Manufacturing Technology Book

M A N U F A C TU R IN G P R O C E S S E S , Second Edition J .P . Kaushish

© 2010 by PH I Learning Private Limited, N e w Delhi. All rights reserved. N o part of this book m ay be reproduced in any form, by mimeograph or any other m eans, without permission in writing from the publisher. IS B N -9 7 8 -8 1 -2 0 3 -4 0 8 2 -4 T h e export rights of this book are vested solely with the publisher.

Second Printing (Second Edition)

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August, 2010

Published by Asoke K. G h o s h . P H I Learning Private Limited. M -9 7 , C o n n augh t Circus, N e w D elhi-110001 and Printed b y M ohan Makhijani at R e kha Printers Private Limited, N e w Delhi-110020.

28. In centrifugal castings, impurities are: (a) uniform ly distributed in casting (b) forced towards outer surface (c) collected close to centre o f casting 29. Centrifugally cast products have (a) large grain structure with high porosity (b) fine grain structures with high density (c) fine grain structure with low density (d) segregation o f slag towards the outer skin o f casting 30. In green-sand m olding process, uniform ram m ing leads to (a) less chance o f gas porosity (b) uniform flow o f m olten metal into the old (c) greater dimensional stability o f casting (d) less sand expansion type o f casting defect

A n s w e r s o f o b je c tiv e ty p e q u e s tio n s 1. 6. 12. 18. 24. 30.

(a) (a) (c) (b) (d) (c).

2. 7. 13. 19. 25.

(b) and (c) 8. (a) (c) 14. (a) (d) 20. (b) (c) 26. (b) (c)

3. 9. 15. 21. 27.

(c) (b) (b) (c) (e)

4. 10. 16. 22. 28.

(d) (a) (b) (b) (c)

5. 11. 17. 23. 29.

(d) (c) (c) (c) (b)

■*u•

Metal Machining Processes and Machine Too

6.1

IN T R O D U C T IO N

Various m anufacturing processes used for transform ing metals into som e usable products are based on basic properties o f metals, for exam ple, the process o f casting is based on the property o f ‘feasibility’ (or melting), forging on the property o f ‘m alleability’, and rolling or form ing on the property o f ‘ductility’. Likewise, the process o f m achining is based on the property o f ‘divisibility’, which is the capability o f metal for getting divided into small bits and separated from the w orkpiece in the form o f chips. Blank is the piece o f metal out o f w hich a product or a com ponent o f some use is m achined out. M achining consists o f forcing a cutting tool o f harder material through the excess (or surplus) material on the workpiece blank; the excess material being progressively separated from the blank in the form o f chips because o f the relative m otion maintained between the tool and the workpiece. T he operation finally results into a transform ed product m achined to the desired shape and size. Metal machining or metal cutting comprises those processes wherein removal o f material from a w orkpiece is effected by relative motion between the cutting tool and the workpiece. T he cutting tool may be (a) sin g le-p o in t cu ttin g to o l as used for turning on lathe or shaping or (b) m ulti-point cutting to o l as used for drilling or milling operations. Basic elem ents o f a m achining operation include (a) w orkpiece, (b) tool and (c) chip. W orkpiece provides the parent metal from w hich unwanted metal in the form o f chip is rem oved by the cutting action o f tool for getting the desired shape and size o f the m anufactured product. T he machining operation is greatly affected by the chem ical com position and physical properties o f workpiece metal. Tool material and tool geom etry play an important role in m achining effectively and economically. Similarly, type and geom etry o f chip are affected by metals o f w orkpieces and tool, geom etry o f tool and cutting fluid. T he process o f machining has gained im portance as it successfully and econom ically m eets the basic objectives o f m anufacturing a product, such as h ig her m etal rem oval rates, high class finish on the w orkpiece, production of com ponents o f intricate shapes, less pow er consumption in comparison to many other production

m ethods, etc. H owever, one m ajor draw back o f machining process is loss o f material in the form o f chips. Metal cutting processes are perform ed on m etal cutting m achines or m achine tools using different types o f cutting tools.

6.1.1

C la s s ific a tio n o f M a c h in in g P ro c e s s e s

M achining processes can be broadly classified as follows: (a) M etal cutting processes using (i) sin g le-p o in t cutting tool include turning, boring, threading, shaping, planing and slotting and (ii) m ulti-point cutting to o l include drilling, milling, tapping, broaching and hobbing. (b) G rinding processes include surface grinding, cylindrical grinding and centreless grinding. (c) Finishing processes include lapping, honing and super-finishing. (d) U n c o n v e n tio n a l m a c h in in g p r o c e sse s in c lu d e e le c tro -d is c h a rg e m a c h in in g , ultrasonic machining, electrochem ical machining, electron beam machining, laser beam machining, etc. Selection o f a suitable machining process depends on workpiece material, shape, size and quantity o f product to be made, expected degree o f accuracy in the dim ensions o f product, requirem ent o f surface finish and finally the cost o f production.

6 .2

C U T T IN G T O O L S A N D T H E IR N O M E N C L A T U R E

As already mentioned that during machining a w orkpiece, a cutting tool o f harder material is forced through the surplus material o f the w orkpiece blank, the surplus material being progressively separated from the blank in the form o f ‘chip* because o f the relative motion m aintained between tool and w orkpiece. The cutting tools are made from high strength and harder materials such as high carbon steel, high speed steel, cem ented carbide, etc. Various cutting tool m aterials have been described under Section 3.18. It may be noted that a cutting tool never peels the material aw ay from the w orkpiece like a knife does. T he tool has a ‘cutting e d g e ’ which is blunt and needs sufficient force to pry the chip from the jo b (Fig. 6.1). In fact, the cutting edge causes the internal shearing action in the metal such that the metal below the cutting edge o f the tool yields and flow s plastically. First o f all, the compression o f the metal under the tool edge takes place [Fig. 6.2(a)] w hich is followed by the separation o f the metal in the form of chip [Fig. 6.2(b)] when the com pression limit o f the metal just under the tool edge has been exceeded. The cutting tools as used on lathes have only a ‘sin g le cutting edge ’ or 'point ’ at one end o f its body, it is then called ‘sin g le-p o in t to o l’. The ‘p oint’, which Fig. 6.1 Turning w ith a is w edge-shaped portion, form s the cutting part o f the tool. There single-point tool. are m ulti-point cu ttin g to o ls ’ also as will be discussed in the following.

Fig. 6 .2

6.2.1

Show ing the principle of metal cu ttin g w ith a sin gle-po in t tool: (a) C om pression of metal under to o l edge and (b) The cu ttin g edge causes internal shearing action in the metal. The metal below the to o l edge yields and flo w s plastically, w hich is follow ed by the separation of sheared metal in the form of a chip.

C la s s ific a tio n o f C u ttin g T o o ls

All cutting tools can be broadly classified as: (i) Single-point cutting tools having only one cutting edge. These tools find wide applications for lathe, shaper, planer, slotter, boring m achine, etc. (ii) M ulti-point cutting tools have more than one cutting edge such as twist drills, reamers, taps, milling cutters, broaches, etc. A m ulti-point cutting tool may differ in overall appearance and purpose but each cutting edge o f the tool acts as and has its basic features o f a single-point cutting tool. Also, the cutting process performed by multi-point cutting tools closely resembles machining as performed by single-point cutting tools. C utting tools are som etim es classified based on their motion during cutting, for example, linear m otion tools as that o f lathe, shaper, planer and slotter; rotary m otion tools as milling cutters and grinding wheels; rotary a n d linear m otion tools as twist drills, ream ers, honing tools, etc. Besides above, a tool may be a solid or forged tool (Fig. 6.3) made from high carbon steel or high speed steel. C utting bits o r inserts made o f high speed steel, stellite or cem ented carbide are available, w hich can be brazed on a high carbon steel shank and tools thus made arc called brazed tools. The cutting bits can be held with the tool shank with som e clam ping system. T h e tool bit is inserted in a slot (in the tool holder) made at 15° to the base, thus reducing the effective clearance angle and increasing the top rake angle by 15°. Tool bit is less expensive than solid tool. Also, the tool can be adjusted to the correct height easily by adjusting the position o f the tool bit in the slot. Regrinding o f tool is easier as only the end cutting edges are required to be ground. It is very easy to withdraw or replace the tool bit without disturbing the setting. T erm s relating to the geom etry o f single-point tool: Important terms relating to the geom etry o f a single-point cutting tool are explained in the following with reference to Fig. 6.4.

Clam ping screw

' ' ' ' -V

Shank (To o l holder)

(iv)

Fig. 6.3

D ifferent types of lathe tools: (i) Solid or forged tool, (ii) Brazed tipped tool, (iii) M echanically held to o l tip o r insert and (iv) Tool bit held in a to o l shank.

Shank

End-cutting edge angle (C*)

Side rake angle +

Main cutting edge or side cutting edge Back rake angle Auxiliary cutting edge or end cutting edge

(a j

Main flank Side relief angle ( 9S)

Front or auxiliary flank

or side clearance angle Side cutting edge angle (0 $ )

Front clearance or end relief angle ( 0 J

Fig. 6 .4

G eom etry of a single-point cutting tool.

Shank is the body o f the tool and is usually rectangular in cross-section. Face is the surface against w hich the chip slides upw ards. Flank (main) is that surface which faces the workpiece. It is the surface adjacent to and below the main cutting edge when the tool lies in horizontal position. Heel is the lowest portion o f the side-cutting and end-cutting edges. N ose or point is the w edge-shaped portion and is the conjunction o f side- and end-cutting edge. Base is the underside o f shank. Rake refers to the slope o f the tool top away from the cutting edge. Tool has side rake and back rake. Besides the body parts o f the tool as mentioned above, the tool geom etry also includes various tool angles which have been explained in the following.

6 .2 .2

A n g le s o f a S in g le -p o in t C u ttin g T o o l

A ngles o f the tool play a significant role in efficient and econom ical machining o f different metals. These tool angles vary according to the metal to be m achined and the tool material. A change in the ch ief angles o f cutting tool will correspondingly change the forces due to the cutting action as also the conditions for heat transm ission through the cutting elem ents o f the tool. Thus, the tool angles o f a cutting tool influence its perform ance and life. Important angles o f a single-point tool are discussed in the follow ing with reference to Fig. 6.5.

•Side cutting edge angle Approach angle

(CJ

as =U ° T V

an9*e \

8

14

0, = 6°

ab Back

6

20

15

To o l designation rake

a , S ide rake 0„ End relief 0S Side relief

Cb E n d cutting edge Cs S ide cutting edge R

Fig. 6.5

N o se radius

Im p o rta n t angles and cu ttin g to o l signature of a sin gle-po in t cu ttin g tool.

1. R ake angle is the rake or slope o f the tool face and is form ed betw een tool face and a plane parallel to its base. W hen this slope is tow ards the shank, it is called back rake or top rake and w hen measured tow ards the side o f the tool, it is called sid e rake. Rake angle has the following functions: (i) A llow s chips to flow in a convenient direction aw ay from the cutting edge. (ii) Reduces chip pressure on tool face and provides keenness to the cutting ed ge and consequently im proves finish on the workpiece. (iii) Reduces cutting forces required to shear the metal and thus helps increasing tool life and reduces pow er consum ption. Provision o f rake angle depends upon following main factors: (i) W orkpiece m aterials as harder m aterials (cast iron) need sm aller rake angle than softer m aterials such as alum inium or steel.

(ii) Tool m a teria l, for exam ple, cem ented carbide permits m achining at very high cutting speeds with little effect o f rake angle on cutting pressure and hence rake angle in such cases may be reduced to zero o r even negative rake may be provided to increase tool strength. (iii) D epth o f cut, for exam ple, higher depth o f cut (as in rough cutting) gives severe cutting pressures on tool and hence rake is decreased to increase tip angle that results in strong cutting edge. Front rake is important when tool removes metal from its front cutting edge (a parting-off tool). Side rake influences m achining when tool removes metal on its side cutting edge only. Side rake allows chips to flow by the side o f the tool and away from tool post. Since the single-point tools generally rem ove metal both on its end and side cutting edges, a slope on the face o f the tool is given suitably com bining the front and side rake together, and this resultant slope is called true rake. T he rake o r slope o f the face o f the tool may be positive, zero or negative as shown in Fig. 6.6.

(a ) Positive rake

Fig. 6 .6

(c) Negative

rake

Positive, zero and negative rake. Note the position and direction of th ru s t on the to o l in each case. R— Rake and T— Thrust.

Positive rake: A tool has positive rake w hen face o f the tool slopes aw ay from the cutting edges and also slants tow ards the back (shank) or side o f the tool [Fig. 6.6(a)]. A rake angle specifies the ease with which a metal is machined. The higher the rake angle, the better is the cutting and less are cutting forces. Since an increase in rake angle reduces the strength o f tool tip, heat dissipation and tool life, it is, therefore, usually kept not m ore than 15° (for high speed steel tool). Zero rake: A tool has zero rake when no rake is provided on tool, i.e. the tool face has no slope and is parallel to the upper surface o f the tool shank [Fig. 6.6(b)!. A zero rake increases tool strength and avoids digging o f the tool into the w orkpiece. Brass is turned well with tools having zero rake angle. Negative rake: A tool has negative rake when the tool face slopes aw ay from the cutting edge and slants upw ards tow ards the side or back o f the tool [Fig. 6.6(c)]. Negative rake is used on cem ented carbide o r ceram ic tools. N egative rake results into a tool with reduced keenness but stronger cutting edge (and hence stronger tool) o r tool tip. Carbide tools with negative rake are used for m achining extra hard surfaces and stronger m aterials in mass production.

Cutting action o f a tool with positive and negative rake is shown in Fig. 6.7.

Built-up edge

(a) Fig. 6 .7

Cutting edge

(b)

Show ing the cutting action of a tool w ith positive rake (a) and negative rake (b). Note that in positive rake cutting, there exists a tendency fo r the metal to build up and also m ore pronounced crater form ation. In negative rake cutting, the tendency of crater form ation is less and the cu ttin g edge in the process gives a burnishing (polish in g) effect on the machined surface of w orkpieces. The th ru st of cut show n by a rro w passes through the cutting edge of the tool at (a) and thus introduces a bending load at the cu ttin g edge, whereas at (b) the th ru st passes through the to o l shank and this gives a com pression load on the stronger portion of the tool.

A dvantage o f using negative rake on tool (i) (ii)

(iii) (iv) (v) (vi)

N egative rake gives larger tip angle and hence a stronger tool. In case o f tipped tools, an advantage with negative rake is that there is a tendency o f the chip pressure to press lip against the body o f tool, a favourable factor since carbide tips are very good for com pressive loads. Negative rake on these tools varies from 5° to 10°. T he point o f application o f cutting force is altered from cutting edge (a w eaker tip) to a stronger section. Very high cutting speeds can be used for faster metal removal. Tool w ear is decreased and hence tool life is increased. H eavier depth o f cut can be taken as negative rake increases tip angle o f the tool.

There are certain limitations o f using negative rake, for exam ple, h ig h er cutting sp e e d should be kept to take full advantage o f negative rake; rig id ity o f the m achine to o l must be ensured against higher cutting speeds and vibrations; high heat generated by negative rake turning must be taken care o f for better tool life and h igher p o w e r requirem ent, above 10 to 15% more than what required for positive rake machining. 2. C learance angles: Clearance angle is the angle between the m achined surface and the Hank faces (Fig. 6.4) o f the tool. It helps preventing the flank o f the tool from rubbing against the surface o f the w orkpiece, thus allow ing the cutting edge o f the tool only to com e in contact with the w orkpiece, for exam ple, front clearance angle (also called end relief angle) prevents the front or auxiliary flank o f the tool from rubbing against the finished surface o f the workpiece. In case the angle is too small, the tool will rub on the surface o f the jo b and spoil surface finish. Too large end relief angle m ay give tool digging tendency and may chatter. The side clearance angle (or side relief angle)

prevents the side or main flank o f the tool from rubbing against the workpiece under longitudinal feeds. Values o f these angles for turning tools vary between 5° and 15°. 3.

Side cutting edge angle: Side cutting edge angle is the angle between the side cutting edge and the longitudinal axis o f tool. Its com plim entary angle is approach angle, (Fig. 6.5) w hich is between feed direction and side cutting edge. Side cutting edge angle helps providing a w ider cutting edge and thus an increased tool life as cutting force, distributed on w ider surface, provides greater cutting speeds and quick heat dissipation and gives a better finish on work surface. It controls direction o f chip flow. Too large side cutting edge angle produces chatter. It is usually kept around 15° although in turning tools, it varies from 0 to 90°, for exam ple, a knife edge turning tool has 0° side cutting edge angle and its cutting edge is perpendicular to the work surface and such a tool is used for turning slender w orkpiece as no bending stress is produced when tool is fed. A square nose tool with side cutting edge angle 90° is used for finish turning.

4.

End cutting edge angle: It prevents the trailing end o f the cutting edge o f tool from rubbing against the workpiece. A larger end cutting edge angle weakens the tool. It is usually kept between 8° and 15°.

5. Lip angle: L ip angle or cutting angle depends on the rake and clearance angle provided on tool and determ ines the strength o f cutting edge. The lip angle is m axim um when rake (positive) and clearance angle are m inim um . But in negative rake, lip angle increases as rake increases. A larger lip angle permits m achining o f harder metals, allows heavier depth o f cut and increases tool life and better heat dissipation. This sim ultaneously calls for reduced cutting speeds, which is a disadvantage. 6. N ose radius: W hile greater nose radius increases abrasion, it also helps in im proving surface finish, tool strength and tool life. Large nose radius may cause chatter. For rough turning, it is kept about 0.4 mm and for finish turning, 0.8 to 1.6 mm. Average recom m ended tool angles for machining different metals are given in Table 6.1. TABLE 6.1

Recom m ended angles fo r high carbon and high speed steel turning tools

Material

Front rake, deg

Front clearance, deg

Side rake, deg

Side clearance, deg

Mild steel Stainless steel Aluminium Brass Cast iron Copper

10-12 5-7 30-35 0-6 3-5 14-16

6-8 6-8 8-10 8-10 6-8 12-14

10-12 8-10 14-16 1-5 10-12 18-20

6-8 7-9 12-14 10-12 6-9 12-14

6 .2 .3

N o m e n c la tu re o f a L a th e T o o l

N om enclature o f a cu ttin g to o l means systematic nam ing o f various parts and angles o f the tool. Com plete nomenclature o f various parts o f a single-point tool is shown in Fig. 6.4 and Fig. 6.5 which includes shank, face, flank, heel, nose, base, back rake, side rake, side clearance,

end clearance, end cutting edge, side cutting edge and lip angle. These elem ents define the shape o f a cutting tool. C utting tool signature: The cutting to o l sig n a tu re (or tool designation) is a sequence of num bers listing various angles, in degrees and the size o f nose radius. The A m erican Standards Association (A SA ) has standardized the numerical m ethod o f tool identification. The seven elements com prising the signature o f a single-point tool are alw ays written in the following order: back rake angle, side rake angle, end relief angle, side relief angle, end cutting edge angle, side cutting edge angle and nose radius. Example:

A tool shape specified as per ASA system is given below (Fig. 6.5): 8-14-6-6-20-15-4

has back rake angle 8°, side rake angle 14°, end relief angle 6°, side relief angle 6°, end cutting edge angle 20°, side cutting edge angle 15° and nose radius 4 mm. Besides the A m erican Standards Association (A SA ) System , also called coordinate system (or X-Y-Z Plane System) w hich has been described in the above, the other systems o f tool designation include British System , Continental System and International System (or O rthogonal R ake System). In O rthogonal R ake System (O R S) o r International System , main parameters o f a single-point tool are designated in the follow ing order: inclination angle (X), orthogonal rake angle (O'), side relief angle ()), end relief angle (y x), auxiliary cutting angle (0,), approach angle (0O) and nose radius (/?). For exam ple, a cutting tool designated as 0-10-5-5-7-90-1 will have the following values o f its parameters. X

= 0°

(inclination angle)

a

= 10°

(orthogonal rake angle)

Y

= 5°

(side relief angle)

Y\

= 5°

(end relief angle)

0> = 7° 0Q = 90° R

6 .3

= 1 mm

(auxiliary cutting angle) (approach angle) (nose radius)

M E C H A N IC S O F M E T A L C U T T IN G

The topics generally covered under the treatm ent on m echanics o f m etal cuttin g include basic m echanism o f metal cutting and shear zone, formation o f chip, orthogonal and oblique cutting, forces on chip (M erchant’s A nalysis), etc. These are discussed in the following.

6.3.1

F o rm a tio n o f C h ip

To understand clearly the fundam entals o f the m echanism o f metal cutting on m achine tools, let us first try to understand a sim ple case o f cutting with an ordinary hand tool, say a flat chisel, under the blows o f h am m er because the cutting principle as applied to any hand tool used in bench w orking or a cutting tool used on a m achine tool is the same.

R efer Fig. 6.8 w herein shearing action o f a cold chisel is shown during the process of cutting surplus metal from a w orkpiece under the blow o f a hammer. The chisel is shown flat on the w orkpiece surface without any clearance angle, primarily to ensure that depth o f cut can be m aintained and secondly, the clearance angle takes no actual part in the cutting or shearing action o f the chisel. Note that the force (F ) o f the h am m er blow is transm itted at approxim ately 90° to the cutting face AC, and this sets up shear stress across a narrow region in the w orkpiece say the shear plane AB. U nder the effect o f heavy blow s o f ham mer, the metal ahead o f the cutting edge o f chisel will shear across the shear plane and m oves up the chisel face A C in the form o f a ‘segm ent o f ch ip ’. Since the energy required to shear or rupture the metal will be the shearing force along the shear plane AB, this shearing force will, therefore, be proportional to the length AB. Hence, the smaller the rake angle o f chisel, the greater will be the length (AB) o f shear plane and the larger will be the energy required to shear the metal.

Fig. 6 .8

Illu stra tin g the shearing action of a cold chisel.

Chip formation may be com pared to the m ovem ent o f card stack when pushed along the tool face. The consecutive displacem ents o f lamellae o f forming chip are depicted in Fig. 6.9 w herein the segm ents o f the chip num bered from 1 to 6 earlier occupied the positions shown by the dotted lines. W hen the tool advances, the segment 7 slips a finite distance relative to the uncut metal. As the tool advances further, the next segm ent 8 slips similarly and previous segm ent 7 m oves over the tool as a part o f the chip. A lthough the card model is a little over sim plification o f w hat happens during metal cutting, it does illustrate some o f the major considerations in the metal cutting process.

T he basic m echanism o f chip form ation, therefore, consists o f a deform ation o f metal lying just ahead o f the cutting edge o f tool, by process o f shear, in a narrow zone (called shear zon e or prim ary deform ation zone) extending from the cutting edge o f the tool obliquely up to the uncut surface o f w orkpiece in front o f the tool (Fig. 6.10). During metal cutting, the metal in the area in front o f the cutting edge o f the tool is severely com pressed causing high tem perature shear stress in the metal, the shear stress being m axim um along a narrow zone or plane called the shear plane (Fig. 6.11). W hen the shear stress in the workpiece metal just ahead o f the cutting ed g e o f tool reaches a value exceeding the ultimate strength o f the metal, particles o f the metal start shearing aw ay (or rupture) and flow plastically along the shear plane, form ing ‘segm ents o f ch ip ’ w hich flow upw ards along the face o f the tool. In this way, m ore and m ore new chip segm ents are form ed and the cycle o f com pression, plastic flow and rupture is repeated resulting into the birth o f a continuously flowing chip. Since the w idth o f shear zone is small, chip formation is often described as a process o f successive shears o f thin layers o f w orkpiece metal along particular surfaces. Chips are highly com pressed body and have burnished and deform ed underside (due to deformation at secondary shear zone on account o f friction between chip and tool face). The primary shear zone deform ations are required for the formation o f chip, w hereas deform ations in secondary shear zone are secondary deform ations w hich, in fact, are disturbances and are not required.

Fig. 6.11

Illu stra tin g the shear zone (ABDC), shear plane and shear angle ().

T he shearing o f the metal in the process o f chip formation does not, however, take place sharply along the shear plane shown by a straight line LM (Fig. 6.11). In actual case, the com plete plastic deform ation occurs over a definite area, represented by ABDC. Form ation o f chip starts when the metal structure begins elongating along the line BA which is below the shear plane and continues to do so until it is com pletely deform ed along the line DC above the shear plane and is bom as ‘ch ip ’. Shear zone (or prim ary>deform ation zone) lies between the lines BA and DC. These two lines m ay not be parallel (giving uniform w idth o f shear zone) but m ay produce a w edge-shaped zone thicker near the tool face at the right and thinner on opposite to it, a feature w hich is considered responsible for ‘curling o f ch ip s’ during machining. A nother cause o f chips to curl away from the cutting face o f tool may be nonuniform distribution o f forces at the tool-chip interface and on the shear plane resulting into a shear plane slightly curved concave dow nw ards. At high speed cutting, shear zone can be assum ed to be restricted to a straight line plane called shear plane inclined at an angle