Surfaces spherical indentation

The equation, unlike that for a spherical indenter, contains no terms relating to the state of the sample surface (flaw population, etc.). Instead, it considers the cone angle as a variable through its influence on the penetration field. 

It should be pointed out that Equation (11) should be modified to Equation (1) when compression of a single particle between two surfaces is modelled, that is, spherical indentation is replaced by compression between two surfaces. Applications in which these models were applied to experimental data from compression testing are described later. 

Figure 12-18. Degree of contact for a hard spherical indenter pressed into the flat, rough surface of an unconstrained deformable body. The data divide into two classes. Homogeneous solids drawn rod aluminum, bead blasted A cold rolled aluminum, bead blasted cold rolled aluminum, bead blasted and then annealed Ygold, bead blasted and then annealed work-hardened turned copper. Degree of 0.007. Solids with hardened surface layers aluminum, bead blasted. Degree of contact ranged Data by Williamson and Hunt [16].

The arrangement of the radial and circumferential-like cracks around spherical indents depends strongly on the surface orientation [33], A schematic representation of the crack pattern on (111) NiAl is shown in Fig.9 together with surface profiles in different crystal directionfMatfiin the surface plane. 

Fig. 9. Arrangement of cracks around a spherical indent on (111) NiAl toghether with surface profiles measured by LSM.

Fig. 10. Results of FliM calculations of the spherical indentation surface profile (a), radial (b) and circumferential (c) surface strains versus radial distance from the centre of the indent for a piecewise linear work hardening (tangent modulus Et - 0.1 E for , < 0.02 and Er -- 0.0044 E for e, >0.02 (full line) T = 0.1 E (dashed line) E - 180 GPa, v =- 0.3,...

The elastic problem of contact between spherical particles was solved by Hertz in 1881 Of interest here is the limiting case of the contact of a sphere, radius / , with a flat surface (blunt contact). The spherical indenter forms a circular contact, radius a, with the surface. The contact area increases with size as the load increases. It can be shown that... 

Brinell Hardened steel ball Brinell hardness number (BHN) Is applied force divided by surface area of Indentation Meyer hardness number (MHN) uses projected area BHN = FtnDt MHN = 4F/tccF Spherical Indenters not used for ceramics... 

Nanoindentation is a technique gaining increasing popularity [74-76]. Actually, the technique is sometimes abused by attempts to calculate the elastic modulus E on the basis of a model valid for fully elastic materials only [74]. While such attempts fail, a connection has been found by Fujisawa and Swain between E and the unloading strain rate [75]. As shown by Tweedie and Van Vliet [76], spherical indentation provides lower contact strains and more reliable results than conical indentation. A modification providing repetitive indenter hits perpendicular to the specimen surface at the same spot and thus nanoindentation fatigue testing (NIFT) exists also [77]. 

Hardness and mechanical moduli of polymer blends were determined with a Micro materials Nano Test 600 apparatus (UK), applying the procedure of spherical indentation with 10% partial unloading. R=5 pm stainless steel spherical indenter probed the surface layer of material with the loading speed of dP/dt=0.2 mN/s, reaching depths up to 8.0 pm. More information on the instrumentation can be found elsewhere [13]. 

The Hertz method of determining Kc involves the use of an optically flat surface and a blunt— i.e., spherical— indenter. The sphere is pressed with a series of loads P until a critical load P ris found that gives a 50% chance of Hertz ring crack formation. In practice this is found by plotting the fracture probability against applied load for any given indenter radius a typical plot would look like Figure 5.18. 

Schematically illustrations of deformation on surface with spherical indenter are shown in Figure 2. The geometrical factor for elastic surface deformation is equal to 2 for spherical indenter. Thus, the contact circle penetration ftp is described as following ...

Figure 2. Schematically illustrations of deformation on surface with spherical indenter.

Formulations for DPIs are required to easily generate the highest FPF possible by dispersion during inhalation. Following these results, the carrier shape is crucial for the performance of interactive mixtures. A spherical shape gives the opportunity to detach dmg particles from all over the surface equally. Indentations in the carrier prevent good DPI performance. 

Figure 8.2 shows a diagram of the elastic loading of a glass surface by a spherical indenter. In such an experiment, a sphere of radius R is loaded under a force F, the contact radius being a. The specimen surface around the contact area also deforms elastically as shown schematically in Figure 8.2. 

Figure 8.2 Diagram of the elastic loading of a spherical indenter on a glass surface.

FIGURE 33.1 Schematic of a depth-sensing indentation (DSI) test. An indenter is pushed with force, F, into the surface an amount, h. The load-depth curve is generated. A schematic for a spherical indenter is shown. Corrections for the contact area calculation are made by finding he = (hmax+hr)/2. The parameters, hj. Fmax HE, and dF/dh are used to find the hardness, modulus, and energy dissipation resulting from indentation. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

The principle of the Brinell hardness test is that the spherical surface area of a recovered indentation made with a standard hardened steel ball under specific load is direcdy related to the property called hardness. In the following, HBN = Brinell hardness number, P = load in kgf,... 

However, for the case of the rigid particle indenting a compliant substrate, the change in area, which arises from the stretching of the surface of the substrate, is given by the expansion in size of a spherical cap. 

The elasticity was quantitatively determined by analyzing the recorded force curves with the help of the Hertz model. The Hertz model describes the elastic deformation of two spherical surfaces touching imder the load, which was calculated theoretically in 1882 by Hertz. Other effects, such as adhesion or plastic deformation, were not included in this model. Sneddon extended the calculation to other geometries. For a cone pushing onto a flat sample, the relation between the indentation 5 and the loading force F can be expressed as ... 

The surface characteristics of excipients have also been studied and related to the dispersion and dissolution of poorly soluble drugs [58]. It was found that excipients with rough surfaces (such as Emcompress, with a porous surface) trap the drug particles in the indentations, which can then be blocked by fine excipient particles and decrease dissolution. Smooth surfaces (such as spherical sugar beads), however, produced high dissolution efficiency of the poorly soluble drugs. 

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