Fatigue fracture planes and expected principal stress directions under biaxial variable amplitude loading

Fatigue behaviour under multiaxial variable amplitude loading can be examined by applying the failure criteria based on the critical plane approach. Positions of the critical plane can be determined in relation to the principal stress or strain directions. In the present paper, the expected directions of the principal stresses under proportional and non-proportional loading have been obtained by averaging the instantaneous values of the Euler angles through special weight functions. The known weight functions based on stress parameters appear not to be efficient for each loading or material being analysed. Thus, the authors consider new weight functions based on energy parameters. The prese…

ESTIMATED AND EXPERIMENTAL FATIGUE LIVES OF 30CrNiMo8 STEEL UNDER IN-AND OUT-OF-PHASE COMBINED BENDING AND TORSION WITH VARIABLE AMPLITUDES

Abstract— Calculated fatigue lives, based on three criteria for multiaxial random fatigue, were compared with lives obtained from tests on cylindrical specimens of 30CrNiMo8 steel subjected to in- and out-of-phase bending and torsion at variable amplitudes. In the chosen fatigue criteria the expected position of the fracture plane, determined from a variance method for the equivalent stress, were taken into account. The equivalent stress history was related to the rain flow method and fatigue damage was evaluated from the Palmgren–Miner hypothesis. It has been shown that the expected fatigue fracture planes agree with those determined by experiments. The most realistic estimations of fatigu…

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.

Comparison of Variance and Damage Indicator Methods for Prediction of the Fracture Plane Orientation in Multiaxial Fatigue

ABSTRACT Two methods that enable prediction of the fracture plane orientation are presented and compared in this paper. The first one is a statistical approach, which is based on the variance of an equivalent stress. It is assumed that the fracture plane is the one where the variance of a linear combination of the shear and normal stresses acting on this plane is maximum. The second one uses the so-called damage indicator of a multiaxial fatigue criterion, which is based on the research of the critical plane. The formulation of the criterion involves shear and normal stress amplitudes and mean normal stress. The fracture plane is the critical plane; That is to say the one where the damage i…

Fracture Plane of Cruciform Specimen in Biaxial Low Cycle Fatigue—Estimate by Variance Method and Experimental Verification

This paper presents the variance method of determining the fracture plane under random multiaxial stress states. The fracture plane was estimated analytically by the variance method with the three fatigue criteria. The estimated fracture planes were compared with experimental results using type SUS 304 and 1Cr-1Mo-1/4V steel cruciform specimens. The variance method with the maximum normal strain criterion, by neglecting the strain in direction in which no external forces act, could estimate the actual fracture planes of cruciform specimens in high temperature biaxial low cycle fatigue.

Fatigue fracture plane under Multiaxial Random Loadings - prediction by variance of equivalent stress based on the maximum shear and normal stresses

It is assumed that the plane in which the maximum variance of the equivalent stress appears is critical for a material and the fatigue fracture should be expected in this plane. The equivalent stress is calculated according to the fatigue criterion of maximum shear and normal stresses in the fracture plane. It was demonstrated that for each stationary random stress state there is one or more critical planes where the fatigue fracture plane can be expected. The variance method together with the discussed fatigue criterion give good results for three analysed types of carbon steels under multiaxial cyclic loadings.

Simulation investigations of the position of Fatigue Fracture Plane in materials with biaxial loads

In the paper three methods of determination of the expected fatigue fracture plane position under random triaxial stress state have been presented. They are: weight function method, variance method and damage cumulation method. The weight function method for biaxial cyclic loadings has been analysed with digital simulation. The fatigue fracture plane position has been determined with mean values of the direction cosines of principal stress axes. Averaging has been done at angle values with use of weights. Eleven various weights have been presented and their usability has been analysed on the basis of experimental results obtained by Rotvel, and Nishihara-Kawamoto. The weights with good agre…

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 fati…

Relations between cavitation erosion resistance of materials and their fatigue strength under random loading

Abstract The paper contains results of tests on fatigue strength under uniaxial random loading and cavitation erosion resistance for three steels: 10HNAP, 18G2A and 15G2ANb. The obtained fatigue and cavitation characteristics were used for determination of relations between these two phenomena. From the analysis it appears that there is correlation between fatigue strength of the material under random loading and its cavitation erosion resistance. It has been shown that fatigue tests under random loading and tests on cavitation erosion of 10HNAP, 18G2A and 15G2ANb steels may be described with a mathematical model of the same type. It has been also found that there is a linear relation, in t…

Comparison of the Rain Flow Algorithm and the Spectral Method for Fatigue Life Determination Under Uniaxial and Multiaxial Random Loading

This paper presents the strain energy density parameter used for fatigue life calculation under random loading by two methods. The first method is based on schematization of energy parameter histories with the rain flow algorithm. The other one is based on moments of the power spectral density function of the energy parameter. The experimental data of fatigue tests of 10HNAP steel under constant amplitude and random uniaxial loading with non-gaussion probability distribution, zero mean value, and wide-band frequency spectrum used for comparison of the rain flow algorithm and the spectral method gave satisfactory results. Next, histories of the random stress tensor with normal probability di…

Estimation of the fatigue life of high strength steel under variable-amplitude tension with torsion: Use of the energy parameter in the critical plane

Abstract The paper concerns application of the energy parameter, being a sum of the elastic and plastic strain energy density in the critical plane, for describing experimental data obtained in fatigue tests of 35NCD16 steel, subjected to constant amplitude tension-compression, torsion and variable amplitude tension-compression, torsion and combined proportional tension with torsion. It has been shown that the normal strain energy density in the critical plane is a suitable parameter for correlation of fatigue lives of 35NCD16 steel under considered kinds of loading. The critical plane is the plane where the normal strain energy density reaches its maximum value.

Elastic-plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading

The paper presents the results of fatigue crack growth on low-alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one-sided sharp notch were used. The tests were performed under the stress ratios R = -1, -0.5 and 0. The test results were described by the ΔJ-integral range and compared with the ΔK stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the ΔJ-integral range.

FATIGUE FAILURE CRITERIA FOR MATERIALS UNDER RANDOM TRIAXIAL STATE OF STRESS

SUMMARY Five fatigue failure criteria are formulated for a random triaxial state of stress whose components have zero mean values. It is assumed that fatigue failure is determined by the stress and strain components that act on an expected fracture plane. It is shown that in some special cases the proposed failure theories reduce to classical theories applied for sinusoidal stresses.

Fatigue life estimation for 30CrNiMo8 steel under in- and out-of-phase combined bending and torsion with variable amplitudes

Fatigue life successively calculated according to three criteria of multiaxial fatigue for randomly varying loading is compared with fatigue life obtained by Sanetra and Zenner in testing cylindrical specimens of 30CrNiMo8 steel by in- and out-of-phase bending and torsion with variable amplitudes. The position of the plane of fatigue fracture is determined using the variance method. The histories of equivalent stresses are schematically represented by the Monte Carlo method. Fatigue damage was computed using the Palmgren-Miner hypothesis. The most realistic estimates of fatigue life in the scatter band of the results with a factor of 3 are obtained on the basis of the criterion of maximum t…

Generalized Fatigue Criterion of maximum shear and normal strains on the fracture plane for materials under multiaxial random loadings

A generalized fatigue criterion for materials under multiaxial random loadings is presented. The criterion is based on the assumption that shear and normal strain on the expected fracture plane – shear strain in one direction on this plane is considered – determine the fracture plane. It has been shown that the well known fatigue criteria of maximum normal strain, maximum shear strain and the criterion of maximum shear and normal strains on the critical shear plane result from the newly formulated criterion.

Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading

The paper contains a new algorithm for estimation of fatigue life in HCF regime under multiaxial random loading using spectral methods. Loading of Gaussian distribution and narrow- and broad-band frequency spectra were assumed. Various characteristic states of multiaxial loading were considered. The equivalent stress history was determined with use of the failure criteria of multiaxial fatigue based on the critical plane. For determination of the critical plane position, the method of variance was applied. During simulation, the authors compared the results obtained by a spectral method in the frequency domain with those from the rain-flow algorithm in the time domain. The paper also contai…

Critical and Fracture Planes of 18G2A Steel Under Nonproportional Combined Bending and Torsion

Many multiaxial fatigue failure criteria of materials are based on the critical plane approach [1, 2, 3]. In these criteria, it is assumed that the fatigue failure of material is caused by stresses and/or strains acting in one plane (called critical) within the material. The proper orientation of that plane in fatigue failure criteria based on the critical plane concept must be established for fatigue life calculation. In the paper the damage accumulation method was used to determine the critical plane orientations. In this method, the critical plane is the plane where the maximum damage degree, computed according to the selected fatigue failure criterion, is the highest. The critical plane…

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.

Reduction of parameters in failure criteria for multiaxial Random Fatigue

In the paper some equivalent methods of determining the expected fatigue fracture plane position have been presented. These methods make use of elements of a full linear rotation group. Replacing nine direction cosines, mutually related, by three Euler angles we obtain a reduced number of parameters used for the description of the excepted fatigue fracture plane position. New mathematical forms of the fatigue criteria with a reduced number of independent parameters have been presented well.

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 accumula…

Covariance between components of biaxial stress state in fatigue life calculations

In this paper influence of correlalions between components of random stress tensor on the calculated fatigue life of the machine element has been analysed. Two groups of covariance matrices for components of biaxial stress state were considered. The first group was arbitrarily assumed and the second one was determined on the basis of the measured strains in the element of the vibrating screen for aggregate. Computer simulation was realized with four criteria of multiaxial random fatigue. Cycles were counted with the method of rain flow and damages were cumulated according to Palmgren-Miner hypothesis. It has been shown that covariances between components of stress state tensor strongly infl…

Fatigue life under non-Gaussian random loading from various models

Fatigue test results on the 10HNAP steel under constant amplitude and random loading with non-Gaussian probability distribution function, zero mean value and wide-band frequency spectrum have been used to compare the life time estimation of the models proposed by Bannantine, Fatemi–Socie, Socie, Wang–Brown, Morel and Łagoda–Macha. Except the Morel proposal which accumulates damage step by step with a proper ethodology, all the other models use a cycle counting method. The rainflow algorithm is used to extract cycles from random histories of damage parameters in time domain. In the last model, where a strain energy density parameter is employed, additionally spectral method is evaluated for …

Statistical Properties of Generalized Strain Criterion for Multiaxial Random Fatigue

ABSTRACT Statistical properties of generalized criterion of the maximum shear and normal strains on the fracture plane have been presented, Functions of probability distribution and spectral density of the equivalent strain have been analysed on the assumption that a random tensor of strain state is a six-dimensional stationary and ergodic Gaussian process. The expected value and variance of the equivalent strain have been determined as well. From spectral analysis a new limitation has been derived for extension of some multiaxial cyclic fatigue criteria to random loadings. It is connected with the fact that in some cases the frequency band of the equivalent strain is greater than that for …

Spectral analysis of the criteria for multiaxial Random Fatigue

In the paper the spectral analysis of several fatigue criteria under simple and complex states of stress has been done and limitations appearing while formulating new criteria for multiaxial random loadings have been shown. The presented analysis includes determination, with digital simulation, of probability density function and power spectral density function of the equivalent stress according to three special linear criteria of multiaxial random fatigue and six nonlinear criteria. Calculations were carried out for four kinds of random stress state. It has been shown that mathematical models for the criteria of multiaxial random fatigue formulated as nonlinear combinations of stress state…

Generalization of Energy-Based Multiaxial Fatigue Criteria to Random Loading

Fatigue Crack Growth for Different Ratios of Bending to Torsion in AlCu4Mg1

The paper contains the fatigue crack growth test results obtained under proportional bending with torsion in AlCu4Mg1 aluminium alloy [1]. Specimens with rectangular cross sections and dimensions: length l = 90 mm, height w = 10 mm and thickness g = 8 mm were tested [2]. Each specimen had an external unilateral notch with depth 2 mm and radius ρ = 0.2 mm. The tests were performed under the stress ratio R = −1. The notches in the specimens were cut with a milling cutter and their surfaces were polished after grinding. The tests were realized on a fatigue test stand MZGS-100 where the ratio of torsion moment to bending moment was \( M_T (t)/M_B (t) = tg\alpha = \sqrt 3 /3,1{\text{ }}and\sqrt …