Analysis of Interfacial Damage and Debonding Life Estimation of Cold Forging Tool Coated with Hard Film

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1 Materials Trasactios, Vol. 45, No. 9 (24) pp to 2837 #24 The Japa Society for Techology of Plasticity Aalysis of Iterfacial Damage ad Debodig Life Estimatio of Cold Forgig Coated with Hard Kuio Hayakawa 1, Tamotsu Nakamura 1, Shigekazu Taaka 1 ad Kuiaki Harada 2 1 Departmet of Mechaical Egieerig, Shizuoka Uiversity, Hamamatsu , Japa 2 NTN Corporatio, Iwata , Japa The behavior of the iterface of a cold forgig tool coated with a hard film is aalyzed by the fiite elemet method (FEM). The mechaical properties of the iterface betwee a hard film ad a tool material are modeled uder the framework of the irreversible thermodyamic costitutive equatio theory with cotiuum damage mechaics. The iterface damage variable ad its evolutio law are itroduced, which express the degradatio of the iterface. The hemispherical tool of SUJ2 i JIS coated with a electroplated coatig of chromium idets ito a cylidrical workpiece of S25C i JIS, which is performed to examie the validity of the proposed model. I FE aalysis, the proposed costitutive equatios are implemeted by the oliear sprigs betwee opposite odes of the iterface. Calculated results show that the maximum iterfacial ormal displacemet is observed close to the frot of the lip of idetatio, whereas maximum iterfacial tagetial displacemet is observed close to the back of the lip of idetatio. The regio where debodig will first occur as idicated by the calculatio results, is similar to the regio of the behavior durig a actual forgig operatio. Fially, a method of evaluatig the iterfacial debodig life of coated tools is proposed. (Received October 6, 23; Accepted Jue 1, 24) Keywords: cold forgig, hard-film-coated tool, iterface, fiite elemet method, oliear sprig model, iterface damage mechaics, iterfacial separatio, debodig life 1. Itroductio Recetly, forgig tools coated with hard films such as electroplated coatigs of chromium, titaium itride (TiN) ad titaium carbide (TiC), are used with the aim of icreasig the service life of tools by about 2 to 1 times. 1 3) I the practical use of coated tools, however, we ofte ecouter debodig at the iterface of the film ad the tool material. It is importat to grasp the behavior of the iterface of a hard film ad a tool material to accurately evaluate iterfacial stregth. Numerical simulatios of the mechaical behavior of materials coated with a hard film have bee performed. 4,5) The objects of the simulatios are flat hard films o a flat substrate ideted with a ideter similar to that used i a scratch test or a idetatio test. 6) Moreover, complete adhesio at the iterface is postulated. However, the deformatio of the film i a scratch test or a idetatio test does ot correspod to that of a actual hard film coated o forgig tools sice the film itself is ideted. Furthermore, because complete adhesio at the iterface is postulated, the deterioratio of the iterface is ot cosidered. I the preset paper, the fiite elemet aalysis of the mechaical behavior of the hard film - tool material iterface of forgig tools uder coditios closer to actual forgig situatios tha those for covetioal scratch or idetatio tests was performed by iterface damage mechaics (IDM). First, the examiatio model of idetatio of hemispherical coated tool was proposed. Next, after itroducig a oliear iterfacial sprig model ad defiig the iterfacial damage variable, the costitutive ad damage evolutio equatios at the iterface betwee the hard film ad the tool material are formulated uder the framework of the irreversible thermodyamic costitutive theory. 8,9,11) To apply the above equatios to the umerical aalysis of the iterface by FEM, the cocept of the oliear iterfacial sprig model is employed. 7) O the basis of the calculated results o the deformatio behavior of the iterface, the probable debodig mechaisms of the preset forgig tool coated with the hard film are discussed. Fially, a method of evaluatig the iterfacial debodig life is proposed. Moreover, the calculated results o the debodig life of the preset forgig tool are show. 2. Examied Model for Iterfacial Behavior of Forgig Coated with Hard I the scratch or idetatio tests, the hard film o the substrate is ideted by a slider or a ideter. The, the aspect of the deformatio of the film does ot correspod to that of actual forgig tools. It is favorable to evaluate the behavior of the iterface at coditios closer to those of actual forgig tha to coditios of these tests. I the preset study, we aalyze the behavior of the iterface betwee the hard film ad the tool material by the examiatio model as show i Fig. 1. I this model, the hemispherical coated tool of 5 mm radius is ideted to the R Thickess t Fig. 1 Schematics of examiatio model of idetatio of hemispherical tool coated with hard film.

2 Aalysis of Iterfacial Damage ad Debodig Life Estimatio of Cold Forgig Coated with Hard 2833 Iterfacial regio h Microdefects workpiece of 2 mm i diameter ad 1 mm i height. The deformatio of the bottom ad the periphery of the workpiece are costraied. The proposed model is itroduced as the simplificatio of the actual forgig. The effect of the plastic flow of the workpiece ad the frictio coditio betwee the film ad the workpiece o the behavior of the iterface ca be take ito accout more effectively. 3. Modelig of Iterface by Noliear Iterfacial Sprig Model 3.1 Noliear iterfacial sprig model Let us postulate the iterfacial behavior that occurs i the iterfacial regio show i Fig. 2(a). I the iterfacial regio, microdefects develop whe the exteral load is subjected, ad adhesio stregth deteriorates. I the preset study, o calculatig the iterfacial behavior by FEM, the adhesio of the iterfacial regio betwee the hard film ad the tool material is modeled usig distributed oliear sprigs proposed by Ma ad Kishimoto, 7) as show i Fig. 2(b). I this model, the displacemet of the iterfacial regio ca be expressed by the differece i displacemet betwee the iitial poits o the opposite sides of the film ad the tool material P ad P across the iterfacial regio, as show i Fig. 2(b). Whe exteral load is applied, poit P will move to poit Q, ad these poits will produce the iterfacial displacemet U ¼ P Q. The iterfacial displacemet vector U ca be expressed by the compoets of the ormal directio, tagetial directio t ad aother directio b accordig to a right-had Cartesia coordiate system i Fig. 2, expressed as U, U t ad U b. Moreover, we defie the iterfacial relative displacemet u as u ¼ðu ; u t ; u b Þ T ¼ 1 h ðu ; U t ; U b Þ T where h is the thickess of the iterfacial regio. Moreover, the superscript T meas traspositio. 3.2 Iterfacial damage variable Whe the iterface is subject to a exteral load, the iterface deteriorates gradually because of the iitiatio ad growth of microscopic cracks ad cavities. Figure 3 shows the odamaged ad damaged states of the iterface. The elemetal area at the udamaged state da is U P U t Q Fig. 2 Schematics of Iterfacial regio with microdefects ad equivalet iterfacial sprig model. (a) Iterfacial regio (b) Equivalet sprig model P b t ð1þ da No-damaged state of iterface deteriorated by the exteral load, ad the elemetal area da becomes d ~a. The, the iterfacial damage variable D is defied as d ~a ¼ð1 D Þda ð3þ where is the uit ormal vector to the iterface. I the preset study, we express the deterioratio of the iterface usig the iterfacial damage variable D. 4. Modelig of Iterfacial Costitutive ad Damage Evolutio Equatios 4.1 Iterfacial stress iterfacial relative displacemet relatioship with iterfacial damage The irreversible thermodyamic costitutive equatio theory 8) is oe of the most ratioal frameworks for the formulatio of the costitutive equatios with irreversible chages of iteral states such as damage ad plastic deformatio. I the preset study, we apply this theory to the formulatio of the costitutive ad damage evolutio equatios of the iterface. If the thickess h is small ad the strai throughout the thickess is uiform, iterfacial strai tesor " is defied as " ¼ 1 2 ðu þ u Þ ð3þ Whe we restrict the adiabatic, costat temperature coditio, Clausius Duhem iequality i the iterfacial regio ca be express as : _" _ ð4þ where ad are the iterfacial stress ad Helmholtz free eergy i the iterfacial regio. Helmholtz eergy is a fuctio of iterfacial relative displacemet u ad iterfacial damage variable D. By use of the iterfacial stress vector T ¼, eq. (4) ca be rewritte as To hold for eq. _D ð5þ For the Helmholtz free eergy, we defie da Damaged state of iterface Fig. 3 Schematics of o-damaged ad damaged states of elemetal area i hard film-tool material iterface. ð6þ

3 2834 K. Hayakawa, T. Nakamura, S. Taaka ad K. Harada ¼ 1 2 ð1 D Þ u K u where K is the iitial iterfacial rigidity tesor at the itact state. Here, we will adopt followig simple form: K 1 t K ¼ B Kb A ð8þ K By usig eqs. (6) ad (7), the relatioship betwee iterfacial stress vector ad iterfacial relative displacemet ca be obtaied as T ¼ð1 D ÞK u ð9þ O the other had, we defie the thermodyamic cojugate force of the iterfacial damage variable R ¼ 1 2 ðk t u2 t þ K b u2 b þ K u2 Þ ð7þ ð1þ 4.2 Evolutio equatio of iterfacial damage variable Uder the restrictio of the framework of the irreversible thermodyamic costitutive equatio, the evolutio equatio of the iterfacial damage variable _D ca be derived usig the ormality rule, so that _D ca develop to the outer ormal directio of the damage dissipatio potetial defied i the space of the cojugate force of the iterfacial damage F d ðr Þ _D ¼ _ d ð _ Þ where _ is a udetermied multiplier that prescribes the magitude of damage developmet. I the preset study, we postulate a simple form for the damage dissipatio potetial F d ðr Þ as F d ðr Þ¼R ð12þ For the multiplier _, we give the followig form so that the iterfacial fatigue behavior uder the cyclic loadig ca be expressed as _ ¼ R R D 1 h _R i ð13þ S S Usig eqs. (11) ad (12), eq. (11) is expressed as _D ¼ R R D 1 h _R i ð14þ S S where, S ad R are material costats. Moreover, the brackets hi are the Macauley brackets. As observed i eq. (13), the iterfacial damage variable D develops whe the cojugate force of the iterfacial damage R exceeds the threshold value R ad the derivative of R with respect to time icreases. Debodig is assumed to occur whe the iterfacial damage variable D reaches the threshold damage variable D cr. Whe debodig occurs, the iterfacial rigidity is reduced to zero. Adhesio stregth ca be evaluated by iterfacial stress i eq. (9). 4.3 Iitial iterfacial rigidity The deformatio of the iterface regio depeds o the hard film ad tool materials. The material that ca deform more easily tha others will give a stroger effect o the deformatio property of the iterfacial regio. Therefore, the iitial iterfacial rigidities Kb, K t ad K are postulated to be expressed as Kt ¼ Kb ¼ 2G f G t =ðg f þ G t Þ ð15þ K ¼ 2E f E t =ðe f þ E t Þ ð16þ where E f ad E t are Youg s moduli of the hard film ad the tool materials, ad G f ad G t are the their shear moduli, respectively. 5. Fiite Elemet Aalysis of Iterfacial Behavior Figure 4 shows the discretized model, boudary coditios ad the equivalet iterfacial sprig of the iterface for aalysis. I the preset study, the axisymmetric model is used. The geometries of the hemispherical coated tool ad the workpiece are the same as show i Fig. 1. For the boudary coditios of the hemispherical tool, the odes o the axisymmetric axis are restricted o the x-coordiate, ad the idetatio depth s o the y-coordiate is give to the odes of the upper edge of the tool. The maximum idetatio depth s max is 4.5 mm. For the parameter idicatig the positio of the iterface, we adopt the agle ( 9 ), as show i Fig. 4. For the boudary coditio of the workpiece, we give the costrait of the x-directio to the odes o the axisymmetric axis ad the outer edge, ad the costrait of the y-directio to the odes o the bottom edge. The commercial fiite elemet code MSC. Marc2 is used i the preset study. The oliear iterfacial sprigs betwee the two material poits o opposite sides of the iterface, as show i Fig. 4, are implemeted usig the user subrouties equipped i the code. For fiite elemets, we use axisymmetric 4-ode isoparametric quadrilateral elemets. The umbers of the elemets x Idetatio y depth s θ Coated tool a =.13mm Equivalet iterfacial sprig Fig. 4 Aalyzed model of idetatio of hemispherical tool coated with hard film. t

4 Aalysis of Iterfacial Damage ad Debodig Life Estimatio of Cold Forgig Coated with Hard 2835 Table 1 Elastic ad plastic properties materials used i FEM. Material Youg s modulus /GPa Poisso s ratio of the hard film, the tool material ad the workpiece are 18, 175 ad 64, respectively. Characteristic legth h is defied as h ¼ :1 mm. The depedecy of h o the umerical results is ot cosidered here because we aim at the validatio of the proposed costitutive equatios of the iterface. For frictio coditios, a coulomb frictio coefficiet of ¼ :3 is employed by assumig coditios of o lubricatio to promote the developmet of the iterfacial damage. Table 1 shows the elastic properties of the materials used i the aalysis. As materials, we employ a chromium electroplatig, a ball-bearig steel SUJ2 (i JIS) ad a lowcarbo steel S25C (i JIS) for the hard film, tool ad the workpiece, respectively. Usig the values i Table 1, the iterfacial rigidity of eqs. (17) ad (18) ca be calculated to be K ¼ 237: GPa ad K t ¼ Kb ¼ 93:92 GPa. Figure 5 shows the flow stress - plastic strai relatioship of the tool material ad the workpiece. Although the material costats D, S D ad R of eq. (15) should be determied experimetally, we employ the followig values, for the purpose of determiig the characteristics of the proposed damage evolutio equatio qualitatively: ¼ 2:, S ¼ 5: ad R ¼ :3. As observed i eq. (14), the evolutio of the iterfacial damage _D is attributed to a form proportioal to the term ðr R Þ=S for ¼ 2:. Furthermore, S ca determie the magitude of iterfacial damage evolutio. However, the ifluece of the value of S to the qualitative characteristics of the iterfacial damage is small. 6. Results ad Discussio Yield stress /MPa Behavior of iterface by iterfacial sprig model Figure 6 shows the distributio of equivalet stress i the hard film, tool material ad workpiece at S ¼ 1 mm. The Equivalet stress σ eq / MPa Equivalet plastic strai ε eq p 1. Fig. 5 Flow stress - plastic strai curves of tool ad workpiece materials used for FEM. Equivalet stress / MPa Fig Idetatio depth s = 1 mm Distributio of equivalet stress at idetatio depth of s ¼ 1 mm. plastic deformatio of the tool material does ot yield. I this figure, high equivalet stress i the tool material ad hard film is observed i the viciity of the lip of idetatio. Compressive stress is take ito accout i the calculatio of equivalet stress show i Fig. 6. For debodig, however, the effect of compressive stress ca be cosidered ot to be high. Figures 7(a) ad 7(b) show the relatioship betwee the iterfacial relative displacemets u ad u t, ad the positio of the iterface with the parameter of idetatio depth s.i these figures, the positios of the cotact edge betwee the tool ad workpiece at each idetatio depth are idicated by solid circles. As observed i Fig. 7(a), the iterfacial relative displacemet i the ormal directio u takes a maximum value at ¼ 42. This positio is close to the back of the cotact edge. A similar relatioship ca be observed at ay idetatio depth. O the other had, the iterfacial relative displacemet o tagetial directio u t is distributed moderately. At ay idetatio depths, the maximum u t is i frot of the cotact edge. Let us ivestigate i more detail the positio of the maximum iterfacial relative displacemets u ad u t. Figure 8 shows the positio of the maximum iterfacial displacemet i the ormal ad tagetial directios u ;max ad u t;max at s ¼ 2 mm. As metioed above, u ;max is located at the back of the cotact edge, whereas u t;max is i frot of the cotact edge as observed i Figs. 7(a) ad 7(b). 6.2 Developmet of iterfacial damage variable Figure 9 shows the chage i the iterfacial relative displacemets u ad u t, ad the iterfacial damage variable D at the idetatio depth s at ¼ 45. The iterfacial relative displacemets u ad u t are plotted as left ordiate, whereas the iterfacial damage variable D is plotted as right ordiate. We ca observe the rapid icrease i u at s = approximately 1.15 mm. The iterfacial relative displacemet i the tagetial directio u t starts icreasig at

5 2836 K. Hayakawa, T. Nakamura, S. Taaka ad K. Harada Relative displacemet u / s = 1. mm s = 2. mm s = 3. mm s = 4. mm Positio of cotact edge Positio of iterface θ / (a) 8 Relative displacemet u, u t / θ = 45 Iterfacial damage D u t (Tagetial) u (Normal) Idetatio depth s / mm Fig. 9 Chage i relative displacemet u, u t ad iterfacial damage variable D to idetatio depth s. at iterfacial positio ¼ Iterfacial damage D / 1-6 Relative displacemet u t / s = 1. mm s = 2. mm s = 3. mm s = 4. mm Positio of cotact edge Positio of iterface θ / (b) B 4 5 A Fig. 7 Effects of idetatio depth o distributio of iterfacial relative displacemets u ad u t. (a) Normal directio (b) Tagetial directio Fig. 1 Schematic of debodig mechaism of iterface betwee tool ad workpiece..2mm u t,max u,max mm Fig. 8 Positio of maximum relative displacemets u ;max ad u t;max at idetatio depth s ¼ 2 mm. s = approximately 1.5 mm, ad it takes the maximum at s = approximately 1.4 mm. Iterfacial damage variable D also icreases as the iterfacial relative displacemets u ad u t icrease. However, the developmet of D ceases after the iterfacial relative displacemets u ad u t stop icreasig. 6.3 Mechaism of debodig of hard film Figure 1 shows the schematic of the iterfacial stresses subjected i the viciity of the lip of the idetatio as well as the iterfacial displacemets obtaied by the calculatio. Let us discuss the mechaisms of the debodig of the coated tool from this figure. The hard film is subjected to stress ` ad its reactio stress. Uder such a coditio, the hard film is subjected to compressio by the force of idetatio À. Cosequetly, the hard film will be i the state of buckig. The mechaism cosidered above ca be observed i the practical cold forgig processes usig tools coated with the hard film, particulary a puch. Debodig from the straight lad of the puch ca be ofte experieced. I these cases, the adhesio stregth is smaller tha the stregths of the tool material ad hard film, ad thus debodig by the mechaism cosidered above will occur. The mechaism of debodig by the bucklig of the film has bee reported by Strawbridge ad Evas. 1) They ivestigated such a mechaism usig a flat film o a flat substrate. I the preset study, it is revealed that a similar mechaism may be a cause of the debodig of the iterface of a practical forgig tool with more complicated geometry, i case that the coditios regardig the mechaical properties of the tool material ad hard film are similar to those i the preset calculatio. The iterface is also subject to iterfacial shear stress by frictioal force ˆ. The, debodig by shear ca occur at the

6 Aalysis of Iterfacial Damage ad Debodig Life Estimatio of Cold Forgig Coated with Hard 2837 positio of the maximum iterfacial relative displacemet u t;max, poit B, i Fig. 1. I practical cases, debodig by shear at poit B will be restricted, as large hydrostatic pressure is subjected to poit B. 7. Evaluatio of Iterfacial Debodig Life of Coated Forgig I covetioal forgig, the debodig of the hard film of a tool occurs after some umber of cycles. The cotiuum damage mechaics may be used to evaluate the above pheomea by calculatig iterfacial damage. I the preset chapter, we attempt to evaluate the iterfacial debodig life of a forgig tool coated with a hard film uder the cyclic idetatio show i Fig. 1. A idetatio depth s of 3 mm is employed. The cyclic idetatio is calculated by FEM as follows: First, the sigle idetatio is calculated. Next, the pressure agaist the hard film at the istataeous idetatio depth s obtaied i the calculatio is coverted to the odal exteral force. The, the calculatio of the cyclic idetatio is simulated usig the coverted odal exteral forces as boudary coditios applied to the surface of the coated tool. Let us ote that calculatio after the iterfacial debodig is ot performed i the preset calculatio, sice the evaluatio of chages i the iterfacial damage variable ad iterfacial relative displacemet util the debodig is maily focused o. Figure 11 shows the distributio of the accumulated iterfacial damage variable D util the cyclic idetatio of N ¼ 22. The maximum accumulated damage ca be observed at a iterface positio of ¼ 28. From this result, the iterfacial debodig is cosidered to occur at this positio. Figure 12 shows chages i the ormal relative displacemet u ad iterfacial damage variable D to umber of idetatio at a iterface positio of ¼ 28. As umber of idetatio icreases, iterfacial damage variable ad ormal relative displacemet icrease. Moreover, as observed i Iterfacial damage D Positio of iterface θ / N = 5 N = 1 N = 15 N = 2 N = 22 Fig. 11 Effects of umber of idetatio N o distributio of iterfacial damage variable D. 8 Relative displacemet u / eq. (1), iterfacial damage variable decreases iterfacial rigidity K. 8. Coclusios I the preset paper, the FE aalysis of the iterfacial behavior of the idetatio of a hemispherical tool coated with a chromium electroplatig ito a workpiece is performed i order to elucidate mechaical behavior of the iterface of the cold forgig tool. The results of the FE aalysis show that the iterfacial relative displacemet i the ormal directio takes its maximum close to the back of the lip of the idetatio at ay idetatio depths. O the other had, the maximum iterfacial relative displacemet i the tagetial directio is located i frot of the edge of the idetatio. The possible mechaisms of the debodig of the hard film are iterfacial displacemet i ormal ad tagetial directios. Fially, iterfacial debodig life is evaluated. The aspect of the local accumulatio of iterfacial damage variables with the icrease i umber of idetatio ca be described. REFERENCES θ = 28 Iterfacial damage D Normal relative displacemet u Number of idetatio N Fig. 12 Chage i relative displacemet u ad iterfacial damage variable D to umber of idetatio N at ¼ 28. 1) Y. C. Lee ad F. K. Che: J. Mat. Process. Techol. 15 (2) ) D. C. Ko, D. H. Kim ad B. M. Kim: Wear 252 (22) ) Ch. Hisel, M. Celeghili, U. Egel ad M. Geiger: Proc. 6th ICTP 1 (1999) ) E. R. Kral, K. Komvopoulos ad D. B. Bogy: J. Appl. Mech., Tras. ASME 62 (1995) ) N. Naka, K. Yamamoto, Y. Isoo, T. Taaka ad N. Terayama: J. JSME, A 66 (2) (i Japaese). 6) P. Bejami ad C. Weaver: Proc. R. Soc., Ser. A 254 (196) ) F. S. Ma ad K. Kishimoto: JSME It. J., Ser. A 39 (1996) ) J. Lemaitre ad J. L. Chaboche: Mechaics of Solid Materials, (Cambridge Uiversity Press, 199). 9) K. Hayakawa ad S. Murakami: It. J. Damage Mech. 6 (1997) ) A. Strawbridge ad H. E. Evas: Egg. Failure Aal. 2 (1995) ) K. Hayakawa, T. Nakamura ad S. Taaka: J. JSTP 43 (22) (i Japaese) Iterfacial Damage D