Metal Machining - Theory and Applications Episode 2 Part 10 pot

In Chapter 3, reference is made to yield and strain hardening behaviours of aluminium, copper, iron, nickel and titanium alloys, as determined by room-temperature, low strain rate, compr

Equilibrium between the forces of the nominal and real contact stresses gives

sn Ar pr

According to equation (A3.16a), Ar/An⇒ t/k as s/k ⇒ 1 From equation (A3.16b), if Ar/An

< (sn/k), pr/k > 1 However, the slip-line field is not valid if pr/k > 1: flow will break through to the free surface and pr/k will be limited to 1 Thus, for a plastic asperity on a plastic foundation, when s/k is close to 1, Ar/Anwill equal (t/k) when (t/k) > (sn/k), and (sn/k) when (sn/k) > (t/k), up to its maximum possible value of 1 Contours of Ar/An= 1, 0.9, 0.8, satisfying this, are added to Figure A3.9(b)

Figure A3.9(b) shows, firstly, the levels of dimensionless hydrostatic stress, pE/k, needed for a combination of (t/k) and (sn/k) to be associated with a bulk plastic flow If

there is bulk plasticity, it then shows how degrees of contact much larger than when the

bulk remains elastic (Figure A3.8a) can be generated at values of (sn/k) < 1 In these

condi-tions the ratio of friction to normal stress (the friction coefficient) becomes greater than 1

A3.6 Friction coefficients greater than unity

In metal machining, and elsewhere, friction coefficients > 1 have been measured in

condi-tions in which asperities have been plastic but (t/k) and (sn/k) have been too low for bulk

plastic flow to be a possibility What could account for this, that has not been considered

in the previous sections?

Work hardening offers two possibilities First, in the same way as it changes the hydro-static pressure distribution along the primary shear plane in metal machining (Figures 2.11 and 6.9(b)), it can modify the pressure within a deforming asperity to reduce the mean

value of prto a value less than k However, there is likely only to be a small effect with the

rake face asperities in machining, already work hardened by previous deformations A second possibility imagines a little work hardening and high adhesion conditions, leading

to the interface becoming stronger than the body of the asperity Unstable asperity flow, with contact area growth larger than expected for non-hardening materials, has been observed by Bay and Wanheim (1976)

There is a second type of possibility In the previous sections it has been assumed that

an asperity is loaded by an amount W by contact with a counterface and that W does not

change as sliding starts For example, in Section 3.4.2 on junction growth of plastic

contacts, it is written that the addition of a sliding force F to a real contact area creates an extra shear stress F/Arwhich, if Ar does not increase, will cause tmax to increase This

assumes that the stress W/Ardoes not decrease

If W is constant, the extra force F causes the two sliding surfaces to come closer to one another: it is this that enables Arto grow Green (1955) pointed out that, in a steady state

of sliding (between two flat surfaces), the surfaces must be displaced parallel to one another In that case any one junction must go through a load cycle Figure A3.10 is based

on Green’s work With increasing tangential displacement, asperities make contact, deform

Friction coefficients greater than unity 373

and break The load rises, passes through a maximum and falls, but the friction force rises and stays constant until failure If, at any one time, there are many contacts in place, each

at a random point in its life cycle, an average friction coefficient will be observed that is obtained from the areas under the curves of Figure A3.10, up to the point of failure Green argued that when conditions were such that junctions failed when the load dropped to zero, the friction coefficient would be unity Higher coefficients require junctions to be able to withstand tensile forces, as shown The exact value of the friction coefficient will depend

on the exact specification of how the surfaces come together and move apart; and on the junctions’ tensile failure laws Quantitative predictions do not exist

References

Bay, N and Wanheim, T (1976) Real area of contact and friction stress at high pressure sliding

contact Wear 38, 201–209.

Childs, T H C (1973) The persistence of asperities in indentation experiments Wear 25, 3–16.

Green, A P (1955) Friction between unlubricated metals: a theoretical analysis of the junction

model Proc Roy Soc Lond A228, 191–204.

Greenwood, J A and Williamson, J B P (1966) Contact of nominally flat surfaces Proc Roy Soc.

Lond A295, 300–319.

Johnson, K L (1985) Contact Mechanics Cambridge: Cambridge University Press.

Oxley, P L B (1984) A slip line field analysis of the transition from local asperity contact to full

contact in metallic sliding friction Wear 100, 171–193.

Sutcliffe, M P (1988) Surface asperity deformation in metal forming processes Int J Mech Sci.

30, 847–868.

Fig A3.10 Qualitative junction load history for zero normal displacement

Appendix 4

Work material: typical mechanical and thermal

behaviours

This appendix holds data that support Chapters 3 and 7, in the first instance In Chapter 3, reference is made to yield and strain hardening behaviours of aluminium, copper, iron, nickel and titanium alloys, as determined by room-temperature, low strain rate, compres-sion testing Information on this is given in Section A4.1 The thermal conductivity, heat capacity and diffusivity ranges of these alloys, and their variations with temperature – also used in Chapter 3 to estimate temperature rises during machining – are tabulated in Section A4.2 In Chapter 7 the idea was developed that it is not the strain hardening behaviour of the work materials at room temperature and low strain rates that is needed What is impor-tant for predicting chip formation in machining is the strain hardening behaviour at the temperatures and strain rates that actually occur Data on this are presented in Section A4.3 This appendix is also a source for applications studies such as are described after Chapter 7

A4.1 Work material: room temperature, low strain rate, strain hardening behaviours

Figures A4.1 to A4.3 contain representative strain hardening data for commercially pure samples of aluminium, copper, iron, nickel and titanium, and their alloys The data have been obtained either from plane strain compression tests or from measuring the depen-dence of yield stress of sheet samples upon reduction of their thickness through cold

rolling In every case, the variation of shear stress, k, with shear strain, g, is shown k has been calculated from s—/
 3 and g from e—
3 The following is a brief commentary on the figures

Copper and aluminium alloys (Figure A4.1)

The copper and copper alloys (left-hand panel) are all initially in the annealed state They show the low initial yield and large amount of strain hardening typical of these face centred cubic metals The aluminium and aluminium alloys (right-hand panel) show a similar behaviour, but generally at a lower level of stress Some aluminium alloys can be hardened

by ageing, either at room temperature (T4 temper) or above room temperature (T6) The examples of Al2024 (an alloy with 4Cu) and Al6061 (an alloy with 0.5Mg0.5Si) show the extent of hardening by this means It could be argued that the 32Cu–66Ni alloy shown in the figure is more properly a nickel alloy: it is included here because Figure A4.3, on nickel alloys, is concerned more with Ni–Cr heat resistant alloys

Ferrous alloys (Figure A4.2)

The left-hand panel contains data for carbon and low alloy steels as received from the hot rolling process In this state their microstructure is a mixture of ferrite and pearlite (or, for the high carbon steel, pearlite and cementite) In contrast with the copper and aluminium alloys, these body centred cubic materials show a large variation in initial yield stress and, relative to the initial yield, less strain hardening The right-hand panel shows two austenitic steels, a stainless steel (18Cr8Ni) and a high manganese steel (18Mn5Cr) These face centred cubic alloys show high strain hardening, both absolutely and relative to the body centred steels

Nickel and titanium alloys (Figure A4.3)

All the nickel alloys (left-hand panel) shown in this figure are for high temperature, creep resistant, use Commercially they are known as Inconel or Nimonic alloys They are face centred cubic, with initial yield stress larger than copper alloys and large amounts of strain hardening The titanium alloys (right-hand panel) are hexagonal close packed (h.c.p.) or mixtures of h.c.p and body centred cubic Their initial yield and strain hardening behav-iours are intermediate between the face centred and body centred cubic materials Further elementary reading on metal alloys, their mechanical properties and uses can be found in Rollason (1973), Cottrell (1975) and Ashby and Jones (1986)

A4.2 Work material: thermal properties

Tables A4.1 to A4.3 contain information on the variation with temperature of the thermal conductivity, heat capacity and diffusivity of a range of work materials The main single

Fig A4.1 Shear stress-strain behaviours of some copper and aluminium alloys

Thermal properties 377

Fig A4.2 Shear stress-strain behaviours of some ferritic/pearlitic and austenitic steels

Fig A4.3 Shear stress-strain behaviours of some nickel and titanium alloys

Table A4.1 Thermal conductivity [W/mK] of some work material groups

Iron and steel

Aluminium

Copper

Nickel

Titanium

*: high and commercial purity; **: including cobalt- and ferrous-base superalloys.

Table A4.2 Heat capacity (MJ/m3 ) of some work material groups

Iron and steel

Aluminium

Copper

Nickel

Titanium

source of information has been the ASM (1990) Metals Handbook but it has been

neces-sary also to gather information from a range of other data sheets

A4.3 Work material: strain hardening behaviours at high strain rates and temperatures

Published data from interrupted high strain and heating rate Hopkinson bar testing (Chapter

7.4) are gathered here Stress units are MPa and temperatures T are ˚C Strain rates are s–1

A4.3.1 Non-ferrous face centred cubic metals

For T from 20˚C to 300˚C, strain rates from 20 s–1to 2000 s–1and strains from 0 to 1, the following form of empirical equation for flow stress, including strain path dependence, has been established (Usui and Shirakashi, 1982)

B

– ——

s— = A (e T+273)(——) ( ∫strain path(——) de— ) (A4.1a)

Strain hardening behaviours at high strain rates 379

Table A4.3 Diffusivity (mm2 /s) of some work material groups

Iron and steel

Aluminium

Copper

Nickel

Titanium

*: high and commercial purity; **: including cobalt- and ferrous-base superalloys.

For the special case of straining at constant strain rate, this simplifies to

B

– ——

e—˘ M+mN s— = A (e T+273

)(——) e–N

(A4.1b) 1000

Coefficients A, B, M, m and N for the following annealed metals are as follows.

A4.3.2 Pearlitic carbon and low alloy steels

In early studies, an equation similar to equation (A4.1a) was used but for a changed expo-nential temperature term and a term dependent on temperature within the strain path inte-gral Later, this was developed to

e—˘ M

e—˘ m

e—˘ –m/N N

s = A(——) eaT

(——) ( ∫strain pathe–aT/N

(——) de—) (A4.2a)

to give a particularly simple form in constant strain rate and temperature conditions:

e—˘ M

1000

A range of measured coefficients is given in Table A4.4, valid for T from 20˚C to 720˚C,

strain rates up to 2000 s–1and strains up to 1

Table A4.4 Flow stress data for annealed or normalized carbon and low alloy steels

Steel Coefficients of equation (A4.2)

0.1C A = 880e –0.0011T+ 167e –0.00007(T–150)2+ 108e –0.00002(T–350)2+ 78e –0.0001(T–650)2

[1]* M = 0.0323 + 0.000014T N = 0.185e –0.0007T+ 0.055e –0.000015(T–370)2

a = 0.00024 m = 0.0019

0.45C A = 1350e –0.0011T+ 167e –0.00006(T–275)2 M = 0.036

[2]* N = 0.17e –0.001T+ 0.09e –0.000015(T–340)2 a = 0.00014 m = 0.0024

0.38C A = 1460e –0.0013T+ 196e –0.000015(T–400)2– 39e –0.01(T–100)2

–Cr–Mo M = 0.047 N = 0.162e –0.001T+ 0.092e –0.0003(T–380)2

[3]* a = 0.000065 m = 0.0039

0.33C A = 1400e –0.0012T+ 177e –0.000030(T–360)2– 107e –0.001(T–100)2

–Mn–B M = 0.0375 + 0.000044T N = 0.18e –0.0012T+ 0.098e –0.0002(T–440)2

[3]* a = 0.000065 m = 0.00039

0.36C A = 1500e –0.0018T+ 380e –0.00001(T–445)2+ 160e –0.0002(T–570)2

–Cr–Mo M = 0.017 + 0.000068T N = 0.136e –0.0012T+ 0.07e –0.0002(T–465)2

Ni[4]* a = 0.00006 m = 0.0025

A4.3.3 Other metals

The behaviour of some austenitic steels and titanium alloys has also been studied An 18%Mn-18%Cr steel’s flow stress behaviour has been fitted to equation (A4.2b), with

(e—/0.3) – replacing e— –, with coefficients (Maekawa et al 1994a)

A = 2010e –0.0018T

M = 0.0047e 0.0036T N = 0.346e –0.0008T+ 0.11e–0.000032(T–375)2

A different form has been found appropriate for an austenitic 18%Mn-5%Cr steel, with

negligible strain path dependence (Maekawa et al 1993):

s— = 3.02e˘—0.00714

[45400/(273 + T) + 58.4 + a(860 – T)e— b]

where, for e— ≤ 0.5 a + 0.87, b = 0.8; e— ≥ 0.5 a = 0.57, b = 0.2 Other forms have been given for a Ti-6Al-4V alloy (Usui et al 1984) and a Ti-6Al-6V-2Sn alloy (Maekawa et al 1994b) For the Ti-6Al-4V alloy:

s— = A(e—˘/1000) MeaT (e—˘/1000) m{c + [d + ∫strain pathe–aT/N (e—˘/1000) –m/N de—]N}

with A = 2280e –0.00155T

M = 0.028 N = 0.5 a = 0.0009 m = –0.015 c = 0.239 d = 0.12

The data for the Ti-6Al-6V-2Sn alloy were fitted to equation (A4.2a) with

A = 2160e –0.0013T+ 29e–0.00013(T–80)2+ 7.5e–0.00014(T–300)2+ 47e–0.0001(T–700)2

M = 0.026 + 0.0000T N = 0.18e –0.0016T+ 0.015e–0.00001(T–700)2

a = 0.00009 m = 0.0055

References

ASM (1990) Metals Handbook, 10th edn Ohio: ASM.

Ashby, M F and Jones, D R H (1986) Engineering Materials, Vol 2 Oxford: Pergamon Press.

Childs, T H C and Maekawa, K (1990) Computer aided simulation and experimental studies of

chip flow and tool wear in turning low alloy steels by cemented carbide tools Wear 139,

235–250.

Cottrell, A (1975) An Introduction to Metallurgy, 2nd edn London: Edward Arnold.

Maekawa, K., Kitagawa, T and Childs, T H C (1991) Effects of flow stress and friction

character-istics on the machinability of free cutting steels In: Proc 2nd Int Conf on Behaviour of Materials in Machining – Inst Metals London Book 543, pp 132–145.

Maekawa, K., Kitagawa, T., Shirakashi, T and Childs, T H C (1993) Finite element simulation of

three-dimensional continuous chip formation processes In: Proc ASPE Annual Meeting, Seattle,

pp 519–522.

Maekawa, K., Ohhata, H and Kitagawa, T (1994a) Simulation analysis of cutting performance of a

three-dimensional cut-away tool In Usui, E (ed.), Advancement of Intelligent Production.

Tokyo: Elsevier, pp 378–383.

Maekawa, K., Ohshima, I., Kubo, K and Kitagawa, T (1994b) The effects of cutting speed and feed

on chip flow and tool wear in the machining of a titanium alloy In: Proc 3rd Int Conf on Behaviour of Materials in Machining, Warwick, 15–17 November pp 152–167.

References 381

Maekawa, K., Ohhata, T., Kitagawa, T and Childs, T H C (1996) Simulation analysis of

machin-ability of leaded Cr-Mo and Mn-B structural steels J Matls Proc Tech 62, 363–369.

Maekawa, K (1998) private communication.

Rollason, E C (1973) Metallurgy for Engineers, 4th edn London: Edward Arnold.

Usui, E and Shirakashi, T (1982) Mechanics of machining – from descriptive to predictive theory.

ASME Publication PED 7, 13–35.

Usui, E., Obikawa, T and Shirakashi, S (1984) Study on chip segmentation in machining titanium

alloy In: Proc 5th Int Conf on Production Engineering, Tokyo, 9–11 July, pp 235–239.