Punch, rigid

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. 

Our aim is to analyze the solution properties of the variational inequality describing the equilibrium state of the elastic plate. The plate is assumed to have a vertical crack and, simultaneously, to contact with a rigid punch. 

A linear approximation for the nonpenetration condition between the rod and rigid punch can be written as follows ... 

Khludnev A.M. (1983) A contact problem of a linear elastic body and a rigid punch (variational approach). Appls. Maths. Mechs. 47 (6), 999-1005 (in Russian). 

Khludneva E.Yu. (1990b) Contact of a nonelastic plate with a rigid punch. In Dynamics of Continuum Media. Novosibirsk (98), 67-79 (in Russian). 

The best products have smooth, natural curves and drawn sections that are spherical or nearly so in shape. Their walls will be more uniform, they will be more rigid, their surfaces will be less apt to show tool marks, and their tooling and molds will be lower in cost. Notches or square holes should be avoided when punching formed products. Round holes are preferred to oval ones for minimizing stress buildup. 

Some ductile plastics, such as PC and ABS, can be fabricated like metals with punching and cold-forming techniques. These processing techniques are analogous to the hardness tests in that a rigid indentor is pressed into a sheet of a less-rigid plastic. 

Screening involves passing stock thorough a perforated screen plate to remove oversized material from the good quality fibres or fines. Screen plates are rigid metal plates in which slots have been cut or punched. There are essentially two characteristics that affect stock behaviour during screening, first the fibres and fines... 

Die Pressing. Pressing of powders in rigid dies is carried out either in mechanical or hydraulic presses. The pressure is applied from the top, or from the top and bottom (double action presses). Die and punches are made of high-speed tool steel or... 

The impact extrusion process is used to produce open-ended collapsible tubes from softer metals such as tin and lead. When aluminium is used, it work-hardens during the forming process and the resultant tubes must be annealed to regain flexibility. Alternatively aluminium tubes may be left in their work-hardened state as rigid containers. Impact extrusion is a particularly useful process to produce containers with a high length to diameter ratio, e.g. up to 7 1. A slug of the metal to be formed is held in a female die and is struck by a punch which has the same form as that of the inside of the ultimate container. Upon impact the metal flows up the outside of the punch. A stripper plate then removes the extruded container on its return stroke. 

For some time now special isostatic (or, more properly, isostatic-effect) die sets have been used to optimise filling homogeneity right across the surface of the die cavity isostatic dies have reduced finished die defects considerably. Compression is exerted by way of a punch with a rigid back and a hard, yet deformable polymer front that comes into contact with the powders to be pressed a chamber between the punch and the polymer membrane contains an incompressible fluid. Fig. 8 illustrates the operating principle behind these punches. 

Keeler SP (1961) Plastic instability and fractine in sheet stretched ovct rigid punches. PhD Thesis. Massachusetts Institute of Technology, Boston... 

Figure 9.5. (a) Hemispherical compressive stress at Hertzian contact spot (b) rigid punch tensile stress distribution (c) resultant pressure distribution obtained by adding (a) and (b). 

The same reasoning applies to an elastic surface coating which is indented by a rigid punch, as shown in Fig. 14.16(a). In this case the crack is caused by the squeezing of the film from the gap between the punch and the substrate. This causes a ring crack to be initiated just outside the punch contact region, as shown by some early experiments in 1974. ... 

Figure 17.6. Different geometries of adhesion test sphere, rigid punch, peel, and butt.

SP Keeler. Plastic Instability and Fracture in Sheet Stretched over Rigid Punches. ScD thesis, Massachusetts Institute of Technology, Cambridge, MA, 1961. 

Johnson et al. (3) have shown how the elastic energy can be computed in the case of a spherical punch by adding a rigid body displacement to the classical elastic solution. In fact, this method is quite general for punches of any shape and can be proved by the general theory of elasticity (4) stresses and discontinuities of displacement are those of fracture mechanics ... 

Adherence of spheres and flat punches was studied by Johnson et al. (3), Kendall (5), and Maugis and Barquins (2,6). For an axisymmetric rigid punch contacting an elastic half-space, under a load P, over an area of radius a, it can be shown (7,4) that... 

PVC is an amorphous polymer (glass transition temperature = 220 °F, 105 °C). As a result, it has good clarity. Another important characteristic is that it can be extruded either as a rigid material or as a flexible material by adding a plasticizer to the polymer. Rigid films can be metallized and punched into sequins for dressmaking applications. Flexible films are used to overwrap clothing and other textile products. 

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