Evaluation of the probability distribution of crack propagation life in metal fatigue by means of probabilistic finite element method and B-models

In this paper, a new model for the prediction of the cumulative distribution function of fatigue life of structural elements during the crack propagation stage is established. This problem is considered as a cumulative damage process following the probabilistic approach of Bogdanoff and Kozin (B-models). The initial and final crack lengths, the crack propagation angle, the material fracture and elastic parameters and the external loads have been the random variables considered here. The theoretical bases of the model and the procedure to construct it are described in the forthcoming paragraphs such as several examples for mode I problems including the comparison with experimental results.     

A modified model for the estimation of fatigue life derived from random vibration theory

When a component is subjected to variable-amplitude loading, if the fundamental stress–life cycle relationship and an accumulation rule are given, then the fatigue damage or fatigue life of the component can be calculated and/or estimated. In the present paper, random vibration theory is incorporated into the analysis of the above problem. Several formulas are thus derived. Experimental work is then carried out to verify the derived formulas. Comparison is made among the results calculated based on different formulas, different accumulation rules and different random loading. It is concluded that the derived formulas do provide us with quick prediction of the fatigue damage or fatigue life when a component is subjected to variable-amplitude loading that has a certain random nature.     

Application of inverse first-order reliability method for probabilistic fatigue life prediction

A general probabilistic life prediction methodology for accurate and efficient fatigue prognosis is proposed in this paper. The proposed methodology is based-on an inverse first-order reliability method (IFORM) to evaluate the fatigue life at an arbitrary reliability level. This formulation is different from the forward reliability problem, which aims to calculate the failure probability at a fixed time instant. The variables in the fatigue prognosis problem are separated into two categories, i.e., random variables and index variables. An efficient searching algorithm for fatigue life prediction is developed to find the corresponding index variable at a certain confidence level. Numerical examples using direct Monte Carlo simulation and the proposed IFORM method are compared for algorithm verification. Following this, various experimental data for metallic materials are used for model prediction validation.     

Damage indices for failure of concrete beams under fatigue

In this study, an analytical method is proposed to correlate local damage variables such as relative crack depth and crack tip opening displacement with a newly defined global damage index for a concrete beam under fatigue loading. This global damage index may be used to assess the response of a degraded concrete beam under service loading. The damage is assumed to appear in the form of a major crack that propagates under constant amplitude fatigue loading. The progressive cracking phenomenon is modeled within a finite element framework using a crack beam element, which takes into account the compliance variation due to discrete cracking within the member. The flexural stiffness degradation of the member is computed based on an Eigen analysis of the global stiffness matrix. It is seen that the degree of flexural stiffness degradation due to discrete cracking is the same for geometrically similar specimens when the relative crack depth is used as a local damage parameter. Further, in order to improve the accuracy of the response prediction using the above global damage index, another global damage parameter is defined based on the nature of applied loading.     

Reliability of reinforced concrete structures under fatigue

This paper focuses on time-variant reliability assessment of deteriorating reinforced concrete structures under fatigue conditions. A strategy combining two time scales, namely the micro-scale of instantaneous structural dynamics (or statics) and the macro-scale of structural lifetime, is proposed. Non-linear response of reinforced concrete structures is simulated by means of the finite element method with adequate material model. A phenomenological fatigue damage model of reinforced concrete is developed and calibrated against experimental results available in the literature. Reliability estimates are obtained within the response surface method using the importance/adaptive sampling techniques and the time-integrated approach. The proposed assessment strategy is illustrated by an example of a concrete arch under fatigue loading. The obtained results show a general inapplicability of local and linear fatigue models to system level of structures.     

Cumulative fatigue damage and life prediction of elastomeric components

Elastomeric components are widely used in many applications due to their good damping and energy absorption characteristics. The type of loading normally encountered by these components in service is variable amplitude cyclic loading. Therefore, fatigue failure is a major consideration in their design. In this work capabilities of Rainflow cycle counting procedure, maximum principal strain as a damage criterion, and Miner's linear cumulative damage rule are evaluated with both specimen and component tests. An automotive cradle mount is used as an illustrative component. Comparison of predicted and experimental fatigue lives in both specimen and cradle mount variable amplitude load tests indicate satisfactory predictions in both cases.     

Stop drilling procedure for fatigue life improvement

This paper investigated how the stop drilling procedure improved the crack initiation life and the total fatigue life in specimens of 6061-T651 aluminium alloy and AISI 304 stainless steel. The crack initiation life was the number of fatigue cycles initiating a 0.2 mm crack at a stophole edge. The larger the stophole diameter, the longer the crack initiation and total fatigue lives. The 2, 2.5, and 3 mm diameter stopholes improved the nonstop-drilled total fatigue life of the 6061-T651 specimen by 187%, 321%, and 443% and that of the AISI 304 specimen by 72%, 121%, and 174%. At each stophole diameter, the 6061-T651 crack initiation life improved over the AISI 304 counterpart because of lower values of the K_f factor and the ΔJ/ρ_c ratio.     

Experiment and modeling of uniaxial tension fatigue performances for filled natural rubbers

A tension fatigue model of filled natural rubbers is investigated to study the contributions of two key factors, namely, the damage parameter and the specimen geometry used in the fatigue experiment. The uniaxial tension fatigue experiments were carried out for three filled natural rubber specimens with different geometry: a dumbbell simple tension specimen (STS), a dumbbell cylindrical specimen (DCS), and a hollow cylindrical specimen (HCS). The commonly used damage parameters for fatigue life prediction are discussed. The fatigue life prediction models are formulated using the measured tension fatigue life of the STS together with different damage parameters. The effectiveness of the models is established in terms of a correlation coefficient characterizing the error between the measured and predicted fatigue lives. It is concluded that all the damage parameters considered in the study can effectively estimate the tension fatigue life with correlation coefficients exceeding 0.9. The fatigue life model formulated for the STS was also found to be appropriate for predicting the fatigue life of specimens with different geometry (DCS and HCS) suggesting that the relationship between the tension fatigue life and the damage parameters is independent of the specimen geometry. One may thus conduct tension fatigue tests with STS alone in order to model the tension fatigue life of rubbers with alternate geometry.     

Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

The research on failure analysis of fluid cylinder and fatigue life prediction

To analyze the reasons of fluid cylinders’ rupture, macro-analysis, SEM, composition inspection, metallographic analysis, hardness test and mechanics performance test of fluid cylinders materials were implemented. Two different kinds of fatigue life prediction methods have been proposed which are based on total life analysis and strain–life methodology. The results indicate that: the failure cylinders’ material quality is satisfactory. Fatigue damage caused by high working, stress and corrosion is the main reason of cracking. The fatigue life prediction illustrates that strain–life methodology is well adapted to fluid cylinders.     

New fatigue life calculation method for quenched and tempered steel SAE 4140

In stress-controlled constant amplitude and service loading tests at ambient temperature mechanical stress-strain hysteresis, temperature and electrical resistance measurements were performed to characterize the fatigue behavior of the quenched and tempered steel SAE 4140. The applied measurement methods use deformation-induced changes of the microstructure in the bulk material and represent the actual fatigue state. A new test procedure combines any kind of load spectra with periodically inserted constant amplitude sequences to measure the plastic strain amplitude, the change in temperature and the change in electrical resistance at the same time. The average values of the measuring sequences are plotted as function of the number of cycles in cyclic ‘deformation’ curves and represent the summation of microstructural changes caused by service loading. On the basis of generalized Morrow and Basquin equations the physically based fatigue life calculation method “PHYBAL” was developed for constant amplitude and service loading. With only three fatigue tests, Woehler (S–N) and fatigue life curves can be calculated in very good agreement with experimental ones determined in a conventional manner. The application of “PHYBAL” provides an enormous saving of experimental time and costs.     

A thermodynamic framework for fatigue crack growth in concrete

The phenomenon of fatigue is commonly observed in majority of concrete structures and it is important to mathematically model it in order to predict their remaining life. An energy approach is adopted in this research by using the framework of thermodynamics wherein the dissipative phenomenon is described by a dissipation potential. An analytical expression is derived for the dissipation potential using the concepts of dimensional analysis and self-similarity to describe a fatigue crack propagation model for concrete. This is validated using available experimental results. Through a sensitivity analysis, the hierarchy of importance of different parameters is highlighted.     

On the need to decompose fatigue strain signals associated to fatigue life assessment of the AISI 1045 carbon steel

The evaluation of a new statistical-based analysis is discussed in this paper, leading to the fatigue life assessment at three different applied stresses during the cyclic testing procedure. Fatigue tests were performed following the standard ASTM: E466-07. These tests involve a strain gauge being attached to the specimen. For this test, AISI 1045 carbon steel was used as material due to its wide application in automotive and machinery industries. Fatigue tests were performed at three different stress levels of 305 MPa, 325 MPa, and 345 MPa with the testing frequency of 8 Hz, and the strain signals were collected accordingly. The Integrated Kurtosis-based Algorithm for Z-filter (I-kaz) approach, which provides its coefficient and three dimensional graphics, was utilised to define a statistically-based fatigue behaviour pattern. The I-kaz technique was used to extract strain signal patterns at the respective low, medium, and high frequency ranges for each signal at specific applied testing stress level. Results showed that highest strain amplitude occur at the low frequency range, suggesting the capability of I-kaz to identify fatigue damage pattern of metallic materials using statistical representation.     

A multifractal analysis of fatigue crack growth and its application to concrete

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structure size, and some theoretical arguments have been proposed to interpret such a phenomenon. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature, particularly for so-called quasi-brittle materials like concrete. In the present paper, by exploiting concepts of fractal geometry, some definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. A multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed and used to interpret relevant experimental data related to concrete.     

A unified fatigue life model based on energy method

A new unified fatigue life model based on the energy method is developed for unidirectional polymer composite laminates subjected to constant amplitude, tension–tension or compression–compression fatigue loading. This new fatigue model is based on static failure criterion presented by Sandhu and substantially is normalized to static strength in fiber, matrix and shear directions. The proposed model is capable of predicting fatigue life of unidirectional composite laminates over the range of positive stress ratios in various fiber orientation angles. By using this new model all data points obtained from various stress ratios and fiber orientation angles are collapsed into a single curve.

The new fatigue model is verified by applying it to different experimental data provided by other researchers. The obtained results by the new fatigue model are in good agreements with the experimental data of carbon/epoxy and E-glass/epoxy of unidirectional plies.     

A plausible strategy for modeling fatigue life variation

In this paper stochastic modeling is used to predict fatigue life uncertainty by simulating small variations in strain-life material constants. The Monte Carlo method,^[1] using either known cumulative distribution functions (CDFs) for the material constants and/or postulated CDFs, provides the mechanism to generate a set of failure data. These data are analyzed, using ordinary statistical techniques, to develop the Weibull CDF for cycles to failure. It is seen that small variations (∼±15%) in values of the strain-life constants result in large variations (∼600%) in predicted fatigue life at moderate strain. The often-observed phenomenon that spread in fatigue data is greater at lower strain is also described by the stochastic model.     

Experimental research on the behaviour of high frequency fatigue in concrete

Calculating the fatigue strength of concrete under the cyclic load of vehicles when designing bridges is an issue which is receiving more and more attention from many engineers and researchers. Based on this fact, fatigue tests of plain concrete under constant-amplitude and stepping-amplitude cyclic loads were conducted. The mechanism which damages plain concrete specimens under high frequency fatigue loads was analysed and a non-linear accumulative fatigue formula that causes the damage was proposed. A fatigue equation P–S–N that considers the failure probability p′ was given. The results of this research are a good preparation for further studies into high frequency fatigue tests of concrete cylinders reinforced with carbon fibre.     

A fatigue reliability analysis method including super long life regime

An affordable and feasible method with moderate accuracy is developed to realize fatigue reliability assessment and life prediction including super long life regime (SLLR) through series of experimental researches on a railway axle steel and real axles. A competition damage mechanism for fatigue crack initiation and growth in SLLR is revealed to fascinate an understanding on wide fatigue damage behavior and to provide a weigh and balance on material primary quality control and on-line inspection capacity. Affordable material probabilistic strength-life (S-N) curves including SLLR are presented by an extrapolation approach on a concurrent probability rule between the S-N relations in mid-long life regime and the fatigue limits with a specified life definition. And then, structural probabilistic S-N curves are deduced by considering scale-induced effect on the material curves. Random cyclic stress-strain (CSS) relations are depicted for constructing structural random stressing history. Reliability assessment and fatigue life prediction are conducted by an interference model of the applied stress deduced from the random CSS relations and the strength capacity derived from the structural probabilistic S-N curves. Availability and feasibility of the present method are indicated by a successful application on a railway axle steel.     

A fatigue life prediction method for coke drum base,weld, and HAZ materials from tensile properties

The importance of material fatigue information in design has been well recognized. There are a few existing fatigue life prediction methods based on materials tensile properties. Some of these fatigue life prediction methods can be successfully applied for non-heat affected materials. However, industrial components, such as pressure vessel and pipelines are commonly constructed by welding parts together. The fatigue lives of welded section and its surrounding material could be greatly affected by the welding process. Therefore, it is beneficial to develop a fatigue life prediction model for the weld and surrounding heat affected zone (HAZ) materials based on their tensile testing data. In this paper, fatigue lives of base material and its weld and HAZ materials for constructing coke drums are studied. Mechanical properties are first obtained from the tensile tests. Then, fully-reversed strain-controlled fatigue tests were performed. It is found that the fatigue life of pure base material is roughly twice of the weld and four time of the HAZ at the same strain amplitude. Four-point correlation (FPC) method by Manson can reasonably predict the life of base material. However, it over-predicts the lives of weld and HAZ. By introducing two reduction factors R_plastic and R_elastic for the weld and HAZ material respectively into the FPC method, the over-prediction can be rectified. Therefore, the proposed modified FPC method could be applied in predicting fatigue lives of weld and HAZ materials.