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Forming, Casting and Welding Technology Forming Technology

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reg. č. CZ.1.07/2.2.00/15.0399

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1 THE PHYSICAL NATURE AND MECHANISM OF PLASTIC DEFORMATION

The forming processing of metal materials makes use of the plasticity of these materials - i.e. the ability of materials to reshape without any disruption. Forming can be therefore defined as follows:

Forming is a manufacturing operation in which the shape of the starting blank undergoes permanent transformation as a result of the effect of external forces (the material is deformed below the solidus curve).

The result of forming: a) change in the shape and dimensions

b) physical changes of the material which manifest themselves in structural transformations and thus also in the changes of the physical and mechanical properties

Forming - plastic deformationIt is necessary to produce such a state of stress in the formed body that the yield strength of the given material is overcome and a permanent deformation of the required direction and size is achieved without any disruption of cohesion.

Internal forces counteract against any external forces which act on the body. These internal forces represent the resistance of the material to its transformation. The resulting effect of forming thus depends not only on the nature of the external forces but also on the factors affecting the internal forces (e.g. the structure of the formed material, temperature). In contrast to elastic deformation, in permanent deformation the distance of the movement of atoms is higher than the lattice constant. Plastic deformation of metals cannot be caused by the normal stress σ, but only by the shear stress τ. In plastic deformation there occurs a permanent displacement of atoms from their equilibrium positions, this displacement is retained even after the effect of the external deformation forces has ceased. The permanent displacement of atoms occurs only after the value of the critical shear stress τkr has been exceeded and only in some active crystallographic planes and directions where the movement of the atoms encounters the fewest barriers.

1.2. The Mechanism of Plastic DeformationSimple slip - translation

The most common mechanism of plastic deformation is a simple slip - translation. Plastic deformation does not take place by the simultaneous movement of all atoms in the active slip plane which would require very high values of the shear stresses at the level of the theoretical shear strength (21.103 MPa in pure Fe, the actually determined value for single crystals of Fe is 29MPa). The structure of real metals contains already in the starting state a large number of lattice defects,

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especially dislocations, a part of which is brought into the slip movement on the slip plane as a result of the effect of τkr. Gradually, some of the potential slip planes take part in the slip. The crystal remains without deformation between these active slip planes until other slip systems are brought into action as a result of the rising stress.

The physical laws of slip

a) Slip usually occurs on the planes which are the most densely occupied by atoms.b) The slip direction is always identical with the direction which is the most densely occupied by

atoms. c) Only such a slip system – out of the given group of possible slip planes and directions – is active

in which the shear stress τ reaches the value of τkr. For the given metal, crystal lattice, temperature and deformation rate this stress is defined by the plasticity constant.

d) Shear stresses reach maximum values in planes which are inclined at the angle of 45° to the so-called primary planes (i.e. in those planes where only normal stresses apply) whose direction is identical to the direction of the external deformation (forming) force in many forming procedures.

The value of the critical shear stress τkr depends on:

- deformation rate - temperature- state of the material prior to the deformation (chemical composition, structure: method of

previous processing)

The τkr value therefore depends on the temperature, deformation rate and on previous deformation of the crystal. The slip occurs first in those planes where the tangential shear stress caused by an external force reaches τkrit.

The equation for calculating the shear stress in the slip plane in the case of the tensile test is as follows (Fig. 1-1):

,

Where σk is the yield strength and φ is the angle between the slip plane and the axis of the cylindrical sample. The shear stress τ which forms an angle λ with the sample axis and thus also with the normal stress σk is active in this plane. There is a dependence between the normal and the shear stress

After modifying, the following equation is achieved:

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If this stress τ reaches the value of the critical shear stress τkrit, there occurs a dislocation slip in those slip planes which are the most densely occupied by atoms.

This value is first reached on the planes forming the angle of 45° with the axis of the cylindrical sample of the tensile test (later, there occurs a triaxial stress state when other slip systems in different planes are activated in the so-called neck).

Fig. 1-1: The relationship between the normal and the shear stress in uniaxial tensile straining of the tested sample.1

Twinning

At very low temperatures and high deformation rates plastic deformation occurs also as a result of the so-called twinning mechanism. In this mechanism, atoms in a part of the crystal move only by a part of the interatomic distance, so that the slip results in a lattice region which is a symmetrical mirror-image of the static lattice according to the twinning plane – the so-called twin (Fig. 1-2). The twinning mechanism does not achieve large plastic deformations. Deformation twins occur only in a

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limited extent during forming, mainly in copper alloys and in the basic ferritic structure formed at a high deformation rate at low temperatures.

Fig. 1-2 Twinning according to the plane A-A2

1.3. Plasticity and Formability

Plasticity is the ability of a material to deform itself plastically (irreversibly) under the effect of external forces without any macroscopic disruption. In metallic materials, these changes are accompanied by changes in the structure.

Formability - the ability of a material to deform itself plastically (irreversibly) without any macroscopic disruption in a specific forming process or an ability bound to a specific test of formability.

Note: The concepts of “tvařitelnost” (“tvářitelnost”), or “tvárnost”,” plastičnost” (“plastičnosť”, “plasticity”, “ductility”,”plasticität”) and technological formability (“ductility”, “workability”,” formability”, “formbarkeit”, “umformbarkeit”) are not fixed in literature.

Formability is a function of:

a) the material:

- its chemical composition

- its structure

b) the temperature and deformation rate

c) the stress state

d) the history of stress and deformation (method of previous processing by forming)

e) the geometric factor

f) the external environment

The extent of these individual "formability" variables differs for each forming process.

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In hot forming, factors a) and b) apply predominantly, i.e. the material with its chemical composition and structure and the influence of temperature and deformation rate. This is the case of the so-called “internal” (metallurgical or structural) formability.

In cold forming, factors c) to f) apply predominantly, i.e. the intensity of the stress and the shape of the deformation zone and also the method which has been used to achieve the final deformation (the deformation history) have a decisive influence. This is the so-called stress (SOS - state of stress) formability.

The behaviour of a material and its reactions to the forming process are thus variable and depend on the specific technological procedure. For the purposes of calculating the forces, deformations and stress during forming, the material is described by means of a curve expressing the dependence of the deformation stress on the size of the deformations (σ-ε) which have a different progress in cold and hot forming (Fig. 1-3).

Figure 1-3 A graph of the dependence of stress on the size of deformation of plastically formed metals3

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THE STUDENT KNOWS:

The mechanism of plastic deformation

Physical laws of the dislocation slip

The concept of twinning

The meaning of the concepts of plasticity and formability

SOURCES OF INFORMATION:

M.Žídek, V.Dědek, B.Sommer: Tváření oceli, SNTL 1988

KEY WORDS IN THE ENGLISH LANGUAGE:

Plastic deformation

Dislocation slip

Formability and plasticity


2. THE EFFECT OF FORMING ON THE PROPERTIES AND STRUCTURE OF METALS

In terms of the forming temperatures and the progress of physical-metallurgical processes, the following processes are distinguished:

a) cold forming

b) hot forming

The criterion for distinguishing between cold and hot forming is the progress of the restoring (softening) processes, i.e. recovery and recrystallization. The softening processes which take place simultaneously with deformation hardening and which are called dynamic softening processes are of a special importance.

2.1. Recovery

In recovery, the stored deformation energy of grains is reduced by a partial annihilation of point defects and dislocations when the "surplus" concentration of point defects (interstitial atoms and vacancies) and dislocations is reduced to an equilibrium value. This partially reduces their density and the stress which is necessary for the plastic deformation. Other dislocations assume more energetically favourable positions, and there occurs the so-called polygonization (Fig. 2-1). Recovery occurs at temperatures lower than the temperatures of the beginning of recrystallization. Recovery of dislocations manifests itself by a substantial decrease of internal stresses in the metal and by a slight decrease of hardness, strength, yield strength, and by an increase of plastic properties.

The progress of recovery is directly dependent on:

a) the degree of deformationb) the temperature and time of heating

Fig. 2-1 A schematic illustration of edge dislocations in a bent crystal

Dynamic recovery is the predominant softening mechanism for forming metals with a cubic body-centred lattice (ferritic steel, Al and its alloys) or for metals with a hexagonal lattice. As a result of

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dynamic recovery equiaxed grains are formed in the elongated grains. The reduction of dislocation density is lower in dynamic recovery than in recrystallization, and thus also the degree of softening is proportionately lower.

2.2. Recrystallization

In recrystallization the original grains are replaced by new grains (there is, however, no change of the crystalline system!) when the amount of lattice defects decreases to the level of the annealed non-deformed state.

The result of recrystallization is a new structure devoid of any signs of deformation and without deformation hardening, this is the case of the so-called primary recrystallization. The metal assumes properties similar to the annealed state. If the heating temperature continues to grow or if the heating time is extended, recrystallization is followed by a phase of growth of the grain in the recrystallized lattice. This is the so-called secondary recrystallization. In some cases, certain grains with a specific crystallographic orientation can start to grow rapidly at the expense of neighbouring grains. The result is a metal with a locally very coarse grain.

Recrystallization can be divided into the following phases:

a) the emergence of new crystal nucleib) their growth till the point when the recrystallized grains replace the previous deformed

structurec) coarsening of the recrystallized graind) additional growth of some grains

The recrystallization temperature for pure metals is 35-45% of the melting temperature, i.e. Trekr = (0.35 to 0.45) Ttav (in Kelvin!). The recrystallization temperature Trekr. usually refers to the temperature of the isothermal heating at which there occurs a complete recrystallization of the metal in 1 hour.

Note.: For pure Fe the temperature of the beginning of the recrystallization is approx. 300 °C.

The nuclei of new grains are mostly sites with a relatively regular lattice (coherent nuclei) to which are added (allocated) neighbouring atoms and from which new grains begin to grow (approximately equiaxed).

Recrystallization occurs at a certain rate which depends on:

a) the degree of deformationb) the temperature

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Recrystallization, much like recovery, is a thermally activated process (the activation energy for their occurrence is supplied by heating), and this is why its progress depends not only on temperature but also on time.

The stored deformation energy is the driving force behind recrystallization. If it is high, the recrystallization of the same metal will occur more easily, i.e. at a lower temperature or faster.

The size of the grain is also an important characteristic of the recrystallized metal. At a specific recrystallization temperature it is dependent on the degree of deformation of the formed metal. A large number of recrystallization nuclei are formed during annealing in a metal which has been intensively formed, and the result is a fine grained structure. After a small deformation new grains grow only from a small number of nuclei and the grain coarsens disastrously. The cold deformation which causes such coarsening during recrystallization is called critical deformation (it is usually around 5 to 10%). It must be avoided in products which will be subjected to recrystallization annealing. The so-called recrystallization diagram describes the dependence between deformation, temperature of recrystallization annealing and the size of the resulting metal grain (Fig. 2-2). The mechanical properties return to their previous level as a result of recrystallization. (Fig. 2-3)

Fig. 2-2 The recrystallization diagram

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Fig. 2-3 The effect of recovery, the primary and secondary recrystallization

During hot forming there occurs dynamic recrystallization, i.e. a recrystallization which takes place during the process of forming. After certain critical values of internal energy have been reached which correspond to the critical stage of deformation, there occurs a favourable state for the formation of nuclei and their growth during plastic deformation. Dynamic recrystallization leads to the formation of new grains, to the elimination of hardening and to an increase of plastic properties. The formation of nuclei – nucleation – takes place first along the boundaries of original grains and in coarse intermetallic phases. The dynamically recrystallized grains grow up to a certain size corresponding mainly to the size of the deformation. This distinguishes them from the grain growth during the static recrystallization where the grains continue to grow until they touch each other.

The development of structure in hot forming is shown in Figure 2-4. If carbides are present in the structure, they do not recrystallize; they break as a result of the forming and move in the direction of the ongoing deformation. After forming, there can be observed a structure of carbidic segregation in which the distribution of carbides shows the material flow during forming.

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Figure 2-4 The progress of structural changes on the stress-deformation curve

2.3. Cold Forming

Cold forming processes are characterized by hardening. In steels this occurs typically at temperatures lower than 0.2 to 0.3 Ttav., i.e. under the temperatures of recovery processes. In cold forming where the basic mechanism of plastic deformation is the dislocation slip, the dislocations moving in the slip planes interact with obstacles in the lattice, especially with substitution atoms, vacancies and other dislocations. The presence of other phases also significantly affects the dislocation slip, and the slip is determined by the size, shape and distribution of these phases. At the beginning of loading (forming) the slip deformation takes place only in grains with the most favourable orientation with regard to the direction of loading. During the interaction of dislocations with obstacles there occur dislocation sources which are the cause of additional dislocations. The density of dislocations (the total length of dislocations in a unit of volume - mm/mm3) grows, and the shear stress necessary for the movement of dislocations in the lattice with such an increased density of dislocations must be increased. As a result of the increasing stress additional slip systems are activated also in grains with a less favourable orientation; thus each grain is deformed into a shape determined by the deformation of its neighbours. The dislocation slip gradually becomes difficult, the slip resistance grows, until no more dislocations are able to pass through the lattice and they begin to accumulate in front of obstacles, most often at the boundaries of grains or at coarse phases. This is how a nucleus of a crack is formed and the material manifests itself as brittle. There are a number of models which describe the behaviour of dislocations in a real crystal lattice (see physical metallurgy). These processes result in the hardening of the material which is manifested by:

a) an increase of the yield strength and the tensile strength; the yield strength grows faster than the tensile strength

b) a reduction of ductilityc) by a change of the physical, electrical and magnetic properties

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Absolute exhaustion of plastic properties is characterized by the fact that yield strength and breaking strength are identical at zero ductility. The breaking strength (and thus also the yield strength) is several times higher than before the forming (up to 300%), the region of elastic deformations is significantly wide. Further forming is not possible, annealing (recrystallization annealing) is necessary for the restoration of plastic properties.Cold forming is often the final forming technology, it makes it possible to obtain exact products with a good level of mechanical properties (strength, flexibility, toughness, resistance to fatigue and corrosion). Figure 2-5 shows an example of the change of mechanical properties in low-carbon steel and brass after cold forming.

Fig. 2-5 The change of mechanical properties after cold rolling

2.4. Hot Forming

According to the classic theory, hot forming takes place above the recrystallization temperature (0.4 Ttav). In practice, however, the temperatures of forming are above 0.6 to 0.7 Ttav (Fig. 2-6).

Two basic processes – hardening and recovery - take place during hot forming. The preference of these processes for the given material (chemical composition, structural state) depends on the thermo-mechanical parameters (temperature, deformation rate, deformation size). Hardening can be eliminated by dynamic recovery processes immediately, i.e. already during hot forming; more often it is eliminated only partially and further recovery takes place through static recovery processes after forming. In this case, the effect of the deformation rate and of the period between the individual deformations plays an important part. As a general rule, formability decreases and the resistance to deformation increases with the rising deformation rate. At a high deformation rate recrystallization is unable to completely eliminate the adverse effects of hardening and thus resistance to deformation grows.

The influence of the deformation (forming) rate is greater in hot forming than in cold.

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During hot forming a metal keeps its plastic properties, and thus it is possible to achieve great levels of deformation. Fundamentally, there are no changes in the mechanical or physical properties. Only in the case of forming a cast structure (ingots), the achieved homogeneity and compaction result in the improvement of the mechanical properties.

Figure 2-6 Forming temperatures of steels – in a simplified Fe–Fe3C diagram. The upper forming temperatures: 1-speed heating, 2-blanks with a casting structure, 3 – blanks with a wrought structure. The lower forming temperatures: 4-hypoeutectoid steels, 5-hypereutectoid steels with a lower formability, 6-hypereutectoid steels with a higher formability

2.5. The Effect of the Structure on the Plastic Properties of the Material

The structure of a formed metal influences the plastic properties and the deformation progress by the size of its grains and also by their homogeneity and the intercrystalline matter.

The size of the grain: the decreasing size of the grain entails not only a rising deformation resistance but also worse formability of the material.

The effect of the intercrystalline matter on the decrease of strength and formability is influenced by the presence of easily meltable additives and by the weakening of the bonding of grains as a result of unevenly distributed intercrystalline matter.

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2.6. The Effect of the Temperature on the Plastic Properties of the Material

Plastic properties (as well as the deformation resistance) change significantly in relation to the temperature.If the structure is made up of one phase, the plastic properties usually improve with the increasing temperature. The decrease of the deformation resistance is explained by an easier movement of dislocations in the lattice due to the increased number of oscillations of atoms in the lattice. At the same time there occurs an accelerated diffusion of atoms which enables a dislocation climb and dislocations can therefore move along the boundaries of grains or pass into other slip planes. In some temperature regions, formability is decreased as a result of physical-metallurgical processes (Fig. 2-7).

Figure 2-7 The change of steel formability according to the temperature

The causes of reduced formability of steels:

a) The region of cold brittleness is associated with the so-called transition between the brittle and tough states. At sufficiently high temperatures dislocations react with obstacles, dislocation sources are formed or activated, and dislocations are capable of further slip. The material presents itself as tough. At low temperatures, dislocations accumulate in front of obstacles which they cannot overcome, there occur nuclei of cracks and the material becomes brittle. The tough – brittle state transition manifests itself in metals with a cubic body-centred lattice.

b) The region of blue brittleness is associated with the elimination of sulfur along the boundaries of the original austenitic grain.

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c) The reduction of formability as a result of phase transformations is characterized by the presence of internal tension due to differences in the distribution of atoms and due to a dissimilar lattice parameter in different crystal lattices.

d) The hot forming region - at high temperatures the susceptibility to the growth of grains increases; if the temperature is increased even further, the steel is overheated and burnt. If the steel is overheated, the grain coarsens and sulfur is eliminated in the form of sulfides (FeS) along the boundaries of grains. The overheating of steel can be removed by full annealing (grain refinement), or possibly by long-term annealing, the so-called homogenization annealing (elimination of chemical heterogeneity). The burning of steel results in an additional elimination of phosphorus along the boundaries of grains and in a subsequent melting of eliminated sulfides and phosphides. The steel is completely depreciated and sometimes it almost falls apart into individual steel grains.

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THE STUDENT KNOWS:

What recovery and recrystallization mean

Processes in cold forming

Processes in hot forming

The influence of forming on the structure of metals


M.Žídek, V.Dědek,B.Sommer: Tváření oceli, SNTL 1988


Recovery and recrystallization

Hot and cold forming


3. THE MECHANICAL PRINCIPLE OF FORMING AND BASIC LAWS OF PLASTIC DEFORMATION

The application of external forces on the formed body results in the occurrence of stresses which – after reaching a certain limit intensity (simply the yield strength for the specific conditions of forming) - cause plastic deformation, but the coherence of the body must not be disrupted.

3.1. The Stress in the Formed Body

The stress σ is defined as the force F acting on a unit of the surface S, therefore . Due to the generally uneven distribution of the force on the surface, it is appropriate to express the stress in a differential form .

In the most commonly used rectangular coordinate system, three normal stresses designated as σx, σy, σz act on the material point; these stresses are at a right angle to the walls of the cubic element which represents the material point, furthermore six shear stresses which are active on the walls of the element and are designated as τxy , τyx , τyz , τzy , τxz , τzx also act on the element (Fig. 3-1). The first index indicates the plane in which the tangential stress is active, i.e. the axis of the coordinate system which is perpendicular to this plane; the second index indicates the direction of the tangential stress. The state of stress is therefore determined by nine constituents and it can be recorded by means of the following matrix:

Shear stresses are subject to the law of conjugate shear stresses, thus τxy = τyx , τyz = τzy , τxz = τzx ..

When calculating the stresses and forces in forming, the studied body is placed in a coordinate system which can be freely chosen. The chosen coordinate system can be rotated to obtain the so-called main coordinate system, this means that only normal stresses σ1 , σ2 , σ3 will apply in the walls of the spatial element and the shear stresses will be equal to zero. The coordinate system is chosen in such a way that the direction of at least one of the stresses is identical to the direction of the external forming force. The state of stress is an invariant quantity, i.e. it does not depend on the spatial orientation of the coordinate system. It is described by means of three so-called invariants:

It is a linear invariant whose physical significance corresponds to the hydrostatic pressure (tension) at which there cannot occur any plastic deformation. It thus determines the elastic deformation.

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It is a quadratic invariant and it specifies the stress intensity (effective stress, reduced stress) which expresses the total effect of all stresses:

If this stress is equal to the constant of plasticity, there occurs plastic deformation (the energy condition of plasticity, see below). Similarly, the intensity of shear stresses

expresses the magnitude of the deformation resistance of the material particle to the change of its shape.

The third invariant

is called a cubic invariant and it is related to the type of plastic deformation. Its practical importance is limited.

Figure 3-1 The stress acting on a spatial element – a material point.

3.2. The Mechanical Diagram – Diagrams of Stresses and Deformations (MSD)

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Mechanical diagrams of deformation are of great importance for the analysis of forming procedures in plastic deformation. They provide a graphic representation of the presence and direction of major stresses and deformations. The mechanical diagram is given by a combination of the state of stress diagram and the deformation diagram, and it is typical for a specific type of forming.

The state of stress diagram:

The state of stress has a significant influence on the formability and deformation resistance of a metal. As a rule, the presence of tensile stresses reduces the formability of a material, because tensile stress leads to the expansion of voids and crack nuclei. By contrast compressive stresses lead to the closure of voids and cracks, and the material is therefore capable of withstanding higher plastic deformation than under the effect of tensile stresses. In the presence of compressive stresses the deformation resistance increases and it reaches its maximum if all the three main stresses are compressive.

The state of stress in the formed body is represented by means of diagrams of the main stresses (shear stresses are omitted). The stresses have a positive (= tension stresses), negative (= compressive stresses) or zero value. In theory, all combinations of the main stresses are possible, i.e. 9 possible diagrams:

1) the uniaxial state of stress (+,0, 0) – one tensile stress, the other stresses are zero,

(-, 0, 0) – one compressive stress, the other stresses are zero,

2) the planar state of stress (+,0.-) (+ +,0) (-,-, 0)

3) the spatial state of stress (+, +, +), (-,-,-) (+, +,-) (+,-,-)

Not all diagrams are of the same importance for forming.

The uniaxial state of stress occurs only in laboratory conditions in the tensile test prior to the formation of the neck or in the test of the uniaxial compression (without friction).

The planar state of stress is typical for flat forming, sheet metal forming, i.e.:

- in cross bending of sheets and strips

- in curling of welded tubes

- in deep drawing of sheet metal

The spatial state of stress applies in volume forming under the condition that

a) the diagram with the all-around tension cannot be used

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b) the triaxial compression exists in extrusion

c) the other diagrams are common in forging, rolling, drawing, etc.

Note.: The designation (+, +, +) or (-,-,-) does not mean that the stresses are of the same intensity – in such a case plastic deformation would be impossible, only elastic deformation would occur. In extrusion all three main stresses are compressive stresses but not of the same intensity.

(+,0,0) (-,0,0) (+,+,0) (-,-,0) (+,-,0) (+,+,+) (-,-,-) (+,-,-) (+,+,-)

The uniaxial state of stress

The planar state of stress The spatial state of stress

Figure 3-2 The diagrams of the main stresses

The diagrams of main deformations

The problems of forming require an examination of the mutual connection between the state of stress and the state of deformation.

Therefore the diagrams of main stresses which express qualitatively the state of stress in the point of the body are allocated diagrams of main deformations which express the progress of deformation in the given point. The deformation diagrams determine the change of dimensions of the formed body (+ the dimension increases, i.e. it is extended, - the dimension decreases, i.e. it is contracted)

Assuming a constant volume of the formed body, there are 3 real combinations of these deformations (out of the total number of 9):

1) the spatial deformation (++-) (the most common: forging operations, rolling of billets)

(- - +) (die forming, extrusion, drawing)

2) the planar deformation (0,-, +) (rolling of metal sheets and wide strips)

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Note: Various combinations of the stress and deformation diagrams are possible, but not arbitrary ones. For example, the following combinations do not exist:

Deformation, state of stress

1) (0 - +) (+ 0 0)

2) (0 - +) (- 0 0)

3) (++-) (+ 0 0) = uniaxial tension + spatial deformation (++-)

4) (--+) (0 0-) = uniaxial compression + spatial deformation (--+)

The mechanical diagram is determined by the combination of the state of stress diagram and the deformation diagram and it is typical for a specific case of forming.

Mechanical diagrams for some forming operations

Figure 3-3 Upsetting without friction

Figure 3-4 Upsetting with friction

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Figure 3-5 Extrusion

Figure 3-6 Die drawing

3.3. Deformation in the Formed Body

A body changes its shape under the influence of an external force, it deforms itself. If the body assumes its original shape after unloading, it is a case of elastic (reversible) deformation. If this does not happen, it is a plastic (permanent) deformation.

Deformation, whether elastic or plastic, can be expressed in the following ways:

Absolute deformation is the difference of dimensions after and before a deformation. If a prism of original dimensions h0, b0 and l0 (fig. 3-7) is upset into the final dimensions of h1, b1 and l1, then the absolute deformation is:

From a practical standpoint, the absolute deformation is calculated in such a way that it can be expressed in terms of a positive number.

In practice, this is used, for example, to express the reduction during rolling, i.e. the difference between the input and the output thickness of the rolled blank expressed in mm.

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Figure 3-7 A schematic illustration of the change in shape and dimensions of a prism in upsetting

The proportional linear strain is defined as the ratio of the change in a dimension in relation to the original dimension:

compression

widening

elongation

The advantage of expressing the intensity of the proportional strain is its clarity. However, it is suitable only for the description of small deformations (up to approx. ε = 0.1), especially in the elastic region; in forming where large deformations occur its use is inappropriate.

The true or logarithmic strain is derived on the basis of mathematical laws when an infinitesimal change of dimensions is being considered:

therefore:

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The true or logarithmic strain is of general application and is suitable for both small and large deformations.

Example:

If we stretch a rod with the length of 1000 mm by 10 mm, then ε = 10: 1000 = 0.01 and φ = ln (1010: 1000) = 0.00995. The error is therefore negligible, so we can count with the proportional linear strain. However, if we stretch a rod with the length of 1000 mm to the length of 10000, for example, by rolling or by drawing, then ε = (10000-1000): 1000 = 9, but φ = ln (10000: 1) = 2.3. We therefore end up with completely different numerical values. The use of the proportional linear strain is not mathematically justified and it is therefore incorrect. In practice, an area reduction is used in such cases, it is expressed in %.

Expression of deformation by means of deformation coefficients has also become common in technical practice:

- coefficient of compression

- coefficient of widening

- coefficient of elongation

The law of volume constancy (see Chapter 3.4) implies that:

The relationship between the true strain and the proportional linear strain can be also expressed as follows:

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Uneven deformation

The diagram of the main deformations gives a somewhat idealized representation of the deformation processes according to which deformation proceeds evenly in the formed body. There is always an uneven deformation in the technological forming processes and the distribution of the deformation in the cross-section varies.

3.4. The Basic Laws of Plastic Deformation

1) The law of volume constancy: In large plastic deformations the change of the volume is negligible, a small change of volume can occur only as a result of the closure of voids, especially in the forming of a cast structure. There is therefore an increase of density (specific weight) of the material.

Note: Substances may have three types of states of matter: solid, liquid and gaseous. In general, at a given temperature and pressure solids do not change either their shape or their volume, the liquid state changes the shape, and the gaseous state changes both shape and volume.

This law can be expressed mathematically by the equation:

where φ 1,φ2 ,φ3 are the real main logarithmic strains. Therefore, it applies that the sum of the logarithmic strain degrees in three main directions of the deformation is equal to 0.

The above given mathematical proposition indicates that the sum of the real - logarithmic strains in all major directions where there are only linear strains is equal to 0.

2) The law of similarity This law has to be respected in physical modelling, for example, if a specific forming technology is being tested in laboratory conditions. An experiment carried out in a laboratory is similar to the actual process only if conditions of similarity are met: the geometric, mechanical and physical similarity must be observed.

The geometric similarity: i.e. the proportion of the corresponding deformed surfaces on similar bodies is constant and it is equal to the coefficient of similarity.

Note: If a cylindrical body is upset in the manufacturing process, then under laboratory conditions a cylinder is chosen for rolling. If a method of forming a prism body is being examined, then the model is again a prism with the same proportion of sides.

The mechanical similarity requires that:

a) the relevant specific pressures are of the same intensityb) the coefficients of friction on the contact surfaces are the same

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c) the main stresses are of the same intensity, they must have the same index (direction) in a coordinate system which has been selected in the same way

The physical similarity assumes that:

a) both bodies have the same chemical and structural composition and phase stateb) the deformation rate and the temperature in deformation are the samec) the stress in both bodies is distributed similarly

All of the above given conditions cannot be fully adhered to in practice, it is necessary to analyze what error can be expected if any of these requirements fails to be observed.

Definition:

If two geometrically similar bodies are formed, it is possible to determine the ratio of forces and work provided there is slow pressing and friction is neglected and provided the force Fm for compressing one body is known (Fig. 3-8).

a ... the linear coefficient of dimension extension

... the force and work for the deformation of a large and a small body

The real ratios are, however, more complex, and tests show that the forces for (pressing) forming of a large body tend to be relatively lower (a lower cooling effect) because the resistance to forming increases with the decreasing body dimensions.

26


Figure 3-8 The geometrical similarity of bodies

3) The law of the least resistance

During plastic deformation particles of the material move in the direction of the least resistance because it is energetically favourable.

An observation of how the shape of an upset prism changes, while considering friction on the contact surfaces of the tool and the body, can serve as an example of the validity of this law. The originally rectangular base of the prism (Fig. 3-9) changes into a shape which is depicted with the dashed line. After further upsetting, the outline of the transverse cross-section of the body gradually assumes the shape which is characterized by the smallest perimeter, a circle.

Figure 3-9 The law of the least resistance

4) The law of the independence of positional (potential) deformation energy on the mechanical deformation diagrams.

The law is based on the theory of plasticity using the hypothesis of the energy condition of plasticity. During the deformation the body accumulates potential energy of deformation. At the given conditions (temperature, deformation rate), this energy, per unit of volume, is a constant quantity independent of the diagram of deformation (i.e. it does not depend on the change of the body shape).

27


5) The law of elastic unloading of a plastically deformed body

If the plastic deformation is interrupted by unloading and then by repeated loading, and the nature and method of loading do not change, the diagram of the dependence of deformation on stress preserves its original shape.

In practice, this means that an elastic deformation occurs after a plastic deformation of the body and its unloading. Therefore, the dimensions, for example, of a forging do not exactly match the dimensions of the cavities of the die.

6) The law of shear stress

The plastic (ductile) deformation can occur only if the shear stress in the body reaches a certain level which depends on the nature of the body and on the conditions of the deformation (temperature, deformation rate, deformation size, diagram of the main stresses).

7) The law of additional stresses

An even deformation does not usually occur during plastic deformation (especially by compression), the individual parts of the formed body undergo different changes in dimensions during forming. A change of dimensions in one area causes a change of dimensions in another area. This mutual influence of the individual areas is manifested by the emergence of additional stresses.

Definition:

In the course of any plastic change of the shape of a material, there occur additional stresses which

try to reduce its dimensions, i.e. there occur additional compressive stresses. In layers and particles

of the body leading to the reduction of its dimensions, there occur, by contrast, additional stresses

which cause the increase of its dimensions, i.e. tensile stresses.

Additional stresses can:

a) remain in the formed body in the form of residual stresses (reduction of fatigue and corrosion properties, possibly problems during machining) after the external force has been unloaded

b) relax in the form of an undesired plastic deformation

c) relax in the form of a disruption of the formed body (cracks, fractures)

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3.5. External Friction

Metal forming is based on the application of a tool on a formed blank. As a result of the application of the force of the tool, the moving metal particles slide along the working surface of the tool, and this causes the formation of friction forces which slow down the sliding movement and thus affect the progress of deformation in the entire formed body. External friction manifests itself in forming both as a passive factor which has an adverse effect on the deformation resistance, force, work and durability of forming tools and as an active factor which makes the forming process possible (the grip of the metal during rolling). A coefficient of external friction μ is introduced for assessing its intensity, it depends on these factors:

a) surface quality of the working surface of the toolb) surface quality of the formed metalc) chemical composition of the formed metald) forming temperature (it is associated mainly with the formation of scales when the

coefficient of friction increases in a certain range of temperatures)e) working rate of the tool (it declines with an increasing rate)f) lubricant

4. Deformation Resistance, Forces and Work Required for Forming

Deformation resistance refers to the stress on the contact surface between the formed body and the tool which is necessary for the formation of plastic deformation.

The deformation resistance σd is determined by the product of:

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THE STUDENT KNOWS:

Types of stress in the formed body

Deformation in the formed body

Basic laws of plastic deformation

External friction




Stress and strain

Basic laws of plastic deformation

External friction


where σp is the natural (basic deformation resistance, yield strength) deformation resistance (MPa) and Qσ is the so-called forming factor. The natural deformation resistance Qp characterizes the resistance of the metal itself against deformation in the uniaxial state of stress under certain thermo-mechanical conditions

where T is the temperature of the forming, ε is the size of the deformation and is the deformation rate. It corresponds to the value of stress intensity (effective stress – see the energy condition of plasticity). The forming factor Qσ expresses the overall effect of all factors in the technological processing (state of stress, external friction, uneven deformation, etc.)

4.1. Determination of the Deformation Resistance in the Case of Upsetting a Circular Plate

The case of upsetting a cylindrical body between straight anvils is a good example for understanding the mutual relationships and connections between the deformation resistance and the forces which are necessary for plastic deformation. In practice, the upsetting technology is used as a basic forming operation of free forging in the production of circles and casings and as an intermediate upsetting operation for increasing the forging effect or reducing the anisotropy of mechanical values.

Approximate equations of equilibrium and the condition of plasticity are used in calculations. The external forces from the forming tool - anvils - are put in equilibrium with the internal forces. Due to the uneven distribution of stress and deformation in the body it is necessary to characterize the body by a delimited spatial element of an infinitesimal thickness. In this case the cylindrical body represents an element in the shape of a hollow cylinder of thickness dx and of a width delimited by the central angle α (Fig. 4-1).

30


Figure 4-1 Upsetting of a circular plate

The element of thickness dx, inner radius x and height h is affected by stress σ1 which is caused by the forming tool. The stress σ2 affects the element in the radial direction. This stress is given by the resistance of the material which “resists” plastic deformation seeking to increase the diameter of the body. The stress σ3 is active in the tangential direction. Due to the axial symmetry of the cylinder the radial and tangential stresses are identical in their intensity:

The equation of the equilibrium of forces is generally determined by the sum of all forces acting in one direction on the delimited element. In this case, the equation of the equilibrium in the direction of x, i.e. in the direction which is at a right angle to the axis of the cylinder (plane A-A) will be solved. The following applies:

,

31


where is the frictional stress between the anvil and the formed body. This stress can be determined as a product of the coefficient of friction and the compressive stress (Coulomb's law):

The following mathematical rules will be used for further adjustment of the equations:

a) applies in very small angles (unit: rad)

b) the multiplication of differentials (infinitesimal quantities) is equal to zero:

After modification:

The following applies from the condition of plasticity:

where σp is the constant of plasticity (which at small deformation rates - to 1 s-1 – corresponds to

the value of the yield strength under the given conditions of forming with respect of the temperature and deformation rate, alternatively the yield strength p).

Another solution by means of the analytical method presupposes a simplifying consideration that the individual compressions are very small, therefore σ2 is very small and it is ignored. The author of this consideration is Siebel, according to him therefore,

And after integration:

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The integration constant is determined from the condition that the radial stress σ2 on the external surface of the cylinder is equal to zero.

The following applies in

therefore

.

After substituting

The resistance in the individual sites of the upset block is linearly dependent on the x coordinate (on the perpendicular distance from the axis of the cylinder).

Substitution into the condition of plasticity:

The pressure distribution on the surface in the upsetting of the cylinder shows a linear dependence (Fig. 4-2) with a maximum value in the centre of the contact surface. The stress σ1 has the meaning of the deformation (forming) resistance σd, which is also designated as po

33


Figure 4-2 Seemingly even distribution of compression on the contact surface during upsetting

In practice, when calculating the force necessary for forming, the compression is taken into consideration as if it were evenly distributed on the whole area. A certain seemingly evenly distributed compression poz is therefore used. In determining the intensity of poz, the notion that the volume of a cone constructed above the surface of the cylinder which has the height of pomax – p is equal to the volume of the cylinder which has the height of poz΄ is used.

(Note: The volume of a cone or pyramid is calculated as where S is the area of the base and v is the height)

The following applies in accordance with Fig. 4-2:

for x = 0

and at the same time

therefore

or:

34


Due to its simplicity and easy orientation this Siebel’s equation is used for calculating the force which is needed for carrying out the upsetting operation. The upsetting force is calculated by multiplying what seems to be an evenly distributed compression by the area on which it operates:

In hot forming the coefficient of friction μ is chosen usually at approx. 0.3.

4.2. The Deformation Rate

The deformation rate refers to a change in deformation which occurred in a specific period of time.

This rate is not the same as the rate at which the body deforms itself. This rate also depends on the dimensions of the body.

If the degree (change) of deformation, in the case of upsetting, is expressed by an elementary change of the proportional linear strain

,

then the ratio of this degree and the deformation time dt states the deformation rate.

where v is the instantaneous speed of the forming tool (anvil) and h is the instantaneous height of the upset blank (fig. 4-3).

By analogy, in elongation the following applies

where l is the instantaneous length of the elongated blank.

35


Figure 4-3 Elementary deformation in upsetting (left) and in elongating (right).

The movement speed of the forming tool v is determined according to the type of the used forming machine.

Forming tool v [m/s]

Hydraulic presses

Crank and eccentric presses

Hydraulic forging machines

Drop hammers

Drop hammers with a high v of impact

0.025 – 0,5

0.3 - 0.6

0.3 - 0.6

5 - 8 (10 - 12)

20%

36


Table 4-1 The speeds of movement of the forming tool for different types of forging machines

The deformation rate, in fact, expresses the rate at which two transverse cross-sections move towards each other. The deformation rate influences the intensity of the deformation resistance especially in hot forming. The deformation rates for individual types of forging machines are listed in Table 4-2.

Forming tool

Hydraulic presses

Crank and screw presses

Drop hammers

0.01 - 10

4 - 25

40 (-100)

Table 4-2 Deformation rates for different types of forging machines

4.3. The Deformation (Forming) Work

37


Figure 4-4 The work in upsetting the body

Assuming a smaller degree of deformation (plastic deformation) during which the deformation resistance does not substantially change, and it is therefore possible to use its mean value, and in which the final shape of the upset cylindrical body will be still of a cylindrical form, it is possible to calculate the ideal deformation work required for the deformation of this section.

The elementary work dA in pressing the blank by the value of dx at the distance x from the beginning of the upsetting can be determined from the equation (Fig. 4-4):

Sx ... cross-section at the distance x

p0 ... deformation resistance

The size of the cross-section Sx in any position can be expressed from the condition of volume constancy of the upset blank

,

where V is the volume of the upset body and h0 the initial height of the upset body.

Using integration in the limits to an equation for the deformation work in upsetting a blank from the initial height h0 to the final height h1 is achieved, provided that the deformation resistance does not change and has therefore the mean value poz:

The calculation is carried out by means of a substitution:

and after derivation

In an integration using substitution the integration limits must be changed according to Table 4-3.

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Table 4-3 The change of the integration limits in substitution

The calculation of the integral:

.

The calculation of the work:

Thus calculated work represents the ideal deformation work Aid.

The ratio of the ideal deformation work Aid and the real work Askut is called the deformation efficiency

Empirical relationships are also used for determining the deformation work with regard to the deformation resistance, e.g. - according to Storozhev

where d0, h0 and d, h are the dimensions of the body before and after upsetting.

39

Change of limits for integration:

x 0 h0 – h1

z h0 h1

THE STUDENT KNOWS:

The definition of deformation resistance

The calculation of deformation resistance, force and work in upsetting




Deformation resistance definition

Calculation of deformation resistance, strength and part of the operation upsetting


5. METALLURGICAL BASICS OF HEATING

Properly conducted heating increases formability and reduces deformation resistance which has a positive effect on the energy aspect of forming, on the durability of forming tools and on the production rate of the forming process. The effect of accelerated diffusion also helps to improve the quality of the heated steel: the chemical composition of the structure homogenizes, precipitates – and possibly also inclusions - are partially or completely dissolved, and the quality of grain boundaries is improved.

The determination of the optimum heating depends on knowing selected physical quantities and their dependence on temperature. These include: the coefficient of thermal conductivity, specific heat capacity, density, coefficient of temperature conductivity, thermal expansion and mechanical characteristics.

5.1. Physical Quantities Affecting the Heating of a Metal

The coefficient of thermal conductivity

The thermal conductivity coefficient λ [W m-1K-1] depends on the oscillation of molecules, on the distribution of atoms in the lattice and on the free path of electrons. The coefficient of thermal conductivity is further negatively affected by an increased density of lattice defects, by a casting structure, a cold formed structure or a quenched structure. Steels can be divided into three groups according to the influence of temperature on the thermal conductivity coefficient:

1) the coefficient of thermal conductivity significantly decreases with the temperature (low-carbon steel, pure iron)

2) the coefficient of thermal conductivity decreases only slightly with the temperature or it does not change at all (medium-alloy steels)

3) the coefficient of thermal conductivity slightly increases with the temperature (high-alloy steels, but also alloys of Cu and Al).

The higher the thermal conductivity coefficient, the faster the heat transfer from the surface into the core of heated body, the smaller the thermal stress and the shorter the heating time.

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Heat capacity

The specific heat capacity c [kJ kg-1K-1] depends significantly on the temperature, its maximum occurs at the temperature of the phase transition. The dependence on the chemical composition of steels at a room temperature is small.

The higher the specific heat capacity (specific heat), the longer the heating time and the greater the energy intensity of the heating.

Note.: The mean specific heat of high-carbon steels for 0-100 °C is:

where wc is the mass concentration of carbon in steel (%).

Specific heat of other metals and alloys (see. physical tables):

Ex.: Al = 8.79

Fe = 5.02 - 5.86

Pt = 0.134 – 0.129

Specific weight (density) of metals

The higher the density ρ [kg m -3 ] , the longer the heating time and the greater the energy intensity of heating.

Note.: Pig Fe: - at a room temperature

Melt Fe: - at 1530° C

It is possible to determine the specific weight in steel also by a calculation according to the chemical composition:

(contents of elements in %)

The values: are used for practical calculations in carbon and alloy steels at t = 0 - 1100° C

Density also depends on the structure of steel according to the formula:

The coefficient of temperature conductivity

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It expresses the ratio of the supplied heat to the heat required for the heating of the body [m2 h-1] :

The higher the coefficient of temperature conductivity, the shorter the heating time and the lower the energy intensity of heating.

Temperature linear expansion

The higher the temperature linear expansion α [K-1], the greater thermal stresses in the heated body and the lower the heating rate.

Note.: In pure iron the temperature linear expansion is The influence of carbon is almost negligible.

Austenitic steels are characterized by the highest linear expansion:

Mechanical properties

The plastic properties of steels also change significantly according to the temperature (Fig. 2-7, p. 14). Steels are divided into three groups according to their drawability A:

- steels with high plasticity: A > 25%

- steels with medium plasticity: A > (15 - 25%)

- steels with low plasticity: A < 15%

The higher the plasticity, the greater the heating rate and the less sensitive steels are to thermal stress.

5.2. Thermal Stress during Heating

In heating or cooling thermal stresses occur as a result of the uneven temperature field, and in some cases these stresses can have a limiting character for the rate of heating. In the specific conditions of heating, thermal stresses occur in the first stage of heating at temperatures from 0-550°C. Above this temperature the steel becomes plastic, stresses are reduced and disappear.

The following relationships apply with regard to the intensity of the thermal stress which does not threaten the coherence of the body:

42


where is an allowed stress in MPa, is the coefficient of linear thermal expansion, E is the modulus of elasticity in tension, K is the coefficient depending on the shape (form) of the detail (blank), t is the average temperature of the body and tx is the temperature in the monitored section.

Note.:

Allowed heating rate: In heating a cold material, the following procedure can be generally used:

Allow the temperature gradient in the range of 1.2 ÷ 3.4 ° C on 1 cm of the diameter

In heating hot ingots it is possible to allow a temperature gradient in the range of 6 ÷ 10 ° C on 1 cm of the diameter.

Classification of steels according to the heating mode:

Classification of steels into 5 groups:

1) non-alloy steels c < 0,4 %

2) non-alloy steels c < 0,4 ÷ 0,7 (possibly low or medium-alloy c = 0.5)

3) eutectoid and hypereutectoid non-alloy steels (possibly low-alloy or medium-alloy tool steels)

4) high-alloy tool steels

5) high-alloy steels of class 17, manganese steels, etc.

5.3 Technological Principles of Heating of Metals

The heating of a blank is carried out as an operation preceding a forming process or as heating for subsequent heat treatment.

The upper forming temperature

Determining this temperature depends on respecting entirely contradictory phenomena: formability improves and deformation resistance decreases with the rising temperature which is positive, but at the same time oxidation and decarburizing of the surface layers intensify and the susceptibility to grain growth, overheating and burning of steel increases. In blanks with a casting structure the upper forming temperature is somewhat increased which supports homogenization of cast steel.

The region of the upper forming temperatures is shown in Fig. 2-6 (p. 13). The top forming temperature usually ranges from 150 to 200°C under the solidus curve.

At high temperatures under the solidus curve there is a risk of steel overheating and burning.

The lower forming temperature

This temperature has a decisive effect on the resulting properties of wrought steel. The following principles must be met at reaching the lower forming temperature:

43


a) the steel must show sufficient formabilityb) the deformation resistance of the steel must be in accordance with the energy quantities of the

forming machinesc) the required properties of the steel are the result of an appropriate combination of the lower

temperature, of the last reduction and of the subsequent method of cooling.

Due to the entirely different properties of ferrite and cementite, the lower forming temperature is determined independently for hypoeutectoid and hypereutectoid steels.

Hypoeutectoid steel

The optimum forging temperature for hypoeutectoid steels is approx. 50° above the A 3 temperature.

Completion of the forming procedure high above the A3 temperature supports static recrystallization and may lead to the coarsening of the grain. Forming between A3 and A1 temperatures is also not recommended because there is not only an increase of stress in the two-phase structure, but also deterioration of formability, segregation, and anisotropy of mechanical properties becomes more pronounced.

Hypereutectoid steel

The lower forming temperature is just above the A 1 temperature in the region of austenite and eliminated secondary cementite. The purpose is to disrupt the network of cementite along the boundaries of grains which helps further heat treatment. The conditions of forming depend on the shape of cementite – the globular shape does not cause any problems in forming. If the lower forging temperature were above Arm, then brittle cementite would be eliminated in the form of a network along the boundaries of grains (between temperatures Arm and Ar1).

The forming temperatures of non-ferrous metals and alloysThe forging temperatures are usually chosen so that the alloy will be homogeneous and the temperature will affect the intercrystalline cohesion. The interval of forming temperatures is more narrow in most cases of these materials, and the temperatures depend on a very different recrystallization ability of individual alloys.

5.4. The Accompanying Phenomena of Heating

Loss by burning

Loss by burning is a consequence of surface oxidation of the heated body in a furnace atmosphere. The formation of scales is limited by the diffusion of iron atoms and takes place through the action of free oxygen, carbon dioxide and water steam. Scales are formed from the temperatures of 600-700°C, at first the formation proceeds almost imperceptibly, but above the temperature of 1000°C the intensity is very high. The scaling results in a loss of metal, in a decline of the durability of the furnace and forming tools, in an increased risk of defectiveness because the scales are pressed into the surface of the formed blanks, in the necessity of removing the scales prior to further cold forming or machining. The reduction of scaling can be influenced by improving the thermal work of the

44


furnace, by complete combustion (suitable burners), by accelerating the heating, by using effective insulation materials, etc.

These measures can reduce the loss by burning by 20-50%.

Heating in protective atmospheres, in salt baths or heating in the lithium atmosphere also affect the quantity and structure of formed scales.

Decarburizing

Decarburizing reduces the content of carbon in the surface layer which leads to reduction of strength and fatigue properties. The decarburized layers deform plastically upon loading, while the remaining material deforms elastically which after a certain time leads to the formation of surface cracks.

Overheating and burning steel

Overheating of steel occurs when the steel is heated just above the upper forming temperature where the austenitic grain coarsens. Strong coarsening of the austenitic grain during heating results in rapid deterioration of the toughness of the steel, especially after quenching and tempering. Correction is possible by full annealing.

In the case of high overheating in an oxidizing atmosphere there occurs rapid diffusion of oxygen along the grain boundaries and their oxygenation. In addition, low-melting eutectics stored in the intercrystalline matter (along the boundaries of grains) are melted at high temperatures. This leads to a complete loss of plastic properties and toughness – the so-called burning of steel. This state cannot be remedied by heat treatment.

the surface of the product, the different elements (metals and non-metals) it is possible to achieve different mechanical or physico-chemical properties of the surface and the core. These properties can be achieved in principle by two ways: ... ....

45

THE STUDENT KNOWS:

The definition of deformation resistance

The calculation of deformation resistance, force and work in upsetting


M.Žídek, V.Dědek,B.Sommer: Tváření oceli. SNTL 1988

Z. Petržela, J. Kučera, R. Březina: Technologie slévání, tváření, svařování. VŠB v Ostravě, 1987.

J. Procházka, M. Zahradník, M. Němec, J. Novotný: Technologie slévání, tváření a svařování.ČVUT Praha, 1982


Deformation resistance definition

Calculation of deformation resistance, strength and part of the operation upsetting


6. THE CLASSIFICATION OF METAL FORMING PROCESSES

Forming processes can be divided according to their temperature into cold forming and hot forming, or according to the state of stress into flat forming and volume forming.

The technological procedures of hot forming include:

1) Forging: - free forging (hydraulic presses, drop hammers)

- die forging (dieing machines, screw and crank presses, forging rollers, etc.)

2) Rolling: - for mass production of objects with simple shapes (plates, sheets, circular cross-sections; wires; tubes; rails, beams, etc.)

3) Extrusion: - for the production of rods, profiles, tubes

The technological procedures of cold forming include:

1) Rolling: - similar to hot rolling (fine sheets and strips)

2) Drawing: - wires, rods, profiles, tubes

3) Pressing: a) shearing (shearing, punching, blanking, etc.) the tool overcomes the breaking strength of the material

b) bending, bulge forming, curling

c) drawing of vessels

d) volume forming - extrusion

With regard to the state of stress, forming processes are divided into volume forming which includes:

46


1) Forging2) Rolling3) Drawing of wires and profiles4) Extrusion

The flat forming procedures include:

1) Rolling of sheets and strips2) Sheet metal drawing3) Shearing (shearing, punching, blanking)4) Bending, bulge forming, curling

47

THE STUDENT KNOWS:

Methods of forming






Forming processes


7. FREE FORGING

Forging refers to hot volume forming carried out by an impact or by a calmly operating force. Forging has a rich history – manual forging with a hammer and an anvil has been known to mankind for several thousand years. It is a discontinuous way of forming and the forging product has a required shape, a favourable macrostructure, advantageous microstructure and improved mechanical and physical properties. Forging can be used for processing of almost all metals. The aim of free forging is to obtain a blank of the required shape with the typical formed structure characterized by the so-called degree of forging. The aim of forging is the removal of the non-homogeneous coarse cast structure and of metallurgical defects in ingots which reduce formability and physical and mechanical values and properties of the metal. As a result of hot forming, the shape of primary crystals, dendrites, changes (they are disrupted) and fibres are formed. Because dynamic recrystallization sets in, deformed grains change into new and finer ones and the texture disappears. However, impurities (including carbides and cementite) in the surface layers of crystals do not undergo recrystallization and therefore they do not change their shape – a fibrous (segregated) structure is formed (Fig. 7-1) which cannot be removed by any forming or heat treatment. The fibrosity has an effect on the anisotropy of properties (mechanical properties, ductility, ...) in the direction of fibres and in the transverse direction and changes according to the degree of forging “Pk” (the practical value of forging is 3 to 4) and according to the degree of deformation. Therefore, the correct direction of fibres must be always remembered in hot forming. The direction of the highest normal stress should correspond to the direction of the fibres and the tangential stress should be perpendicular to it. The fibres should not be disrupted and they should agree with the shape of the part.

The problems of forging are connected to the influence of friction between the forming parts of the tool and the material which causes a barrel-like character of the forging product or bulging in long bodies and also different degrees of forging in the individual regions of the forging product (rotation is necessary) - the so-called forging cross.

48


Figure 7-1 An example of a fibrous texture after forging

Free forging is a process in which the material is processed sequentially using multi-purpose tools and instruments. The free forging operations can be divided as follows:

1. upsetting – the cross-section of a blank is increased at the expense of its height, or rather local upsetting is performed (Fig. 7-2),

2. elongation – characterized by extending the length of the blank with the simultaneous reduction of its cross-section (Fig. 7-3),

3. joggling – elongation of the delimited parts of the blank while preserving the coaxiality of all of its parts (Fig. 7-4),

4. other operations – necking (Fig. 7-4, 7-5), punching with a full (Fig. 7-6) and a hollow mandrel, etc

3. flattening on a mandrel – used in forging rings when both the inner and the outer diameter and the height of the ring are increased at the expense of the thickness of the wall (Fig. 7-8)

6. forging on a mandrel – elongation on a mandrel (Fig. 7-7) when a hollow (punched) forging product is extended in the direction of the longitudinal axis of the mandrel while at the same time the inner diameter and the wall are decreased (length forging – hollow bodies); flattening on the mandrel (diameter forging - rings)

7. cutting (burring), tipping, planishing

49


According to ČSN EN free forged products are divided into forged rods, longitudinal forgings (e.g. cylinders, crankshafts, etc.), discs and circular plates, rings and hollow bodies. All of them are blanks which have an uneven scaling surface with forging allowances.

Hammer forging is carried out either on presses or on drop hammers.

Figure 7-2 Upsetting of an ingot with a pre-forged handling pin

Figure 7-3 Extension into a quadrate

50


Figure 7-4 Joggling

Figure 7-5 Necking

Figure 7-6 Punching by a full mandrel

51


Figure 7-7 Extending on a mandrel

Figure 7-8 Flattening on a mandrel

52

THE STUDENT KNOWS:

Operations of free forging






Free forging operation


8. DIE FORGING

Die forging is used for manufacturing a large number of components with the same shape from steels or formable alloys. A die is usually a two-part tool. The main advantages of die forging include high effectiveness and easy operation. The forging products are, however, limited in their size and weight.

The heated material is formed in the cavity of the die whose shape is identical to the shape of the forged product. The dimensions are, however, increased by the value of the shrinkage of the cooled forging product. In contrast to free forging, die forging achieves more exact shapes of the forging product. Precision and quality of the surface can be significantly improved by subsequent calibrating so that machining does not have to be used. Die forging achieves a high degree of forging and the flow of fibres follows the outline of the forging product. The procedure of die forging is as follows: the starting blank which has been heated to the required forging temperature is inserted into the cavity of the die and it is subjected to compression or impacts of the forming machine (Fig. 8-1). Die forging uses drop hammers (forging by impact) or presses (forging by quiet compression).

Figure 8-1 The forging procedure in a single-cavity die on the drop hammer

53


Dies can be divided into

1) single-cavity (simple) dies - for simple shapes of forging products which do not need pre-forging (in the case of more complex shapes pre-forging is carried out outside the die)

2) multi-cavity dies - progressive dies – for more complex shapes of forging products

The cavity of a die can be filled either by extrusion or by upsetting – with upsetting being the better option. In drop hammer forging the die cavity is filled gradually during several impacts of the ram, in press forging the forging product is made in the course of one stroke or several strokes (a progressive die). The forging are often combined in multiple cavities. After the completion of forging, the forging products are connected between themselves by a burr, they are separated after the burr has been cut off. Friction presses can be also used for forging. This concerns primarily forging products of rotary shapes which are forged in the vertical position.

The following rules apply basically for more complex shapes of forgings:

a) a metal should not be deformed in the transverse and longitudinal direction at the same time in one cavity

b) the material is first divided in the longitudinal direction and then in the transverse direction

c) the shape of the pre-forging should be designed so that during forging the particles can move in the cross-sections and the pre-forging will have a rotary shape

In die forging the number of forging cavities depends on the shape of the forging but also on the shape of the source material. It happens only rarely that a single cavity suffices for the forging of the product. The individual cavities are often placed in a common block of steel – a tool which is advantageous for the work with the drop hammer. The transfer of the forging from one cavity to another does not take too long and the forging does not cool down quickly. In the case of more complex shapes it is therefore necessary to forge in more cavities which will ensure flow of the material in the cavity of the die – forging in progressive dies.

The progressive die can be sometimes constructed by means of replaceable shape inserts of a rectangular or circular shape. This leads to significant saving of the material of the die. The die forging without burrs is referred to as the closed-die forging. It is very demanding because the volume of the material must be set very precisely. Figure 8-2 shows an example of a progressive die for a drop hammer. In a progressive die the cavities are not located in a line according to the technological procedure. The forging (finishing) – the last – cavity is located in the middle so that its centre of gravity is near to the centre of gravity of the whole block. This is because the force (or energy) for the forging of the products is higher than in the forging of the blanks, the forging product cools down and thus its deformation strength increases, and also because the forging product together with its burr groove has the largest surface. Other cavities are distributed around this finishing cavity.

INCLUDEPICTURE "http://www.ksp.tul.cz/cz/kpt/obsah/vyuka/skripta_tkp/sekce/03-kovani/10.jpg" \* MERGEFORMATINET

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Figure 8-2 The progressive die for a drop hammer (on the left: cavities of the die: 1 – extending, 2 – dividing, 3-pre-for-ging, 4-forging, 5 – finishing cavity; on the right: a technological procedure: a – blank, b – lengthening, c-dividing, d-bend-ing, e – forging in the 1st finishing cavity, f-post-forging)

The cavities of the progressive die can be divided into:

a) pre-forging cavities, in many cases these are open cavities

b) finishing closed cavities

The pre-forging cavities are used for transferring material (preliminary forming) into the places of the more complex future shape of the forging

The pre-forging cavities include:

- extending- upsetting- dividing (open or closed)- narrowing- bending- shaping

The last finishing (final) cavity is fitted with a burr groove around the outline of the forging shape (Fig. 8-3). Its cross-section for the selected forging machine is shown in the picture. The narrow part is called the bridge, the wide part is called the tank. The function of the product is twofold. On the one hand to hold the excess material because the cavity of the die must be fully filled, and on the other hand to affect the flow of the material inside the die when the increased resistance of the fast cooling material in the narrow part of the burr groove leads to perfect filling of the upper part of the die (it ensures the “climb of material”). The burr is afterwards removed by cutting.

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Figure 8-3 The burr groove in the die (on the left for the drop hammer, on the right for the press)

The final treatment of the forgings therefore includes the cutting of the burr (Fig. 8-4), possibly cutting the membranes in the holes, straightening of the forging, scales are removed from the forging (pickling, blasting), it is heat treated (full annealing ) or subjected to cold calibration (Fig. 8-5).

Figure 8-4 Treatment of forgings: cutting of the burr

Figure 8-5 Treatment of forgings: calibration

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THE STUDENT KNOWS:

Die forging






Die forging operation


9. ROLLING

Rolling refers to a continuous process in which the formed material is deformed between rotating working rolls under the conditions of a predominant all-around compression. The rolled material is deformed between the rolls, its height is reduced; the material is extended in length and at the same time also extended in width and the speed at which the material leaves the mill also changes. The gap between the working rolls is smaller than the input dimension of the material. Rolling is carried out primarily as hot, but also as cold. The process results in the production of a rolled product. According to the position of the rollers and the workpiece rolling is divided into the following types from the point of view of the main deformation:

a) Longitudinal rolling (Fig. 9-1) — the roll axes are parallel; the blank is drawn between the rolls; the direction of the rotation of the rolls is opposite – the rolls rotate “against each other”. The blank is pressed to the required cross-section, the longitudinal axes of blanks and rolls are per-pendicular to each other.

Examples of products: rolled semi-finished products with a rectangular (blocks, slabs) or square (billets) cross-sections, sheets

b) Longitudinal shape rolling: continuous – the shape of the calibre determines the cross-section of the rolled product; discontinuous – the forming is carried out in the calibre made on a part of the roll; periodic – the forming process takes place in the calibre, its shape determines the repeating shape of the product.

Examples of products: profile steel (I, H), rails, rolled rods, wires

c) Cross rolling – the axes of rolls and the workpiece are parallel, the direction of the rotating rolls is identical, the blank rotates between the rollers on its axis, the diameters of the rolled blank change.

Examples of products: moulded shafts, threaded rods, spindles

d) Oblique rolling (Fig. 9-2) – the axes of rolls are not parallel, they form the angle of approx. 5°. The workpiece rotates around its axis and at the same time it moves forward (rolling of seamless tubes). As a result of tensile stresses a void is formed inside the workpiece. It is divided into punching by oblique rolling – the cavity is made with the use of a mandrel, and into oblique peri-odic rolling – the shape of the rolled product is determined by a screw calibre on the perimeter of the rolls.

Examples of products: seamless tubes

e) Flattening – a punched workpiece is flattened by a pressing roll into the required cross-sectionf) Grooving – production of grooves on the surface of the rotating workpieceg) Thread rolling – thread rolls produce a thread on the workpiece

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Figure 9-1 Schematic illustration of types of rolling: A- longitudinal rolling, B1 – longitudinal rolling in a calibre, B2 – lon-gitudinal rolling using forging rolls, B3 – periodic rolling, C to F – different types of cross rolling.

Figure 9-2 Oblique rolling: A – tube rolling, B – oblique periodic rolling (e.g. spheres)

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9.1. The Rolling Train and Mill

The main production unit of the rolling mill plant is the rolling train which includes a comprehensive, interconnected set of machines and machine parts, transport and handling mechanisms which are necessary for carrying out the rolling process. In addition, the rolling train must be fitted also with other equipment, for example, with heating and annealing furnaces, with equipment for cooling, straightening and surface treatment of rolled products. Rolling trains are composed of a varying number of rolling mills into production lines ranging from one to twelve mills, or even more. They are classified most often according to the following aspects:

1) according to the design of the rolling mill and the number of rolls in the mill2) according to the type of the rolled product and the diameter of the work rolls3) according to the rotation of the rolls4) according to the arrangement of the rolling mills

The rolling mill is the basic machine unit of the rolling train in which the forming is carried out. The rolling mill must be firm and stiff but at the same time it must be so simple as to allow an easy and fast replacement of rolls and of other required or damaged parts.

According to the number of rolls, rolling mills are divided into two-high, three-high, four-high, cluster, universal and special mills:

1) two-high rolling mills belong among the most widespread mills and they are characterized by two parallel work rolls (Fig. 9-3 a). The engine usually powers both rolls. The rolls can be non-reversing (continuous) – both rollers turn in only one direction – or they can be reversing (the direction of the rotation changes after each pass of the rolled workpiece between the rolls – rolling of billets)

2) three-high rolling mills are characterized by three parallel work rolls (Fig. 9-3b). The drive is transmitted to the central, fixed roll, the remaining rolls which are usually adjustable are driven by gear.

The Lauth mill represents a special type of a three-high rolling mill. Its middle roll has a diameter of 1/3 smaller than the top and bottom rolls. This roll is towed, i.e. it rotates only as a result of friction. In each pass it leans against either the top or the bottom roll.

The lower and upper rolls are powered. A considerable wear of the middle roll constitutes a disadvantage.

3) four-high rolling mills are characterized by four parallel rolls. The inner rolls are work rolls and their smaller diameter supports elongation and increases the precision of the thickness of the rolled product. The outer rolls are supporting – they prevent the middle rolls from sagging. The work rolls are powered, while the supporting rolls are towed. They are constructed both in the non-reversing and reversing design and they are used for hot and cold rolling of sheets and strips.

4) cluster rolling mills are further divided into:

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a) classic arrangement, i.e. two rolls are working, the other rolls are supporting (max. 20 rolls). The two middle rolls of a smaller diameter are mostly powered. This type of rolling mills enables cold rolling of thin sheets, strips and foils.

b) planetary rolling mills (Fig. 9-3 h) have two parallel supporting rolls of a large diameter and two systems of work rolls which freely-- like planets – run around the supporting rolls which enables the reduction of up to 95% in one pass. They are used in hot rolling of sheets and strips.

5) universal rolling mills are mills with four work rolls (two rolls are in the horizontal position and two rolls in the vertical position). The vertical rollers are used for adjusting the widening, i.e. the width profile is adjusted. The rolled product is of a rectangular cross-section, and the extension in a single passage is higher in this type of the rolling mill than in the regular two-high mill.

Figure 9-3 Rolling mills: a) two-high rolling mill, b) three-high rolling mill c) Lauth three-high mill, d) four-high rolling mill, e) six-high rolling mill, f) seven-high rolling mill, g) twelve-high mill, h) planetary rolling mill, i) universal mill, j) universal mill for rolling wide-flange beams

According to the type of rolled products and the diameter of the work rolls , rolling trains are divided into:

a) billet trains which are used for rolling billets (blocks, slabs, billets) which are used as a blank for finishing mills.

Examples

A slabbing train - a massive two-high mill train equipped with two-high rolling mills with smooth rolls (the first mill is usually universal).

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A blooming train – it is equipped by one or two reversing two-high mills with grooved rolls which are cooled by water.

A cogging train – it processes rough billets into finer billets. It is fitted with 2 x 6 mills behind each other or next to each other.

b) finishing trains which are used for rolling finished products in a very diverse range of sizes and shapes

Examples

a) heavy – a reversing design for rolling heavy shaped and rod rolled products; D = 700 to 950 mmb) rough - for rolling of rough shaped and rod rolled products; D = 650 to 900 mmc) medium - for rolling of medium shaped and rod rolled products; D = 400 to 600 mmd) fine – for rolling of fine shaped and rod rolled products; D = 250 to 350 mme) for rolling wiref) for rolling thick sheetsg) for rolling thin sheets in platesh) for hot and cold rolling of narrow and wide stripsi) universal – for rolling of wide steel with a rectangular cross-sectionj) for hot and cold rolling of seamless tubesk) special for demanding shapes of rolled products (wheels and tires of rail vehicles, rolled products of a changing

cross-section)

9.2. Production of Metallurgical Blanks

The rolling technology of basic metallurgical blanks can be divided into three groups according to the type of product:

a) Sheet rolling

From the point of view of production and consumption, sheets are divided into thick and thin. The standard mentions the thickness of 3. 75 mm as the borderline between the two.

Thick sheets are hot rolled. The train is usually equipped with a reversing two-high mill, in the case of greater widths by a four-high mill or by a non-reversing three-high mill (Lauth mill).

Thin sheets are cold rolled up to the thickness of 0.15 mm. An older method of production was carried out by rolling in several layers on top of each other. This increased the total height of the rolled product and decreased the consumption of deformation forces. The disadvantages of this method include:

1) The sheets get sometimes welded together during rolling and it is difficult to separate them

2) The thickness of the individual sheets is not always the same

Advantages:

1) The possibility of reloading during rolling – i.e. a change in the direction of rolling by 90° and thus a reduction of the surface anisotropy of sheet metal.

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Today, sheets are mainly produced as strips on the so-called wide strip continuous trains and they are shorn into plates after rolling.

b) Rolling of profiles

Profiles are rolled on profile trains. The profile mills are two-high or three-high mills equipped with the so-called profile (calibrated) rolls. The calibres are in the form of perimeter grooves on the rolls.

The calibres can be open or closed when one roll has a groove and the other roll fits inside it with a profile collar.

c) Rolling of seamless tubes

The production of seamless tubes can be divided into three basic operations:

1) Punching of workpieces (by forging or rolling): oblique rolling in which the diameter is reduced and the length of the rolled product is increased is used most widely for punching. The application of rolls whose axes are not parallel leads to tensile stresses in the central part of the billet and these tensile stresses are the cause of internal cracks – therefore of punching. The internal hole has an irregular shape and it is therefore calibrated by a mandrel.

2) Rolling of a punched workpiece (reduction of the diameter, extension). Rolling on a profile rolling mill with the billet placed on the mandrel is used for further reduction of the diameter. The profile rolling mill for tubes which is equipped, apart from work rolls, also with transporting rolls is called an automatic. Another equipment for reduction is the so-called pilger mill in which the rolled product is moved there and back along its axis in the individual stages of the rolling (from there its meaning: “pilger” = “pilgrim”). Slight surface waves in the distance of the rolling step are noticeable on the surface of products rolled in the pilger mill, these waves have to be removed by calibration.

3) Calibration of dimensions

There are several recognized technological modes of producing seamless tubes:

a) the Mannesmann system – long oblique rolls are used for punching, reduction is carried out on pilger mills b) the Stiefel system - punching is performed on short oblique rolls, the subsequent rolling is carried out on trains

with pilger mills with longitudinal and cross calibration rolling

c) the Erhardt system – punching of blanks by forging, i.e. by a mandrel under a press, reduction and calibration are carried out on a continuous train equipped with many pairs of calibrated discs.

9.3. The Conditions for the Grip (Drawing) of the Rolled Workpiece

The grip angle

The grip angle is determined by the angle between the connecting line where the material enters between the rolls and the centre of the roll and the connecting line of the point where the material

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comes out of the gap in the rolls and the centre of the roll. It is designated by the symbol α - (see Figure 9-4, the ASC angle). In rolling the height of the rolled workpiece is reduced by the so-called removal which is expressed by the equation:

,

where H1 is the input height of the rolled blank and H2 is the output height of the rolled product.

Figure 9-4 The grip angle

The size of the grip angle depends on the diameter of the roll D and on the difference between the input and the output height of the blank – the so-called removal. The following applies in determining the grip angle:

Where h0 is the input height of the blank, h1 is the output height of the blank and h is the removal.

If the diameter of the roll is given and the removal is selected, it is possible to determine the grip angle α. On the other hand, if the grip angle and removal are given, it is possible to determine the diameter D of the roll by means of the equation:

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Note: The maximum gripping angle varies according to the type of the rolling mill. In billet rolling mills it ranges from 27 to 34 °, in profile trains from 22 to 24°, in hot rolling of sheets the angle of 15 to 22° is used, in cold rolling this angle is very

small, in the range of 3 to 8°.

The Condition of Drawing the Workpiece Between the Rolls (Condition of Gripping)

The material is loaded into the rolls at a specific rate. A compression force N which is at a right angle to the surface of the roll is formed when the material gets into contact with the rolls at the point A which represents the contact edge of the billet and the roll. A force of the same intensity but of the opposite direction acts against it according to the action-and-reaction principle. The force acting on the surface of the billet in point A can be divided into two mutually perpendicular constituents – a vertical constituent and a horizontal constituent. The horizontal constituent tends to push the rolled piece from the roll; the vertical constituent leads to the reduction of the height of the piece (it helps the removal of the machine).

The friction force T which is at a right angle to the compression force N is formed as a result of the friction between the rolled workpiece and the rotating rollers. The following relationship applies between the friction and the compression forces:

,

where f is the coefficient of friction between the roll and the blank. The friction force T can be once again divided into two constituents: the horizontal constituent draws the blank between the rolls and the vertical constituent leads to the reduction of the height of the blank.

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Figure 9-5 The condition for drawing the blank between the rolls

The following three cases can occur in forces acting in the horizontal direction:

1) ….. the blank will not be gripped by the rolls

2) ….. a limit case (the blank may or may not be drawn between the rolls)

3) ….. the blank will be drawn between the rolls.

By modifying the inequality the following is reached:

The expression can be substituted by the value f ( )

And therefore:

Definition of the gripping condition:

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The rolling workpiece may be pulled between the rolls only if the coefficient of friction between the roll and the workpiece is higher than the tangent of the grip angle.

In a graphical analysis of the condition of gripping the blank is drawn between the rolls if the direction of the resultant of forces N and T (designated by the letter R in Figure 9-5) leads between the rolls.

The coefficient of friction is influenced by:

1) direct proportion:a) by the material of the rolls and the roughness of their surface (artificially roughened rolls on

blooming trains)2) indirect proportion:

a) by the surface temperature and the chemical composition of rolling workpiece b) by the peripheral speed of the rolls

Conclusion - The smaller the diameter of the rolls and the rougher their surface, the higher the removal (and thus also the productivity of the process). With regard to stiffness, the rolls of a small diameter can be used only with smaller widths of the rolled material (otherwise it is necessary to use the supporting rolls), the rough surface of rolls is not suitable for finishing operations because the surface of the rolled product would be damaged by it.

10. wire drawing, profiles and tubes

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THE STUDENT KNOWS:

Ways of rolling

The condition of drawing the blank between the rolls






Rolling operations

The condition of drawing the blank


10. Drawing

10.1. WIRE DRAWING

Drawing is a process of pulling a blank through the hole of a die (Fig. 10-1) during which the cross-section is reduced and the length increased with a simultaneous change of mechanical properties (increase of breaking strength and yield strength). It makes it possible to achieve exact dimensions and shapes, and the quality of the surface improves (fatigue properties). The tool is immobile, the complete deformation is carried out gradually in several consequent dies (10-20 passes). It is a cold process. If plasticity is exhausted and the required dimension still has not been reached (diameter of the drawn wire), intermediate annealing must be carried out.

Figure 10-1 A schematic illustration of the die.

The geometry of the die whose work part is made of cemented carbides (hardmetal) or synthetic diamond is shown in Figure 10-2. Sufficiently effective lubricating must be ensured during drawing; the lubricant must reduce the coefficient of friction, separate the blank and the die from each other, conduct heat and ensure a smooth surface. In the lubricating cone, lubricant is placed on the surface of the drawn blank (wire). The deformation itself takes place in the drawing cone which is characterized by the draw angle (8-16°); the calibrating cone ensures precision of dimensions, reduction of internal stresses after drawing and sufficient durability of the die.

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Figure 10-2 Zones in the die: 1 – input cone (loading), 2 – lubricating cone, 3-drawing cone, 4-calibrating cone, 5-output cone

The deformation in a single die (partial removal) is relatively small and amounts to 15-25% of the input cross-section. However, if technology is chosen well, it is possible to achieve the total deformation (the total removal Uc) at the level of 90-95% with regard to the input cross-section without intermediate annealing; therefore it is possible to write:

where Sp is the initial cross-section of the drawn wire and Sk is the final cross-section of the drawn wire. After modification:

where Dp and Dk are the input and output diameters of the wire. If the total removal is expressed by means of a logarithmic (true) strain, then it reaches the value of up to:

where lk and lp express the final and initial (unit) lengths of the wire. This substantial deformation without intermediate annealing is made possible by the state of stress in the die where significant radial compression – caused by the resolution of forces in the cone part of the die (Fig. 10-3) leads to the reduction of the diameter. The mechanical diagram shown in Fig. 3-6 (p. 21) corresponds to this: the predominant stress state is a combination of two compressive and one tensile stress and a diagram of deformations (tensile) corresponding to it. Equality of the main compressive stresses and of the main compressive deformations (σ2=σ3, ε2=ε3) is characteristic for this process.

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Figure 10-3 A schematic Illustration of wire drawing: Ro is the initial (input) radius of the wire, Rf is the output radius of the drawn wire.

The input blank is a rolled wire or a wire which has been processed by previous drawing and which has been heat-treated, its surface is of a good quality. Prior to drawing, scales on the wire must be removed by pickling and further, for example, by phosphating where the surface of the wire is covered with a finely crystalline layer of phosphates.

Note.: There are gaps and pores between the individual crystals which is particularly favourable for holding the lubricant on the surface. The phosphatized surface is about 13 times better in holding oil (lubricant) than a bare surface!

During drawing, there is the so called drawing drum after each die which is powered and exerts the main deformation force (tensile). This method of deformation is suitable only for well formable materials with an appropriate structure (usually steels of class 12 with a pearlitic structure and the content of carbon in the range of 0.5 to 0.8%).

10.2. Tube and Profile Drawing

A discontinuous process is used for drawing seamless tubes and profiles which unlike a wire are drawn in their final length. Usually it is a cold process and it is intended for tubes of small to medium dimensions (from 0.1 up to 250 mm), thin-walled and thick-walled, with demands on dimensional accuracy and surface quality (both the outer and the inner surface is shiny and smooth). These tubes are sometimes referred to as precision tubes. The blank is a tube produced by rolling up to the length of 4.5 m with an adjusted end for pulling through the die.

The basic methods of tube drawing are as follows (the individual methods of drawing are distinguished according to the way the internal diameter of the tubes is determined during the drawing process because the external diameter is always determined by the diameter of the die):

a) die drawing in which the tensile force is transferred by the tube, neither the internal diameter nor the thickness of the wall are determined by any tool (Fig. 10-4)

b) drawing on a fixed mandrel in which the tube transfers the tensile force and the mandrel is fixed to a mandrel rod (Fig. 10-5)

c) drawing on a free mandrel in which the tensile force is transferred by the tube, the mandrel must have such a cone shape which prevents it from being pushed out or pulled in (Fig. 10-6)

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d) drawing on a rod in which the tensile force is transferred by a rod; it is followed by rolling so that the rod can be pulled out - there is no dimensional accuracy; in the case of small tube diameters drawing is carried out on a string (Fig. 10-7)

e) profiles of irregular shapes are drawn by means of multi-part dies assembled in a mounting frame and they have more precise dimensions than rolled profiles. Some of them are intended for special engineering production, e.g. for lock inserts.

Figure 10-4 Die drawing

Figure 10-5 Drawing on a fixed mandrel

Figure 10-6 Tube drawing on a free mandrel

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Figure 10-7 Tube drawing on a rod

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THE STUDENT KNOWS:

The basic principle of wire drawing

The mechanical diagram in wire drawing

Tube and profile drawing



http://www.ksp.tul.cz/cz/kpt/obsah/vyuka/skripta_tkp/index.htm , Technical University in Liberec, 2011

S.H.talbert, B.Avitzur: Elementary Mechanics of Plastic Flow in Metal Forming. John Wiley & Sons, 1996.


wire drawing

tube drawing

http://www.ksp.tul.cz/cz/kpt/obsah/vyuka/skripta_tkp/index.htm


11. Extrusion

Extrusion is a technology which can be carried out

a) as a hot process

b) as a cold process in which an extrusion billet of an exact shape, with minimum allowances for machining and with modified mechanical properties (hardening) is obtained.

In the course of extrusion the material is deformed by passing through a fixed extrusion die under the effect of a force caused by a moving tool – the extrusion ram (Fig. 11-1).

Figure 11-1 The principle of the extrusion technology

The state of stress in the formed material element is triaxial, all-around compressive. The formed material moves and the direction of its movement is determined by the design of the tool – the ex-trusion press. The product is called an extrusion billet.

This technology can be divided into two groups. The first concerns the production of final products, the second concerns the production of blanks (tubes, rods, profiles, etc.). This production method is used, for example, for the production of cartridges, plugs for engines, and more.

11.1 Methods of Extrusion

Extrusion – the blank is formed under the influence of compressive stresses in the extrusion die. It makes it possible to form materials which are characterized by low formability. It is divided into:

a) Forward extrusion in which the material moves in the direction of the movement of the extru-sion ram (Fig. 11-2). It is used for forming of pins, bolts, casings, etc., that is, of products which do not have a constant cross-section.

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http://www.ksp.tul.cz/cz/kpt/obsah/vyuka/skripta_tkp/sekce/video/01-direct.swf


Figure 11-2 The principle of forward extrusion

b) Backward extrusion in which the material moves against the direction of the movement of the extrusion ram (Fig. 11-3). It is used for the manufacture of hollow extrusion billets and also of bil-lets with ribs in which the thickness of the wall is very small compared to the diameter or vice versa.

Figure 11-3 The principle of backward extrusion (1,3-extrusion die, 2,4-extrusion ram, a-ram, b-wiper, c-die, d-puller).

c) Combined extrusion in which the material moves simultaneously in the direction and against the direction of the movement of the extrusion ram (Fig. 11-4).

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Figure 11-4 The principle of combined extrusion

d) Side and radial extrusion (Fig. 11-5) – the material moves at a right angle to the direction of movement of the extrusion ram.

It is used for the production of extrusion billets with an external and internal mounting. Radial extru-sion refers to forming in which the material and parts of the tool move in a radial direction with re-gard to the axis of the material.

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Figure 11-5 The principle of side (at the top) and radial extrusion

e) Cavity extrusion – for forming functional cavities of tools

11.2 The Mechanical Diagram, Force and Work in Extrusion

In extrusion the material is loaded with a triaxial compression, all three main stresses are compressive. The stress and deformation diagram is shown in Fig. 11-6.

Figure 11-6 The diagram of the state of stress and deformation during extrusion

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Note: Caution! The main compressive stresses do not have the same intensity – if the compressive stresses were the same, it would be a case of stressing by hydrostatic pressure and plastic deformation would not be possible in such stress. The resistance to elastic deformation would theoretically grow to infinite values.

High deformation forces which depend on the chemical composition of the material , on preparation and heat treatment, on lubricating, geometry of the tool (the higher it is, the higher the force is), the size of the reduction (the higher it is, the higher the force is), the thickness of the wall (the thinner it is, the higher the force) and on the type of the machine are necessary for cold extrusion. Due to the compressive state of stress extrusion can be used also for forming materials whose formability is difficult and which cannot be processed, for example, by drawing. The required forces and work are difficult to calculate and empirical relationships and numerical calculations are often used. The limiting factor for extrusion machines is the intensity of the force needed for deformation under the influence of compression where the deformation resistance of a material grows especially in cold extrusion. Materials with low deformation strength, aluminium and its alloys, can be extruded in one operation. Steels and other metals are extruded in more operations. Sometimes it is necessary to carry out intermediate annealing (first recrystallizing annealing and then soft annealing).

Friction which significantly affects the process itself, the quality of the product and economy of production, especially in the case of steels, constitutes another decisive factor in the extrusion process – appropriate surface treatment must be carried out otherwise there is dry friction and the tool can seize. The surface treatment includes:

a) elimination of surface defects (blasting, grinding, pickling for Al, etc.), b) chemical and mechanical cleaning (washing, drying, etc.),

c) phosphating (the phosphated surface has a high adhesion to the starting material which is most often a disc or a disc with a hole, the so-called calotte, which enables lubrication of the material surface due to the porosity of the phosphated layer in high pressures, this was used for the first time in the 1930s),

d) application of a lubricant layer (e.g. by immersion in a solution of an organic oil and soap).

The intensity of the friction forces also depends on the roughness of the ram and die surfaces and on their wear at critical points.

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78

THE STUDENT KNOWS:

Extrusion methods

Mechanical diagrams in extrusion





extrusion methods



12. DIVISION OF MATERIALS BY SHEARING AND TEARING - FLAT FORMING

The division of materials is carried out, in practice, most frequently by the following methods:

1. cutting at sawmills

2. parting on a lathe

3. tearing on special mechanical breakers

4. cutting under a drop hammer or press

5. shearing with shears

Shearing of material is carried out by means of shears with straight shear blades – parallel or inclined – or by means of circular shears.

Shearing consists of dividing a material by the shear effect of two blades with a previous elastic or plastic deformation of the place of shearing. This method of division is suitable especially for formable soft materials.

Division of shearing: shearing through the section, notching, blanking, trimming, cropping, etc.

Figure 12-1 The stress at the point of shearing, A-B the diagram of the main stresses in points A and B, R – the shear sur-face

The principle of shearing: At the beginning of shearing, the material is stretched and pushed to the sides between the moving shear blades of the frames, first at the point of the blades and then the area inside are affected. Longitudinal layers are extended and during the movement of the sheared part they bend and tilt. The outer contour of the material undergoes deformation and the thickness of the sheet in the area of the shear decreases.

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The application of the shear blades causes a vertical compressive normal stress σz and a horizontal tensile normal stress σr (Fig. 12-1). The theory of plasticity states that plastic deformation and subsequent forming disruption of the material are caused by the effect of the shear stress in the direction in which this shear stress reaches its highest values. The maximum shear stress is acting in the direction which forms an angle of 45° with the directions of the main normal stresses (in this case σz and σr ). At this angle a crack starts to grow at the beginning of the shearing process. As the shearing progresses, the direction of the main stresses changes, the maximum shear stress also changes its direction and the direction of the crack turns into the vertical direction. The result is an S-shape of the shear line R- see Fig. 12-1.

Figure 12-2 The forces in shearing with parallel blades

In the actual shearing process, the shear forces Fc are not acting ideally in a single plane, there has to be a certain gap z between the blades (Fig. 12-2). The force is not acting on the edges of the blades, but in the middle of the “shear surface”.

The force Fc with which the blade acts on the material can be divided into the constituents F1 and F2.

These constituents cause moments: and

where l is the instantaneous distance of the points of forces F1 in the vertical direction, a is the distance of the points of forces in the horizontal direction. The moment M1 causes the rotation of the material in the course of shearing. The sheared material continues to turn until the equality of the moments has been reached.

→

In order to prevent the wedging of the material in between the blades and its winding as a result of the M1 moment, it is necessary to use a holder.

The force of the holder Fp can be determined from the following relationship:

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and further

The M2 moment caused by the effect of the force F2 tries to push the blades from each other. Therefore, it causes separation of the blades and their bending which can lead to breaking if they are not sufficiently dimensioned.

The clearance between the blades z (Fig. 12-2) must be of optimum size so that the cracks spreading from the two opposite blades link in the middle without producing an undesired burr. If the clearance between the knives is either too big or too small, the cracks do not connect in the middle and the material tears off with a poor-quality shear surface.

Figure 12-3 A look at the shear surface

Several zones can be observed on the shear surface (Fig. 12-3):

a) a deformation zone which corresponds to the original plastically deformed surface

b) a plastic shear zone – the division of the material in this area is the result of the direct application of the blades on the material

c) a fracture zone – after the blades have cut the material up to a certain depth typical for the given material and the geometry of the blades, there occurs a spontaneous tearing of the sheared material without a direct application of the blades

d) an abrasion zone – this zone is a part of the fracture zone and it is where the shear surface is sheared off and the divided parts wear against each other.

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In shearing the blades do not pass through the entire cross-section of the material, they cut only to a critical depth and the shear is completed spontaneously. In cold shearing the effect of deformation causes hardening of the shear surface which can show itself in the following processing by drawing or bending.

The geometry of the blade is defined by the clearance angle α (max 3°), by the back rate β (75 – 85°) and by the rake γ (Fig. 12-4)

Figure 12-4 Geometry of the shear blade

12.1. Calculation of the Shear Force and Shear Work in Cutting on Shears with Parallel Blades

In shearing a material of the thickness t and width l (Fig. 12-5) it is possible to determine the ideal shear force Fsid from the following relationship:

,

where is the shear strength which in the case of steel corresponds to the value

Rm is the tensile strength. In the case of other materials, it is possible to find their shear strength from relationships given in tables (Table 12-1).

In calculating the real shear force, it is necessary to take into account the effect of blunting of the blade, the size of the clearance between the blades, thickness and surface quality of the material, etc., thus the ideal shear force must be multiplied by coefficient K1:

.

In practice, the value of the coefficient K1 ranges from 1.2 to 1.5.

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Figure 12-5 A schematic illustration of shearing with parallel blades

Material Formula for calculation

BRASS

DURALUMIN

ZINC

Al, Sn, Cu, Ni

Table 12-1 The relationship between the shear strength and tensile strength in selected materials1

The dependence of the shear force on the path of the blade is shown in Fig. 12-6.

Figure 12-6 The dependence of the shear force on the path of the blade in shearing with parallel blades

In shearing the material is first elastically deformed – zone I in Fig. 12-6 in which the force acting on the blades increases linearly. After the yield strength of the sheared material has been exceeded, there occurs plastic deformation of the surface of the material which corresponds to zone II. Zone III

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is a zone of plastic shear, it is followed by zone IV – tearing of the material. The depth im is the so-called proportional depth of the penetration of the blade at the maximum force and ik is the proportional penetration depth of the blade in cross-shearing. The thickness of the material t is greater than the path of the blade. In the shearing of soft materials the maximum shear force is small and the blades cut deep into the material, in the shearing of hard materials the shear force is high and the blades penetrate less deep into the material.

In calculating the shear work which is determined by the surface under the curve of the dependence of the shear force on the path of the blade (Fig. 12-6), the actual progress is replaced with an idealized curve – a half of an ellipse (Fig. 12-7). The depth of the penetration of the blade is expressed by means of the coefficient which depends on the properties of the sheared material and its values can be found in tables. As a rule, the harder the shorn material is, the smaller the coefficient (coefficient of filling in the diagram).

Note.: The thickness of the material is always greater than the path of the blade.

The shear work will be calculated as a surface under the half of the ellipse with half axes Fs – a:

.

Figure 12-7 The real and ideal progress of the shear force depending on the path of the blade

7.6 Calculation of the Shear Force and Shear Work in Cutting with Shears with Inclined Blades

Shearing with angled, inclined blades which form a certain angle during shearing is advantageous because the total necessary shear force required in this method of shearing is lower compared to shearing with parallel blades. The material is sheared gradually. The size of the shear edge and thickness – the area of the triangle – will be decisive for the intensity of the shear force.

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Figure 12-8 Shearing with angled, inclined blades

The calculation of the shear work in shearing with inclined blades

Figure 12-9 The path of the blade in shearing with inclined blades

The shear force can be generally calculated from the following relationship

,

where is the area of the delimited element and is the shear strength.

By integration in the limits from zero to the value of b (Fig. 12-8) and using the relation

,

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where t is the thickness of sheared material and is the inclination angle of the upper blade, a relationship for the calculation of the ideal force for shearing is reached:

.

After substituting for

and with regard to the technological factors – the effect of friction, bending, etc., which are included in the calculation by multiplying the ideal force by the coefficient K2, the relationship for the calculation of the real shear force in shearing with inclined blades is achieved as follows:

Note.: The inclination angle of the upper blade for lever shears is in the range of φ= 7- 12°, and for squaring shears φ= 2-6°.

The calculation of the shear work in shearing with inclined blades

Figure 12-10 A schematic illustration for the calculation of the shear work in shearing with inclined blades

Figure 12-10 can be used for calculating the theoretical value of work which is required for shearing with inclined blades as the area of a rectangle with the sides z and Fsmax:

,

where

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and after substitution

.

Assuming that the work performed in shearing the same workpiece with parallel blades and inclined blades must be the same, the relationship between the technological coefficients K1 and K2 can be derived:

7.6 Shearing in Blanking Dies and Punches

The most widespread method of processing sheet metal is shearing in blanking dies and punches. The basic operations are blanking and piercing in which punching blanks for further processing (e.g. by bending) or finished components (e.g. gears, etc.) are achieved. The diagram of the shearing tool is shown in Figure 12-11. The size of the shear surface in cross-shearing is calculated by multiplying the circumference of the punching product with the thickness of the sheared sheet; in the case of a circular punching product the following applies:

and in the shear force

Where the coefficient k also includes the force needed for the removal of the punching product from the blanking punch.

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Figure 12-11 A schematic layout of the blanking die

7.7 Shearing on Circular Shears

Circular shears are designed for longitudinal shearing of long strips. It is a shearing tool with rolling blades. The use of circular blades extends the time of shearing but reduces impacts during shearing. The inclination of the shear edge changes from the highest value at the point of the grip to zero.

Circular shears are divided according to the number of discs into single-disc, two-disc and multi-disc shears:

1) Single-disc shears are used mostly in ironworks for trimming of long plates of thick metal sheets on both sides. The lower blades are fixed (edge of the shearing table), the upper blades are mobile.

2) Double-disc shears are divided according to the mutual position of the blades and of the shorn sheet metal:

a) discs of a large diameter (strip shears), parallel axes, for straight shears up to the thickness of 30 mm

b) blades of very small diameters, parallel axes, shearing on curved lines

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c) circular shears with one inclined blade (by about 30 to 40°) up to the thickness of 30 mm.

d) shears with two inclined blades, the so-called curved shears, for shearing strongly curved contours.

3) multi-disc shears – with more pairs of disc blades (cutting of plates into narrower strips - Fig. 12-12).

4) other types – shears for cutting profiles, shearing on presses

Figure 12-12 The arrangement of circular shears in cutting strips

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90

THE STUDENT KNOWS:

The principle of shearing

The calculation of the shear force and shear work in shearing with parallel blades

The calculation of the shear force and shear work in shearing with inclined blades

The schematic layout of a shearing tool

Types of circular shears


F.Blaščík: Teória a metodika tvárnenia. Alfa Bratislava. 1971

Z.Petržela, J. Kučera, R. Březina: Technologie slévání, tváření, svařování. VŠB v Ostravě, 1987.

J.Procházka, M. Zahradník, M. Němec, J. Novotný: Technologie slévání, tváření a svařování.ČVUT Praha, 1982



Cutting and shearing

Cutting force and power



13. BENDING AND STRAIGHTENING

Bending is a forming process in which the material is permanently deformed into various angles of bending with a higher or lower degree of rounding of edges. In bending there occurs an elastic plastic deformation which is caused by the moment of the external forces. It affects a relatively small volume of the workpiece and in this volume stress and deformation significantly change their intensity and direction. The layers (fibres) of metal on the inner side of the bend are compressed and shortened in the longitudinal direction and stretched in the transverse direction. The layers of metal on the outer side of the bend are stretched and elongated, in the transverse direction they are compressed. In between the elongated and shortened layers (fibres), there is a neutral layer whose length does not change during bending. The neutral layer does not pass through the centre of the cross-section. The distribution and intensity of stress in the material is shown in Figure 13-1.

Figure 13-1 The distribution of stress in bending

8.1 Calculation of the Force in V-Shape Bending

The bent product is considered to be a beam with two supports and loaded with a force in the centre between the two supports (Fig. 13-2)

Figure 13-2 V shape bending

The cross-section of the material is stressed with a bending moment at a distance x from the support.

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,

where F0 is the acting force.

If the stress rises and reaches the yield strength in the outer fibres, a permanent deformation of the

component commences. This state occurs at the site of the maximum moment under the point of the

force F0 which reaches the value

where W is the cross-section modulus of bending, lv is the distance between supports (Fig. 13-2) and

σk is the yield strength of the material.

Further increase of the force F0 causes expansion of the permanently deformed region both in the

depth and in the direction of the supports. At the point of bending the cross-section shows three

zones:

a) a zone of elastic deformations which is the cause of the so-called elastic recovery of the bent

component and which is located around the neutral axis

b) an outer zone with a permanent extension

c) an inner zone with a permanent compaction

If the external forces cease to act on the body, the dimensions of the body will partially return to the original values, i.e. the body recovers or springs back. While in the previously examined technologies elastic recovery was negligible, in bending it has a significant importance. Elastic recovery in bending manifests itself as an angle displacement whose importance grows with the length of the arms (Fig. 13-3). The reverse elastic recovery of bent components is caused by the influence of elastic deformation of the material around the neutral axis. The size of the angles of elastic recovery depends on:

a) the type of material

b) the shape of the bent part

c) the material thickness

d) the radius of the bending

e) the final size of the bent component and on the method of bending.

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It is usually in the range of 3 to 15°.

Figure 13-3 Elastic recovery of the material in V and U shape bending

8.2 Straightening

Straightening is a technology which is used to remove an undesired deformation which occurred

either as a result of handling or in the production. Straightening by compression under a press can be

imagined as “inverted” bending in which uneven parts are straightened (Fig. 13-4). The rule of the

simultaneous effect of elastic and plastic deformations applies here too – therefore after external

forces cease to exert their effect, the body undergoes elastic recovery which manifests itself by

residual unevenness.

Figure 13-4 Straightening of a pressing product by compression between straight plates

In very thin materials and in hard materials the pressing force rises to impossible values. Therefore

another route is chosen in these cases. The straightened body is not introduced into the plastic state

in its entire volume but only at certain regularly distributed points. This is the so-called point or pro-

jection straightening. Figure 13-5 shows the jaws in detail. Jaws with sharp tips are used for very hard

materials or for materials where punctures are not a problem.

Figure 13-5 Point straightening (left) and projection straightening (right)

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A method of repeated bending is often used for straightening of materials. It is common, for

example, in straightening of wires or strips before the material is loaded into a processing machine.

The material is straightened by alternating bending during its passage between rolls (Fig. 13-6). The

remaining stresses will be lower if smaller and smaller alternating straightening bends are used. The

presence of residual stresses has a significant impact on the strength of components and the

intensity of elastic recovery.

Figure 13-6 Straightening of sheet metal by rolling

The disadvantages of straightening technologies include especially the risk of damaging the surface of products with surface cracks and notches which can result in a significant lowering or degradation of the fatigue parameters (cold rolled sheet metal, drawn wire).

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95

THE STUDENT KNOWS:

The principle of deformation in bending

Calculation of the force in W shape bending

Causes of elastic recovery/springing


F.Blaščík: Teória a metodika tvárnenia. Alfa Bratislava. 1971

J.Procházka, M. Zahradník, M. Němec, J. Novotný: Technologie slévání, tváření a svařování.ČVUT Praha, 1982



bending

bending force

springing



14. Sheet Drawing – Flat Forming Technology

Sheet and strip drawing results in the production of a spatial pressing of an unrollable shape. According to the shape of the pressing it is possible to distinguish between shallow and deep drawing, drawing with and without reduction of the wall, drawing of rotary and non-rotary shapes and also drawing of irregular shapes (the so-called bodywork pressings). The starting workpiece is a flat blank of sheet metal, a sheet strip or otherwise processed blank which can be processed by the following technologies: plain drawing, drawing with a reduction of the wall, reverse drawing, fluting, widening and hemming, narrowing, stretch forming, stretching and in special ways (Fig. 14-1).

Figure 14-1 Technological methods of drawing: A, B-drawing without a blank holder, 1st and 2nd draw; C, D-drawing with a blank holder, 1st and 2nd draw; E – reverse drawing (turning); F-drawing with a reduction of the wall; G – narrowing; H –widening; I – hemming (stretch forming); J – stretching

Drawing is such a technological way of forming in which a hollow body – a half-closed container - is formed in one or more draws from a straight sheet metal. Sometimes this technological process is called deep drawing. The instrument is the drawing tool (Fig. 14-2) which is composed of a punch and a die and other structural parts, the product is a drawn cup.

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Figure 14-2 The drawing tool

14.1 The Drawing Process, Mechanical Diagram

It is ideal to explain the principle of drawing on the drawing of a simple cylindrical shape with a bot-tom. The acquired results can be subsequently applied in a similar way to drawn parts of angular or irregular shapes. If the punch is pressed into the die, the sheet metal moves over the draw edge which is the first part of the tool to wear out. The force required for the drawing issues from the strength condition of the cylindrical part of the container which must not break during the drawing. It is necessary to take into consideration the effect of friction and hardening of the material.

During drawing the annular ring of the flat blank (D-d) changes into a cylinder with the diameter d and height h from the earlier dimension of the flat blank D (Fig. 14-3). As a result of the law of volume constancy, the volume of the metal does not change during the process and, therefore, the height h will be greater than the width of the annular ring D-d.

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Figure 14-3 The principle of drawing a cylindrical shape

The state of stress in drawing varies in the individual places of the drawn cup, and there occurs an anisotropy of the mechanical properties of the sheet metal. The bottom (A) is pulled slightly and evenly in two directions. The cylindrical part (C) is stretched in one direction, but at the bottom (B) there is a biaxial or triaxial state of stress. The material which passes over the draw edge (D) is stressed by radial bending and tangential compression. The material under the blank holder (E) is stressed by tension in the radial direction, by compression in the tangential direction and by compression at a right angle on the surface of the flange. If the tool does not have a holder, the compression under the holder is omitted. The most disadvantageous conditions are at the site of the bending at the bottom of the cup, there is high tensile stress. This results in thinning of the wall and that leads to the risk of the bottom breaking off.

Figure 14-4 A schematic illustration of stresses and deformations in drawing with a blank holder: 1-blank holder, 2-punch, 3 – die, 4 – flat blank

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http://www.ksp.tul.cz/cz/kpt/obsah/vyuka/skripta_tkp/sekce/09-tazeni/03-napjatost%20pri%20tazeni.jpg




14.2. Calculation of the Force and Work

The mathematical relationships for calculating the force are relatively complicated and they are therefore simplified. Practical formulas are based on the fact that the allowed stress in the dangerous cross-section must be lower than the stress on the breaking strength. Therefore the highest tensile force must be lower than the force which causes the breaking of the cup bottom from the side walls. The progress of the tensile force in the individual phases of drawing is shown in Figure 14-5. The graph clearly shows that the force changes from zero to maximum roughly in the middle of the tension and then it falls down again.

Figure 14-5 The progress of the tensile force in the individual phases of drawing

For a tool without a holder, the intensity of the tensile force for the rotary shape of the cup in the first and subsequent draws is calculated in a simplified way according to the following relationship:

,

where S is the area of the material which is stressed by tension (S = π . d . s) and is the breaking strength of the material.

For a tool with a holder, the intensity of the tensile force in the first and subsequent draws is calcu-lated in a simplified way according to the relationship:

,

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where L is the length of the blank perimeter, Rm is the breaking strength of the material, s is the thickness of the sheet metal, Sp is the area of the holder [mm2], and p is the specific pressure of the holder (from 0.8 to 3 MPa).

The intensity of the work in drawing is calculated according to the relationship

,

where h is the height of the cup and C the coefficient of filling the surface.

14.3. DETERMINATION OF THE DIMENSIONS OF THE FLAT BLANK, THE NUMBER OF DRAWS

The total deformation of the sheet metal is considerable, the entire cup usually cannot be drawn in a single operation. Therefore the first draw is made shallow and of a large diameter. The drawing then proceeds with another draw of a smaller diameter. The height of the cup grows simultaneously (Fig. 14-6). When plasticity has been exhausted, it is necessary to carry out intermediate annealing.

Figure 14-6 Drawing of a product in three draws

The coefficient of drawing, or the degree of drawing, is used in order to determine the maximum deformation in one draw and the number of drawing operations, it is calculated for the first draw from the relationship:

where m is the coefficient of drawing, d is the diameter of the cup, D is the diameter of the flat blank, and K is the degree of drawing.

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The coefficient or degree of drawing for further draws is calculated in a similar way. The total coeffi-cient of drawing is equal to the multiplication of the individual coefficients. The values of the coeffi-cients of drawing for cylindrical containers are given in tables. If the shape is different, the coefficient of drawing is determined according to the point where the curvature of the wall and the relative depth reach their maximum values. Generally, it depends on the type of material, on previous hardening, on proportional width, shape of the cup, drawing rate, compression of the holder, lubrica-tion and especially on the geometry of the drawing tool.

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THE STUDENT KNOWS:

Sheet drawing methods

Mechanical diagrams in sheet drawing

Calculation of tensile forces and work

The concept of the coefficient of drawing





sheet drawing

deep drawing



Contents

1. THE PHYSICAL NATURE AND MECHANISM OF PLASTIC DEFORMATION ... ... ... ... ... ... ... ... ... ...1

1.2. The Mechanism of Plastic Deformation ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...1

1.3. Plasticity and formability....................................................................................4

2. THE EFFECT OF FORMING ON THE PROPERTIES AND STRUCTURE OF METALS ... ... ... ... ... ... ... ... 7

2.1. Recovery........................................................................................................ 7

2.2. Recrystallization................................................................................................8

2.3. Cold Forming ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...11

2.4. Hot Forming............................................................................................ 12

2.5. The Effect of the Structure on the Plastic Properties of the Material ... ... ... ... ... ... ... ... ... ... ... 13

2.6. The Effect of Temperature on the Plastic Properties of the Material ... ... ... ... ... ... ... ... ... ... ... 14

3. THE MECHANICAL PRINCIPLE OF FORMING AND THE BASIC LAWS OF PLASTIC DEFORMATION 16

3.1. The Stress in the Formed Body ...............................................................................16

3.2. The Mechanical Diagram - Diagrams of Stresses and Deformations (MSD).......................... 18

3.3. Deformation in the Formed Body....................................................................... 21

3.4. The Basic Laws of Plastic Deformation ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 24

3.5. External Friction.................................................................................................... 28

4. DEFORMATION RESISTANCE, FORCES AND WORK REQUIRED FOR FORMING ... ... ... ... ... ... ... 29

4.1. Determination of the Deformation Resistance in the Case of Upsetting a Circular Plate ... ... ...29

4.2. The Deformation Rate ..................................................................................... 34

4.3. The Deformation (Forming) Work ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... 36

5. METALLURGICAL BASICS OF HEATING ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..... 39

5.1. Physical Quantities Affecting the Heating of Metals ........................................................... 39

5.2. Thermal Stress during Heating ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... 41

5.3. Technological Principles of Heating Metals ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...42

5.4. The Accompanying Phenomena of Heating ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...43

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6. THE CLASSIFICATION OF METAL FORMING PROCESSES ................................................................. 45

7. FREE FORGING............................................................................................... 47

8. DIE FORGING...................................................................................... 52

9. ROLLING.................................................................................................... 57

9.1. The Rolling Train and Mill ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 59

9.2. Production of Metallurgical Blanks ........................................................................61

9.3. The Conditions for the Grip (Drawing) of the Rolled Workpiece ................................................. 62

10. DRAWING …………………………………………………………………………………………...67

10.1. Wire Drawing ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...67

10.2. Tube and Profile Drawing .................................................................................. 69

11. EXTRUSION ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..... 72

11.1. Methods of Extrusion ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...72

11.2. The Mechanical Diagram, Force and Work in Extrusion ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 75

12. DIVISION OF MATERIALS BY SHEARING AND TEARING – FLAT FORMING ...........................78

12.1. Calculation of the Shear Force and Shear Work on Shears with Parallel Blades .........81

12.2. Calculation of the Shear Force and Shear Work on Shears with Inclined Blades ........... 83

12.3. Shearing in Blanking Dies and Punches ........................................................... 86

12.4. Shearing on Circular Shears ................................................87

13. BENDING AND STRAIGHTENING ....................................................................................90

13.1. Calculation of the Force in V-Shape Bending ...............................................................90

13.2. Straightening......................................................................................................92

14. SHEET DRAWING – FLAT FORMING TECHNOLOGY ... ... ... ... ... ... ... ... ... ... ... ... .... 95

14.1. The Drawing Process, Mechanical Diagram ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... 96

14.2. Calculation of the Force and Work .................................................................................. 98

14.3. Determination of the Dimensions of the Flat Blank, the Number of Draws ............................... 99

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