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# Ch 3-process parameters 1of3

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### Ch 3-process parameters 1of3

1. 1. 41 3. PROCESS PARAMETERSThe data obtained in a uniaxial tensile test has limited use for metal forming calculations asmetal forming conditions are far different from those available in uniaxial tensile test.Stress−strain characteristic are affected by two types of factors.1. Factors related to deformation process(i) amount of deformation (∈)(ii) strain rate (∈) (iii) operating temperature (t)2. Factors not related to deformation process(i) chemical composition and metallurgical structure(ii) average grain diameter(iii) pre strain history of materials.I. AMOUNT OF DEFORMATIONFlow stress increases with amount of deformation and relationship between these is defined byHollomon equation and Ludwik equation. σ = K (t ) n ………. Hollomon equation σ = σi + K (∈) n ……… Ludwik equation
2. 2. 42 Fig. 1n = 1 is valid for metals which are heavily deformed.Larger the amount of deformation, greater will be value of flow stress. Table 1Typical values for k and ‘n’ at room temperature. Material K(MPa) N Aluminium 1100−0 180 0.2 2024−T4 690 0.17 6061−0 200 0.2
3. 3. 43 Brass 70/30 annealed 900 0.5 85/15 cold rolled 580 0.33 copper, annealed steel 315 0.55 Low Carbon 530 0.25 4135 annealed 1015 0.18 4135 cold rolled 1100 0.14 304 stainless steel (annealed) 1275 0.45 410 stainless steel (annealed) 960 0.1 C 60 quenched/temnp 1600 0.1 Table 2 σ = C(∈) m 1. Strain hardening exponent ‘n’ is useful in determining the behaviour of materials during many working operations.2. When deformation exceeds abilities of a material to undergo uniform straining, strain get localized and necking takes place. The strain hardening exponent is a measure of materials abilities to distribute strain uniformly and resist localization of strain and thereby delays necking.
4. 4. 44 Materials which have a high work hardening exponent such as copper and brass (n ≥ 0.5) can be given a large plastic deformation move easily than those which have smaller n, such as heat treat steel (n ≈ 0.15) . Materials having higher n value are desirable in wire drawing.3. ‘n’ represent limiting strain for uniform and homogenous deformation.4. High value of 302 austenitic steel (n = 0.3) n is an indication of poor machinability. This is because the cutting action of the tool causes strain hardening a head of the tool. Due to the high ‘n’ value, this causes a large increase in strength and hardness. Thus the cutting tool is always working against higher strength material, reaviring larger cutting forces.5. In contrast, a high value is desirable for sheet formation, in which resistance to local necking or reduction in sheet thickness is necessary. When a high ‘n’ value material begins to neck, the deforming region rapidly strain hardens, causing subsequent plastic deformation to occur in the surrounding softer metal. This produces a long diffusion neck. In contrast, neaking in a material with a low value occurs move locally, causing failure at a lower strain. Fig. 2Comments on Hollomon equation1. It is found that the work hardening of many metals approximates to a parabolic form. For annealed metals with cubic lattice, the stress−strain relation is well defined by Hollomon
5. 5. 45 equation. For pre-worked materials, this equation gives less accurate results. The values of stress are valid from yield point to maximum load point.2. Strain hardening exponent for many metals range between 0 to 0.5. It is zero for non hardening rigid plastic metals. The higher the value n, more pronounced is the strain hardening of the material.3. The stretching capacity [strain forming, deep drawing] of metals is related to its ability to delay or resist necking. One measure of this resistance to neck is strain-hardening exponent. The higher the value of ‘n’, larger is the uniform elongation and greater is resistance to necking. A higher value of n improves the ability of metal to resist localisation of strain in presence of stress gradient. This generates move uniform distribution of strain and permits more effective utilisation of available metal. A high value of n indicates good stretch formability and cold formed grade steels have n value in the range of 0.22 to 0.5. On the other hand, hot rolled materials can have n values as low as 0.1 and may undergo excessive thinning or fracture in severely strained region of processing. Time does not enter as a parameter and ordinarily, the deformation characteristics is taken as independent of time.4. A simple guide for calculating n for steels is 70 n = σ 0 ( N / mm 2 )5. Many a times, strain hardening exponent is considered as strain hardening rate, which is not true. σ = K (∈) n log σ = log K + n log ∈ Taking derivative dσ d∈ d∈ = 0 + n. = n σ ∈ ∈
6. 6. 46 ∴ strain hardening rate dσ σ = n. d∈ ∈ dσ σ ∴ strain hardening rate is not simply equal to n but equal to n . . d∈ ∈6. Limitations of Hollomon equation: i. This equation is quite reliable when induced strain is greater than 0.04 but less than the strain at which necking begins. ii. Use of this equation to predict initial yield strength of the metal should be avoided. Instead, a method such as offset should be used. iii. Most metal working operations imparts strain far in excess of 0.04 and the exclusion of the elastic and transition strain region leads to little error in this regard. II. EFFECT OF TEMPERATURE ON FLOW STRESSFlow stress in influenced by temperature. Flow stress decreases with increase in temperature.Ductilities also increases with temperature. This characteristic is fully utilised in hot workingwhere large reduction are obtained at relatively lower flow stresses. Fig. 3 : Effect of temperature on flow stress.3. Strain rateStrain rate (∈) does not influences flow stress in cold working. It is a significant factor in determing flow stress in hot working. Flow stress increases with strain rate and dependence offlow stress on strain rate increases with temperature.
7. 7. 47 Fig. 4 log σ = m log ∈ + log c  σ = c (∈) m where m = strain rate sensitivity exponent c = strain rate strength constant σ = c (∈) m 
8. 8. 48As the temperature increases the slope of the curve increases. Thus the strength becomes moveand more sensitive to strain rate as temperature increases. Slope is relatively flat at roomtemperature m Cold working upto 0.05 Hot working 0.05 to 0.4 Super plastic 0.3 to 0.85High the value of m, more the capacity of the material to delay the necking and more stretchingis possible at elevated temperature before failure.2. When strain rate is of high order, the stress−strain curve change as a function of strain rate in accordance with equation σ = C (∈) m  m = 0 stress is independent of strain rate m = 0.2 common metals = 0.4 to 0.9 superplastic metals Fig, 5The dependence of flow stress on strain rate increases with temperature.Larger the value of m, more postponement of necking will be. The reason for this is that as soonas necking starts in some region, the strain rate (∈) increases locally resulting in a rapid increase 
9. 9. 49in the stress required to cause further deformation in that region. The deformation then shits toother region of the material, where there is no necking. Here the strain rate and hence the stressto cause deformation is smaller stainless steel, aluminium and titanium alloys exhibitsuperplastic behaviour.Principal effects of strain rate in metal forming: -1. Flow stress of metal increases with strain rate, especially at temperatures above recrystallisation temperature.2. At higher strain rates, the temperature of workpiece increases abnormally as there is little time available for heat transfer. It is adiabatic heating.3. Lubrication at the tool-work interface improves as long as lubrication is maintained – At higher strain rates there is possibility of breakage of lubrication film, resulting in poor surface finish.Deformation velocity of commercial equipments used in metal forming is much higher thanobserved in tension test. For wire drawing at speed of 40 m/s result in strain rate of 10 5 s −1 .However, there is a group of newer metal working processes which utilises velocities as high as200 m/s to carry out forging, sheet forming, extrusion etc. They are known as High VelocityForming [HVF] and High Energy Rate Forming processes. These processes have strain ratemuch higher than the conventional methods. For many materials elongation limit (upto fracture)increases with strain rate, upto limit. Beyond this limit of strain rate ductility falls sharply, thislimit is called as critical strain rate.At the other extreme of strain rate spectrum, there is superplastic forming. Materials having highstrain rate sensitivity index ‘m’ (0.3 <m ≤ 1) exhibits pronounced resistancefor necking. Superplasticity behaviour is observed when operating temperature is above 0.4 Tmand strain rates are below 0.01 sec −1 .• Very fine grain (grain size <10 µm)• High operating temperature (T > 0.4 Tm)• Very low strain rate ( ∈< 0.01 S −1 ). 
10. 10. 50The chief advantages of superplasticity(i) Very low How stress 5 – 30 MPa(ii) Very large deformations can be obtained.The effect of m on hot deformation behaviour is somewhat analogous to that of strain hardeningexponent for cold deformation. A high ‘m’ value causes a considerable increase in strength andhardeness of the material at high strain rates, leading to a requirement for higher forming forces.Alternatively, for high m materials a slow strain rate is necessary for forming. This can lead tounacceptably long and often, uneconomical forming time. An important advantage of a high mvalue, like a high n value is improved formability resulting from forming a diffuse neck ratherthan a local neck.A positive value of ‘m’ reduces localisation of strain and thus necking. A large and positivevalue of ‘m’ opposes rapid localisation of strain and causes neck to be more diffused. In reverseway, a negative value of ‘m’ promotes localisation of strain and thus generate severe straingradient. Thus both sign and magnitude of ‘m’ is important.In sum a positive value of strain rate sensitivity index.1. Higher stresses are required to form part at higher strain rates.2. At a given forming rate, the material resists further deformations in regions that are being strained more rapidly than adjacent region by increasing the flow stress in these regions. This helps in distributing strain more uniformly.In many forming operation, need for higher stress for deformation is not a major considerationbut ability to distribute strain uniformly is one. Generally, metal have value – 0. 01 to 0. 06.Metals in superplastic region have high ‘m’ values, which is one to two orders higher thantypical steel. High ‘m’ and ‘n’ values is of little use in deep drawing as they strengthen wall aswell as flange which make it harder to draw.Mean strain rate (∈m ) for various metals forming processes: 
11. 11. 511. For up setting and tension test v ∈m =  v = cross head hvelocity h =instantaneous height of the specimen.2. For extrusion and wire drawing 2 6 V d 0 log R ∈m =  V = extrusion velocity (d 3 − d 1 ) 0 3 d 0 = billet diameter d1 = extrusion diameter R = extrusion ratio.3. For rolling V h ∈m =  × log 0 h 0 = thickness of slab before rolling h h1 h 1 = thickness of slab after rolling.Superplastic behaviour of metals and alloysConventioned metals and alloys exhibit elongation in the range of 10 to 60%. Some metals andalloys exhibit very large deformations, more than 100% and even upto 3000% with out fracture.This behaviour of metals is termed as superplastic behaviour. It has enabled the economicalproduction of large, complex shaped products with compound curves. Deep or complex shapescan now be made as one piece [rather than joining /welding many pieces into a assembly], singleoperation pressing rather than multistip conventional pressings. Precision is excellent and finedetails or surface texture can be reproduced accurately. Springback and residual stresses are nonexistent and products have a fine, uniform grain size.Main characteristics of superplastic behaviour are:i. Very large deformations are obtained without fracture. It permits forming of metals as if they are polymer or glass.
12. 12. 52ii. The other characteristics normally observed concurrently is substantial reduction in flow stress. The flow stress is about 5 to 50% of the conventional method flow stress.Following are requirements if the material is to exhibit superplstic behaviour:1. The operating temperature should be more than the half of melting point. T > 0.5 Tm Tm = melting point k.2. Small and stable grain size. Grain size should be less than 10 µm. The presence of second phase particles inhibit grain growth at high operating temperature. Further, the strength of second phase should be similar to that of matrix to avoid excessive cavity formation.3. Flow stress of superplastic material is very sensitive to the strain rates. High value of strain rate sensitivity index is necessary. Strain rate sensitivity index should be in the range of 0.3 to 0.9 i.e. 0.3 < m < 0.94. Superplasticity is observed within specified range of strain rates. Ductility reduces dramatically on either side strain rate range is 10 −5 to 10 −2 / Sec. of this range.Superplastic deformation occurs predominantly by grain boundary sliding and grainrearrangement. Both of these mechanisms require a large grain area and hence the need for asmall grain size. They are accommodated by grain boundary diffusion which is a temperatureactivated process and hence the requirement for elevated temperature.The strain rate sensitivity index (m) itself is function of strain rates and strain rate range shouldbe 10 −5 to 10 −2 / sec . Within this range of strain rate, m is sufficiently large for superplasticbehaviour of metal. It is observed that the high value of m is obtainable with fine grainmicrostructure or m value increases with decrease in grain size. Such a fine grain structure iseasily obtained and maintained in eutectic and eutectoid alloys. For these materials differentmicrostructure/phases are formed simultaneously at subeutectic or subeutectoid temperatures and
13. 13. 53then precipitate in a fine dispersion. It is, however, demonstrated that superplastic behaviour isnot confined to these two phase structures, but even fine grained pure metals also exhibit thesame.A characteristics feature of superplastic deformation is that large macroscopic elongations arepossible without significant elongation of individual grains. In superplstic alloy, grain boundarysliding constitutes the greatest contribution to deformation in superplastic region. Fig. 6 : Dependence of m on strain rate.Superplastic alloysSmall and stable grain size is requirement for superplastic behaviour of metal and therefore notall commercially available alloys are superplastic. Following alloy exhibit superplasticbehaviour. Alloy Temperature ∈  m % elongation Titanium Ti – 6 Al – 4V 850 10 −3 0.75 750 – 1150 Ti – 6 Al – 4V- 2Ni 815 2 × 10 −4 0.85 720% Aluminium Al – 33 Cu 450 8 × 10 −4 0.8 400 – 100% Zn 78% + 22% Al 240 C  - 0.5 Al 67% + 33% Cu 480  C - 0.9 Cu 90 + 10% Al 500 - 0.5
14. 14. 54Advantages1. Commercial development of superplastic materials has made it possible the production of large, complex shaped products often in limited avantity economical. Deeper or complex shaped can be made from one piece in a single operation rather than multistep conventional pressing or multipiece assemblies.2. Drastically deduced flow stress of the material.3. Because of the low forming pressures, forming blocks can be used in place of die set and hence tooling is relatively inexpensive.4. It requires shorter production lead time.5. Many applications of superplasticity eliminates a considerable number of subsequent operations. The weight of the products can be reduced and there are fewer fastening holes. These holes generally initials cracks on repeated loads.6. Precision obtained is excellent and fine details are produced− products have fine and uniform grain size.LimitationA major limitations to superplastic forming is the low forming rate that is required to maintainsuperplastic forming, cycle time range from 2 min to 2 hours per part is too long compared toseveral seconds that is typical of conventional press work. As a result, application tend to belimited to low volume products such as those common to aerospace industry. By makingproducts larger and eliminating assembly operations, the weight of products can be reduced.There are fewer fastening holes to initiate fatigue cracks, tooling and fabrication costs arereduced.
15. 15. 55Strain hardeningStrain hardening is a phenomenon whereby the yield stress of a metal increases with increasingdeformation (strain). It occurs at low temperature, below recrystallisation temperature which isabout 0.5 Tm (Tm is melting point temperature K). This applies to forming temperatures that areso low that thermally activated processes play no significant role. Strain hardening results inhigher forming force and forming energy requirement, thus increasing load/stresses acting on thetool. Strain hardening increases strength and hardness but cause decrease in ductility andtherefore in many cases, annealing become necessary to restore ductility and formability toobtain the required deformation. To negate the effect of strain hardening, forming can be carriedout at elevated temperatures, the accuracy and surface quality obtained would be inferior to theone obtained in cold forming.Besides these undesirable side effects of strain hardening there is an increase in the strengthvalues of the finished components through forming which is very desirable. Strain hardeningcan be used for practically all metals and alloys to increase hardness and strength. The increasedstrength permits the use of materials with lower initial strength compared to componentsproduced by machining. Moreover, in many cases heat treatment (costly and time consuming) isunnecessary because of strain hardening.Strain, hardening is a result of a large number of dislocations participating simultaneously.During metal forming the dislocation density increases by several order from 10 7 to 1012 / cm 2 .By this zones of higher dislocation density emerge, which represent a hindrance for movingdislocations. Presence of dislocations lowers the shear stress required to cause slip. Butdislocations can:(i) become entangled and interfere with each other.(ii) be impeded by barriers, such as grain boundaries and inclusions in the material.As dislocation density increases, the stress required for moving dislocation increases due tointerfering effect of stress fields surrounding the dislocations. Entanglement and impedimentsincrease the shear stress required for slip. The effect is an increase in shear stress that causes an
16. 16. 56increase in the overall strength of the metal, known as strain hardening or work hardening. Thisphenomenon forms basis for work hardening, described by means of equation:The shear stress τ to move a dislocation increases with increasing dislocation density e,according to the following equation. τ = τ0 + A ρwhere τ 0 = base stress to move the dislocation in the crystal in the absence of other dislocations. A = constantThis equation describes the work hardening behaviour. For a soft crystal, the CRSS (criticallyresolved shear stress) for initiation of plastic deformation is typically 0.5 N / mm 2 . 10 A = 0.01 N/mm = N / mm 1000low dislocation density = 10 4 / mm 2CRSS for annealed crystal = T0 = 0.5 1 = 0.5 N / mm 2 + × 10 4 100 = 1.5 N/mm 2heavily cold worked, the dislocation density increases to 10 8 / mm 2 1 = 0.5 + × 10 8 100 = 100 N / mm 2 .Strain hardening depends on :1. Lattice structure. Strain hardening rate is greater for cubic crystal.
17. 17. 57 (i) Strain hardening rate in FCC metals is affected more than for HCP crystals by stacking fault energy. Therefore, copper, nickel, austenitic steel harden more rapidly than aluminium. (ii) HCP (Hexagonal close packed) metals subjected to “twinning” and strain hardening rate is much rapid as there is only one plane for easy glide.(2) Strain hardening rate increases with complexity of structure − impurities, grain size, second phase particles etc. Therefore, final strength of the cold worked solid solution alloy is always greater than that of pure metal cold worked to the same extent.Strain hardening capacityTwo measures of strain hardening capacity yield strength 240i. ratio of = = (for ms) = higher the ratio. ultimate strength 380ii. uniform elongation eu which is the elongation at max load. n = log (1 + eu) value of ‘n’ is highest when the material is normalised. It is lowered by cold working. A typical low carbon steel has ‘n’ value 0.2 to 0.22. A value of 0.25 is considered high for these steels while those below 0.18 are considered to have low ductility and poor strain hardening capacity.Strain hardening is an important industrial process used for strengthening and hardening metals[Cu, Al] or their alloys which do not respond to heat treatment process. Of course, the productmust not be used at temperature that will anneal the metals.Strain hardening has important place in industry.
18. 18. 58i. It alters the properties of metal. Cold working improves strength and hardness of metal, but reduces elongation. Fig. 7 Cold work reduces the amount of plastic deformation that a metal can undergo subsequently during shaping operation. The hardened, less ductile, cold worked metal require more power for further working and is subjected to cracking. Therefore cold work anneal cycles are used to assist production i.e. formation limit is extended through annealing. The loss of ductilities has useful side effect − improvement in machinability by 25% in low−medium carbon steel. With less ductility, chips break move readily thus facilitating cutting operation. Cold work stock is used for machining screw stock.ii. The preferential orientation of second phase particles and structural discontinuities [voids, inclusions, segregations] in the principal direction of deformation give rise to mechanical fibering. A important consequence of mechanical fibering is that mechanical properties in different directions. In general, tensile strength, ductility, fatigue strength is more in longitudinal direction than transverse. But shear strength is greater in transverse direction.FRICTION IN METALSFriction is defined as the resistance to relative motion between two bodies in contact, under anormal load. Friction plays an important role in metalworking and manufacturing processesbecause of the relative motion and forces that are always present on tools, dies, and workpieces.
19. 19. 59Friction dissipates energy, thus generating heat, which can have detrimental effects on anoperation. Furthermore, because friction impedes free movement at interfaces, it cansignificantly affect the flow and deformation of materials in metalworking processes. On theother hand, friction is not always undesirable; without friction, for example, it would beimpossible to roll metals, clamp workpieces on machines, or hold drill bits in chucks.Friction plays a great role in all engineering applications whenever solid surfaces are in slidingcontact with each other. This is particularly true in metal working processes where the slidingpair of surfaces are metals and where plastic deformation of the softer of two metals usuallytakes place. Friction conditions between the deforming tool and workpiece in metal working ofgreatest importance as it decides force required and mode of deformation, properties of thefinished specimen, resulting surface finish etc.The friction stress, τ is measured in force per unit area. The surface area of contact is aboundary of the deformed metal.I. Coulomb’s Friction Law F N F=µ×N ⇒ =µ× A A T= µ × PF = Frictional forceA = Apparent area of contact Fig. 8
20. 20. 60The tangential stress, Tat any point on that surface is proportional to the pressure p between thetwo bodies and is directly in opposite direction to the relative motion between these bodies. Thecoefficient of friction ‘µ’ is taken as constant for given die and the workpiece (under constantsurface and temperature conditions) and is said to be independent of the velocity, applied load,and area of contact. Fig. 9µP > kIt is expected that this relation is sufficient to describe the conditions until the product of µ and P(µP) becomes higher than the yield stress in pure shear (k) of the material. The material will thenstick to the tool and yielding takes place in the interior of the material. Modern theory of frictionis based on premise that flat surface is not flat but consists of numerous peaks and valleys.
21. 21. 61 Apparent Actual surface Fig. 10A commonly accepted theory of friction is the adhesion theory, developed by F.P. Bowden(1903 − 1968) and D. Tabor (1913 −). The theory is based on the observation that two clean anddry surfaces, regardless of how smooth they are, contact each other (junction) at only a fractionof their apparent area of contact (Fig. 8). The maximum slope of the hills on these surfacesranges typically between 5  and 15 .In such a situation, the normal (contact) load, N, is supported by the minute asperities (smallprojections from the surface) that are in con tact with each other. The normal stresses at theseasperities are, therefore, high; this causes plastic deformation at the junctions. Their contactcreates an adhesive bond: the asperities form microwelds. Cold pressure welding is based on thisprinciple.Sliding motion between two bodies which have such an interface is possible only if a tangentialforce is applied. This tangential force is the force required to shear the junctions; it is called thefriction force, F. The ratio of F to N (see Fig. 8) is the coefficient of friction, µ.
22. 22. 62Fig. 11: Schematic illustration of the interface of two bodies in contact, showing real areas ofcontact at the asperities. In engineering surfaces, the ratio of the apparent to real areas ofcontact can be as high as 4 − 5 orders of magnitude.In addition to the force required to break these junctions by shearing, a plowing (or ploughing)force can also be present if one surface scratches the other (abrasive action). This force cancontribute significantly to friction at the interface. Plowing may (a) cause displacement of thematerial and/or (b) produce small chips or slivers, as in cutting and abrasive processes.Depending on material and processes involved, coefficients of friction in manufacturing varysignificantly, as is obvious in Table 1. Table 1: Range of Coefficients of Friction in Metalworking Processes Coefficient of friction (µ) Process Cold Hot Rolling 0.05 − 0.1 0.2 − 0.7 Forging 0.05 − 0.1 0.1 − 0.2 Drawing 0.03 − 0.1 − Sheet−metal forming 0.05 − 0.1 0.1 − 0.2 Machining 0.5 − 2 −Almost all of the energy dissipated into heat (a small fraction becomes stored energy in theplastically deformed regions; raising the interface temperature. The temperature increases withfriction, sliding speed, decreasing thermal conductivity, and decreasing specific heat of thesliding materials. The interface temperature may be high enough to soften and even melt thesurfaces, and sometimes to cause microstructural changes.
23. 23. 63Temperatures also affects the viscosity and other properties of lubricants, causing theirbreakdown. Note, for example, how butter and oil burn and are degraded when temperatures areexcessive. These results, in turn, adversely affect the operations involved, and cause surface tothe object.When two surfaces are in touch, sufficient contact is established to support the applied load. A = Apparent area of contact After application ofload Ar = real area of contact Fig. 12Ar, real area of contact increases with increases in load. N Ar = σ 0 = yield strength of weaker material in contact. σ0Large stresses and plastic deformation causes the tear off upper contaminated layers present onthe surfaces. Then the real materials come in contact. This results in welding of the asperityjunction and the sliding of one body above the other will be possible only after these asperityjunctions are sheared:Force required to shear Fs = T × Ar T = shear strength of weak Fs τ × Ar T µ= = = N σ 0 × Ar σ0 T = µ σ0
24. 24. 64From this, µ depends only on material in contact. For better results, T and σ 0 should be taken for Talloy formed at the junction due to heavy cold work and welding. But µ = is valid only when σ0Ar <<< A 0 . As Ar attains the value of A (apparent area), the force required to slide will notincrease even if N is increased. Under such situation, mechanism other than welding of asperityjunctions become active making friction phenomenon quite complex. One such mechanism islocking of asperities.Resistance to sliding motion is due to:i. The force necessary to plough the peaks of harder material through softer material.ii. The force required to break welding weldaments. Ar < A Fig. 132. When real area of contact approximates apparent area, movement w.r.t. each other continues but due to subsurface shearing in softer and weaker material. The frictional force, then, equals the shear strength of the material.
25. 25. 65 Fig. 14 Such type of friction is called “sticking friction”. σ Ts = 0 (As per Von miser) σ 0 = yield strength of softer material [Aluminium]. 3 T =µP P = normal pressure.A very low value of ‘µ ’ = 0.05 is possible with highly polished tool surface and flood lubricationwith soluble oils. ‘µ’ between 0.05 to 0.15 are usually found in cold working operations such aswire drawing, tube drawing and extrusion − while rolling thin stripswith mirror finish rolls, a value of 0.05 is common. However, in cold rolling with goodlubrication µ can range between 0.07 − 0.15. In hot rolling, presence of scale increases thevalue of ‘µ’and depends on rolling temperature. A value of 0.4 is quite common in rolling at400  C. ArAmonton’s law is a good approximation for ordinary sliding where << 1. Aa
26. 26. 66But in metal forming, areal area of contact approximates apparent area of contact. Fig. 15Zone I: ArPlastic deformation is confined to asperties only and thus << 1. Amonton’s law is obeyed. AaZone II:Ar increases with deformation but ‘µ’ decreased.Zone III:T does not vary with normal pressure and become independent of normal stress. Sliding Friction Sticking Friction 1. One surface slides over the other 1. In sticking friction the metal surface and friction exist there is no welding adjacent to the tool surface does not slide, of two surfaces at the contact instead it moves due to shearing. interface. Fig. SubSurface shearing occur in aluminium.
27. 27. 67 2. The definition of coefficient of 2. Under such conditions the coulomb’s law friction implies that the frictional ceases to apply and the magnitude of shear force is directly proportional to stress is controlled by the shear strength of normal force and there must be the work material. For the case of sticking relative movement between the friction the frictional stress workpiece and die surfaces. σ  Interfaces at which these conditions T= 0  2     exists undergo sliding friction. σ 0 = yield stress of the material in tension. It is valid when Due to high interface pressure P, the frictional µ P << k shear stress Ti = µP is greater than shear stress required for shearing the workpiece (workpiece has lower shear strength compared to die metal). If this occurs, less tangential force is required for metal to shear within the body of the workpiece than for the workpiece to move relative to the die. This is referred as sticking friction, through no actual sticking together of the die and workpiece necessarily occur. Ti = µP > k (shear strength of workpiece) when this inequality is satisfied, ‘µ’, the coefficient of friction becomes meaningless. Hence sticking friction represents an upper limit to the interface frictional stresses. The interface pressure developed in the most metal working process is at least equal to uniaxial yield stress and may appreciably exceed K (shear strength). As K is K independent of applied pressure, µ = is σ0 not correct to describe sticking friction, leads to misinterpretation. 3. Usually present in cold working. 3. Usually present in hot working.Sticking deformation is undesirable.i. Deformation with sticking friction requires greater energy.
28. 28. 68ii. Because localised internal shearing of the workpiece occurs, results in less deformation homogeneity compared to sliding friction.Q. Show that the maximum meaningful friction coefficient is 0.5.Soln: The interface shear stress is τ i = µP. The interface pressure P is the same as the normal interface stress σ 0 . ∴τ i = µ σ 0 . From the Tresca or maximum shear stress yield criterion, τ i max ≈ 0.5 σ 0 . The internal shear stress τ i cannot exceed τ i max, because when τ i = τ i max yielding of the workpiece in shear will occurs. Therefore τ i = µP = 0.5 σ 0 = τ i max; the maximum µ = 0.5. A coefficient of friction above 0.5 is not attainable as the shearing of the workpiece will have occurred.Effect of friction in metal forming:1. Force required for deformation increases with friction. 1 + B  B σ x = σ0   B  [1 − R ]     4µL  Pt = σ 0  log R +   Ram travel  d0  1. Direct extrusion 2. Indirect extrusion 3. Hydrostatic extrusion Fig. 16
29. 29. 69 Fig. 17 In extrusion, friction exists between billet and die and between billet and container. Friction between die and container is eliminated in indirect extrusion but between die and billet exists. In hydrostatic extrusion, friction is eliminated altogether and lower amount of force is required for extrusion.2. Excess load capacity is provided and load perse is not important aspect from practical point of view. Effective lubrication decreases the load requirement but it also serves other more important functions. i. prevention of pickup: If too much surface contact occurs, metal pickup on the tooling can damage product finish and size. ii. minimizes tool wear and thus better control over size and lower maintenance cost. iii. Frictional energy is converted into heat and raises the temperature of workpiece. To keep the temperature at lower level, extrusion velocity is reduced in hot extrusion of M.S.3. Friction plays positive role in rolling. Rolling is not possible without adequate friction between the rolls and bloom−billet. For rolling µ ≥ tan α α = angle of bite.  1   1  i. ∆h max = De 1 −  = De 1 −   1 + µ2   1 + (tan α) 2     
30. 30. 70 ii. ∆h min = 0.035 µ R σ  σµ R  =   12.8  α = 5  for cold rolling = 20 − 30  for hot rolling.4. Proper distribution of friction improves the deformation process.i. Deep drawing The coefficient of friction around punch corner should be high and that around die corner should be low. It prevents thinning of the sheet metal.ii. Tube drawing If the friction between tube and mandrel is high, then drawing load is shared by the mandrel and thereby reducing the stress in the tube wall. This allows for large reduction ratios. Fig. 18 µ − µ2 B= 1 tan α
31. 31. 715. Friction causes more wastage of material especially in extrusion. The dead zone formed in direct extrusion is result of friction and redundant work. It causes 20−30 % wastage of material which is quite large compared to indirect extrusion where friction between container and billet is eliminated.LubricationThe surfaces of tools, dies and workpieces are subjected to(i) forces and contact pressure, ranging from very values multiples of the yield stress of the workpiece material.(ii) relative speeds, from very low to very high.(iii) temperatures, which range from ambient to melting.Metal working fluids should be applied to reduce friction and wear effectively workingtemperature. Lubrication is the process of applying these fluids and solids. There are four typesof lubrication: Lubrication mechanism1. Boundary 2. Thick Film 3. Thin Film 4. Mixed Lubrication (full film lubrication) LubricationLubrication Fig. Fig. Fig.A thin layer of low shear • Completely prevent • Some metal to metalstrength material adheres at metal to metal contact. contact occurs.surface interface. Adherencemay be physical or chemical[Sulphur, chlorine] or both. • film thickness is about 10 • film thickness is about 5 Ra (Ra = surface Ra roughness)
32. 32. 72 (a) Thick film (b) Thin film (c) Mixed (d) Boundary Fig. 19: Types of lubrication generally occurring in metalworking operations.a. In thick− film lubrication, the two mating surfaces are completely separated by a fluid film as in hydrodynamic lubrication, and lubricant viscosity is the important factor. Such films can develop in some regions of the workpiece in high−speed operations, and can also develop from high−viscocity lubricants that become trapped at die−workpiece interfaces. The film thickness is 10 Ra.There is no metal to metal contact and therefore no wear of parts. The coefficient of friction isbetween 0.001 to 0.02 and depends on viscosity of lubricant and contact pressure. Coefficient offriction increases with normal pressure [double with every increase in pressure by 35 MPa] anddecreases with increase in temperature [every rise of temperature by 15  C decreases it to half].
33. 33. 73 Conditions favourable for thick film lubrication are somewhat rare in metal working but they do occur at higher sliding speed. High speed wire drawing and rolling are best examples this. A thick lubricant film results in a dull, grainy surface appearance on the workpiece, whereby the degree of roughness depends on grain size (Fig. 19). In operations such as coining and precision forging, trapped lubricant are undesirable because they prevent accurate shape generation.b. Thin film lubrication As the load between the die and workpiece increases or as the speed and the viscosity of the metal working fluid decrease, the lubricant film becomes thinner (thin film lubrication). The film thickness decreases to 3 to 5 Ra. This causes some metal to metal contact and raises the friction at the sliding interfaces and result in slight wear.c. Mixed lubrication In most liquid lubricated metal working operations. Some asperity contact is unavoidable. A significant part of the load is carried by the metal to metal contact and rest is carried pockets of liquid in the valleys of the asperities. This mixed film lubrication is common in metal working. Boundary lubricants with extreme pressure (EP) are added to the fluid at the points of metal contact.d. Boundary lubrication In boundary lubrication, the load is supported by contacting surfaces covered with a boundary film of lubricant. These are thin organic films physically adhered to the metal surfaces or chemically adsorbed on the metal surface, thus preventing direct metal to metal contact of the two bodies and hence reducing wear. The boundary lubricants are typically polar substances, natural oils, fats, fatty acids, esters or soaps. These films are firmly adhered to the metallic surfaces and have lower shear strength, thereby sliding surfaces takes place easily.
34. 34. 74Solid lubricationProduct resulting from the reaction of liquid lubricant and parent metal can be termed as solidlubricant because solid phase formed of it is effective as lubricant.Sometimes interposing film of molybdenum disulphide, graphite, teflon is used as lubricant.These films have lower shear strength which is temperature and pressure dependent. Boundaryfilm forms rapidly and as the film thickness decreases, metal to metal contact occurs. Dependingon the boundary film shear strength and its thickness, the coefficient of friction varies between0.1 to 0.4.Boundary films can break as a result of:i. desorption caused by high temperatures at the sliding interfacesii. being rubbed off during sliding.Deprived of this protective film, the metal surfaces may then wear and score severely.Other ConsiderationsThe valleys in the surface roughness of the contacting bodies can serve as local reservoirs orpockets for lubricants, thereby supporting a substantial portion of the load. The workpiece, notthe die, should have the rougher surface; otherwise, the rougher and harder die surface, acting asa file, may damage the workpiece surface. The recommended surface roughness on most dies isabout 0.4 µm .The overall geometry of interacting bodies is also an important consideration in ensuring properlubrication. The movement of the workpiece into the deformation zone, as duringwire drawing, extrusion, and rolling, should allow a supply of lubricant to be carried into thedie−workpiece interface. With proper selection of process parameters, a relatively thick lubricantfilm can be entrained and maintained.METALWORKING FLUIDSThe functions of a metalworking fluid are to:a. reduce friction, thus reducing force and energy requirements, and temperature rise.b. reduce wear, seizure, and galling.
35. 35. 75c. improve material flow in tools, dies, and molds.d. act as a thermal barrier between the workpiece and tool and die surfaces, thus preventing workpiece cooling in hot−working processes.e. act as a release or parting agent, a substance which helps in the removal or ejection of parts from dies and molds.Several types of metalworking fluids are now available which fulfill these requirements andwhich have diverse chemistries, properties, and characteristics. This section describes the generalproperties of the most commonly used lubricants.General properties of most commonly used lubricantsOils have high film strength on the surface of the metal and it is effective in reducing friction andwear. Oils have lower thermal conductivity and specific heat. Thus they are not effective inconductivity away the heat generated by friction and plastic deformation in metal formingoperations. Oils are difficult to remove from component surfaces that are subsequently bepainted or welded, and they are difficult to dispose off. The source of oils are mineral(petroleum), animal, vegetable and fish−oils may be compounded with variety of additives orwith other oils to impart special properties.Metal working oils are blended with several additives. Important additives are sulphur, chlorine,and phosphorus known as EP [Extreme Pressure] additives and used singly or in combination,they react chemically with metal surfaces and forms adherent films of metallic sulphides andchlorides. These films have lower shear− strength and good antiweld properties and thuseffectively reduce friction and wear. While EP additives are important in boundary lubrication,these lubricant attack the cobalt binder in tungsten carbide tools and dies, causing increase intheir roughness and integrity.Emulsions [or water soluble fluids] are two types: direct and indirect. In direct emulsions,mineral oil is dispersed in water as very small droplets. Direct emulsions are important fluidsbecause the presence of water gives them high cooling capacity and useful in high speed cutting.Oils maintain high film strength on the surface of a metal, as we can observe when trying toclean an oil surface. Although they are very effective in the reduction of friction and wear, oils
36. 36. 76have low thermal conductivity and low specific heat. Consequently, they do not effectivelyconduct away the heat generated by friction and plastic deformation. In addition, it is difficultand costly to remove oils from component surfaces that are to be painted or welded, and it isdifficult to dispose of them.The sources of oils can be mineral (petroleum), animal, vegetable, or fish. Oils may becompounded with any number of additives or with other oils; this process is used to change suchproperties as viscosity−temperature behavior and surface tension, heat resistance, and boundarylayer characteristics. Mineral (hydrocarbon) oils with or without additives, used undiluted, areknown as neat oils.Oils can be contaminated by the lubricants used for the slideways and various components of themachine tools and metalworing machinery. These oils have different characteristics than thoseused for the process itself, and thus can have adverse effects. When present in the metalworkingfluid itself, these oils are known as tramp oil.EmulsionsAn emulsion is a mixture of two immiscible liquids, usually of oil and water in variousproportions, along with additives. Emulsifiers are substances that prevent the dispersed dropletsin a mixture from joining together (hence the term immiscible).Milky in appearance, emulsions are also known as water− soluble oils or water− base coolants,and are of two types: direct and indirect. In a direct emulsion, mineral oil is dispersed in water inthe form of very small droplets. In an indirect emulsion, water droplets are dispersed in the oil.Direct emulsions are important fluids because the presence of water gives them high coolingcapacity. They are particularly effective high−speed machining where temperature rise hasdetrimental effects on tool life, the surface integrity of workpieces, and the dimensional accuracyof parts.Synthetic and Semisynthetic SolutionsSynthetic solutions are chemical fluids that contain inorganic and other chemicals dissolved inwater; they do not contain any mineral oils. Various chemical agents are added to a particular
37. 37. 77solution to impart different properties. Semisynthetic solutions are basically synthetic solutionsto which small amounts of emulsifiable oils have been added.Soaps, Greases, and WaxesSoaps are typically reaction products of sodium or potassium salts with fatty acids. Alkali soapsare soluble in water, but other metal soaps are generally insoluble. Soaps are effective boundarylubricants and can also form thick film layers at die−workpiece interfaces, particularly whenapplied on conversion coatings for cold metalworking applications.Greases are solid or semisolid lubricants and generally consist of soaps, mineral oil, and variousadditives. They are highly viscous and adhere well to metal surfaces. Although used extensivelyin machinery, greases are of limited use in manufacturing processes.Waxes may be of animal or plant (paraffin) origin; compared to greases, they are less “greasy”and are more brittle. Waxes are of limited use in metalworking operations, except as lubricantsfor copper and, as chlorinated paraffin, as lubricants for stainless steels and high−temperaturealloys.AdditivesMetalworking fluids are usually blended with various additives, such as the following:a. oxidation inhibitors.b. rust−preventing agents.c. foam inhibitors.d. wetting agents.e. odor−controlling agents.f. antiseptics.Sulfur, chlorine, and phosphorus are important oil additives. Known as extreme− pressure (EP)additives and used singly or in combination, they react chemically with metal surfaces and formadherent surface films of metallic sulfides and chlorides.
38. 38. 78These films have low shear strength and good anti−weld properties and, thus, effectively reducefriction and wear. On the other hand, they may preferentially attack the cobalt binder in tungstencarbide tools and dies (selective leaching), causing in the surface roughness and integrity oftools.SOLID LUBRICANTSBecause of their unique properties and characteristics, several solid materials are used aslubricants in manufacturing operations. Described below are four of the most commonly usedsolid lubricants.GraphiteGraphite is weak is shear along its basal planes and thus has a low coefficient of friction in thatdirection. It can be effective solid lubricant, particularly at elevated temperatures.However, friction is low only in the presence of air or moisture. In a vacuum or an inert gasatmosphere, friction is very high; in that, graphite can be abrasive in these situations. We canapply graphite either by rubbing it on surfaces or by making it part of a colloidal (dispersion ofsmall particles) suspension in a liquid carrier such as water, oil, or an alcohol.There is a more recent development in carbon called fullerenes or Buckyballs. These are carbonmolecules in the shape of soccer balls. When placed between sliding surfaces, these moleculesact like tiny ball bearings. They perform well as solid lubricants, and are particularly effective inaerospace applications as bearings.Molybdenum DisulfideThis is a widely used lamellar solid lubricant; it is somewhat similar in appearance to graphite.However, unlike graphite, it has a high friction coefficient in ambient environment. Oils arecommonly used as a carriers for molybdenum disulphide and are used as lubricant at roomtemperature. Molybdenum disulfide can be rubbed onto the surfaces of a workpiece.
39. 39. 79Metallic and Polymeric FilmsBecause of their low strength, thin layers of soft metals and polymer coatings are also used assolid lubricants. Suitable metals include lead, indium, cadmium, tin, silver, polymers such asPTFE (Teflon) polyethylene, and methacrylates. However, these coatings have limitedapplications because of their lack of strength under high contact stresses and at elevatedtemperatures.Soft metals are also used to coat high−strength metals such as steels, stainless steels, andhigh−temperature alloys. Copper or tin, for example, is chemically deposited on the surface ofthe metal before it is processed. If the oxide of a particular metal has low friction and issufficiently thin, the oxide layer can serve as a solid lubricant, particularly at elevatedtemperatures.GlassesAlthough it is a solid material, glass become viscous at elevated temperatures and, hence, canserve as a liquid lubricant. Viscosity is a function of temperature, but not of pressure, anddepends on the type of glass. Poor thermal conductivity also makes glass attractive, since it actsas a thermal barrier between hot workpieces and relatively cool dies. Glass lubrication istypically used in such applications as hot extrusion and forging.CONVERSION COATINGSLubricants may not always adhere properly to workpiece surfaces, particularly under highnormal and shearing stresses. This property has the greatness effects in forging, extrusion, andwire drawing of steels, stainless steels, and high−temperature alloys.For these applications, the workpiece surfaces are first transformed through chemical reactionwith acids (hence the term conversion). The reaction leaves a somewhat rough and spongysurface, which acts as a carrier for the lubricant. After treatment, any excess acid from thesurface is removed using borax or lime. A liquid lubricant, such as a soap,is then applied to the surface. The lubricant film adheres to the surface and cannot be scraped offeasily.
40. 40. 80Zinc phosphate conversion coatings are often used on carbon and low−alloy steels. Oxalatecoatings are used for stainless steels and high−temperature alloys.Friction and lubrication in rollingThe friction between the roll and the metal surface is of great importance. Frictional force isrequired to pull the metal into the rolls. A large fraction of rolling load comes from the frictionalforces. High friction results in high rolling load, a steep friction hill and great tendency for edgecracking. The friction varies from point to point along contact arc of the rolls. However, it isvery difficult to measure this variation in µ.i. For cold rolling with lubricant µ varies from about 0.05 to 0.1.ii. But for cold rolling friction coefficient from 0.2 upto the sticking conditions are common [0.5 to 0.6].Lubrication in hot rolling1. Hot rolling of ferrous alloys is usually carried out without lubricant, although graphite may be used, waterbased solution are used to cool the rolls and break up the scale on rolled material. Nonferrous alloys are hot rolled with variety of compounded oils, emulsions and fatty acids.2. Cold rolling is carried out with water soluble oils or low viscosity lubricants such as mineral oils, emulsions, paraffins and fatty oils.3. Heating medium used in heat treating billets and slabs also act as lubricant. e.g. residual salts from molten salt baths.Lubrication in forgingForging1. Lubricants greatly influence friction, wear, force required and metal flow in the cavities. They also act as a thermal barrier between the hot workpiece and relatively cool dies, slowing the rate of cooling of the workpiece and improves the metal flow.2. It acts as a parting agent, that is, one which inhibits the forging from sticking to the dies and helps in its release from the die.
41. 41. 813. For hot forging graphite, MoS 2 , and sometimes glass are used as lubricant. In hot forging, the lubricant is usually applied directly to the dies.4. For cold forging, mineral oils and soaps are commonly used as lubricants, applied after conversion coatings of the blanks. In cold forging lubricant is directly applied to the WP.5. The method of application and uniformity of the lubricant’s thickness blank is important.HOT WORKINGTemperature of work material is resultant of following contributing factors:1. Initial temperature of work and toolings.2. Heat generated due to plastic deformation which is proportional to strain induced.3. Heat generation due to friction at work−tool interface4. Heat transfer from work material to tool and surrounding.• Effect of temperature on metal forming processes:1. Flow stress decreases with increase in work material temperature and therefore power required deformation decreases. For this reason, hot working is used for primary forming processes [rolling, extrusion, forging] where primary objective is to reduce cross sectional area and refine grain size.2. High operating temperature increases the deformation limit before fracture. True strain of fracture of tungsten is increased from 1% at room temperature is 55% at 1000°C.Very large reductions are possible at elevated temperatures because recovery process neutralisesthe strain hardening effect of deformation.∈1 , ∈2 , ∈3 are limiting strain at T3 , T2and T1 temp. ∈3 > ∈2 > ∈1 T1 > T2 > T3
42. 42. 82 Fig. 20Hot working refers to deformation carried out under conditions of temperature and strain ratesuch that recovery process occurs substantially and is predominant over the strain hardening,thereby neutralising the effect of the later.It is important to note that distinction between cold working and hot working does not dependson any arbitrary temperature of deformation. Hot working is usually carried out at temperatureabove recrystallisation temperature and approx. equals to. 0.6 Tm where Tm = melting point temperature at in KTypically hot working temperature range Material temperature °C M.S. 900−1200 Aluminium 350−450 zinc, lead, Tin room temperatureHot working temperature is high for commercial metals, but lead, tin, zinc recrystallise rapidly ateven room temperature and therefore working of these metals even at room temperatureconstitutes hot working. In contrast, working of tungsten even at 1100°C, a hot workingtemperature for steel, constitutes cold working because this high melting point metal hasrecrystallisation temperature above this working temperature.Recrystallisation TemperatureRecrystallisation does not occur unless the degree of cold work is sufficient and temperature issufficiently high. The minimum degree of cold work necessary for recrystallisation to occur iscalled the critical degree of cold work. This is of the order of 2 to 3% for most of the metals landalloys. The temperature at which a metal or alloy with normal degree of cold work completely(i.e. 95 % or above) recrystalizes in a reasonable period (usually 1 hour) is called as therecrystallisation temperature of metal. Recrystalisation temperature of a metal is dependent onfollowing factors:
43. 43. 831. Degree of cold workRecrystallisation is a process of nucleation and formation crystals. Deformed grains have morefree energy than undeformed one. The free energy difference between the cold workeddeformed crystals and the undeformed crystals is driving force behind recrystallization.Therefore, applied deformation prior to recrystallization should be more than the crystal degreeof cold work. Further, the deformed grains and grain boundaries provide preferred sites fornucleation. Larger the degree of cold work, lower is recrystalisation temperature. For example, Amount of cold work Recrystallization temp time 20 % 3200 C 1 hour 60 % 2800 C 1 hour2. Melting PointHigher the melting point, higher is the recrystallisation temperature. It has been observed thatthe recrystallisation temperature of most of metals and alloys are in the range of 0.4 to 0.6 oftheir melting point temperatures in degree kelvin Tcr = 0.5 Tm 0K , where Tm = melting point temperature in Kelvin. Metal Recrystallization Melting point 0 C Re crystallization temp  K = temperature melting po int  K Tin Below Room Temp 232 0.6 Lead Below Room Temp 327 0.5 Zinc Below Room Temp 419 0.43 Aluminium 150 660 0.45 Magnesium 200 650 0.51 Silver 200 960 0.38 Gold 200 1063 0.41 Copper 200 1083 0.35 Iron/Steel 450 1539 0.40 Platinum 450 1760 0.35 Nickel 600 1452 0.51 Tungsten 1200 3410 0.403. Purity of metalPresence of soluble impurities or addition of small amount of soluble alloying elements raise therecrystallisation temperature.
44. 44. 84(i) Six nine (99.9999 %) pure aluminium has recrystallization temperature below room temperature and therefore cannot be strain hardened at room temperature. But commercially pure aluminium has recrystallization temperature of 150 0C.(ii) Recrystallization temperature of commercial purity copper is 150 0C but addition of 0.5 % impurity of arsenic raises recrystallization temperature above 500 0C. Therefore, arsenic copper is used for high temperature applications such as boiler tubes.4. Grain sizeFiner the original grain size, lower is the recrystallization temperature.5. Heating timeIt has little influence on recrystallization temperature. Recrystallization temperature is far moreimportant than recrystallisation time. One expects such results as flux of atoms is proportional todiffusivity which in turn is strongly dependent on temperature.Time and temperature required for recrystallization of 75 % cold worked aluminium alloy. Time Temperature 1 minutes 350 0C 60 minutes 300 0C 40 days 250 0CThe effect of degree of cold work on recrystallized grain size.
45. 45. 85 Fig. 21The grain size of the material obtained at the end of recrystallisation depends temperature ofheating, time, degree of prior cold work and level of impurities. Lower temperature of heating(above Tcr), higher degree of prior cold work and insoluble and fine impurity particles givesmaller grain size.• LIMITS OF TEMPERATURE1. The lower limit of temperature for hot working is the lower temperature for hot working is the lowest temperature at which recrystallisation rate is rapid enough to eliminate strain hardening effect. This temperature depends on − (i) the amount of prior deformation. The greater the amount of prior deformation, lower is the recrystallisation temperature. (ii) duration for which the material is held at that temperature.2. The upper limit of hot working is determined by the temperature at which melting or excessive oxidation occurs. Generally the maximum working temperature is limited to 50°C below the melting point to avoid hot shortness.Hot ShortnessIt is caused by local melting of a constituent or an impurity in the grain boundary at atemperature below the melting point of a metal itself. When subjected to plastic deformation atelevated temperature, the piece of metal crumbles and disintegrates along grain boundaries.Examples of impurities. antimony in copper sulphur in steel lead leaded steel leaded brassBeneficial effects of hot working1. Lower flow stress and hence lower power requirement of deformation machines.2. Large deformations are possible.
46. 46. 863. Removal of structural inhomogeneity. Rapid diffusion at hot working temperatures decreases chemical inhomogeneity of the cast ingot structures. Blowholes and porosity are eliminated by welding together these discontinuities and the coarse columnar grains of the case ingot are broken down and refined into smaller equiaxed recrystalled grains. These changes improves the ductility, toughness and strength of the material.PROBLEMS WITH HOT WORKING1. Additional heating facilities are required2. Material handling in hot condition becomes difficult and risky.3. As high temperature is involved, surface reactions between the metal and the furnace atmosphere becomes a problem. Ordinarily, hot working is done in air, oxidation results and considerable amount of material is lost. The work metal tends to oxidise. Scaling of steel and copper alloys causes loss of metal and roughned surfaces while processing under inert atmosphere is possible, it is prohibitively expensive and is avoided in the case of very reactive metals. Reactive metal like titanium are severely embrittled by oxygen and therefore they must be hot worked in an inert atmosphere, which is prohibitively expensive. Surface decarburisation of hot worked steel can be serious problem and frequently extensive finish machining is required to remove the decarburised layer. Because of pilling of oxide scale leaving pits and embedding α − roll−in−oxide in the surface finish obtained is poor and require further machining operation.4. The dimensional control on hot worked products is poor. The dimensional tolerances has to be large to take into account the expansion and contraction of metal.5. Lubrication is more difficult. Lubricants used for hot working should be stable at elevated operating temperature and should bot decompose. Viscous glasses are used in hot extrusion of steels. Although molybdenum di sulphide, graphite is used as lubricants for hot working, much hot working is done without lubrication.6. Tool life is shortened because of heating, the presence of abrasive scales, and the lack of lubrication. Sometimes, scale breakers are employed and rolls are cooled by water spray to minimize tool damage.7. Poor surface finish and loss of precise gauge control result from the lack of adequate lubrication, oxide scales, and roughened tools.
47. 47. 878. The lack of work hardening is undesirable where the strength of cold worked product is needed.METALLURGICAL ASPECTS OF METAL WORKING1. CompositionResistance to deformation and ductility depends on chemical composition. Alloys have alwaysbetter strength than the pure constituents taken singly. For steel, increase in carbon content oralloying constituent increases resistance to deformation and decreases ductility and therebydecreases deformability. Carbon content should not exceed 0.5% for steels to be used in coldextrusion and 1.5% for cold forging.(ii) Impurities such as sulphur, oxygen, phosphorous and nitrogen decreases deformability.(iii) The strength of a cold worked solid solution alloy is always greater than that for a pure metal, cold worked to the same extent.2. Microstructure also affects deformabilitySoft annealing [spherodising] of steel prior to cold working improves its cold workability. Thelarge grains are easier to deform.(i) Crystal structureFormability depends upon the ductility which in turn is dependent on crystal structure. Crystalstructure which provides more number of slip planes have more ductility. Strain hardening rateis more for cubic crystals than for HCP.FCC − has greatest opportunity for slip as it has four (4) distinct non parallel planes and threedirections for slip. Therefore materials with FCC structure are relatively weak and possessexcellent ductility. Aluminium Platinum Copper Silver Gold ξ − iron
48. 48. 88BCC − structure has fewer slip planes and therefore more difficult to deform metals with thisstructure generally possess high strength with moderate ductility. Molybdenum Vanadium Tungsten ChromiumHCP: Metals with HCP structure tend to have a low ductility and are often appear brittle.Example − Magnesium, Zinc, Zirconium.(ii) Grain sizeGrain size significantly influences mechanical properties of metal. At room temperature, a largegrain size is generally associated with low strength, low hardners and low ductility. Largegrains, particularly in sheet metals, also cause a rough surface appearance on stretching e.g.orange peel.Grain boundaries are more reactive than the grains themselves, because the atoms along the grainboundaries are packed less efficiently and are more disordered. As a result, they have higherenergy than the atoms in the orderly lattice within the grains. Size of grain is not that importantas the length of the grain boundary. Grain boundaries restrict the amount of slip that can occurfine-grained materials have greater length of grain boundaries than coarse-grained material.Thus coarse grained material has lower strength and yield point. This relationship can beexpressed in the form of equations: σ0 = σi + k / d σ 0 = yield strength σ i = the frictional stress of crystal lattice for dislocation movement. k = locking parameter which measures relative hardening contribution. d = average grain diameter k = 0.1 BCC crystal = 0. 7 FCC crystal
49. 49. 89For ductile materials, hardness and strength are related.For steel S u = 0.36 BHN kgf / mm 2 . Large grained metals are more ductile.Direction of slip changes more rapidly in smaller grain and therefore it is difficult to propagatecrack and difficult to break.Grain refinementGrain size is an outcome of relative rates of nucleation and grain growth − combination of highnucleation rate and slow grain growth yield fine grain size. The driving force behind thesolidification is reduction in free energy from liquid to solid rate. Small grained material Large grained material Fig. 1: a, b.Nucleation can be homogenous or heterogeneous. Homogenous nucleation Heterogeneous nucleation 1. Degree of undercooling is essential 1. Nucleation starts at preferred sites. homogenous nucleation. These sites are provided by (i) container walls. (ii) intensional inclusions. − Boron (Bo) and titanium are added in aluminium alloys for grain Fig. refinement cooling curve for homogenous nucleation. − Ferrosilicon is added to cast Iron.
50. 50. 90 Tm = melting point temperature − Zirconium in Magnesium alloys. when liquid approaches melting point temp, atoms begins to join together to form unit cells and lattice formation takes place. Undercooling causes forming of stable lattice. The energy released during solidification raises the temp to the true melting point. Undercooling is needed to start nucleation. Solid nuclei grow in all direction with result that number of crystals compete the same space and perfect external shape is difficult to obtain. This results in formation of crystals which do not have regular external shape.In hot working processes, fine grain size is obtained by a low finishing temp and arapid cooling rate. Grain size determines strength and fracture toughness. In processingsteel which undergo a structural transformation on cooling from the finishing temperature, theferrite grain size obtained depends on achieving a fine austenite grain size.GRAIN SIZE AND YIELD STRENGTHHall petch equaiton: The equation defines relationship between yield strength of the material andits average grain diameter. k σo = σi + dwhere, σ i = yield stress for a crystal of the same material where there are no grain boundaries.It measures resistance of the material to dislocation motion due to effects other than grainboundary.
51. 51. 91k = constantd = average grain diameter.Material σ i ( N / mm 2 ) k ( N / mm 3 / 2 )Aluminium 16 2.2Copper 26 3.5Zinc 33 7.0Iron 48 22.44Grain boundaries provide obstacles to dislocation movement. In addition, the crystals areseparated by a thin non−crystaline region, which is the characteristics structure of a large anglegrain boundaries. Hence dislocations are stopped by a grain boundary and pile up against it.The smaller the grain size, the more frequent is the pile up of dislocations.‘k’ value for BCC iron is 22.44 (N/ mm 3 / 2 ) where as only 2.2. and 3.5 for FCC matts such asAluminium and Copper. So for a given amount of grain refinement greater strengthening effectis produced from BCC metals than FCC.At temperatures below 0.5 Tm (Tm is melting point in k) and at higher strainrates, grain boundaries increases rate of dark hardening and increases thestrength. At high temperatures and slow straining rates, deformation is localisedat the grain boundaries. Thus a grain boundary sliding and stress inducedmigration takes place. Finally fracture takes place at the grain boundaries.ASTM NumberThe ASTM grain size number (n) is related to the number of grains (N) per square inch at amagnification level of 100x N = 2 n −1
52. 52. 92The grain dia can be approximately calculated from the ASTM specification for grain size. Foran ASTM number (n). The number of grains per square inch (645 mm 2 ) at a magnificaiton of100x is given by N = 2 n −1Grain size number ASTM 1 corresponds to 1 grain per square inch at a magnification of 100x 25.4 25.4 645 Actual area = × = mm 2 100 100 10 4If, d is average grain diameter, and N is number of grains Fig. 23 π 2 25.4 25.4 a N= × 4 100 100 28.66 0.2866 ∴ d= = mm. 100 × N NGrain sizes between 5 and 8 are generally considered fine. A grain size of 7 is generallyacceptable for sheet metal forming car bodies, appliances and kitchen utensils.
53. 53. 93A distinction between a coarse grained steel and fine grained steel is not clearly define.However, a grain size number below ASTM number 3 represents a definitely coarse grainedsteel and above As TM number 6 represents a reasonably fine grained steel. Steels havingASTM grain size number greater than 8 are called ultra fine grained steels. Fig. 241. The yield strength of a polycrystalline material increases from 120 N / mm 2 on decreasing the average grain diameter from 0.04 mm to 0.01 mm. fine the yield strength for a grain size of 0.025 mm.Solution:Hall petch equation states the relationship between yield strength of a material and grain size. σ o = σi + k / d σ o = σ i + | k / 0.04 = σ i + 5k = 120 N / mm 2 σ o = σ i + k / 0.01 = ∂ i + 10 k = 220 N / mm 2 ∴ K = 20 N / mm 3 / 2 , ∂ i = 20 N / mm 2 . Therefore Hall petch equation for this polycrystalline material is 20 σ o = 20 + d When average grain diameter is 0.025 mm 20 σ o = 20 + = 146.5 N / mm 2 . 0.025∴ The yield strength of the given material at average diameter is 146.5 N / mm 2 .
54. 54. 942. A yield strength of a polycrystalline material increases from 120 MPa to 220 MPa on decreasing the grain diameter from 0.04 to 0.01 mm. Find the yield strength for a grain size of ASTM 9.Solution: d1 = 0.04 mm σ1 = 120 N / mm 2 d 2 = 0.01 mm σ 2 = 220 N / mm 2 σ = σo + k / d 120 = σ o + k / 0.04 = σ o + 5k (1) 220 = σ o + k / 0.01 = σ o + 10 k (2) (1) − (2) 100 = k ∴ k = 20 N / mm 3 / 2 ∴ σ i = 20 N / mm 2 20 ∴ σ o = 20 + N / mm 2 d For ASTM No. 9, n = 9 ∴ N = 2 9 −1 = 256 28.66 d= = 0.0179 mm 100 N k σ = σo + d 20 = 20 + 0.0179
55. 55. 95 σ = 170 N / mm 2 ∴ Yield strength of ASTM 9 material will be 170 N / mm 23. Estimate the yield strength of polycrystalline Fe − 3% si alloy when grain size is ASTM 1, 4, 8 respectively. Assume, σ i = 80 MN / m 2 k = 0.63 MN / m 3 / 2Solution: σ i = 80 MN / m 2 k = 0.63 MN / m 3 / 2 = 80 mpa = 20 N / mm 2 = 80 N / mm 2 28.66 d= 100 N (i) n − 1 N = 2 n − 1 = 2 = 1 28.66 ∴ d1 = = 0.2866 mm 100 1 σ1 = σ i + k / d1 = 80 + 20 / 0.2866 = 117 N / mm 2 . (ii) n = 4 N = 2 n −1 = 2 3 = 8 28.66 ∴ d2 = = 0.1 mm 100 8 σ 2 = σ i + k / d 2 = 80 + 20 / 0.1 = 143.2 N / mm 2
56. 56. 96(iii) n = 8 N = 2 n −1 = 2 7 = 128