Generalized nonlinear Shanley-Ryder failure concepts, Deterministic margins and factors of safety with their relations to failure probabilities, and elastic and viscoelastic structural health monitoring

  • Harry H. Hilton University of Illinois at Urbana-Champaign
  • Jonathan Pignard Institut Supe ́rieur de l’Ae ́ronautique et de l’Espace E ́cole Nationale Supe ́rieur de Me ́canique et d’Ae ́rotechnique (ISAE-ENSMA) Te ́le ́port 2, 1 Avenue Cle ́ment Ader, 86360 Chasseneuil-du-Poitou, France


An investigation of heuristic failure theories based on the Shanley--Ryder (S--R) stress ratio formulations and their extensions to ratios of stress invariants is undertaken. The deterministic structural margin (MS) and factor of safety (FoS) are re-examined and their multiple valued relevances to probabilistic analyses based on statistical loads as well as statistical material failure properties are discussed. MS's have no unique meaning in stochastic analyses while factors of safety effectively increase allowable loads thereby decreasing failure probabilities.

Several stress invariant failure criteria built on the S-R protocol are evaluated. It is shown that their use reduces the number of independent contributors to as few as three fundamental stress invariants. Whereas the S-R interaction relations can have upward of eight independent failure stress ratios for isotropic media and up to 168 for anisotropic materials. While formulations of both the S-R stress ratios and of the various forms of stress invariant ratios are nonlinear, the economy of scales in number of stake holders definitely favors the invariant protocol.
The importance of using realistic nonlinear probability density functions (PDFs) ranging from minimum to maximum data values, rather than those extending beyond this interval, is analyzed. Wavelet analysis for noninvasive structural health monitoring is developed for elastic and viscoelastic aerospace structures and a plea for missing, and sorely needed, multi--axial experimental modulus and failure data is included.