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MACHINE TOOLDetermining mechanical characteristics of material resistanceto deformation in machiningValerii KushnerMichael StorchakReceived: 14 April 2014/Accepted: 4 July 2014/Published online: 22 July 2014? German Academic Society for Production Engineering (WGP) 2014AbstractThis paper analyses experimental results anddifferent hypotheses about the resistance of the machinedmaterial to plastic deformation in machining. It is neces-sary to take into account that strain rate and temperatureaffects the mechanical properties of the material. It isuseful to describe the regularities of material resistance toplastic deformation with differential equations, determin-ing a dependence of the specific deformation work ondeformation. For machining processes, the correlationsbetween yield point and deformation or rather flow curvesare analytically deduced from the differentiation of thespecific deformation work. It has been found out that theflow curves are vaulted for the adiabatic conditions ofdeformation in the chip forming area and the accumulationzones near the cutting edge. The yield point here reaches itsmaximum for deformations that are usually lower than thetrue final shear of the material penetrating through the chipforming area. It is suggested to take these maximum valuesof the yield point as mechanical properties of the materialto be machined. The main goal of the theoretical andexperimental investigations presented in this paper is toestablish the analytical dependence of the specific defor-mation work and therefore also of yield point and specifictangential forces on deformation, taking account of theeffect of temperature on yield point. The main advantagesof applying the specific deformation work is not only itsdirect relation to deformation temperature but also thepossibilityofexperimentallydeterminingthisworkthrough specific tangential forces and true final shear. Inthis way it is possible to establish how deformation tem-peratureaffectsyieldpointbymeansofempiricalconstants.KeywordsMachine tool ? Cutting ? Mechanicalproperties ? Flow curve1 IntroductionThe resistance characteristics of the machined material todeformationincuttingareusuallydeterminedbymechanical test methods for tension and pressure and thesubsequent extrapolation to the necessary amount of plasticdeformation occurring during machining. However, thedeformation of the material and hence the specific defor-mation work during machining is usually higher by oneorder of magnitude, and the strain rate is higher by abouteight orders of magnitude than in standard test methods fortension and pressure. In addition, large plastic deformationand an inhomogeneous deformation distribution in theprimary shear zone cause a heterogeneous temperaturedistribution. In turn, this leads to an uneven resistance ofthe machined material to plastic deformation. It has to betaken into account that the conditions differ for the defor-mation of the material in the chip forming area or ratherprimary and secondary shear zones as well as in theaccumulation zones and in the areas of the plastic contactbetween chip and wedge 1. It must also be taken intoconsideration that the resistance of the material to plasticdeformation in the shear and accumulation zones variesvery much.V. KushnerDepartment of Mechanical Engineering and Materials Science,Omsk State Technical University, pr. Mira 11, 644050 Omsk,RussiaM. Storchak (&)Institute for Machine Tools, University of Stuttgart,Holzgartenstrae 17, 70174 Stuttgart, Germanye-mail: michael.storchakifw.uni-stuttgart.de123Prod. Eng. Res. Devel. (2014) 8:679688DOI 10.1007/s11740-014-0573-8Deformation, strain rate and temperature are linked toeach other during the machining process. When deter-mining the mechanical properties of a material with astandard test, an operator establishes these factors irre-spective of such interactions. This leads to substantialerrors when determining the mechanical properties of thematerial to be machined. How the above-mentioned factorsinfluence the dependence of yield point on deformation inmachining is not taken into sufficient account. Such con-siderations are necessary because the conditions of thematerials deformation in machining processes differ con-siderably from standard tests. At present, analysing theregularities of the machined materials resistance to plasticdeformation in cutting is limited to examining only themean values of yield point, which are extended to a widerange of change in deformation. This range includes boththe areas of the hardening of the material to be machinedand the areas of the softening 26. Many investigationsare exclusively restricted to the experimental determinationof specific tangential forces in the chip forming area orprimary shear zone 35, 7, 8. This is, however, insuffi-cient to be able to establish a dependence of yield point ondeformation or rather a flow curve for machining processesand to evaluate maximum values of yield point.For different machining conditions, deformation partlyoccurs in a relatively large region of the chip forming area.This deformation is partly located in a narrow regionimmediately at the boundary of the chip forming area 5.The localisation of deformation in this narrow area has aconsiderable effect on the softening of the material to bemachined. Such an effect must absolutely be taken intoconsideration when determining the flow curve.Itisimpossibletodetermineaflowcurveofthemachinedmaterial by experiment under cutting conditions due to theuneven distribution of deformation in the shear zones.Moreover, the yield point of the material to be machineddoes not only depend on the size of deformation but also onthe change in temperature, which involves changes indeformation and yield point. The parameters mentionedhave a certain interaction with each other, which cannot beestablished by experiment. That is why not only experi-mental but also theoretical or analytical examinations haveto be carried out to determine flow curves.The main goal of the theoretical and experimentalinvestigations presented in this paper is to establish theanalytical dependence of the specific deformation work andtherefore also of yield point and specific tangential forceson deformation, taking account of the effect of temperatureon yield point.2 Analysis of hypotheses about the regularitiesof material resistance to deformation in machining2.1 Effect of strain, strain rate and temperatureon the yield pointMany researchers assumed that there are uniform regular-ities, applying to the resistance of the material to bedeformed to plastic deformation, for different cutting lay-outs of a material, including tension, forming and materialremoval, see, e.g., 35. A large number of investigationson tensile tests assume that stress intensity depends onstrain ei, strain rate _ eiand an increase in homologoustemperature DT0913:ri f ei;DT0; _ ei1Among other things, the equation (called conditionalequation in the following) representing a dependence ofshear yield point spon deformation ep, strain rate _ e and anincrease in homologous temperature DT0is defined asfollows 15:spSbffiffiffi3p ?epffiffiffi3p?ln1d=100 !m?_ e_ e0?k?DT0?exp?B?DT0;DT0DTTmT?T0Tm;2where Sbis true tensile strength, epis current value of thetrue shear, e0ffiffiffi3p? ln 1 d=100 is true shear defor-mation at a specific strain d, is strain shear rate in tension,T is the temperature of a deformable material, m, n, k, Bare empirical constants representing an effect of deforma-tion, strain rate and temperature on a current value of theyield point sp, D?T0is the mean value of increase in thehomologous temperature in the chip forming area, DT isthe change in absolute temperature, T is the current tem-perature, T0is room temperature, Tmis the melting tem-perature of the material.The conditional equation in the form of (2) cannot bedirectly applied as material model for machining processes,as an increase in temperature during cutting is not anindependent variable and depends on deformation epaswell as the current yield point sp. Hence, the conditionalequationformeetingthedeformationconditionsinmachining has to be searched for in the form of a flowcurve sp(ep) containing empirical constants. These con-stants represent effects of deformation, strain rate andtemperature.680Prod. Eng. Res. Devel. (2014) 8:6796881232.2 Hypothesis about an application of the simple formof loading by cuttingThe dependences of specific tangential forces stin theconditional shear plane on true final shear ewwhen turningdifferent steels were compared with the dependences ofshear yield point on shear deformation in tension sp(ep) 3.The specific tangential forces stwere interpreted here asmaximum values of the yield point in the chip formingarea. It is, however, more correct to interpret the specifictangential forces st, obtained by experiment, as quotient ofthe specific deformation work in relation to true final shearewor rather as average of the yield point. This follows froma definition of the specific tangential force stin the chipforming area by the projection Fsof the forces Rnand Rmon the rake face of the wedge onto the shear plane A andthe deformation capacity in the chip forming area throughthis force Fsand the specific deformation work AwFig. 1.The following dependences can be deduced from theabove-mentioned and Fig. 1:Fs? v2 ss?a ? bsin uy? v2 Aw? Sb? a ? b ? v3where b is width of cut.AwZew0spSbdep4The following can be concluded from (3):ssSb1ew? Aw;ssv ? sinuyv2? Aw? Sb;v2 v ?cos ccos uy? c?;ewv2v ? sinuyK 1=K ? 2 ? sin ccos c5where m2is the velocity of the chip shear relative to theworkpiece in the direction of the shear plane A, ewis truefinal shear, K is chip compression ratio.To extrapolate the dependences sp(ep), a law of singleload was used which does not take account of an effect ofstrain rate and temperature on yield point 15:spSbffiffiffi3p ?epe0?m62.3 Hypothesis about the stability of specific tangentialforces in the chip formation zone and their relationto material strength by tensile testIt was detected that specific tangential forces stinmachining were close to the shear yield point in tensionin several cases 3. This yield point was established hereby extrapolating the dependence (3) on the size ofdeformation of the true shear during machining. For thisreason an empirical correlation was suggested to estimatespecific tangential forces stin the shear plane duringmachining 3:st? A ? 2:5m A2:5;7where A is the empirical coefficient; A2.5is the shear yieldpoint in tensile tests, which is extrapolated to a deformationof e = 2.5.Regarding the majority of several examined steels, theforces stdid nevertheless not increase with growingdeformation as required by the law of single load (see 6).They rather remained constant or even decreased.Apart from the dependence (7), other correlationsbetween forces stand strength characteristics in tensiletests were suggested as well. Among other things, thefollowing empirical correlations were obtained for estab-lishing specific tangential forces stin the chip forming areaand on the rake face qFwhen turning different steels usingtools with shortened rake faces 1, 16:Fig. 1 Layout for establishing the specific tangential force ssin thechip forming area (a), velocity diagram and cutting scheme (b)Prod. Eng. Res. Devel. (2014) 8:679688681123st 0:8 ? Sb;qF 0:6 ? Sb8These correlations obtained by experiment are presentedin Fig. 2.These constant and decreasing dependences st(ew) showthat the flow curves sp(ep) for tensile tests and machiningdo not agree with each other. This corresponds with theexperimental investigations on machining and pressure ofaluminium in the range of changes in shear deformationbetween 0.6 and 1.5 9. The specific tangential forces inthe shear plane during machining were considerablygreater here than the compression strength.That the flow curves for pressure and machining in therange of smaller deformations do not agree can beexplained by the effect of strain rate on the stresses in theshear plane during machining. The effect of temperature onthe yield point and the specific tangential forces inmachining are assessed differently as well. One side con-tests that temperature affects the specific tangential forcesin the chip forming area and on the rake face of the wedge3, 4, 14. This is confirmed by the fact that the temperaturein the chip forming area does not exceed a limit of 400 ?Cas a rule 15. In addition, it was assumed that a decrease inyield point during machining is completely compensatedby its increase on account of a major effect of strain rate athigher temperatures 16. Assuming that temperature hasno substantial effect was accepted regarding both the spe-cific tangential forces in the chip forming area and thespecific tangential forces on the rake face of the wedge 8,13, 17. Another side confirms that strain rate and tem-perature have a considerable effect on the yield point inmachining 1, 15.The following analysis of the experimental data is pre-sented to justify the latter point of view.3 Effect of strain rate and temperature on specifictangential forces in the chip forming area3.1 Effect of strain rateOwing to the analysis of results obtained by experiment, itis detected in 3 that the ratio of strain rates in tension andmachining affects the mean value of yield point. Specifictangential forces stare examined when machining differentsteels at a depth of cut of a = 0.22 mm and a toolorthogonal rake angle of the wedge of c = 20?. Experi-mental analyses were carried out at extremely low cuttingspeeds of m = 0.2 m/min to rule out an effect of temper-ature on specific tangential forces st3. In addition, tensiletests were simultaneously conducted at the same strainrates. A quotient of the strain rates in machining and tensiletests was approximately two powers smaller than withconventional cutting parameters. This quotient is, however,great enough and reaches about 106.In view of the fact that specific tangential forces stin thechip forming area are characterised by mean values of yieldpoint, they are compared with extrapolated mean values oftensile strength:st;m1ew?Zew0Sbffiffiffi3p ?epe0?mdep1ew? Aw;t? SbA ? Sbm 1? emw;9Aw;tZew0spSbdep;10where Aw,tis the dimensionless specific deformation workin tensile tests, which is extrapolated to deformations of thetrue final shear during machining ew.If the strain rate is taken into account and an effect oftemperature is ruled out, a dependence of specific tangen-tial forces stin the chip forming area at mean values ofFig. 2 Mean specific tangential forces stin the chip forming area andon the shortened rake face of the wedge qFdepending on true tensilestrength Sbin machining 16682Prod. Eng. Res. Devel. (2014) 8:679688123tensile strength can be approximated by the followingfunction:st Ke? st;m;11where Keis the coefficient of deformability, determiningthe differences between the deformation conditions of themachined material in the chip forming area for machiningand tensile tests.Table 1 shows the experimental data and results whencomparing specific tangential forces stin the shear planewith the mean values of yield point ss,m.In the machining of the examined steels, the forces stareapproximately 1.3 times greater than the mean values oftensile strength extrapolated to the deformation of true finalshear in machining (see Table 1). Hence, the coefficient Keis 1.3. According to this coefficient, an increase in strainrate by about 106, which corresponds to a transition fromtensile tests to machining at relatively low homologoustemperatures T0= 0,165), is capable of causing a consid-erable rise in the mean value of yield point st,m.To estimate the effect of homologous temperature on thecoefficient of deformability Ke, it is analysed how relativechanges in strain rate affect the yield point in the machiningof different materials 4 such as lead, aluminium and steel.The results of the analysis are shown in Fig. 3.Hence,thecoefficientofdeformabilityKeinmachining and other kinds of deformation such as, e.g.,tensile tests does not only depend on changes in strainrate _ e/_ e0but also on changes in homologous temperatureDT0. For modern machining processes, the difference incutting speed is within one degree of power at most.Contrary to this, the difference between the speed of astandardised tensile or pressure test and the cutting speedin machining is eight degrees of power. A change indeformation speed within in one degree, which impliesthe change in cutting speeds for different machiningprocesses, changes the derived coefficient of deformabi-lity from 1.258 to 1.344. This change in the coefficientof deformability can be ignored. Therefore, a quotient ofstrain rates for machining in the range of conventionalcutting parameters and for tensile tests is about 108andcan be assumed as constant 15. Accordingly, the valuesof the coefficient Kehave to be greater with growinghomologous temperature (see Fig. 3). This coefficient canbe represented as a function of the increase in homolo-gous temperature:Ke 108k?DT0123.2 Effect of the deformation temperatureOwing to the experimental data of specific tangential forcesin the chip forming area and on the rake face of the wedge,it can be inferred that there is a hardening effect of themachined material due to the change in coefficient Keaswell as a softening effect of the temperature in machining1. For example, it can be concluded from the experi-mental data shown in Fig. 2a, that yield point rises roughlyproportionally to the increase in true breaking point as wellas that the quotient st/Sbdecreases with increasing truetensile strength Sbor correspondingly increasing defor-mation temperature hD:hD?st? ewCV;13where CVis the specific volumetric heat capacity of thematerial to be machined.Figure 4 shows how temperature affects the mean yieldpoint when machining different steels. Specific tangentialforces in the area of plastic contact between tool and chipare lower than in the chip forming zone, when machiningsteels with a shortened rake face of the wedge (see 8):qF& 0.75 ? st16. Such a ratio of the values of meanspecific tangential forces in the chip forming area and inthe area of plastic contact can be interpreted in favour ofthe decrease in yield point of the machined material on therake face with growing temperature (see Fig. 4b). Thisresults in the uneven distribution of the specific tangentialforces on the rake face of the wedge, involving an increaseTable 1 Experimental data for machining and tensile tests (rbelastic limit)No.Kind ofsteeld, %rb,MPamss,m,MPaewst,MPa1St00383180.33564.14602C10423620.33803.3490320Cr354800.34773.15804Cr18Ni9Ti636340.56702.51,030Fig. 3 Effect of homologous temperature on the coefficient ofdeformability KeProd. Eng. Res. Devel. (2014) 8:679688683123in temperature. This leads to the effect of temperature onyield point in machining.It is assumed that the maximum value of yield point isreached in the accumulation zone B (see Fig. 1a) near thecutting edge at lower temperatures. Accordingly, themaximum value of yield point in the accumulation zones ofthe rake face q0and the flank face should be considerablygreater than stand qF.Regarding todays state of the measuring technology, itis impossible or very difficult to determine the directexperimental reason why there is such a maximum bymeans of establishing the change in specific tangentialforces in the very small area of the accumulation zone B.However, this can be indirectly accounted for by estab-lishing specific tangential forces in the accumulation zoneG of the flank face (see Fig. 1a), where the deformationconditions are very similar to the corresponding conditionsof the accumulation zone B 16. Such changes in specifictangential forces in the accumulation zone G of the flankface were investigated for the machining of steel C45 1.It was found out that the specific tangential forces in theaccumulation zone G are greater than in the chip formingareaFig. 5.In the experimental examinations of forces and chipcompression ratios 18 during the machining of steel C45,the quotient of the specific tangential forces qF/stdid notFig. 4 Effect of temperature on the mean yield point when machin-ing different steelsFig. 5 Comparison between specific tangential forces on the rakeface, in the area of plastic contact, in the accumulation zone of theflank face and in the wear chamfer of the flank face for the machiningof steel C45Fig. 6 Quotient of the specific tangential forces qF/stdepending onPe clet number (a) and cutting temperature on the rake face of thewedge (b) 1684Prod. Eng. Res. Devel. (2014) 8:679688123remain constant but decreased in accordance with thecalculated cutting temperature on the rake face or thePe clet number 1, 19Fig. 6.The experimental results indicate that there are consid-erablechangesinspecifictangentialforces,ifthemachining conditions differ. Yet changes in yield point,which could be even greater due to the effect of defor-mation, strain rate and temperature, may show consider-ably greater deviations than changes of its mean values.Due to the complexity of mathematically modelling wholeflow curves sp(ep), it is useful in the first stage to restrict theexamination of the regularities of the machined materialshardening to balancing the intensity of hardening caused bydeformation and strain rate as well as the intensity ofsoftening caused by temperature.4 Theoretical determination of the flow curveof the machined material in cuttingThe main advantages of applying the specific deformationwork is not only its direct relation to deformation tem-perature but also the possibility of experimentally deter-mining this work through specific tangential forces and truefinal shear. In this way it is possible to establish howdeformation temperature affects yield point by means ofempirical constants.4.1 Determining the flow curve for adiabaticdeformation conditions in the chip forming areaEquation (2) defines the yield point as a function of threeindependent variables: ratio of deformations ep/e0, ratio ofstrain rate_ e=_ e0and ratio of homologous temperatureDT0 DhD=Tm. Due to the analysis carried out (seeChapter 3), it can be assumed that the ratio of strain rates inmachining and tensile tests is constant and approximately108. Characterising this ratio, the coefficient of deforma-bility Kecan be represented here as a function of theincrease in homologous temperature (see 12).If the deformation conditions are very close to adiabaticprocesses, an increase in homologous temperature DT0(ep)can be made up for a current value of deformation epby acurrent value of the specific deformation work Aw,tcorre-sponding to this deformation as follows:DT0ep? A1? Aw;tAw;tZep0spSbdeA1SbCV? Tm14Compared to the shear yield point sp, the advantage ofputting in the specific work Aw,tis that the specific workcan be established from the specific tangential force stobtained by experiment, from the true tensile strength Sband the true final shear ewIn contrast to the work Aw,t, theyield point sp(ep) cannot be directly determined by exper-iment in machining. Putting in the specific deformationwork as a parameter of the machined materials deforma-tion condition also allows excluding not only temperaturebut also yield point from the conditional Eq. (2):spSbdAwdep:15If (14) and (15) are taken into consideration, the con-ditional Eq. (2) is transformed as follows:dAwdep A ? Ke? emp? f Aw16For example, in the case off Aw exp ?B ? A1? Aw17specific deformation work is defined as follows:Aw1B ? A1? ln 1 A ? A1? B ? Ke1 m? e1mp?:18The values of the specific work as calculated accordingto Eq. (18) were compared with those established byexperiment according to the measured values of the forcesand the chip compression ratios in machining 1. Theyshow a good agreement of the results obtained by experi-ment and in theoryFig. 7.The specific work Aw,tin tensile tests is definedaccording to Eq. (10). These values, which are extrapolatedin accordance with the usual deformations in machiningaccording to the law of single load, differ more from theexperimental results than the values calculated in view ofFig. 7 Comparison between calculated and experimentally deter-mined values of the specific deformation work in machining andtensile testsProd. Eng. Res. Devel. (2014) 8:679688685123the effect of strain rate and temperature (see Fig. 7). It isvery important for the comparison to take into account thatit is more reasonable to use the experimental data aboutresultant forces and chip compression ratios for directlydetermining the dependence of specific work on true shearthan the characteristics of the flow curve sp(ep).Owing to the ratio (15), Eq. (18) can be differentiatedfor establishing the flow curve sp(ep) for the deformationconditions in machining, taking the effect of strain rate andtemperature 20 into consideration:spSb A ? Ke? emp?1 A ? A1? B ? Ke1 m? e1mp?119Comparing the flow curves for machining and tensiletests with the same deformations and at temperatures cor-responding to different strain rates shows that strain rateconsiderably affects yield pointFig. 8.Analysing Fig. 8 shows that there is no considerablecorrelation between deformation and the dependences ofyield point on current true shear epand of specific tan-gential forces ston true final shear ewin the machining ofsteel C45. Other researchers came to this conclusion aswell 3, 9. In this case, the current and maximum values ofyield point differ only marginally from the mean value st/Sb. These data also indicate that flow curves for machiningand tensile tests do not correspond for a wide range ofchange in deformation. Hence, the correlations betweenyield point and final deformation can prove to be increas-ing, decreasing and constant for different machined mate-rials, depending on the tendency of these materials towardsdeformation hardening and temperature softening.The maximum value of yield point s and the corre-sponding value of deformation shear e are attained if thematerial to be machined has the same intensities of hard-ening and softening:dspdep 0 ord2Awde2p 020 sSbA ? Ks? ems1 m esm ? 1 mA ? Ke? A1? B?11m:21where B = 1.25 and Ke= 1.3 are empirical constantstaking account of the effect of temperature and strain rateon yield point.4.2 Determining the flow curve for isothermaldeformation conditions in the chip forming areaThe condition that there is no hardening (20) is absolutelynecessary for localising deformation in a narrow regionclose to the boundary of the chip forming area 21. Owingto the localisation of deformation, yield point cannot begreater than a value corresponding to the highest temper-ature for true final shear ew:spep? ?spep? ?by spep? ?spewspew by spep? ? spew?:22The phenomenon of localising deformation in a narrowregion and the involved softening of the material to bemachined may considerably affect the dependences of thespecific work and the specific tangential forces in the chipforming area on true final shear. Figure 9 presents such anexample for the machining of steel 35Cr3MoNi.According to the calculations, the ratio of shear yieldpoint to true tensile strength attains a maximum value of s/Sb= 0.726 at a localised shear of es= 0.41 whenmachining steel 35Cr3MoNi. If final shear is ew= 2, theratio s/Sbof yield point to true tensile strength stabilises ata value of 0.649. By contrast, this ratio stabilises at valuesof 0.593 and 0.544 if final shear is ew= 3 and ew= 4Fig. 8 Comparison between calculated and experimentally obtainedvalues of the ratio of yield point to shear for machining and truetensile strengthFig. 9 Effect of localising deformation in a small area on thedependence of the specific work in the machining of steel 35Cr3MoNi3686Prod. Eng. Res. Devel. (2014) 8:679688123respectively. Hence, the decreasing dependence of thespecific tangential forces in the chip forming area on truefinal shear results from the effect of deformation temper-ature on the level of the yield points stabilisation whenlocalising deformations in a narrow areaFig. 10.Hence, material resistance to plastic deformation inmachining as well as differences in the regularities of howtrue final shear affects the specific tangential forces in thechip forming area are connected with such factors as atendency of the machined material to deformation hardening(factor m) as well as a degree of the deformation tempera-tures effect on yield point Bsand true tensile strength Sb.Information about the specific tangential forces in thechip forming area is not sufficient to completely describethe resistance of the machined material to deformation inmachining. The experimental results presented in Fig. 3show that the coefficient of deformation conditions maytake on different values for the deformation zone areas withdifferent temperature distributions and thus with differentmean values of temperature increase DT0even if final shearewis constant.Concerning machining, it is useful to distinguishbetween the quantity of the coefficient of deformationconditions for the chip forming area and the one for theaccumulation zones B and G (see Fig. 1): Kesfor the chipforming area and Keqfor the accumulation zones. ThusKes& 1.3 for the homologous temperature T0= 0.167,characteristic of the chip forming area, in which defor-mations are unevenly distributed 15.4.3 Determining the flow curve for adiabaticdeformation conditions in accumulation zonesat the rake and flank faces of the wedgeIf the temperature is more evenly distributed in the accu-mulation zone B (see Fig. 1) at T0= 0.33, the coefficientof the deformation conditions can attain greater values ofKeq& 1.6. The uneven distribution of temperature alsoinfluences the coefficient of the deformation conditionshere. Correspondingly, the dependence of yield point q oncurrent true shear epis established for the accumulationzones B and G with the coefficient of the deformationconditions Kqby using the following equation:qSb A ? Kq? emp1 A ? A1? B ? Keq1 m? e1mp?1:23Similar dependences are characteristic of the yield pointin the chip forming area and in the accumulation zones aswellFig. 11. Among other things, the maximum yieldpoint can attain a value of s = 663 MPa for a true finalshear of ep= es= 1.6 in the machining of steel C45.As it follows from Eq. (9), the maximum value of yieldpoint s, which can be reached in the chip forming area,only depends on constants of the material to be machined.These constants determine the materials strength charac-teristics in tensile tests, a tendency towards hardening ofdeformation and strain rate as well as a tendency towardstemperature softening. Hence, the maximum value of yieldpoint characterises the resistance of the machined materialto plastic deformation under the conditions prevailing inthe chip forming area. In the accumulation zone B, thevalue of maximum yield point q has to be determined withthe following equation due to the greater strain rate hard-ening, owing to the more evenly distributed temperature: qSbA ? Kq? emq1 m eqm ? 1 mA ? Kq? A1? B?11m:24Under these deformation conditions, the material to bemachined is characterised by a varying resistance to plasticdeformation. The maximum value of yield point q is usedas a characteristic of the materials resistance to plasticFig. 10 Different flow curves and the dependence of the specifictangential forces in the chip forming area on true final shear whenmachining steel 35Cr3MoNi 3Fig. 11 Yield point depending on current true shear for themachining of steel C45Prod. Eng. Res. Devel. (2014) 8:679688687123deformation in the accumulation zone B. The maximumyield point reaches a value of q = 794 MPa in the accu-mulation zones B and G at a true final shear ofew= eq= 1.36 for steel C45 with mechanical propertiescorresponding to the experimental data described inFig. 11. The maximum yield point of 794 MPa in themachining of steel C45 is 1.76 times higher than shear truetensile strength (stw Sb?ffiffiffi3p= 452 MPa).Schematising the distribution of the yield point and thusthe heat flow density in the accumulation zone G of thewedges flank face and the wear chamfer D is of decisiveimportance for calculating the temperature on the flankfaces of the tool. It is equally important to establish themaximum value of the yield point at the boundary betweenzones B and C (see Fig. 1). This information is to be usedfor calculating the temperature distribution and the yieldpoint, which are connected to each other, in the zone C ofplastic contact between the chip and the rake face of thewedge.5 ConclusionThe conducted experimental results confirm that the spe-cific tangential forces change considerably under differentmachining conditions, resulting from the effect of defor-mation, strain rate and temperature. They affect the yieldpoint of the material to be machined if the mass is greater.If the intensities of the cutting materials hardening andsoftening are balanced out, deformation is localised in anarrow region of the chip forming area and leads to changein yield point as well as to its decrease due to the effect offinal temperature on the whole localised area. It was provenby experiment that yield point reaches a maximum in thechip forming area and in the accumulation zones, whereyield point is greater than in the chip
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