Strength ultimate theory

By definition, a brittle material does not fail in shear failure oeeurs when the largest prineipal stress reaehes the ultimate tensile strength, Su. Where the ultimate eompressive strength, Su, and Su of brittle material are approximately the same, the Maximum Normal Stress Theory applies (Edwards and MeKee, 1991 Norton, 1996). The probabilistie failure eriterion is essentially the same as equation 4.55. 

In many cases, a product fails when the material begins to yield plastically. In a few cases, one may tolerate a small dimensional change and permit a static load that exceeds the yield strength. Actual fracture at the ultimate strength of the material would then constitute failure. The criterion for failure may be based on normal or shear stress in either case. Impact, creep and fatigue failures are the most common mode of failures. Other modes of failure include excessive elastic deflection or buckling. The actual failure mechanism may be quite complicated each failure theory is only an attempt to explain the failure mechanism for a given class of materials. In each case a safety factor is employed to eliminate failure. 

The strength and extensibility of a noncrystallizable elastomer depend on its viscoelastic properties (28,29), even when the stress remains in equilibrium with the strain until macroscopic fracture occurs. In theory, such elastomers have a time- or rate-independent strength and ultimate elongation, but such threshold quantities apparently have not been measured, though rough estimates have been made (28,30). 

Load Sharing of Filler Particles. Comparison of ultimate strength of a propellant and its unfilled binder matrix almost always shows that the propellant has up to several times the tensile strength of the matrix. This filler reinforcement is presently thought to stem from additional crosslinks formed between filler particles and the network chains of the binder matrix (5, 8, 9, 34). Effective network chains are defined as the chain segments between crosslinks. From the classical theory of elasticity, the strength and/or modulus of an elastomer is proportional to the number of effective network chains per unit volume, N, or... 

By metallurgists in terms of the mechanical properties, such as modulus, fracture toughness, ultimate tensile strength. And they came up with a theory that deals with dislocation, fracture mechanic and continuum mechanics. 

The mosaic structure of a crystal is intimately connected with its mechanical strength. If we consider the lattice theory of a simple ionic crystal, such as sodium chloride, it is easy to calculate the stress necessary to rupture the crystal by separating it into two halves against the forces of interionic attraction. Such calculations lead to estimates of the tensile strength which are hundreds or thousands of times greater than those actually observed. If, however, the crystal possesses a mosaic structure the mechanism of fracture will be different. The two halves of the crystal will not now be separated simultaneously at every point instead there will be local stress concentrations at which the crystal will fail, the stress concentrations will then be transferred to other points and ultimately the crystal will break in two. The process may be likened to the tearing of a sheet of paper it is not easy to sever a piece of paper by means of a uniformly applied stress, but if a tear is started the stress is concentrated at the end of the tear, failure at that point takes place and the tear is rapidly propagated across the sheet. 

These and similar results led to the formulation of the statistical theories of fiber endurance and strength which assume that the ultimate properties of fibers are controlled by the properties of the weakest cross section of the specimen. The problem with this theory is that it does not lead to an estimate of the ultimate properties of a flawless specimen. Consequently, it is impossible to speculate at present about the strength and endurance of specimens manufactured under ideal conditions from the properties of a given sample. 

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