Classical Fracture Mechanics Research Articles

On the computation of energy release rates by a peridynamic virtual crack extension method

A new peridynamic virtual crack extension (PVCE) method is developed to predict the energy release rate G in fracture mechanics, and the directionally and virtually broken bonds are uniquely applied to constitute the virtual crack for crack extension in the numerical implementation. An algorithm of the PVCE method considering serial crack extensions and quasi-static analysis is proposed, and the modified PVCE method is further introduced to reduce the computational error. As validation and application examples, the developed PVCE method is applied to compute the energy release rates of single edge-notched tension (SENT), double cantilever beam (DCB), and end loaded split (ELS) tests, and the results are compared with the existing analytical solutions and numerical finite element analysis. The new PVCE method builds a natural “bridge” for peridynamic fracture analysis between the peridynamics and classical fracture mechanics, and it is capable of accurately and effectively computing the energy release rates for both mode I and mode II fracture cases as well as predicting the critical load and displacement in fracture analysis.

Finite element modeling of single-lap joint between GdBa2Cu3O7-x-coated conductors using cohesive elements

Both the initiation of cracking and delamination growth have been observed in the joints between the GdBCO-coated conductors, which causes the degradation of electrical property irreversibly. In this paper, firstly, the tension (lap-shear) test of the single-lap joint is simulated to verify the selected material properties and the numerical model. Then, the delamination behavior of the single-lap joint between the GdBCO-coated conductors is investigated based on the cohesive model. The multiple layers of zero thickness cohesive elements are implemented within the tapes and interfaces between the tape and solder. Different boundary conditions are also considered to determine the corresponding delamination position and value of debonding load. With the classical beam theory and linear elastic fracture mechanics, the approximate analytical solution is given to throw light on the behavior of the joint. The numerical results show that the interface parameters such as cohesive strength can affect the positions of crack formation and stable extension of crack. In addition, the debonding load is influenced by the overlap length of the joint and constraint condition.

The Effects of Fatigue Cracks on Fastener Loads during Cyclic Loading and on the Stresses Used for Crack Growth Analysis in Classical Linear Elastic Fracture Mechanics Approaches

High strength threaded fasteners are widely used in the aircraft industry, and service experience shows that for structures where shear loading of the joints is significant, like skin splices, fuselage joints or spar caps-web attachments, more cracks are initiated and grow from the edges of the fastener holes than from features like fillets radii and corners or from large access holes. The main causes of this cracking are the stress concentrations introduced by the fastener holes and by the threaded fasteners themselves, with the most common damage site being at the edge of the fastener holes. Intuitively, it is easy to visualize that after the crack initiation, during the growth stages, some of the load transferred initially by the fastener at the cracked hole will decrease, and it will be shed to the adjacent fasteners that will carry higher loads than in uncracked condition. Using currently available computer software, the method presented in this paper provides a relatively quick and quantitatively defined solution to account for the effects of crack length on the fastener loads transfer, and on the far field and bypass loads at each fastener adjacent to the crack. At each location, these variations are determined from the 3-dimensional distribution of stresses in the joint, and accounting for secondary bending effects and fastener tilt. Two cases of a typical skins lap splice with eight fasteners in a two rows configuration loaded in tension are presented and discussed, one representative for wing or fuselage skins configurations, and the second case representative for cost effective laboratory testing. Each case presents five cracking scenarios, with the cracks growing from approx. 0.03 inch to either the free edge, next hole or both simultaneously.

An overview of application of micromechanical models in ductile fracture analysis of welded joints

Fracture of welded joints has been an important research and industrial topic for a long time, having in mind the key role of welded joints in ensuring the safe operation and integrity of welded structures. This work contains an overview of application of micromechanical models to ductile fracture of welded joints. The main benefit of these models, in comparison with the classical fracture mechanics approach, is consideration of the local quantities (stress and strain) in prediction of damage development. The damage is quantified through the value of the damage parameter, which is typically related to the void nucleation, growth and coalescence for ductile fracture of metallic materials, i.e. the description of the material can be related to the actual material behaviour during fracture. Most of the presented studies, including those published by the present authors, are performed on steel as the base material, and the rest deal with aluminium alloys.

Anti-plane fracture mechanics analysis of a piezoelectric material layer with strain and electric field gradient effects

The problem of an anti-plane crack in a polarized ceramic layer with both the strain and electric field gradient effects is studied. This model includes two characteristic length parameters l and m which describes the strain gradient and the electric field gradient effects, respectively. The analysis demonstrates that the near-tip asymptotic stress and electric displacement are governed by r−3/2 singularities. Due to stain gradient effect, stresses ahead of the crack tip are significantly higher than those in the classical linear piezoelectricity fracture mechanics. When the strain and electric field gradient parameters decrease to sufficiently small, the solutions reduce to the conventional linear elastic fracture mechanics results. The new contribution of this research is that it includes the effects of the strain gradient and electric field gradient simultaneously for a finite crack in a finite piezoelectric layer.

Understanding the Fracture Behaviors of Metallic Glasses—An Overview

Fracture properties are crucial for the applications of structural materials. The fracture behaviors of crystalline alloys have been systematically investigated and well understood. The fracture behaviors of metallic glasses (MGs) are quite different from that of conventional crystalline alloys and have drawn wide interests. Although a few reviews on the fracture and mechanical properties of metallic glasses have been published, an overview on how and why metallic glasses fall out of the scope of the conventional fracture mechanics is still needed. This article attempts to clarify the up-to-date understanding of the question. We review the fracture behaviors of metallic glasses with the related scientific issues including the mode I fracture, brittle fracture, super ductile fracture, impact toughness, and fatigue fracture behaviors. The complex fracture mechanism of MGs is further discussed from the perspectives of discontinuous stress/strain field, plastic zone, and fracture resistance, which deviate from the classic fracture mechanics in polycrystalline alloys. Due to the special deformation mechanism, metallic glasses show a high variability in fracture toughness and other mechanical properties. The outlook presented by this review could help the further studies of metallic glasses. The review also identifies some key questions to be answered.

Thermodynamic entropy to detect fatigue crack initiation using digital image correlation, and effect of overload spectrums

Current approaches to fatigue life prediction are mostly based on classical fracture mechanics and it is difficult to predict lifetime under different loading conditions, particularly under overload spectrums. A thermodynamic entropy-based approach is less sensitive to variability in loading conditions and provides a dependable measure of damage. Volumetric thermodynamic entropy is utilized in this study to measure damage. Digital Image Correlation-DIC is used to measure plastic deformation in close vicinity of the notch in AA7075-T6 specimens. The plastic deformations are converted to a corresponding thermodynamic entropy, using a modified Clausius-Duhem inequality. A comparison of thermodynamic entropy generation using global measurement consisting of load frame data and Linear Variable Differential Transformer-LVDT extensometer, and local measurement using DIC data is done. The entropic-endurance level for fatigue crack initiation regardless of loading spectrums is shown to scatter within a short interval and is represented by a Weibull distribution.

Stress distribution in front of the crack – analytical solutions vs. numerical. Can the differences be minimized?

It is shown that it is possible to obtain such parameters as α and Q, which, when used in the analytical formulae proposed by O’Dowd and Shih, can lead to stress distributions similar to those obtained numerically. The numerical solution obtained after calibration of the stress-strain uniaxial curve and assuming large strains is expected to be close to the stress distribution. Thus, the analytical solution, after correction is also close to the “real” stress distribution. These new values of α and Q can now be used in fracture criteria proposed within the scope of classical nonlinear fracture mechanics.

Stress Distribution in Front of the Crack - Analytical Solutions vs. Numerical. Can the Differences be Minimized?

It is shown that it is possible to obtain such material parameters as α and Q, which, when used in the analytical formulae proposed by Hutchinson, Rice and Rosengren and O’Dowd and Shih, can lead to stress distributions similar to those obtained numerically (except for the region at the immediate crack front). The numerical solution obtained after calibration of the stress-strain uniaxial curve and assuming large strains is expected to be close to the “"real” stress distribution. Thus, the analytical solution is also close to the “real” stress distribution. These new values of α and Q can now be used in fracture criteria proposed within the scope of classical nonlinear fracture mechanics.

Ab initio aided strain gradient elasticity theory in prediction of nanocomponent fracture

The aim of the paper is to address fracture problems in nanoscale-sized cracked components using a simplified form of the strain gradient elasticity theory aided by ab initio calculations. Quantification of the material length scale parameter l1 of the simplified form of the strain gradient elasticity theory plays a key role in the analysis. The parameter l1 is identified for silicon and tungsten single crystals using first principles calculations. Specifically, the parameter l1 is extracted from phonon-dispersions generated by ab-initio calculations and, for comparison, by adjusting the analytical strain gradient elasticity theory solution for the displacement field near the screw dislocation with the ab-initio calculations of this field. The obtained results are further used in the strain gradient elasticity modeling of crack stability in nano-panels made of silicon and tungsten single crystals, where due to size effects and nonlocal material point interactions the classical linear fracture mechanics breaks down. The cusp-like crack tip opening profiles determined by the gradient elasticity theory and a hybrid atomistic approach at the moment of nano-panels fracture revealed a very good mutual agreement.

The ab-initio aided strain gradient elasticity theory

When the width of cracked nanocomponents made of brittle or quasi-brittle materials is less than approximately , the size of the - dominance zone becomes smaller than and comparable to the fracture process zone ( ). The fracture process starts to be dominated by far-stress field terms and the critical stress intensity factor can no more represent the total fracture driving force. This means a breakdown of a classical linear elastic fracture mechanics suffering from the undesirable crack-tip stress singularity. The contribution presents a new concept expected to properly predict the critical crack driving force for nano-components: The ab-initio aided strain gradient elasticity theory (AI-SGET). In contrast to the Barenblatt cohesive model, the strain gradient elasticity theory does not require to prescribe a suitable field of cohesive tractions along the crack faces in order to eliminate the stress singularity and to exhibit cusp-like profiles of crack flanks close to the crack front in accordance with atomistic models. The only unknown and necessary quantity is the material length scale parameter which can be, e.g., determined by best strain gradient elasticity fits of ab-initio computed phonon-dispersions and near-dislocation displacement fields. Atomistic approaches can also be employed to determine fracture mechanical parameters (crack driving force, crack tip opening displacement) related to the moment of crack instability in a given material. Such AI-SGET codes can then be utilized to a successful prediction of fracture of cracked nanocomponents made of brittle or quasi-brittle materials.

Application of new constraint based Master Curve in fracture assessment of pressure vessels

This paper represents the ability of the recently developed methodology for evaluating fracture probability of the ferritic steel components based on the Master Curve methodology. Due to crack-tip constraint, a cracked component may experience a significant change in its effective fracture toughness under a given load and temperature, whereas the Standard Master Curve (SMC) method cannot take into account this change. In this study the conservatisms associated with SMC method for low constraint geometries is investigated for a pressurized cylindrical vessel containing an internal semi-elliptical axial crack. A modification of SMC is developed based on the Q parameter as the crack-tip constraint. The usability of the Modified Master Curve (MMC) approach for structure integrity assessment of the pressure vessel is demonstrated. Three different assessment methodologies including, classical fracture mechanics, SMC, and MMC are compared for failure assessment of a cracked pressure vessel in ductile-to-brittle transition (DBT) region. It is shown that the developed MMC approach has appropriate capability to reduce the overly conservatism in failure assessment results obtained from the other two methods.

Virtual estimation of the Griffith’s modulus and cohesive strength of ultra-high performance concrete

This investigation presents a computational methodology to estimate the unit fracture energy (Griffith’s modulus) and the cohesive strength of ultra-high performance concrete (UHPC). The hydration of plain UHPC mixtures is simulated using the National Institute of Standards and Technology (NIST) Virtual Cement and Concrete Testing Laboratory (VCCTL) hydration simulator. The Young’s modulus of elasticity of the hardened concrete is obtained via finite-element analysis of a sample cube of its micro-structure. Applying the Extended Finite Element modeling capabilities of ABAQUS to previously grooved simple structural elements under gradually-increasing load, the results of computational simulations of the start of crack growth are linked to the corresponding predictions by regressions on experimental observations in classical linear elastic fracture mechanics physical tests. A procedure is developed to estimate both the Griffith’s modulus and the cohesive strength of the UHPC, which are difficult to assess experimentally. As an application, the effect on the horizontal thrust at the abutments of a two-hinged symmetric arch with a crown crack and uniformly loaded is analyzed using the data provided by the pure-bending test on a pre-grooved simply supported beam.

Zero stress aging in notched multi‐component glass fibers

AbstractDegradation of glass under zero applied load in the presence of humidity at ambient temperature is of great interest to the container and fiber glass industries. The phenomenon is well documented for fused silica used in optical fibers, but has not been studied in detail for multi‐component glasses. In this work notches of varying length (500‐1500 nm) were placed with a focused ion beam into two types of multi‐component glass fibers, E‐glass (48 μm diameter) and soda‐lime‐silicate (35 μm diameter). Notched specimens were exposed to dry and humid conditions for up to 32 days. Transmission electron microscopy revealed the presence of extensive reaction products within the root of the notch, even after only 1 day of aging in the nominally dry environment for the soda‐lime‐silicate glass. Surprisingly, the extensive reactions have no measurable effect on the fiber strength. The uniaxial tensile strength of the notched glass fibers, measured with the fracture surface mirror radius method, does not follow a classic fracture mechanics prediction, implying that the notches are not classic Griffith flaws. Fracture mechanics is applied to show that sharpness at the notch base may be important, especially when subcritical crack growth is present during the strength measurement.

Central crack tearing test and fracture parameter determination of PTFE coated fabric

Abstract Catastrophic failure caused by crack propagation is the most common failure mode of tensile fabric structure, the tearing resistance of the coated fabric is the key issue of structural design. This study concerns the residual strength and fracture resistance of PTFE coated fabric. Central crack tearing (CCT) tests are conducted, experimental results shown that the existence of initial crack significantly reduces the residual strength. Furthermore, fracture parameters which can be treated as material constants are obtained to estimate the tearing resistance. The available theoretical solutions, based on the classical linear elastic fracture mechanics (LEFM) theory, are adopted to calculate the fracture parameters. Results indicated that these theoretical solutions cannot estimate the fracture parameters properly due to the nonlinear stiffness of the coated fabric. Therefore, the numerical method virtual crack closure technique (VCCT) is introduced to the fracture parameters determination of PTFE coated fabric. Combined with the nonlinear material constitutive model, critical energy release rate GIC obtained from VCCT effectively reducing its dependence on crack length and thus can be treated as material tearing resistance. Finally, the influence of boundary condition and shear modulus are discussed. Results shown that uniform displacement boundary condition should be used in VCCT. When the shear modulus decreases, the GIC increases gradually and the dependence on the crack length is reduced due to the decrease of stress concentration zone.

Nonclassical Problems of Fracture/Failure Mechanics: on the Occasion of the 50th Anniversary of the Research (Review)

The main results of research on some nonclassical problems of fracture/failure mechanics are analyzed. These results have been obtained by the author and his followers at the Department of Dynamics and Stability of Continua of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review: – first problem is fracture of composites compressed along the reinforcement; – second problem is short-fiber model in stability and fracture of composites under compression; – third problem is end-crush fracture of composites under compression along the reinforcement; – fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks; – fifth problem is shredding fracture of composites stretched or compressed along the reinforcement; – sixth problem is fracture of materials under compression along parallel cracks; – seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces); – eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling. About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review. This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials; it is published in Prikladnaya Mekhanika (55, No. 3, 2019). The third part is Other Nonclassical Problems of Fracture/Failure Mechanics; it is published in Prikladnaya Mekhanika (55, No. 4, 2019).

Theoretical Investigation on Failure Strength and Fracture Toughness of Precracked Single-Layer Graphene Sheets

Young’s modulus, failure strength, and failure strain of precracked graphene are investigated via finite element method based on molecular structure mechanics in this research. The influence of distribution, length, and orientation of precrack and graphene sizes on these mechanical properties is analyzed. The ratio of precrack length and graphene width is defined as P value, and its particular value Pc can be found, at which the variation trends of Young’s modulus, failure strength, and strain have changes with increasing P value. In addition, the fracture toughness of precracked graphene is investigated, and the stress intensity factor (SIF) is calculated according to the Griffith criterion in classical fracture mechanics. The numerical values of the SIF are about 3.20-3.37 MPa√m, which are compared with the experimental results, and the simulations verify the applicability of the classical fracture mechanics to graphene.

Numerical Investigation of the Fracture Properties of Pre-Cracked Monocrystalline/Polycrystalline Graphene Sheets.

The fracture properties of pre-cracked monocrystalline/polycrystalline graphene were investigated via a finite element method based on molecular structure mechanics, and the mode I critical stress intensity factor (SIF) was calculated by the Griffith criterion in classical fracture mechanics. For monocrystalline graphene, the size effects of mode I fracture toughness and the influence of crack width on the mode I fracture toughness were investigated. Moreover, it was found that the ratio of crack length to graphene width has a significant influence on the mode I fracture toughness. For polycrystalline graphene, the strain energy per unit area at different positions was calculated, and the initial fracture site (near grain boundary) was deduced from the variation tendency of the strain energy per unit area. In addition, the effects of misorientation angle of the grain boundary (GB) and the distance between the crack tip and GB on mode I fracture toughness were also analyzed. It was found that the mode I fracture toughness increases with increasing misorientation angle. As the distance between the crack tip and GB increases, the mode I fracture toughness first decreases and then tends to stabilize.

Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures

While hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as current commercial software, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000×. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. However, their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nanocracking or microcracking damage. It is numerically demonstrated that seepage forces and a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on a recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings [Rahimi-Aghdam S, et al. (2018) arXiv:1212.11023].

A computational study of the mixed-mode crack behavior by molecular dynamics method and the multi-parameter crack field description of classical fracture mechanics

The overarching objective of the paper is to analysis the mixed-mode crack propagation direction angles by molecular dynamics method and to investigate the validity of continuum-based linear elastic fracture mechanics crack growth criteria. For this purpose, an embedded atom potential (EAM) available in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics (MD) software is utilized to accurately pinpoint mixed-mode crack growth. The study is focused on the application of the different approaches for the determination of the initial crack propagation angle. Copper and aluminum plates with the central crack under complex mechanical stresses (Mode I and Mode II loading) are studied by extensive MD simulations. Williams’ expansion for the crack tip fields containing the higher-order terms is used. The crack propagation direction angles for combinations of Mode I and Mode II loadings are obtained by 1) the multi-parameter fracture mechanics approach based on three fracture mechanics criteria: maximum tangential stress (MTS), maximum tangential strain and strain energy density (SED); 2) atomistic modeling for the mixed-mode loading of the plane medium with the central crack. The temperature effects during fracture processes in MD simulations are considered and the temperature field distributions for mixed-mode crack propagation are obtained.