On a thermomechanical model of shear instability in machining

In this investigation, based on the analysis of cyclic chip formation in machining, possible sources of heat including preheating effects by these heat sources contributing toward the t

On a Thermomechanical Model of Shear Instability in Machining

Hou Zhen-Bin, Ranga Komanduri (1) Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, USA

Received on January 4,1995

ABSTRACT

Shear instability was observed experimentally in machining some of the difficult-to- machine materials, such as hardened alloy steels, titanium alloys, and nickelbase superalbys yielding cyclic chips Recht in 1964 developed a classical model of catastrophic shear instability in machining In this investigation, based on the analysis of cyclic chip formation in machining,

possible sources of heat (including preheating effects by these heat sources) contributing toward the temperature rise in the shear band were identified The temperature rise was calculated using Jaeger's classical solutions of stationary and moving heat sources Recht's

original catastrophic shear instability model for shear localization was extended by predicting analytically the conditions for the onset of shear localization

Key Words: machining, cutting, shear

"I often say that when you can measure what you are

speaking about, and express it in numbers, you know

something about it; but when you cannot measure it,

when you cannot express it numbers, your knowledge is

of a meagre and unsatisfactory kind; it may be the

beginning of knowledge, but you have scarcely, in your

thoughts, advanced to the stage of Science whatever !he

matter may be" Lord Kelvin

1 INTROOUCTlON

Machining of conventional metals and their alloys,

such as low carbon steels, aluminum alloys, carbon

steels in the practical cutting speed range is charac-

terized by a continuous (Type II) chip [l] These

materials exhibit high ductility (having a bcc or a fcc

crystal structure) and good thermal properties There

are, however, other materials, such as titanium alloys,

nickelbase superalloys, hardened alloy steels which

produce cyclic chips when machined due to shear

instability [2-7l For some of these materials, as in the

case of hardened alloy steels, a transition from a

continuous to a shear localized chip occurs as the cutting

speed is increased 61 However, once the transition from

transition or reversal to a continuous chip was observed

with further increase in speed For other materials, such

as titanium alloys, shear localization seems to occur

throughout the cutting speed range, i.e from an

extremely low speed to very high speeds Materials that

tend to form shear localized chips can be characterized

by poor thermal properties and/or limited ductility (as in

the case of materials with a hcp crystal structure)

Shear localization causes cyclic variation of force

(both cutting and thrust) and consequent vibration or

chatter in the metal cutting process Consequently, an

understanding of the process, the criteria for shear

instability, and the conditions leading to shear locali-

zation are im rtant considerations in our quest for

of the cutting operation

2 CRITERIA FOR SHEAR INSTABILITY

Recht in 1964 [a] developed a classical model of

catastrophic shear instability in machining Accordingly,

catastrophic shear occurs at a plastically deforming

a continuous to a s F, ear localized chip occurs, no further

improving pr o r uctiviiy, part quality, and overall efficiency

region within a material when the slope of the true stress- true strain curve becomes zero, i.e., the local rate of change of temperature has negative effect on strength which is equal to or greater than the positive effect of strain hardening Assuming an approximate value of the temperature generated in machining, Recht estimated the values of thermo-mechanical properties and calculated the shear strength In this paper, this model was further developed based on the experimental results obtained usin h' h-speed photo raphy, in situ machining inside

an #Elf, and a metahrgical analysis of the chips

generated in conventional machining tests over a range

of cutting speeds Recht's original thermo-mechanical model for shear localization in metal cutting was extended and an attempt was made to predict quantitatively the conditions for the onset of shear localization The temperature raise in the shear band due to the three heat sources as well as the preheating effects by these heat sources on the following segment being generated was calculated A reasonably ood correlation of the experimental work with the aniytical modeling was found Samiatin and Rao (91 developed another model for shear localization which incorporates a heat transfer analysis and materials properties, such as the strain- hardening rate, the temperature dependence of the flow stress and the strain rate sensitivity of the flow stress to establish the tendency towards localized flow Using the data available in the literature, they found the non-uniform flow in metal cutting is imminent when the ratio of the normalized flow softening rate to the strain rate sensitivity is equal to or greater than 5

In addition to thermo-plastic instability (strain hardening versus thermal softening) leading to shear localization, there can be other mechanisms where an actual reduction in the shear stren th in the shear band example, the generation of microcracks in the shear band and a reduction in the actual area undergoin stress

proposed this as a possible mechanism for chip segmentation in machining Recent1 , Shaw and Vyas

[12] proposed it for machining an A l l 1 4340 steel at low

cutting speeds This concept seems to be valid parti- cularly for the case of cyclic chips generated in machining of titanium alloys at very low speeds These

can take place without the therma B softening effect For

Walker and Shaw [lo] pro sed this for materia 9 s under- going large shear and R" omanduri and Brown [ll]

speeds are so low that the heat generated in the shear

band could diffuse on either side with the result thermal

softening would be rather difficult Instead, the actual

shear strength may be lowered by the presence of

microcracks Other mechanisms proposed for shear

instability include structural transformation, as in the

reversion of marten-site to austenite in some steels [13]

In this paper, only the first mechanism of shear

instability, name1 , thermal softening versus strain

hardening is consdered

3 PHYSICAL MODEL OF SHEAR LOCALIZATION IN

MACHINING

The followin is the sequence of events leading to

shear-localized c l i p formation This model is developed

based on the ex erimental results obtained using high-

s eed photograpiy, in d u machining inside a scanning

erectron microscope and metallur ical analysis of the

materials over a range of cutting speeds There are

basically two stages involved in this process One stage

involves shear instability and stain localization in a

narrow band in the primary zone ahead of the tool The

other stage involves u setting of an inclined wed e of

mation, forming a chip segment During upsetting of the

segment ahead of the tool in the primary zone, intense

shear takes place at approximately 4!5O to the direction of

cuttin This occurs not between the chi and the tool

formin Thermo-mechanical response of these drfficult-

to-mac%ine materials under the conditions of cutting tend

to localize the heat generated due to strain localization

and subsequent shear in a narrow band Thus, thermal

softening takes place resulting in the shear stress being

lower than that of the bulk material With increase in

cutting speed, this intense shear takes place so rapidly

that the contact area between any two se ments

gradually decrease to a stage when the in8ividual

segments of the chip are actually separated Such a

phenomenon was observed at higher cuttin speeds

and nickelbase superalloys

Figure I (a) to (c) show various stages of shear

localization in machining, Figure 1 (a) shows the inltial

stage where chip segment I has just formed and under the

essure exerted by the tool face on the weakest plane a

r Figure 1 (b)], shear S1 commences on the main shear

plane This high1 intense, narrow shear zone is

designated as ABZD Note that svgment ll.(i.e in the

s ment to be deformed) undergoes very little plastic

where the cutting tool has moved a distance e T e

width of the shear zone has increased from AB [Figure 1

(a)] to AC Figure 1 (b)] Also, the shear zone has rotated

deformation of segment II takes place by the movement

of the cuqing tool This deformation is caused by the

shear S2 in the weakest plane b of that part of the chip

segment which has its own shear angle @ * and moves

forward together with the cutting tool tip Figure 1 (c)

shows the final stage where the chip segment I has

sheared along the main shear plane to its maximum

extent and the weakest lane in segment II has reached

its extreme position Aler that, the weakest plane will

shift to a' as shown in the figure Thus the next chip

segment is formed It asain will begin to shear along the

new main shear lane a At this instant the length of the

segment has its maximum value A'C or ABC [Figure 1 (cf

It may be noted that the chip formation process

yielding shear localization is far different from that with a

continuous chip In the case of a continuous chip, strain

hardening always predominates ove! thermal softening

Once shear takes place along the main shear plane a, the

stress required for further deformation is higher than

before, so the weakest lane will be shifted to the next

his leads to a uniform1 distributed deformation in the

chi s on a macroscale ut in the case of chip formation

wit[ shear localization thermal softening predominates

chips obtained in conventional mac a ining tests of these

work material by the a 8, ancing tool, with negligible 8 efor-

face gut between the last segment an s the one just

(above 1,000 m/min) in the case of hardened al B oy steels

6

de 7 ormation Figure l b shows an intermediate sta e

due to pastic I indentation (or upsetting) and the

shear zone on t R e main shear plane of the former chi

lane Thus shear will aso P be shifted to the next plane

?

r!

over strain hardening Once shear takes p h c e along the

70

main shear plane a, the strength there becomes lower than before So, the main shear plane is still the weakest plane and hence the shear continuous on the same ane In other words, shear is localized in a narrow plane

#l is results in an inhomogeneous deformation in the chips on a macroscale Figure 2 shows ty ical micro- different cutting speeds illustrating these features

4 CRITERION FOR THERMO-MECHANICAL SHEAR graphs of a continuous and a shear localize 8 chip at two

INSTABILITY IN MACHINING

In this investigation the criterion for shear instability formulated by Recht in 1964 was further developed by predicting analytically the conditions for the onset of shear localization Based on the analysis of cyclic chip formation in machining described earlier, possible sources of heat (including preheatin effects of these heat sources) in the shear band contrguting towards the temperature rise were identified Using Jaeger's classical solutions for stationary and moving heat sources as

bases (141, the temperature rise in the shear band due to various heat sources was calculated Knowing this temperature, the shear stress in the shear band at the shear band tem erature was estimated and compared with the strengtE of the work material at the preheating temperature A thermo-mechanical model was developed wherein if Q' 2 Q, no shear localization takes place but instead strain hardenin occurs If Q ' C 6, then shear localization is imminent The model proposed redicts the onset of shear instability (i.e cutting speed a k v e which shear localization takes place) reasonably well with the experimental results reported in the literature [3.6]

5 THERMO-MECHANICAL PROPERTIES OF THE WORK MATERIAL

Based on experimental materials property data available in the literature on the strain hardening and thermal softening characteristics, relationships were developed for the calculation of true stress, Q, in terms of true strain, E and temperature, T Only temperature and strain effects were considered here as the strain rate effects could not be considered due to lack of materials properties data Similarly, thermal properties of the work material at different temperatures were obtained from the literature and used in the analysis

6 HEAT TRANSFER MODELING

To predict the conditions for the occurrence of shear localization quantitatively, the tem erature rise in the shear band during cutting has to determined Based on an analysis of the cyclic chip formation, the tem erature rise in the shear band is identified as due to effects of these sources The three primary heat sources are: 1 The main shear band heat source, a [see Figure 1

at igher cutting speeds, (2) the secondary shear band heat source b [see Figures 1 (b) and (c)] This is the heat enerated durin the upsetting stage of cyc!ic chip krmation, and (38 the frictional heat source, c (Figure 1) between the s ment already formed and the rake face of the cutting to? In addition, all the three heat sources also effect the temperature on the new shear band of the next chip segment That is, every new segment, where shear localization begins to takes place, will occur at a temperature higher than the room temperature This is the preheating effect on the main shear band Thus, in this

r all the heat sources are identified and used in the

!%ulation of shear band temperature-rise It will be shown later that depending on the cutting speed used, the influence of some of these heat sources will be more prominent than others Some can be neglected at higher speeds but becomes more significant at lower speeds Jaeger's classical instantaneous, infinitely long line heat source solution is taken as the startin point for all the sources The temperature rise at any point M and at any instant t due to each of the heat sources is obtained In this investigation, temperatures at 15 locations along the shear band are calculated The mean of these values

is taken as the temperature rise The mean temperature rise in the shear band (Ze) caused by the three heat sources and that due to three preheating effects are

the P ollowing three heat sources as well as the preheating (b)l; $A is will be the predominant heat source especially

three heat sources as well as the t 7l ree preheating

designated as 6.6, &, Q, 6, and %respectively

Due to limitations of space only the final results are given

here; details of the analytical modeling are given

elsewhere [15]

The first heat source is the main shear band heat

source a [in Figure l(a)] It is assumed as an infinitely

long, stationary, continuous heat source with a variable

intensity of heat liberation This heat source includes the

heat generated in the shear band (i.e between the

segments) and the shear between the segment and the

tool face [see Figures 1 (b) and (c) for details] The

second heat source is the seconda shear plane heat

source b, caused by the upsetting of #e undeformed part

of the material ahead of the tool face which begins

simultaneously with the be inning of the localized shear

in the main shear band, a !Figure 11 During shear, the

shear plane provides a moving plane heat source with

variable width moving along the direction AB Figure 1 b)

between the chi segment already form+ and rake face

of the tool, c I! is assumed as a moving plane heat

source with variable intensity of heat liberaton A similar

approach is taken for calculating the temperature rise due

to each of the three preheating sources

7 RESULTS AND DISCUSSION

Figures 3 and 4 show the variation of temperature

rise due to various heat sources with cutting speed for an

AlSl 4340 steel and a Titanium 6AI-4V work material,

respectively They were obtained using the analytical

models proposed earlier It can be seen that at the low

speeds the temperature rise in the shear band depends

very much on the contributions of the various heat

sources Also, at the lower speeds, reheating effects

predominate At the higher speeck however, the

temperature rise due to the first heat source, namely, the

shear band heat source predominates

Figures 5 and 6 show the variation of shear stress

with cutting speed for an AlSl4340 steel and a Titanium

6AI-4V work material, respectively 6' is the shear stress

at the shear band temperature and 6 is the shear strength

of the bulk material at the preheating temperature Except

at very low speeds, 6' decreases (due to thermal

softening effect) while 6 increases (due to decreasing

preheating effect with increasing cutting speed below the

difference between them decreases with increase in

speed At the critical speed for shear localization, i.e 6

= b', strain hardening effect equals thermal softening

Beyond this speed, thermal softening predominates over

strain hardening with the result a' c 6

It can be seen that the critical speed for shear

localization for Titanium 6A14V is about 8 mlmin while that

for AlSl4340 steel is much higher (about 116 m/min) as

originally predicted by Recht Also, the ex erimental

results reported earlier for the onset of shear kalization

(namely, 125 mlmin) for AlSl 4340 steel [6] agrees with

the analytical results presented here However, in the

case of titanium alloys, cyclic chip formation was

observed at speeds much lower than the value reported

here This difference can be attributed to several factors

It is possible that the criterion for the onset of shear

localization presented here is somewhat simplistic or

other factors of relevance may not been considered in the

analysis For exam le, cut thickness may have some

effect in that the preKeatin effects would be different for

source (and the preheating effect of this heat source)

between the nascent chip and the tool face during the

indentation of the wedge shaped section of the chip

segment has not been considered in the first

ap roximation The basic approach and the conclusions

wil P still valid These modifications may move the speed at

which shear localization takes place slightly lower than

what is sreported in this paper

It is reasonable to assume that at very low cutting

speeds, the conditions in the shear band are far from

adiabatic Consequent1 , adiabatic (or near adiabatic)

shear instability is unlkely at the very low speeds

Perhaps, some other mechanism may have to be invoked

to explain for the observed cyclic chip formation at very

The third heat source, namely, the frictional I, eat source

critical speed 1 or shear localization, a' > 6 The

a thin chip than a thick c a ip Also, the frictional heat

low speeds with titanium alloys It is possible that this phenomenon is due to a difference in the mechanism of shear localization from that of a thermal origin to a mechanical origin, for example, involving microcracks, as originall proposed by Professor Shaw This would effediveyy reduce the stress due to reduced area Work

is under rogress in this direction and it is hoped that the resutts orit will be communicated soon

8 CONCLUSIONS

In this investigation Recht's catastrophic shear instabilit model was extended by predicting analytically the codtions for the onset of shear localization

Based on an analysis of the shear localized chip formation process, three primary heat sources and reheating effects of these heat sources were identified [sing Jaeger's stationary and moving heat source solutions the temperature rise in the shear band due to these heat sources was calculated

3 Shear stress in the shear band, o', was calculated at the shear band temperature and compared

with the value of shear strength, 6, at the preheating tem rature for both AlSl4340 steel and Titanium 6AI4V worpmaterials It was found that if 6' c 6, then shear localiza?ion is imminent The cutting s eed at which this occurs is the critical speed for shear kcalization Shear localization continues at all speeds above this Cutting speed for the onset of shear localization was found to be much lower for Titanium 6A14V (about 9 m/min) than for AM4340 steel (130 m/min)

4 Values of a' and 6 were calculated for AlSl4340 steel over a ran e of practical cutting speeds No shear localization wasyound up to a speed of about 120 mlmin with the onset of shear localization above 130 mlmin Experimental results reported in the literature agrees reasonably with the anal tical values Values of 6' and 6

were also calculated for fitanium 6 AI-4V over a range of cutting speeds up to 10 m/min No shear localization was found up to a speed of about 8 m/min with the onset of shear localization above 9 m/min

ACKNOWLEDGMENTS The authors would like to acknowledge the continuing support of the National Science Foundation in the area of manufacturing at OSU Thanks are due to Drs B M Kramer, K Narayanan, W DeVries, and A Hogan of NSF for their interest Thanks are also due to many of the collaborators of the Air Force roject on Advanced Manufacturing which was funded wlen one of the authors (R.K.) was with G.E In particular, the many valuable discussions with Prof B F von Turkovich, Mr

R F Recht, Dr R A Thompson, Dr M Lee and Dr D G Flom are gratefully acknowled ed Thanks are also due to some of the graduate stutents who helped in the reparation of the drawings Finally, thanks are due to the

R4 OST Chair funds that enabled this work Thanks are also due to Prof M F DeVries for his review and comments

1

2

REFERENCES Merchant, M E., 1944, Basic Mechanics of the Metal Cutting Process, Trans ASME, 66: A65-A71

LeMaitre, F., 1970, Contribution a I'etude de I'usinage

du titane et de ses alliages, Annals of CIRP, 23: 413-

424 Komanduri, R and B F von Turkovich, 1981, New Observations on the Mechanism of Chip Formation When Machining Titanium Alloys, Wear, 69: 179-1 88 Komanduri, R., 1982, Some Clarifications on the Mechanics of Chip Formation When Machining Titanium Alloys, Wear, 76:15-34

Komanduri, R and R H Brown, 1981, On the Mechanics of Chip Segmentation in Machining, Trans ASME, J of Engg for Ind 103 : 33-51

Komanduri, R and T A Schroeder, 1986, On Shear Instability in Machining a Nickel-Iron Base Super- alloy, Trans ASME, J of Engg for lnd.,108: 93-100

71

[7] Komanduri, R., Schroeder, T A Hazra, J., von

Turkovich, B F., and D G Flom, 1982, On the Cata-

strophic Shear Instability in High-speed Machining of

an AlSl4340 Steel, Trans ASME, J of Engg for Ind.,

[8] Recht R F., 1964, Catastrophic Thermoplastic

Shear, Trans ASME 86:189-193

[9] Semiatin, S L and S B Rao "Shear Localization

During Metal Cutting," Materials Science and

Engineering, fi (1 983) 185-1 92

[lo] Walker, T J and M.C Shaw, 1969 On Deformation

at Large Strains, Proc of the 10th M.T.D.R

Conference, 241

[l 11 Komanduri, R and R H Brown, 1972, The Formation

of Microcracks in Machining a Low Carbon Steel,

Metals and Materials, 6: 531

(121 Shaw, M C., and A Vyas, 1993, Chip Formation in

the Machining of Hardened Steel Annals of CIRP,

42/1: 29-33

[13] Lemaire, J C and W A Backofen, Feb 1972,

Adiabatic Instability in the Orthogonal Cutting of

Steel, Metallurgical Trans, 3: 477-481

[14] Jaeger, J C., 1942,Moving Sources of Heat and the

Temperature at the Sliding Contacts, Proc of the

Royal Society of NSW 76: 203-224

[15] Hou Zhen-Bin and R Komanduri, 1995, Thermo-

Mechanical Modelling of Shear Instability in

Machining, Part I: Thermo-mechanical Instability and

Part II Thermal Analysis, papers to be submitted for

publication

104: 121-131

(b)

Figure I (1) to (c) Schematic showing various stages of

shear localization in machining

72

Figure 2 (a) and (b) Typical micrographs of a continuous

and a shear localized chip when machining AlSl

4340 steel (Rc 35), at two different cutting

speeds illustrating these features

(a) 125 m/min and (b) 250 m/min [A

z e i

' I ' , I , ,

0 25 50 75 100 125 150

Cutting Speed, m/min

Figure 3 Variation of temperature rise due to various heat

sources with cutting speed for an AlSl4340

steel

v) 200

ti

Q, 150

9 100

L

c 3

Q,

a 50

Cutting Speed, m/min

0

Figure 4 Variation of temperature rise due to various heat

sources with cutting speed for Titanium 6AI4V

Z 230

a

s

220 F ' " ' " " " " ' " ' 4

Cutting Speed, V m/min

Figures 5 Variation of shear stress with cutting speed for

an AlSl4340 steel S.L.: shear localization and No S.L : no shear localization

140 ~ ~ , ~ ~ I I , I , ,

.-

y 1 35 I

Cutting Speed, V m/min

Figures 6 Variation of shear stress with cutting speed for

Tiianium 6AI-4V S.L.: shear localization and No S.L : no shear localization

73