Failure compressive shear stresses

Ductile Failure of Brittle Polymers under Compressive Shear Stresses... 

If the component T of an applied compressive shear stress orthogonal to the plane of fracture combines with the normal component o-yy of the local stress at the tip of a crack, then the combined higher stress will minimize (AH — U0)/ductile failure ensues. This can occur if the orthogonal compressive stress is locally inhomogeneous. Hence, a polymer can fail in a more ductile fashion under orthogonal compressive shear stresses than in their absence. 

That is, if the local tensile, compressive or shear stresses exceed the materials tensile, compressive or shear strength then failure will occur. Some typical values for the strengths of uni-directional composites are given in Table 3.5. 

The failure of a simple structural element under unidirectional stress (tensile or compressive) is easy to relate to the tensile strength of the material, as determined in a standard tensile test, but for components subjected to combined stresses (normal and shear stress) the position is not so simple, and several theories of failure have been proposed. The three theories most commonly used are described below ... 

DIF values vary for different stress types in both concrete and steel for several reasons. Flexural response is ductile and DIF values are permitted which reflect actual strain rates. Shear stresses in concrete produce brittle failures and thus require a degree of conservatism to be applied to the selection of a DIF. Additionally, test data for dynamic shear response of concrete materials is not as well established as compressive strength. Strain rates for tension and compression in steel and concrete members are lower than for flexure and thus DIF values are necessarily lower. 

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

The second important assumption in the analysis is that interfacial failure occurs only in shear, i.e. that any peeling stress, normal to the interface, is negligible. Analysis of an elastic bilayer (5) shows that, for the experimental parameters employed here, the peeling stress is, in fact, an order of magnitude less than the shear stress. Furthermore, finite element analysis (6) shows that the normal stress is compressive rather than tensile for the thicknesses of PET and Ni used here. Finally, it will be shown that the experimental results are consistent with the one-dimensional analysis presented above. 

The strength of most materials is greater in compression than in tension. It is therefore unfortunate that technical difficulties prevent the direct application of tensile stresses. The compressive stresses commonly used in comminution equipment do not cause failure directly but generate by distortion sufficient tensile or shear stress to form a crack tip in a region away from the point of primary stress application. This is an inefficient but unavoidable mechanism. Impact and attrition are the other basic modes of stress application. The distinction between impact and compression is referred to later. Attrition, which is commonly employed, is difficult to classify but is probably primarily a shear mechanism. 

Height of drop causing complete failure Compression parallel to grain Fiber stress at proportional limit Maximum crushing strength Compression perpendicular to grain Fiber stress at proportional limit Shear parallel to grain... 

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). 

Gcy Stress required to cause failure by shear yielding under uniaxial compression. 

Some agglomerates of different materials have been observed to fail because of internal flaws driven by a number of stresses (e.g., internal tensile stress cracks in the surface plastic flow at the surface between the agglomerate and platen and shear stress within the sphere). For brittle particle agglomerates with significant internal flaws, the tensile strength is small compared to the compressive and shear strength, and failure is likely initiated by the internal tensile stress. In any case, a careful microscopic examination of failed pieces can provide much information on the dominant failure mode (Bika et al., 2001). 

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. 

For materials such as mild steel, w hich fail in shear rather than direct tension, the maximum shear theory of failure should be used. For internal pressure only, the maximum shear stress occurs on the inner surface of the cylinder. At this surface both tensile and compressive stresses are maximum. In a cylinder, the maximum tensile stress is the circumferential stress, (70. The maximum c ompressive stress is the radial stress, These stresses would be computed as... 

The UFS test is useful screening method, since if seripus compressive weakness is present it will become obvious from failure of the tensile face in three point bend test. In this test a span-depth-ratio of 40 1 ensure true flexural failure and minimese the effect of shear stress and traverse crushing by loading envill. The dimension of specimen according to ASTM D-790 as illustrated in figure 2. 

LaRC 03 failure criterion The LaRC 03 failure criterion [12] consists of a family of six criteria. It is an extension of the Puck [11] and Hashin [13] failure criteria. Like the Puck criterion, it focuses on the fiacture plane that is determined by maximizing the Mohr—Coulomb stresses. In the LaRC 03 criterion, failure due to matrix compression is the result of local interaction of shear stresses on a fracture plane. This perspective comes from soil mechanics situafions where the compression strength is different than the tension strength. It is parficularly useful in cases where, on a certain plane in the material, there are both normal and shear stresses acting. The interaction line that... 

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