Fully rationalized Tsai-Wu failure criterion for transversely isotropic materials

Li, Shuguang

Abstract

By examining the quadratic function of the original Tsai-Wu failure criterion for transversely isotropic materials from the perspective of analytic geometry, two of the troublesome coefficients associated with the interactive terms, one describing interaction between in-plane direct stresses and one between transverse direct stresses, can be determined based on mathematical and logical considerations. An appropriate exploration of the quadratic failure function, whilst enhancing the mathematical rigour of the subject, reveals some useful physical relationships as intrinsic properties of a quadratic failure function. Two clear statements can be drawn: (i) To maintain a basic degree of consistency, a failure criterion based on a single quadratic failure function for transversely isotropic materials can only accommodate five independent strength properties, viz. the tensile and compressive strengths in directions along fibres and transverse to fibres, and the in-plane shear strength, and (ii) Amongst the transverse tensile, compressive and shear strengths, only two are independent. In presence of experimentally measured transverse shear strengths, they should be utilised to validate the fully rationalised Tsai-Wu criterion or to recalibrate the remaining transverse strength properties. A practical scheme to this effect has been proposed. To complete the development in the rationalisation of the Tsai-Wu criterion, the criterion has also been extended to offer its fully rationalised strain-based counterpart, unifying the approaches based on stresses and strains in a consistent manner.

Citation

Li, S. (2022). Fully rationalized Tsai-Wu failure criterion for transversely isotropic materials. In S. W. Tsaï (Ed.), Double-Double: a new perspective in the manufacture and design of composites (173-206). Stanford & JEC

• Publication Date: 2022-06
• Deposit Date: Jul 29, 2022
• Pages: 173-206
• Book Title: Double-Double: a new perspective in the manufacture and design of composites
• Chapter Number: 9
• ISBN: 978-0-9819143-3-6
• Keywords: A. Quadratic failure function; B. Tsai-Wu criterion; C. Failure envelope; D. Strength; E. Transverse shear strengths; F. Transversely isotropic material; G. Strain-based criterion
• Public URL: https://nottingham-repository.worktribe.com/output/9409527
• Publisher URL: https://www.jeccomposites.com/product/double-double/