It is 100 years since the well-know Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.

Advances in strength theories for materials under complex stress state in the 20th Century

Recent research on the yield behaviour of polymers is reviewed. Particular attention is given to the importance of the hydrostatic component of stress, the viscoelastic nature of the yield process, and the behaviour of oriented polymers.

Review: The yield behaviour of polymers

This paper reviews the existing theories of failure of laminated fiber-reinforced composite materials. The failure theories of isotropic materials are also reviewed. There exist at least 30 failure theories for laminated composites. Some of these theories are applied directly to the laminate while the rest of the theories are applied to the individual layers of the laminate. In addition, the paper reviews the theories of the post-failure behavior of laminated composites, that is, the behavior of laminated composites beyond first ply failure. For this analysis there exist at least twelve theories, which are included in this survey.

Survey of Failure and Post-Failure Theories of Laminated Fiber-Renforced Composites

An apparatus has been designed and constructed that will allow determination of the mechanical behavior of polymer specimens subject to applied tensile and compressive loading, while the sample is simultaneously subject to a hydrostatic pressure environment. The moduli of high‐density polyethylene and polypropylene determined from compressive tests show a significant increase with pressure. Tensile nominal stress‐strain curves have been obtained at various pressures up to 100 000 psi. These show that the yield stress also increases significantly with increasing pressure for both materials. The nature of yielding and fracture is found to be quite different for the two polymers studied. Polyethylene tends to deform more by shear, and the necked region at high pressures reduces to a fine point before separation. In polypropylene, fracture occurs by plastic tearing across the cross section. An attempt is made to account for the experimental results by use of yield criteria that includes a hydrostatic pressure...

Effects of Hydrostatic Pressure on the Mechanical Behavior of Polyethylene and Polypropylene

Classical lamination theory for fiber composites is inherently limited to the 2-dimen sional conditions appropriate to thin shell configurations. A new derivation with ap propriate tensor transformations is given which provides a fully 3-dimensional lamination theory that is applicable to thick laminates involving "out-of-plane" stress terms. In con nection with this work a new failure criterion is derived for fiber composites, one which involves a minimum number of failure parameters, and offers insight into the modes of failure. The key to both derivations is the restriction of the five properties form of transversely isotropic media to a special form involving three independent properties. The reduced theoretical forms and the failure criterion are evaluated with respect to standard experimental data for fiber composites.

Tensor Transformations and Failure Criteria for the Analysis of Fiber Composite Materials

The paper discusses a yield condition which takes into consideration the influence of hydrostatic stresses. It is shown that many experimental observations made in plasticity can be described satisfactorily by such a yield condition. An application to the determination of the burst pressure of a perfectly plastic spherical shell is given.

Inclusion of the hydrostatic stress component in formulation of the yield condition

A modified Tresca's yield condition with associated flow rules for anisotropic materials was suggested. By using this approach, it was shown that problems of which the principal axes of anisotropy coincide with the principal axes of stress, can be solved simply. Examples having known solutions for isotropic cases were solved. The results demonstrated that great error may be resulted by postulating the plastic flow of a strained body of anisotropic material on the basis of its behavior if it were isotropic.

Modified Tresca's yield condition and associated flow rules for anisotropic materials and applications

A method for the stress analysis of wire drawing using dies of any given profile is described. Examples of straight, concave, convex and bell-shape dies are investigated. Results indicate that the die profile has a significant effect on the distribution of die pressure and comparison shows that the bell-shape die has the lowest draw stress and the most uniformly distributed pressure and frictional force.

L.W. Hu

Papers

Inclusion of the hydrostatic stress component in formulation of the yield condition

Modified Tresca's yield condition and associated flow rules for anisotropic materials and applications

Analysis of die profiles in wire drawing