main shear band, a !Figure 11 During shear, the shear plane provides a moving plane heat source with variable width moving along the direction AB Figure b) The third heat source, namely, the frictional eat source between the chi segment already form+ and rake face of the tool, c !I is assumed as a moving plane heat source with variable intensity of heat liberaton A similar approach is taken for calculating the temperature rise due to each of the three preheating sources I, RESULTS AND DISCUSSION Figures and show the variation of temperature rise due to various heat sources with cutting speed for an AlSl 4340 steel and a Titanium 6AI-4V work material, respectively They were obtained using the analytical models proposed earlier It can be seen that at the low speeds the temperature rise in the shear band depends very much on the contributions of the various heat sources Also, at the lower speeds, reheating effects predominate At the higher speeck however, the temperature rise due to the first heat source, namely, the shear band heat source predominates Figures and show the variation of shear stress with cutting speed for an AlSl4340 steel and a Titanium 6AI-4V work material, respectively 6'is the shear stress at the shear band temperature and is the shear strength of the bulk material at the preheating temperature Except at very low speeds, 6' decreases (due to thermal softening effect) while increases (due to decreasing preheating effect with increasing cutting speed below the critical speed or shear localization, a' > The difference between them decreases with increase in speed At the critical speed for shear localization, i.e = b', strain hardening effect equals thermal softening Beyond this speed, thermal softening predominates over strain hardening with the result a'c It can be seen that the critical speed for shear localization for Titanium 6A14V is about mlmin while that for AlSl4340 steel is much higher (about 116 m/min) as originally predicted by Recht Also, the ex erimental results reported earlier for the onset of shear kalization (namely, 125 mlmin) for AlSl 4340 steel [6] agrees with the analytical results presented here However, in the case of titanium alloys, cyclic chip formation was observed at speeds much lower than the value reported here This difference can be attributed to several factors It is possible that the criterion for the onset of shear localization presented here is somewhat simplistic or other factors of relevance may not been considered in the analysis For exam le, cut thickness may have some effect in that the preKeatin effects would be different for a thin chip than a thick c ip Also, the frictional heat source (and the preheating effect of this heat source) between the nascent chip and the tool face during the indentation of the wedge shaped section of the chip segment has not been considered in the first ap roximation The basic approach and the conclusions wil still valid These modifications may move the speed at which shear localization takes place slightly lower than what is sreported in this paper a P It is reasonable to assume that at very low cutting speeds, the conditions in the shear band are far from adiabatic Consequent1 , adiabatic (or near adiabatic) shear instability is unlkely at the very low speeds Perhaps, some other mechanism may have to be invoked to explain for the observed cyclic chip formation at very low speeds with titanium alloys It is possible that this phenomenon is due to a difference in the mechanism of shear localization from that of a thermal origin to a mechanical origin, for example, involving microcracks, as originall proposed by Professor Shaw This would effediveyy reduce the stress due to reduced area Work is under rogress in this direction and it is hoped that the resutts orit will be communicated soon CONCLUSIONS In this investigation Recht's catastrophic shear instabilit model was extended by predicting analytically the codtions for the onset of shear localization Based on an analysis of the shear localized chip formation process, three primary heat sources and reheating effects of these heat sources were identified [sing Jaeger's stationary and moving heat source solutions the temperature rise in the shear band due to these heat sources was calculated Shear stress in the shear band, o', was calculated at the shear band temperature and compared with the value of shear strength, 6,at the preheating tem rature for both AlSl4340 steel and Titanium 6AI4V worpmaterials It was found that if 6' c 6, then shear localiza?ionis imminent The cutting s eed at which this occurs is the critical speed for shear kcalization Shear localization continues at all speeds above this Cutting speed for the onset of shear localization was found to be much lower for Titanium 6A14V (about m/min) than for AM4340 steel (130 m/min) Values of a'and were calculated for AlSl4340 steel over a ran e of practical cutting speeds No shear localization wasyound up to a speed of about 120 mlmin with the onset of shear localization above 130 mlmin Experimental results reported in the literature agrees reasonably with the anal tical values Values of 6'and were also calculated for fitanium AI-4V over a range of cutting speeds up to 10 m/min No shear localization was found up to a speed of about m/min with the onset of shear localization above m/min ACKNOWLEDGMENTS The authors would like to acknowledge the continuing support of the National Science Foundation in the area of manufacturing at OSU Thanks are due to Drs B M Kramer, K Narayanan, W DeVries, and A Hogan of NSF for their interest Thanks are also due to many of the collaborators of the Air Force roject on Advanced Manufacturing which was funded wlen one of the authors (R.K.) was with G.E In particular, the many valuable discussions with Prof B F von Turkovich, Mr R F Recht, Dr R A Thompson, Dr M Lee and Dr D G Flom are gratefully acknowled ed Thanks are also due to some of the graduate stutents who helped in the reparation of the drawings Finally, thanks are due to the OST Chair funds that enabled this work Thanks are also due to Prof M F DeVries for his review and comments REFERENCES R4 Merchant, M E., 1944, Basic Mechanics of the Metal Cutting Process, Trans ASME, 66: A65-A71 LeMaitre, F., 1970, Contribution a I'etude de I'usinage du titane et de ses alliages, Annals of CIRP, 23: 413424 Komanduri, R and B F von Turkovich, 1981, New Observations on the Mechanism of Chip Formation When Machining Titanium Alloys, Wear, 69: 179-188 Komanduri, R., 1982, Some Clarifications on the Mechanics of Chip Formation When Machining Titanium Alloys, Wear, 76:15-34 Komanduri, R and R H Brown, 1981, On the Mechanics of Chip Segmentation in Machining, Trans ASME, J of Engg for Ind 103 : 33-51 Komanduri, R and T A Schroeder, 1986, On Shear Instability in Machining a Nickel-Iron Base Superalloy, Trans ASME, J of Engg for lnd.,108: 93-100 71 [7] Komanduri, R., Schroeder, T A Hazra, J., von Turkovich, B F., and D G Flom, 1982,On the Catastrophic Shear Instability in High-speed Machining of an AlSl4340 Steel, Trans ASME, J of Engg for Ind., 104:121-131 [8] Recht R F., 1964, Catastrophic Thermoplastic Shear, Trans ASME 86:189-193 [9] Semiatin, S L and S B Rao "Shear Localization During Metal Cutting," Materials Science and Engineering, fi (1983) 185-192 [lo]Walker, T J and M.C Shaw, 1969.On Deformation at Large Strains, Proc of the 10th M.T.D.R Conference, 241 [l11 Komanduri, R and R H Brown, 1972,The Formation of Microcracks in Machining a Low Carbon Steel, Metals and Materials, 6: 531 (121Shaw, M C., and A Vyas, 1993,Chip Formation in the Machining of Hardened Steel Annals of CIRP, 42/1: 29-33 [13]Lemaire, J C and W A Backofen, Feb 1972, Adiabatic Instability in the Orthogonal Cutting of Steel, Metallurgical Trans, 3:477-481 [14]Jaeger, J C., 1942,Moving Sources of Heat and the Temperature at the Sliding Contacts, Proc of the Royal Society of NSW 76: 203-224 [15]Hou Zhen-Bin and R Komanduri, 1995, ThermoMechanical Modelling of Shear Instability in Machining, Part I:Thermo-mechanical Instability and Part II Thermal Analysis, papers to be submitted for publication (b) Figure I(1)to (c) Schematic showing various stages of shear localization in machining 72 v) ti Q, L 200 150 c 100 Q, a 50 10 15 20 Cutting Speed, m/min 25 Figure Variation of temperature rise due to various heat sources with cutting speed for Titanium 6AI4V Z 230 a Figure (a) and (b) Typical micrographs of a continuous and a shear localized chip when machining AlSl 4340 steel (Rc 35), at two different cutting speeds illustrating these features (a) 125 m/min and (b) 250 m/min [A ' I ' , I , , ze i s 220 F ' 50 " ' " " " " ' " 75 100 125 Cutting Speed, V m/min ' 150 Figures Variation of shear stress with cutting speed for an AlSl4340 steel S.L.: shear localization and No S.L : no shear localization 140 ~ ~ , ~ ~ I I , I , , - y 135 I 25 50 75 100 Cutting Speed, m/min 125 150 Figure Variation of temperature rise due to various heat sources with cutting speed for an AlSl4340 steel 10 15 20 Cutting Speed, V m/min 25 Figures Variation of shear stress with cutting speed for Tiianium 6AI-4V S.L.: shear localization and No S.L : no shear localization 73 ... involves shear instability and stain localization in a narrow band in the primary zone ahead of the tool The other stage involves u setting of an inclined wed e of work material by the a ancing tool,... mechanism of shear instability, name1 , thermal softening versus strain hardening is consdered PHYSICAL MODEL OF SHEAR LOCALIZATION IN MACHINING The followin is the sequence of events leading... formed It asain will begin to shear along the new main shear lane a At this instant the length of the shear zone on t e main shear plane of the former chi segment has its maximum value A' C or ABC