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The hardness properties of materials are tracked from early history until the present time. Emphasis is placed on the hardness test being a useful probe for determining the local elastic, plastic and cracking properties of single crystal, polycrystalline, polyphase or amorphous materials. Beginning from connection made between individual hardness pressure measurements and the conventional stress–strain properties of polycrystalline materials, the newer consideration is described of directly specifying a hardness-type stress–strain relationship based on a continuous loading curve, particularly, as obtained with a spherical indenter. Such effort has received impetus from order-of-magnitude improvements in load and displacement measuring capabilities that are demonstrated for nanoindentation testing. Details of metrology assessments involved in various types of hardness tests are reviewed. A compilation of measurements is presented for the separate aspects of Hertzian elastic, dislocation-mechanics-based plasticity and indentation-fracture-mechanics-based cracking behaviors of materials, including elastic and plastic deformation rate effects. A number of test applications are reviewed, most notably involving the hardness of thin film materials and coatings.

In this paper, we study the stability of static charged anisotropic cylindrically symmetric compact object through cracking. The Einstein–Maxwell field equations and conservation equation are formulated. We then apply local density perturbation and study the behavior of force distribution function. Finally, the cracking is explored for two models satisfying specific form of Chaplygin equation of state. It is found that these models exhibit cracking and the instability increases as the value of charge parameter is increased.

This paper is devoted to examine the cracking of spherically symmetric anisotropic fluid configuration for polytropic equation of state. For this purpose, we formulate the corresponding field equations as well as generalized Tolman–Oppenheimer–Volkoff equation. We introduce density perturbations in matter variables and then construct the force distribution function. In order to examine the occurrence of cracking/overturning, we consider two models corresponding to two values of the polytropic index. It is found that the first model exhibits overturning for the considered values of polytropic constant while the second model neither exhibits cracking nor overturning for larger values of polytropic constant.

In the first part of this paper, elastostatic stability of cracked conservative flanged concrete beam-columns has been analyzed. Using the derived expression for the lateral stiffness under constant axial force, their elastodynamic stability is investigated in this second part. As expected, the instantaneous values of the stiffness and the damping coefficients of the lumped-mass underdamped SDOF nonlinear structures are found to depend upon the vibration amplitude. The natural frequency has been found to vanish at the two critical axial loads defined in the first part. For axial load exceeding the second critical value, the concrete beam-columns in the second equilibrium state are shown to exhibit loss of dynamic stability by divergence. Depending upon the initial conditions, the phase plane has been partitioned into dynamically stable and unstable regions. Under harmonic excitations, the nonlinear dynamical systems exhibit subharmonic resonances and jump phenomena. Loss of dynamic stability has been predicted for some ranges of damping ratio as well as of peak sinusoidal force and forcing frequency. Sensitivity of dynamic stability to the initial conditions and the sense of the peak sinusoidal force have also been predicted. The theoretical significance and the methodology adopted in this paper are also discussed.

The cracking of GaN films and the associated cracking of substrates are described. The geometry, structure, and evolution of fracture demonstrate that GaN films crack under tensile stress during growth and are subsequently overgrown and partially healed. The film cracks channel along the (1010)_GaN planes and also extend a distance of ~5 μm into the sapphire substrate. These incipient cracks in the substrate form a set of initial flaws that leads to complete fracture through the sapphire during cooling for sufficiently thick films. Each stage of this cracking behavior is well described by a fracture mechanics model that delineates a series of critical thicknesses for the onset of cracking that are functions of the film and substrate stresses, thicknesses, and elastic properties. Similar cracking behavior is found to occur independently of the choice of substrate between sapphire and SiC and is traced to a tensile stress generation mechanism early in the growth process, such as that provided by island coalescence. Cracking is the dominant stress relief mechanism, as opposed to dislocation generation or diffusion, because of the island growth mode and because of optimized growth temperatures at or below the brittle-to-ductile transition. Lateral epitaxial overgrowth (LEO) of GaN is shown to minimize substrate fracture even though film cracking remains unaffected. This effect explained in terms of the limits placed on the initial extent of insipient substrate cracks due to the LEO geometry.

Ceramic injection moulding is a well established processing technique, but is still limited to thin section components. This paper gives an overview of a variety of defects which appear preferentially in thick moulding sections. The generation of porosity and voidage during packing and solidification are discussed and related to the conditions prevailing during solidification. The use of an insulated sprue extended gate solidification and eliminated voids in thick sections and the use of a polyoxymethylene binder system enabled the progressive removal of binder from large 35 mm sections. Low hold pressure, applied by using a modified injection moulding machine reduced residual stress-induced cracking. Pronounced differential sintering was traced to particle alignment during mould filling and could be eliminated by using equiaxed powders.