Compressibility uniaxial compression

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

Fig. 9.28 Model results for the normalized equivalent macroscopic flow stress 5e/ro as a function of the equivalent macroscopic strain Se for several deformation histories of tension, plane-strain compression, uniaxial compression, and simple shear compared with experimental results of plane-strain compression (o) and uniaxial compression ( ), where To = 7.8 MPa is the plastic-shear resistance of HDPE (from Lee et al. (1993a) courtesy of Elsevier).

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

The structure/property relationships in materials subjected to shock-wave deformation is physically very difficult to conduct and complex to interpret due to the dynamic nature of the shock process and the very short time of the test. Due to these imposed constraints, most real-time shock-process measurements are limited to studying the interactions of the transmitted waves arrival at the free surface. To augment these in situ wave-profile measurements, shock-recovery techniques were developed in the late 1950s to assess experimentally the residual effects of shock-wave compression on materials. The object of soft-recovery experiments is to examine the terminal structure/property relationships of a material that has been subjected to a known uniaxial shock history, then returned to an ambient pressure... 

The microstructure/property relationships observed in shock-recovered samples have been often tacitly assumed to result solely from the shock compression, duration, and rarefaction due to the imposed uniaxial-strain shock. Recent shock-recovery studies have, however, shown that the degree of residual strain in the sample significantly influences the measured struc-... 

For example, a 10 GPa (total strain = 0.06) shock wave in copper has a maximum total strain rate 10 s [21] the risetime would thus be (eje) 0.6 ns. For uniaxial-strain compression, y averaged over the entire shock front. The resolution of the shock wave in a large-scale, multidimensional finite-difference code would be computationally expensive, but necessary to get the correct strength f behind the shock. An estimate of the error made in not resolving the shock wave can be obtained by calculating dt/dy)o with y 10 s (the actual plastic strain rate) and y 10 s (the plastic strain rate within the computed shock wave due to a time step of 0.06 qs). From (7.41) with y = 10 s (actual shock wave) and y = 10 s (computation) ... 

J.J. Dick and D.L. Styrus, Electrical Resistivity of Silver Foils Under Uniaxial Shock-Wave Compression, J. Appl. Phys. 46, 1602-1617 (1975). 

Type of stress. A uniaxial tensile creep test would not be expected to give the required data if the designer was concerned with torsional or compressive creep. 

For a component subjected to a uniaxial force, the engineering stress, a, in the material is the applied force (tensile or compressive) divided by the original cross-sectional area. The engineering strain, e, in the material is the extension (or reduction in length) divided by the original length. In a perfectly elastic (Hookean) material the stress, a, is directly proportional to be strain, e, and the relationship may be written, for uniaxial stress and strain, as... 

Thomas, D.A. Uniaxial compressive creep studies. Plastics and Polymers, Oct(1969) p. 485. 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

Fig. 4.10. The conductivity of uniaxially compressed (111) and (100) high purity germanium crystals leads to a determination of the shear deformation potential for the designated valley minima in the energy band (after Davison and Graham [79D01]).

For each of the failure criteria, we will generate biaxial stresses by off-axis loading of a unidirectionally reinforced lamina. That is, the uniaxial off-axis stress at 0 to the fibers is transformed into biaxial stresses in the principal material coordinates as shown in Figure 2-35. From the stress-transformation equations in Figure 2-35, a uniaxial loading obviously cannot produce a state of mixed tension and compression in principal material coordinates. Thus, some other loading state must be applied to test any failure criterion against a condition of mixed tension and compression. 

Most components of the strength tensors are defined in terms of the engineering strengths already discussed. For example, consider a uniaxial load on a specimen in the 1-direction. Under tensile load, the engineering strength is Xj, whereas under compressive load, it is (for example, Xg = -400 ksi (-2760 MPa) for boron-epoxy). Thus, under tensile load. 

Figure 5-18 Simply Supported Laminated Rectangular Plate under Uniform Uniaxial In-Plane Compression...

Figure 5-26 Buckling Loads for Anfisymmefric Cross-Ply Laminated Plates under Uniform Uniaxial Compression (After Jones [5-19])...

In pi actice, loads are not necessarily uniformly distributed nor uniaxial, and cross-sectional areas are often variable. Thus it becomes necessary to define the stress at a point as the limiting value of the load per unit area as the area approaches zero. Furthermore, there may be tensile or compressive stresses (O,, O, O ) in each of three orthogonal directions and as many as six shear stresses (t, , T ). The... 

Foam Density lb./ft.3 Glass Microballoons Epoxy Macroballoons Uniaxial Compressive Yield Strength, psi Hydrostatic Compressive Strength, psi Method of Preparation Resin System... 

Results of uniaxial strain static and gas gun compression tests on syntactic foam have been conducted. The foam was buoyant and composed of hollow glass microspheres (average diameter 100 microns) embedded in an epoxy plastic. Static testing consists of compressing a 0.25 cm x 2.5 cm dia. wafer between carefully aligned 2.5 cm dia. steel pistons. Lateral expansion of the wafer is... 

The first group of tests is carried out on specimens generally fabricated into a dumb-bell shape, with forces applied uniaxially. The usual apparatus consists of a machine with a pair of jaws, which during the test are moved relative to each other, either together or apart, in a controlled manner. A chart recorder is employed to give a permanent record of the results obtained, so that the force at fracture can be determined. Whether this kind of set up measures tensile, compressive, or flexural strength depends on how the sample is oriented between the jaws, and on the direction that the jaws are set to travel relative to one another. 

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