Failure theories elasticity

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. 

As a pipeline is heated, strains of such a magnitude are iaduced iato it as to accommodate the thermal expansion of the pipe caused by temperature. In the elastic range, these strains are proportional to the stresses. Above the yield stress, the internal strains stiU absorb the thermal expansions, but the stress, g computed from strain 2 by elastic theory, is a fictitious stress. The actual stress is and it depends on the shape of the stress-strain curve. Failure, however, does not occur until is reached which corresponds to a fictitious stress of many times the yield stress. 

Alternatively, if detachment is associated with a brittle failure, then one must first determine if the fracture followed an elastic loading where an elastic model such as the JKR theory is appropriate or if it follows a plastic or elastic-plastic loading. In this latter case, the force needed to detach the particle from the substrate depends on the specific properties of the materials and the details of the deformations [63]. 

The simplified failure envelopes differ little from the concept of yield surfaces in the theory of plasticity. Both the failure envelopes (or surfaces) and the yield surfaces (or envelopes) represent the end of linear elastic behavior under a multiaxial stress state. The limits of linear elastic... 

Whereas the quasi-chemical theory has been eminently successful in describing the broad outlines, and even some of the details, of the order-disorder phenomenon in metallic solid solutions, several of its assumptions have been shown to be invalid. The manner of its failure, as well as the failure of the average-potential model to describe metallic solutions, indicates that metal atom interactions change radically in going from the pure state to the solution state. It is clear that little further progress may be expected in the formulation of statistical models for metallic solutions until the electronic interactions between solute and solvent species are better understood. In the area of solvent-solute interactions, the elastic model is unfruitful. Better understanding also is needed of the vibrational characteristics of metallic solutions, with respect to the changes in harmonic force constants and those in the anharmonicity of the vibrations. 

More or less implicit in the theory of materials of this type is the assumption that all the fibers are straight and unstressed or that the initial stresses in the individual fibers are essentially equal. In practice this is quite unlikely to be true. It is expected, therefore, that as the load is increased some fibers will reach their breaking points first. As they fail, their loads will be transferred to other as yet unbroken fibers, so that the successive breaking of fibers rather than the simultaneous breaking of all of them will cause failure. As reviewed in Chapter 2 (SHORT TERM LOAD BEHAVIOR, Tensile Stress-Strain, Modulus of elasticity) the result is usually the development of two or three moduli. 

The smaller expansion factor predicted by the theory of Hoeve originates from neglecting the tail portions of the adsorbed polymer chain, while the larger expansion factor predicted by Jones and Richmond is due to their failure of correctly evaluating the elastic free energy, as has been pointed out by Kawaguchi and Takahashi74. ... 

It is easy to see that these models are all based on the same (microstructural) principle, viz. that there is an elementary structural unit that can be described and then used for calculation. Remember that the corresponding unit cell for foamed polymers is the gas-structure element8 10). Microstructural models are a first approximation to a general theory describing the deformation and failure of gas-filled materials. However, this approximation cannot be extended to allow for all macroscopic properties of a syntactic foam to be calculated 166). In fact, the approximation works well only for the elastic moduli, it is satisfactory for strength properties, but deformation... 

The thickness of the TDCB specimens (S = 10 mm) is sufficient to ensure plain strain conditions. It should be noted that during the test the arms remain within their elastic limit. Therefore, from simple beam theory [7], and by the use of linear elastic fracture mechanics, the strain energy release rate of the adhesive can be obtained using Eqn. 2, where P is the load at failure and E, is the substrate modulus. The calculated adhesive fracture energy was employed in the simulation of the TDCB and impact wedge-peel (IWP) tests. 

Applications of linear elastic fracture mechanics (primarily) to the brittle fracture of solid polymers is discussed by Professor Williams. For those not versed in the theory of fracture mechanics, this paper should serve as an excellent introduction to the subject. The basic theory is developed and several variants are then introduced to deal with weak time dependence in solid polymers. Previously unpublished calculations on failure times and craze growth are presented. Within the framework of brittle fracture mechanics and testing this paper provides for a systematic approach to the faOure of engineering plastics. 

In a solid beam, the compressive and tensile stresses are not confined to the surfaces. The compressive stress in a section is highest at the upper surface and gradually diminishes to zero at the neutral plane. Similarly, the tensile stress is highest on the lower surface and diminishes to zero at the neutral plane (Figure 10.6a). While the beam deforms elastically, the compressive and tensile stresses increase proportionately with distance from the neutral plane. The compressive stress at a distance, d, above the neutral plane will be the same as the tensile stress at a distance, d, below the neutral plane. Further, as the modulus of elasticity is the same in compression and tension, the strain at both positions will be similar. Simple beam theory assumes that the beam behaves elastically until failure. However, the limit of proportionality in compression is quite low and once exceeded the fibres near the upper surface will start to buckle, crash, and strain at a greater rate while... 

As mentioned already, the main consideration In this work will be the failure occurring as a result of necking during the uniaxial creep of polyethylene at relatively high loadings. Recently, Bernstein and Zapas [2] have extended the work of Erlcksen [3] on the instability of elastic bars to the case of viscoelastic materials, more specifically to the class of materials which behave according to the BKZ theory [4]. 

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