Based on an analysis of four different types of stress state, the incorrectness of application of the maximum stress strength and maximum strain strength criteria, which are widely used in the world practice and modern commercial application packages, for the strength analysis of isotropic, transtropic and composite materials with at least one plane with low degree of anisotropy is theoretically proved. For the composites with the plane of medium-degree anisotropy, the application of these criteria can also result in significant errors. This incorrectness is due to the non-fulfilment of invariance conditions in the plane of isotropy, if any, and can lead to the fact that the value of the strength function at the same stress-strain state can change by a factor of almost two (and perhaps more) depending on the rotation of the coordinate system. It is pointed out that these two criteria are conceptually constructed so that it is very difficult, if not impossible, to modify them to avoid the above incorrectness. They can be used, with a certain degree of reliability, only for essentially orthotropic composites. It is shown that the quadratic generalized von Mises strength criterion, which is also commonly used in applications, is void of these disadvantages and can be correctly used in the strength analysis of both orthotropic and trans- and isotropic materials if the invariance conditions are met. Other quadratic Tsai–Wu strength criteria, one of whose particular cases is the generalized von Mises criterion, will also be correct if the necessary and sufficient conditions for the existence of a limiting failure surface and invariance conditions are met.
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Translated from Problemy Prochnosti, No. 6, pp. 18 – 24, November – December, 2019.
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Romashchenko, V.A. Limitations Of Some Strength Criteria For Composite Materials. Strength Mater (2020). https://doi.org/10.1007/s11223-020-00131-8
- maximum stress criterion
- maximum strain criterion
- the Tsai–Wu strength criterion
- generalized von Mises strength criterion
- invariance conditions