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  1. Mechanics of Sheet Metal Forming
  2. 2nd Edition
  3. Forming processes and mechanics of sheet metal forming
  4. Mechanics of Sheet Metal Forming Material Behavior and Deformation Analysis

Plastic deformation in the surface is much more pronounced than in the thickness. The lankford coefficient r is a specific material property indicating the ratio between width deformation and thickness deformation in the uniaxial tensile test. Materials with very good deep drawability have an r value of 2 or below.

The positive aspect of formability with respect to the forming limit curve forming limit diagram is seen in the deformation paths of the material that are concentrated in the extreme left of the diagram, where the forming limits become very large. Another failure mode that may occur without any tearing is ductile fracture after plastic deformation ductility. This may occur as a result of bending or shear deformation inplane or through the thickness.

The failure mechanism may be due to void nucleation and expansion on a microscopic level. Microcracks and subsequent macrocracks may appear when deformation of the material between the voids has exceeded the limit. Extensive research has focused in recent years on understanding and modeling ductile fracture.

The approach has been to identify ductile forming limits using various small-scale tests that show different strain ratios or stress triaxialities. Knowledge of the material formability is very important to the layout and design of any industrial forming process. Simulations using the finite-element method and use of formability criteria such as the forming limit curve forming limit diagram enhance and, in some cases, are indispensable to certain tool design processes also see: Sheet metal forming simulation and Sheet metal forming analysis. One major objective of the International Deep Drawing Research Group IDDRG , from is the investigation, exchange and dissemination of knowledge and experience about the formability of sheet materials.

Table of Contents Material properties General deformation processes Deformation of sheet in plane stress Simplified stamping analysis Load instability and tearing Bending of sheet Simplified analysis of circular shells Cylindrical deep drawing Stretching over axisymmetric punches Bending under tension Hydroforming Yielding in three dimensional stress state Large strains Customer Reviews Average Review. See All Customer Reviews.

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Mechanics of Sheet Metal Forming

Add to Wishlist. USD Sign in to Purchase Instantly. Temporarily Out of Stock Online Please check back later for updated availability. Overview The basic theory of sheet metal forming in the automotive, appliance and aircraft industries is given. Presents the fundamentals of sheet metal forming - bending, stretching, press forming, deep drawing and hydroforming Shows how deformation, loads and process limits can be calculated using simple equations Concentrates on simple, applicable methods rather than complex numerical techniques Contains many exercises, worked examples and solutions Used as a reference text in undergraduate manufacturing courses, as a required text in specialist graduate courses and as a course text for industrial short courses Is supported by a separate, but related simulation software package described below.

About the Author S. This consists of a punch, and drawring and blank-holder assembly, or binder. This process is widely used to form auto-body panelsand a variety of appliance parts. Die design requiresthe combination of skill and extensive computer-aided engineering systems, but for thepurpose of conceptual design and problem solving, the complicated deformation systemcan be broken down into basic elements that are readily analysed. In this book, the analysisof these macroscopic elements is studied and explained, so that the reader can understandthose factors that govern the overall process.

Deep drawing.

Operations of shearing and bending sheet metals

Asxvi Introduction. To form deeper parts, much more material must be drawn inwards to form thesides and such a process is termed deep drawing. Forming a simple cylindrical cup isshown in Figure I. Lubrication is importantas the sheet must slide between the die and the blankholder. Deeper cups can be made by redrawingas shown in Figure I. Tube forming. Again, these operations can be broken down into a fewelements, and analysed as steady-state processes. Fluid forming. As the pressure to form thesheet into sharp corners can be very high, the forces needed to keep the container closedare much greater than those acting on a punch in a draw die, and special presses arerequired.

Tubular parts,for example frame structures for larger vehicles, are made by bending a circular tube,placing it in a closed die and forming it to a square section as illustrated in Figure I. Coining and ironing. In all of the processes above, the contact stress between the sheetand the tooling is small and, as mentioned, deformation results from membrane forces inthe sheet. In a few instances, through-thickness compression is the principal deformationforce. Coining, Figure I. Ironing, Figure I. The cylindrical cup is forcedthrough an ironing die that is slightly smaller than the punch plus metal thickness dimen-sion.

Using several dies in tandem, the wall thickness can be reduced by more than one-halfin a single stroke. DieFluid Tube a b Figure I. Coining tool Sheet DieFigure I. Only very simple examples of industrial sheet forming processes have beenshown here. An industrial plant will contain many variants of these techniques and numer-ous presses and machines of great complexity.

It would be an overwhelming task to dealwith all the details of tool and process design, but fortunately these processes are all madeup of relatively few elemental operations such as stretching, drawing, bending, bending Introduction xix. CupPunch Ironing dieFigure I. This book presentssimilar models for the deformation of sheet. In this way, the engineer can apply a familiarapproach to problem solving in sheet metal engineering. Application to designThe objective in studying the basic mechanics of sheet metal forming is to apply this topart and tool design and the diagnosis of plant problems.

It is important to appreciatethat analysis is only one part of the design process. Determining how toachieve this comes later. This is typically an iterative process inwhich the designer makes some decision and then determines the consequences. A gooddesigner will have a feeling for the consequences before any calculations are made and thisability is derived from an understanding of the basic principles governing each operation.

For sheet mate-rial, the ability to be shaped in a given process, often called its formability, should also beconsidered. To assess formability, we must be able to describe the behaviour of the sheetin a precise way and express properties in a mathematical form; we also need to knowhow properties can be derived from mechanical tests.

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As far as possible, each propertyshould be expressed in a fundamental form that is independent of the test used to measureit. The information can then be used in a more general way in the models of various metalforming processes that are introduced in subsequent chapters. In sheet metal forming, there are two regimes of interest — elastic and plasticdeformation.

Whenever there is a stress on a sheetelement, there will also be some elastic strain. This will be small, typically less than onepart in one thousand. A tensile test-piece is shown in Figure 1. This is typical of a number of standardtest-pieces having a parallel, reduced section for a length that is at least four times thewidth, w0. The initial thickness is t0 and the load on the specimen at any instant, P , ismeasured by a load cell in the testing machine.

In some tests, a transverse extensometer may also be usedto measure the change in width, i. Some of these are described below. The elastic extension is so small that it cannot be seen. The diagram doesnot represent basic material behaviour as it describes the response of the material to aparticular process, namely the extension of a tensile strip of given width and thickness.

Nevertheless it does give important information. One feature is the initial yielding load,Py, at which plastic deformation commences. Initial yielding is followed by a region inwhich the deformation in the strip is uniform and the load increases. The increase isdue to strain-hardening, which is a phenomenon exhibited by most metals and alloys inthe soft condition whereby the strength or hardness of the material increases with plasticdeformation.

During this part of the test, the cross-sectional area of the strip decreaseswhile the length increases; a point is reached when the strain-hardening effect is justbalanced by the rate of decrease in area and the load reaches a maximum Pmax.. Beyondthis, deformation in the strip ceases to be uniform and a diffuse neck develops in thereduced section; non-uniform extension continues within the neck until the strip fails.

The extension at this instant is lmax. This had the advantagethat a curve was obtained which was independent of the initial dimensions of the test-piece,but it was still not a true material property curve. During the test, the cross-sectional areawill diminish so that the true stress on the material will be greater than the engineeringstress. The engineering stress—strain curve is still widely used and a number of propertiesare derived from it. Figure 1. The elongation at maximum load is called the maximum uniformelongation, Eu.

If the strain scale near the origin is greatly increased, the elastic part of the curvewould be seen, as shown in Figure 1. The strain at initial yield, ey, as mentioned, isvery small, typically about 0. There is a residual plastic strain when the load has beenremoved as shown in Figure 1.

2nd Edition

Material properties 3. Engineering strainEngineering stress b sproof 0. Engineering strain c Figure 1. If this is the case, a proof stress may bequoted. Certain steels are susceptible to strain ageing and will display the yield phenomenaillustrated in Figure 1. This may be seen in some hot-dipped galvanized steels andin bake-hardenable steels used in autobody panels. The amount of discontinuousstrain is called the yield point elongation YPE. Also engineering strain is not a satisfactorymeasure of strain because it is based on the original gauge length.

True stress can be determined from theload—extension diagram during the rising part of the curve, between initial yielding and Material properties 5. The volume of the gauge section is constant,i. If the straining process con-tinues uniformly in the one direction, as it does in the tensile test, the strain increment canbe integrated to give the true strain, i.

Whennecking starts, deformation in the gauge length is no longer uniform so that Equation 1.

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The curve in Figure 1. The empirical equation or power law Equation 1. As may be seen from Figure 1. Empirical equations of this form are often used to extrapolatethe material property description to strains greater than those that can be obtained in thetensile test; this may or may not be valid, depending on the nature of the material. The initial yield load is 1.

At a point, A, the load is 2. The maximum load is 2. The test-piece fails at an extension of Note that the maximum uniform strain, 0.

Forming processes and mechanics of sheet metal forming

This can be anticipated, as shown in a later chapter. This variation isknown as planar anisotropy. In addition, there can be a difference between the average ofproperties in the plane of the sheet and those in the through-thickness direction. In tensiletests of a material in which the properties are the same in all directions, one would expect,by symmetry, that the width and thickness strains would be equal; if they are different,this suggests that some anisotropy exists.

The rate at which this damage progresses varies greatly with different materials. Itmay be indicated by a diminution in strain-hardening in the tensile test, but as the rate ofdamage accumulation depends on the stress state in the process, tensile data may not beindicative of damage in other stress states. Positive rate sensitivityusually improves forming and has an effect similar to strain-hardening. As well as beingindicated by the exponent m, it is also shown by the amount of extension in the tensiletest-piece after maximum load and necking and before failure, i.

Measurement ofhomogeneity and defects may require information on population, orientation and spatialdistribution. Many industrial forming operations run very close to a critical limit so that smallchanges in material behaviour give large changes in failure rates. When one sample ofmaterial will run in a press and another will not, it is frequently observed that the materialscannot be distinguished in terms of tensile test properties.

For example, in the study of bulk forming processes such asforging and extrusion, compression tests are common, but these are not suitable for sheet. The elastic properties of sheet are not easily measured in routine tensile tests, but they do affect springback in parts. For this reason a variety of springback tests have been devised where the sheet is bent over a former and then released. An indenter is pressed into the sheet under a controlled load and the size of the impression measured.

Mechanics of Sheet Metal Forming Material Behavior and Deformation Analysis

This will give an approximate measure of the hardness of the sheet — the smaller the impression, the greater the hardness. For strain-hardening materials, this yield strength will be roughly the average of initial yield and ultimate tensile strength. The correlation is only approximate, but hardness tests can usefully distinguish one grade of sheet from another.