Linear Elastic Fracture Mechanics Methods Research Articles

Comparing linear damage hypothesis to linear elastic fracture mechanics in the estimation of fatigue life in a high speed light craft

Linear elastic fracture mechanics methods provide a more comprehensive representation of crack propagation compared to traditional methods such as the linear damage hypothesis (or SN curve approach). These techniques have been widely adopted in the aerospace industry, however, their usage in the design of marine structures remains limited. The presented research uses full-scale trial data measured onboard a 111 m wave-piercing catamaran to compare the results obtained from linear elastic fracture mechanics and SN curve-based methods. The results reveal significant differences in estimated fatigue life between SN curve-based methods and fracture mechanics methods. These differences are likely due to limitations in the fracture mechanics model during the crack initiation phase. Changes in fracture mechanics parameters also had a significant effect on fatigue life, suggesting that if accuracy is important then material specific parameters are required. Despite the limitations shown, linear elastic fracture mechanics methods have a higher level of tailor-ability when compared to SN curve based methods and could offer benefits in situations such as the tracking of known flaws or in the assessment of changes to vessel configuration, or usage profiles.

Fracture process zone development and length assessment under the mixed-mode I/II load analysed by digital image correlation technique

In this paper, the fracture process zone (FPZ) of high-performance concrete (HPC) is investigated under mixed-mode I/II load conditions, and its formation is studied by applying digital image correlation (DIC). The experimental tests are performed on Brazilian disc specimens with central notch (BDCN). The traction-free crack and the FPZ extent ahead of the crack are localised. This is done by modification of the existing methodology for mode I cracks to account for various mixed-mode I/II loading conditions. Analytical and linear elastic fracture mechanics (LEFM) methods for the critical strain are used to find the FPZ extension. Lastly, this paper revisits the analytical formulas used in the prediction of mode I FPZ lengths. These formulas are adjusted to allow for the prediction of the FPZ length in the whole range of mixed-mode I/II load conditions. Experimental results show that the FPZ has a different size for various mixed-mode I/II load conditions.

Crack Growth in Ni-Cr-Mo-V Steel Using ΔCTOD Elastic–Plastic Model

Many studies have shown that the linear elastic fracture mechanics (LEFM) method based on the stress intensity factor range (ΔK) has limitations that cannot be ignored. Due to neglecting the influence of plastic deformation near the crack tip, LEFM shows apparent deviations in evaluating the fracture behaviour. Therefore, in this study, the crack tip opening displacement range (ΔCTOD) is chosen as an alternative to ΔK and based on the elastic–plastic fracture mechanics (EPFM) to develop a new fracture behaviour assessment approach for marine structures. Firstly, a ΔCTOD model based on the HRR (Hutchinson, Rice, and Rosengren) solution is proposed considering the crack closure effect. Secondly, a series of compact tension (CT) specimen crack growth experiments under constant amplitude loading is carried out. According to the experimental results, the prediction accuracy of the HRR model and traditional Irwin and Dugdale models is compared and analysed. The rationality of ΔCTOD as an alternative to ΔK is verified. The results show that ΔCTOD can describe the crack propagation behaviour well. The proposed HRR model shows better accuracy and a more comprehensive application range than the traditional models, which has a guiding significance for studying fracture behaviour for marine structural applications.

Investigation of a secondary bonded pultrusion composite laminate containing a ply-drop, Part 1: Experimental study of a structural element specimen

This is the first of two papers which presents a novel numerical method to predict the debond failure of a secondary bonded pultrusion laminate. In this paper, experimental work will be described that will later be used in the development, calibration and validation of the numerical model, which will be discussed in the second paper. The structure investigated in this work may be represented by a bonded composite laminate with external ply-drops. The laminate is composed of unidirectional pultrusion carbon fiber reinforced polymer cured plies bonded together to produce a secondary bonded laminate. In order to investigate the different failure modes of the ply-drop structure, an element specimen denoted as a ply-drop specimen, was tested under two types of loadings: axial tension and bending. Testing procedures of this type of specimen are not well established. Thus, test protocols will be suggested. In addition, finite element analyses are carried out using established linear elastic fracture mechanics methods to investigate the conditions during debond failure and in order to assess the ability of the methods to predict the debond failure.

Prediction of rolling contact fatigue crack propagation in bearing steels using experimental crack growth data and linear elastic fracture mechanics

Rolling contact fatigue (RCF) is a major life limiting factor for machine elements that employ non-conformal, rolling sliding, lubricated contacts such as rolling bearings and gears. This paper explores the application of linear elastic fracture mechanics (LEFM) principles, as commonly used in structural fatigue, for prediction of RCF crack propagation. A triple-disc contact fatigue machine is used to generate RCF cracks of varying lengths in AISI 52100 bearing steel roller specimens. Crack propagation rates across the surface are measured using optical inspection of test specimens and the final crack geometry is established through specimen sectioning. A numerical finite element model of surface breaking RCF cracks based on LEFM methods is devised to predict the evolution of stress intensity factors (SIFs) during over-rolling of the contact over the experimentally observed crack geometries. The model employs a suitable fracture mechanics mesh to resolve stresses at the crack tip and accounts for Hertzian contact stresses, contact friction and crack face friction. Potential effects of lubricant pressurisation within the crack are not modelled. The predicted SIFs are then related to the experimentally measured crack propagation rates to establish the applicability of the LEFM principles to RCF crack propagation. Results show that LEFM can be used to predict the growth of surface braking RCF cracks. For cracks longer than about 100 μm, a Paris law relationship with the stress intensity exponent of about 4 is derived. Mode II was seen to be the dominant mode of propagation for surface braking RCF cracks. Mode I SIFs are much smaller but can exhibit significant values when the contact is located just ahead of the crack mouth. Decreasing the crack face friction significantly increases mode II stress intensity suggesting that this is one important mechanism by which lubricant entry into the surface braking crack can accelerate its propagation. The findings can help in improving the reliability of mechanical systems by supporting the development of new tools for prediction of remaining useful life of machine components such as bearings and gears.

Accurate experimental determination of rock fracture toughness under simulated reservoir confining pressures

Rock toughness under confining pressure is recognized as a key mechanical property to understand brittle fracture in oil and gas projects. This article discusses a linear elastic fracture mechanics method to assess the critical stress intensity factor (KIC) of shale rocks subjected to confining pressure. Linear elastic fracture toughness (KIC) is determined in Round Bar Straight-Notch (RBSN) samples by a novel experimental set up. The device uses a primary chamber to apply a fluid-driven load to induce Mode-I opening. A secondary and independent chamber ensures variable hydraulic confinement pressures, up to 80 MPa, and both systems are isolated by O-rings. This allows analyzing the influence of fluid composition, temperature and confinement pressure. Early testing and finite element modelling allowed validating experimental results and identifying possible sources of experimental errors. Experimental assessment is discussed in terms of KIC tests. The effects of confinement on KIC in terms of crack closure mechanisms are recognized, pointing out a plausible cause for increased toughness as confinement rises.

A Numerical Simulation of UIC60 Rail-Weld's Fatigue and Crack Growth under Wheel Frictional Contact and Bending

In service condition rail joints, especially the weldments are under the action of various loadings which are not only working in multiple axis direction but also time-dependent having a cyclic and mixed-mode in nature and non-relative to each other. The surface of the rail and its weldment is acted by very high repetitive stress through the wheel and because of this contact stress the running surface or subsurface may have cracks or fractures due to fatigue. This work is based on numerical simulation of an aluminum thermite weldment on a UIC 60 rail under multi-axial fatigue crack propagation under the friction with surficial interaction between weldment and wheel with bending load due to vertically applied load through the wheel on the weld. Since contact is highly influenced by vertical load and also for minimizing the simulation time the lateral and longitudinal traction forces are not included in this study. The work formulation and discretization have been done with the finite element method and a non-linear lagrangian algorithm solver is applied. A 3-D rail-weld wheel model assembly and a semi-elliptical crack as a flaw on the weld surface are used to identify 3-Modes of SIFs along with its graphical plot generation. Simulation is performed under multi-axial weld wheel surface contact at different locations on weld running surface, taking into account varying position of fracture crack on weld 3-D model to calculate fracture life of weld joint and observation of fatigue crack propagation. This work involves the numerical and theoretical approach of fracture mechanics on created FE fatigue model using the Linear Elastic Fracture Mechanics (LEFM) method following Paris law for fracture mechanics. All the numerical simulation for critical fracture dimension and cycle count with stress intensity factor for weld failure data is estimated using software ANSYS 2020 academic and plotted, then comparison of predicted and observed transverse crack growth behavior and fatigue life of weld, based on Millions Gross Tonnes (MGT) is discussed.

Применение метода J-интеграла к оценке вязкости разрушения полимерных композиционных материалов

This paper discusses a relevant topic of improving the approaches to fracture toughness determination of layered composites. Current ASTM regulations imply the calculation of critical value for fracturing viscosity as per the test data following the classic approach of linear-elastic fracture mechanics (LEFM). For some materials, however, LEFM-based estimates are not realistic. As an alternative to LEFM in calculation of critical failure viscosity value, this paper suggests a method of J-integral. The data needed to apply this method were obtained through numerical experiments in ANSYS finite-element software package. The results of numerical experiments were used to construct load-displacement curves and compare them with the test data. The difference between critical viscosity fracturing values yielded as per LEFM and J-integral method might be as high as 33 %. This study revealed that J-integral method offers more accurate fracture toughness estimates for layered composites be- cause maximum design load results based on critical fracturing viscosity value obtained using J-integral deviated from average loads recorded during physical tests by not more than 2% whereas LEMF-based in certain cases had this deviation as high as 15 %. Still, J-integral method applied in this study required the inputs from numerical analysis, so it needs additional experimental verification.

Machine-learning-based investigation into the effect of defect/inclusion on fatigue behavior in steels

Fatigue tests were conducted under constant amplitude loading with a stress ratio of R = −1 to evaluate the effect of defect/inclusion on fatigue life of welding martensitic stainless steel (13Cr-5Ni) and KSFA90 steel (manufactured for crankshaft). An analysis based on the combined areaeff of defect/inclusion and linear elastic fracture mechanics (LEFM), was performed. The results indicate that defect/inclusion dominated the fracture mode for both materials utilized. Moreover, the combined areaeff and LEFM methods lose their accuracy for predicting fatigue life. Final, random forest machine-learning approach provided acceptable precision for unified predicting the fatigue of materials utilized in the current study.

Low-Temperature Fracture Toughness Study for Hot Mix Asphalt and Warm Mix Asphalt Under Pure Mode I and II Loading Condition

A linear elastic fracture mechanics method is proposed to investigate the fracture behavior of hot mix asphalt and warm mix asphalt; this method was used in this study to calculated the fracture toughness of hot mix asphalt and warm mix asphalt containing 3% Sasobit at low temperatures (0, − 10, and – 20 °C) and two types of bitumen (60/70 and 85/100). A semi-circular specimen with an edged crack under three-point bending load mode was used to create different loading modes, including pure mode I and pure mode II, to test the fracture toughness. The critical stress intensity factor was calculated using the critical load obtained from the failure test. The shape factor was determined from finite element analysis. The results show that hot mix asphalt has a higher fracture toughness against crack growth than the warm mix asphalt containing Sasobit. In addition, the fracture toughness of asphalt mixture with a penetration grade of 85/100 against crack growth is more than that of the mixture with a penetration grade of 60/70. The minimum fracture toughness of hot mix asphalt and warm mix asphalt occurred in pure mode I loading condition.

Mode I stress intensity factors for semi-elliptical fatigue cracks in curved round bars

Some cyclically loaded components such as mooring chains can develop fatigue cracks in locations where the shape of the part is equivalent to that of a curved or bent round bar. Here we consider a semi-elliptical crack growing from the surface of a curved round bar. This geometry can for example represent a chain link segment with a crack located at its inner- or outer radius. The surface crack can be either almond shaped, sickle shaped or straight-fronted. Stress intensity factors (SIFs) over the fronts of such crack geometries are in the present work investigated for several elementary mode I stress distributions. Finite element analysis and linear elastic fracture mechanics methods are used to develop semi-analytical solutions for the SIF at any point on the crack front. Effects of relative bar curvature on numerical results are demonstrated. Relative to otherwise identical cracks in straight bars, SIFs for cracks in the curved bars considered here are found to differ by up to 8%. With an offshore mooring chain model as a case example, the estimation of SIFs for cracks in a complex residual stress field is furthermore demonstrated using a cubic polynomial stress approximation.

Device for rock fracture toughness testing under hydrocarbon reservoir conditions

The effect of confinement pressure on fracture toughness may be significant in materials with poor tensile strength, as is the case of most rocks. In fracking wells for hydrocarbon exploitation, rock fracture is induced by a pressurized fluid. Indirect estimates of rock toughness based on injected pressure and volume records are much larger than laboratory-measured toughness values. This article discusses the design, fabrication and use of a linear elastic fracture mechanics method to assess the critical stress intensity factor (KI) of rocks under real well bottom conditions. Apparent Fracture Toughness (KIf) is determined using notched 1.5″ plugs machined from rocks. In this novel experimental set up, KI is applied by means of a hydraulic pressure inside the crack, so that fracturing fluid chemistry can be modified in order to optimize fracability. A secondary hydraulic system ensures variable confinement pressures, up to 80 MPa. Preliminary tests carried out in shale rocks at well bottom pressures show that rock toughness more than doubles those found at atmospheric pressure. It is shown that increasing triaxial pressure confinement allows to accurately model the conditions of rocks in oil & gas reservoir conditions.

Finite element analysis on the effect of martensitic transformation and plastic deformation on the stress concentration factor in a thin notched superelastic NiTi ribbon

The severe nonlinear behavior caused by the martensitic transformation (MT) and subsequent plastic deformation (PD) of detwinned martensite leads to a complex local stress redistribution at the location of stress risers of superelastic shape memory alloy (SMA) components. Nevertheless, in the literature, the simple linear elastic fracture mechanics (LEFM) equations are widely used in the evaluation of the fracture response of superelastic components which has resulted in obvious conflicts between the conclusions regarding the effect of MT on the fracture parameters, i.e. stress intensity factor (SIF) and material toughness. Furthermore, the linear elasticity method is frequently used in the literature to calculate the stress intensity range ([Formula: see text]) when the fatigue crack growth rate dependence on [Formula: see text] ([Formula: see text]) is being evaluated. Moreover, the PD followed by MT is poorly considered in the fracture mechanics of SMAs. This paper presents a numerical investigation on the role of both MT and PD, as well as the notch acuity, on the evolution of notch-tip stresses and strains and stress concentration factor ([Formula: see text]) upon the incremental application of the macroscopic tensile load on a thin NiTi notched superelastic ribbon, to mimic the effects of MT and PD on the SIF of superelastic parts. It is revealed that MT results in drastic deviations of the notch-tip stress, as well as the stress concentration factor ([Formula: see text]), from that obtained in LEFM. Due to the heterogeneous evolution of MT, the trend of the deviations is not regular and unique upon monotonic external loading. Accordingly, the results represent the ineffectiveness of the LEFM method in the evolution of the stress concentration factor (hence, the SIF) and toughness in monotonic loading, as well as the stress intensity range ([Formula: see text]) under fatigue loading in SMA components.

A DIC method to determine the Mode I energy release rate G, the J-integral and the traction-separation law simultaneously for adhesive joints

The quasi-static Mode I fracture behaviour of joints bonded with either a brittle or toughened epoxy adhesive or a ductile polyurethane adhesive has been investigated by means of digital image correlation (DIC). A novel method to measure the crack length using DIC analysis is proposed. By measuring the crack tip separation, beam rotation and crack length, the energy release rate G and the J-integral are obtained and are compared to analyse the validity of Linear Elastic Fracture Mechanics (LEFM) methods. Simultaneously the traction-separation laws (TSLs) for the adhesive joints were measured. The TSLs were then used as input data for FE modelling to evaluate their accuracy by comparing with experimental results. It is shown that LEFM is valid for the joints bonded with either the brittle or toughened epoxy adhesives but is invalid for joints bonded with the polyurethane adhesive. The procedure proposed here to measure the crack length via DIC shows great promise and can be automated readily in practice.

Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths in Anisotropic Microcracked Materials

Abstract Statistical volume elements (SVEs) are used to homogenize fracture strength of rock, based on the microcrack statistics of a real-world Yuen-Long marble sample. The small size of SVEs enables maintaining inhomogeneities in fracture properties with lower computational cost compared to methods that explicitly model microcracks at macroscale. Maintaining inhomogeneity is important to capture realistic fracture patterns in rock as a quasi-brittle material. Uniaxial tensile, uniaxial compressive, and shear strengths are derived for arbitrary angle for loading and orientation of a single crack by using the linear elastic fracture mechanics (LEFM) method and incorporating frictional effects. Mesoscopic fracture strength fields are generated for different strengths and angle of loading by traversing the spatial domain with circular SVEs. Increasing the SVE size smoothens the spatial inhomogeneity and angular anisotropy of homogenized strengths. Spatial and angular covariance functions of the random fields are obtained to demonstrate how fracture strength varies in space and by changing the angle of loading. Two isotropic and anisotropic rock domains are studied and shown to have very different single- and two-point statistics. Macroscopic fracture simulations by an asynchronous spacetime discontinuous Galerkin (aSDG) method demonstrate that most macroscopic cracks for the anisotropic domain are aligned with the weakest strength planes.

Mode II interlaminar fracture of hybrid woven carbon-Dyneema composites

Recently, there has been renewed interest in interwoven hybrid composites. Hybridization of different fiber types within composite laminates provides opportunities to extend the design space and optimize properties such as strength and toughness. In this paper, the Mode II fracture behavior of a hybrid carbon-Dyneema fiber-reinforced composite is studied experimentally. The usual linear elastic fracture mechanics (LEFM) methods for measurement of interlaminar toughness are not readily applicable to hybrid composites due to the presence of large fracture process zones and extensive fiber bridging. Continuously increasing R-curves are obtained from standard data reduction approaches, resulting in poor estimates of Mode II interlaminar toughness values. A more general J-integral-based method coupled with digital image correlation technique is proposed here to obtain more consistent and accurate results. Specimens with different intralaminar and interlaminar hybridization schemes are explored, and the delamination process as well as toughening mechanisms is examined through a fractographic analysis.

Effect of morphology alteration on mechanical properties and fracture toughness of polypropylene/polyamide 6/ethylene polypropylene diene monomer graft maleic anhydride (PP/PA6/EPDM-g-MA) reactive ternary blends

Morphology, mechanical properties and fracture behavior of polypropylene/polyamide 6/ethylene polypropylene diene monomer graft maleic anhydride (PP/PA6/EPDM-g-MA) ternary blends containing various amounts of the EPDM-g-MA rubbery phase (from 0 to 9 wt%), with special attention to the structure–property relationships through the core–shell morphology development, were studied. The fracture surface, deformation micro-mechanisms and mechanical properties of the blends were examined using field emission scanning electron microscopy technique, tensile and impact tests, respectively. The fracture properties were characterized in detail by the linear elastic fracture mechanics method. The fracture energy (GC), fracture toughness (KIC) and impact strength were improved monotonically up to some EPDM-g-MA content, above which the characteristics were appreciably enhanced. These results were attributed to an alteration of this morphology from dispersion of PA6/EPDM-g-MA core–shell particles at low EPDM-g-MA contents to the aggregated structure of core–shell particles at higher EPDM-g-MA contents. The micro-void formation via activation of internal cavitation or debonding of the rubbery phase was found to be responsible for the stress whitening phenomenon that occurred during the impact fracture process and, hence, increased impact toughness.

Fatigue Precracking Time Estimates for Three-Point Bending Specimens

Specimens containing sharp cracks are needed in certain types of mechanical tests, first and foremost for fracture toughness measurement of materials. Their use, however, is not just limited to this type of test. Another category of experiments deals with characterizing nonlinear vibrations of beams containing breathing cracks. To produce cracked beam specimens, fatigue cracks can be grown ahead of sharp notches under controlled loading. ASTM E399 and ASTM E1820 standards provide guidance on such procedures for preparation of fracture toughness test specimens. However, certain issues which might become important in testing of vibrations of cracked beams, such as the time required for specimen preparation is not addressed in these standards. In this article, both low cycle fatigue methods and linear elastic fracture mechanics methods are used to estimate the number of loading cycles required to have a crack of desired length at the notch tip. Calculation results are compared with experimental ones, and the effects of various factors influencing the required number of loading cycles for a certain crack size are discussed.

Fracture Analysis of a Three-Dimensional Functionally Graded Multilayered Beam

Delamination fracture behavior of the three-dimensional functionally graded multilayered crack lap shear (CLS) beam configuration was studied analytically in terms of the strain energy release rate with linear-elastic fracture mechanics methods. The CLS under consideration can consist of an arbitrary number of layers, each having different thickness and material properties. The material of each layer is functionally graded along its width, thickness, and length. A delamination crack is arbitrarily located along the beam height. The strain energy release rate was derived by analyzing its density in the beam cross section ahead and behind the crack front. It was additionally analyzed using the strain energy release rate was performed by using the beam strain energy for verification. The effect of the material gradient and crack location along the beam height on the delamination fracture behavior was evaluated.

Delamination in a Two-Dimensional Functionally Graded Beam

An analytical study of delamination in the crack lap shear beam is performed. It is assumed that the material is functionally graded along the width and height of the beam. Delamination is studied in terms of the total strain energy release rate by applying methods of linear-elastic fracture mechanics. An additional analysis of the total strain energy release rate is performed by considering the strain energies in the beam cross sections ahead of and behind the crack front for verification. The effects of the crack location and material gradient on delamination are evaluated.