Effect of Shear/Axial Stress Ratio on Multiaxial Non-Proportional Loading Fatigue Damage on AISI 303 Steel

In this paper, we investigate the cyclic response of AISI 303 stainless steel subjected to non-proportional loads with different amplitude ratios between shear stresses and normal stresses. Based on the experiments, a relationship between the proportional reference load and a varied range of non-proportional loads was established. To achieve this objective, an experimental program was implemented to evaluate the non-proportional parameter Y. Then, the evolution of this parameter was analyzed with the number of cycles to failure and with the ratio between shear and normal stresses, finally, the evolution of the non-proportional parameter Y was mapped by two functions. The results show that the non-proportional response of the AISI 303 can be estimated using the two functions obtained. This allows the estimation of the relationship between non-proportional and proportional stresses as a function of the number of cycles to failure together with the relationship between shear and normal stresses. The results obtained have direct application in the evaluation of accumulated damage, assessed in real-time, resulting from variable amplitude loading spectra. This is of particular interest for the evaluation of structural health monitoring of structures and mechanical components.

Constitutive relations for materials with strain state dependent properties

Many materials demonstrate a dependence of mechanical properties on the type of stressed or deformed states. This is most noticeable in the dependence of the processes of shear and bulk deformation. Such materials include rocks, structural graphite, concrete, some grades of steel, cast iron, and aluminum. The main properties of these materials are an absence of a "single curve" relationship between the intensity of stresses and the intensity of deformations. Under shear conditions, bulk deformations can occur. Such materials can be described by constitutive equations that depend on the parameter of the type of a stress state, which is the ratio of the first invariant of the stress tensor to the stress intensity. Thus, these defining relations give the dependence of the strain tensor components on the stress tensor components. Such defining relations can be quite cumbersome, and therefore do not allow an analytical treatment to obtain defining relations that give the dependence of the components of the stress tensor on the components of the strain tensor. The paper proposes the constitutive relations obtained from the analysis of test results of various materials, which properties depend on the type of deformed state. Conditions are derived for material constants that ensure the uniqueness of the solution of boundary value problems. Based on experimental data obtained under the conditions of the proportional loading of various rocks: limestone and talcochlorite, as well as the results of mechanical tests of several grades of concrete, the constants of the mathematical model are determined. The results of the experimental studies are compared with theoretical dependencies predicted by the model. The limited applicability of the proposed constitutive relations is established.

Fatigue Damage Map of AZ31B-F Magnesium Alloys under Multiaxial Loading Conditions

In this work, the mechanical behavior of the AZ31B-F magnesium alloy under cyclic loading is analyzed with the goal of contributing to the advancement of its use in the design of AZ31B-F components and structures. To achieve this goal, an experimental program was implemented to evaluate the cyclic response of the AZ31B-F under specific proportional loads with different stress amplitude ratios. Afterwards, regression methods were applied to extend the experimental data to a wide range of proportional loads. As a result, the AZ31B-F damage map, a material property that stablishes the damage scale between normal and shear stresses for finite life loading regimes, was obtained. In addition, a safety factor was developed for the AZ31B-F material when subjected to proportional loading. The achieved results have a direct application in mechanical design of components/structures made of AZ31B-F contributing to its reliability.

Buckling Pattern Transition Of Periodic Porous Elastomers Induced By Proportional Loading Conditions

This paper focuses on the buckling instabilities of periodic porous elastomers under combined multiaxial loading. A numerical model based on the periodic boundary condition (PBC) for the 2D representative volume element (RVE) is proposed, in which two proportional loading parameters are employed to control the complex stressing state applied to the RVE model. A homogenization-based orthogonal transformation matrix is established by satisfying the equality of the total work rate to realize a proportional multiaxial loading on the RVE. First, the transition behavior of buckling patterns of periodic porous structures is revealed through instability analysis for the RVE consisting of [Formula: see text] primitive cells with circular holes subjected to different proportional loading conditions. Simulation results show that the first-order buckling mode of RVE may change suddenly from a uniaxial shearing buckling pattern to a biaxial rotating buckling pattern at a critical loading proportion. Then the influences of the number of primitive cells in the enlarged RVE on the buckling behavior are discussed. When the number of primitive cells in any enlarging direction is odd, the points of buckling pattern transition of the enlarged RVEs vary significantly with the number of cells in RVE. When the number of primitive cells is even in both enlarging directions, there is no apparent difference for the critical buckling stresses of the enlarged RVEs.