Strength Theories of Failure for Anisotropic Materials

Abstract

A discussion of several failure criteria from their initial application to homogeneous, orthotropic materials to their extension to “quasi-homogeneous,” anisotropic materials is presented. Also discussed are the assumptions, general limitations, and the physical and analytical significance of the respective “material constants.” The basic criteria include the Lame'-Navier maximum stress theory, Henky-von Mises distortional energy theory, Tresca maximum shear stress theory, and the St. Venant maximum strain stream theory.

Nonlinear Stress-Strain Response of Laminated Composites

“…The structural behavior of laminated composites, which are composed of linear elastic laminae, is well discussed [1,2,3]. Also the failure mechanism or criterion of anisotropic materials is treated merely for a failure phenomenon [4,5] and no discussions are made on the domain of inelastic response leading to the failure. In this investigation, techniques are available for using linear elastic analysis.…”

An Investigation of the Biaxial Failure Envelope of Paper: Experimental Study and Theoretical Analysis

“…Tubular specimens subjected to axial loading, combined with internal pressure, were used by de Ruvo, Carlsson, and Fellers (1 1 ) in the determination of the failure envelope of kraft paper and sack paper in the biaxial tensile mode . bi-axial failure envelope of paper Several theories for yielding and failure in materials under combined stresses have been proposed (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) . The aim of these theories is to define a function of all stress components that reaches a critical value for different combinations of stress .…”

“…The severity of the imposed stress state may be expressed by the strength ratio R which indicates the quantitative measure-ofsafety margin( 7 ), defined according to R = ß i / o~ (13) where ßi is the allowable stress vector satisfying equation ( 12) and csi is the imposed stress vector . Instead of solving for the failure criterion, we now solve for the strength ratio.…”

Non-linear stress-strain behaviour of carbon fibre reinforced plastic laminates

“…including the effects of built-in thermal strains. The theory predicts the thermal strains and stresses present in a laminate due to a temperature difference from cure, and for a step-wise applied loading calculates the resulting The theory which has been programmed for a digital computer uses empirical lamina stress-strain curves which are stored in secant modulus form as polynomial functions. Various orthotropic failure criteria have been developed to predict the failure of composite laminates (13). It is usually assumed that yield and failure are synonymous.…”