# A study on a die wear model considering thermal

A study on a die wear model considering thermalsoftening: (I) Construction of the wear modelJ.H. Kanga, I.W. Parkb, J.S. Jaec, S.S. Kangd,*aCentral Corporation, South KoreabDepartment of Mechanical and Precision Engineering, Graduate School, Pusan National University,Pusan, South KoreacMando Machinery Corporation, South KoreadEngineering Research Center for Net-Shape and Die Manufacturing, Pusan National University,Pusan, South KoreaReceived 3 March 1998AbstractThe service lives of tools in metal forming processes are to a large extent limited by wear, fatigue fracture and plastic deformation, etc. Inelevated temperature forming processes, wear is the predominant factor in the operating lives of tools. To predict tool life by wear,Archard’s wear model is generally applied. Usually the hardness of a die is considered to be a function of temperature in Archard’s model,but the hardness of a die is a function not only of temperature, but also of the operating time of the die. To consider the softening of a die byrepeated operations, it is necessary to express the hardness of the die by a function of temperature and operating time. By experiments intothe reheating of dies, die-softening curves have been obtained. Finally a modified Archard’s wear model, in which the hardness of the die isexpressed as a function of the main tempering curve, is proposed. # 1999 Elsevier Science S.A. All rights reserved.Keywords: Wear coefficient; Archard’s wear model; Die-softening test1. IntroductionIn general, the possible causes of die failure in metalforming processes are catastrophic fracture, excessive plas-tic deformation and an intolerable amount of wear, etc.Catastrophic fracture is not generally regarded as an aspectof wear, however it interacts with the mechanisms of gradualwear and must be considered in the analyses of wearproblems. Failures due to catastrophic fracture or excessiveplastic deformation may be eliminated by implementing anappropriate tool design with adequately selected tool mate-rials, and by limiting the use of die under specification. Thereduction of tool life caused by die wear is very difficult tocontrol, because die wear is caused by contacts of the die andthe workpiece.A large number of studies on the optimization of die lifeby predicting die wear have been carried out to reduce thereduction of tool lives by wear. The factors influencing dielife are thermal fatigue, plastic deformation, wear, etc.Amongst these, wear is the predominating factor in warm-and hot-forming processes. Lange reported that wear is thedominating failure mechanism for forging dies, beingresponsible for approximately 70% of failures [1].A large number of researches have been done on wear byadopting Archard’s wear model [2,3]. However, theseresearches had limitations on predicting tool life by con-sidering the hardness of the die to be a constant in coldforming processes and a function of temperature in warm-and hot-forming operations [4–6]. Also results by simula-tions had qualitative agreement, but considerable differencesin qualitative agreement by ignoring changes in the wearcoefficients from surface treatments, and considering thendie hardness softening effects to be constants.Therefore, to predict the amount of die wear accurately inhigh temperature forming operations it is necessary tomeasure the wear coefficients of the dies, considering diesurface treatments and obtaining die-softening curves fordifferent temperatures and operating times. In this study, thewear coefficients of H13, which is applied widely for warm-Journal of Materials Processing Technology 96 (1999) 53–58*Corresponding author.E-mail address: kangss@hyowon.cc.pusan.ac.kr (S.S. Kang)0924-0136/99/$ – see front matter # 1999 Elsevier Science S.A. All rights reserved.PII: S 0924-0136(99)00103-Xand hot-forging dies, were measured applying various heat-treatments, and die-softening by reheating was quantified inthe main tempering curve. A new wear model was proposedby modifying the hardness in Archard’s wear model to be afunction of operating time and temperature.2. Experiments2.1. Die wear testsWear tests of pin-on-disk types had been done to acquirethe die wear coefficients using H13 die steel, applied widelyin industry, as the pin and AISI 1010 as the disk. Thechemical compositions of H13 die steel and AISI 1010are shown in Table 1, whilst the experimental conditionsare shown in Table 2. Experiments were done at 5008Ctohave similarities with the operating conditions for actualdies. Fig. 1 shows the dimensions of the specimens for thewear tests.Tests have been done for six types of heat-treatments tomeasure the wear coefficients of actual heat-treatments usedin industry. The six heat-treatment processes what wereapplied are listed in Table 3, whilst the heat-treatment cyclesare shown in Fig. 2. Generally, a white layer, a diffusionlayer and base metal are formed from the surfaces whennitriding treatment had been done to the dies, as shown inFig. 3. Each layer has a different chemical composition, sothat the wear coefficients are unlike. Symbols A and B inTable 3 are for the same heat-treatments: A does not have awhite layer; whilst B does. The wear coefficients for variousheat-treatments are calculated from the weights of the pinsapplied in the tests. The calculated results of wear coeffi-cients are listed in Table 4.In Table 4, specimen A without a white layer has a 1.83 -times greater wear coefficient than specimen B with a whitelayer, but A and B have the same heat-treatment history.Specimen C has the same heat-treatment history as B, but thepost heat-treatment is not same. By comparison of speci-mens B and C, it is seen that the ion nitrided specimen has anearly three-times greater wear coefficient than that for thegas nitrided specimen. In the case of F, applying ComplexHeat Treatment which is applied to warm- and hot-formingdies by Dongwoo Heat-Treatment Corporation, Korea,results in a higher value of wear coefficient than that ofthe nitrided specimen, but also gives a more uniform hard-Table 1Chemical compositions of the H13 and AISI 1010 steels (wt%)Material C Si Mn P S Ni Cr Mo W VH13 0.32–0.42 0.08–1.20 0.5 0.03 0.03 1.30–2.0 4.50–5.50 1.00–1.50 0.50–1.00 0.80–1.20AISI 1010 0.08–0.13 0.15–0.35 0.30–0.60 0.03 0.03 – – – – –Table 2Experimental conditions for the wear testsOperating variablesMovement SlidingNormal force 300 NVelocity 50 mm/sSystem structurePin H13Disk AISI 1010Atmosphere AirTemperature 5008CLubrication NoneFig. 1. Dimensions (mm) of the disk and the pin for wear tests.Table 3Heat treatments of the H13 steel for the wear testsPin Quenching(1 h)First tempering(8C 1h)Second tempering(8C 1h)Post heattreatmentWhite layer(mm)DiffusionlayerHardness(HRC)A 10308C 530 520 Ion nitriding 0 0.2 54B 10308C 530 520 Ion nitriding 2–4 0.2 54C 10308C 530 520 Gas nitriding 2–4 0.2 54D 10308C 580 570 Ion nitriding 2–4 0.2 48–50E 10308C 580 570 Gas nitriding 2–4 0.2 48–50F 10308C 530 520 Complex treatment 2–4 0.2 6054 J.H. Kang et al. / Journal of Materials Processing Technology 96 (1999) 53–58ness distribution from the surface than that of the other heat-treated specimens. Therefore the resistance to wear is pre-dicted to be higher than that for other heat-treated specimenswhich has been verified by Jae [7], who pronounced in histechnical report that die life was increased by 200–500%after applying Complex Heat Treatment.2.2. Die-softening testsHeat-treatments as shown in Fig. 4 were carried out toacquire the die-softening curves of H13 die steel for actualheat-treatments.Dies of H13 that had been subjected to quenching,tempering and 15, 30, 45 and 60 h of nitriding, werereheated to 6008C, 6258C and 6508C for 20, 40 and 60 h.Die softening related to time and temperatures was mea-sured using a Vickers hardness tester and converted to theRockwell C scale (HRC). The results of the die-softeningtests are classified in Table 5. The hardness decreases withthe passage of time at each reheating temperature, as shownin Figs. 5–7.The tempering parameter related to heat-treatment can beexpressed as Eq. (1)M T 20 log t ; (1)where t is tempering time (h) and T is the temperingtemperature (K).The main tempering curve according to reheating can beobtained by the use of the tempering parameter expressed asEq. (1). Relationships between this tempering parameterand hardness can be approximated to one equation by themain tempering curve. The die-softening rates according toFig. 2. Heat-treatment cycles of H13 steel for wear tests.Fig. 3. The layers of the nitrided die.Table 4The results of the wear testsPin Length (mm) Weight (g) Area ( 102mm2) k ( 106)Initial Final Initial Final Initial FinalA 14.30 14.00 4.3707 4.3641 2.0854 28.375 1.37B 14.28 14.1 4.3763 4.3726 2.9634 1.5525 0.74C 14.29 14.2 4.3636 4.3618 2.5052 7.626 0.27D 14.26 14.15 4.3530 4.3501 3.9951 9.66 0.62E 14.28 14.20 4.3646 4.3632 2.9634 6.879 0.27F 14.29 14.20 4.409 4.4104 2.5052 7.2475 0.86Fig. 4. The heat-treatment processes for obtaining the die-softeningcurves.J.H. Kang et al. / Journal of Materials Processing Technology 96 (1999) 53–58 55temperature and time can be obtained from the main tem-pering curve. The main tempering softening curve can beexpressed as Eq. (2)H A exp B M 0:001 CD; (2)where M is tempering parameter and A, B, C and D are die-softening constants.Constants A, B, C and D were obtained by means ofEq. (1) and Figs. 5–7. Relationships between the temperingparameter and the hardness for various heat-treatments wereobtained from the acquired constants and are shown inFig. 8.3. Suggestion of a new wear modelThe conventional model applied to wear prediction inmetal forming processes is Archard’s model, in which thehardness of the die is expressed as a function of temperatureonly. However, the hardness of the die generally decreaseswith increasing number of operations. In this study, theTable 5Results of the hardness softening of the die steel after different reheating timesHeat treatment Hardness (HRC)20 h 40 h 60 h6008C 6258C 6508C 6008C 6258C 6508C 6008C 6258C 6508C10308C 60 min 5808C, 5708C (Q t : (3)Eq. (3) can be expressed in integration form as Eq. (4) forfinite-element analyses:d k3H T;t ZTtot0nv dt on C10tool: (4)Eq. (4) can be arranged as Eq. (5):dt tdtk3H T;t vn v tt on C10tool: (5)To apply Eq. (5) to finite-element simulation, repeatedanalyses are necessary. Therefore, it is suggested to useEq. (6) where the amount of wear can be predicted by onlyone finite-element analysis. Generally, the allowable amountof wear for dies are fixed in industry because of the requireddimensional accuracy of the products, so the operating timecan be predicted by just one analysis from Eq. (6) if theallowable amounts of wear are considered as constantsdfinHH T;t Ztfin0kPL3Hdt on C10tool; (6)where H is the hardness of the die at steady-state tempera-tures, H T;t is a function of hardness softening consideringthe tempering parameter and dfinis an allowable amount ofwear of the dies in industry.Eq. (6) can be simplified as Eq. (7)dfinXnfin1kPL3HHH T;tcyclenfin: (7)Since an accurate description of hardness decreases byoperating time and tempering parameter is necessary, thehardness distributions of the initial die surface were notconsidered in Eq. (7). The hardness of the initial die surfacewas assumed to be that of a worn die during operation.Eq. (7) was modified into Eq. (8) to obtain the final amountof wear from one finite-element analysis.dfinXnfin1kPL3HHH T;t;winitial: (8)From Eq. (8), the operating times of warm- and hot-forging processes can be acquired by adding the amountof wear for the time increment. The operation number wasobtained by dividing the operating time into the cycle time,but the proposed equation has a meaning only if the tem-perature of the die is a steady-state temperature. Thus theassumption of the initial input temperature for obtainingsteady-state is an important variable.In calculating the amount of wear, the wear coefficient forthe white layer, 0.74 106, must be changed into that of thediffusion layer, 1.37 106, when the amount of wearexceeds the white layer. The amount of wear in the diffusionlayer can be obtained by multiplying the ratios of the twowear coefficients, 1.83, to initial result of analysis. Also, thehardness was obtained from the initial hardness in wornparts by considering increments of the tempering parameter,as shown in Fig. 9, to consider the hardness decreases inFig. 9. Flow chart for the calculation of the die hardness distributions.Fig. 10. Flow chart for the calculation of the final amount of wear.J.H. Kang et al. / Journal of Materials Processing Technology 96 (1999) 53–58 57operation. Wear amounts per unit time were obtained by theacquired hardness from Eq. (8), the former calculationprocedures being repeated to obtain the final amounts ofwear. The flow chart for the calculation of the amounts wearis shown in Fig. 10.4. ConclusionsTo predict the die life of warm- and hot-forging diesprecisely, the differences in the amounts of wear by thecharacteristics of the dies and the materials must be con-sidered. It is necessary to consider the hardness and the heat-softening of worn parts at the same time by deliberating thehardness distributions from the die surface after the initialheat-treatment of the die. In this study, experiments werecarried out considering these factors and a new wear modelwas proposed. From this work, the following conclusionscan be drawn:1. The wear coefficients of H13 die steel, applied widely inindustry were measured according to the heat-treat-ments. By experiment, wear coefficients related to thesurface heat-treatment layers were obtained. From theseresults, wear coefficients could be selected based on thedegree of the amount of wear amounts from the diesurface.2. A tempering parameter of dies was introduced to con-sider the simultaneous heat-softening of dies by time andtemperature. Relationships between the temperingparameter a