Yielding under multiaxial stress

One simple criterion for yielding under multiaxial stresses is known as the Tresca yield criterion. This approach recognizes that the maximum shear stress is one-half the difference between the maximum and minimum principal stresses. In terms of the uniaxial yield stress [Pg.187]

The yielding of solids under multiaxial stresses gives rise to question about the 5deld criteria. One of the simplest yield criteria was proposed by Tresca already in 1864. It states that yielding occurs when the maximum shear stress exceeds a critical value. In terms of principal stresses we have (23) ... 

The simplified failure envelopes differ little from the concept of yield surfaces in the theory of plasticity. Both the failure envelopes (or surfaces) and the yield surfaces (or envelopes) represent the end of linear elastic behavior under a multiaxial stress state. The limits of linear elastic... 

A polymer is more likely to fail by brittle fracture under uniaxial tension than under uniaxial compression. Lesser and Kody [164] showed that the yielding of epoxy-amine networks subjected to multiaxial stress states can be described with the modified van Mises criterion. It was found to be possible to measure a compressive yield stress (Gcy) for all of their networks, while the networks with the smallest Mc values failed by brittle fracture and did not provide measured values for the tensile yield stress (Gty) [23,164-166]. Crawford and Lesser [165] showed that Gcy and Gty at a given temperature and strain rate were related by Equation 11.43. 

The preceding is a general overview of the main features of yield in pol5uners. From a practical point of view, structures are rarely subjected to simple imiaxial or shear loads and it is instructive to be able to determine when a material might yield under more complicated stress states. The following yield criteria attempt to do this from a phenomenological point of view, that is they do not address the fundamental mechanisms of yield but rather provide yield criteria for multiaxial loading conditions. 

Steel Under Earthquake Excitations Reinforcing steel in external reinforced crmcrete jackets for the retrofit and strengthening of existing reinforced concrete or steel members comes mainly in the form of bars. Usually, the stress-strain behavior under tension-compression is cmcial to assess the longitudinal bars contribution. The stress-strain behavior under tension is of interest for the transverse reinforcement (stirmps). Steel dowels and stud shear connectors may involve shear (or tensile) behavior of steel- or bond-related issues. External steel plates may be considered under multiaxial loading (i.e., in cases of shear strengthening in order to estimate their yield stress). Bond-related issues may concern bar-concrete interfaces, bar-resin-concrete interfaces (NSM applications), or plate-resin-concrete interfaces under cyclic loading. 

---