Compressive measurement stress

Curran [61C01] has pointed out that under certain unusual conditions the second-order phase transition might cause a cusp in the stress-volume relation resulting in a multiple wave structure, as is the case for a first-order transition. His shock-wave compression measurements on Invar (36-wt% Ni-Fe) showed large compressibilities in the low stress region but no distinct transition. 

Figure 59.19 Measurements used in calculating shear and compressive key stress...

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

Interesting deviations from Gaussian stress-strain behaviour in compression have been observed which related to the Me of the networks formed, rather than their degrees of swelling during compression measurements. 

Some measured values of hardness are given in Table 8.1 which shows how the hardness varies with stoichiometry (Qian and Chou, 1989). The values in the table are averages of 30 measurements for each composition. The stoichiometric value is 16X the yield stress (albeit from different authors). Since hardness numbers for metals are determined by deformation-hardening rates, the latter is very large for Ni3Al causing the hardness numbers to be 16X the compressive yield stress instead of the 3X of pure metals. 

In the same way that close-packed directions in a crystal have larger refractive indices, so too can the application of a tensile stress to an isotropic glass increase the index of refraction normal to the direction of the applied stress. Uniaxial compression has the reverse effect. The resulting variation in refractive index with direction is called birefringence, which can be used as a method of measuring stress. 

Compressive measurements provide a means to determine specimen stiffness, Young s modulus of elasticity, strength at failure, stress at yield, and strain at yield. These measurements can be performed on samples such as soy milk gels (Kampf and Nussi-novitch, 1997) and apples (Lurie and Nussi-novitch, 1996). In the case of convex bodies, where Poisson s ratio is known, the Hertz model should be applied to the data in order to determine Young s modulus of elasticity (Mohsenin, 1970). It should also be noted that for biological materials, Young s modulus or the apparent elastic modulus is dependent on the rate at which a specimen is deformed. 

Fig. 26. Comparison of the predicted (solid lines [46]) and measured (points [45]) strain rate dependence of the compressive yield stress of silica filled epoxy at different filler concentrations...

Glass transition temperature Secondary transition Extension ratio Maximum extension ratio Craze intensification stress Craze initiation stress Tensile strength Compressive yield stress Drop in after yielding A measure of strain softening Test frequency... 

Figure 14.8 shows stress-strain curves for polycarbonate at 77 K obtained in tension and in uniaxial compression (12), where it can be seen that the yield stress differs in these two tests. In general, for polymers the compressive yield stress is higher than the tensile yield stress, as Figure 14.8 shows for polycarbonate. Also, yield stress increases significantly with hydrostatic pressure on polymers, though the Tresca and von Mises criteria predict that the yield stress measured in uniaxial tension is the same as that measured in compression. The differences observed between the behavior of polymers in uniaxial compression and in uniaxial tension are due to the fact that these materials are mostly van der Waals solids. Therefore it is not surprising that their mechanical properties are subject to hydrostatic pressure effects. It is possible to modify the yield criteria described in the previous section to take into account the pressure dependence. Thus, Xy in Eq. (14.10) can be expressed as a function of hydrostatic pressure P as... 

Flow Functions and Flowabilily Indices Consider a powder compacted in a mold at a compaction pressure Oi. When it is removed from the mold, we may measure the powder s strength, or unconflned miiaxial compressive yield stress L (Fig. 21-38). The unconfined yield and compaction stresses are dietermined directly from Mohr circle constructions to yield loci measurements (Fig. 21-36). This strength increases with increasing previous compaction, with this relationship referred to as the powder s flow function FF. 

The effective P may be determined with the electron beam apparatus. When the sample (slab geometry) is thick enough to absorb all of the incident electrons, a compressive stress wave propagates from the irradiated region into the sample bulk. A transducer, located just beyond the deposition depth, may be used to record the stress pulse. Alternatively, the displacement or velocity of the rear surface of sample may be observed optically and used to infer the initial pressure distribution from the experimentally measured stress history. Knowledge of the energy-deposition profile then permits the determination of the Gruneisen coefficient. 

A polymer is more likely to fail by brittle fracture under uniaxial tension than under uniaxial compression. Lesser and Kody [164] showed that the yielding of epoxy-amine networks subjected to multiaxial stress states can be described with the modified van Mises criterion. It was found to be possible to measure a compressive yield stress (Gcy) for all of their networks, while the networks with the smallest Mc values failed by brittle fracture and did not provide measured values for the tensile yield stress (Gty) [23,164-166]. Crawford and Lesser [165] showed that Gcy and Gty at a given temperature and strain rate were related by Equation 11.43. 

The easiest way to measure stress in thin films after deposition is to analyze the change in the radius of curvature of the wafers before and after film deposition on one side, as first proposed by Stoney [7]. However, this technique usually requires the use of test wafers. After complete processing of the wafers, the stress can be obtained by measuring the deflection of membranes or indicator structures [8], To measure compressive stress, the buckling technique on double-side supported bridges [9] and harp-like structures [10] can be applied. 

Fig. 16 Typical stress-strain behavior of mPVA (a) and mPDMS (b) gels in unidirectional compression measurements. In both cases, three samples having the same amount of filler particles are compared, but the distribution of the particles is different...

The cross-linking density cannot be estimated from the stoichiometric relation between monomer and cross-linker, e.g., NlPAAm and MBAAm, since the possibility of cychzation during NlPAAm polymerization is high (see Sect. 2, in chapter General properties of hydrogels ). A more realistic number of net chains can be determined by compression or stress-strain measurements, preferred on a gel swollen in organic solvent. 

The aim of an investigation determines the method to obtain contrast " in NMR. Let us consider the case of evaluating the distribution of cross-linking density inside a network. By classical mechanical measurements, e.g., compression or stress-strain experiments, we can calculate a cross-linking density, which represents a mean value over the sample volume we used in measurements. NMR enables the characterization on a microscopic level if we can investigate the properties of network chains at different sample positions. 

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