Fracture multiaxial stress

The stored strain energy can also be determined for the general case of multiaxial stresses [1] and lattices of varying crystal structure and anisotropy. The latter could be important at interfaces where mode mixing can occur, or for fracture of rubber, where f/ is a function of the three stretch rations 1], A2 and A3, for example, via the Mooney-Rivlin equation, or suitable finite deformation strain energy functional. 

A polymer is more likely to fail by brittle fracture under uniaxial tension than under uniaxial compression. Lesser and Kody [164] showed that the yielding of epoxy-amine networks subjected to multiaxial stress states can be described with the modified van Mises criterion. It was found to be possible to measure a compressive yield stress (Gcy) for all of their networks, while the networks with the smallest Mc values failed by brittle fracture and did not provide measured values for the tensile yield stress (Gty) [23,164-166]. Crawford and Lesser [165] showed that Gcy and Gty at a given temperature and strain rate were related by Equation 11.43. 

Since the flow stress increases due to hardening, failure by cleavage fracture may occur even after plastic yielding. In this case, a (macroscopi-cally) ductile (but microscopically brittle) cleavage fracture develops, a rather seldom case that can occur only in a multiaxial stress state (90. ... 

These statistical approaches can not be applied directly to the experimental results in this study, because the fracture was occurred under biaxial stress in Disk-on-Rod tests and Piston-on-Ring tests. The statistical approaches for multiaxial stress state have been studied by several investigators. In order to determine the suitable equivalent stress more precisely, further investigation is needed for the widely variable stress states. However, it is considered that uniaxial statistical approach by eqs. (2) (5) are available for the comparison of the critical stress for maincrack formation under... 

Further investigation is needed for the application to complex multiaxial stress states and the fracture mechanical analysis of crack arrest and propagation process. However, new experimental technique of thermal shock fracture (Disk-on-Rod test), by which the indispensable information for the structural application of ceramics at high temperature, was established in the present study. 

To predict component reliability for multiaxial stress states the Batdorf the-ory ° is used. Batdorf theory combines the weakest link theory with linear elastic fracture mechanics. It includes the calculation of the combined probability of the critical flaw being within a certain size range and being located and oriented so that it may cause fracture. 

Manjoine, M.J. Multiaxial stress and fracture. Fracture, vol. 3, Eng. Fund, and Environm. Effects,, Academic, New York (1970)... 

Notched monotonic tensile specimens can be a useful approach to begin to understand the effect of structural notches on the behavior of UHMWPE total joint replacement components. Therefore, we developed a testing methodology to characterize the stress strain and fracture behavior of a notched tensile specimen. Additionally, the stress-strain behavior of notched tensile specimens can be used to challenge the Hybrid Constitutive Model for UHMWPE (see Chapter 35) with a multiaxial stress state. Accurate prediction of the behavior of a notched specimen by a simulation utihzing the Hybrid Model would be one vahdation of its accuracy in describing the mechanical behavior of UHMWPEs. 

Despite the rationale for the above general formulations, it has proven remarkably difficult to quantify them in terms of crack tip plasticity and to independently verify their accuracy. For instance, uniaxial creep deformation laws at low homologous temperatures are not necessarily applicable to the multiaxial stress conditions in the surface region adjacent to the crack tip, and the use of linear-elastic fracture mechanics must have limitations for the near-crack-tip, high-plastic-deformation conditions. 

Criteria 2, 5, and 6 are generally used for yielding, or the onset of plastic deformation, whereas criteria 1,3, and 4 are used for fracture. The maximum shearing stress (or Tresca [3]) criterion is generally not true for multiaxial loading, but is widely used because of its simplicity. The distortion energy and octahedral shearing stress criteria (or von Mises criterion [4]) have been found to be more accurate. None of the failure criteria works very well. Their inadequacy is attributed, in part, to the presence of cracks, and of their dominance, in the failure process. 

Kaufman, R.P., Topper, T. The influence of static mean stresses applied normal to the maximum shear planes in multiaxial fatigue. In Carpinteri A., de Freitas M., Spagnoli A. (Eds.) Biaxial/Multiaxial fatigue and fracture. Elsevier, Oxford, 133 (2003)... 

The term Uo in Eq. (8.21) has been taken to represent the macroscopic uniaxial stress Uo in the event of uniaxial stretching — or the largest principal stress component Oy in the event of multiaxial states of stress. This does not mean that the times to fracture of tubular and uniaxial specimens are always identical if only Oy is equal Uo. As discussed above the creep functions in these two cases are described by different potential laws, namely by Eqs. (8.16) and (8.17) respectively. 

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