Compressive loading, yield stresses

Plastic Forming. A plastic ceramic body deforms iaelastically without mpture under a compressive load that produces a shear stress ia excess of the shear strength of the body. Plastic forming processes (38,40—42,54—57) iavolve elastic—plastic behavior, whereby measurable elastic respoase occurs before and after plastic yielding. At pressures above the shear strength, the body deforms plastically by shear flow. 

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). 

Compression Test. Compression tests similar to that described in (5) were conducted for yield stress C and modulus E measurement. Rectangular neat resin specimens (1.27 cm x 1.27 cm x 2.54 cm) cut from the cast resin plates were tested under compression, as shown in Figure 1, in an universal testing machine at a loading rate of 0.05 cm/min. For each resin system studied, tests were conducted at several temperature levels between -60 and 60 degree C. All specimens were instrumented with strain gages for... 

PP bead foams of a range of densities were compressed using impact and creep loading in an Instron test machine. The stress-strain curves were analysed to determine the effective cell gas pressure as a function of time under load. Creep was controlled by the polymer linear viscoelastic response if the applied stress was low but, at stresses above the foam yield stress, the creep was more rapid until compressed cell gas took the majority of the load. Air was lost from the cells by diffusion through the cell faces, this creep mechanism being more rapid than in extruded foams, because of the small bead size and the open channels at the bead bonndaries. The foam permeability to air conld be related to the PP permeability and the foam density. 15 refs. 

The compression of uniform samples to the point where the force exceeds the structural capacity causes it to permanently deform and essentially break (4). A typical load-deformation curve can be used to derive values for yield stress, yield strain, and compressive yield work, and depending on the linearity of the onset of compression, a compressive modulus may be obtained (4). These measurements can be used to provide an index of hardness for fats, which have been successfully correlated to the textural attributes of hardness and spreadability obtained through sensory evaluation (4). Unfortunately, these tests are destructive in nature and yield minimal information about the native microstructure of the system. 

As explained earlier, most authors quote nominal mbber contents rather than mbber phase volumes, and there is therefore very little information in the literature on the relationship between Oyc and 0 for mbber-modified plastics. A rare exception occurs in the work of Oxborough and Bowden vdio measured yield stresses in tension and compression for a series of HIPS polymers ccmtaining composite rubber particles. Their results are presented in Fig. 7. Equation (9) underestimates the yield stresses both in tension and compression, and it must be concluded fiiat the effective area model does not provide a satisfactory basis for correlating yield data in this class of material. Either the model itself must be modified in some way, or some allowance must be made for load sharing with the mbber particles, if the effective area apprcrach is to be retained. 

The effective area modd predicts that the stress concentration factor 7 should be independent of composition in conqmsites containing well-bonded rigid filler paitides. This prediction is supported by the compressive yield data for silica-loaded epoxy resins presented in Fig. 8 yield stress is linear with log (strain rate) for eadi material, and the dopes are identical in each case. The increase of yield stress with silica content must therefore be interpreted as a decrease in the pre-exponential factor rather than in 7. Young and Beaumont observed a similar large increase in the yidd stress of silica-loaded epoxy resins, and suggested an analc with precipi-taticm-hardening in metals ... 

Powders can withstand stress without flowing, in contrast to most liquids. The strength or yield stress of this powder is a function of previous compaction, and is not unique, but depends on stress ap ication. Powders fail only under applied shear stress, and not isotropic load, although they do compress. For a given apphed horizontal load, failure can occur by either raising or lowering die normal stress, and two possible values of failure shear stress are obtained (active versus passive failure). 

Both destructive and nondestructive measurements can be done on an Instron Material Tester. In this system, the sample is loaded in a test cell, and the compression or tension force is measured when the upper part of the cell is moved over a given distance (time). Within the elastic limit of the gel, the elastic modulus E (or gel strength) is obtained from the initial slope of the nondestructive stress/strain curve additional deformation results in the breakage of the sample, giving the characteristic parameters—yield stress and breaking strain. 

Investigation of the deformation relief occurring on the surface of samples additionally subjected to by 15% strain after different number of compression steps have shown that plateau on the initial portion of strain curves is result of strain localization (Fig. 2a) in macro shear bands (MSB). Its appearance is result of scattering some dislocation boundaries onto individual dislocations (Baushinger effect) and formation of avalanche of mobile dislocations (Fig. 2b). So, in this case yield of titanium is controlled by substructure that, probably, leads to weak dependence of yield stress on strain. Macrobands formed at the beginning of the cycle of loading remain until the end of loading. So, plastic flow of titanium is localized. 

Comments on the Compression Tackiness Tester This is clearly a fingerprinting method of a proven practical value. The result does not represent, however, the unconfined yield stress corresponding to the compression load because the compression stress varies within the height of the briquette. This is because the load during the sample compression is partly taken up by wall friction and the stress (and the bulk density) therefore reduces in... 

Compressive properties include compressive strength, modulus of elasticity, yield stress, and deformation beyond yield point. The ASTM procedure covers determinations of all of them. In all cases, tested specimens are loaded in compression at relatively low uniform rates of straining or loading. Compressive yield point is the first point on the stress-strain curve at which an increase in strain occurs without an increase in stress. In other words, it is the load under which the specimen starts to move continuously without an increase in the load. Also, many plastic materials will continue to deform in compression until a flat disk is produced, without breaking of the specimen. In those cases the compressive stress (nominal) increases steadily in the process, without failure of the material. Compressive strength typically has no meaning in such cases. 

The compressive strength is calculated by dividing the maximum compressive load by the original minimum cross-sectional area of the specimen. The compressive yield strength is calculated in the same manner, but instead of compressive load at break, the compressive load at the yield point is used. The compressive modulus of elasticity is calculated in the usual manner, by dividing the compressive stress taken as a point on the initial linear portion of the load-deformation curve by the corresponding strain. 

Sample Load direction compression strength (psi) Yield stress (psi) Yield strain (%)... 

The same phenomenon occurs in the deflection of a column imder a compression loading. In this type of failure, a critical load is reached beyond which collapse occurs as a result of a rapid increase in the stresses beyond the yield point of the material. The critical pressure that causes collapse is not a simple function of the induced stress, as with tensile loads. In fact, it is directly proportional to the modulus of elasticity of the material and the moment of inertia of the shell and is inversely related to the cube of the radius of the curvature. 

Where a, is the uniaxial tensile yield stress and for polymer-based materials this is usually taken as the maximum load if a distinet yield point is not exhibited. However shear yielding in tensile tests with most polymers can be achieved by carefully polishing the specimen edges in order to remove surface blemishes and thus avoid premature failure. If yielding does not oecur and brittle failure is obtained, the stress at failure should be used in the criteria which gives a conservative size value. Alternatively 0.7 times the compressive yield stress may be used. The loading time to yield (or equivalent) should be within 20% of the loading duration in the fracture test. 

FEA of the stresses in the UHMWPE cup is difficult, as the stresses exceed the elastic limit. Teoh et al. (2002) considered an 8 mm thick cup with a metal backing, a 32 mm diameter ball and a peak load of 2.2 kN (about 2.5 X body weight) for walking. Using the unrealistic condition that the compressive stress on the ball/UHMWPE interface could not exceed the uniaxial compressive yield stress (of 8 MPa), they predicted the compressive stress to be at this level over a surface region of diameter about 8 mm. However, a von Mises type yield criterion should be used. It requires a pressure of nearly three times the uniaxial yield stress to extrude the PE to the side of the joint (Section 8.2.4). 

The fundamental difference between mechanical stresses and tliermal stresses lies in the nature of the loading. Thermal stresses as previously stated are a result of restraint or temperature distribution. The fibers at high temperature are compressed and those at lower temperatures are stretched. The stress pattern must only satisfy the requirements for equilibrium of the internal forces. The result being that yielding will relax the thermal stress. If a part is loaded mechanically beyond its yield strength, the part will continue to yield until it breaks, unless the deflection is limited by strain hardening or stress redistribution. The external load remains constant, thus the internal stresses cannot relax. 

S = code allowable stress, tension, psi N = number of anchor bolts Fp = allowable bearing pressure, concrete, psi Fy = minimum specified yield stress, sldrt, psi Fs = allowable stress, anchor bolts, psi fLT = axial load, tension, Ib/in.-circumference fLc= axial load, compression, Ib/in.-circumference Ft = allowable stress, tension, sldrt, psi Fc = allowable stress, compression, sldrt, psi Fb = allowable stress, bending, psi... 

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