Flat punch

However, use of the loss tangent in Eq. (13) is an oversimplification. Instead, we shall make use of an empirical dissipation law obtained in the study of rate-dependent adhesion of elastomers (19). Maugis and Barquins [19], in order to explain the dynamic adhesion of elastomers in a variety of test configurations (peel, flat punch, etc), proposed the following relation ... 

Tablets of 250 mg with starch concentrations of 5%, 15% and 25% w/w respectively, were prepared. Starch and lactose were mixed for 15 minutes in a Turbula mixer at a rotation speed of 90 rpm.. Magnesium stearate (0.5% w/w) was added and mixing was continued for 2 minutes. The tablets were prepared on a single punch tabletting machine, using 9 mm flat punches. From each mixture tablets were produced at three compression load levels 157,314,472 MPa.

Precompression using a Frogerais 0A single-punch instrumented press (Ets. Ed. Frogerais), equipped with flat punches 11,28mm in diameter (surface area, 1 cm2). The speed ofthe machine was adjusted to one tablet s... 

Compact density and its distribution is also strongly influenced by interactions between the solid particles and of the particulate mass with equipment features (e.g. die walls, punch surfaces, roller press pockets, etc.). If a perfectly lubricated particulate solid (i.e. featuring no interparticle friction) were compacted in a cylindrical die with frictionless walls, it could be expected that the force exerted by the smooth, flat punch is transmitted through the entire volume of material resulting in uniform pressure and, therefore, uniform density throughout the compact. In reality, the presence of frictional and shear forces leads to a non-uniform pressure distribution and irregular particle movement (displacement) causing variations in compact density. 

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... 

The load P corresponding to the limit of stability will be called the adherence force of the two elastic bodies, and thus will generally depend on the stiffness of the measuring apparatus. In some geometries (unstable geometries), equilibrium is always unstable, and thus the criterion for adherence force is simply G = w. li is the case for the double cantilever beam at fixed load, or for a flat punch on an elastic half-space. It is also the classical Griffith case of a crack in an infinite solid. 

The case of an axisymmetric flat punch of radius a on an elastic half-space was solved by KendalK7) by evaluating the elastic energy = iPb and the potential energy Up = —from the elastic displacement under the load P ... 

Figure 3.32- Coordinate system for calculation of a stress field from a long flat punch. After...

The new theory makes use of old established work by ignoring plasticity and modeling elastic stress fields around a long, flat punch of finite width subjected to a uniform pressure. Stresses are calculated with the variables shown in Figure 3.32 and the following equations ... 

The same arguments apply to adhesion of two spheres where the contact spot is much smaller than the sphere diameter. In this case the stress inside the contact is the sum of the Hertzian hemispherical distribution and the flat punch Boussinesq distribution. This problem was solved by Johnson, Kendall and Roberts in 1971 [22] to give the diameter d of the equilibrium contact spot for equal spheres diameter D... 

Fig. 5 Maximum indentation force and standard deviation as a function of the number of measured silica model aggregates (Xprimary = 50 nm) using a flat punch indenter geometry [39]...

For a cylindrical flat punch indenting an elastic half-space with the flat side parallel to the plane of the half-space, the contact area is simply given by na, where a is the radius of the cylinder. For an applied load P, the indentation 8 (i.e., the change in distance of the center points beyond the first contact of the bodies) of the punch becomes... 

Here, E and v are the Young s modulus and Poisson s ratio of the half space material. The indentation of a flat punch on an elastic half-space is proportional to the applied load. The contact area stays constant independent of load. We obtain a linear relation between load and displacement with an effective spring constant of E a/(l — v ) = E a. The vertical surface displacement Az(r) of the elastic half-space is given by... 

If we introduce an adhesion between the surfaces of the flat punch and the elastic half-space, all equations of Section 8.2.1 remain valid and can also be applied for the situation where the load l becomes negative, that is, a traction force (Figure 8.6). 

The problem of the elastic contact of a flat cylindrical punch is less complex than that of a sphere due to the fact that for the flat punch, the contact radius is just given by the radius of the cylinder and thus known a priori. The problem of the elastic contact between a sphere and a planar surface and between two spheres was solved by Hertz in 1882 [846]. Under the assumption that the contact radius a is small compared to the sphere radii, that the contact is frictionless and no tensile stress exists within the area of contact. Hertz derived an equation for the contact radius a between the spheres ... 

The indentation force increases with a power of 3/2 with indentation depth. The contact area jta increases as and the mean contact pressure Fi/na increases with applied load as In contrast to the flat punch case, the contact does no longer act as a linear spring since Fl is proportional to due to the fact that the contact area... 

The last result was obtained by combining Eqs. (8.52), (8.53) and (8.55). The distribution of the normal stress across a JKR contact is just the sum of the distributions for a Hertzian contact with compressive load Fi and a flat punch with a tensile load Fi—Fl (Figure 8.10) ... 

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