Comparative analysis of three thermal fatigue experiments

This paper presents an analysis of the ability of different criteria to predict fatigue crack initiation under thermal loading. More precisely the predictions of the number of cycles to crack initiation are compared with experimental results obtained using five different fatigue criteria in three types of thermal fatigue tests (namely the FAT3D, JRC and SPLASH test campaigns). This analysis has revealed that:

• ? The conventional criteria based on equivalent strain variation substantially overestimate the lifespan of a structure subjected to thermal loading.
• ? A criterion making account for loading multiaxiality is required to estimate thermal fatigue life.

Three of the criteria studied give satisfactory results: the Zamrik criterion, the Park and Nelson criterion and a criterion taking hydrostatic pressure into consideration proposed by Amiable et al. The latter should be preferred for the accuracy of its results and the Zamrik criterion for its simplicity.     

Crack initiation under thermal fatigue: An overview of CEA experience. Part I: Thermal fatigue appears to be more damaging than uniaxial isothermal fatigue

For nuclear reactor components, uniaxial isothermal fatigue curves are used to estimate the crack initiation under thermal fatigue. However, such approach would be not sufficient in some cases where cracking was observed. To investigate differences between uniaxial and thermal fatigue damage, tests have been carried out using the thermal fatigue devices SPLASH and FAT3D: a bi-dimensional (2D) loading condition is obtained in SPLASH and crack initiation is defined as the first 150-μm surface cracks, whereas a tri-dimensional (3D) loading condition is obtained in FAT3D and crack initiation refers to the first 2-mm surface crack.All the analysed tests clearly show that for identical levels of strain, the number of cycles required to achieve crack initiation is significantly lower in thermal fatigue than in uniaxial isothermal fatigue.The enhanced damaging effect probably results from a pure mechanical origin: a nearly perfect biaxial state corresponds to an increased hydrostatic stress. In that frame, a Part II accompanying paper will be dedicated to investigate accurately on multiaxial effect, and to improve thus estimation of crack initiation under thermal fatigue.     

On the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loading

In this paper, the modified Wöhler curve method proposed by Susmel and Lazzarin is employed to predict the fatigue life of welded connections subjected to biaxial cyclic loading. This criterion is reformulated here in order not to take into account the mean stress effect, as suggested by several design codes (at least when welded connections are not completely stress relieved). The accuracy of the proposed method in fatigue lifetime estimation was evaluated by using a number of data sets taken from the literature. The modified Wöhler curve method was applied in terms of nominal stresses and was calibrated using the uniaxial and torsional fatigue curve determined by reanalysing the experimental data, as well as using the standard fatigue curves of the Eurocode 3. The proposed approach was seen to be successful, giving multiaxial fatigue life predictions located within the widest scatter band related either to uniaxial or to torsional data, independently of both out‐of‐phase angle and load ratio value. Finally, the accuracy of the modified Wöhler curve method was compared to the one obtained by applying the procedure suggested by the Eurocode 3: the proposed criterion is demonstrated to be much more accurate and reliable than the standard one.     

Multiaxial fatigue of rubber: Part II: experimental observations and life predictions

Fatigue experiments were conducted with an axial‐torsion specimen covering a wide range of stretch biaxiality and a range of fatigue lives between 10³ and 2 × 10⁶ cycles. These experiments include combined torsion–compression, pure torsion, combined torsion–tension and pure axial tension. Both in‐phase and out‐of‐phase combinations of axial and torsion loading were considered. The multiaxial fatigue experiments described provide empirical evidence from which an understanding of the mechanics of the fatigue process in rubber can be developed. Each of the four equivalence parameters described in Part I has been applied to the axial‐torsion fatigue experiments described in this paper (Part II). These results provide the basis for an analysis of the effects of multiaxial loading on fatigue life, and an assessment of the degree to which the various equivalence parameters are able to rationalize the results in a unified way. For the combined axial and shear strain histories in this study, the maximum principal strain criterion gave the best correlation to fatigue life. Strain energy density gave the worst correlation. The cracking energy density criterion was generally found to give good correlation of fatigue crack nucleation lives from combined axial‐torsion tests. Because it provides a plane‐specific analysis, this criterion appears to be particularly well suited for use in crack nucleation analyses of multiaxial strain histories.     

Multiaxial fatigue criterion for a high‐density polyethylene thermoplastic

The multiaxial fatigue behaviour of a high‐density polyethylene was investigated at room temperature and constant frequency. As a consequence of the mode of failure, an end‐of‐life criterion for fatigue tests is discussed in the first part of the work, in order to define the number of cycles to failure. Based on force controlled fatigue tests under tension, compression and torsion at two stress ratio, a multiaxial fatigue criterion including the stress‐ratio effect is proposed for the fatigue design of this polymer. This criterion is based on the maximum and mean values of the second invariant of the stress tensor.     

Selection of the critical plane orientation in two-parameter multiaxial fatigue failure criterion under combined bending and torsion

The present paper is focused on engineering application of the algorithm of fatigue life calculation under multiaxial fatigue loading. For that reason, simple two-parameter multiaxial fatigue failure criterion is proposed. The criterion is based on the normal and shear stresses on the critical plane. Experimental results obtained under multiaxial proportional, non-proportional cyclic loading and variable-amplitude bending and torsion were used to verify the proposed two-parameter criterion and other well-known multiaxial fatigue criteria. Elastic–plastic behaviour of the bulk material was taken into account in calculation of the stress/strain distribution across the specimen cross-section. It is shown that the proposed two-parameter multiaxial fatigue failure criterion gives the best correlation between the experimental and calculated fatigue lives.     

An application of the implicit gradient method to welded structures under multiaxial fatigue loadings

This paper deals with the problem of fatigue strength assessment of welded joints subjected to multiaxial loading. Three-dimensional solid modelling and linear elastic stress analysis, by means of numerical methods, are used to investigate the local stress field at weld toes and roots, geometrically regarded as sharp notches. Starting from the stress field obtained from a linear elastic analysis and taking advantage of the so-called implicit gradient approximation, an effective stress index connected with the material strength is calculated. In particular, there will be an investigation into the possibility of applying the implicit gradient approach to welded structures, under both uniaxial and multiaxial loading conditions, by introducing a multiaxial criterion into the implicit gradient framework. The multiaxial criterion consists of an improvement of the well-established Crossland-like criteria. It will deal with multiaxiality caused by external loadings as well as multiaxial stress fields caused by severe stress raisers. In order to validate the devised approach, theoretical fatigue damage estimations are compared with experimental data. In particular, the proposed approach is applied to a series of applicative examples taken from scientific literature and related to welded joints subjected to uniaxial or in-phase multiaxial fatigue loading.     

Criteria of multiaxial random fatigue based on stress,strain and energy parameters of damage in the critical plane

In this paper generalized criteria of multiaxial random fatigue based on stress, strain and strain energy density parameters in the critical plane have been discussed. The proposed criteria reduce multiaxial state of stress to the equivalent uniaxial tension–compression or alternating bending. Relations between the coefficients occurring in the considered criteria have been derived. Thus, it is possible to take into account fatigue properties of materials under simple loading states during determination of the multiaxial fatigue life. Presented models have successfully correlated fatigue lives of cast iron GGG40 and steel 18G2A specimens under constant amplitude in‐phase and out‐of‐phase loadings including different frequencies.     

A method for low-cycle fatigue life assessment of metallic materials under multiaxial loading

A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0.6, 0.8, and 1.0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. __________ Translated from Problemy Prochnosti, No. 1, pp. 56–59, January–February, 2008.     

Fatigue behavior of laminated composites with a circular hole under in-plane multiaxial loading

A modified fiber failure fatigue model is presented for characterizing the behavior of laminated composites with a central circular hole under in-plane multiaxial fatigue loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane multiaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Analytical predictions are compared with the experimental results for uniaxial and multiaxial fatigue loading cases. A good match is observed. Further, studies are carried out for different in-plane biaxial tension–tension and biaxial compression–compression loading cases.     

The effects of stress and temperature gradients on fatigue life

A method is developed that establishes a lower bound on fatigue life due to non-uniform multiaxial stress (strain) and temperature distributions. The method allows prediction of fatigue crack initiation at notches, where stress (strain) gradients are always present, from isothermal uniaxial fatigue tests. In addition, the method enables prediction of fatigue life due to multiaxial, non-uniform thermal stresses (strains) associated with temperature gradients. By considering the strain energy density distribution associated with the non-uniform stress (strain) field, it is shown that if the actual distribution is replaced by a series of thin strips, each at an average temperature with a chordwise linear strain energy density distribution, then the actual strain energy is always less than that associated with the chordwise approximation. The concept of “specific damage” (per cycle) is then introduced as linearly proportional to strain energy. Specific damage is then related to fatigue life through the life fraction rule, which leads to a lower bound on actual fatigue life.     

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

Prediction of rubber fatigue life under multiaxial loading

The process of fatigue failure of materials is generally described by two phases: crack initiation and crack propagation. This study concerns the crack initiation in rubbers submitted to a cyclic loading. A parameter based on the strain energy density (SED) and predicting the onset of primary crack and its probable orientation has been identified for such materials according to the investigations of Mars and Fatemi. More precisely, this criterion has been analytically developed in the cases of simple tension, biaxial tension and simple shear loadings by assuming large strains. The results denote the possibility to predict the orientation plane in which the primary crack would be expected to occur in a material. Then, it was implemented in a finite‐elements (FE) program in order to be applied to structures under any kind of the strain states. A good agreement was obtained between FE and analytical results for the usual strain states. Finally, to evaluate lifetime up to crack nucleation, we have achieved a set of experimental fatigue tests using uniaxial tension (UT) and pure shear (PS) test specimens containing a hole in order to localize the crack initiation. The obtained results proved the efficiency of the criterion to describe the fatigue life of rubbers under multiaxial loading.     

Multiaxial fatigue of rubber: Part I: equivalence criteria and theoretical aspects

This paper investigates commonly used approaches for fatigue crack nucleation analysis in rubber, including maximum principal strain (or stretch), strain energy density and octahedral shear strain criteria. The ability of these traditional equivalence criteria, as well as a recent equivalence criterion (the cracking energy density) to predict multiaxial fatigue behaviour is explored. Theoretical considerations are also introduced relating to the applicability of various fatigue life analysis approaches. These include the scalar nature of traditional equivalence criteria, robustness of the criteria investigated for a wide range of multiaxial loadings, effects of crack closure and applications to non‐proportional multiaxial loadings. It is shown that the notion of a stress or strain amplitude tensor used for the analysis of multiaxial loading in metals is not appropriate in the analysis of rubber due to nonlinearity associated with finite strains and near incompressibility. Taken together, these considerations illustrate that traditional criteria are not sufficiently consistent or complete to permit confident analysis of arbitrary multiaxial loading histories, and that an analysis approach specific to the failure plane is needed. Of the three traditional criteria, maximum principal strain is shown to match most closely to the cracking energy density criterion, in terms of a failure locus in principal stretch space.     

A computational lifetime prediction of a thermal shock experiment. Part II: discussion on difference fatigue criteria

The SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref. [ 1 ]. The purpose of this paper is to discuss the application of different fatigue criteria in this case. The fatigue criteria: dissipated energy, Manson Coffin, Park and Nelson, dissipated energy with a pressure term, are determined for the experiment using results from FEM computations presented in the first part of the paper (Part I) 2 and compared with results from uniaxial and multiaxial experiments from literature. The work emphasizes the evolution of the triaxiality ratio during the loading cycle.     

Multiaxial fatigue life prediction method in the ground vehicle industry

The extensive progress which has been made in the multiaxial fatigue area over the past 5 to 10 years has allowed wider application of the multiaxial fatigue method in component durability design in the ground vehicle industry. The method adopts the long established local strain–life approach and includes several new features. (1) A three-dimensional cyclic stress–strain model, used to simulate the elastic–plastic material behavior under complicated loadings. (2) The critical plane approach, which requires the fatigue analysis to be performed on various potential failure planes before determining the lowest fatigue life. (3) A biaxial damage criterion, to better quantify fatigue damage under various loading conditions. (4) A multiaxial Neuber equivalencing technique, used to estimate, from the elastic finite element stress results, the multiaxial stress and strain history of plastically deformed notch areas. This paper examines the application of the above features to the fatigue analyses of three generic service/test histories: a constant amplitude (baseline) test history, a history directly recorded by strain gages mounted on the critical location of a structural component, and a loading history recorded in multichannels for a complex structure.     

Multiaxial fatigue damage parameter and life prediction for medium-carbon steel based on the critical plane approach

The tension–torsion fatigue characteristics were investigated under proportional and non-proportional loading in this paper. The fatigue cracks on the surface of multiaxial fatigue specimens were observed and analyzed by a scan electron microscope. On the basis of the investigation on the Kindil–Brown–Miller and Fatemi–Socie’s critical plane approaches, a shear strain based multiaxial fatigue damage parameter was proposed by von Mises criterion based on combining the maximum shear strain and the normal strain excursion between adjacent turning points of the maximum shear strain on the critical plane. The proposed multiaxial fatigue damage parameter does not include the weight constants. According to the proposed multiaxial fatigue damage parameter, the multiaxial fatigue life prediction model was established with the Coffin–Manson equation, which is used to predict the multiaxial fatigue life of medium-carbon steel. The results showed that the proposed multiaxial fatigue damage parameter could be used under either multiaxial proportional or non-proportional loading.     

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. Technical University of Opole, Opole, Poland, Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 86–96, May–June, 1996.