Metal Machining Episode 14 docx

Appendix 5 Approximate tool yield and fracture analyses This appendix supports Section 3.2. The material of Section A5.1 is also referred to in Appendix 1.2.4. A5.1 Tool yielding The required tool hardnesses to avoid the yielding shown in Figure 3.19 have been obtained by a method due to Hill (1954).The requirement that the tool does not yield at its apex, together with force equilibrium in the tool, limits the difference between the rake face contact stress and the zero stress on the clearance face and hence places a maximum value on the allowable rake face contact stress. With the cylindrical polar coordinate system shown in Figure A5.1(a), in which the origin is at the tool apex and the angular variable q varies from 0 on the rake face to b on the clearance face, and in which the stresses s r , s q and t are positive as shown, the radial and circumferential equilibrium equations are ds r dt r —— + (s r – s q ) + —— = 0 (A5.1a) dr dq Fig. A5.1 Coordinate systems and definitions for the analysis of tool (a) yielding and (b) fracture (a) (b) Childs Part 3 31:3:2000 10:43 am Page 383 dt ds q r —— + 2t + —— = 0 (A5.2a) dr dq At the apex, where r = 0, these become dt (s r – s q ) + —— = 0 (A5.1b) dq ds q 2t + —— = 0 (A5.2b) dq To avoid yielding of the tool, the shear yield stress of which is k t , 1 — (s q – s r ) 2 + t 2 < k t 2 (A5.3) 4 If t is written as a fraction of k t t = k t sin 2f (A5.4) where f varies between ± p/4, it may be shown, after substituting (s r – s q ) from equation (A5.1b) into equation (A5.3), that equation (A5.3) leads to a limitation of the rate of change of f with q df | —— | < 1 (A5.5) dq Furthermore, an expression for the contact stress s n on the rake face relative to the value zero on the clearance face is found by integrating equation (A5.2b). After dividing both sides of equation A5.2b by k work s n k t ——— = – 2 ——— ∫ 0 b sin 2fdq (A5.6) k work k work The largest value of s n /k work is obtained when the integral takes its largest negative value. Figure (A5.2) shows the variation of f with q that gives that largest negative value: at q = b, f = 0; and at q = 0, f is determined by the friction contact stress on the rake face. In Chapter 3 (Figure 3.18) extreme examples of friction stress were considered, up to k work during steady chip creation, but zero at the start of a cut: f ≡ f 0 = 0, t f = 0 (A5.7a) 1k work f ≡ f 0 = – — sin –1 ( ——— ) , t f = k work (A5.7b) 2k t For 0 < q < b, f takes the smallest values allowed by equation (A5.5). Figure A5.2(a) is for the case b > p/2 – f 0 . If b < p/2 – f 0 , Figure A5.2(b) applies. Integration of equation (A5.6) for the dependence of f on q shown in Figure A5.2(a) or (b) as appropriate gives a maximum value of s n /k work depending on k t /k work and b. Inversely, for a specified s n , for example 384 Appendix 5 Childs Part 3 31:3:2000 10:43 am Page 384 5k work or 2.5k work , a minimum ratio of tool to work shear yield stress to avoid yield can be derived. Taking the tool’s Vickers Hardness HV to equal 5k t , relations between tool hard- ness, k work and b to avoid tool yielding can be derived. Thus, the HV/b relations dependent on k work shown in Figure 3.19 are obtained. A5.2 Tool fracture Figure A5.1(b) shows a wedge-shaped tool with a line force R per unit length acting at a friction angle l at a distance d from the apex of the wedge. This force is equivalent to a force R acting at the apex, with a moment M = Rd. A classical result of stressing a wedge (Coker and Filon, 1931) is that on the rake face the tensile stress at a distance r from the apex is bb bb cos — sin ( l + — ) sin — cos ( l + — ) 2R 22 22 s r = – —— [ ————————— – ————————— ] r b + sin bb– sin b 2M sin b + —— ——————— (A5.8) r 2 b cos b – sin b The sizes of tool transverse rupture stress (TRS) relative to the k work required to avoid fail- ure, and which are presented in Figure 3.19, have been obtained by replacing the distrib- uted tool rake face contact stresses by their equivalent line force and moment at the apex, substituting these in equation (A5.8) and differentiating with respect to r to obtain the posi- tion and hence the value of the maximum tensile stress. It is supposed that a tool will frac- ture when the maximum tensile stress is the TRS. The results presented in Figure 3.19 are for the case of a tool entering a cut, assuming that t f = 0 and s n is constant and equal to 5k work over the contact length l between the work and tool. It is found for this example that the maximum tensile stress occurs at r ≈ l. To replace the distributed stress by the equiva- lent line force and moment is only marginally justifiable: the treatment is only approxi- mate. Tool fracture 385 Fig. A5.2 Variations of φ with θ that maximize σ n / k work Childs Part 3 31:3:2000 10:43 am Page 385 References Coker, E. G. and Filon, L. N. G. (1931) A Treatise on Photoelasticity. London: Cambridge University Press, pp. 328, 367. Hill, R. (1954) On the limits set by plastic yielding to the intensity of singularities of stress. J. Mech. Phys. Solids, 2, 278–285. 386 Appendix 5 Childs Part 3 31:3:2000 10:43 am Page 386 Appendix 6 Tool material properties More detail is given here than in Chapter 3 of the materials that make up the main tool groupings. A6.1 High speed steels The high speed steels are alloy steels with about 0.75% to 1.5% carbon (C), 4% to 4.5% chromium (Cr), between 10% and 20% tungsten (W) and molybdenum (Mo); they can also have vanadium (V), up to 5%, and cobalt (Co), up to 12%. They are strengthened by heat- ing to high temperature (around 1150 to 1250˚C), just below the solidus; then quenching in two stages (to avoid thermal cracking) – to the range 500˚C to 600˚C and then to room temperature; and then tempering typically between 500˚C and 560˚C. Tempering causes hardening by the precipitation of fine carbides. More details may be found in metallurgi- cal texts such as those by Trent (1991) and Hoyle (1988). There are two series of materials, the T series which is based on W (with no Mo), and the M series which substitutes Mo for some of the W. There are no major technical advan- tages of one series over the other. The choice is one of cost, varying with the availability of these two elements. The basic grades in each series contain 0.75% to 0.85% C and 4% to 4.5% Cr, with a small amount of V (<2%) but no Co. The addition of extra V, with extra C as well, results in the formation of hard vanadium carbides on tempering. These increase the alloy’s room temperature hardness and abrasion resistance but at the expense slightly of its toughness. The addition of Co improves hot hardness, also at the expense of tough- ness. Table A6.1 gives the nominal compositions of a range of grades. Table A6.1 Sample compositions of some high speed steels Grade Composition (wt. %, balance Fe) CCrWMoVCo T1 0.75 4 18 – 1 – M2 0.85 4 6.5 5 2 – T6 0.8 4 20.5 – 1.5 12 T15 1.5 4.5 13 – 5 5 M42 1.05 4 1.5 9.5 1 8 Childs Part 3 31:3:2000 10:43 am Page 387 Figure A6.1(a) shows how the room temperature Vickers Hardness (HV) of M2, T15 and M42, and the room temperature tensile rupture stress (TRS) of M2 and M42, typically vary with tempering temperature after quenching from the recommended austenitizing temperatures for these alloys. Figure A6.1(b) shows, for M2, how HV and TRS vary with austenitizing temperature after tempering at 560˚C. The data have been derived mainly from Hoyle (1988), converting from Rockwell to Vickers Hardness, with additional data from other sources. The data are presented to show the sensitivity of mechanical proper- ties to composition and heat treatment. Traditionally, high speed steels have been shaped by hot working. Now, powder metal- lurgy technology is used to make high speed steel indexable inserts. HV and TRS values are not much changed but there is evidence that fracture toughness (K IC values) can be higher for powder metallurgy than wrought products. Sheldon and Wronski (1987) give K IC at room temperature for sintered T6 as 30 MP m 1/2 whereas wrought T6 heat treated in the same way has K IC = 15 to 20 MP m 1/2 . This paper also gives the temperature depen- dence of TRS quoted in Chapter 3 (Figure 3.22). A6.2 Cemented carbides and cermets Cemented carbide and cermet cutting tools consist of hard carbide (or carbo-nitride) grains, bonded or cemented together by up to around 20% by weight of cobalt or nickel, 388 Appendix 6 Fig. A6.1 Variations of room temperature HV and TRS with (a) tempering and (b) austenitizing temperature, for a range of high speed steels as indicated (a) (b) Childs Part 3 31:3:2000 10:44 am Page 388 with minor additions of other metals (such as molybdenum or chromium) possible. The hardness of the tools reduces and the toughness increases as the proportion of the metal binder phase is increased. Cemented carbides and cermets are manufactured by sintering. The reactions that take place during sintering are extremely complex and the creation of good cutting tool grades requires a close attention to detail. A comprehensive monograph has been published (Schwarzkopf and Keiffer, 1960) and since then research reviews have appeared at regular intervals (Exner, 1979; Gurland, 1988). However, from a user’s point of view, the elements of cemented carbide tool development are quite clear. The earliest cemented carbides, developed in the 1920s, consisted of tungsten carbide (WC) cemented together by cobalt (Co). It soon became clear that this material was not suitable for machining steels at high cutting speeds. The WC dissolved in the steel at the temperatures generated by cutting, leading to rapid cratering of the rake face of the cutting tool. It was found that the system titanium carbide (TiC)-Co was more chemically resistant to steel, although cemented carbides based on TiC alone were more brittle than WC-Co. Toughness could be recovered by adding tantalum carbide (TaC). During the 1930s, cemented carbides based on WC-TiC-TaC-Co started to be developed. Tools based on WC-Co, suitable for cutting non-ferrous metals (and also cast iron, which does not get hot enough in machining to trigger rapid dissolution of WC, so tool life remains deter- mined by flank wear) are now known as K-type carbides and those based on WC-TiC- TaC-Co, for steel cutting, as P-type. (In practice, the tantalum carbide often includes niobium; one should then refer to Ta(Nb)C.) During the 1950s, an alternative system for steel cutting began to be studied, based on TiC cemented mainly by nickel (Ni). These have developed to titanium carbo-nitrides (Ti(C,N)) bonded by Ni (with minor amounts of WC and Co), and are known as cermets. Much more detailed data are available on the composition and properties of the K- and P-type carbides (and M-type as well – see later) than on the cermets. The remainder of this section will concentrate mainly on the carbide grades. The description K-, P- and M-type carbides, although it closely relates to carbide composition, in fact refers not to composition but to performance. An international Standard (ISO 513, 1991) classifies cemented carbide cutting tools by type and grade. Type refers to suitability for steel cutting (P) or non-ferrous materials (K) or to a compro- mise between the two (M). Grade refers to whether the tool material’s mechanical proper- ties have been optimized for hardness and hence abrasive wear resistance, or for toughness. Wear resistance is more important than toughness for low feed, finishing cuts. Toughness is more important for high feed, roughing or interrupted cuts. Grades run from 01 to 50, as properties change from hard to tough. Different manufacturers achieve a particular tool performance by minor differences of the processing route, so that there is not a one-to-one relation between a tool’s type and grade on the one hand and its composition on the other. This is illustrated in Figure A6.2. Each row of the figure presents data on composition, hardness and transverse rupture stress (at room temperature) for one manufacturer’s range of tool materials, according to infor- mation published by Brookes (1992). The first row is data from a German manufacturer, the second is from a major international company and the third is from a Japanese producer. Each data point in the left hand column represents the TiC-TaC and Co weight % of one tool material (the balance is WC). What type and grade is assigned to the mater- ial is indicated by the solid and dashed lines. The ranges of compositions giving P-, Cemented carbides and cermets 389 Childs Part 3 31:3:2000 10:44 am Page 389 M- and K-types are slightly different for each producer. So are the ranges of compositions giving the different grades. The right-hand column shows the relation between transverse rupture stress and hard- ness for all the grades. It can be seen that the relation depends on the carbide grain size. All three manufacturers produce tool materials of 1 to 2 mm grain size. These have the same relation between transverse rupture stress and hardness, independent of K-, M- and P-type. However, one set of data, in the first row, is for material of sub-micrometre 390 Appendix 6 Fig. A6.2 Composition and mechanical property differences of cemented carbide cutting tools classified according to ISO 513 (1991) by three different manufacturers Childs Part 3 31:3:2000 10:44 am Page 390 grain size: it shows a greater transverse rupture stress for a given hardness than the coarser grained material. Such a fine grain size is only achievable with WC-Co (K-type) materials. The mechanical and physical properties of commercial cemented carbide cutting tools broadly depend on the wt. % of Co, the wt. % of TiC-TaC and the grain size of the mater- ial. Rather than describe the material by type and grade, the remainder of this section will describe it by these quantities. For convenience, the classification by amount of TiC-TaC will be by whether the amount of this by weight is in the range 0–3%, 8–15% or 19–35%. The data presented in Brookes (1992) show that very few cutting tool materials have amounts of TiC-TaC outside these ranges. Figure A6.3 shows that the room temperature hardness of a cemented carbide depends mainly on cobalt content and grain size. Figure A6.4 shows that quantities such as thermal conductivity, K, heat capacity, rC, thermal expansion coefficient, a e , Young’s modulus, E, and thermal shock resistance, (TRS.K)/(Ea e ), are most influenced by the type of carbide present. Figures A6.2 to A6.4 are the main source of information for the cemented carbide data presented in Chapter 3. Such detailed information on the properties of cermets is not available in the open liter- ature. Table A6.2 presents data for one manufacturer’s products. TiC and TiN are the major hard phase, with WC as a minor part. Ni is the major binder metal, with Co as a minor part. Less complete or differently presented data from other manufacturers, extracted from Brookes (1992) are gathered in Table A6.3. The densities of the cermets are almost half those of the cemented carbides (the densi- ties of which, because of the high specific weight of tungsten, are around 14 000 to 15 000 kg/m 3 for the WC-Co types and 10 000 to 13 000 kg/m 3 for the high TiC-TaC-Co types). The cermets are mainly described as P-types, although some manufacturers also recom- mend them as K-types, but because of their limited toughness (TRS < 2.5 GPa, compared with up to 4 GPa for fine grained WC-Co materials), none of them are recommended for heavy duty use, above 30-grade. Cemented carbides and cermets 391 Fig. A6.3 Hardness dependence on % Co and grain size, for cemented carbides Childs Part 3 31:3:2000 10:44 am Page 391 392 Appendix 6 Fig. A6.4 Composition dependence of some properties of cemented carbides Table A6.2 One manufacturer’s range of cermet tool materials Wt. % ——————— Grain ISO Ti(C,N) Ni + size ρ HV TRS K E α e code + WC Co [ µ m] [kg/m 3 ] [GPa] [GPa] [W/mK] [GPa] [10 –6 K –1 ] P/K01–05 95 5 1 6800 18.1 1.3 11 410 6.7 P10–P15 86 14 1 7100 15.5 1.65 12 400 7.2 P/K05–15 89 11 <1 7000 16.5 1.65 14 410 7.6 P10–P25 85 15 <1 7000 15.2 2.0 19 390 7.4 Childs Part 3 31:3:2000 10:44 am Page 392 [...]... [W/mK] P01–10 P05–25 P01–15 50 49 48 . 16 15 8 12 < 2 7000 14. 2 1.8 20 P01–15 48 16 20 5 11 –* 7000 15.7 –* 20 P05 Total carbide: 94 Total metal: 6 –* 6100 17.2 1.8 –* P10 Total carbide: 86 Total metal: 14 –* 7000 15.7 2.3 11 P20. 2.3 11 P20 Total carbide: 82 Total metal: 18 –* 7000 14. 2 2.5 16 P01–20 Total carbide: 87 Total metal: 13 2 6600 16.7 1.5 25 P10–30 Total carbide: 83 Total metal: 17 2 7000 15.2 1.8 27 P10–30. ultimate hardness or metal- based for toughness. For PcBN, the ceramic base is Al 2 O 3 and the metal base is sintered carbide or cermet. For PCD, the ceramic is based on SiC and the metal on Co. References Brookes,