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Bulk Metal Forming Processes in Manufacturing Ehsan Ghassemali a,b,c *, Xu Song a , Mehrdad Zarinejad a , Danno Atsushi a and Ming Jen Tan b a Singapore Institute of Manufacturing Technology (SIMTech), Singapore, Singapore b School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore, Singapore c School of Engineering, Jönköping University, Jönköping, Sweden Abstract Among the manufacturing methods, bulk metal forming processes are recognized as classical methods with unique advantages for related industries. Despite many emerging technologies, these advantages have made them a hot topic in industrial applications. In this chapter, various types of bulk metal forming processes are described. The main processes including rolling, extrusion, and forging with their sub-categories are covered. Particular attention is given to the metallurgical aspects of these processes such as the effect of initial blank properties and interfacial friction on the in-process material behavior. Different approximation methods for modeling of these forming processes are explained and compared. The main challenges in nite element simulation of the bulk metal forming processes are also introduced and discussed. This chapter may serve as a good reference for forming process selection and identication for researchers, engineers, and students. Introduction: An Overview on Bulk Metal Forming Processes Introduction The broad topic of bulk metal forming includes many processes both as classical and modied categories. These classical bulk metal forming processes are still in great demand in many industry sectors. It does not seem that this trend will slow down as new technologies have been developed over recent years. These technologies are continuously modied for new demands, such as higher precision (near-net shape) forming, micro-/nano-forming for micro-components, and bulk-sheet metal forming processes for complex workpieces. Thus, it is important to have a broad knowledge of the classical theories of metal forming which was mainly an overview of metal forming processes and their fundamentals, some of the modication of these processes in the current work. Specically, effects of material behavior on the forming processes which are of paramount importance are discussed. The classical modeling techniques to describe the forming processes will also be addressed, with a focus on the challenges in this area. Classification of Metal Forming Processes Based on the type of the workpiece and deformation mode, the metal forming processes are generally categorized into two subgroups of bulk metal forming and sheet metal forming, as indicated in Table 1. *Email: [email protected] *Email: [email protected] Handbook of Manufacturing Engineering and Technology DOI 10.1007/978-1-4471-4976-7_44-31 # Springer-Verlag London 2013 Page 1 of 50

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Page 1: Handbook of Manufacturing Engineering and Technology || Bulk Metal Forming Processes in Manufacturing

Bulk Metal Forming Processes in Manufacturing

Ehsan Ghassemalia,b,c*, Xu Songa, Mehrdad Zarinejada, Danno Atsushia and Ming Jen TanbaSingapore Institute of Manufacturing Technology (SIMTech), Singapore, SingaporebSchool of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore, SingaporecSchool of Engineering, Jönköping University, Jönköping, Sweden

Abstract

Among the manufacturing methods, bulk metal forming processes are recognized as classicalmethods with unique advantages for related industries. Despite many emerging technologies,these advantages have made them a hot topic in industrial applications. In this chapter, varioustypes of bulk metal forming processes are described. The main processes including rolling,extrusion, and forging with their sub-categories are covered. Particular attention is given to themetallurgical aspects of these processes such as the effect of initial blank properties and interfacialfriction on the in-process material behavior. Different approximation methods for modeling of theseforming processes are explained and compared. The main challenges in finite element simulation ofthe bulk metal forming processes are also introduced and discussed. This chapter may serve asa good reference for forming process selection and identification for researchers, engineers, andstudents.

Introduction: An Overview on Bulk Metal Forming Processes

IntroductionThe broad topic of bulk metal forming includes many processes both as classical and modifiedcategories. These classical bulk metal forming processes are still in great demand in many industrysectors. It does not seem that this trend will slow down as new technologies have been developedover recent years. These technologies are continuously modified for new demands, such as higherprecision (near-net shape) forming, micro-/nano-forming for micro-components, and bulk-sheetmetal forming processes for complex workpieces. Thus, it is important to have a broad knowledge ofthe classical theories of metal forming which was mainly an overview of metal forming processesand their fundamentals, some of the modification of these processes in the current work. Specifically,effects of material behavior on the forming processes which are of paramount importance arediscussed. The classical modeling techniques to describe the forming processes will also beaddressed, with a focus on the challenges in this area.

Classification of Metal Forming ProcessesBased on the type of the workpiece and deformation mode, the metal forming processes aregenerally categorized into two subgroups of bulk metal forming and sheet metal forming, asindicated in Table 1.

*Email: [email protected]

*Email: [email protected]

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Besides the above categories, metal forming processes can be classified based on the formingtemperature as shown in Table 2. Indeed, to increase the formability of hard-to-deform metals, theprocess temperature is occasionally increased.

It is noteworthy that majority of the bulk metal forming processes are performed in compressionmode rather than tension or bending. This is different from sheet metal forming in which theworkpiece is most commonly subjected to tensile stresses. As a result, the typical problemsencountered in sheet metal forming such as anisotropy of the workpiece and material fracturecaused by tensile stresses are commonly avoided in bulk metal forming.

RollingBefore conducting a forming process, there is a need for primary processes to provide the bulkyworkpieces with defined configuration, dimensions, and properties. In fact, rolling of a raw materialinto a slab or plate is considered as one of the most important primary processes (Avitzur 1968). It isimportant to note that in sheet or strip rolling, where the thickness is relatively low, the deformationoccurs in plane-strain condition (no change in the width of the strip during the process). However, inbulk rolling of thick plates, deformation occurs in all three directions.

Rolling is also used for forming of more complicated parts such as rounds or squares or complexsections such as L, U, T, or H. These processes are mostly done in multi-pass rolling by using thegrooved rolls or universal mill.

Rolling is a mechanical process whereby the metal is deformed by passing through the gapbetween rotating rolls. Depending on the process and the metal type, there might be only two or morenumber of rolls to be used for the process, as shown in Fig. 1.

The rolls in contact with the deforming metal are called the work rolls, while the others are calledbackup rolls (Mielnik 1991). As will be explained in later sections, there are definite advantages ofusing small diameter work rolls. However, small rolls could be deflected easily by formingpressures. To resolve the issue, a four-mill rolling process is used for prevention of the verticaldeflection.

Table 2 Classification of metal forming processes based on deformation temperatures (Mielnik 1991)

Category Characteristic Remark

Hot metal forming 0.7TMa < deformation

temperature < 0.8TM

No work hardening, dynamic recovery, andrecrystallization

Warm metalforming

0.3TM < deformationtemperature < 0.5TM

Partial strain/participation hardening

Cold metalforming

deformation temperature < 0.3TM Work hardening

aTM ¼ melting temperature

Table 1 Classification of the metal forming processes based on deformation type

Category Characteristic Examples

Bulk metal forming Semifinished (bulky) initial workpiece Forging, extrusion, rolling

Small surface-to-volume ratio

Large amount of deformation

Sheet metal forming Large surface-to-volume ratio of the initial workpiece Deep drawing, bending

Small change in the thickness during the process

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Side/edge or so-called universal mills with Hu or U cross section are used for precise directionalcontrol of the workpiece and obtaining more accurate width dimensions.

Based on the amount of the metal to be rolled, reduction amount, final part shape, and desiredmechanical properties, the rolling procedure and sequences (pass schedule) can be planned.

In comparison with other bulk metal forming processes, rolling is a relatively uniform orhomogenous process, since the plastic deformation proceeds continuously/in-continuously andplastic zone is penetrated to the center line of the workpiece. However, during the process, asshown in Fig. 2, in practice, a sort of backward metal flow occurs at the rolling entry zone (bendingof the grid line outwards) and a forward metal flow at the rolling exit (bending back the grid lines tothe straight position), which pushes the metal during the process (Mielnik 1991). Under thiscircumstance, a rise in redundant deformation occurs, which in return decreases the relative processefficiency.

In the case of large workpieces and small thickness reductions, there is a probability of havingmore deformation at the surface, while the center of the specimen remains undeformed, causinga nonuniform deformation through the thickness. Application of proper pass schedule (reduction inthickness) could minimize the nonuniformity in such cases. Nonuniform microstructure can alsolead to alligatoring as shown in Fig. 3c.

Fig. 1 Typical arrangement of rolling mills for slab and thick plates: (a) 2-high single pass, (b) 2-high reversing mills,(c) 4-high

Fig. 2 Distortion of vertical lines in the central vertical section during rolling in case of (a) homogenous deformationand (b) inhomogeneous deformation

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Fig. 3 Nonuniform deformation in plate rolling (a) skin rolling, (b) normal (proper) rolling, (c) central alligatoring

Table 3 Special metal forming processes

Process Definition Schematic Applications

Ring rolling A hollow circular blank is formedinto a ring with larger diameter byreducing the blank thicknessbetween the main roll at theoutside of the blank and a mandrelat the inside of the blank. Theheight of the ring is controlled byan auxiliary roll

Huge rings, flanges,bearing races, gear rims,wheel bearings, nuclearreactor components

Mannesmannmethod

A hollow is formed at the center ofa cylindrical hot billet byperipherally rolling over a conicalpiercer point. The billet is drivenby a pair of cone-shaped rolls. Thefrictional forces between the rollsand the billet cause the billet torotate and force it to advancethrough the process

Seamless thick tubes

Form rolling(gear rolling/thread rolling)

Rolling with profiled rolls to formgear teeth on a round or cylindricalsolid blank

Gears, sprockets

(continued)

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ForgingForging is usually defined as plastic deformation of a bulk metal to a predetermined shape bycompressive forces using a hammer or press.

Forging in conventional way is classified as (i) open-die and (ii) closed-die forging.Open-die forging is the term that is used for processes in which there is no lateral constraint for the

material movement in the die set. These processes are practically used under the circumstancesbelow (Altan et al. 2004):

1. As a preforming process for closed-die forging2. For simple desired shapes3. To justify the operation cost and time in small number of forgings

Open-Die Forging If the open-die forging is used as the final forming process, a post-forgingoperation such as machining is required to obtain the desired shape. However, in case the open-dieforging is used as a preforming operation, it is effective to optimize the forging sequence for near-netshape forming.

Based on the operation used, the open-die forging processes can be categorized as indicated inTable 4.

Since all the above mentioned operations are fundamentally connected to upsetting or compres-sion, the deformation mode in compression is discussed here in detail. In upsetting of a bulk piece,the main issues could be the barreling (Fig. 4-a) and the buckling of the workpiece (Fig. 4-b). Thebarreling is caused by inhomogeneous deformation. When the initial height-to-diameter ratio of theworkpiece is larger than 2.5, the lateral buckling appears (Fig. 4).

The behavior of the inhomogeneous deformation in the forging can be analyzed by variousmethods such as (i) grid pattern distortion (Altan et al. 1983a), (ii) hardness distribution, and (iii)microstructural observation on the cross section.

Table 3 (continued)

Process Definition Schematic Applications

Orbital/rotary/swingforging

An upper die rotates aroundinclined axis and a nonrotatinglower die for incremental forgingof a slug. The lower die onlymoves axially up towards theupper die

Bevel gears, claw clutchparts, bearing rings

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Table 4 Different types of open-die forging process according to the operation (Mielnik 1991)

Process Definition Schematic Applications

Cogging Compression of an ingotbetween narrow dies

Forged billets from castproducts and elongation of barstock

Upsetting Compression between two flatdies

Disks

(continued)

Fig. 4 Typical deformation of workpiece in the upsetting process: (a) barreling, (b) buckling

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Table 4 (continued)

Process Definition Schematic Applications

Heading(upsetforging)

Localized upsetting of theworkpiece between two flatdies

Flanged shafts, finishedforging, shafts with head

Swaging Radial compression betweenlongitudinal, semicircular dies

Bar elongation, stopped shafts

Punching Indentation with mating dies Preform forgings

(continued)

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The cross section of the workpiece after upsetting deformation is schematically illustrated inFig. 5. Due to the interfacial friction forces at the both end surfaces of workpiece, the material at thecenter of the workpiece has relatively more freedom to flow laterally, causing a barreling. Theamount of this barreling depends directly on the friction. To reduce the amount of barreling and therequired forming load, usually application of a proper lubrication during the process is advised.

Table 4 (continued)

Process Definition Schematic Applications

Piercing Punch indentation into theworkpiece

Preforming, cavity forming

Extrusionforging

Extrusion of a bulk metal intoa die

Boss

Bending Bending of a bulk betweenmating dies

Bend forged parts

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The so-called dead metal zones in the microstructure appear near the end surfaces of workpiecewhen the high friction exists at both end surfaces during upsetting.

Closed-Die Forging The closed-die forging is a process in which the metal has the restriction inflowing laterally during the process. It usually involves filling a cavity between the punch (upper partof the die) and the die (lower part of the die). Due to that, the load-displacement curve for the closed-die forging cycle is usually divided into three main stages, as typically is shown in Fig. 6:

1. Upsetting which corresponds to lateral and vertical flow of the material.2. Die filling, in which the die cavities start to be filled and the flash begins to form.3. End stage in which the dies are completely filled. Due to restriction of the metal flow, the pressure

inside the die increases rapidly.

As shown in Fig. 6, normally the dies are not completely closed in the closed-die forgingprocesses. The purpose of the flash land is to control the back pressure to obtain a desired fill-upof metal in the cavity. The design of the flash land is critical though to have a good control over theprocess.

Fig. 5 Deformation pattern in upset forging of cylindrical billet

Fig. 6 Typical load-stroke behavior during closed-die forging process

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It is important to reduce the material cost, in conventional forging processes. Therefore, the diedesign and the initial material (stock) volume must be optimized to minimize the material wastage.However, technically the stock is usually provided with a bit of an excess metal (Mielnik 1991).There are some special closed-die forging processes that are summarized in Table 5.

ExtrusionExtrusion is basically categorized as a compression forming process, since the main forming stresscomes from the compressive stresses which are applied from the punch, as shown in Fig. 7.

Extrusion is usually either performed at room temperature (cold extrusion) to obtain the final partwith close dimensional accuracy or at elevated temperatures (hot extrusion) for extreme conditionssuch as high punch pressure and high degree of deformation.

The extrusion products are typically axisymmetric solid bars or hollow pipe/tube, and parts withanomalous shape of cross Sections.

Extrusion ProcessesDirect Extrusion (Forward Extrusion) The flow of the material is in the same direction of the punchmovement. Thus, the punch pushes the material to be extruded through the die orifice. The cross-sectional shape of the extruded product is dictated by the geometry of the interior shape of the die.

Table 5 Special types of closed-die forging process

Process Definition Schematic Applications

Coining/hobbing

A closed-die forging processfor imprinting on a restrainedworkpiece

Metallic coins, decorative items,medallions, sizing of automobileor aircraft engine components

Nosing Closing the open end of a shellor tubular component by axialpressing with a shaped die

Gas pressure containers

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Indirect Extrusion In indirect extrusion process, the die set is designed in a way that the materialcould only flow in the opposite direction of the punch movement, through the hole at the punchcenter.

Backward Can Extrusion In this type of extrusion, the material flow is also in the opposite directionof the punch movement, but only through the gap between the punch and die walls. Lateral flow isconstrained by the die walls, to distinguish this method by the heading process. This technique isused for forming a can by piercing from a bulk billet.

The schematic of the abovementioned types of extrusion process is shown in Fig. 8.There is a slight difference between the forming-load behaviors of the direct and indirect extrusion

processes. As shown in Fig. 9, the forming pressure in backward extrusion is slightly lower. This isbecause in backward extrusion, there is no load necessary to overcome the container friction.

The extrusion force is influenced by the following process variables:Extrusion ratio, R ¼ A0/Af, where A0 and Af are cross-sectional areas of the workpiece before and

after extrusion, respectively. Since the average strain increases by increasing the reduction ratio, i.e.,average strain, the amount of deformation stress goes up.

Die geometry (die angle, a in Fig. 7). The material flow during the process highly depends on thedie angle, which is reflected on the forming load. In forward extrusion, increasing the die entranceangle leads to an increase in the volume of the metal undergoing shear deformation, which in returnincreases the deformation load. On the other hand, increasing the die entrance angle decreases the

Fig. 7 Schematic of the extrusion process

Fig. 8 Different types of extrusion processes: (a) direct extrusion (forward extrusion), (b) indirect extrusion,(c) backward can extrusion

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die-metal interface and results in the decrease in the die friction load. As a consequence, for a givenreduction and friction, there is an optimum die angle that minimizes the extrusion load.

Lubrication. It has been proven that efficient lubrication can lower the extrusion loads.

Defects in Extrusion Products One of the most common defects in forward extrusion process iscenter-burst or chevron cracks, occasionally called cupping. This defect appears on the longitudinalcross section of the extruded part. The chevron defect is mainly caused by nonhomogenousdeformation which requires an abrupt acceleration of the metal in the extrusion die. Thus, it canbe prevented by (i) increasing the extrusion reduction ratio (R0/Rf), (ii) decreasing the die entranceangle, (iii) decreasing the friction, and (iv) application of interval annealing (Tschaetsch 2005).

Improvement in ductility of the material at the center of the billet is also important to prevent thisdefect.

In addition to chevron cracking, dead metal zone formation is another defect that may result innonuniformity in the final part properties. This defect is caused by selection of a large die entranceangle.

At the critical die entrance angle, the internal shear deformation causes the formation of the deadmetal zone next to the die surface. This zone does not participate in the flow process but insteadadheres to the die surface, considered as a material wastage. In some cases, dead metal zone couldleak to the die orifice, causing a nonuniform microstructure. Increasing the die entrance angle to thesecond critical angle causes the dead metal zone to move backwards, forming metal chips. This isinteresting because as the rod proceeds through the die, the outer surface is shaved off and the coremoves through the die without plastic deformation, making the process similar to the blankingprocess. This is the main reason for decreasing the relative forming pressure with an increase in dieentrance angle in the shaving region.

In case the external force applies as pulling forces on the metal, the process is called drawing. Thedeformation principles are very similar to extrusion processes. This process is mainly used for wireor tube drawing.

Cold and Hot Bulk Forming ProcessesAccording to forming temperature, the bulk metal forming processes are divided into two maingroups of cold and elevated temperature forming processes. The elevated temperature bulk formingitself is somehow can be sub-categorized into warm and hot forming processes. The direct effect oftemperature is on the plastic deformation of the metal.

Fig. 9 Difference between load-stroke behaviors of direct and indirect extrusion processes

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Cold Metal FormingCold bulk forming is defined as forming of a bulk metal at room temperature without initial orinterstage heating. The plastic deformation of the metal is developed by the slip on multiple slipplanes in each grain. This develops a network of dislocations in the grains and a series of dislocationpile-ups at the grain boundaries, inclusions, and internal defects. These obstacles inhibit thedislocation movement inside the metal, and thus increase the flow stress and hardness by workhardening. This, nevertheless, decreases the ductility in certain amount. The plastic deformationchanges the grain shape along the deformation route as shown in Fig. 10 for the cold rolling process.

Moreover, due to possible inhomogeneous deformation in some conditions, the final part prop-erties could be nonuniform. To adjust the mechanical properties of the cold-formed parts, annealingis advised. Figure 11 shows the typical change in the mechanical properties and the microstructure ofthe metal due to the annealing. In some cases, recovery annealing is conducted to eliminate theresidual stress in the cold-formed parts.

Fig. 11 The effects of annealing on the material properties

Fig. 10 Evolution of the grains shape during typical cold forming processes

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In general, due to the low temperature, the main work limits in cold forming processes could becategorized as Fig. 12.

Due to these limitations, and also due to geometry complexity of the formed part, the cold bulkforming processes need to be designed by highly experienced process designers with broadknowledge about the in-process material behavior, tooling properties, lubrication, process costs,and FE simulation for design optimization. Typical metal alloys that can be cold-formed are listedin Table 6.

Elevated Temperature Metal FormingAlthough metals exhibit good ductility at room temperature, some alloys such as medium to highcarbon steels, different grades of stainless steel, titanium alloys, and magnesium alloys cannot beeasily formed in bulk due to low formability or/and higher flow stress. For these alloys, elevatedtemperature forming is suitable.

In warm forming processes, the metal is heated to temperatures below the recrystallizationtemperature, for instance, up to around 750–850 �C for different types of steels. An exceptioncould be austenitic stainless steels that are warm-formed at around 250–450 �C. Such a warmtemperature can ease the movement of the dislocations within the microstructure, increasing theformability of the metal. Furthermore, since the temperature is yet below the recrystallizationtemperature, the grain growth and phase transformations can be controlled through the process.The work hardening appears in warm forming process, but its extent is smaller than that in the coldforming process. As an example of warm forming, magnesium alloys such as Mg-3%Al-1%Zn(AZ31) and Mg-6%Al-1%Zn (AZ61) can be formed at 250–450 �C.

Fig. 12 Limitations in cold metal forming processes

Table 6 Typical alloys that can be cold-formed

Metal type Example

Steels Low and medium carbon steels (<0.45 %C)

Low alloy steelsa

Stainless steels

Aluminum Almost all alloy types

Copper Almost all alloy types

Nickel Inconel alloy

Titanium Pure titanium, b-Ti alloysaSpheroidize annealing might be required to improve the formability

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In the forming of hard-to-machine alloys such as high carbon steels and titanium- and nickel-based superalloys, the hot forming process is used at temperatures above the recrystallizationtemperature. The hot forming is also used to form large size components.

The isothermal hot forming processes can provide a near-net shape product of titanium- andnickel-based superalloys (to reduce the material cost), with a well-controlled microstructure andproperties.

In isothermal forming processes, the dies are heated up to the same temperatures as the workpiece(e.g., more than 1,000 �C for nickel-based superalloys), preventing the temperature drop in theworkpiece, which in return provides better formability. Moreover, to maintain the superplasticmaterial behavior, the strain rate must be kept low. This prolongs the forming process. However,since the process is isothermal, there is no die chilling required.

In hot forming processes, since the temperature is higher than the recrystallization temperature ofthe workpiece, dynamic recovery and recrystallization occur in the microstructure during the process(Fig. 13).

The effect of the dynamic recrystallization on the flow stress of the metal during the process isshown below. The elevated temperature affects the metal yielding behavior. Moreover, as can beseen, high temperature eliminates the work hardening effects (shown by the straight-line portion ofthe high-temperature curve in Fig. 14).

Typical metals that are usually hot-formed are listed in Table 7. As discussed, based on the amountof the deformation, other easy-to-form alloys might also be considered to be formed at highertemperatures.

Fig. 13 Schematic of the microstructure evolution in hot rolling process

Fig. 14 The effect of dynamic recrystallization on the metal flow

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Material Deformation Analysis in Bulk Metal Forming

IntroductionIn bulk metal forming processes, the materials usually experience a significant amount of plasticdeformation. As the bulk forming processes are marching towards near-net-shape manufacturing,the deformation mode, material flow, and product geometry are increasingly becoming complexbeyond the levels to be addressed by simple analytical solutions. It is widely accepted that suchcomplexity is contributed from the nonlinearity of the geometry, material, and boundary conditionsin the process. Therefore, the main objectives of material deformation analysis in metal formingoperations are:

To establish the kinematic relationships between the undeformed and deformed parts. Most prom-inently, to predict the metal flow during the forming process (geometry)

To establish the forming limits, i.e., to determine the possibility of performing the forming operationwithout causing any surface or internal cracks or folds (material)

To estimate the load required to carry out the forming operation, which provides necessaryinformation for tool design and equipment selection (boundary condition)

Therefore, approximation methods, either analytical or numerical, are required for analysis of bulkmetal forming processes.

There are numerous approximation methods available to analyze the metal forming processes.However, none of these methods are robust enough to cover all the processes with great precision.This is partially because some necessary assumptions have been made in order to facilitate thedevelopment of a mathematical approach. Moreover, their accuracy also depends on the quality ofthe inputs, which are essentially (i) flow stress data and (ii) friction coefficient. These two quantitiesare usually determined experimentally and difficult to obtain accurately. Thus, any uncertainty inthem may impose additional error to the result of the analysis. In this section, various models tomathematically describe the material stress-strain curve and friction coefficient will be presented in

Table 7 Typical alloys that are usually hot-formed

Metal type Example

Steels High carbon steels (>0.45 %C)

Low and high alloy steels

Stainless steels (ferritic, austenitic, martensitic)

Super alloys Almost all alloy types, e.g., iron-based, nickel-based, cobalt-based

Copper alloys Pure copper

Brass

Bronze

Aluminum alloys A3000 series

A2000 series

A6000 series

A4000 series

Titanium alloys Ti-6Al-4 V

Ti-4Al-4Mn

Ti-5Al-2Cr-1Fe

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future sections. The choice of suitable test for obtaining the flow stress data is covered in this chapter,and friction conditions and their implication to the bulk forming are to be discussed in sectionsahead.

Approximation Methods for Deformation AnalysisThe approximation methods have changed significantly over the last 30 years since Altanet al. (1983b) first attempted to summarize all the common methods used and list them in terms ofapplications and limitations. Some of Altan’s predictions on their future applicability are quiteinsightful. Authors here would like to reorganize the chart in order to reflect the progresses peoplehave made over the last three decades in metal forming (Table 8).

From the above chart, it is not difficult to point out that despite the long computational time, thefinite element, finite volume, and finite difference take the lead in terms of accuracy and availabilityof the result outputs (field variables). Their advantages go further when complex shape parts areconsidered, where other methods cannot compete. Furthermore, long computational time problemhas also been alleviated over the last three decades by the advances of the computer science, whichmakes large-scale computing possible and affordable (within minutes or hours). Therefore, these“finite” methods dominate the current metal forming simulation practice, among which it is alsowidely believed that finite element method is superior compared to the other two, since it canaccurately follow material interfaces. This is widely used in engineering problems when deforma-tion of complex isolated objects is modeled and material flow needs to be accurately traced.Therefore, most of the modern simulation software for metal forming analysis employ finite elementmethod as the backbone algorithm, and in the Section “Tool Manufacturing and Material Selectionfor Bulk Metal Forming,”we will focus on this method and its application to the bulk metal formingprocess simulation.

Deformation Modes in Bulk Metal Forming and Their CharacterizationThe deformation mode of the process refers to the dominating stress state in the workpiece that theprocess uniquely possesses. As mentioned in the Introduction section, bulk metal forming is

Table 8 Brief summary of various analysis methods

Method

Input Output

CommentFlowstress Friction

Velocityfield

Stressfield

Temperaturefield

Stresses on thetools

Slab Aa (a)(b) N Y N Y Ignore redundant work

Uniformenergy

A (b) N N N A Approximate redundant work

Slip line A (a)(b) Y Y N Y Valid for plane strain

Upper bound D (b) Y N N A Gives upper bound on loadand pressure

Hill’s D (a)(b) Y N N A 3D possible

Finitedifference

D (a)(b) Y Y Y Y Long computing time

Finiteelement

D (a)(b) Y Y Y Y Long computing time

Finite volume D (a)(b) Y Y Y Y Long computing time

Weightedresidual

D (a)(b) Y Y Y Y Very general approach

aA Average value only, D Distribution field value, Y Yes, available, N No, not available. (a) Coulomb (b) Shear

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dominated by compressive stress state. Figure 15 illustrates the applied force and primary stress stateof the four typical bulk forming processes.

The aim of such deformation mode study is to (i) simplify the model into 2D or even 1D case sothat the analytical solution can be obtained and (ii) identify the suitable material workability test forits formability study and characterization.

From Fig. 15, it can be concluded that rolling experiences a biaxial compressive stress state (planestrain) when operating without front or back tension. Forging and upsetting in closed die hasa uniaxial compressive stress state, and extrusion shows a triaxial compressive stress state. In the

Fig. 15 Illustration on the applied force and primary stress state in (a) rolling, (b) forging, (c) extrusion, and (d) drawing

Fig. 16 Typical deformation modes in the bulk metal forming

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wire drawing, the deformation zone indicates a uniaxial tension-biaxial compression stress state.The common deformation modes in the bulk forming process are summarized as in Fig. 16.

Although the names of uniaxial and axisymmetric are quite self-explanatory, the biaxial stressstate plane stress and plane strain are not and they need special attention. Plane stress occurs whenthe stress states lie in the plane of the workpiece (no stress in third dimension). This typically occurswhen one dimension of the blank is very small compared to the other two and the workpiece isloaded by a force lying in the plane of symmetry of the body. Thin wall pressure vessel is a goodexample for this type of analysis.

Plain strain occurs when the strain in one of the three principal directions is zero, as in anextremely long member subjected to lateral loading or a thick plate with a notch loaded in tension.A common plane-strain condition in the bulk metal forming is the rolling of a wide sheet. It is worthnoting that although there is no strain in the width direction, there is stress acting in that way.

In most cases of bulk forming, the stress state is complex. Therefore, a triaxial stress term isneeded to evaluate the material performance during forming process. The most common one isdefined by the von Mises criteria (von Mises stress ¼ sv), or effective stress s.

sv ¼ s ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2sxx � syy

� �2 þ syy � szz

� �2 þ sxx � szzð Þ2 þ 6 sxy þ syz þ szx

� �2� �r(1)

Another important stress term is the mean or hydrostatic stress sm, as explained by Eq. 2

sm ¼ 1

3s1 þ s2 þ s3ð Þ (2)

Hence, a general workability parameter can be formulated using those two stress terms as Eq. 3(Venugopal Rao et al. 2003).

b ¼ 3sm

s(3)

This parameter can be used to evaluate the workability of the material in bulk forming processesas well as in testing methods, including tension, compression, and torsion tests.

Schematics of the material testing methods are shown in Fig. 17, with their deformation characterslisted in Table 9. In Fig. 18, we link the bulk forming processes with those workability tests in termsof their deformation modes.

It is clearly stated that for wire drawing, it is recommended to use tensile test to evaluate thematerial formability in this process, while the compression test works well when extrusion, rolling,and forging are the dominating processes. Torsion test is mainly designed for measuring flow stressunder hot-working conditions, as the deformation is similar to the torsion test where excessivematerial reorientation occurs at large strains. These three tests are the main workability tests for bulkmetal forming, and their test procedures have been standardized in ASTM-E8 (for tension), E9 (forcompression), and A938 (for torsion) (ASTM 2009). An example of the compression test result ofstainless steel 304 L is presented in Fig. 19. It is worth noting that we use the term “true strain” torepresent the amount of deformation experienced by the material. Normally, we measure thematerial extension or contraction by “engineering strain,” which is the ratio of total deformationto the initial dimension of the material. It is expressed as Eq. 4

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e ¼ DLL

¼ l � L

L(4)

where l is the material final dimension and L is the material initial dimension. However, to trulyreflect the amount the deformation that material experiences, its incremental form has to be adopted

Fig. 17 Illustration of common material formability tests

Table 9 Material formability tests with their deformation characters

Test Principle stress Effective stress Mean stress b

Tension sx;sy ¼ sz ¼ 0 sx sx/3 1.0

Torsion sx ¼ �sy; sz ¼ 0ffiffiffi3

psx 0 0

Compression �sx;sy ¼ sz ¼ 0 �sx �sx/3 �1.0

Fig. 18 The influence of process stress state on the workability and strain at fracture

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and it is in the logarithmic form due to integration. It is often called logarithmic strain or true strainand in the form of

e ¼ðde ¼

ðlL

dl

L¼ ln

l

L

� �(5)

It is widely considered that the compression test is the most important and commonly used test forcharacterizing the material stress-strain curve and formability in bulk metal forming processes.Details of various material flow stress models based on the compression test data will be covered insections ahead.

Load Prediction for Bulk Metal FormingOne of the main questions that a bulk metal forming study has to answer is the load prediction. Suchexercise provides necessary information on tool design and equipment selection. Nowadays most ofsuch studies are carried out using finite element simulation software, e.g., DEFORM, ABAQUS,PAMSTAMP, FORGE, etc., due to complex workpiece geometry involved. However, a few simpleanalytical solutions, derived from slab analysis, still provide useful information and good approx-imation on the load during bulk forming process. Some of the most popular equations are providedhere as a guideline for quick load estimation (Kalpakjian 1997).

Force in Open-Die ForgingThe deformation mode of the open-die forging process is uniaxial compression. If the material isstrain hardening with a stress-strain curve following power law (see section on “Tool Manufacturingand Material Selection for Bulk Metal Forming” for details),

Y ¼ Ken (6)

The expression for force at any stage during deformation becomes

DIMENSION, MATERIAL AND QUANTITYMATERIAL LUBRICATION

Enclosing TeflonQUANTITY D (mm) H (mm)

1

00 0.2 0.4 0.6

True Strain

SS304L

0.8

∅ D ± 0.05

± 0.1

1

200

400

600

800

1000

1200

1400F

low

Str

ess

(MP

a)

1600

6.0 9.0 SS 304L

q

Fig. 19 Compression test of ss304L for its stress–strain curve

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F ¼ YA (7)

The Yand A are instant values of flow stress and cross-sectional area at the given time. If a solidcylindrical workpiece is considered, the instant average pressure on the workpiece can be expressedas

pav ffi Y 1þ 2mr3h

� �(8)

where m is the friction coefficient, r is the diameter of workpiece, and h is the height at that stage(Fig. 20). The forging force is thus

F ¼ pav pr2� �

(9)

Force and Power in RollingFor rolling without front or back tension, the contact length curves (red highlighted in Fig. 21), L,multiplied by the strip width, w, are the contact area under pressure on the strip. A simple way ofcalculating the roll force is to multiply the contact area with average flow stress Y:

Fig. 20 Illustration of an open-die forging process

Fig. 21 Schematic of the rolling process

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F ¼ LwY (10)

The average flow stress, if based on power law s ¼ Ken, can be given as

Y ¼K

ðe10ende

e1¼ Ken1

nþ 1(11)

Moreover, the dimension L as the projected area is approximated using Eq. 12.

L ¼ffiffiffiffiffiffiffiffiffiRDh

p(12)

where R is the roll radius andDh is the difference between the original and final thickness of the strip(draft) (Fig. 21).

As the friction in the rolling process is comparatively small, the friction force is ignored here forfirst-order approximation. The torque per roll then can be obtained from Eq. 13:

T ¼ FL

2(13)

and the power required per roll is

Power ¼ Tw ¼ pFLN60, 000

kw (14)

where w ¼ 2pN w ¼ 2pN and N is the revolutions per minute of the roll.

Pressure in the ExtrusionThe extrusion ratio is defined as

R ¼ Ao

Af(15)

where Ao is the billet cross-sectional area and Af is the area of the extruded product (Fig. 22). Thenthe extrusion pressure at the ram can be given as

p ¼ YlnAo

Af

� �¼ Yln Rð Þ (16)

where Y is the average flow stress. If friction at the die-billet interface (but not the container wall) isconsidered, for small die angles a, the pressure is given as

Fig. 22 Variables in the extrusion process

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p ¼ Y 1þ tan tan am

� �Rm coscos a � 1ð Þ (17)

Drawing Force in the Wire/Rod DrawingThe drawing of the wire/rod is similar to extrusion except that instead of the pressure (p) on the Ao,there is a drawing stress sd on the exit Af (Fig. 23). Such drawing stress for the simplest case of idealdeformation (no friction or redundant work) is

sd ¼ YlnAo

Af

� �(18)

where Y again is the average flow stress, and the drawing force F then is

F ¼ YAf lnAo

Af

� �(19)

Similarly, if friction is considered, the drawing stress becomes

p ¼ Y 1þ tan tan am

� �1� Af

Ao

� �m coscos a (20)

This section briefly lists the available approximation methods and their application on the dieforce prediction. Material deformation modes and their test methods during bulk metal forming arealso included in this section. This is to provide an overview to the bulk metal deformation studymethodology. More details on the respective methods can be found in the references listed at the endof the Section.

Modeling and Simulation of Bulk Metal Forming Processes

IntroductionMost of the numerical simulations of the bulk metal forming processes nowadays are carried outusing finite element method. It has been extensively applied to the metal forming industry to enablea more scientific approach to forming process development and optimization. In this section,a particular interest was paid on the critical challenges in finite element simulation with the aim to

Fig. 23 Variables in drawing round rod wire

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help the handbook users to identify the key issues in this area. Such issues include the materialfriction behaviors, mechanical properties, microstructure evolution, and fracture prediction.

Friction in the Finite Element SimulationIn metal forming process, workpiece deformation is brought about during contact between a tool anda workpiece. This inevitably results in friction if there is any tangential force at the contactingsurfaces. Numerous analytical models have been proposed to describe the frictional behaviorsbetween the workpiece and die; below are the some of the most popular ones used in the finiteelement simulation software. Their areas of application are also presented.

Coulomb Friction ModelCoulomb friction model is used when contact occurs between two elastically deforming objects(could include an elastic-plastic object, if it is deforming elastically), or an elastic object and a rigidobject. Generally, it is used to model sheet metal forming processes. The frictional force in theCoulomb law model is defined by

f ¼ mp (21)

where f is the frictional stress, p is the interface pressure between two bodies, and m is the frictioncoefficient. However, the use of coulomb friction model gives occasion of an overestimation of thefriction stresses at the tool-workpiece interface, as the normal pressure is often considerably greaterthan the yield stress of the material. Consequently, the friction stress becomes greater than the yieldstress of the material in pure shear.

Shear Friction ModelThe constant shear friction is used mostly for bulk metal forming simulations. The frictional force inthe constant shear model is defined by

f ¼ mk (22)

where f is the frictional stress, k is the shear yield stress (of the workpiece), and m is the frictionfactor. This states that the friction is a function of the yield stress of the deforming body. A generalbenchmark of friction coefficients for different bulk metal forming processes are listed in Table 10. Itis important to note that the lubricant used on the tooling may play a large role in the value of frictionstress. The friction will in turn affect the metal flow at contact surfaces.

Table 10 Typical friction coefficient values using constant shear friction model

Bulk forming process Shear friction coefficient

Cold forming (carbide dies) 0.08

Cold forming (steel dies) 0.12

Warm forming 0.25

Hot forging (lubricated) 0.3

Hot forging (dry) 0.7

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Hybrid Friction ModelA hybrid friction model (combination of the coulomb and the constant shear models) is often usedwhen rolling or elastoplastic deformation (for springback) is considered. The general function is asEq. 23.

t ¼ mp mp < mkð Þt ¼ mk mp � mkð Þ

�(23)

This model describes that at low normal pressure, the friction is proportional to the normalpressure whereas at high normal pressure, the friction is proportional to the workpiece shear stress.The frictional behavior is illustrated in Fig. 24.

General Friction Model (by Wanheim and Bay)The general friction model proposed by Bay and Wanheim (1976) is a very popular friction modelwhich also takes into consideration the different friction behaviors under low/high normal pressure.

t ¼ f ak (24)

where t and k represent the friction stress and shear yield stress of the material, respectively. f is thefriction factor and a is the real contact area ratio. This equation can also be treated as a combinationof coulomb and constant shear models as at high normal pressure, both f and a stay constant, whichimplies a constant m value:

tk¼ f a ¼ m (25)

At low normal pressure, the real contact area ratio a exhibits a linear relationship with normalpressure p. With constant f and k, t has a linear relationship with p, which turns into a typicalcoulomb friction model. An illustration of the general friction model showing such a combinednature can be found in Fig. 25.

Advanced Friction ModelsThere are numerous advanced friction models to accurately capture the interaction between theworkpiece and die under varying processing conditions. These models take into consideration the

Fig. 24 Illustration of hybrid coulomb and constant shear friction model

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influence of the time, interface pressure, interface temperature, and surface stretch of the deformingworkpiece or even a combination of these. Normally, the empirical models for the pressure, strainrate, and sliding-velocity-dependent friction coefficients can be obtained, as listed below.

Pressure-dependent friction coefficient:

m ¼ m0 1� e�apð Þ or=and m ¼ m0 1� e�apð Þ (26)

where p is the normal pressure and a is a constant with typical values ranging from 0.012 to 0.06.Strain-rate-dependent friction coefficient:

m ¼ m0 1þ a_e� �

or=and m ¼ m0 1þ a_e� �

(27)

where _e is the effective strain rate and a is a constant with typical values ranging from 0.0012 to0.0045.

Sliding-velocity-dependent friction coefficient:

m ¼ m0 usj ja or=and m ¼ m0 usj jas ¼ Ee (28)

where us is the sliding velocity and a is a constant with typical values ranging from 0.0016 to 0.014.These models provide additional options for users to accurately capture the friction behaviors

during bulk metal forming process if such a process exhibits a strong sensitivity to friction.However, most conventional processes are not extremely sensitive to friction, and the typical valueslisted above may be adequate for initial process design and load prediction.

Material Mechanical Properties RepresentationThe material mechanical properties here are mainly the material’s flow stress during the formingprocesses. It is a fundamental parameter to determine toque and power of metal forming equipmentand is defined as a stress that results in the material flow in a one-dimensional stress state. Initially wefocus on the models that describe the material flow stress curves. Subsequently, multiple-dimensional stresses are introduced, with their anisotropy (orientation-dependence) considered interms of yield function.

Fig. 25 Illustration of the general friction model function

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Elastic RegionA classic ductile metal stress-strain curve resembles that in Fig. 26, in which the two distinct materialbehaviors, elastic and plastic regions, are shown. For elastic region (till yield stress), Hooke’s lawapplies to relate the stress s with strain e,

s ¼ Ee (29)

where E is the modulus of elasticity, or Young’s modulus. As it is a linear relationship, the moduluscan be determined from the slope of the engineering stress–strain curve in the elastic region.

Power LawIn the plastic region, work hardening is observed for plastic materials. Work hardening is thestrengthening of a metal by plastic deformation. This strengthening occurs because of dislocationmovements and dislocation pile-up within the crystal structure of the material. Perhaps the mostcommon mathematical description of such work hardening phenomenon is the power law, which isan empirical stress–strain relationship obtained by fitting an exponential curve to the experimentaldata points of the flow stress curve.

s ¼ Ken þ s0 (30)

whereK is the strength coefficient and n is the strain-hardening exponent coefficient, while s0 can beseen as the initial yield value. Figure 27 provides an example of the power law fitting of Inconel718 alloy flow stress data.

Linear HardeningAnother popular (but to a lesser extent accurate) work hardening rule is the linear hardening law. Itassumes that the flow stress is proportional to the strain in the plastic region with hardeningcoefficient of H, which in principle is smaller than the value of the material Young’s modulus.Such rough approximation is especially helpful when limited material data are available (i.e., onlyyield stress, UTS, and elongation are provided). The linear hardening rule is presented as

Fig. 26 Stress–strain curve of a typical ductile metal

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s ¼ s0 þ He (31)

where both s0 and H are dependent on temperature and the dominating atom content (in steel, thedominating atom content is carbon percentage). Figure 28 gives an illustration of the linearhardening flow stress curve.

In this law, if the linear hardening coefficient H is set to 0, the material behavior becomes elastic-perfect plastic, which is a special case of the linear hardening law.

Johnson-Cook Flow Stress ModelJC flow stress model is perhaps the most famous empirical flow stress model that takes strain rate andtemperature effects into consideration. Such rate-dependent inelastic behavior of solids is calledviscoplasticity in continuum mechanics theory. The general form of a JC flow stress law looks like

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

200

400

600

800

1000

1200

1400

1600

1800

Str

ess

(MP

a)

Strain

04 May 2012Inconel 718, Annealed, F6.0¥9mmCross head speed: 60mm/min

s = Kenn 0.235

INCONEL 718, Annealed

1713K

Fig. 27 Flow stress of INCONEL 718 (annealed)

Fig. 28 Illustration of the linear hardening law

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s ¼ Aþ Benð Þ 1þ Cln _e�Þð Þ 1� T�ð Þmð Þð (32)

where e is the equivalent plastic strain, _e� is the normalized plastic strain rate, T* is the normalizedequivalent temperature, and A, B, C, n, and m are material constants.

The normalized strain rate and temperature in the equation above are defined as

_e� ¼ _e�

_e�0and T� ¼ T� T0ð Þ

Tm � T0ð Þ (33)

where _e�0 is the effective plastic strain rate of the quasi-static reference test used to determine the yieldand hardening parameters A, B, and n. T0 is a reference temperature, and Tm is a reference meltingtemperature. For conditions where T* < 0, t is assumed that m ¼ 1.

It is also worth noting that in JC flow stress rule, if the influences of the strain rate (second term inthe equation) and temperature (third term in the equation) are ignored, the equation becomesa classic power law mentioned before.

Microstructure-Based Flow Stress ModelThis flow rule or the so-called Taylor equation (Taylor 1934) is relatively new to the industry.However, it is very popular among the academia in solid mechanics research field, which providesa good link between the microscopic and macroscopic levels by explaining the strain-hardeningphenomenon using the dislocation pile-up theory. A general form of the equation is

s ¼ s0 þ aGbffiffiffir

p(34)

where a is a dimensionless coefficient, G is the shear modulus, b is the Burgers vector, and r is thedislocation density. The strain hardening occurs when the dislocations are piling-up during plasticdeformation, by which their density increases and results in increment of material flow stress. Therelationship between plastic deformation and dislocation density needs to be provided alongside thisEquation.

Poisson’s RatioThe equations above are all for one-dimensional stress state. If multiaxial stress state is considered,the material may behave differently from that of the one-dimensional. In the elastic region, forinstance, the material may show different Young’s modulus if uniaxially loaded in differentdirections. This is so-called anisotropy in elasticity. Most of the metals exhibit such anisotropy inelastic region but not in a large amount. More often, when a piece of metal is tensile loaded in onedimension, the other two dimensions will shrink accordingly to accommodate such shape change.Such phenomenon is called Poisson’s effect, with ratio of transverse to axial strain named asPoisson’s ratio. Most materials have Poisson’s ratio values ranging between 0.0 and 0.5.Majority of steels and rigid polymers when used within their elastic limits (before yield) exhibitPoisson ratio values of about 0.3, increasing to 0.5 for plastic deformation. Rubber has a Poissonratio of nearly 0.5.

Yield Function: Von MisesYield function is a function describing the material yield point when triaxial stress is presented. Foruniaxial loading, the yield point can be easily identified in the stress–strain curve as the transitionpoint between linear elastic and plastic regions. When triaxial stress state is considered, if the

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material is isotropic, the yield condition should be based on the von Mises yield stress value sy.When the von Mises stresses or equivalent tensile stress sv > sy, then the material plasticallydeforms. If sv < ¼ sy, then the material only deforms elastically.

sv ¼ s ¼ 1

2sxx � syy� �2 þ syy � szz

� �2 þ sxx � szzð Þ2 þ 6 sxy þ syz þ szx� �2� �

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2sx � sy� �2 þ sy � sz

� �2 þ sx � szð Þ2� �r

(35)

where s1s2s3 are the principle stresses (normal stresses in the directions without any shear stresses)and

sv � sy, elastic deformationsv > sy, plastic deformation

It is worth noting that in this case, if uniaxial stress is considered, s1 6¼ 0, s2 ¼ s3 ¼ 0, thereforethe von Mises criterion simply reduces to s1 ¼ sy, which is the yield point of uniaxial loading.

Yield Function: Hill’sThe quadratic Hill’s yield criterion has the form

F sxx � syy� �2 þ G syy � szz

� �2 þ H sxx � szzð Þ2 þ 2Ls2yz þ 2Ms2zx þ 2Ns2xy ¼ 1 (36)

Here F, G, H, L, M, and N are constants that are needed to be determined experimentally. Thequadratic Hill yield criterion depends only on the deviatoric stresses and is volumetric stressindependent. It predicts the same yield stress in tension and compression. It is especially usefulwhen the material has strong texture, for instance, for rolled plates or hot-extruded billets. Inmaterials science, texture is the distribution of crystallographic orientations of a polycrystallinesample. Aworkpiece in which these orientations are fully random is said to have no texture. If thecrystallographic orientations are not random, but have some preferred orientation, then the samplehas a weak, moderate, or strong texture depending on the number of crystallites sharing the sampleorientation. The material properties show a strong anisotropy because of the texture, and thephenomenon of anisotropic yield can be accounted for using Hill’s yield criterion. The disadvantageassociated with the criterion is that there are quite a number of coefficients (six in the quadratic form)to be determined (hence multiple tests are required) before it can be applied to finite elementsimulation.

Lankford CoefficientEarlier we briefly discussed the anisotropy in elasticity and anisotropy in yield. The anisotropy inplasticity is in no way simpler than that of elasticity or yield. A commonly used plastic anisotropyindicator is the Lankford coefficient (also called Lankford value or R-value). This scalar quantity isused extensively as an indicator of the formability of recrystallized low-carbon steel sheets. Itsdefinition follows:

If x and y are the coordinate directions in the plane of rolling and z is the thickness direction, thenthe Lankford coefficient (R-value) is given by

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R ¼ epxyepz

(37)

where exyp is the plastic strain in-plane and ez

p is the plastic strain through the thickness. In practice, theR-value is usually measured at 20 % elongation in a tensile test.

For sheet metals, the R-values are usually determined for three different directions of loadingin-plane (0�, 45�, and 90� to the rolling direction) and the normal R-value is taken to be the average

R ¼ 1

4R0 þ 2R45 þ R90ð Þ (38)

The planar anisotropy coefficient or planar R-value is a measure of the variation of R with anglefrom the rolling direction. This quantity is defined as

Rp ¼ 1

2R0 � 2R45 þ R90ð Þ (39)

It has been widely recognized that anisotropy is closely linked with the material microstructure.The evolution of material microstructure during bulk forming process may greatly influence the endproduct’s structural integrity. Hence, understanding the microstructural behavior, before and duringthe forming process, is one of the main focuses.

Simulation of Microstructure Evolution During Bulk Metal Forming ProcessesThe finite element simulation of microstructure evolution is a very hot topic in research communi-ties. Divided opinions exist in many areas, even on the definitions of some fundamental mecha-nisms. Therefore, in this section, only the most popular definitions and generalized equation formsare provided.

To start, an introduction on the metal microstructure has to be provided. Metal alloys areunusually polycrystalline solids, which consist of many crystallites that are small, often microscopiccrystals that are held together through highly defective boundaries. Metallurgists often refer to thesecrystallites as grains (grain size �30 mm). Figure 29 provides an example of the grain structure in thesteel.

Fig. 29 Optical micrograph of AA6061 aluminum alloy showing polycrystalline structure

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They are normally of different orientations and separated by grain boundaries. Grain boundariesare interfaces where crystals of different orientations meet. Grains in the metal change shapes andorientations during forming process, which in turn influence the material mechanical properties.Modeling such changes may not be easy as there are thousands of grains in the workpiece andcapture of individual behavior becomes computationally impossible. Therefore, such changes arealways modeled using statistical methods. To represent the grain structure before deformation,methods like cellular automata (Wolfram 1983) and voronoi tessellation (Voronoi 1908) arecommonly employed. A value of average grain size is of course another option (although veryrough).

For the grain structure evolution during deformation, numerous phenomenological models havebeen developed in this area, and controversies exist on the definitions of various recrystallizationmechanisms. However, the computational algorithms behind them are similar: in each time step,local temperature, strain, strain rate, and evolution history, the mechanism of evolution is deter-mined, and then the corresponding grain variables are computed and updated. In the condition thatall the phenomena can be divided into the following three microstructural evolution groups, then ineach group the corresponding mathematical function can be used to describe such evolution.

Dynamic recrystallization (DRX) occurs during deformation and when the strain exceeds thecritical strain. The driving force is dislocations annihilation.

Static recrystallization occurs after deformation and when the strain is less than the critical strain.The driving force for static recrystallization is dislocations annihilation. The recrystallization beginsin a nuclei-free environment.

Grain growth occurs before recrystallization begins or after recrystallization is completed. Thedriving force is the reduction of grain boundary energy.

Dynamic RecrystallizationThe dynamic recrystallization is a function of strain, strain rate, temperature, and initial grain size,which change in time. It is very difficult to model dynamic recrystallization concurrently duringforming as this has the possibility of creating numerical instability. Instead, the dynamic recrystal-lization is computed in the group immediately after the deformation stops. The average temperatureand the strain rate of the deformation period are used as inputs of the Equations.

Activation Criteria The onset of DRX usually occurs at a critical stain ec

ec ¼ a2ep (40)

where ep denotes the stain corresponding to the flow stress maximum:

ep ¼ a1dn10 _em1e Q1=RTð Þ þ c1 (41)

in which d0 is the initial grain size, R is the gas constant, T is the temperature in Kelvin, and Q isactivation energy.

Kinetics The Avrami equation (Avrami 1939) is used to describe the relation between the dynam-ically recrystallized fraction X and the effective strain.

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X drex ¼ 1� exp �bde� a10ep

e0:5

� �hd" #

(42)

where e0.5 denotes the strain for 50 % recrystallization:

e0:5 ¼ a5dn50 _em5e Q5=RTð Þ þ c5 (43)

Grain Size The recrystallized grain size is expressed as a function of initial grain size, strain, strainrate, and temperature

drex ¼ a8dh80 e

n8 _em8e Q8=RTð Þ þ c8 (44)

if drex � d0 then drex ¼ 0ð Þ

Static RecrystallizationWhen deformation stops, the strain rate and critical strain are used to determine whether staticrecrystallization should be activated. The static recrystallization is terminated when this elementstarts to deform again.

Activation Criteria When strain rate is less than _esr , static recrystallization occurs afterdeformation.

_esr ¼ Aexp b1 � b2d0 � Q2=Tð Þ (45)

Kinetics The model for recrystallization kinetics is based on the modified Avrami equation.

X srex ¼ 1� exp �bst

t0:5

� �hs" #

(46)

where t0.5 is an empirical time constant for 50 % recrystallization:

t0:5 ¼ a3dh3en3 _em3e Q3=RTð Þ (47)

Grain Size The recrystallized grain size is expressed as a function of initial grain size, strain, strainrate, and temperature

drex ¼ a6d0h6en6 _em6e Q6=RTð Þ þ c6 (48)

if drex � d0 then drex ¼ 0ð Þ

Grain GrowthGrain growth takes place before recrystallization starts or after recrystallization finishes.

The kinetics is described by equation

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dr ¼ dmrex þ a9texpQ9

RT

� � 1=m(49)

Retained Strain When recrystallization of a certain type is incomplete, the retained strain availablefor following another type of recrystallization can be described by a uniform softening method:

ei ¼ 1� lX rexð Þei�1 (50)

Temperature Limit The temperature limit is the lower boundary of all grain evolution mecha-nisms. Below this temperature, no grain evolution occurs.

Average Grain Size The mixture law is employed to calculate the recrystallized grain size forincomplete recrystallization:

d ¼ X rexdrex þ 1� X rexð Þd0 (51)

Based on the abovementioned equations, the evolution of the microstructure during bulk formingprocess can be estimated.

Fracture Prediction in Bulk Metal FormingPerhaps one of the most important questions that mechanical engineers would like to ask is when thematerials will fracture/damage during the forming process. The answer to this question depends onthe geometry of the workpiece, the boundary condition, and the material properties. As the first twofactors have already been taken into consideration during simulation using finite element method,the focus here will be placed on the materials. There are many numerical models available whichintend to provide the material damage criteria under different loading conditions. They may considerdamage as a progressive process with initiation and evolution at different stages of loading. Indeed,in most of the metals, the ductile damage dominates, which is a process due to nucleation, growth,and coalescence of voids in ductile metals. However, in our case, the damage is treated as aninstantaneous event with a single-value indicator to determine that particular damage for ease ofapplication. Below listed are some of the most commonly used ones in the bulk forming areas:

Maximum Principle Stress/Ultimate Tensile StrengthPerhaps the easiest criterion that one can immediately think of is the comparison between the currentstress (s) state and the maximal principle stress or UTS (sUTS). The critical value is given by the ratiobetween them as

a ¼ ss1

� ac or a ¼ ssUTS

� ac (52)

Cockcroft and LathamThis is the most commonly used fracture criterion with bulk deformation (Cockcrof and Latham1968), which states

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ðef0s�de � C (53)

where s* is the maximum tensile stress in the work piece, ef is the strain at fracture, andC is the C&Lconstant. This method has been used successfully to predict fracture in edge cracking in rolling andfree-surface cracking in upset forging under conditions of cold working.

Rice and TracyThis model is defined as a function of mean stress and effective stress. a is the model coefficient.

ðef0easms de � C (54)

BrozzoBrozzo model is defined as a function of principal stress and mean stress:

ðef0

2s�

3 s� � smð Þ de � C (55)

The disadvantage associated with above criteria is that all these methods predict the damage basedon a certain critical value, which can only be determined experimentally. Moreover, the damagepoint in the experiment is not easy to identify as it is a progressive process. To make the situationeven worse, the critical value varies from material to material, and sometimes different setups mayalso contribute to such deviation. Therefore, these fracture/damage values can only be used asa rough guideline for the process design.

In this section, we had a brief overview of the challenges in utilization and application of FEsimulation to design and optimize the forming processes. Issues such as the material frictionbehaviors, mechanical properties, microstructural evolution, and fracture prediction were covered.Surely the challenges in the simulation are far greater than those presented here. However, thisprovides a flavor to the readers of this handbook on the complexity the bulk metal forming processeshave in terms of modeling and simulation.

Lubrication in Bulk Metal Forming

IntroductionFriction in bulk metal forming is defined as the resistant force against relative movement of the dieand workpiece. This can affect the metal flow, surface quality, and stresses on dies. In most cases,friction is undesirable, except in some rare cases such as rolling, which could not proceed withoutfriction.

The characteristics of frictional condition in bulk metal forming are as follows:

• Sliding under high pressure, larger than yield stress of the workpiece• Plastic deformation in the workpiece• Surface expansion of the workpiece• High temperature of the workpiece (hot forming)

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Although there have been a lot of reports on the subject of friction in metal forming processes, itsmechanism is still not fully understood. It is preferred to reduce the friction in bulk metal deforma-tion by using proper types of lubricants to lower the frictional resistance between the die and theworkpiece and to present wear as well as galling on the tools.

Based on the form of the contact between the tool and the workpiece, the various friction andlubrication conditions can be summarized as in Table 11.

The relative friction coefficient of various friction regimes is typically shown in Fig. 30. Thisso-called Stribeck curve is useful for the determination of the optimum lubricant based on theprocess parameters.

Various types of friction regimes at the interface have been shown schematically in Fig. 31.Boundary lubricants have significant effects especially in microscale forming processes, since theycan trap the lubricants in this scale and reduce the forming load.

Table 11 Different friction regimes (Mang et al. 2011)

Frictionregime Definition Remarks

Relativefrictionlevel

Solidfriction(dry)

When there is no separating layer (except oxidelayers) between two solids in direct contact inmetal forming

Desirable in only rare situations such as hotrolling of plates and slabs

High

Boundaryfriction

There is a molecular layer of chemicalsubstances covering the contacting surfaces.The lubricant layer is created from surface-active substances and their chemical reactionproducts

Practical when thick long-lasting lubricantfilms are technically impossible to achieve ina variety of geometrical and thermal conditions

Medium

Fluid filmfriction

When a thick layer of a hydrodynamicallyformed lubricant is present between contactingpartners

Only works when the interfacial normalpressure, temperature, and relative speed of dieand the workpiece are low

Medium

Mixedfriction

Combination of the fluid and boundary frictions Using the appropriate lubricants containingspecial organics, the machine elementsexperience mixed friction when starting andstopping their operation

Low

Fig. 30 Typical Stribeck curve for evaluation of liquid lubricants

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Lubricant SelectionThe selection of the lubricant type depends on many factors, hence is empirical, with a very littleanalysis-based information. For instance, the lubricant choice in cold forging depends on the processparameters such as normal pressure and surface expansions. In that sense, upsetting of smallspecimens does not need the same lubricant efficiency as conventional backward extrusion. Scalingdown the bulk forming process to microscale sometimes brings up the size effect on the frictionbehavior, which makes the matter more complicated.

There are many types of lubricants in use in the industry. The most common types may becategorized as listed in Table 12.

Poor selection or poor application of the lubricant type may cause partial direct contact with highpressure between tool and workpiece (Fig. 32). This arises microscale adhesion which leads togalling or seizure or scratch on the final part’s surface.

Application of LubricantsThe most commonly used lubricant application methods can be summarized in Table 13.

Fig. 31 Schematic of differences between mixed and boundary lubrication

Table 12 Typical lubricants being used for different forming processes

Type of lubricant Typical lubricant

Liquid lubricant for cold working Mineral, synthetic, and vegetable oil; wax

Solid lubricant for cold/hot working Graphite; MoS2; BN; metallic soap, glass

Chemical conversion coating for cold working Zinc phosphate + metallic soap

Aluminum fluoride + metallic soap

Fig. 32 Schematic of disadvantages of using improper lubricants

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Post-Metal Forming Considerations in Lubricant SelectionWith increasing demand from industries, it is vital to protect the environment from pollutingchemical lubricants during or after metal forming. To do so, some procedures for using biodegrad-able lubricants have been proposed especially for Euro-zone countries. As an alternative, technol-ogies towards reusing of the waste lubricants have been developing.

Furthermore, lubricants remained on the part surface may affect the subsequent processes such aswelding and painting. Thus, the lubricants must be easily removable from the formed parts after theprocess, without environmentally hazardous effects.

Methods for Evaluation of LubricantsTo have the optimum lubricant selection, it is essential to evaluate the lubricants. There are manymethods that have been proposed for lubricant evaluation. These methods have been designed basedon the nature of the forming process (e.g., ring compression test is the best for evaluation of the upsetforging process, since both methods involve compression stresses on the workpiece, while for moresevere deformation conditions in extrusion, the double-cup backward extrusion test is a properchoice). Here only two of the most common tests are presented.

In general, for evaluation of the friction in hot metal forming, it is advised to consider the diechilling effect, contact time, and forming speed.

In ring compression test, a flat ring shape specimen is compressed to a defined reduction. Thechange in internal and external diameters of the ring depends significantly on the friction at theinterface. Thus, changing the friction factor would change the behavior of the internal radiusdimension during compression test.

To obtain the friction value for a specified lubricant, the change in the internal diameter of the pinin the experiment is compared with that obtained from finite element simulation (i.e., FE simulationof the ring compression test in similar dimensions using different friction factors). One typicalexample is plotted in Fig. 33.

The outcome could be considered as universal as changes in material properties (i.e., strainhardening) have no significant effect on the result.

For more severe deformation conditions (e.g., extrusion), the double-cup backward extrusion testmay provide a more accurate evaluation for lubricant behavior. As shown in Fig. 34, this test consistsof a forward and backward extrusion processes. The ratio of the cup heights (H1/H2) is verysensitive to the frictional behavior. With increasing friction, the cup heights ratio increases. Againhere the FE simulation helps in finding the exact value of the friction coefficient.

Table 13 Different methods for applying lubricants on the surface (Mang et al. 2011)

Applicationmethod Definition Remarks

Dripping Dripping the liquid lubricant on the blank during theprocess

Cheap and simple, but difficult to control theproper amount of desired lubricant

Roll coating Lubricant is applied on the blank moving betweentwo rollers with a certain pressure

Precise control of the amount of lubricant, butapplicable only for rolling processes

Physical/chemicalcoating

Physical/chemical or electrical deposition of a layerof solid lubricant on the blank

No lubricant wastage, but relatively moreexpensive

Spraying Spraying a controlled amount of liquid lubricant onthe blank during the process

Minimal lubricant wastage, but it does not workfor high viscous lubricants

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It is important to note that the upper punch is moving while the lower punch is stationary duringthe test. This leads to a relative velocity between the upper punch and the container, while there is norelative movement between the container and the lower punch. Consequently, the material flowbehavior is different in upper and lower portions, which explains the reason behind the difference inthe upper and lower cup heights. This test is relatively more dependent on the material properties.

As mentioned, many factors may affect the value of the friction factor. Thus, it is important toknow the region where the friction test has been done.

Tool Manufacturing and Material Selection for Bulk Metal Forming

IntroductionSince a considerable portion of the bulk forming process cost is from die manufacturing, the tool (dieand punch) must be manufactured by modern manufacturing methods using appropriate material toprovide a reasonable tool lifetime at an affordable cost.

Initial Ring

High Friction

DryWisuraFuchsTeflon

Red

uctio

n in

inte

rnal

dia

met

er, %

−200 20 40 60

Reduction in height, %

80

m=0.1

m=0.2

m=0.4

m=0.6

m=0.8

m=1.0

100

−10

0

10

20

30

40

50

60

70

80

ab

Low Friction

Fig. 33 (a) Schematic of the friction effects on the final inner radius in the ring compression test; (b) determination ofthe shear friction factor using ring compression test and finite element simulation

Fig. 34 Schematic of the double-cup backward extrusion test

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For a given forming process, the type of the tool material depends mainly on the maximum toolstress and the temperature of forming. Dies need to be changed before their lifetime expires. Thelifetime of a die is affected by wear, plastic deformation, galling/seizure, corrosion, and fatiguecracking, etc. Many of these defects occur due to high temperature, high stress, and severe friction.Thus, to prevent severe deterioration of dies in bulk metal forming, special materials must be usedand proper tool design employed. Using a proper lubricant can also help increase the die lifetime.

Tool Material SelectionIn general, the material properties that determine tool material selection for the metal formingprocess can be summarized as listed in Table 14.

In cold bulk metal forming, tool material selection depends mainly on the stress levels (type ofdeformation). For instance, in forward extrusion, the punch needs to have high compressivestrength, whereas in backward extrusion, it needs to have high wear resistance as well. Normally,in conventional cold bulk forming, based on the deformation type and tool stress level in the process,the cold working die steels (such as D2, D3), or high speed steels (such as M2), are used for diematerial.

Tool materials that are used for hot bulk metal forming processes can be summarized as listed inTable 15.

Besides the material selection, other parameters such as tool design and the workpiece propertiesmay affect the tool lifetime. For instance, it is advised to prevent sharp corners in tool making. Thisprevents stress accumulation on the corners, reducing the possibility of cracking. The proper heattreatment to the tool is of importance for increasing the tool life. The hard coatings of tools by PVD,CVD, and plasma nitriding are the useful methods to improve tool life by reducing the galling/seizure and wear.

Manufacturing TechniquesAfter computer-aided design of the tool geometry, the bulk metal forming tools are usuallyfabricated by machining processes. The main die manufacturing process may be divided into diedesign, rough machining, heat treatment, finish machining, manual finishing (polishing), orbenching and hard coating (if necessary).

Table 14 Tool material selection criteria

Materialproperties Definition Remarks

Hardenability The depth to which a metal can be hardened(it is not related to the hardness value)

Higher alloying elements increases the hardenability

Wearresistance

A gradual change in tool dimensions or shapedue to corrosion, dissolution, or abrasion

A high hot hardness value is required for wear resistancein hot forming – Mo and W alloys improve the wearresistance

Yieldstrength

Resistance to plastic deformation measuredby yield strength

Higher hardness leads to higher strength, but lowertoughness

Toughness Ability to absorb the forming energy withoutcracking – combination of strength andductility

Higher hardness lowers the impact strength; thusmedium-alloy steels are the best in this case

Resistance toheat cracking

Caused by nonuniform thermal expansion atthe surface and center of the tool

It is critical for hot metal forming process to have a diematerial with high thermal conductivity; Mo alloyingelement increases this resistance

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High Speed and Hard MachiningIn conventional die-making techniques, the die is hardened after rough machining. This could causedistortion. To resolve the issue, the hard machining method has been replaced nowadays. Instead,the hardened metal (45–62 HRC) is machined, preventing the possible distortion, and providesbetter surface finish.

Electro-Discharge Machining (EDM)EDM is a process that consists of a current-passing-through electrode which provides a voltagepotential between itself and the workpiece. Decreasing the gap between the electrode and theworkpiece creates the spark that is required for vaporizing the workpiece surface. The removedmaterial is flushed away by the EDM fluid. The hardness of the metal does not influence theefficiency of the process. Due to its good accuracy and its relative higher required process time,EDM functions on much smaller scales than conventional machining.

The only disadvantage of this method may be the time needed for electrode design. Moreover, thesparking process consumes the electrode, limiting the repeatability of the process.

The surface of tool sometimes needs to be polished after EDM for removing the surface damagescaused by EDM and to improve surface roughness.

Based on the operation, this process is divided into two types of sink and wire EDMs.In the sink EDM, the internal cavities are made by a copper of graphite electrode. The die cavity

gets its shape from the electrode (Fig. 35).The wire EDM (Fig. 36) is similar to the sink EDM in case of functioning. The primary difference

is that the electrode is a wire ranging in diameter from 0.05 to 0.3 mm.In the case of superalloy dies, since the hardness value is high, occasionally it is better to cast these

dies and subsequently obtain the final shape by EDM.

Table 15 Typical tool material selection for hot metal forming processes (Altan et al. 1983a)

Designation Alloy type Main Characteristics Application

6G, 6F2, 6F3 (ASM) Low alloy steel Good toughness Not good for higher formingtemperatures of 500 �CShock resistant

Reasonable wearresistant

6F5, 6F7 (ASM) Low alloy steel – higheramount of nickel (2–4 %)

Good hardenability Could be used for more severeapplications than the first groupGood toughness

6F4 (ASM) Low alloy steel – higheramount of molybdenum

Age hardeningcapability

Good for warm forming up to around600 �C

H10, H11, H12, H13,H14, H19 (AISI)

Chromium-based steel alloy High resistance tosoftening

Good for hot metal forming in highertemperatures than 600 �C

High resistant to heatcracking and wear

H21, H22, H23, H24,H25, H26 (AISI)

Tungsten-based steel alloy High resistance tosoftening

Good for hot metal forming at severeforming load and speed

Adequate toughness

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New Technologies in Bulk Metal Forming Processes

Press TechnologiesThe application of servo-presses goes back to the 1950s where they were used for the cuttingprocesses. With the development of transistor controllers, their power capacity was improved forforming technologies during 1990s. Prior to that, conventional mechanical presses were broadlyused for metal forming. These presses are categorized in three categories as summarized in Table 16.

All the above mentioned features can be driven by a servomotor without requiring a flywheel andclutch. In other words, the mechanical servo-presses offer a combination of the flexibility ofhydraulic presses with speed, accuracy, and reliability of mechanical presses. In Fig. 37, theoperation mechanism of both types of presses is shown.

Normally the major part of the overall forming energy is required during punch acceleration. Inconventional mechanical presses, a portion of this energy is stored in flywheels, while in hydraulic

Fig. 35 Schematic of the sink EDM process

Fig. 36 Schematic of the wire EDM process

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presses, this energy is wasted. In servo-presses, however, this energy is stored in electroniccapacitors, with relatively higher efficiency.

By precise control of the punch speed, the hitting velocity of the punch to the specimen can becontrolled. This can help in decreasing the noise due to punch-workpiece impact. Furthermore, itimproves the die lifetime and results in higher efficiency of the presses.

Moreover, with a programmed punching velocity throughout the process, heat generation due tohigh strain rate can be controlled which provides better die lifetime with consistent product quality.Furthermore, the control over punch velocity can increase the forming process speed, in casea progressive forming process is desired. Table 17 compares different presses.

Bulk-Sheet Metal Forming ProcessesWith the growing competitive industrial vibe, it is important to develop into cost-effective produc-tion processes. Especially for some automotive components, it is suggested to incorporate bulkmetal forming processes into sheet metals to produce high-quality sheet metal componentscommercially.

Sheet-bulk metal forming (SBMF) processes are defined as sheet metal forming where the flowoccurs in three dimensions similar to bulk metal forming. The main characteristic of these processesis that the final product has the dimensions of a magnitude similar to the sheet thickness, projecting

Table 16 Typical conventional presses according to the performance (Altan et al. 1983a)

Feature Typical presses

Stroke-controlledpresses

The rotational movement of the motor is mechanically stored in theflywheel, and by starting the forming it is converted into the linear slidemovement

Crank press, knuckle-jointpress, linkage press

Energy-controlledpresses

The rotational movement of the flywheel is changed to the linear motionwith a screw, and the slide stops when the energy stored in the flywheelis consumed completely

Screw press, hammer

Force-controlledpresses

The pressure of the working oil is raised by the motor, and the pressvelocity and position is controlled by the oil pressure

Hydraulic press

Ram or slide

Capacitor

Power Supply

a

b Balance Tank Main Gear

Drive ShaftBrake

Servo Motor

Flywheel

Fig. 37 (a, b) Comparison of the conventional mechanical press and mechanical servo-presses

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out of the plane of the sheet. Based on this characteristic, only some special bulk forming processescan be applied on sheet metals as summarized in Table 18.

Micro-Bulk-Sheet Metal FormingProduction of very small parts is a trend in many technical areas such as electronics and medicalindustries (Chinesta et al. 2007). In general, metal forming is well suited for efficient production ofmicro-parts. Near-net shape and excellent mechanical properties of the final product, together withthe mass production capability and lower manufacturing cost, have made this route an interestingalternative. A few years after the introduction of microforming processes by Geiger et al. (1996),many studies have been conducted towards the development of micro-parts manufacturing (Engeland Eckstein 2002; Okazaki et al. 2004; Ghassemali et al. 2011).

Despite the relatively wide range of research in this field, microforming processes have not beenadopted extensively for mass production in the industry. This is related to issues such as handling ofmicro-parts and even removal of the formed parts without damage which require further process andmanufacturing system design and development. It was stated by Engel et al. (2007) that handling ofparts is less difficult in sheet-bulk metal forming processes, since the parts usually remain connectedto the strip. This is a big advantage for the sheet metal forming processes as they are scaled down tothe micron level.

Hirota (2007) suggested the use of sheet metal for production of micro-billets. However, a discspecimen with a predefined diameter was used as the initial raw material for the process in his study.A counterpunch was used under the formed pin to the push up after the pin forming process.However, as the pin diameter decreases in size and the surface area-to-volume ratio increases, sucha pin removal method will become a challenge due to the greater risk for damage caused to the pin.

Table 17 Comparison of the different types of presses

Conventional mechanical press Conventional hydraulic press Mechanical servo-press

Speed control Low Medium High

Flexibility Low Good High

Accuracy Medium Medium High

Energy consumption High Medium Low

Noise High High Low

Maintenance cost High High Low

Table 18 Different types of SBMF processes

SBMF Process Application Remarks

Upsetting/ironing/flow forming

Sheet thinning,sizing

Combined upset/forging/drawing of sheets can be used for production offeatures such as nails, screws, and flanges

Forging Sheet thinning andthickening

Usually done in closed-die manner to have deformation flow normal to thesheet surface. Notebook cases or cell phone shields can be named as productexamples

Orbital forming Sheet thinning andthickening

Relatively smoother surfaces, lower forming load, and less noise comparedto forging and extrusion, but longer process time. Bevel gears and hollowring gear parts are some product examples

Coining/embossing Sheet thickening Efficient process for production of small features at the sheet surfaces

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Based on the concept by Hirota, a progressive micro-bulk-sheet pin forming system was designedand developed by Ghassemali et al. (2012). The system has the following advantages: (i) it cancircumvent the handling issues of small billets needed for extruding pins of very small diameter;(ii) such a process uses a strip as the workpiece and is more productive as a progressive process canbe implemented; and (iii) instead of ejecting the formed pin, the system uses a blanking process toremove the formed pin from the strip material, eliminating the possibility of buckling damage ifa counterpunch is used as an ejector. Figure 38 shows the schematic of the process.

Fig. 38 Schematic of the progressive microforming process

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As can be seen in this figure, the process setup consists of two stages: (i) pin forming by forwardextrusion and (ii) blanking. In the first step, the strip is deformed by a punch of a defined diameterand specified displacement. As a result, a portion of the material is forward extruded into the diecavity. The strip is inserted via guides on the setup. To ensure the precise positioning, guide holes arecreated on the edge of the strip and guide pins are used along the different stages of the die setup. Thespring-loaded blank holder was used in this lab-scale study to distinguish the forming load from theblank-holder load. In industrial applications, the blank holder is usually attached to the press.

After extrusion in stage I, the strip with the attached extruded pin is ejected by springs and can bemoved to the next stage.

It is noteworthy that the forming process only occurs in stage I of the process. In other words,stage II is only used for detaching the pins from the strip. Thus, the formed micro-pin at stage I is stillattached to the strip which makes it easier for handling and transferring to the next stage either forblanking or for subsequent measurements. No counterpunch is used in this process, and the ejectionby the springs on the strip only leads to the withdrawal of the formed pin from the forming die. Thefeasibility of this process for production of micro-pins of diameters between 100 mm to macro-scalehas been proven (Ghassemali et al. 2012, 2013a). It is important to note that due to its axisymmetricgeometry, the progressive microforming process has a good capability of producing other symmet-rical micro-parts such as hollow pins, stepped pins, or cups.

After stage I, no significant damage in terms of pin fracture and buckling was observed in theexperiments, as can be seen from Fig. 39. This was indicative that the ejection process of the formed

Fig. 39 Micro-pins produced by progressive microforming process: (a) before and (b) after the blanking process.(c) FESEM micrograph of the final micro-pins

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micro-pin by the ejecting springs on the strips does not cause any damage on the formed pin in thisprocess, although there were galling effects on the pins’ surface. Developing hard-coating tech-niques seems essential to be able to coat the very small die orifice (Ghassemali et al. 2013a).

The three stages in the process can be seen also in the load-stroke curves. Figure 40 showsa typical load-stroke curve for the progressive microforming process. Almost a similar behavior wasobserved in the punch reaction of other processes, in which the first stage was contributed to theelasticity and the last two stages in the curve was related to the plasticity behavior of material in theprocess (Jiang and Chen 2011).

In the first stage, loads are relatively low, which corresponds to the elastic forming initiation andindentation process. The portion of this stage is relatively small. At stage II, upsetting is the mainphenomenon mainly due to the less force required for this phenomenon compared to that of theextrusion. Till this stage, the material mainly flows towards the outside of the punching area ratherthan moving towards the die cavity. After reaching stage III, the load increases rapidly. In this stage,the required extrusion force is less than the upsetting, and therefore, the extrusion becomes thedominant phenomenon occurring in the process. Therefore, the metal will mostly flow towards thedie cavity rather than moving outwards, after this stage. The unloading portion of the curve presentsthe elastic deflection of the material and punch essentially due to the force in stage III. This shape ofthe load-stroke curve is similar to what happens in the common impression-die forging process(Altan et al. 1983b) as reported also for bending process (Jiang and Chen 2011).

Based on this phenomenological study, this process has been optimized using upper bound theory(Ghassemali et al. 2013b). Using the developed model, it is possible to predict the material behaviorduring the process, with the least material wastage and competitive production rate.

References

Altan TO, Oh S-I, Gegel HL (1983a) Metal forming: fundamentals and applications. AmericanSociety for Metals, Metals Park

Altan T, Oh S-I, Gegel HL (eds) (1983b) Metal forming: fundamentals and applications. AmericanSociety for Metals, Metals Park, pp 156–158

Fig. 40 Load-stroke curve for the 0.8 mm pin produced by 3.2 mm punch

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Altan T, Ngaile G, Shen G (2004) Cold and hot forging; fundamentals and applications. ASMInternational, Materials Park

ASTM (2009) Standard test methods of compression testing of metallic materials at room temper-ature. ASTM International, West Conshohocke

Avitzur B (1968) Metal forming: processes and analysis. McGraw-Hill, New YorkAvrami M (1939) Kinetics of phase change. I general theory. J Chem Phys 7(12):1103–1112Bay N, Wanheim T (1976) Real area of contact and friction stress at high pressure sliding contact.

Wear 38(2):201–209Chinesta F et al (2007) Microforming and nanomaterials advances in material forming. Springer,

Paris, pp 99–124Cockcrof MG, Latham DJ (1968) Ductility and workability of metals. J Inst Met 96(Part 2):33–39Engel U, Eckstein R (2002) Microforming–from basic research to its realization. J Mater Process

Technol 125–126:35–44Engel U, Rosochowski A, Geißdörferfer S, Olejnik L (2007) Microforming and nanomaterials.

Springer, Paris, pp 99–124Geiger M, Vollertsen F, Kals R (1996) Fundamentals on the manufacturing of sheet metal

microparts. CIRPAnn Manuf Technol 45(1):277–282Ghassemali E et al (2011) Dead-zone formation and micro-pin properties in progressive

microforming process. In: 10th international conference on technology of plasticity(ICTP2011), Steel Research International, Germany

Ghassemali E et al (2012) Progressive microforming process: towards the mass production of micro-parts using sheet metal. Int J Adv Manuf Technol 66:611–621

Ghassemali E et al (2013a) On the microstructure of micro-pins manufactured by a novel progres-sive microforming process. Int J Mater Form 6(1):65–74

Ghassemali E et al (2013b) Optimization of axi-symmetric open-die micro-forging/extrusion pro-cesses: an upper bound approach. Int J Mech Sci 71:58–67

Hirota K (2007) Fabrication of micro-billet by sheet extrusion. J Mater Process Technol191(1–3):283–287

Jiang C-P, Chen C–C (2011) Grain size effect on the springback behavior of the microtube in thepress bending process. Mater Manuf Process 27(5):512–518

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engineering, lubrication. Wiley-VCH, WeinheimMielnik EM (1991) Metalworking science and engineering. McGraw-Hill, New YorkOkazaki Y, Mishima N, Ashida K (2004) Microfactory–concept, history, and developments.

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Soc Lond Ser A 145(855):362–387Tschaetsch H (2005) Metal forming practise; processes, machines, tools. Springer, BerlinVenugopal Rao A, Ramakrishnan N, Krishna kumar R (2003) A comparative evaluation of the

theoretical failure criteria for workability in cold forging. J Mater Process Technol 142(1):29–42Voronoi G (1908) Nouvelles applications des paramètres continus à la théorie des formes

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Index Terms:

container 11, 23, 40extrusion 1–2, 8, 10–12, 18–19, 23–24, 38–41, 45, 47–48forging 1–2, 5–10, 18–19, 21–22, 25, 36, 38–39, 45, 48metal forming 1–4, 12, 14, 16–19, 21, 24–25, 27, 36–37, 39, 41–45modeling 1, 33, 36rolling 1–4, 13, 15, 18–19, 22–23, 26, 31–32, 36–37, 39simulation 1, 14, 17, 21, 24–25, 31–32, 35–36, 39–40

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