A Model for Chip Formation During Machining of Hardened Steel

A Model for Chip Formation During Machining of Hardened Steel M.A. Elbestawi ( l ) ,A. K. Srivastava, T. I. El-Wardany, Mechanical Engineering Department, McMaster University, Hamilton, Ontario, Canada Received on January 8,1996

Abstract Saw-toothed chips are formed during machining of hardened steel (H,,-60-63). This paper presents a new analytical approach for modelling the chip formation mechanism in hard-turning. It has been observed that the chip formation starts with initiation of a crack at the free surface of the workpiece which further propagates towards the cutting edge of the tool. The crack soon ceases to grow at a point where severe plastic deformation oi the material exists under higher level of compressive stresses. The chip segment caught up between the tool rake face and the crack is pushed out while the material in the plastic region just below the base of the crack is displaced along the tool rake face thus forming saw-toothed chips. The direction of crack initiation and propagation are predicted using the surface layer energyktrain energy density criterion. The maximum value of surface layer energy,\(,, can be used to evaluate the angle of crack initiation whjle the strain energy density criterion predicts the corresponding crack propagation angle. Here, the process of chip formation is considered to be a mixed mode crack problem of Mode I and Mode II. The theoretical predictions are verified by the resultant chip contours obtained experimentally. The predictions made are shown to be in good agreement with those measured experimentally.

Key Words: Hard turning, Strain energy density, Chip formation, Crack

1. Introduction With the development of super-hard cutting materials such as ceramics, CBN, PCBN, and P C D etc., the technology of hard turning has created considerable interest to several leading manufacturers. In order to specify the potential of this new production technology, several issues of the hard turning such as cutting mechanism, tool wear, machined surface integrity etc. have been recently studied [l-111. One of the significant observations during hard turning which is different from machining of ductile materials is that consistently cyclic 'saw-toothed' chips are produced, essentially, without any deformation at the shear plane. An excellent overview of 'saw-toothed' chip formation has been provided by Komanduri and Brown [IZ].They have shown that the cyclic chips are formed through a variety of mechanisms and based on a particular mechanism, the chips can be categorized into four types; the wavy chip, the catastrophic shear chip, the segmental chip, and the discontinuous chip. Nakayama et al. [I, 51 discussed the mechanisms of 'saw-toothed' chip formation during turning of hardened steel and showed that the chip formation starts with the initiation of crack on the free surface when the shear strain at that point attains an ultimate shear strain value over which the work material can not afford. Since the deformation adjacent to free surface was assumed to be the result of pure shear, the shear crack was assumed to intersect the free surface at an angle of 45'. Shaw and Vyas [8] reviewed the formation of various types of 'sawtoothed' chips and proposed that the 'saw-toothed' chips during hard turning of case carburized AlSl 8620 hard steel (H,,= 61) are formed due to periodic gross fracture extending part way from free surface of chip to tool tip. Again, the gross fracture plane shear angle was considered as 4.5'. Konig et al. [9] also presented similar concept of chip formation during hard turning and explained the chip formation mechanism on the basis of extended shearing stress hypothesis.

Annals of the ClRP Vol. 45/7/1996

Literature survey reveals that the fracture due to shearing process is mainly used to explain the formation of 'saw-toothed' chip during hard turning. In this paper, the surface energy concept and strain-energy density criterion first proposed by Sih 113, 141 are used to predict the direction of crack initiation and propagation and a simple hypothesis is presented. The problem is tackled as a mixed mode crack problem of Mode I and Mode I I . Based on the experimental observations in our laboratory and as described by Konig [9],it is assumed that the crack initiates at the free surface and propagates towards the tip of the cutting edge. It is arrested in the region where material is in severe plastically deformed state. The cyclic 'saw-toothed' chip formation starts with the movement of the material caught up between the tool rake face and the crack. At the same time, the plastically deformed material close to the cutting edge is pushed out just like an extrusion process without breaking continuity. The theoretical predictions are confirmed by the experimental observations. I

2, C riterion f or crack initiation and m q x i q t'&! u It is often helpful to develop a model which has the characteristics of the phenomenon observed. Steels when heat treated, induce hardness due to martensitic structure. With increasing hardness, the ductility decreases and the materials start behaving in a brittle manner. Such materials are, specially, sensitive to surface characteristics. It is known from common experience that ali the surfaces to be machined are not perfectly smooth but rough composed of microscopic ridges, cracks, voids etc. When such case hardened materials are machined, the high compressive stress, though, create sub-surface material flow but mainly lead to the formation of crack at the free surface owing to the brittleness of material, The irregularities on the free surface play a major roll in crack initiation. Sih [15] tried to incorporate the surface effects into a ccntinuum in an averaged way by considering a boundary layer thickness, 6, to separate surface and interior regions

71

and suggested a 'surface layer energy' failure criterion. According to this criterion, the crack will initiate at a location along the boundary layer of the workpiece where the local energy caused by loading (dynamicktatic) exceeds some experimentally determined material constant. Sih assumed this layer to be in continuum such that its gross properties may be treated as an isotropic and homogeneous medium. The strain energy, ye, per unit surface layer area is given as [151:

where, E is the Young's modulus, v is the poisson's ratio, 6 is the order of magnitude of a continuum element, CT, is the applied stress, and 8, is the corresponding strain, the term 2Ey$(l -v2))6, can be treated as an experimentally determined material constant. Workpiece surface is never perfectly smooth but notched with a zig-zag pattern. To a first approximation, the workpiece surface may be assumed to have very small narrow elliptical notch boundaries with a boundary layer of uniform thickness, b all over the surface [Figures l ( a ) , l(b)]. At each point along the layer, the magnitude of the surface layer energy, ye can be calculated from equation (1). If the cutting pressure p, is applied at certain angle @ from the major axis of the elliptical notch [Figure 1 (c)], the surface layer energy at each point along the layer can be obtained using the relation [15]:

Y, = [

6( 1 -v2)p2 2E

(2) ( a + f ~(sinqcos@-cosqsin@)2-a2sin2@-b2cos2@ )~ a2sin2q + b2cos2q

l2

where a and b are the semi-major and semi-minor axes of the elliptical notches, q is the eccentric angle for the ellipse, and @ is the angle of loading (the loading may be tensile or compressive). free surfam

workpiece surface physical boundaG.7 c-" boundary layer ti

'

b) continuum element on a free surface

a) free surface boundary layer

Y

stresses in the workpiece material during machining. With further advancement of the tool, the stress as well as deformation levels in the work material in front of the cutting edge also increase. The direction of applied cutting pressure is fixed, however the local regions (notches) on the workpiece free surface change their orientationsthus passing through continuously varying angle of loading @ (Figure 2 ). It is proposed that a crack at the free surface initiates at a critical angle, QCi such that the surface layer energy, ye, reaches the maximum value,ye, , at the minimum applied cutting pressure. The position of maximum surface layer energy, Ye-,, which determines the point of crack initiation on the notch boundary, may be obtained analytically by setting the first derivative of ye in equation (2) equal to zero with respect to eccentric angle q i.e., 6 y e / 6 q = 0. This gives tan

=

a2sin2@ b2cos2@] (3) b [ a s h 2 @- bcos2@+ a(a + b)sin@cos@ 7

The direction of cutting

4u

\

Wokpiece

Tool

/ i'

Fig. 2 Process of saw toothed chip formation Substitution of equation (3) in (2) gives a relation and 41for a workpiece under compressive between ,Ye loading. The value of QCrcan be obtained from this relation at a point where applied cutting pressure is minimum. This angle will represent the inclination of crack against the cutting direction during chip formation. Having known the location of crack initiation on the free surface, the knowledge of crack propagation inside the workpiece material can be obtained using Sih's 'strain energy density' theory [15] which assumes that in a twodimensionai case, the crack extension takes place in the direction along which the strain-energy-density, S is a minimum i. e.,

aCr

where 8, is between -n and n and marks the direction of crack propagation. Sih [15] has analytically obtained a relation of 'strain energy density' factor, S for the case of a relatively sharp elliptical notch under a plane strain conditions. Due to limitation of space, without going into details only relevant equations to find fracture angle with notch at the boundary are given here which are:

s2 + s = s,+ r

s 3 r2

(5)

in which

S,

=

a,,k,2

2a,,k,k2

c) elliptical notch under compression

S, =

bilk,'

+

S,

C,,k,2

- 2ct2k,k2

Fig. 1 Continuum element and stresses on workpiece free surface During hard turning, the tools with negative rake angles are commonly used which generate compressive

72

=

+

a2,k,"

(6)

-

2b12k,k2 b,,k22 + C22k22

where k,, and & are the stress intensity factors in Mode I and Mode II, respectively, and dependent upon loading and

geometric conditions. The coefficients a,,, b plane strain conditions are given as: a,,

=

2 [(3-4v-c0s0)(1 rcose)] 16I-J

a,2

J-

=

,,

and c , for

2sine [cose-(i -2v)l

19) (10)

16lJ 1 a2,=---[4(1 16I-J b,,

=

0,

-v)(l - c o s 6 ) ~ (Al C O S ~ ) ( ~ C O S € ? - ~ ) ] (1 1)

b?,

=

-2 sine, 8v

b,,

=

--&os6

(13)

4v

where p is the shear modulus of elasticity, v is the poisson's ratio, 6 is the direction of crack propagation, and p = a(b/a)'. The solution of equation (5),satisfying the condition of equation (4), provides a relation between loading angle @ and the fracture angle 6,. Thus, the angle of crack propagation, 0, corresponding to crack initiation angle, @cr can be predicted using the above analysis. These are the two important angles during the formation of 'saw-toothed' chip in hard turning. Now, according to the present hypothesis the crack initiated from the free surface ceases at a point where transition takes place from brittleness to ductility due to severe plastic deformation in the region close to the tip of the cutting edge. Let t be the total undeformed chip thickness and t,, be the plastically deformed portion where the crack ceases (Figure 3). The chip volume between t and t,, will be pushed out without any deformation along the rake face on one side and off the crack on the other side. At the same time, the material within the plastically deformed portion will be displaced through the gap between the base of the crack and the rake face. The volume of this plastically deformed portion of the chip will gradually decrease with further advancement of the tool until a new crack develops for the next chip formation. The movement of the plastically deformed work material along the rake face can be expressed in differential form as: 1 = - cos( -Yo) * fpl (14) d Yr tl pi where t, is the deformed chip thickness at any point y , and yo is the rake angle. As the chip starts moving along the rake face, at y,= 0, the maximum plastically deformed chip thickness will be tpmar=tlp,cos(yo-@,,)/sin(@c,). Solving equation (14) with this initial condition gives: 9

The maximum 'saw-toothed' chip thickness, , t in terms of undeformed chip thickness t can be given as t cos(yo-0,)/sin(B0) which will first decrease linearly along the developed crack upto the crack base and then, in the plastically deformed portion, it will start decreasing exponentially according to equation (15). 3. Experimental procedure Hard turning tests, both in orthogonal and oblique cutting conditions, were conducted on a standard 10HP CNC lathe machine. The work material used was AlSl 1550 case-hardened steel (HQ,- = 60) with a case-

hardened layer of 4 mm The workpieces were prepared in the form of bars for oblique cutting tests, and in the form of tubes for the orthogonal cutting tests The bar workpieces were 25 mm in diameter and 200 mm in length. The dimensions of the tube workpieces were 25 mm outside diameter, 200 mm length, and 4 mm wall thickness. All the tests were conducted using TNG (70% A1,0~30%T1C) ceramic indexable tips with zero degree clearance angle and 1.2 mm nose radius The tools with two different rake angles of -6' and -26O, and zero approach angle were used during the tests. No cutting fluid was used. The cutting speeds (V) between 66 to 120 m/min, feeds (f) between 0 025 to 0.2 mm/rev., and depths of cut (d) between 0 5 to 2 mm were used in oblique cutting. The width of cut during orthogonal cutting tests was 4 mm. The cutting, thrust, and radial force components (Fc, F,, and F,, respectively) were measured with a piezoelectric 3component dynamometer. Each test was run as short a time

Workpiece

Fig. 3 Different parameters for specifying the chip geometry where, ,,t = maximum chip thickness (mm) tpmax= chip thickness where plastic deformation starts R, = tpmax , ,/, t 0, = the fracture angle QCr = the inclination of crack against cutting direction as possible in order to minimize the effects of cutting edge wear. The time, however, was sufficiently long to give steady state conditions. No built-up edge was observed in any test. Each test was repeated three times. The signal sampling frequency used for data acquisition was 8.08 KHz. This enabled us to measure the maximum cutting force at the chip segmentation frequency. To study the chip geometry, some chips were collected from each cutting test and mounted in an epoxy metallurgical mount, ground, mechanically polished, etched, and examined under bright field illumination by optical microscopy at magnifications 1OOX and 1600X. In addition, some of these polished and mounted samples were also examined in the SEM using back scattered electrons analysis to determine the region of plastic deformation. All observations on mounted chips were made in the longitudinal mid-section direction. The chip thickness measurements were made at different points along the chip segment using an optical comparator and plotted. The crack

73

initiation angle, QCr , and fracture angle, % were measured for each case to verify the theoretical analysis. 4. Results and discussion Figures 4(a) and 4(b) show the optical micrographs of a new case-hardened workpiece and corresponding 'sawtoothed' chip produced during hard turning. A very fine lath martensitic microstructure is observed in both the cases with, essentially, no strain or plastic deformation all along the chip contour except in the teeth of the chips and in the area around the cutting edge tip where severe plastic deformation occurs due to high compressive stresses [Figures 4(c) and 4(d)]. The heavy plastic flow within a very narrow zone is recognisable as structureless unetched white layer. These observations were consistent during all the fifty seven orthogonal and oblique cutting tests conducted under various cutting conditions.

during hard turning may be assumed to start with initiation of a crack near the free surface which further propagates and ceases in the plastically deformed region close to the tip of the cutting edge. If the present hypothesis is correct, the crack at the free surface will initiate at a critical angle against the cutting direction when the surface layer energy reaches its maximum value at the minimum applied cutting pressure. This angle of crack initiation will remain constant and will not be affected by changing cutting conditions provided the work material is very hard, brittle, and homogeneous. Figures 5 and 6 show the variation of maximum surface layer energy and cutting pressure (both in dimensionless form), respectively, with the angle of loading Q, for a typical value of b/a = 0.1. The ratio b/a determines the shape of the eilipse and thus, reflects the workpiece surface characteristics. Variation in ratio b/a changes the maximum amount of surface layer energy /minimum cutting pressure required to initiate a crack but will make no significant change in the value of angle QCr. The above figures provide the predicted value of as 33'

acr,

aCr

I-nIb

a8

N

20 pm a) microstructure of the case hardened laver

I I

/

l a \

crilicat angle for

I

cr?ck injtiation 33" t

0

1

40

20

60

80

angle of cutting force applied

-

50 pm b) microstructure of the saw tooth chip

Fig. 5 Variation of maximum surface layer energy with loading angle 1.o 0.8

lu)

-.0.6 (v

h

N

0.4 Y

v

5

r

0.2-

critical angle for crack initiation 33" I I

c) SEM image of region A

50 pm

d) white layer in saw tooth chips Fig. 4 Optical micrographs of workpiece and chips

It is evident from these results that the chip formation

74

observations are helpful in assigning this value. The experimental values of crack initiation angle, QCr and fracture angle, 0,, obtained during tests under various conditions of cutting speeds, depths of cut, and two different rake angles of -6' and -26' are plotted against undeformed chip thickness (feed) in Figure 8. The figure shows that for all the cutting conditions, the average value of varies between 31.8' to 33.2'. Earlier, Nakayama et al. [5]also had similar observations during the machining of hard material (bearing steel) in which case the inclination of crack against the cutting direction was almost constant (about 30') in spite of wide variation of rake angles (-lo', -3@, -50' ). The average values of 8, lie between 52 and 570 for various cutting conditions. The results are close to the predicted values. The important point to be noted here is that, in no case, fracture angle is 45' which means that the fracture does not occur due to pure shear at a plane of maximum shear stress but, essentially, at a point on the free surface where the surface layer energy first reaches maximum at a minimum cutting pressure. The fracture angle is more accurately predicted using Sih's ' strain energy density' theory applied to notches under the conditions of mixed mode of kind I and II. It is worth mentioning here that the cutting pressure exerted in the direction of tool movement is considered responsible for the crack initiation. This is because no chip sliding along the rake face is possible until the crack initiates and propagates. The tool face friction which gives rise to a compressive stress near the tool tip and assists in

aCr

'

--. E -

5 II

8

Actual

,P ,

. Average P,,,

6,-

Undeformed chip thickness t (mm)

Fig. 9 Effect of undeformed chip thickness on the maximum pressure determined from different cutting conditions (V=66-120 m/min, f=0.025-0.2 mmhev, d=0.5-4 mm, ~ , = - 6 ~ , - 2 6 ~ )

1001

applied cutting pressure angle @ Fig. 7 Variation of fractyre angle with angle of loading ,for b/a = 0.1 100,

1

Nakayama et al. [5] without providing any reasonable explanation indicated that unlike machining of ductile material, a large chip length ratio over 1.0 (chip thickness ratio <1.0) is obtained during hard turning. This is explainable from the present analysis which gives a fracture angle greater than 45' for most of the cutting conditions and thus, a chip thickness ratio less than 1.0. The ratio of maximum 'saw-toothed' chip thickness to the undeformed chip thickness for several cutting conditions is shown in Figure 10. This ratio, in most of the cases, is found to be less than 1 except at very low feeds. The geometry of typical 'saw-toothed' chips obtained using tool with rake angles of -6' and -2$ are shown in Figure 3.

; 1.6

[.

V

4 .-.I-

0.8

*

t-

201

2 a

u

0.4-

m

=

!

I

I ii

t

f

i

I I

m

1

3

II I

b

++

I

1

I oL

'0

0.04

0.08

0.12

0.16

0.2

0.24

Undeformed chip thickness t (mm)

'

O.b4

'

0:08

'

0.12

'

0.'16

'

0.2

'

0:24

'

Undeformed chip thickness t (mm)

Fig. 8 Effect of undeformed chip thickness on angles 8,and @crfor oblique and orthogonal cutting

Fig. 10 Effect of undeformed chip thickness on R,, and tmax/t ratio

(V=66-120 m/min, f=0.025-0.2 mmhev, d=O.5-4 mm, y,=-6°,-260)

(V=66-120 m/min, f=0.025-0.2 mmhev, d=0.5-4 mm, y,=-6",-26")

75

.

10,

1

measured predicted

u = u,/ to.6' U,= 7.4 E+08

; o 0r , ,0.04 ,

,

,

,

,

,

,

0.08

,

,

,

0.12

,

,

,

,

0.16

,

'

,

0.2

1

Undeforrned chip thickness t (mm)

Fig. 11 Variation of specific energy with undeformed chip thickness for orthogonal cutting (V=66-120 mimin, f=0.025-0.2 mmhev, d=4 mm, yo =-6",-26")

The portion from A to B shows the fractured surface which has been pushed out without any deformation and is approximately linear while the area under the line BC is the plastified portion whose shape is analytically governed by equation (15). It has been found that the ratio of maximum plastically deformed chip thickness, tpmW to the maximum 'saw-tooth' chip thickness, , , t is close to 0.4 except at a very low feed of .025 mm (Figure 10). This result also favours the present analysis because if the angles of crack initiation and fracture 9 are fixed, and the cutting pressure is almost constant, the proportion of plastic deformation to the maximum 'saw-toothed' chip thickness will also remain constant. During hard turning, it can be assumed that the crack propagation ceases at a point in the plastically deformed subsurface layer where maximum shear stress level exists. The cutting pressure on the tool can be considered similar to Hertzian stresses. Shaw and DeSalvo [16] has shown that in case of a blunt axi-symmetric indenter, the plastic flow occurs first at a point beneath the surface corresponding to maximum shear stress = 0.468 p. Using the approach presented in their paper, a ratio close to 0.4 can be obtained for plastically deformed chip thickness to the maximum 'sawtooth' chip thickness. At very low feeds, the undeformed chip thickness is considerably less than the radius at the tool tip and the effective rake angle becomes largely negative. The material ahead of the tool rake face is under intense compressive stress state. In such a case, large volume of material becomes fully plastic before a very small chip is formed. This causes an exponential increase in specific energy with smaller undeformed chip thickness values as shown in Figure 11. Under these circumstances, hard turning seems to be similar to grinding process. However, it is still different from grinding due to fracture being the root cause of chip formation in hard turning.

aGr

5. Conclusions An analytical approach to study the mechanism of 'sawtooth' chip formation during hard turning has been presented here. From the chip configuration, the measured fracture angle is always found to be greater than 45' which shows that the chip formation mechanism can not be fully explained on the basis of pure shear

76

deformation process only. The concepts of surface layer energy/ strain energy density first proposed by Sih are more useful in predicting the initiation and propagation of crack during the process. Several oblique and orthogonal turning tests were performed with IS1 1550 case hardened steel as the workpiece material . All the tests (except at very low feeds) conducted under various cutting conditions confirm the present hypothesis for 'saw-toothed' chip formation mechanism. Many experimental observations, specifically, chip thickness ratio, chip contour. ar?d plastic deformation in Subsurface layer during hard turning have also been discussed with proper explanation for their occurrences. 6. References [ 11 Nakayama, K., 1974, The Formation of Saw-Toothed Chip in Metal Cutting, Proc. Int. Conf. on Prod. Eng.,Tokyo: 572-577. [2] Narutaki, N., and Yamane, Y., 1979, Tool Wear and Cutting Temperature of CBN Tools in Machining of Hardened Steels, Annals of CIRP, 2811: 23-28. [3] Hodgson, T., Trendler, P. H. H., and Micheletti, G. F., 1981, Turning Hardened Tool Steel with CBN Inserts, Annals of CIRP, 3011: 63-66. [4] Konig, W., Komanduri, R., Tonshoff, H. K., and Ackerschott, G., 1984, Machining of Hard Materials, Annals of CIRP, 33/2: 417-427. [5] Nakayama, K., Arai, M., and Kanda, T, 1988, Machining Characteristics of Hard Materials, Annals of CIRP, 37/11 89-92. [6] Konig, W., Klinger, M., and Link, R., 1990, Machining Hard Materials with Geometrically Defined Cutting Edges-Field of Applications and Limitations, Annals CIRP, 3911: 61 -64. [7] El-Wardany, T. I., Elbestawi, M. A., Attia, M. H., and Mohammed, E., 1992, Surface Finish in Turning of Hardened Steel, ASME, WAM, PED- 62, Engineered Surfaces: 141-1 57. [8] Shaw, M. C., and Vyas, A., 1993, Chip Formation in the Machining of Hardened Steel, Annals of the CIRP,

4211 : 29-33. [9] Konig, W., Berktold, A., and Koch, K. F., 1993, Turning versus Grinding-A Comparison of Surface Integrity Aspects and Attainable Accuracies, Annals of CIRP, 42/1: 39-43. [lo] Tonshoff, H. K., Brandt, D., and Wobker, H. G. , 1995, Potential and Limitation of Hard Turning, 1 st lnt. Mach. and Grind. Conf., SME, MR 95-215: 965-978. [ l l ] Tonshoff, H. K., Wobker, H. G., and Brandt, D., 1995, Hard Turning-Influences on the Workpiece Properties, Trans. NAMRVSME, XXIII: 21 5-220. [12] Komanduri, R., and Brown, R. H., 1981, On the Mechanics of Chip Segmentation in Machining, J. of Eng. for Ind., Trans. ASME, 103: 33-51. [13] Sih, G. C., 1973, Some Basic Problems in Fracture Mechanics and New Concepts, Engineering Fracture Mechanics, 5: 365-377. [14] Sih, G. C, 1974, Strain-Energy-Density Factor Applied to Mixed Mode Crack Problems, Int. J. of Fracture, 1 0/3: 305-321 . [15] Sih, G. C. , 1974, Surface Layer Energy and Strain Energy Density for a Blunted Crack or Notch, Prospects of Fract. Mech., Noordhoff International Publishing, Leyden: 85-102. [16] Shaw, M. C. and G. J. DeSalvo, 1970, On the Plastic Flow Beneath a Blunt Axi-symmetric Indenter, Trans. ASME, J. of Engg. for Ind.: 480-494.