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.     

Fatigue crack propagation at concrete–concrete bi-material interfaces

This paper presents experimental and analytical studies on fatigue crack propagation in concrete–concrete cold jointed interface specimens. Beams of different sizes having jointed interface between two concretes with different elastic properties are tested under fatigue loading. The acoustic emission technique is used for monitoring the fatigue crack growth. It is observed that the interface having a higher moduli mismatch tends to behave in a brittle manner. The CMOD compliances at different loading cycles are measured and the equivalent crack lengths are determined from a finite element analysis. An analytical model for crack growth rate is proposed using the concepts of the dimensional analysis.     

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.     

Fatigue crack propagation from a cold-worked hole

The cold expansion process is widely used to enhance the fatigue life of structures with fastener holes. Various studies assert that the cold expansion improves the fatigue strength of fastener holes; however, the improvement of fatigue life is difficult to quantify. Therefore, the influence on fatigue life of cold-worked process was studied by numerical and experimental tests. Then, a parametric study on material hardening behavior and Bauschinger’s parameter was performed for several loading conditions in order to determine their effect on crack growth propagation. The results of the numerical tests have exhibited a good prediction of the fatigue life of the component.     

Cohesive crack analysis of size effect

This paper deals with the analysis of size effect in concrete. An extensive campaign of accurate numerical simulations, based on the cohesive crack model, is performed to compute the size effect curves (CSEC) for typical test configurations. The results are analyzed with reference to the classical Ba?ant’s size effect law (SEL) to investigate the relationship between CSEC and SEL. This analysis shows that as specimen size tends to infinity, the SEL represents the asymptote of the CSEC, and that the SEL parameter known as the effective fracture process zone length is a material property which can be expressed as a function of the cohesive crack law (CCL) parameters. Finally, the practical implications of this study are discussed in relation to the use of the CSEC or the SEL for the identification of the CCL parameters through the size effect method.     

Fatigue crack propagation in cellular metals

Two types of cellular metals were investigated: a closed-cell aluminium foam with a cell size of about 3.5 mm and densities ranging from 0.25 to 0.40 g/cm³ and hollow sphere structures made of a stainless steel (316L) with sphere sizes of 2 and 4 mm and a density of about 0.3 g/cm³. Fatigue and fatigue crack propagation tests were performed on these materials using an electro-dynamic resonance fatigue testing machine. The crack extension was monitored by a potential drop technique. Additionally, investigations were carried out inside the scanning electron microscope (SEM) using an in situ loading device. All tests were accompanied by local deformation measurements and fracture surface analyses. From the fatigue crack propagation tests it is evident that these materials show a relatively high Paris-Exponent m in the range of 6 to 25 compared to common ductile solid metals. Additional tests were performed to estimate the influence of crack closure, crack bridging and micro cracking on the da/dN versus ΔK curve for these materials. The in situ fatigue tests and the fracture surface analyses revealed a difference in the fatigue crack propagation mechanisms between the closed-cell foam and the hollow sphere structure: in the closed-cell foam a contiguous fatigue crack can be found, where in the case of the hollow sphere structure the fatigue crack propagation is concentrated in the vicinities of the sintering necks.     

Fatigue crack propagation in 7050-T7451 plate alloy

A study has been accomplished to characterize the fatigue crack growth rates and mechanisms in thin and thick plate commercial 7050-T7451 aluminum plate in the L-S orientation. Crack growth and crack shielding with branching behavior of long, through thickness cracks is examined and compared to L-T and T-L oriented growth data. Compact tension specimens and the compliance method were used to determine crack growth rates. Constant ΔK data showed significant retardation of growth rate curves for the L-S orientation in the range of 10-13 MPa√m where branching and splitting parallel to the load axis are dominant growth mechanisms.     

Mixed-mode crack propagation through reinforced concrete

This paper presents the results of a very recent experimental research program aimed at investigating mixed-mode fracture of reinforced concrete. The tests were designed so that only one single mixed-mode crack generates and propagates through the specimen, as opposed to the usual dense crack pattern found in most of the tests in scientific literature. The specimens were three-point-bend beams of three different sizes. They were notched asymmetrically and reinforced with various ratios of longitudinal and inclined reinforcement. These experiments may help to understand the mechanisms of crack initiation and propagation through reinforcing bars under mixed-mode load conditions.     

Fatigue crack growth simulation in heterogeneous material using s-version FEM

A fully automatic fatigue crack growth simulation system is developed using the s-version Finite Element Method (s-FEM). This system is extended to fractures in heterogeneous materials. In a heterogeneous material, the crack tip stress field has a mixed-mode condition, and the crack growth path is affected by inhomogeneous materials and mixed-mode conditions. Stress intensity factors (SIFs) in the mixed-mode condition are evaluated using the virtual crack closure method (VCCM). The criteria for the crack growth amount and crack growth path are based on these SIFs, and the growing crack configurations are obtained. At first, the basic problem is solved, and the results are compared with some results available in the literature. It is shown that this system gives an adequate accurate estimation of the SIFs. Then, two-dimensional fatigue crack growth problems are simulated using this system. The first example is a plate with an interface between hard and soft materials. The cracks tend to grow in soft materials through the interface. A second example is a plate with distributed hard inclusions. The crack takes a zig-zag path by propagating around the hard inclusions. In each case, the crack growth path changes in a complicated manner. Changes of the SIFs values are also shown and discussed.     

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris’ law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena.     

Cohesive crack model description of ductile to brittle size-scale transition: dimensional analysis vs. renormalization group theory

The present paper is a review of the research works carried out on the cohesive crack model and its applications at the Politecnico di Torino during the last decade. The topic encompasses experimental, numerical and theoretical aspects of the cohesive crack model. The research work followed two main directions. The early work concerns the development and the implementation of the cohesive crack model, which has been shown to be able to simulate experiments on concrete specimens and structures. It is referred to as the dimensional analysis approach, since it succeeds in capturing the ductile-to-brittle transition by increasing the structural size owing to the different physical dimensions of two material parameters: the tensile strength and the fracture energy.On the other hand, the later research direction aims at extending the classical cohesive model to quasi-brittle materials showing (as they often do) fractal patterns in the failure process. This approach is referred to as the renormalization group (or fractal) approach and leads to a scale-invariant cohesive crack model. This model is able to predict the size effects even in tests where the classical approach fails, e.g. the direct tension test.The two research paths, therefore, complete each other, allowing a deeper insight into the ductile-to-brittle transition usually detected when testing quasi-brittle material specimens or structures at different size-scales.     

Fatigue crack propagation in short-carbon-fiber reinforced plastics evaluated based on anisotropic fracture mechanics

The influence of fiber orientation on crack propagation was studied with single edge-notched specimens cut from injection-molded plates of fiber-reinforced polyphenylene sulfide (PPS). Fracture mechanics parameters were calculated by FEM based on anisotropic elasticity. For mode I crack propagation in specimens parallel (MD) and perpendicular (TD) to molding direction, difference in crack propagation rate, dc/dN, among specimens becomes small when correlated to a crack-tip-opening radius parameter, H_IΔG_I, where H_I is a compliance parameter. Including crack propagation under mixed loading, all the data tend to merge a single relation when correlated to total energy-release-rate range divided by Young’s modulus, ΔG_total/E_θ.     

An improved model for predicting the crack size and plasticity dependence of fatigue crack propagation

The angled crack problem has been given special attention in the recent years by fracture mechanics investigators due to its close proximity to realistic conditions in engineering structures. In this paper, an investigation of fatigue crack propagation in rectangular steel plates containing an inclined surface crack is presented. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. During the fatigue tests, the growth of the fatigue crack was monitored using the AC potential drop technique. A series of modification factors, which allow accurate sizing of such defects, is recommended. Paris power law is normalized and adopted for data analysis. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The results obtained are compared with those obtained using the commonly employed fracture criterion and the experimental data.     

Fatigue crack growth simulation in a first stage of compressor blade

A first-stage rotary compressor blade of a Model GE-F6 gas turbine failed due to vibration in early March 2008. Initial investigations showed that pitting on the pressure side of the blade caused micro cracks, leading to larger cracks due to high cycle fatigue. To assess this failure, a series of experimental, numerical, and analytical analyses were conducted. Fractography of the fractured surface of the blade indicated that two semi-elliptical cracks incorporated and formed a single crack. In this study, static and dynamic stress analyses were performed in Abaqus software. Moreover, fracture mechanics criterion was accomplished to simulate fatigue crack growth. This was carried out using a fracture analysis code for 3-dimensional problems (Franc3D) in two states. Firstly, stress intensity factors (SIFs) for one semi-elliptical surface crack and then SIFs for two semi-elliptical surface cracks were taken into account. Finally, the Paris and Forman–Newman–De Koning models were used to predict fatigue life. Since stress level and crack shape in both conditions are the same and the SIF at the crack tip reaches the fracture toughness of the blade, SIFs results indicate that insertion of a second crack has no effect on the final SIF, however, the second crack facilitates the process of reaching the critical length. So, fatigue life in two-crack condition is less than in the one-crack state.     

Fatigue crack propagation in rocker and roller-rocker bearings of railway steel bridges

In this work, a method is proposed for rolling contact fatigue crack propagation analysis using contact and fracture theories in conjunction with fatigue laws. The proposed method is used in the fatigue analysis of rocker and roller-rocker bearings of a railway open web girder bridge which is instrumented with strain gages. Using a contact algorithm based on the minimum energy principle for bodies in rolling contact with dry friction, the normal and tangential pressure distribution are computed. It is seen that the most critical location of a crack in bearings is at a point very close to the contact region, as expected.     

Age-dependent size effect and fracture characteristics of ultra-high performance concrete

This paper presents an investigation of the age-dependent size effect and fracture characteristics of ultra-high performance concrete (UHPC). The study is based on a unique set of experimental data connecting aging tests for two curing protocols of one size and size effect tests of one age. Both aging and size effect studies are performed on notched three-point bending tests. Experimental data are augmented by state-of-the-art simulations employing a recently developed discrete early-age computational framework. The framework is constructed by coupling a hygro-thermo-chemical (HTC) model and the Lattice Discrete Particle Model (LDPM) through a set of aging functions. The HTC component allows taking into account variable curing conditions and predicts the maturity of concrete. The mechanical component, LDPM, simulates the failure behavior of concrete at the length scale of major heterogeneities. After careful calibration and validation, the mesoscale HTC-LDPM model is uniquely posed to perform predictive simulations. The ultimate flexural strengths from experiments and simulations are analyzed by the cohesive size effect curves (CSEC) method, and the classical size effect law (SEL). The fracture energies obtained by LDPM, CSEC, SEL, and cohesive crack analyses are compared, and an aging formulation for fracture properties is proposed. Based on experiments, simulations, and size-effect analyses, the age-dependence of size effect and the robustness of analytical-size effect methods are evaluated.     

Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate

The effects of applied compressive stress on the crack tip parameters and their implications on fatigue crack growth have been studied. Four center-cracked panel specimens with different crack lengths are analysed using finite element method. The results show that under tension–compression loading the local crack tip parameters are determined by two loading parameters. The two loading parameters are the maximum stress intensity and the maximum compressive stress in the applied stress cycle. Predictions of fatigue crack propagation behaviour based on the maximum stress intensity and maximum compressive stress agree well with experimental observations.     

A methodology for automatic crack propagation modelling in planar and shell FE models

This paper describes a fast and reliable algorithm for automatic simulations of crack propagation in bi-dimensional and non-planar shell FE models. Thanks to its simplicity, the algorithm can be coded with little effort and in a relatively short time. Moreover, it can be interfaced with the existing FE analysis environment. An automatic iterative process makes it possible to achieve the highest degree of accuracy in the results for the FE model used. Good accuracy can also be achieved for quite coarse meshes.     

Fatigue and creep crack growth behaviour of Inconel MA 6000

Crack growth in MA 6000 under cyclic loading was studied at 24, 760, and 1000°C and under static loading at 1000°C in two matenal onentatwns. Correlatwns of fattgue crack growth rate with parameters ?K and ?J were examined. Also comparisons were made of experimental and predicted growth rates.

The rate of growth was influenced by temperature and onentatwn m addttwn to the loading mode. Fatigue crack growth rate generally increased with temperature. However in the L-T orientation at 1000°C secondary cracks developed perpendtcular to the primary crack and significantly altered its behaviour. Creep crack growth at 1000°C was strongly orientation dependent, mainly due to secondary crackmg m the L-T oriented specimen in the direction perpendicular to the main crack.

Fracture surfaces were examined by scanning electron microscopy. Also, comparisons were made between crack growth behaviour of MA 6000, MA 754 and MA 956.     

疲劳裂纹扩展预测模型及其应用

在分析了灰色预测方法和支持向量机各自的优缺点基础上,提出了将二者相结合的一种新的预测模型———灰色支持向量机裂纹扩展预测模型.新模型发挥了灰色预测方法中"累加生成"的优点,弱化了原始序列中随机扰动因素的影响,增强了数据的规律性,同时避免了灰色预测方法及模型存在的理论缺陷.工程实例表明,文章所提出的裂纹扩展预测模型较传统的GM(1,1)模型、等维GM(1,1)模型精度都有所提高,为预测疲劳裂纹扩展提供了一种新的方法.