Proportional Multiaxial Loading Research Articles

Consideration of Fatigue Evaluation of SUS316 and SUS430 Steels under Multiaxial Stresses Combined Internal Pressure and Axial Load using Hollow Cylinder Specimen

This study focuses on discussing fatigue life evaluation method of SUS316 and SUS430 steels under wide ranged proportional multiaxial loading conditions. Fatigue tests under 7 types of loading path which are combined axial stress and inner pressure were carried out using hollow cylinder specimens at room temperature. It has been considered that the proportional loading does not cause additional hardening, however this study shows that the complex loading path causes additional hardening without principal direction change of stress and strain in a cycle. The Itoh-Sakane model which evaluates loading and lives under non-proportional multiaxial fatigue by only considering the maximum and the minimum principal stress or strain and their principal directions. However, this model is also needed to consider middle principal stress because change of the middle principal stress influence fatigue life under current loading paths. Therefore, the Itoh-Sakane model was modified to evaluation fatigue life of SUS316 and SUS430 under combined internal pressure and axial loading conditions.

The dislocation-based fatigue deformation mechanism of a RAFM steel under multi-axial loadings

Reduced Activation Ferritic/Martensitic (RAFM) steel is a candidate blanket material for a fusion reactor, which should have outstanding performance under extreme environments containing complex thermal and stress damage during operation. To date, the properties under a single-axial loading type of tensile, creep and fatigue have been extensively reported, while the multi-axial loadings were rarely studied. Here, the multi-axial fatigue behaviors of a RAFM steel were investigated in an axial-torsional cyclic tester with controlled strain and different loading paths. The results show that the fatigue behavior of the RAFM is strongly determined by the shear-stress condition, where the lifetime under the pure torsional loading is only 16% of the uniaxial cyclic loading one. The fatigue life of the specimens under multi-axial loadings with a phase angle of 0° or 180° are comparable to that of uniaxial tension-compression one. However, it was decreased by ∼28% as the loading angle changed to 90° with a circular path. Besides, we found the fatigue softening under the proportional multi-axial loading while additional hardening in the non-proportionally multi-axial cyclic loading related to the dislocation activities during loadings. Under the proportional-multiaxial loading and uniaxial tension-compression loading and torsion loading, the high density of dislocation was rearranged and annihilated by the cyclic shear stress, while the tempered martensite lath structure was mainly retained. However, under the non-proportional multi-axial loading, dislocations transform the lath structure into a finer cell structure, improving the resistance upon fatigue deformation.

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.

Crane runways – Fatigue evaluation of crane rail welds using local concepts

The introduction of the wheel loads into a crane runway with a hot rolled I-section and a block rail fastened by longitudinal fillet welds forms a multiaxial fatigue problem. At the point of wheel load application the top region of the runway girder is subjected to a stress field comprising local stress components induced by the concentrated load, i.e. local transverse pressure and local shear stress in addition to the direct and shear stress components due to global bending. The superposition of all aforementioned stress components (and stress ranges, resp.) during each single crane pass results in a so-called non-proportional cyclic stressing of the rail welds with alternating principal stress direction. Due to the variation of the principal stress direction the conventional fatigue evaluation procedures appear not to be reliable. To approach the complex issue two crane runway girders were tested under proportional multiaxial loading, i.e. under flexural bending and stationary wheel load, both simultaneously pulsating. The paper presents the fatigue evaluation of these tests using different local concepts.

Multiaxial low-cycle fatigue of 63Sn-37Pb solder

A series of low-cycle fatigue experiments of tubular specimens under uniaxial, torsional, and proportional multiaxial loading was performed on 63Sn-37Pb solder. Several criteria of multiaxial low-cycle fatigue life were evaluated based on the fatigue life data of 63Sn-37Pb solder. It was shown that the maximum normal strain approach gives life prediction on the unconservative side, but the maximum shear strain approach presents quite good predictions. The Lee-Kim-Nam (LKN) parameter gave an acceptable prediction, but the prediction for uniaxial fatigue life was on the conservative side. The shear-based critical plane parameters, Kandil-Brown-Miller (KBM) parameter and Chen-Xu-Huang (CXH) parameter, presented good predictions of multiaxial fatigue life.

Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading: statistical analysis and size effect

An extensive experimental programme and detailed mechanical analysis were performed to test and model the statistical response of metallic foams under complex loading conditions. Tensile tests were performed on more than 80 specimens of closed-cell aluminium foams with four different specimen sizes. These test results show a large scatter and a significant size effect especially on standard deviation. The average fracture stress and, more significantly, the corresponding scatter decrease for increasing volume sizes. An attempt is made to use the Weibull statistical analysis to interpret these variations. A Weibull modulus close to 8 is found. Compression tests were also carried out. Both mean fracture stress in tension and mean peak stress in compression and the corresponding dispersions are correctly described by a single set of Weibull parameters. The statistical model is extended to multi-axial loading conditions by introducing an effective stress measure involving both the deviatoric part of the stress tensor and its trace. One additional parameter is identified using the average shear yield stress obtained from pure shear tests and torsion tests on solid bars. It is shown that the model is able to predict the dispersion found for the shear strength. Two types of combined tension/compression–torsion loading conditions were then tested experimentally. The non-proportional loading path consists of a tension test followed by torsion, keeping the axial stress constant. In the proportional loading path, shear and axial stress follow a straight line in the stress space. The corresponding surface of average yield/fracture stress is found to be symmetric. The experimental results are in good agreement with the predictions of the statistical model. The model predicts a bell-shaped surface for the first loading path and a quasi-elliptic one for the proportional one. The scatter found in the description of this surface is also accounted for accurately by the model. A brief discussion of an extension of Beremin's micromechanical model to the statistical failure of brittle foams is presented.

Simulation des Mikrorisswachstums unter Schwingbeanspruchung. Teil 2: Simulationsergebnisse - Einfluss des Spannungszustandes und Reihenfolgeeffekte

In part one the modelling of micro crack growth due to alternating loading has been presented. Simulation results for tension/compression, torsion and proportional multiaxial loading, the scatter of the simulated lifetimes to a macroscopic crack length of 500 μm as well as the influence of the density of crack seeds and the grain size have been presented. In part two the influence of the stress state under proportional and non-proportional loading is examined. Additionally the sequence effect of High-Low and Low-High as well as consecutive load sequences will be discussed. The comparison of the simulation results to experimental results shows that the influences of multiaxial loading and sequences can be simulated qualitatively correctly. The simplifications of the modelling have been to be considered. If the length of the maximum crack is interpreted as a measure of the damage, it can be concluded that the damage accumulation is non linear and non continuous. The main proportion of lifetime from the crack seed to the macro crack is contributed in the phase in which the length of the maximum micro crack comes close to the size of the grain size.