Fatigue crack growth in CFRP-strengthened steel plates

In this paper fatigue crack growth in steel plates reinforced by using carbon fiber reinforced (CFRP) strips is investigated from the experimental, numerical and analytical point of view. Single edge notched tension (SENT) specimens were strengthened with different reinforcement configurations and tested at a stress ratio R of 0.4. Different initial damage levels were considered and the experimental results showed that the reinforcement application can effectively reduce the crack growth rate and significantly extend the fatigue life. Numerical models (finite elements) were also developed to evaluate the stress intensity factor (SIF) and the crack opening displacement (COD) profile. Based on the numerical results, an analytical model was proposed to predict the fatigue crack growth rate and the fatigue crack growth curves. The analytical results are validated by comparing the fatigue crack growth curves to the experimental ones.     

Fatigue crack propagation model for plain concrete - An analogy with population growth

In this work, an analytical model is proposed for fatigue crack propagation in plain concrete based on population growth exponential law and in conjunction with principles of dimensional analysis and self-similarity. This model takes into account parameters such as loading history, fracture toughness, crack length, loading ratio and structural size. The predicted results are compared with experimental crack growth data for constant and variable amplitude loading and are found to capture the size effect apart from showing a good agreement. Using this model, a sensitivity analysis is carried out to study the effect of various parameters that influence fatigue failure.     

MODELLING THE CONDITIONS FOR FATIGUE FAILURE IN METAL MATRIX COMPOSITES

Abstract— An investigation on the fatigue crack growth (FCG) and fatigue failure in metal matrix composites (MMCs) has been conducted using a model based on micromechanical elasto-plastic fracture mechanics (EPFM) principles. To evaluate the model, comparisons between experimental and predicted fatigue life have been made for two silicon carbide strengthened (SCS)-6/Ti-based MMCs. Conditions for crack arrest and crack instability have also been considered in order to define the fatigue damage limits. Crack arrest occurs from the added effects of fibre bridging and the constraint provided by the fibre on matrix microplasticity, while crack instability is achieved when the fibre constraint effect is minimum and the fatigue resistance of the material is reduced due to the accumulation of fatigue damage. Comparisons of the predicted fatigue damage limits with experimental results show good agreement which underlines the usefulness of a microstructural fracture mechanics model.     

UNSTABLE FATIGUE CRACK PROPAGATION AND FATIGUE FRACTURE TOUGHNESS OF STEELS

This paper presents the results of fatigue crack growth and fatigue fracture toughness studies of a high-pressure vessel steel with particular emphasis on the influence of heat treatment, low temperatures, plastic prestraining, the stress ratio and specimen dimensions. It has been shown that steels in an embrittled state, caused primarily by thermal treatment and low-temperatures, exhibit unstable fatigue crack growth which is characterized by alternate crack jumps (cleavage zones) and zones of fatigue crack growth. The fatigue fracture toughness, which corresponds to the first crack jump, and final fracture can be appreciably lower (i.e. up to 50%) than the static fracture toughness under plane strain conditions at the corresponding temperature. An analysis has been performed of unstable and stable fatigue crack growth and a model of unstable crack propagation is proposed which accounts for the observed experimental behaviour.     

Numerical modeling the effects of overloading and underloading in fatigue crack growth

In this paper, the effects of overloading and underloading on fatigue crack growth were investigated. Numerical modeling was done by using finite element software. In this software, without using the remeshing technique, effect of crack tip plasticity in fatigue crack growth life was analyzed. Plasticity effects were considered by using three methods: COD method, U correction factor and J-integral. Calculated results for crack growth rates were compared with experimental data in literature. Results were obtained by COD method and U correction factor have good agreement but results form J-integral have not. We also study the effects of stress ratio (R) in plane stress and plane strain conditions. With increasing R, the fatigue life was increased. The extent of crack retardation is greater under plane stress than plane strain conditions. Underloading has not significant effects on fatigue crack growth rate. Underloading cause a little variation in plastic zones and so little effects on fatigue life.     

Discussion on “A Mixed Mode Crack Growth Model Taking Account of Fracture Surface Contact and Friction” by Bian Et al. (2006)

A mixed-mode fatigue crack growth model with taking account of fracture surface contact and friction was developed recently by Bian et al. (2006), in reference to the general three-dimensional tensile stress solution for an elastic elliptical crack that was given by Kassir and Sih (1975). However, this general stress solution contains an error, and thus all equations for the fatigue crack growth model proposed by Bian et al. (2006) involve the error. The correct three-dimensional stress field for the elastic elliptical crack is then presented, and three fatigue crack growth models are corrected and expressed as simple functions in this paper.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Fatigue crack propagation model and size effect in concrete using dimensional analysis

It is well known that fatigue in concrete causes excessive deformations and cracking leading to structural failures. Due to quasi-brittle nature of concrete and formation of a fracture process zone, the rate of fatigue crack growth depends on a number of parameters, such as, the tensile strength, fracture toughness, loading ratio and most importantly the structural size. In this work, an analytical model is proposed for estimating the fatigue crack growth in concrete by using the concepts of dimensional analysis and including the above parameters. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between different parameters involved. It is shown that the proposed fatigue law is able to capture the size effect in plain concrete and agrees well with different experimental results. Through a sensitivity analysis, it is shown that the structural size plays a dominant role followed by loading ratio and the initial crack length in fatigue crack propagation.     

Three-dimensional mixed-mode fatigue crack growth in a functionally graded titanium alloy

The implementation of unitized structure in the aerospace industry has resulted in complex geometries and load paths. Hence, structural failure due to three-dimensional mixed-mode fatigue crack growth is a mounting concern. In addition, the development of functionally graded materials has further complicated structural integrity issues by intentionally introducing material variability to create desirable mechanical behavior. Ti-6Al-4V β-STOA (solution treated over-aged) titanium is a functionally graded metallic alloy that has been tailored for superior fatigue crack growth and fracture response compared with traditional titanium alloys. Specifically, the near-surface material of Ti β-STOA is resistant to fatigue crack incubation and the interior is more resistant to fatigue crack growth and fracture. Therefore, Ti β-STOA is well suited for applications where surface cracking is a known failure mode. Advances in experimental testing have shown that complex loading conditions and multi-faceted materials can be tested reliably. In this paper, the authors will experimentally generate three-dimensional mixed-mode surface crack data in functionally graded Ti-6Al-4V β-STOA and comment on the effect of the material tailoring.     

FORMULATION OF A STOCHASTIC MODEL OF FATIGUE CRACK GROWTH

Based on a global/local energy balance a deterministic model of fatigue crack growth under constant amplitude loading is derived. The energy terms resulting from the continuous plasticity and localized fracture around the crack tip are determined for small scale yielding leading to the fatigue crack growth equation involving the stress intensity factor and its amplitude. Four material parameters which should be identified from experimental data have a physical interpretation; these are eventually assumed to be random variables and model the statistical scatter of the crack growth versus N curves observed in experiments. A Gaussian white noise random field is additionally assumed to describe the stochastic material non-homogeneity within a specimen. Its effect on the crack growth is derived and results in a positive non-stationary random function depending on the crack length. Statistical parameters of the random fields are identified. Verification of the model by comparison with experimental results is undertaken in a subsequent paper.     

Fracture mechanics assessment of railway axles: Experimental characterization and computation

The results of a joint research project aiming at developing validated fracture mechanics assessment procedures for railway axles are presented. Experimentally determined fatigue crack growth parameters for the commonly used axle steel 25CrMo4 (A4T) and the high strength steel 34CrNiMo6 are included in the range of stable crack propagation and near threshold. The results are employed for predicting fatigue crack growth for cracks initiating at the axle shaft. For the computational modelling of fatigue crack propagation a generally applicable solution for stress intensity factors has been derived. Furthermore, the influence of variable amplitude loading (block loading) on the crack propagation behaviour has been studied and is discussed. The computational results are in good agreement with experimental data determined on standard fracture mechanics specimens as well as down-scaled and geometrically similar axle specimens.     

A NOTE ON MODELLING SHORT FATIGUE CRACK BEHAVIOUR

Based upon experimental short fatigue crack growth data and adopting the Brown–Hobson model, new crack growth equations have been derived in an attempt to describe more precisely short fatigue crack growth behaviour that separates the physically small crack regime from the long crack regime. An empirical model for physically small crack growth was developed by employing elastic–plastic fracture mechanics parameters.
By considering the proposed approach to short fatigue crack modelling, a new second 'microstructural' threshold condition has been established using only short fatigue crack growth data. In the case of fatigue in an aggressive environment it is suggested that three transition (threshold) conditions can be identified representing: (i) a stress-assisted pitting/pit-to-crack transition; (ii) a microstructurally short shear crack/physically small tensile crack transition; and (iii) a physically small crack/long crack transition.
A comparison of this approach with that of existing models has been made, and predictions of total fatigue lifetime using the model have been presented. A reasonable agreement has been observed between predicted and experimental crack growth rates.     

Fatigue crack growth in welded beams

The fatigue behavior of welded steel beams is evaluated using the fracture mechanics concepts of stable crack growth. A fracture mechanics model for cracks originating from the pores in the web-to-flange fillet weld is developed. Estimates of the stress-intensity factor are made that numerically describe the initial flaw condition. With the final crack size known, a theoretical crack-growth equation was derived from the fatigue test data of the welded beams. The derived relationship compares well with actual crack-growth measurements on a welded beam and available data from crack growth specimens. The regime of crack growth where most of the time is spent growing a fatigue crack in a structural element is shown to correspond to growth rates below 10^?6 in. per cycle. Little experimental crack growth data is available at this level. It is concluded that the fracture mechanics concepts can be used to analyze fatigue behavior and to rationally evaluate the major variables that influence the fatigue life of welded beams.     

Stochastic analysis of fatigue crack growth for metallic structures

In order to estimate the statistical variability of fatigue crack growth in metallic structures, a stochastic model is proposed by combining stochastic theory with experimental results. A stochastic differential equation is derived from the stochastic model for fatigue crack growth. By using the solution of the stochastic differential equation, some distribution functions related to fatigue crack growth were derived. Sample functions of fatigue crack growth time histories have been simulated as random processes.     

Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

Fracture simulation of ferroelectrics based on the phase field continuum and a damage variable

Domain switching in the vicinity of a crack tip is known as one of the major aspects of local nonlinear behavior of ferroelectrics, and it plays an important role in the fracture behavior. In the present paper, a fracture model based on a phase field continuum and a damage variable is presented to study the fracture behavior of ferroelectrics and its interaction with the domain structures. In this model the energy of fracture is regularized by the damage variable. When the damage variable equals one, it represents undamaged material. In this case, the energy reduces to the phase field potential with the spontaneous polarization being an order parameter, and the system of equations becomes the same as that of a conventional phase field continuum. When the damage variable becomes zero, it represents a crack region, and the potential becomes the energy density stored in the crack medium. The evolution of the damage variable is governed by a Ginzburg-Landau type equation. In this way, the fracture model can simulate the fracture behavior such as crack growth, kinking and formation, with no a priori assumption on fracture criteria and predefined crack paths. The model is implemented in a 2D Finite Element Method in combination with implicit time integration and non-linear Newton iteration. As example, the fracture model is used to simulate the fracture of an edge crack in a ferroelectric single crystal under mechanical mode-I loading. In the simulation crack propagation, kinking and formation are observed. In particular, the results show the interaction between the domain structure evolution and the crack propagation.     

Weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Analysis of fiber bridging phenomenon in the composites and determination of stress intensity factors due to non-uniform stress distributions such as residual and thermal stresses generally require the use of a weight function. This paper describes the development and verification of a weight function for the single edge cracked geometry with clamped ends. Finite element analyses were conducted to determine the stress intensity factors (K) and crack opening displacements (COD) due to different types of stress distributions. The weight function was developed using the K and COD solution for a constant stress distribution. K and COD predicted using this weight function correlated well with the finite element results for non-uniform crack surface stress distributions.     

Modeling fatigue crack and spalling for rolling die under hot milling

In hot milling process, rolling die is subjected to nonsteady conditions which can rise the combinations of fatigue and spalling damage mechanism. An understanding about the failure mechanism of the rolling die is essential under hot rolling process. Fatigue crack growth and spalling process are governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic‐plastic fracture mechanics, an analytical model are presented in this paper to determine the elliptical crack growth rate and spalling damage mechanism. The model includes new proposed constitutive equations for fatigue and spalling crack growth. To verify the models, finite element simulation and experimental data are considered. The results show good agreement with finite element simulation and experimental data.     

Microscopic and Macroscopic Growth Rates of Fatigue Cracks in Steels and Alloys under the Influence of Crack Closure

On the basis of the experimental data, we show that the difference between the macroscopic and microscopic fatigue crack growth rates in the second section of the kinetic diagram of fatigue fracture is caused by the effect of crack closure within the limits of its existence. We establish the relationships between the macroscopic and microscopic fatigue crack growth rates and the structure of the material in the second section of the diagram for various values of the load ratio with regard for the effect of crack closure and propose a procedure of examination of the fracture processes in structural materials based on the analysis of microscopic and macroscopic fatigue crack growth rates.     

A strip yield model for two collinear cracks in plates of arbitrary thickness

As two cracks grow and approach each other under fatigue loading, a deleterious interaction between them can considerably affect the crack growth rate, making theoretical evaluations and experimental data from a single isolated crack case considerably inaccurate. The aim of the present study is to investigate the interaction between two collinear cracks of equal length, taking into account the plate??s thickness effect, which was demonstrated to have a large effect on fatigue crack growth in the case of a single crack. The obtained solution to the problem is based on the Dugdale strip yield model and the distributed dislocation technique. In addition, a fundamental solution for an edge dislocation in a finite thickness plate is utilised. The present solution shows a very good agreement with previously published results for some limiting cases. The obtained results confirm a significant dependence of the interaction and stress intensity factors on the plate thickness, which can dramatically affect the plastic collapse conditions as well as fatigue crack growth rates.