Ewald Macha

A critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime

Abstract In this paper the energy parameter, defined for random loadings, is analysed. Under uniaxial loading this parameter distinguishes between the strain energy density for tension (positive) and the strain energy density for compression (negative). As a consequence, if there is no mean component in the random loading, we obtain a random history of strain (elastic and plastic) energy density with zero expected value. Under multiaxial loadings the normal strain energy density in the critical plane (i.e. the plane of the maximum damage) is understood as the energy parameter. The history of strain energy density is schematized with use of the rain-flow algorithm. Fatigue damage is accumulated according to Palmgren-Miner hypothesis and the standard fatigue characteristic of the material, rescaled with use of the considered energy parameter. The proposed parameter was verified during fatigue tests of cruciform specimens made of 10HNAP steel, subjected to biaxial non-proportional random tension-compresion. The calculated fatigue lives are included in the scatter band of the experimental data of a factor of 3. Thus, the normal strain energy density in the critical plane seems to be an efficient fatigue parameter under random non-proportional loadings for high-cycle fatigue.

Expected principal stress directions under multiaxial random loading. Part I: theoretical aspects of the weight function method

As has been observed experimentally by many authors, the position of the fatigue fracture plane appears to strongly depend on the directions of the principal stresses or strains. In Part I of the present work the expected principal stress directions under multiaxial random loading are theoretically obtained by averaging the instantaneous values of the three Euler angles through some suitable weight functions which are assumed to take into account the main factors influencing fatigue behaviour. Then, in Part II, it is examined how such theoretical principal directions determined by applying the proposed procedure are correlated to the position of the experimental fracture plane for some fatigue tests reported in the literature.

Expected principal stress directions under multiaxial random loading. Part II: numerical simulation and experimental assessment through the weight function method

In Part I of the present work, the theoretical aspects of a proposed procedure to determine the expected principal stress directions under multiaxial random loading have been discussed. This procedure consists of averaging the instantaneous values of the three Euler angles through weight functions. In Part II here, a numerical simulation is presented to illustrate the above theoretical method. As an example, the algorithm proposed is applied to some experimental biaxial in- and out-of-phase stress states to assess the correlation between the expected principal stress directions and the position of the experimental fatigue fracture plane for such tests.

The influence of the mean stress on fatigue life of 10HNAP steel under random loading

Abstract This paper contains the results of uniaxial random load fatigue tests with different mean values performed on 10HNAP steel specimens. The experimental fatigue life was compared with the life determined according to different methods of amplitude transformation of the cycles. Cycles were counted with the rain flow algorithm and damage was cumulated with the Palmgren–Miner hypothesis. It has been shown that in the case of “symmetric” stress histories with zero expected values, the mean values of selected cycles do not strongly influence the calculated fatigue life and transformation of the cycle amplitudes; hence, no mean stress correction for cycle mean values different from zero is required. As for the “asymmetric” histories, the algorithm of transformation of the stress history (because of its global expected value different from zero) gives similar results to the algorithm of amplitude transformation of cycles. A suitable choice of the transformation relationship is very important. In the case of 10HNAP steel, stress amplitude transformation according to the Goodman relationship gives good results.

Expected position of the fatigue fracture plane by using the weighted mean principal Euler angles

The expected principal stress axes under multiaxial fatigue loading are determined by averaging the instantaneous Euler angles through suitable weight functions. Then, the fracture plane position is derived from such expected principal stress directions. Three weight functions based on stress parameters are discussed by comparing theoretical predictions with available test results related to six metallic materials under proportional and non-proportional loading. The fatigue fracture plane position under multiaxial loading may be established on the basis of the averaged direction of the maximum principal stress, with such a direction deduced by employing proper weight functions.

Digital control systems based on Matlab/Simulink software for strength machines

This paper presents the stands for strength tests of materials and structures with digital control systems, designed and built at the Department of Mechanics and Machine Design, Opole University of Technology. The authors described electrohydraulic strength stands for tests under uniaxial tension – compression, biaxial tension – compression of cruciform specimens, and electromechanical stands for tests under cyclic bending and torsion with phase shift, and under polyharmonic bending with torsion. Fatigue tests which could be performed on these stands as well as algorithms of controllers were presented.

Critical Planes in Multiaxial Fatigue

The paper includes a review of literature on the multiaxial fatigue failure criteria based on the critical plane concept. The criteria were divided into three groups according to the distinguished fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the applied the critical plane position. The multiaxial fatigue criteria based on two critical planes seem to be the most promising. These two critical planes are determined by different fatigue damage mechanisms (shear and tensile mechanisms).

Critical Fracture Plane Under Multiaxial Random Loading by Means of Euler Angles Averaging

ABSTRACT Several authors have experimentally observed that the position of the fatigue fracture plane strongly depends on the directions of the principal stresses or strains. The expected principal stress directions under multiaxial random loading are obtained herein by averaging the instantaneous values of the three Euler angles through some suitable weight functions, in order to take into account the main factors influencing the fatigue fracture behaviour. Then the correlation between such theoretical principal directions and the experimental fracture plane is examined for some biaxial random fatigue tests.

Energy Based Characterization of Fatigue Behaviour of Cyclically Unstable Materials

The paper presents a definition of a new energy based parameter which allows to better describe fatigue proprieties of materials, especially cyclically unstable materials in comparison with the Lagoda-Macha parameter. The proposed parameter distinguishes positive and negative work of external force and depends on the sign of the stresses in paths of strain in materials. It is used in laboratory tests for control of a fatigue process on hydraulic stand. A close-loop control system has been equipped with computer program based on MATLAB/Simulink module.

Spectral method of fatigue life calculation under random multiaxial loading

We develop a new spectral method for the evaluation of fatigue life under random multiaxial loading. This method is a generalization of the known formulas of Miles, Kowalewski, Raikher, and Bolotin based on the power spectral density function of stresses under uniaxial random loads. The power spectral density function of the equivalent stress determined according to a linear criterion of multiaxial random fatigue is introduced in the indicated formulas. It is shown that, in reducing the multiaxial state of loading to the uniaxial state according to linear criteria, the frequency bands of the components of the stress state are transformed into the frequency band of the equivalent stress without increasing its width. This favorable result cannot be obtained if the equivalent stress is calculated according to nonlinear multiaxial fatigue criteria.