Application Of Fracture Mechanics Research Articles

Experimental investigation of fracture process zone of rock in dynamic mode I fracturing and its effect on dynamic crack initiation toughness

Fracture process zone (FPZ) is critical to the applicability of linear fracture mechanics (LEFM) in rock fracturing, but little attention has been given to quantify the FPZ under dynamic loading condition in previous studies. This study presents the experimental results of notched semi-circular bending (NSCB) tests undertaken by split Hopkinson pressure bar (SHPB) to investigate the FPZ evolution for red sandstone under dynamic mode I fracturing and its effect on dynamic crack initiation toughness. A hybrid displacement–strain calibration method was proposed to characterize the FPZ with high-speed digital image correlation (DIC) technique. Results show that the FPZ initiation in dynamic fracturing is much earlier than that in quasi-static cases, and the FPZ length fully develops when crack initiation taking place at the pre-peak stage. The FPZ in dynamic fracturing is of a semi-elliptical shape with a width independent from the loading rate. The opening displacement exhibits a nonlinear decreasing trend along the FPZ boundary. LEFM theory underestimates the inherent dynamic crack initiation toughness, and the corrected dynamic crack initiation toughness was approximately 1.6 ∼ 2.1 times the uncorrected one within the loading rate ranging from 8.5 ∼ 78.2 GPa•m1/2/s in present study. The FPZ length in dynamic mode I fracturing lies in between the values predicted by Schmidt model and Irwin model, which indicates a non-linear cohesive stress with higher gradient near the FPZ tip is distributed along the FPZ.

A computational investigation of applicability of nonlinear fracture mechanics in nano-scale fracture of graphene

One of the main concerns for large-scale applications of graphene is unwanted fracture due to its low fracture toughness, close to that of an ideally brittle solid. However, graphene fracture properties and criteria have not been fully understood yet and the related understanding at the continuum-mechanics level is mostly limited to the linear elastic fracture mechanics (LEFM) investigations. In this paper, the applicability of nonlinear fracture mechanics (NLFM) to describe the fracture behavior of graphene is investigated through modeling the graphene sheets, including a center crack along the armchair and zigzag directions under mode I and mode II loading. A hyperelastic high-order continuum description is developed to be used in the nonlinear finite element simulations at the continuum level, by expanding the elastic strain energy in terms of the Lagrangian strains up to the seventh-order terms. The proposed continuum model is parameterized using the molecular dynamics (MD) simulation results to accurately reproduce the nonlinear mechanical behavior of graphene in uniaxial strain, equi-biaxial strain, and simple shear deformations. Finally, the applicability of NLFM, compared to LEFM, is investigated for graphene fracture through the continuum mechanics and MD fracture simulations. © 2001 Elsevier Science. All rights reserved

Retraction: Fracture investigation of U‐notch made of tungsten–copper functionally graded materials by means of strain energy density, H. Mohammadi, H. Salavati, Y. Alizadeh, A. Abdullah, F. Berto, Fatigue and Fracture of Engineering Materials and Structures, Volume 40, issue 12, pp. 1984–1993

The above article, published online on 12 April 2017 in Wiley Online Library (wileyonlinelibrary.com) has been retracted by agreement between the authors, the journal and John Wiley and Sons, Ltd. The retraction has been agreed due to considerable overlap with a previously published article (1).(1) Mohammadi H, Salavati H, Alizadeh Y, Berto F. (2017) Prevalent mode II fracture assessment of inclined U‐notched specimens made of tungsten‐copper functionally graded material. Theoretical and Applied Fracture Mechanics, 89, 90–99.REFERENCEMohammadi H, Salavati H, Alizadeh Y, Abdullah A, Berto F. Fracture investigation of U‐notch made of tungsten–copper functionally graded materials by means of strain energy density. Fatigue Fract Engng Mater Struct. 2017;40(12):1984‐1993. doi:10. 1111/ffe.12616

Effect of edge cracks on critical current degradation in REBCO tapes under tensile stress

The slitting process for manufacturing REBa2Cu3O7-δ (REBCO, RE = Rare earth) tapes of required width significantly improves the production efficiency and reduces production costs. However, edge cracks induced by the slitting process of wide REBCO tapes may cause premature degradation under high tensile stress in high-field magnets. Therefore, it is necessary to evaluate the effect of edge cracks of REBCO tapes on the critical current (Ic) degradation. Firstly, Ic degradation under artificial cracks was measured to validate the applicability of linear elastic fracture mechanics for the REBCO layer. The maximum circumferential stress criterion was used to derive the mixed-mode stress intensity factor of multiple oblique edge cracks. A semi-analytical model considering edge crack properties such as angle β, spacing d, and length a, was built to evaluate the critical load and critical crack. We found that when the stress intensity factor at the crack tip is below KIC=2.3 MPam, edge cracks did not propagate. We examined commercial REBCO tapes manufactured by two different processes, concluding that edge cracks in these tapes will not cause premature degradation.

Hydrogen-assisted cracking (HAC) of high-strength steels as a function of the hydrogen pre-charging time

This work demonstrates that by performing hydrogen-assisted cracking (HAC) as a function of hydrogen pre-charging time, highly symmetric circumferential cracks can be generated in circumferentially notched or grooved round bars made of high-strength steels, which can be used to study HAC in terms of fracture mechanics. Using the simple-to-perform method, control over hydrogen-assisted crack initiation is achieved by applying low hydrogen pre-charging times and by determining a threshold minimum preload to failure LHAC. The uniaxial tensile testing at LHAC under constant displacement results in a characteristic load-time-curve as well as a high-symmetry circumferential crack for each material investigated in this study. Finally, the minimum preload to failure, the time to failure and the critical crack length are each exhibited as a function of hydrogen pre-charging time and an approach to the application of fracture mechanics with the aim of determining the threshold stress intensity KIHAC is discussed.

Estimating the reliability of forestry machine elements with possibility theory application

The working conditions of forestry machines differ from those of agricultural machines. The presence of obstacles during the clearing of forest areas increases loading of machine components and assemblies and, consequently, leads to their failures. This paper deals with an improvement of probabilistic methods of forestry machine design by applying fracture mechanics and possibility theory. The main fracture mechanics expressions linking stress intensity factor with crack-like defect length are presented in the introduction. Fracture toughness and crack-like defect length are viewed as Gaussian random values, maximum applied stress is presented as a fuzzy variable with unknown distribution law in the second part of the paper. Analytical equations for reliability evaluation are obtained by estimation of upper and lower bounds of reliability function. The real value of reliability function is located within this interval. The proposed approach may be applied to give recommendations for engineering of forestry machine and equipment elements in the case of limited statistical information.

Effects of BFRP Bar Diameter and Cover Thickness on Fracture Behavior of BFRP Bar–Reinforced Ecological High-Ductility Cementitious Composites

Abstract To obtain the design parameters of bridge deck link slabs made of ecological high-ductility cementitious composite (Eco-HDCC) material reinforced with a basalt fiber-reinforced plastic (BFRP) by applying fracture mechanics concepts, the reinforcing effects of a BFRP bar on the fracture properties of BFRP bar–reinforced Eco-HDCC specimens were studied. First, cracking load, crack mouth opening displacement (CMOD), and deflection of specimens were monitored, and BFRP bar diameter and cover thickness were considered. The results indicate that both the diameter and cover thickness of BFRP bar have an obvious influence on the crack kinking angle. In addition, as the diameter of BFRP bar increases, the peak load, peak CMOD, peak deflection, and fracture energy of Eco-HDCC specimens increase, and these peak values of Eco-HDCC specimens after reloading also show the same trend. In addition, the peak load, peak CMOD, peak deflection, and fracture energy are larger if the Eco-HDCC specimen has a smaller cover thickness. However, the Eco-HDCC specimen with a BFRP bar cover thickness of 25 mm has a higher peak load after reloading than the specimen with a cover thickness of 15 mm when the bar diameters are 10 and 12 mm, respectively. In conclusion, BFRP bar diameters from 10 to 14 mm and a cover thickness of 25 mm are recommended when designing bridge deck link slabs.

Fracture assessment of polycarbonate parts produced by fused deposition modeling in the out-of-plane printing direction – effect of raster angle

PurposeThe purpose of this paper is to study the Mode I fracture behavior of polycarbonate (PC) parts produced using fused deposition modeling (FDM). The focus of this study is on samples printed along the out-of-plane direction with different raster angles.Design/methodology/approachTensile and Mode I fracture tests were conducted. Semi-circular bend specimens were used for the fracture tests, which were printed in four different raster patterns of (0/90), (15/−75) (30/−60) and (45/−45). Moreover, the finite element method (FEM) was used to determine the applicability of linear elastic fracture mechanics (LEFM) for the printed PC parts. The fracture toughness results, as well as the fracture path and the fracture surfaces, were studied to describe the fracture behavior of the samples.FindingsFinite element results confirm that the use of LEFM is allowed for the tested PC samples. The fracture toughness results show that changing the direction of the printed rasters can have an effect of up to 50% on the fracture toughness of the printed parts, with the (+45/−45) and (0/90) orientations having the highest and lowest resistance to crack propagation, respectively. Moreover, except for the (0/90) orientation, the other samples have higher crack resistance compared to the bulk material. The fracture toughness of the tested PC depends more on the toughness of the printed sample, rather than its tensile strength.Originality/valueThe toughness and the energy absorption capability of the printed samples (with different raster patterns) were identified as the main properties affecting the fracture toughness of the AM PC parts. Because the fracture resistance of almost all the samples was higher than that of the base material, it is evident that by choosing the right raster patterns for 3D-printed parts, very high resistance to crack growth may be obtained. Also, using FEM and comparing the size of the plastic zones, it was concluded that, although the tensile curves show nonlinearity, LEFM is still applicable for the printed parts.

Application of fracture mechanics for the characterization of poly(vinyl chloride) pipes. II. Evaluation of a ring‐type specimen for fracture mechanics testing

AbstractAn unplasticized poly(vinyl chloride) (U‐PVC) pipe sample used in infrastructure applications in Brazil (nominal diameter DN 100, outside diameter 110 mm) was evaluated according to different fracture mechanics methodologies, including essential work of fracture (EWF) and other fracture toughness parameters such as the stress intensity factor and plane strain energy release rate . This pipe sample was also tested for the quality of processing (degree of gelation) via differential scanning calorimetry (DSC) and tensile strength. The comparative evaluation of different specimen configurations—curved specimens in three‐point bending (CTPB) and full rings in tension (SNRT), in thicknesses varying from 5 to 30 mm, showed initial evidence of the suitability of ring‐type specimens for the evaluation of EWF and . Results also indicate that the full ring geometry, at least in the present experimental setup, presents some drawbacks probably due to the storage of large amounts of elastic energy throughout the test. This fact leads to relevant deviations in both load–displacement behavior and results for strain energy release rate (), and the results found here will guide future research using full and split rings in different loading modes and improved experimental setups. It was also confirmed that the value of , determined by a modified Charpy test, is independent of the type of specimen tested, as long as the test mode and specimen width are the same. Both the experimental value of and the estimated value for the plane strain stress intensity factor () showed excellent agreement with values reported for other U‐PVC compositions.

Applicability of linear elastic fracture mechanics to compressive damage in carbon fiber reinforced epoxy matrix composites

The failure of carbon fiber reinforced epoxy matrix composites has been attributed to different mechanisms involving tensile, compressive and shear failure of the fibers or the matrix. This research serves to understand whether linear elastic fracture mechanics can explain the matrix behavior under compressive loading. Experiments and finite element analysis (FEA) are used to confirm that the matrix under compressive loads follows the relationships established by linear elastic fracture mechanics. The failure load is related to the corresponding notch length, and the observed relationship is compared to the relationship defined by linear elastic fracture mechanics.

Stress intensity factors for external corrosions and cracking of buried cast iron pipes

The municipal water distribution systems across the world include a significant amount of cast-iron pipes. Many of the buried cast-iron pipes are over fifty years old and require rehabilitation. Municipalities decide on a rehabilitation solution between the replacement and re-use of the existing pipes based on the remaining strengths of the pipes. Fracture mechanics has appeared as the most viable tool for remaining strength assessment of the deteriorating pipes. However, a method of assessing the stress intensity factor (SIF) is often not available to municipal engineers to apply fracture mechanics. This paper presents a method for calculating the SIFs of buried cast iron pipes subjected to corrosion and crack on the exterior surface. Different semi-elliptical-shaped defects were characterized using various aspect ratios (crack-depth to crack-length ratio) and relative depths (crack-depth to pipe thickness ratio). The SIFs were assessed for invert/crown and springline position cracks under internal pressure and vertical surface loads. A simplified method is proposed for evaluating the SIFs of buried pipes subjected to the exterior surface defects.

The Overview of Fracture Mechanics Models for Concrete

Abstract Fracture mechanics of concrete is a complex matter still thoroughly researched from different angles. It is not an easy task to describe fracture process in concrete, as there are many factors affecting crack development and propagation. Practical applications of fracture mechanics could allow engineers to design concrete structures more effectively and safely. At the minimum, it could help estimate the “safe” period of time left before the unstable, dangerous crack propagation. This utilitarian goal was the reason for many researchers to invent numerous theoretical models in order to describe the crack occurrence better. However, dealing with various analytical problems was not a simple matter and thus existing models of fracture mechanics for concrete have different limitations. Over the years first fracture theories for concrete were reviewed repeatedly. All of these investigations lead to modifications of older models in order to overcome found drawbacks, which proved not to be an easy task. Recently, new approaches to fracture analyses seemed to produce promising results, like universal size effect law (USEL) or modified two parameter fracture model (MTPM) with alternative ways for evaluating fracture parameters. In the paper some of them will be discussed together with other fracture models, starting from some of the very first ones introduced for concrete, like fictitious crack model (FCM) and crack band model (CBM).

Crack propagation in flexural fatigue of concrete using rheological-dynamical theory

The concrete fatigue analysis can be performed with the use of fracture mechanics. The fracture mechanics defines the fatigue crack propagation as the relationship of crack growth rate and stress intensity factor. In contrast to metal, the application of fracture mechanics to concrete is more complicated and therefore many authors have introduced empirical expressions using Paris law. The topic of this paper is development of a new prediction of fatigue crack propagation for concrete using rheological-dynamical analogy (RDA) and finite element method (FEM) in the frame of linear elastic fracture mechanics (LEFM). The static and cyclic fatigue three-point bending tests on notched beams are considered. Verification of the proposed approach was performed on the test results taken from the literature. The comparison between the theoretical model and experimental results indicates that the model proposed in this paper is valid to predict the crack propagation in flexural fatigue of concrete.

Jive: An open source, research-oriented C++ library for solving partial differential equations

A majority of physical models are written as partial differential equations. For most of these equations, analytical solutions cannot be obtained and they can be solved only numerically using e.g. the finite element method. To not waste time programming, it is vital for researchers working on state-of-the-art numerical methods to adopt a flexible, efficient, open source and research-oriented library designed to solve partial differential equations for their work. This paper describes such a library named Jive . This numerical library, written in C++, can be used to implement any numerical method. Here, we describe the overall features of Jive . Moreover, as Jive has proven to be well adapted to finite element methods, in particular, we go on to present ofeFRAC, our in-house finite element code for damage and fracture mechanics applications written on top of Jive . We demonstrate that using Jive allows us to quickly write efficient codes for testing new models and methods.

Fracture Mechanical Characterization of Adhesively Bonded Wood-Ceramic Interfaces for Mode I Loading

Abstract This study introduces a novel approach for investigating the fracture behavior and technical quality of adhesively bonded wood-ceramic interfaces for Mode I loading. For that, a special test arrangement originally used for quasi-brittle materials was applied. The key benefit of this innovative concept is the ability to describe postcracking behavior that is due to stable and steady recording of load-displacement diagrams. This is a big benefit over common practice techniques from both a mechanical and fracture mechanical point of view. The reason for this is that the quasi-brittle material’s nature of unstable cracking comes into place when the test setup is not stiff enough. Another reason to apply fracture mechanics over continuum mechanics is the ability to identify quantitative parameters that describe the softening process in terms of fracture energy. This is a great benefit over stress-based concepts, such as the stress intensity approach (K-concept), which is not appropriate for adhesively bonded multimaterial interfaces. To demonstrate this new approach, bonded wood-ceramic composites were investigated using four different industrial adhesives from Sika AG (Baar, Switzerland) and Murexin (Wiener Neustadt, Austria). The findings indicated interesting relationships between adhesive bonding strength and crack growth resistance when it comes to changing the material of one bonding partner from wood to ceramic. Polyurethane-based adhesives especially show the highest potential of bonding power and fracture resistance when Mode I loading is applied. Furthermore, acrylate-based adhesives are capable of high improvement gains of both mechanical and fracture mechanical parameters when adhesively bonded wood-ceramic interfaces are investigated. This is a remarkable effect and should be part of future investigations by also incorporating the economical aspects of adhesive selection in terms of benchmarking. Finally, these findings could be used for optimizing the mechanical and chemical properties of hybrid adhesives in the future.

Application of fracture mechanics for the characterization of PVC pipes. I. Evaluation of the applicability of the EWF technique in specimens produced directly from pipes

AbstractUnplasticized (U‐PVC) and modified (M‐PVC) pipes used in irrigation and infrastructure applications in Brazil (nominal diameter DN 300, outside diameter 326 mm), were evaluated according to various fracture mechanics methodologies, including essential work of fracture (EWF), C‐ring toughness and fracture toughness parameters (stress intensity factor KC and energy release rate GC, both at plastic collapse). These pipes were also evaluated for the quality of processing (degree of gelation) via DSC and tensile strength. Results show that the differences in behavior against fracture propagation are sensitive, depending on the technique, when comparing the results between the different types of pipes, opening up new possibilities for testing this product. This possibility is particularly interesting in the case of the evaluation of the degree of gelation in industrial process controls, since the dichloromethane (DCMT) solvent immersion method still in use tends to be replaced in the future by alternative methodologies due to chemical exposure factors.

Parametrized reduced order modeling for cracked solids

SummaryA parametrized reduced order modeling methodology for cracked two dimensional solids is presented, where the parameters correspond to geometric properties of the crack, such as location and size. The method follows the offline‐online paradigm, where in the offline, training phase, solutions are obtained for a set of parameter values, corresponding to specific crack configurations and a basis for a lower dimensional solution space is created. Then in the online phase, this basis is used to obtain solutions for configurations that do not lie in the training set. The use of the same basis for different crack geometries is rendered possible by defining a reference configuration and employing mesh morphing to map the reference to different target configurations. To enable the application to complex geometries, a mesh morphing technique is introduced, based on inverse distance weighting, which increases computational efficiency and allows for special treatment of boundaries. Applications in linear elastic fracture mechanics are considered, with the extended finite element method being used to represent discontinuous and asymptotic fields.

Application of fracture mechanics to weld fatigue

The application of fracture mechanics to the determination of the fatigue behavior of weldments is discussed with the focus on classic fatigue, i.e., the overall fatigue life and the fatigue strength in terms of an S-N curve and the endurance limit. The following issues are addressed: specific features of short fatigue crack propagation, an adequate initial crack size, multiple crack propagation and its statistical treatment as well as welding residual stresses. As an example, an approach of the authors is applied to the determination of FAT classes for a butt weld with varying weld toe geometry.

Thermal fracture characteristics of an interface crack subjected to temperature variations

Abstract Thermal fracture characteristics – the thermal energy release rate and thermal stress intensity factor of a semi-infinite crack at an interface between the two elastic isotropic materials, subjected to the temperature variations, are considered in this paper. Those characteristics are determined based on application of the linear elastic fracture mechanics (LEFM) concept. Expressions for obtained theoretical solutions are compared to solutions from literature and they are found to be more concise. Influence of the materials change on these two thermal fracture properties were observed, as well as the influence of the thickness ratio of the two layers constituting the interface.

Fracture toughness evaluation for Zr-4 clad tubing structure with pellet inserts

Applying fracture mechanics approach to spent nuclear fuel (SNF) system reliability investigation is warranted due to the inherent flaws and hydride structures existed in a SNF system after nuclear reactor operation. However, none of the existing fracture toughness data deal with fuel cladding specific geometry or spent fuel material conditions, such as cladding structure with the pellet-inserts and the associated pellet clad mechanical interactions induced mixed-mode damage mechanisms. Thus, the development of an intrinsic fracture mechanics approach that is suitable for SNF materials is needed. Due to thin wall and small dimension of clad tubing structure, the spiral notch torsion test (SNTT) method of small specimen approach was used to estimate the clad tubing structure fracture toughness. The estimated fracture toughness for Zr-4 cladding with alumina-pellet inserts are presented in this report. For SNTT samples with a short or medium crack length, between 5.4-mm and 8-mm, the estimate JIQ upon fracture initiation for the baseline Zr-4 cladding is at 50 kJ/m2 with 2-sigma uncertainty of 3.26 kJ/m2, and the associated KIQ is at 67.46 MPa√m. For SNTT samples with a long crack length, around 13-mm, the crack initialization is deviated from that of the Mode-I tensile fracture and appears to be a mixed-mode fracture of Mode I – tensile stress and Mode III – out of plane shear stress; the estimated JMQ is at 18.9 kJ/m2, the associated KMQ is at 41.4 MPa√m.