Linear Elastic Fracture Mechanics Research Articles

Experimental Study on Fracture Behavior of Adhesive-Bonded Structure with V-notch Based on Digital Gradient Sensing Method

In this paper, a comparative study of the mode-I fracture behaviors of two types of specimens with a V-notch defect under plane stress conditions was performed using the digital gradient sensing (DGS) method. First, two types of specimens (namely one-piece specimen and bonded specimen) with the same V-notch defect were both made of polymethyl methacrylate (PMMA), and three different V-notch angles’ defect were considered for each type of specimen. Then, three-point bending tests were performed on both types of specimens. The angular deflection field of light near the V-notch region was recorded using a CCD during the experiments. Finally, by utilizing the relationship between the stress gradient and angular deflection as established by the elasto-optic effect, in conjunction with the principles of linear elastic fracture mechanics theory, the stress intensity factors (SIFs) of two types of specimens under different stress conditions were calculated using the least square method. According to the experimental results, the influence of V-notch angle on fracture load and fracture toughness of two kinds of specimens was discussed. Meanwhile, the experimental results show the significant differences in the fracture behaviors of the two types of specimens under mode-I loading conditions.

USAF Characteristic K Approach: A Robust Tool for Predicting Fatigue Crack Growth under Various Underload Spectra.

This paper forms part of an ongoing investigation into the tools required in linear elastic fracture mechanics (LEFM) for evaluating the durability of components designed for limited life replacement. In this study, we demonstrate that the USAF 'Characteristic K' method, when combined with the Hartman-Schijve adaptation of the NASGRO crack growth formula, can predict the impact of underloads on the propagation of small cracks in aluminum alloy AA7050-T7451 with reasonable accuracy. The published da/dN versus ΔK small crack growth curves associated with five specific underload spectra are examined. It is found that, in each case, there is reasonably good agreement between the predicted and the measured curves. To the best of the author's knowledge, this paper is the first to highlight the ability of the USAF Characteristic K approach, when coupled with the Hartman-Schijve equation, to reasonably accurately predict the growth of small cracks subjected to a range of underload spectra.

Synergistic impact of corrosion pitting on the rotating bending fatigue of additively manufactured 316L stainless steel: Integrated experimental and modeling analyses

In this study, the ex-situ rotating bending corrosion fatigue behavior of laser powder bed fused stainless steel (SS) 316L has been studied incorporating experimental analyses and modeling. The findings revealed significant variations (almost 20 %) in fatigue lifetime in pre-corroded specimens relative to non-corroded (virgin) specimens because of corrosion-derived pitting phenomena on the surface. To this end, the fatigue strength of virgin (non-corroded) and pre-corroded SS 316L were recorded at 242 MPa and 203 MPa, respectively. Upon conducting the fatigue tests and extracting stress-life trends, advanced microstructural characterization and postmortem analyses were used to quantify fatigue crack behavior and fracture surface. An empirical model is also developed employing depth-sensing indentation testing, linear elastic fracture mechanics, and computer tomography scans to propose an optimum predictive trend. The analysis comparing existing models with our proposed model demonstrates reasonable agreement between experimental findings and the predicted life for the studied laser powder bed fused SS 316L material exposed to corrosion rotating bending fatigue test. The findings of this research carry important contributions to the structural integrity and longevity of marine engineering, ship construction, naval operations, and naval aviation where materials and components are exposed to cyclic loading and corrosion.

Tensile fracture of blunt V-notches in rectangular plates additively manufactured from Acrylonitrile Butadiene Styrene with different raster angles

In this research, the tensile fracture behavior of rectangular specimens made of Acrylonitrile Butadiene Styrene (ABS) containing double-edge blunt V-notches is evaluated. The specimens are printed using the fused deposition modeling (FDM) technique with five different raster angles and three different notch tip radii. To simplify the complex calculations related to the anisotropic behavior of these specimens, the Virtual Isotropic Material Concept (VIMC) is used in conjunction with three well-known linear elastic notch fracture mechanics (LENFM) criteria, i.e., the mean stress (MS), point stress (PS), and averaged strain energy density (ASED) criteria as well as the extended finite element method (XFEM). It is shown that all these fracture models can predict the load-bearing capacity of the 3D-printed notched specimens by acceptable accuracies, where the best predictions belong to the MS criterion with the critical distance obtained directly from the finite element method, and the least accurate predictions belong to the XFEM method.

Cyclic inelastic behaviour of a bonded patch repair system used for pipes with through-wall corrosion damage

Repairs of through-wall corrosion damage in pipes conveying liquids using bonded metallic patches are becoming common in the oil and gas industry. Usually, this kind of patch is used in association with a composite sleeve, and it is essential to assure that the repair wońt leak. The use of bonded metallic patches associated with the composite sleeve is not forbidden in the standards for the design of composite repair systems (such as ASME PCC-2 and ISO 24817). However, they do not address this very frequent practice adopted in industry. Since the patch is responsible for sustaining most of the pressure of the repair, it becomes necessary to further understand its behaviour. This paper investigates the cyclic inelastic behaviour of a metal patch/adhesive system and its effect on the failure pressure. Hydrostatic tests were performed regarding how pressure variations can generate cyclic inelastic strains in the adhesive layer that bonds the metal patch to the pipe, and how this cyclic loading–unloading process ultimately affects the failure pressure. The failure pressure in monotonic burst tests can be reasonably modelled using basic concepts of linear elastic fracture mechanics. Although the assumption of a brittle-elastic behaviour of the repair system seems adequate in the case of monotonic loading, it is not in the case of cyclic tests with high pressure amplitudes. Repairs in steel pipes under pressure with a 25 mm diameter hole failed after a very small number of cycles with pressure amplitude of 80% of the average failure pressure obtained in monotonic burst tests. To help understanding the behaviour of the system, single lap joints were studied. The patch and pipe are not subjected to significant permanent deformations, while the adhesive layer has an inelastic behaviour. Results show that the lap joints present a rate-dependent behaviour in tensile tests and may present highly different cyclic responses which are quite sensitive to very small perturbations in the manufacturing process.

Fatigue design of stress relief grooves to prevent weld root fatigue in butt-welded cast steel to ultra-high-strength steel joints

In the welded joints, fatigue failures typically originate from defects or notch-like geometries under cyclic loading. This study investigates the impact of stress relief grooves (SRG) on the fatigue performance of butt-welded cast steel to ultra-high-strength steel components using experimental fatigue tests and finite element method. The experiments examined the fatigue properties of hybrid joints between G26CrMo4 cast steel (t = 20 mm) and S960 steel plate (t = 6 mm) with and without SRG. Gas metal arc welding process was used to weld the butt joints that had a permanent root backing machined on the cast steel part, causing a crack-like defect to the weld root. Additionally, the top surfaces of the welded parts were aligned, resulting in a significant axial misalignment in the butt joint. The SRG, positioned close to the weld root, was found to have a beneficial influence on the joint’s fatigue performance by a factor of 1.2 when using the nominal stress criterion. However, the fatigue capacity was still roughly 35% lower compared to the symmetrical equivalent due to the secondary bending stress, caused by axial misalignment. The finite element analyses indicated that the SRG reduces the amount of secondary stresses at the weld root leading to lower total structural stress. The study recommends using the FAT80 (m = 3) design curve in the structural stress method, for similar butt-welds having a crack-like defect, parallel to the loading direction, at the weld root. However, for welded joints with crack-like defects, it is advisable to use linear elastic fracture mechanics rather than relying solely on stress-based local approaches.

Measurement of the interfacial energy release rate (ERR) and cohesive law parameters of polyvinyl butyral laminated glass using a novel beam-type test specimen

The polyvinyl butyral (PVB) laminated glass (LG) structures are widely used in architectural and automotive sectors. Determination of the interfacial fracture energy (i.e. G) between the PVB layer and glass is one of the most vital procedures for ensuring the structural safety and fracture resistance of these kinds of components. The present study investigates the adhesion characteristics between glass and PVB interface in a LG composite structure. A new simple test fixture is introduced to measure the mixed-mode fracture energy from pure mode I (i.e. GI) to pure mode II (i.e. GII). By making use of the concept of Equivalent material Concept (EMC), linear elastic fracture mechanics (LEFM) formulations together with finite element (FE) analysis can be used to compute the compliance parameter of the system and pure modes I/II fracture energies. Besides, the interaction of cohesive forces between the PVB layer and glass are simulated by using a FE method based on a bi-linear cohesive zone model (CZM) technique. In this regard, the cohesive law parameters are computed for mode I and mode II in an iterative process. Then, the obtained pure mode cohesive law parameters are utilized to predict the mixed-mode load–displacement diagrams. The obtained results demonstrate the satisfactory accuracy of the cohesive law parameters and fracture energies in predicting the mixed-mode loading results across four different loading rates (i.e. LR = 2, 5, 10, and 15 mm/min).

Micromechanical properties characterization of 4H–SiC single crystal by indentation and scratch methods

Growth and micromachining of single crystal silicon carbide (SiC) have drawn extensive attention in wide bandgap semiconductors and remained challenging. The micromechanical properties (i.e., hardness, elastic modulus, fracture toughness), which are the key to machinability and machining quality (and therefore the yield of the grown SiC), of 4H–SiC were assessed by nanoindentation, microhardness, and microscratch tests. Consistent values of true indentation hardness of 4H–SiC can be obtained by different approaches without the need for the area function of the indenter. Accurate determination of elastic modulus (i.e., 583.5 GPa) and indentation hardness (i.e., 38 GPa) of 4H–SiC by the instrumented indentation technique requires low loads with slight indentation-induced damage. Consistent values of fracture toughness Kc of 4H–SiC were obtained by different methods such as the Vickers/Berkovich indenter-induced cracking method (2.1 MPa·m1/2), energy-based nanoindentation approaches (the critical void volume fraction of 0.062 should be used for 4H–SiC when the deterioration of indentation hardness is used), and linear elastic fracture mechanics (LEFM)-based scratch approach with a spherical indenter (2.6 MPa·m1/2). This work provides the guidance for the mechanical machining of 4H–SiC wafers and the paradigm of micromechanical characterization of brittle solids by indentation and scratch technologies.

How Stress Barriers and Fracture Toughness Heterogeneities Arrest Buoyant Hydraulic Fractures

AbstractIn our study, we investigated the impact of changes in Mode I fracture toughness and stress barriers on fully developed planar, buoyant hydraulic fractures assuming linear elastic hydraulic fracture mechanics. We present scaling-based arguments to predict the interaction type and use numerical simulations to validate our findings. Through a two-dimensional simplification, we estimate the lower limit for the fracture to feel a change in fracture toughness (so-called immediate breakthrough). Our simulations show that this approach only captures the order of magnitude of the toughness jump necessary for immediate breakthrough compared to the actual value due to three-dimensional solid effects, emphasizing their importance in such systems. We show that we can estimate the occurrence of indefinite containment at depth by considering that lateral spreading occurs at an approximately constant height. However, timing predictions in the case of a transient containment suffer from our simplified approach, which cannot model the injection history of the spreading constant height fracture. The same observations regarding immediate breakthrough and indefinite containment hold when considering stress barriers using pressure-scale-based arguments. Our study shows that the required toughness changes for fracture arrest are more significant than the observed values in the field. In contrast, stress barriers with a magnitude of around 1 MPa are generally sufficient to contain buoyant hydraulic fractures indefinitely. Stress barriers, in combination with other arrest mechanisms, are thus the most prominent mitigation factor of buoyant growth in industrially created hydraulic fractures.

Tensile-Tear cracking resistance of RAP incorporated asphalt Mixtures, enhanced by Warm mix asphalt additive and nano calcium carbonate

Asphalt mixture is a commonly used material for road paving. However, its production is expensive and requires significant amounts of virgin materials. To address this issue, adopting a less harmful production process and incorporating recycled materials can be beneficial. In this study, the focus was on investigating the cracking resistance parameters of warm mix asphalt (WMA) mixtures prepared with high contents of reclaimed asphalt pavement (RAP), along with the use of nano calcium carbonate (NC) as a modifier. In this context, the cracking resistance of the mixtures was studied in two −12 and + 25 °C temperatures under pure mode I, two mixed modes I/III, and pure mode III loading. The results revealed that adding RAP increased the fracture toughness and fracture energy, with an average increase of 30 and 20 %, respectively. Incorporating NC also improved the mixture’s resistance to cracking, enhancing fracture energy by up to 30 % and fracture toughness by up to 20 %. The optimal content of NC was determined to be in the range of 2 to 4 %, depending on the variables considered. Considering the linear elastic fracture mechanics, several theoretical criteria were used to predict the fracture data, and accurate predictions were achieved. Statistical analyses were also conducted to evaluate the impact of variables on cracking resistance; as an example of outcomes, it is seen fracture energy of pure mode III is about twice the mode mode I.

Mechanics of abrasion-induced particulate matter emission

Microplastic pollution constitutes a substantially detrimental type of environmental contamination and poses threats to human health. Among the sources of airborne and marine microplastics, evidence indicates that non-exhaust emissions resulting from tire abrasion and other organic materials have emerged as a notable contributor. However, the mechanistic understanding of abrasion emission of organic materials has remained elusive. To fill the gap, we here develop a multi-scale abrasion mechanics model using the principles of linear elastic fracture mechanics. Macroscopically, material wear and tear can be viewed as a process of macro-crack propagation associated with the fatigue fracture. Microscopically, we consider the effect of microcracks propagating under cyclic loading on the material modulus and energy release rate during fatigue fracture. This framework leads to an evaluation of the effective energy release rate for the abrasion-induced emission of particulate matter, thus leading to a calculation of the concentration of the emitted particulate matter with varied sizes. The theory is validated by corresponding experiments and high consistency is exhibited between the theoretical and experimental results. This research constructs a quantitative relationship between fracture mechanics and abrasion emissions. This research not only paves the way for a mechanistic understanding of particulate matter pollution from a solid mechanics perspective but also offers rational guidance for modern society to alleviate airborne particulate matter and marine microplastic abrasion emissions.

Estimating the remaining service life of in-situ grouted post-tension anchors using flaw tolerance limit plots

Brittle failure of grouted post-tensioned anchors used in trunnion girders at dams has given rise to concerns and questions surrounding their continued use and remaining service life. This paper reviews the brittle failure of five grouted post-tensioned anchor rods due to stress corrosion cracking at dams in California. To provide an early warning system to dam owners and expand on available resources for practicing engineers, this study derives plain strain fracture toughness from the failed grouted post-tension anchors using cross sectional photos. Using derived and available fracture toughness values, flaw tolerance limit plots, which can quickly illuminate the severity of a defect for various anchor diameters, were developed for semicircular and straight fronted flaw types using linear elastic fracture mechanics and stress intensity factors for both ASTM A322 and ASTM A722 materials. To help demonstrate the use of flaw tolerance limit plots and estimate the remaining service life of an in-situ anchor, an example problem was developed.

Optimising fatigue crack growth predictions for small cracks under variable amplitude loading

The fatigue cracks in a fighter aircraft that pose the greatest threat to structural integrity and availability are usually less than 1 mm for most of their lives. However, it has long been recognised that small cracks can grow significantly faster than long cracks at the same stress intensity range (ΔK). This means predictions for small cracks growing under realistic spectrum loading can be significantly non-conservative when using linear elastic fracture mechanics and long crack-based empirical rate data. Previous work showed empirical rate data based on small cracks grown under constant amplitude (CA) loading could significantly improve predictions. However, such data still have limitations related to an inability to predict the spectrum history effects that influence small cracks. This paper presents a method to optimise a model to predict fatigue crack growth rates for cracks loaded with realistic spectra. This method is demonstrated for small cracks in Aluminium Alloy 7050-T7451 grown under fighter wing root spectrum loading. Numerical optimisation is used to select model parameters that minimise fatigue crack growth rate prediction errors for a training dataset. This purpose-built model consistently outperformed a generic model based on the growth of small cracks under CA loading.

Universal slope-based J-integral methods for characterization of the mode I, mode II and mixed mode I/II fracture behaviour of adhesively bonded interfaces

Universal slope-based J-integral methods have been developed for the determination of the energy release rate for adhesively bonded joints under mode I, mode II and mixed-mode (I/II) loading conditions. The individual J components corresponding to the mode I and mode II loading were separated based on the J-integral decomposition theory. The proposed methods use the slopes of the substrates at various locations to characterize the energy release rate and thus avoid the measurement of crack lengths, which are especially suitable for characterizing the tough interfaces associated with large fracture process zones ahead of crack tips. Under linear elastic deformation, the slope-based J equations were found to be equivalent to classical G equations based on linear elastic fracture mechanics (LEFM). Both experimental and numerical testing of adhesively bonded joints were undertaken to validate the slope-based J equations. The universal slope-based J-integral methods provide a reliable alternative to the measurement of G for adhesive joints or laminated composites undergoing nonlinear or inelastic deformations where conventional LEFM is not valid. It is shown that LEFM, even when coupled with an effective crack length approach, can be inaccurate when damage occurs in a test specimen away from the fracture process zone, as was seen here in mode II. Slope-based J equations can avoid these inaccuracies with a careful selection of contour paths. Slope based methods are therefore strong candidates for selection in future test standards for mode II fracture characterisation of structural adhesive joints.

Mode I fracture propagation and post-peak behavior of sandstone: Insight from AE and DIC observation

Microcracks generated at the crack tip, particularly in quasi-brittle materials such as sandstone, give rise to a non-linear region known as the fracture process zone (FPZ), which cannot be analyzed using linear elastic fracture mechanics (LEFM). To gain insights into the nonlinear fracturing behavior of rock, this study conducted three-point bending experiments on sandstone beams with prefabricated notch. Stable mode-Ⅰ fracture propagation during the post-peak stage was achieved by the monotonic increment of crack mouth opening displacement (CMOD) measured by a clip gauge. The acoustic emission (AE) and digital image correlation (DIC) techniques were utilized to visually track the detailed crack propagation process from both micro and macro perspectives. Nonlinear fracture parameters, including FPZ length, were identified by AE and DIC measurements and compared with the theoretical calculation. A nonlinear fracture criterion relating applied load, equivalent crack length, and stress intensity factor were established, from which the theoretical CMOD-P curve at the post-peak stage were obtained and validated with experimental measurement from MTS machine. The results reveal that microcracks formulating the FPZ materialize in the pre-peak stage, with the majority emerging post-peak to facilitate the propagation of the traction-free crack and FPZ in the loading direction, as evidenced by AE locations and DIC displacement gradient. Throughout the crack propagation process, over 65 % of microcracks are estimated to be tensile mode based on both AF/RA and polarity analysis, aligning with anticipated outcomes from macroscopic three-point bending fracture tests. Energy dissipation primarily occurs within the FPZ to facilitate separation of crack faces, with the dissipated energy region advancing towards the beam boundary. By integrating AE source locations and DIC displacement gradient, the FPZ length of the 3-point-bending sandstone specimens is determined to be lp = 8.1 mm, slightly exceeding the theoretical FPZ lengths calculated by the Irwin model (lp = 7.0 mm) and the Dugdale-Barenblatt model (lp = 7.6 mm). Using a non-linear fracture criterion that incorporates the FPZ and employing the in-time equivalent crack length measured by AE and DIC as an intermediate variable, the theoretical applied load-crack length curve during the post-peak stage is calculated, showing close agreement with load cell measurements with a negligible error of approximately 2 %. Furthermore, the theoretical post-peak CMOD vs. load curve aligns with experimentally obtained results, demonstrating a non-linear crack propagation speed at a constant CMOD rate, wherein crack propagation speed decreases as crack length increases.

Applicability investigation on failure assessment diagram of ASME code section XI - Appendix H for ferritic nuclear piping

The failure assessment diagram (FAD) is a widely used tool for evaluating the fracture acceptance of structural components. In addition to linear elastic fracture mechanics, elastic-plastic fracture mechanics, and limit load analysis, the ASME Code incorporated FAD as an alternative safety evaluation method for flaws in nuclear pipes starting from 2004 edition. This paper conducts a series of finite element elastic-plastic fracture mechanics analyses to establish the specific J–based FAD curves considering various loading and geometry conditions for ferritic pipes containing various circumferential flaws. By comparing with the suggested FAD of ASME Code Section XI - Appendix H, it is found that the radius-to-thickness ratio of pipes and the flaw depth influence the applicability of FAD, but with minor effects of crack length. In addition, the effects of material properties between base metal and weld materials on FAD are also discussed. The result of this work could be a reference when applying the FAD to evaluate the flawed piping for nuclear power plants.

The demarcation problem in the applied sciences

The demarcation problem in the applied sciences refers to the challenge of discerning between progressive, stagnant, and improper model development programs. We examine the demarcation problem from the perspectives of two influential philosophers of science, Imre Lakatos and Thomas Kuhn, using the evolutionary development of linear elastic fracture mechanics (LEFM) for illustration. We propose objective criteria.

Fracture toughness testing of metallic materials based on scratch tests

As a crucial parameter for determining a material's resistance to crack propagation, the convenient characterization of fracture toughness has attracted much attention. The scratch test is an alternate method for determining fracture toughness because it does not require notches or pre-existing cracks and only requires a minimal sample volume. In this study, the product of strength and elongation of materials is incorporated into a modified model based on the energy size effect law to calculate the fracture toughness of metallic materials using scratch tests. To validate the proposed model, scratch tests of DP800, 18CrNiMo7-6, 4140, and 4340 are performed to characterize their fracture toughness. The fracture toughness of these four metallic materials determined from scratch tests utilizing the proposed model, Akono's linear elastic fracture mechanics (LEFM) model, Akono's microscopic energetic size effect law (MESEL) model, Hubler's MESEL model, and Liu's MESEL model are compared with the results from a compact tensile test or single edge notched beam test. Our results indicate that our modified approach is applicable to metallic materials. The proposed model could be reduced to the linear elastic fracture mechanics model. This study offers an efficient way of characterizing the fracture toughness of materials using the scratch method.

Structural design against brittle fracture: Optimizing energy release rate and experiment

Despite substantial advancements in optimizing structural designs for stiffness, the field of design against fracture is still in its early stages. This paper introduces a fundamental and standardized paradigm for structural design against brittle fracture, achieved through the minimization of the energy release rate G within the framework of linear elastic fracture mechanics (LEFM). By leveraging the Griffith criterion expression and the total potential energy in LEFM, we propose an efficient approach for structural optimization that enhances the toughness of architected materials. The energy release rate G is evaluated a synergistic application of finite element analysis and finite difference methods, yielding a precision of 0.6% compared to benchmarks in published handbooks. We demonstrate significantly reduced G values compared to standard stiffness and stress-oriented topology optimization, which directly contributes to increased toughness. To comprehensively analyze the fracture process encompassing damage, crack initiation, propagation, and failure, we employ post-processing phase field fracture modeling on the optimally designed architected materials. By performing multi-objective optimization of the stiffness and energy release rate G, the toughness and extreme load-bearing capacity can be simultaneously improved. The resulting perforated architecture effectively outperforms homogeneous structures in both toughness and peak load. Additionally, we extend our analysis to various configurations, such as non-center cracks, pure shear loading, and adherence to the standard 3D compact tension ASTM E-399-72. The designed structures are additively manufactured and experimentally validated, demonstrating a toughness increase of over 10 times compared to stress-based design. These contributions offer promising prospects for advancing the design of future engineering structures and materials with a favorable balance of critical fracture resistance characteristics.

Data-Driven Dynamic Inversion Method for Complex Fractures in Unconventional Reservoirs

Abstract Hydraulic fracturing is a crucial technology for enhancing the recovery of oil and gas from unconventional reservoirs. Accurately describing fracture morphology is essential for accurately predicting production dynamics. This article proposes a new fracture inversion model based on dynamic data-driven methods, which is different from the conventional linear elastic fracture mechanics model. This method eliminates the need to consider complex mechanical mechanisms, resulting in faster simulation speeds. In the model, the fracture morphology is constrained by combining microseismic data and fracturing construction data, and the fracture tip propagation domain is introduced to characterize the multi-directionality of fracture propagation. The simulated fracture exhibits a multi-branch fracture network morphology, aligning more closely with geological understanding. In addition, the influence of microseismic signal intensity on the direction of fracture propagation is considered in this study. The general stochastic approximation (GSA) algorithm is employed to optimize the direction of fracture propagation. The proposed method is applied to both the single-stage fracturing model and the whole well fracturing model. The research findings indicate that in the single-stage fracturing model, the inverted fracture morphology aligns closely with the microseismic data, with a fitting rate of the fracturing construction curve exceeding 95%, and a microseismic data fitting rate exceeding 93%. In the whole well fracturing model, a total of 18 sections were inverted. The fitting rate between the overall fracture morphology and the microseismic data reached 90%. The simulation only took 5 minutes, demonstrating high computational efficiency and meeting the needs of large-scale engineering fracture simulation. This method can effectively support geological modeling and production dynamic prediction.