SHEET FORMING In stamping, drawing, or pressing, a sheet is clamped (sujeta, anclada) around the edge and formed into a cavity by a punch. The metal is stretched (estirada) by membrane forces so that it conforms to the shape of the tools. The membrane stresses in the sheet far exceed the contact stresses between the tools and the sheet, and the through-thickness stresses may be neglected except at small tool radii. Figure 1 shows a stamping die with a lower counter-punch or bottoming die, but contact with the sheet at the bottom of the stroke will be on one side only, between the sheet and the punch or between the die and the sheet. The edge or flange is not usually held rigidly, but is allowed to move inward in a controlled fashion. The tension must be sufficient to prevent wrinkling (arrugas), but not enough to cause splitting (cortes).Figure 1 Figure 1. A schematic section of a typical stamping die. The sheet contacts only the punch or the die at any point. Membrane stresses stretch the sheet over the tools.

Límites de conformado The limits of deformation, or the window for stamping, are shown in Figure 2. It is assumed that the failure limits are a property of the sheet. This assumption is reasonable if through-thickness stresses are negligible, and if each element follows a simple, linear path represented by a straight line radiating from the origin.Figure 2 Figure 2. A schematic plot of the window of safe straining for simple pathsthe forming- limit diagram. With an isotropic material, the limits for e2 > e1 mirror those in the region where e1 > e2.

Pasos de deformación en un estampado real rectangular The path in stampings is described by the ratio of the membrane strains β=e 2 /e 1 which vary from equal biaxial stretching (β = 1) to uniaxial compression (β = -2.) Figure 3 shows the strain paths along two lines (A to J and A to E) in a rectangular pressing. Such diagrams are strain signatures of the part. The concept of the forming limit curve is that all possible strain signatures are bounded by an envelope that is a characteristic only of the material.Figure 3

Inestabilidad plástica en tracción equibiaxial

Inestabilidad plástica en tracción con deformación plana

Ecuación se Swift para inestabilidad plástica según diversos pasos de deformación

Gráfico de la ecuación de Swift en espacio ε 1 - ε 2

Inestabilidad en presencia de defectos en la plancha

Inestabilidad en presencia de defectos en la plancha

Límites de conformado empleando un criterio de fractura

Mecanismos de fractura dúctil. Metales puros

Mecanismos de fractura dúctil. Metal puro monocristalino

Mecanismos de fractura dúctil. Metales con partículas de segunda fase grandes.

Mecanismos de fractura dúctil. Metal con partículas de segunda fase de mediano tamaño.

Mecanismos de fractura dúctil

Inicio y crecimiento de la fractura dúctil

Criterio de Kobayashi para la fractura dúctil

Criterio de Cochroft y Latham para la fractura dúctil

Diferentes criterios de fractura dúctil donde  p representa la deformación plástica equivalente,  p f es la deformación plástica equivalente en el instante de la fractura,  es la tensión equivalente,  h es la tensión hidrostática,  I es la tensión principal máxima y los C i (i=...6) son constantes del material a determinar experimentalmente. En la forma aquí presentada, los criterios expuestos predicen que el fallo del material por fractura dúctil se produce cuando el valor de la integral (término izquierdo de la igualdad) alcanza un valor igual a la unidad.

Diagramas de deformaciones límites (DDL) (Forming limit diagrams). Herramienta para evaluar la formabilidad de planchas metálicas y la posibilidad de estampar una determinada forma. Los diagramas de deformaciones límites (DDL) son herramientas desarrolladas a nivel de taller para evaluar la posibilidad de estampar planchas delgadas sin rupturas para producir piezas de diferentes formas. Cuando se estampan piezas de formas complejas, diversos puntos de la plancha se deforman según diferentes pasos de deformación (k = e 2 /e 1 ); e 1 y e 2 son deformaciones de ingeniería máxima y mínima en una pequeña área del plano de la plancha. Se ha usado deformación de ingeniería porque se han generado a nivel de taller, pero por supuesto también se puede utilizar deformaciones verdaderas. En procesos de estampado industriales los pasos de deformación van desde k = -1/2 ( tracción uniaxial), k = 0 (tracción con deformación plana) hasta k= 1 (tración equibiaxial). El proceso de embutido produce un paso de deformación k= -1. El DDL señala las máximas deformaciones que se pueden aplicar, siguiendo diferentes pasos de deformación, hasta que se produzca una fisura. La figura siguiente muestra un DDL

Ensayos para obtener DDL. Se estiran hasta la falla : cuello localizado o fisura probetas de diferentes formas iniciales, las que generan diferentes pasos de deformación

Probetas de diferentes formas iniciales producen diferentes pasos de deformación al ser estiradas por el conjunto matriz - punzón

Se imprime sobre la superficie de la probeta una grilla de círculos y cuadrados; los primeros de transforman en elipses con un semieje mayor ( e 1 ) y un semieje menor (e 2 ); la probeta se estira hasta que en alguna zona se produce un cuello localizado o ruptura.

Deformaciones de una grilla circular y deformaciones límites

Se imprime sobre la superficie de la probeta una grilla de círculos y cuadrados; los primeros de transforman en elipses con un semieje mayor ( e 1 ) y un semieje menor (e 2 ); la probeta se estira hasta que en alguna zona se produce un cuello localizado o ruptura.

Los DDL dividen el espacio e 1 – e 2 en dos regiones: bajo el DDL es una región segura para deformar la plancha y sobre el DDL se producen fallas; entre las dos hay una franja ambivalente.

Cómo encontrar el DDL (límite entre zona segura y zona de fallas)

Es importante el punto mínimo del DDL (FLD 0 ) ; el cual corresponde a deformación plana (e 2 o ε 2 = 0)

Las dos figuras sirven para estimar el DDL de un acero para estampado. La Figura de la izquierda es estandar y de sube o baja paralela según el valor de FLD 0 calculado con la Figura de la derecha, en función de n y del espesor de la plancha.

Variación del DDL al variar la tensión de fluencia del acero y el espesor de la plancha para un mismo acero Espesor (in)

Ensayos practicados en el Lab. de Ing Mecánica para obtener pasos de deformación: tracción uniaxial, tracción con deformación plana y tracción biaxial.

Fig. 2 Bulge test specimen holder Dispositivo para el bulge test

Probetas para producir pasos de tracción uniaxial y tracción con deformación plana.

Otras probetas para producir tracción uniaxial, tracción con deformación plana, tracción biaxial circular y elíptica

Configuración óptica para medir deformaciones con interferometría laser speckle

Ensayos para caracterizar la formabilidad de planchas

Ensayo para LDR (razón límite de embutido) o ensayo Swift

Limited Draw Ratio (LDR) The Limiting Draw Ratio test is a single mode draw test. This test evaluates the ability of a sheet metal to be drawn into a cylindrical cup. Typically, however, circular disks of increasing diameter are machined or punched. After deburring, they are inserted into the draw fixture. A clamping force is applied which is sufficient to prevent wrinkling but which is not so large as to add an unnecessarily large component to the draw load. Cups are drawn with increasing blank diameter until the blank diameter is reached at which breakage is encountered. The Limiting Draw Ratio is defined as that maximum ratio of blank diameter to punch diameter for the onset of breakage. The LDR has been shown to depend linearly on the normal anisotropy of the steel

Ensayo simulativo de la expansión de un agujero en la plancha

Hole Expansion The hole expansion test measures the ability of a sheet edge to be elongated. No standard test procedures have been developed for this test. Thus, various combinations of hole diameters and punch diameters, as well as different punch configurations, are used by different laboratories. Many test units in operation today have a common diameter of four inches (102mm). The diameter of the hole depends on the sheet metal being tested; a typical hole diameter of two inches (51mm) allows a maximum hole elongation of 100 percent. Hole expansion is continued until a predefined end point is reached. This usually is the onset of edge “checks” or edge notches. Deformation beyond this stage will rapidly lead to cracking. The formula for the hole expansion is: % H.E. = [(Df – Di)/ Di]x 100 where Df is the final hole diameter and Di is the initial hole diameter. El %HE depende mucho de la terminación del agujero

Curvas tensión – deformación con diferents valores de n y m. Un alto valor de “n” da alta deformación homogénea (previa al cuello) un alto “m” da alta deformación post cuello.

Correlación entre deformación post cuello y valor de “m”.

Ensayo de la Altura límite del domo

Ensayo de la altura límite del domo The Limiting Dome Height (LDH), strips of varying widths are clamped on end by a lock bead and then deformed with a four-inch (102mm) diameter hemispherical punch. The different widths generate different minor strains at failure. The height at failure (height at maximum load) can be plotted as a function of strip width or minor strain. LDH curves for two different steels are schematically shown in the Figure. Superimposed on the LDH curves are the strain paths commonly followed by three traditional laboratory tests. The total height of the dome depend on two factors: The first is the maximum amount of strain the metal can withstand before failure. Obtained from the Forming Limit Diagram (FLD), this strain represents a limiting (ceiling) value. The second factor is how uniformly the strain is distributed without exceeding the ceiling. A high uniform strain will generate the largest dome height. The distribution of strain is governed both by the stretchability of the steel and the strain distribution characteristics of the blank-punch interface. These are also the characteristics which lead to good stretchability in a production stamping. Therefore, it is argued that the height in the LDH test can be related to the stretchability of production stampings.

Ensayo Domo de Olsen Se permite deslizamiento de la plancha entre matrices.

Olsen/Erichsen Dome The Olsen Dome test is used as a stretchability evaluation test in North America. The Erichsen Dome test is a similar test used in Europe and Japan. The simple test procedures makes these two tests popular in the sheet metal forming industry. The operational procedures of the Olsen Dome test are few. Specimen preparation requires only sharing a small rectangular blank. The test apparatus consists of a hydraulic cylinder to force a small diameter hemispherical punch into a sheet clamped by an annular die set activated by another hydraulic cylinder. Measurements are made of punch load and punch travel. Punch travel is stopped when the end-point is detected. The correct end-point is the maximum in the punch load-punch travel curve. This can be determined from a graphical plot of punch load versus punch travel. Total punch travel is measured in thousandths of an inch; the Olsen value is the dome height in thousandths. Therefore, a 425 Olsen value is really inches of punch travel to the point of test cutoff. In theory the Olsen Dome test is a pure biaxial stretch test. As such the Olsen values should correlate with common stretchability parameters,

Correlación entre altura del Olsen dome y la elongación total (mm) de la plancha

Marciniak test. El punzón empuja la placa inferior perforada, la que a su vez estira la placa superior. Es un modo de estirar de manera plana la plancha ensayada.

The Marciniak Stretch test, It was designed to overcome the severe strain gradients developed by the traditional dome tests using a hemispherical punch. If a flat sheet of metal is simply clamped and a flat-bottom punch is pushed into the sheet, a very limited amount of stretch is possible, usually around the punch radius, before the strain level reaches failure and tearing occurs over the radius. To increase the level of straining in the flat bottom, metal must slide over the punch radius and transmit increasing force to the metal in the flat bottom. Strain can not be allowed to localize in the radius. This is extremely difficult to accomplish with a single sheet of metal. A carrier blank between the test blank and the punch has to be added. A central hole punched in the carrier blank easily expands allowing metal to slide over the punch radius with relatively small applied force. The metal of the test blank on top of the carrier blank rides with the carrier blank. The metal of the test blank within the circumference of the carrier blank hole elongates in all directions. A common size of the tested blank is eight inches (203mm) for a four-inch (102mm) diameter punch. The carrier blank can be made from any stock steel or other metal with excellent formability; the test bank must fail before the edge of the enlarged hole in the carrier blank checks or tears. Carrier blank thickness is not specified, but must be on the same order as the test blank or else fracture can occur in the carrier blank.

Ensayos de formabilidad simulativos. Estirado cónico de Fukui.

Fukui Conical Cup Very few stampings can be identified as being pure stretch or pure draw. Therefore, it can be argued that laboratory simulative tests which are intended to be pure stretch (such as the Olsen Dome test) or pure cup drawing tests (such as the Limiting Draw Ratio) should correlate poorly with actual press performance. A laboratory simulative test is needed which incorporates both modes of deformation. Fukui Conical Cup test was designed to overcome this problem. In this test, a circular disk of metal is blanked in a separate operation; its diameter depends on the sheet metal thickness. This disk is then placed into a conical die. No holddown is used. This is possible because the ratio of blank diameter to sheet thickness is such that buckling does not occur. The absence of holddown eliminates many of the test variables associated with draw type tests, such as holddown load, die radii, roughness of the holddown surfaces, lubrication under the holddown, etc. The deformation forces are generated by pushing a spherical ball into the center of the blank. Two deformation modes occur. The central portion of the blank is stretched over the ball. This loading also causes the blank to be pulled down the conical cavity. The circumference of the blank must decrease, generating the compressive stress component found in cup drawing. This test sums all the various components to produce a final cup height at failure. The higher the maximum height, the more formable the steel. The traditional Fukui Conical Cup Values (CCV) – the ratio of final cup diameter to blank diameter – strongly depend on the product of n m times r m.

The diameter ratio of the Fukui conical cup test correlates well with the product of n m and r m