Forming Limit Diagram
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Forming Limit Diagram
A forming limit diagram, also known as a forming limit curve, is used in sheet metal forming for predicting forming behavior of sheet metal. The diagram attempts to provide a graphical description of material failure tests, such as a punched dome test. In order to determine whether a given region has failed, a mechanical test is performed. The mechanical test is performed by placing a circular mark on the work piece prior to deformation, and then measuring the post-deformation ellipse that is generated from the action on this circle. By repeating the mechanical test to generate a range of stress states, the formability limit diagram can be generated as a line at which failure is onset (see also formability). Description The semi-axes of the ellipse formed in this circle allow for the measurement of relative strain in two primary directions, known as the major and minor directions, which correspond to the major and minor semi-axes of the ellipse. Under the assumption of path in ...
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Sheet Metal
Sheet metal is metal formed into thin, flat pieces, usually by an industrial process. Sheet metal is one of the fundamental forms used in metalworking, and it can be cut and bent into a variety of shapes. Thicknesses can vary significantly; extremely thin sheets are considered foil or leaf, and pieces thicker than 6 mm (0.25 in) are considered plate, such as plate steel, a class of structural steel. Sheet metal is available in flat pieces or coiled strips. The coils are formed by running a continuous sheet of metal through a roll slitter. In most of the world, sheet metal thickness is consistently specified in millimeters. In the U.S., the thickness of sheet metal is commonly specified by a traditional, non-linear measure known as its gauge. The larger the gauge number, the thinner the metal. Commonly used steel sheet metal ranges from 30 gauge to about 7 gauge. Gauge differs between ferrous ( iron-based) metals and nonferrous metals such as aluminum or copper. Cop ...
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Formability
Formability is the ability of a given metal workpiece to undergo plastic deformation without being damaged. The plastic deformation capacity of metallic materials, however, is limited to a certain extent, at which point, the material could experience tearing or fracture (breakage). Processes affected by the formability of a material include: rolling, extrusion, forging, rollforming, stamping, and hydroforming. Fracture strain A general parameter that indicates the formability and ductility of a material is the fracture strain which is determined by a uniaxial tensile test (see also fracture toughness). The strain identified by this test is defined by elongation with respect to a reference length. For example, a length of is used for the standardized uniaxial test of flat specimens, pursuant to EN 10002. It is important to note that deformation is homogeneous up to uniform elongation. Strain subsequently localizes until fracture occurs. Fracture strain is not an engineering st ...
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Deformation (mechanics)
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of ''relative'' displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the temperature field of the body. The rel ...
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Yield (engineering)
In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. In such a case, the offset yiel ...
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Cold Forming
In metallurgy, cold forming or cold working is any metalworking process in which metal is shaped below its recrystallization temperature, usually at the ambient temperature. Such processes are contrasted with hot working techniques like hot rolling, forging, welding, etc. The same or similar terms are used in glassmaking for the equivalents; for example cut glass is made by "cold work", cutting or grinding a formed object. Cold forming techniques are usually classified into four major groups: squeezing, bending, drawing, and shearing. They generally have the advantage of being simpler to carry out than hot working techniques. Unlike hot working, cold working causes the crystal grains and inclusions to distort following the flow of the metal; which may cause work hardening and anisotropic material properties. Work hardening makes the metal harder, stiffer, and stronger, but less plastic, and may cause cracks of the piece. The possible uses of cold forming are extremely v ...
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Probabilistic Forming Limit Map
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ...
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Strain Hardening
In materials science, work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context. This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material. Many non-brittle metals with a reasonably high melting point as well as several polymers can be strengthened in this fashion. Alloys not amenable to heat treatment, including low-carbon steel, are often work-hardened. Some materials cannot be work-hardened at low temperatures, such as indium, however others can be strengthened only via work hardening, such as pure copper and aluminum. Undesirable work hardening An example of undesirable work hardening is during machining when early passes of a cutter inadvertently work-harden the workpiece surface, causing damage to the cutter during the later passes. Certain alloys are ...
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Strain Rate
In materials science, strain rate is the change in strain (deformation) of a material with respect to time. The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point. It comprises both the rate at which the material is expanding or shrinking (expansion rate), and also the rate at which it is being deformed by progressive shearing without changing its volume (shear rate). It is zero if these distances do not change, as happens when all particles in some region are moving with the same velocity (same speed and direction) and/or rotating with the same angular velocity, as if that part of the medium were a rigid body. The strain rate is a concept of materials science and continuum mechanics that plays an essential role in the physics of fluids and deformable solids. In an isotropic Newtonian fluid, in particular, the viscous stress is a linear function of the ...
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Strain Hardening Exponent
The strain hardening exponent (also called the strain hardening index), usually denoted n, a constant often used in calculations relating to stress–strain behavior in work hardening. It occurs in the formula known as Hollomon's equation (after John Herbert Hollomon Jr.) who originally posited it as \sigma=K\epsilon^nJ. H. Hollomon, Tensile deformation, Trans. AIME, vol. 162, (1945), pp. 268-290. where \sigma represents the applied true stress on the material, \epsilon is the true strain, and K is the strength coefficient. The value of the strain hardening exponent lies between 0 and 1, with a value of 0 implying a perfectly plastic solid and a value of 1 representing a perfectly elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ... solid. Most metals have an n-value betw ...
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Lankford Coefficient
The Lankford coefficient (also called Lankford value, R-value, or plastic strain ratio) is a measure of the plastic anisotropy of a rolled sheet metal. This scalar quantity is used extensively as an indicator of the formability of recrystallized low-carbon steel sheets.Ken-ichiro Mori, ''Simulation of Materials Processing: Theory, Methods and Applications'', (), p. 436 Definition If x and y are the coordinate directions in the plane of rolling and z is the thickness direction, then the R-value is given by : R = \cfrac where \epsilon^p_ is the in-plane plastic strain, transverse to the loading direction, and \epsilon^p_ is the plastic strain through-the-thickness. ISO 10113:202/ref> More recent studies have shown that the R-value of a material can depend strongly on the strain even at small strains . In practice, the R value is usually measured at 20% elongation in a tensile test. For sheet metals, the R values are usually determined for three different directions ...
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Anisotropy
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.). An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it. Fields of interest Computer graphics In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal, as is the case with velvet. Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and steeply angled with respect to the point of view. Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or bl ...
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