Linear Elastic Fracture Mechanics Approach Research Articles

Determination of opening stresses for railway steel under low cycle fatigue using digital image correlation

Crack closure phenomenon is important to study as it provides an estimation to fatigue life of the components. It becomes even more complex under low cycle fatigue (LCF), since under LCF high amount of plasticity is induced within the material near notches or defects, as a result the assumptions used by linear elastic fracture mechanics (LEFM) approach become invalid. Evaluation of opening stresses for mechanical components undergoing LCF phenomenon requires a robust methodology to correctly predict the fatigue life. In this study, an experimental campaign was carried out for determination of opening stresses of railway steels (25CrMo4 and 30NiCrMoV12) subjected to LCF using digital image correlation (DIC) technique. The concept of crack opening displacement (COD) was used for the analysis. Two different methodologies were introduced to analyze experimental data for the identification of opening levels. Experimental results were then compared with crack closure prediction model, Newman model. Results from Newman model agreed well with the experimental analysis. Newman model provided very good prediction for strain ratio Rε = −1, however, for the materials undergoing strain ratio Rε = 0, stress ratio must be considered rather than strain ratio, because Newman model can’t predict stress relaxation behaviour.

Fracture mechanics testing and crack propagation modelling in polypropylene pipes

PurposeThe main aim of this study is to determine the fracture toughness and accordingly to predict the fracture initiation, crack propagation and mode of crack extension accurately in polypropylene subsea pipes subjected to internal pressure.Design/methodology/approachTensile test was performed following the ISO 527–1 standard. An elastic-plastic constitutive model was developed based on the tensile test results, and it is implemented in the FEA model to describe the constitutive behaviour of the polypropylene material. Three-point bend tests with linear-elastic fracture mechanics (LEFM) approach were conducted following ISO-13586 standard, from which the average fracture toughness of the polypropylene pipe material in crack-opening mode was found as KIc = 3.3 MPa√m. A numerical model of the experiments is developed based on the extended finite element method (XFEM), which showed markedly good agreement with the experimental results.FindingsThe validated XFEM modelling approach is utilised to illustrate its capabilities in predicting fracture initiation and crack propagation in a polypropylene subsea pipe subjected to an internal pressure containing a semi-elliptical surface crack, which agrees well with existing analytical solutions. The XFEM model is capable of predicting the crack initiation and propagation in the polypropylene pipe up to the event of leakage.Originality/valueThe methodology proposed herein can be utilised to assess the structural integrity and resistance to fracture of subsea plastic pipes subjected to operational loads (e.g. internal pressure).

Apparent fracture toughness for LEFM applications in hydraulic fracture modeling

Linear Elastic Fracture Mechanics (LEFM) is a widely applied theory to numerically simulate hydraulic fracture initiation and propagation in the subsurface. However, LEFM with the typical fracture toughness measured from unconfined laboratory tests does not apply to hydraulic fracturing applications under subsurface conditions because the fracture toughness is affected by the confining stress and fluid lag at the fracture tip. Thus, the apparent fracture toughness was proposed by Rubin (1993) to consider the contributions of fluid lag and confining stress.The main objective of this study is to validate the applicability of LEFM with the apparent fracture toughness in simulating hydraulic fracture under subsurface conditions. We utilized the finite element models to compare the near-tip stress state between the LEFM approach and the cohesive zone model (CZM), which considers the effect of confining stress and fluid lag. In addition, we compared the analytical solutions of fracture energy between LEFM and CZM. This study showed that the near-tip stress state of CZM outside the fluid lag and cohesive zone is comparable to the stress field predicted by LEFM with the apparent fracture toughness. However, LEFM with the fracture toughness measured from standard unconfined laboratory tests underestimates the near-tip stress state of fractures under confining stress. This study also revealed that the fracture energy of fluid-driven fractures calculated by CZM is identical to the fracture energy estimated from the approach of LEFM with the apparent fracture toughness. Thus, this study demonstrated that LEFM with the apparent fracture toughness is an appropriate and accurate method to simulate hydraulic fracture propagation in the subsurface.

Linear elastic analysis of the loading rate dependency of the fracture properties of structural adhesives in the mixed mode I+II plane

In this paper, the fracture properties of a structural adhesive are investigated via the Tapered Double Cantilever Beam (TDCB) and the Mixed Mode Bending (MMB) tests. The experiments were performed at low to fairly low loading rates. The results were analyzed using Linear Elastic Fracture Mechanics (LEFM). It is shown that the testing speed has considerable impact on the fracture behaviour when close to mode II. Nonetheless, TDCB and MMB Load-Unload tests revealed significant non-linearities. Arcan tests demonstrated the important sensibility of the adhesive material properties to the strain rate. Therefore, the relevance of the LEFM approach is also discussed.

Fracture Mechanism in Human Teeth

Materials’ cracking is a first step of the fracture. Enamel and dentin like other materials suffering from the cracks. During life or even through the denture treatments, the damage can be started. In this work, the crack path and fracture behavior of the teeth have been monitored. It was shown that the linear elastic fracture mechanics approach (LEFM) could evaluate the fracture toughness in teeth. The vertical crack is a traditional path of the fracture. The crack due to the cyclic loading like chewing will be propagated. The understanding of failure in teeth like another solid body, aims to decrease the failure risk. In addition, gives an insight for repairing treatments. Hence, early observations of the cracks will protect the teeth. Due to the brittleness of enamel and a little toughness of dentin, the dentin-enamel margins resist the crack propagation due to their fracture toughness and the cohesive properties. The crack path in teeth was simulated using the finite element software (FE).

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.

Lifetime Calculation of Soil-Loaded Non-Pressure Polymer Pipes

Outstanding durability of plastic pressure and non-pressure pipes can cause difficulties, when a reasonable lifetime estimation is needed. It is impossible to prove the lifetime by testing, but there is a method of calculation that can provide a certain idea about the expected lifetime. The lifetime estimation is based on the assumption that the failure occurs as a result of the slow crack growth mechanism and it is calculated using the linear elastic fracture mechanics approach. Numerical simulations of crack growth in the pipe are necessary for this calculation. These simulations must consider various effects that can play a role in the lifetime. This paper deals with the lifetime calculations of a pressure and a non-pressure corrugated pipe considering the soil loads acting on pipes when they are buried. In the simulation of the pressure pipe, a combination of loads is applied that consists of internal pressure, residual stress and the soil loads. The influence of the loads is discussed. The non-pressure corrugated pipe is loaded by the soil loads only.

Cohesive-zone effects in hydraulic fracture propagation

Hydraulic fracture presents an interesting case of crack elasticity and fracture propagation non-linearly coupled to fluid flow. Hydraulic fracture (HF) is often modeled using the Linear Elastic Fracture Mechanics (LEFM), which assumes that the damaged zone associated with the rock breakage near the advancing fracture front is small compared to the lengthscales of other physical processes acting during propagation. The latter include dissipation in viscous fluid flow in the fracture channel, of which the fluid lag - a region adjacent to the fracture tip filled with fracturing fluid volatiles and/or infiltrated formation pore fluid - is the extreme manifestation. In this study we address the validity of the LEFM approach to hydraulic fracturing by constructing the solution for the near tip region of a cohesive fracture driven by Newtonian fluid in an impermeable linear-elastic rock. We show that the near HF tip solution has an intricate structure supported by a number of nested lengthscales on which different dissipation processes are realized. This structure is bookended by the solid ‘c’ or fluid lag ‘o’ process zone immediately near the tip and by the viscosity ‘m’ asymptote away from the tip, while the LEFM ‘k’ asymptote may emerge at intermediate distances within the c/o to m transition. Realization of the k asymptote, and, therefore, the viability of the LEFM in HF, depends on two parameters: the cohesive-to-fluid-lag fracture energy ratio Gc/Go and the cohesive-to-in-situ stress ratio σc/σo. For representative values of the former, we show that the LEFM-behavior emerges only when the cohesive stress is large compared to the in situ confining. Since σc ∼ few MPa for most rocks, it follows that the LEFM may only be applicable to laboratory hydraulic fracture conducted under low confining stress, and, conversely, is not applicable to the field hydraulic fracturing characterized by larger values of σo. We further use an approximate “equation of motion” approach based on the continuation of the tip solution onto the entire fracture to solve for the propagation of a penny-shaped HF driven by a point source fluid injection and quantify the prominence of the non-LEFM effects.

FATIGUE LIFE ANALYSIS OF RAIL-WELDS USING LINEAR ELASTIC FRACTURE MECHANICS

The initiation and growth of fatigue cracking is mainly due to high stress concentration, heterogeneity and poor quality of weld. The detection and rectification of such weld defects are major concerns of rail network managers to reduce potential risk of rail breaks and derailments. To estimate the fatigue life of welded joints and to analyze the progress of fatigue cracks, a fracture mechanics-based analysis and fatigue models were developed using Finite Element Analysis. The initial flaw is obtained from a sample weld using ultrasonic flaw detecting machine test. Linear Elastic Fracture Mechanics (LEFM) approach based on the Paris law was applied to determine critical crack size and the number of cycles to failure using FRANC3D software. The inspection interval of rail welds before fracture (failure) was suggested based on reliability and life cycle analysis that correspond with minimum overall cost and frequency interval. It is recommended that fracture-based models in combination with reliability analyses can be a sustainable infrastructure decision-making algorithm.

Fracture analysis in plane structures with the two-scale G/XFEM method

Generalized or extended finite element method (G/XFEM) uses enrichment functions that holds a priori knowledge about the problem solution. These enrichment functions are mostly limited to two-dimensional problems. A well-established solution for problems without any specific types of analytically derived enrichment functions is to use numerically-build functions in which they are called global-local enrichment functions. These functions are extracted from the solution of boundary value problems defined around the region of interest discretized by a fine mesh. Such solution is used to enrich the global solution space through the partition of unity framework of the G/XFEM. Here it is presented a two-scale/global-local G/XFEM approach to model crack propagation in plane stress/strain and Reissner–Mindlin plate problems. Discontinuous functions along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly represent its geometries. Under the linear elastic fracture mechanics approach, the stress intensity factor (obtained from a domain-based interaction energy integral) can be used to either determine the crack propagation direction or propagation status, i.e., the crack can start to propagate or not. The proposed approach is presented in detail and validated by solving several linear elastic fracture mechanics problems for both plane stress/strain and Reissner–Mindlin plate cases to demonstrate its the robustness and accuracy.

Linear Elastic Fracture Mechanics Characterization of an Anisotropic Shale

The existence of bedding planes in natural shale formations makes the fracture characterization remarkably complicated. To achieve a further understanding of the anisotropic crack extension behaviors of shale using a linear elastic fracture mechanics approach, four groups of three-point bending tests on Longmaxi shale from southeast Chongqing were conducted in this study with different bedding plane inclination angles. The fracture propagation paths were observed using a scanning electron microscope. The results indicated that cracks initiated along the bedding plane when the bedding plane inclination angle (i.e., the angle between the loading direction and the normal direction of the bedding plane) was relatively large; in contrast, cracks penetrated into the matrix and induced higher fracture toughness in cases with lower bedding plane inclination angle. Brittle fractures occurred in the tested shale, and the fracture strength was strongly dependent on the bedding plane inclination angle. Meanwhile, the stress field around the crack tip was analyzed theoretically. The results indicated that the crack tip stress field of anisotropic shale is not only determined by the stress intensity factor but also related to the elastic constants and bedding plane inclination angle. Furthermore, a criterion for determining whether a crack extends along the bedding plane was developed by distinguishing the differences in the strengths of the shale bedding and the matrix.

Three-Dimensional Poroelastic Modeling of Multiple Hydraulic Fracture Propagation from Horizontal Wells

Numerical simulations of multistage hydraulic fracturing usually neglect poroelastic effects. However, in case of low permeability reservoirs, where hydraulic fracturing is usually carried-out using relatively low viscosity fluids and high injection rates, coupled poroelastic mechanisms need be included for better understanding of the fracturing process, which can involve rock failure and/or reactivation of natural fractures. In this paper, we present a fully coupled three-dimensional poroelastic analysis of multiple fracture propagation from horizontal wells. The numerical model uses the indirect boundary element method of displacement discontinuity for poroelastic response of the rock, the finite element method for fracture fluid flow, and the linear elastic fracture mechanics approach for fracture propagation. The model accounts for the mechanical interactions among multiple fractures, mixed-mode propagation, fluid diffusion into the reservoir matrix, and the effects of fluid diffusion on the rock mechanical response. The model is verified with analytical solutions, and numerical examples of simultaneous and sequential fracturing of single and multiple horizontal wells in the Niobrara Chalk formation are presented. The results show the created fracture network geometries are strongly influenced by the mechanical interactions among the fractures. It is also demonstrated that the poroelastic effect increases the net fracture pressure and causes a reduction in fracture volume. The poroelastic model illustrates the transient character of stress shadow, and is particularly useful for re-fracturing analysis since it readily calculates the stress variations due to reservoir depletion.

Calculation of Mechanical Fracture Parameters of Chevron Notched Core Based Concrete Specimen: Software <i>CheF</i>

The structural concrete can be also characterized via parameters obtained by evaluation of fracture tests. Therefore, this paper presents software CheF developed in Java programming language, designed for evaluation of three-point bending fracture tests of core based concrete specimens with chevron type notch. The records of fracture tests in form load vs. displacement and load vs. crack mouth opening displacement diagrams are analysed by software CheF to obtain values of selected mechanical fracture parameters: modulus of elasticity E, fracture toughness KIc, and fracture energy GF, determined based on the linear elastic fracture mechanics approach and work-of-fracture method.

Computational Investigation on the Crack in Kevlar Based Composite Materials at Cryogenic Temperatures to be used in Superconducting Motors

The compatibility of Kevlar based composites at cryogenic temperatures made it possible to be used in various superconducting applications including superconducting motors. The torque tube used in the superconducting motors is made up of Kevlar due its capability to hinder the heat transfer between driving to the driven end of the motor. However, at cryogenic temperatures brittle fracture is highly pronounced due to contraction of the Kevlar. Hence, in the present work, the fracture behaviour of Kevlar-49/Epoxy with 60% fibre volume fraction at cryogenic temperatures is investigated using a commercial code namely ABAQUS. This code uses extended finite element method (XFEM) of formulation in solving the stiffness matrix with realistic boundary conditions. A uniaxial tensile load of 700MPa is considered with one end as fixed. Further, Kevlar-49/Epoxy is considered to be isotropic with the magnitude of Young’s modulus to be 99GPa and the poison’s ratio to be 0.34 at 75K. The consideration of isotropic properties would be valid as the XFEM assumes linear elastic fracture mechanics (LEFM) approach. Further, the accuracy of XFEM is superior over contour integral method due to the enrichment of elements in the entire computational domain including the crack tip. A Kevlar specimen of 50X30 mm is modeled and meshed (quadrilateral) in ABAQUS. The mesh size is considered to be 2 mm to capture the results at maximum number of nodes. Three cases of edge crack, one being towards the loading end, the second being at the middle and the last being towards the fixed end of the specimen are considered. It is found that significant changes in Von Mises stress, strain and strain energy density exist according to the initiation of crack location. Further, the computational results are validated with the obtained analytical results.

Fracture analysis of multi-osteon cortical bone using XFEM

Fracture analysis of a cortical bone sample from a tibia of a 70 years-old human male donor is conducted computationally using an extended finite element method. The cortical bone microstructure is represented by several osteons arranged based on bone microscopy image. The accuracy of results is examined by comparing a linear elastic fracture mechanics approach with a cohesive segment approach and varying the finite element model mesh density, element type, damage evolution, and boundary conditions. Microstructural features of cortical bone are assumed to be linear elastic and isotropic. We find that the accuracy of results is influenced by the finite element model mesh density, simulation increment size, element type, and the fracture approach type. Using a relatively fine mesh or small simulation increment size gives inaccurate results compared to using an optimized mesh density and simulation increment size. Also, mechanical properties of cortical bone phases influence the crack propagation path and speed.

Effects of recycled HDPE and nanoclay on stress cracking of HDPE by correlating Jc with slow crack growth

The effects of recycled high density polyethylene (HDPE) and nanoclay on the stress crack resistance (SCR) of pristine HDPE were evaluated using the Notched Constant Ligament Stress (NCLS) test. The test data were analyzed by both linear elastic fracture mechanics (LEFM) and elastic plastic fracture mechanics (EPFM). The LEFM approach uses the stress intensity factor K to define the two failure mechanisms: creep and slow crack growth (SCG). In contrast, using the J‐integral in EPFM, which emphasizes the nonlinear elastic‐plastic strain field at the crack‐tip, revealed a short‐term failure stage prior to the creep failure. In this article, a power law correlation between the fracture toughness Jc and SCG was found under a plane‐strain condition. Increasing recycled HDPE content lowered the SCG resistance of pristine HDPE by decreasing Jc. Adding nanoclay up to 6 wt% also decreased Jc while simultaneously, lowering the stress relaxation of nanocomposites, leading to longer SCG failure times at low J values. POLYM. ENG. SCI., 58:1471–1478, 2018. © Published [2017]. This article is a U.S. Government work and is in the public domain in the USA.

Evaluation of fatigue crack propagation behaviour in Ti-6Al-4V manufactured by selective laser melting

Total fatigue life performance of high strength titanium alloy Ti-6Al-4V manufactured by Additive Manufacturing (AM) based methods such as Selective Laser Melting (SLM) is of significant interest and has gained much attention recently. Researchers often compare the total fatigue life of materials manufactured from SLM with conventional manufacture, and often the SLM lives are reduced because cracks initiate from “defects” such as porosity or Lack of Fusion (LOF). But for repair and alternative manufacture of complex and critical aerospace structures for example, the crack growth/propagation phase of the fatigue process is also very important and it has not been studied as extensively. The aim of the work presented here was to evaluate and better understand crack propagation under constant amplitude loading in Ti-6Al-4V samples manufactured using SLM with a variety of layer thicknesses and build directions (vertical or horizontal). The “as-manufactured” condition was studied, with no post heat treatment. Cracks typically initiated at LOF features which had a negative impact on the total fatigue life. The focus here was on the crack growth phase. Modelling was performed with a conventional Linear Elastic Fracture Mechanics approach using literature data obtained from testing on Compact Tension (C(T)) specimens which were also in the as-manufactured condition with a variety of build directions. The modelling provided a very useful correlation of the data and provided a way of assessing the LOF features in terms of an equivalent initial crack. The crack growth properties of the SLM cases were also compared against literature data for conventionally manufactured material. The work will lead to a better understanding of fatigue crack growth characteristics for components manufactured by AM methods such as SLM. That understanding is an essential requirement for full certification and acceptance into service for critical applications such as aerospace structures.

Mixed-mode fracture toughness evaluation of a copper single crystal using atomistic simulations

The fracture toughness and kinking of a cracked Cu single crystal under mixed-mode loads are investigated via atomistic simulations. The embedded-atom-method potential is adopted for modeling the Cu single crystal. The displacement conditions imposed on the simulation cells are the near-tip K-field displacements of a crack in a cubic symmetry material obtained from linear elastic fracture mechanics (LEFM). For comparison, an asymptotic problem of a kinked crack in a Cu single crystal is solved by finite element analysis under the LEFM framework. The mixed-mode fracture toughness and preferred orientation of the crack extension for the LEFM approach are evaluated on the basis of a proposed mixed-mode fracture criterion. The crack extension is determined by maximizing the crack extension force, which defined as the ratio of the normalized energy release rate to the normalized surface energy. The discrepancies between the results obtained from the atomistic simulations and the LEFM approach are discussed. The transition of fracture patterns from brittle fracture to fracture after dislocation emission with an increase in mode mixity is the primary reason for such discrepancies.

Adaptive Gaussian process regression as an alternative to FEM for prediction of stress intensity factor to assess fatigue degradation in offshore pipeline

The linear elastic fracture mechanics (LEFM) based remnant fatigue life (RFL) assessment of offshore pipeline is used to determine the inspection interval frequency of the aforementioned asset. One of the vital factors of the LEFM approach that determines the accuracy of the RFL estimate (and in turn of the inspection interval frequency) is the Stress Intensity Factor (SIF), which must be evaluated as accurately as possible. For simple crack geometries numerous closed-form equations available in various handbooks and industrial standards provide accurate SIF results. However, it is a common industry practice to utilize finite element method (FEM) for evaluating the SIF for the intricate crack geometries and the complex loading conditions. Although, FEM is known for its accurate SIF calculation, but due to its high computational expense and time-consumption, cycle-by-cycle SIF evaluation (required for the LEFM based RFL assessment) makes the aforementioned method quite laborious. Furthermore, using FEM to evaluate SIF for thousands of pipeline location (undergoing fatigue degradation) on an offshore platform seems to be impractical. Thus, in this manuscript authors have proposed a computationally inexpensive adaptive Gaussian process regression model (AGPRM) which may be utilized as an alternative to FEM for prediction of SIF to assess fatigue degradation in offshore pipeline. The training and testing data for AGPRM consists of 105 and 50 data points (load (L), crack depth (a), half-crack length (c) and SIF values), respectively. Latin Hypercube Sampling (LHS) is used to generate (L, a and c) values while SIF values are evaluated using FEM by carefully accounting for the discretization error emanating due to the finite mesh size in the FEM simulation. After the GPRM has been adaptively trained, it is used to predict the response of the 50 data points. On comparing the values of the SIF (obtained by AGPRM) with the SIF values obtained from FEM, the average residual percentage between the two is found to be 1.76%, thus indicating a good agreement between the AGPRM and FEM model. Furthermore, the time required to predict the SIF of 50 test points is reduced from 50 min (for FEM) to 12 s with the help of the proposed AGPRM, thus making RFL assessment less laborious and time consuming.

Interfacial crack arrest in sandwich beams subjected to fatigue loading using a novel crack arresting device – Numerical modelling

A novel crack arresting device is implemented in foam-cored composite sandwich beams and tested using the Sandwich Tear Test (STT) configuration. A finite element model of the setup is developed, and the predictions are correlated with observations and results from a recently conducted experimental fatigue test study. Based on a linear elastic fracture mechanics approach, the developed FE model is utilised to simulate crack propagation and arrest in foam-cored sandwich beam specimens subjected to fatigue loading conditions. The effect of the crack arresters on the fatigue life is analysed, and the predictive results are subsequently compared with the observations from the previously conducted fatigue tests. The FE model predicts the energy release rate and the mode mixity based on the derived crack surface displacements, utilising algorithms for the prediction of accelerated fatigue crack growth as well as the strain field evolution in the vicinity of the crack tip on the surface of the sandwich specimens. It is further shown that the developed finite element analysis methodology can be used to gain a deeper insight onto the physics and behavioural characteristics of the novel peel stopper concept, as well as a design tool that can be used for the implementation of crack arresting devises in engineering applications of sandwich components and structures.