Critical Energy Release Research Articles

Investigation of crack propagation behavior on shales with different inclination based on ultra-fast time resolution method

The layer structures of shale greatly influence its crack propagation behavior. Nevertheless, the correlation between crack extension rates and mechanical parameters has not been well studied, especially, the relationship between the energy release rate and crack propagation rates. Consequently, there are unresolved issues regarding the effects of layer structure on the propagation of cracks in shale. In this paper, a series of three-point compressive loading tests were conducted on seven groups of shale semi-circular bend (SCB) samples with an inclination angle of 0°-90°. The entire fracture process was captured using the ultrafast time-resolution method with a resolution capability of up to 15 picoseconds. In addition, fracture surface information was obtained by a high-precision laser three-dimensional scanning system, and this information was utilized to categorize crack propagation behaviors, such as propagation along weak planes, intermittent penetration, and deflection penetration. Furthermore, a quantitative relationship was established between the energy-release rate and crack propagation rate, based on the first law of thermodynamics and the maximum energy release rate (MERR) criteria proposed by Griffith. The experimental results showed that there is a linear relationship between the energy-release rate and the propagation rate, which meets well with the established relationship. The experimental results indicated that symmetric loading does not result in significant angle localization during crack initiation. This suggests that crack propagation behavior in shale is a reflection of the interplay between energy-release rates and fracture resistance. Finally, this study evaluated the influence of the bedding angle on dissipated energy, and absorbed energy.

Experimental characterization of tensile and compressive translaminar fracture toughness coupling multi-physics measurements

The study of the failure modes of carbon fiber reinforced polymers is essential due to their extensive use in industry. Translaminar failure (at the scale of the laminate) has been studied extensively the main goal being to compute the critical strain energy release rate in mode I of the ply GIC_ply but large variations can be observed between papers. This study investigates this failure mode of a carbon/epoxy laminate, using Compact Tension (CT) and Compact Compression (CC) specimens. The stacking sequence used is [45/-45/(0/90)4]s where 45° plies on the outside efficiently prevented the buckling of the specimen to be observed, as well as plasticity of the matrix. Moreover, this layup is rather similar to real-life industrial stacking sequences. Strains fields and axes displacement were obtained using digital image correlation. Infrared images were used to follow the crack propagation during the loading of the specimen and compared to DIC and X-ray tomography crack length measurements. IR measurements studied from a qualitative point of view were thus shown to be an efficient and reliable method. GIC of the laminate GIC_lam was computed with both the ASTM-E399 and compliance methods, and finally GIC_ply was computed using a rule of mixtures. Secondary damage was detected and its effects on the energy dissipated were quantified using strain fields, X-ray and infrared images. This enabled a more accurate rule of mixtures to be redefined. The failure scenarios of all specimens were eventually exhibited. GIC_ply values in tension were found to be higher than in the literature whereas in compression it was found to be lower than in the literature, due to crack propagation being detected earlier by means of IR measurements.

Experimental and numerical investigation on the failure behavior of multi-spar composite box under bending and shear

Multi-spar composite boxes (MSCB) are common elements in structural design due to their high load capacity in different loading conditions. This paper presents an experimental and numerical investigation of the failure behavior of MSCB subjected to a combined bending-shearing load. Quadratic failure criteria and mixed-mode strain energy release rate criteria are used to predict the onset and propagation of damage at the inter-laminar interfaces of the MSCB, which was implemented into Abaqus/Explicit analysis via a user-defined material subroutine VUMT. At last, a good agreement between tests and numerical prediction was observed.

Mutual dependence of experimental and data analysis features in characterization of fiber‐matrix interface via microdroplets

AbstractThe accurate determination of interfacial strength in composites poses a significant challenge, a critical factor yet often complex due to the multitude of unknowns that affect the microbond (MB) test. This complexity arises not only from different individual parameters, but also from the combined effects of these parameters interdepending with each other. This study presents a thorough analysis of the MB test, carried out through numerous finite element simulations that take into account a wide range of parameters. This was achieved in the context of an experimentally validated reference test. In this study, 624 different numerical simulations were performed, each using a unique set of parameters defined for this investigation. The study demonstrates that even minor modifications to features such as a change in droplet behavior (change in ductility – simulated via different material models), the normalized error can range from −2.5% to 20.6% and −10% to 80%, for peak force () and force‐displacement area (), respectively. The negative percent values indicate lower magnitudes than the reference experimental data, while positive values suggest higher predicted magnitudes. In addition, residual stresses are identified as the second strongest in terms of mutual interaction and a key feature that interacts with other parameters. The results also show that typical comparisons using and are inadequate and misleading, suggesting the use of critical stress and critical energy release rate for more accurate qualitative comparisons about the interface. In this work, the interdependencies between the selected features are investigated with the reasoning based on the interfacial crack propagation and associated dissipative phenomena of the droplet.

Kinking prohibition enhancement of interface crack in artificial periodic structures with local resonators

In this study, the propagation and kinking of an interface crack between two dissimilar artificial periodic structures with local resonators is investigated. By Fourier transform, the dynamic fracture problem is derived as an equation with Wiener–Hopf type. An additional band gap can be created by local resonators. During the dynamic failure, elastic waves will be excited continuously from the crack tip and result in the energy dissipation. Moreover, the energy release ratio which characterizes the fracture resistance is obtained. The meta-arrest property of the artificial periodic structure with local resonators is illustrated. Based on inverse Fourier transform, the displacement field is given to further understand the deformation and oscillation of crack faces. Based on the crack-tip field, the maximum energy release rate criterion is presented to discuss about whether the crack can propagate through kinking out of the interface. Comparing with the model without local resonators, we find that crack kinking can be prohibited in the proposed artificial periodic structures. Finally, finite element simulation and experiment are performed to show the good agreement with the theoretical predictions.

Simulation of fluid driven crack propagation along metal/elastomer interface - Application to the numerical analysis of the rubber cord adhesion inflation test

The Rubber Cord Adhesion Inflation Test (RCAIT) has been proposed as an alternative technique to more standard pull out protocols such as H, T or pull out tests for characterizing the adhesion between cord/cable reinforcement and rubber. During this test, a fluid is injected in between a wire and a rubber cylindrical envelope to provoke the interface separation once a critical pressure is reached. A simple energy balance analysis is used to evaluate the critical strain energy release rate, GC, which drives the crack propagation from measurable quantities. However, some assumptions should be assessed to ensure reliable GC evaluation. Then, a predictive finite elements simulation of the RCAIT is proposed to simulate the fluid driven crack nucleation and propagation process along the rubber cord interface. These results are compared with the ones obtained from the RCAIT simplified analysis.

Microstructural fatigue fracture behavior of glycated cortical bone.

The current study aims to simulate fatigue microdamage accumulation in glycated cortical bone with increased advanced glycation end-products (AGEs) using a phase field fatigue framework. We link the material degradation in the fracture toughness of cortical bone to the high levels of AGEs in this tissue. We simulate fatigue fracture in 2D models of cortical bone microstructure extracted from human tibias. The results present that the mismatch between the critical energy release rate of microstructural features (e.g., osteons and interstitial tissue) can alter crack initiation and propagation patterns. Moreover, the high AGEs content through the increased mismatch ratio can cause the activation or deactivation of bone toughening mechanisms under cyclic loading. The fatigue fracture simulations also show that the lifetime of diabetic cortical bone samples can be dependent on the geometry of microstructural features and the mismatch ratio between the features. Additionally, the results indicate that the trapped cracks in cement lines in the diabetic cortical microstructure can prevent further crack growth under cyclic loading. The present findings show that alterations in the materials heterogeneity of microstructural features can change the fatigue fracture response, lifetime, and fragility of cortical bone with high AGEs contents. Cortical bone models are created from microscopy images taken from the cortical cross-section of human tibias. Increased glycation contents in the cortical bone sample can change the crack growth trajectories.

Strength damage behavior analysis of silicon carbide(SiC) ceramic cylindrical shells under hydrostatic pressure based on the state-based peridynamics

Ceramics are one of the most promising materials for pressure-resistant shells of submersibles due to their exceptional mechanical properties. However, ceramics are brittle materials, and the occurrence of strength damage is inevitably accompanied by the generation and propagation of cracks. A new state-based peridynamic damage model is established, the relation between critical elongation and critical energy release rate for tensile and compression fracture is deduced innovatively, to investigate the strength damage behavior of silicon carbide (SiC) cylindrical shells under hydrostatic pressure. The findings demonstrate that by increasing cylinder thickness, the structural damage pressure can be significantly improved. Moreover, the initial damage zones, are located on the internal surface of shell and induced by the compression fracture, and evenly scattered at 90° around the circular direction. As pressure increases, tensile damage zones emerge on the external surface of cylinder. The failure zones on the interior and exterior walls of the shell propagate along the circumferential direction firstly, then extend toward the middle surface until the damage zones completely penetrate the entire thickness, and the cylinder loses its load-bearing capacity.

Discussion on three forms of coupled criterion for notch fatigue limit prediction: Comparison between point-wise and averaged stress (energy) criteria

In the framework of finite fracture mechanics, two coupled criteria were proposed by Leguillon and Carpinteri, respectively. Leguillon’s criterion uses the point-wise stress criterion, whereas Carpinteri’s criterion uses the averaged stress criterion. Both criteria employ the same incremental energy release rate criterion which can be considered as an averaged energy criterion. Mathematically, the averaged energy criterion can be transformed into an equivalent point-wise criterion. In this paper, a new coupled criterion based on the point-wise stress and energy criteria was proposed. The proposed criterion is equivalent to Carpinteri’s criterion when predicting notch fatigue limits. All the three forms of coupled criteria were checked and compared by a large number of experimental results including V-shaped and central hole specimens. When performing the coupled criteria, power functions derived from finite element analysis were used to express the energy release rate and notch stress distributions. The effect of notch size on the crack extension lengths were investigated.

Experimental and computational models for simulating the oral breakdown of food due to the interaction with molar teeth during the first bite

The first bite involves the structural breakdown of foods due to the interaction with teeth and is a crucial process in oral processing. Although in vitro experiments are useful in predicting the oral response of food, they do not facilitate a mechanistic understanding of the relationship between the intrinsic food mechanical properties and the food behaviour in the oral cavity. Computer simulations, on the other hand, allow for such links to be established, offering a promising design alternative that will reduce the need for time consuming and costly in vivo and in vitro trials. Developing virtual models of ductile fracture in soft materials, such as food, with random and non-predefined crack morphology imposes many challenges. One of the most important is to derive results that do not depend on numerical parameters, such as Finite Element (FE) mesh density, but only physical constants obtained through independent standard mechanical tests, such as fracture strain and/or critical energy release rate. We demonstrate here that this challenge can be overcome if a non-local damage approach is used within the FE framework. We develop a first bite FE modelling methodology that provides mesh independent results which are also in agreement with physical first bite experiments performed on chocolate. The model accounts for key features found in chocolate and a wide range of compliant media, such as rate dependent plasticity and pressure dependent fracture initiation strain. As a result, our computational methodology can prove valuable in studying food structure-function relationships that are essential in product development.

Experimental study on fracture damage and seismic performance of loose through-tenon joints in ancient timber structures

A looseness is typical damage of mortise-tenon joints in ancient timber structures. Brittle fractures of loose joints are likely to occur, leading to joint failure during earthquakes. This study conducts pseudo-static tests on three groups of full-scaled through-tenon joints to examine the fracture damage and seismic behavior of the loose mortise-tenon joints and determines fracture damage modes of through-tenon joints with different looseness. It uses the acoustic emission method to measure the ring count on the tenon surface, along with each joint's critical load and critical energy release rate and then analyzes the fracture damage performance of different tenon joints. In addition, this research investigates the hysteretic and skeleton curve, stiffness degradation curve, and tenon pulling quantity of the joint under various fracture damage states. The results showed that the fracture failure mode of the through-tenon joint is a fracture in the variable cross-section and along the local tenon neck. During the loading process, the critical energy release rate initially increases and then decreases as the looseness grows. In addition, with the increase of crack mouth opening displacement (CMOD) and crack length, the bending moment of the joint firstly increases and then decreases. When the variable cross-section breaks and the tenon neck partially cracks, the joints' bending moment and stiffness reduce with increasing looseness. With the increase in local embedment compression in the lower side of the beam end and the mortise, the amount of tenon pull-out of loose joints decreases under positive and negative loading.

Enhanced interlaminar mechanical behavior of advanced fiber metal laminates via nano Al2O3‐IPN formation and surface pre‐treatments

AbstractThe inferior delamination resistance and out‐of‐plane performance of fiber metal laminates (FMLs) are of serious concerns. This work employs two modification methods, namely metal surface's chemical pre‐treatment and nano Al2O3 embedded interpenetrating polymer network (IPN) formation for improving the delamination resistance of aluminum and glass fiber‐reinforced polymer (GFRP) composite‐based FMLs. The synergetic effect of the two modification techniques resulted in high degrees of improvement in delamination resistance that were ~28% for critical strain energy release rate during mode‐I interlaminar fracture toughness (ILFT), that is (GIC) and ~37% for GIIC. Simultaneously, the flexural strength, tensile strength, and interlaminar shear strength improved by ~23%, ~17%, and ~24%, respectively. Scanning electron microscopy, atomic force microscopy, and surface energy measurement studies showed that the chemical pre‐treatment significantly influenced the surface morphology, surface roughness, and surface energy responses of aluminum, respectively. Fractographic study validated the effect of modification methods on the failure behavior under various testing modes.

On the mechanistic driving force for short fatigue crack path

The growth of fatigue cracks at the microstructural level is significant for many engineering industries. The multifarious nature of crack propagation at microstructure length scales necessitates the use of advanced modelling techniques to predict fatigue life accurately. A key contributor to this is the path of the crack, which also remains challenging to predict; the maximum slip criterion has been used widely in the literature but is not fully adequate. This paper tests the hypothesis that for short crystallographic cracks, there is some other factor responsible for guiding their extension on a particular plane. With this, using a crystal plasticity finite element modelling framework, two new energy-based methods are developed: a microstructure-sensitive maximum energy release rate criterion, and a maximum normal stored energy density criterion. Results demonstrate, for the two cases studied, both methods offer a significant improvement over the maximum slip criterion when applied to real microstructures. In particular, the maximum normal stored energy method gives closest agreement with experiments, while maximum energy release rate offers new insights into a mechanism for crack bifurcation.

Use of Random Forest to Predict Intermediate Temperature SCB Jc Parameter of Long-Term Aged Asphalt Mixtures

With the growing use of reclaimed asphalt pavement (RAP), recycled asphalt shingles (RAS), and other innovative additives in asphalt mixtures, there are concerns about the accuracy of Superpave volumetric-based mixture design. Performance tests in mix design procedures are needed to ensure desirable pavement performance. The Louisiana Department of Transportation and Development (LADOTD) has adopted the semi-circular bend (SCB) critical strain energy release rate parameter, Jc, to evaluate the cracking resistance of asphalt mixtures. To address practical shortcomings, this study aims to develop a predictive model to estimate SCB Jc at intermediate temperature of long-term aged (LTA) asphalt specimens from volumetric properties of plant-produced asphalt mixtures, and rheological and chemical properties of unaged asphalt binder by using a machine-learning model, random forest. Asphalt mixture SCB test and asphalt binder rheological and chemical properties tests were conducted. Stepwise correlation analysis was used to determine the most influential variables to SCB Jc. Random forest model was optimized using grid search with hyperparameter combinations. Results show that the developed random forest model was able to predict the SCB Jc fracture parameter of asphalt mixtures and a good agreement was observed between predicted and measured SCB Jc values. Variable importance scores based on mean decrease in impurity (MDI) showed that the Δ Tc had the most influence on SCB Jc prediction accuracy, and other inputs such as coarse aggregate type, LTA days, Fourier transform infrared spectroscopy test carbonyl index, and linear amplitude sweep test ALas also had significant effects on SCB Jc.

Cracking direction in graphene under mixed mode loading

Crack branching in graphene under complex stresses is investigated by molecular dynamics simulations and boundary-layer models. Using the maximum energy release rate (MERR) criterion, an analogy of Wulff curve is plotted considering the anisotropic fracture toughness of hexagonal graphene, which shows the direction of crack kinking (local bump on the curve) is consistent with that of the weak fracture toughness (along zigzag edge). The angle of crack kinking prefers 0°/30°/60°, rather than the angle predicted by maximum circumferential stress criterion. The T-stress along crack front, obtained by the over-deterministic method, can indicate the possibility of kink by its transformation between positive and negative, especially for zigzag cracks. This study incorporates Wulff-like curve and MERR criterion to provide an accurate prediction of nanocrack paths in graphene.

On the mixed mode I/II translaminar fracture of plain-weave carbon, E-glass and Kevlar reinforced laminated composites

The main aim of this study is to investigate the influence of long fiber types on the translaminar fracture behvior of epoxy-based composites subjected to pure mode I, mixed mode I/II and pure mode II using a combined experimental study and finite element (FE) analysis. Compact tension shear (CTS) test configuration was used to determine the critical strain energy release rate (CSERR) of the laminated composites reinforced with three types of high-performance fibers: Carbon, E-glass and Kevlar fiber. We believe that this is the first published report on the full combination of mode I, mixed mode I/II and mode II translaminar fracture toughness of laminated composites reinforced by three types of fiber. The translaminar fracture envelopes of the tested materials were illustrated. The results revealed that the translaminar CSERR of the composite systems is strongly dependent on the reinforcement type and the loading condition. The mode I translaminar CSERR of E-glass, Carbon and Kevlar fiber reinforced composites are equal to 16.87, 13.52, and 18.29 kJ/m2, respectively. Besides, under mode II loading condition, the translaminar CSERR of the laminated composites reinforced by E-glass, Carbon and Kevlar is obtained as 15.21, 7.82, and 8.45 kJ/m2, respectively. Fractographic analysis manifested that fiber pull-out clustering, fiber splitting, fiber breakage and matrix cracking are the main energy dissipating mechanisms happened on the fracture surface of the laminated composites.

Mode I fatigue threshold energy assessment of a polyurethane adhesive: effects of temperature and Paris law relation

ABSTRACT In this study, the effect of temperature (below and above Tg) on the rate of crack growth and on the fatigue threshold energy release rate of a polyurethane (PU) adhesive is analysed. The effect on the results of the Paris law relation used is also investigated. Tests were performed under a displacement-control strategy and at different temperatures. Out of the experimental data, the threshold energy release rate was determined as a function of temperature, something which up until now has been much more common for adhesive systems other than polyurethane. Results showed that the threshold energy release rate diminishes with increasing temperature, while the crack growth rate increases for a given strain energy release rate. The ratio between the threshold energy release rate and critical strain energy release rate remained constant for tests above the Tg, indicating that fatigue tests need only be performed at one temperature when above the Tg at least for the range of temperatures considered in this study and for the adhesive tested. A Paris law relation taking into account the effect of R-ratio during the displacement-control fatigue tests proved effective in unifying results at different temperatures.

A phase-field-based multi-physics coupling numerical method and its application in soil–water inrush accident of shield tunnel

The mixed-mode cracking of brittle materials in multi-physics coupling problems has always been a research hotspot. In this study, a phase-field-based multi-physics coupling numerical method is established to simulate the mixed-mode cracking of brittle materials under fluid–structure coupling. The proposed method is available to simulate the mixed-mode cracks of arbitrary topology, and the cracking behavior is governed by a crack evolution equation. To ensure consistency of the crack evolution equation, the crack-driving force is innovatively unified with the critical energy release rate. The phase-field-based multi-physics coupling numerical method is implemented in the finite element framework. Then, the proposed method is applied to simulate the structural discontinuous crack damage (SDCD) induced by soil–water inrush in shield tunnel under complicated geological conditions with confined water. Compared with the field inspection and monitoring, the numerical model performs well in simulating the SDCD and deformation of tunnel lining. It is also found that the soil–water inrush has a significant effect on the distribution of water-earth pressure acting on the tunnel lining, and the internal force of tunnel lining is redistributed during the evolution of SDCD.

Mode-II progressive fracture of sawn timber and timber-adhesive bond: experimental evaluation of end notched flexure (ENF) testing using DIC

The end-notched flexure (ENF) testing technique has been used in this paper to investigate the Mode II fracture behaviour of sawn timber and timber-adhesive bonds. Mode-II strain energy release rates were obtained by using classical data reduction schemes based on actual crack lengths captured using digital image correlation (DIC) technique. The compliance-based beam method (CBBM), which does not require the actual crack length measurements, was also evaluated for its suitability for Mode-II fracture of timber. Utilizing forward shear slip measurement from DIC at every millimetre of crack length, a simple yet effective and innovative technique to identify crack tip opening and to monitor crack length has been proposed herein. Three different initial notch widths were used in the current study to examine their suitability in producing reliable crack initiation and consistent bond delamination in solid timber and glued timber. The strain energy release rates calculated from the actual crack and equivalent crack length values showed similar trends in fracture resistance curves, which are commonly known as R curves, but the initial strain energy release rate (GII0) and the critical strain energy rate (GIIC) obtained from the two methods showed some discrepancies. Equivalent crack method CBBM was found to be inadequate in determining a consistent initial strain energy release rate despite producing a stable and steady fracture energy after crack initiation. Experimental results showed that Mode-II timber-adhesive bond line fracture is relatively more brittle than timber fracture, and the average critical strain energy release rate of timber-adhesive bond (GIIc) was 14% greater than that of sawn timber. Based on experimental observations, specific test criteria for ENF testing of timber structures are proposed in this paper.

Edge chipping damage in lithium silicate glass-ceramics induced by conventional and ultrasonic vibration-assisted diamond machining.

Diamond machining of lithium silicate glass-ceramics (LS) induces extensive edge chipping damage, detrimentally affecting LS restoration functionality and long-term performance. This study approached novel ultrasonic vibration-assisted machining of pre-crystallized and crystallized LS materials to investigate induced edge chipping damage in comparison with conventional machining. The vibration-assisted diamond machining was conducted using a five-axis ultrasonic high-speed grinding/machining machine at different vibration amplitudes while conventional machining was performed using the same machine without vibration assistance. LS microstructural characterization and phase development were performed using scanning electron microscopy (SEM) and x-ray diffraction (XRD) techniques. Machining-induced edge chipping depths, areas and morphology were also characterized using the SEM and Java-based imaging software. All machining-induced edge chipping damages resulted from brittle fractures. The damage scales, however, depended on the material microstructures; mechanical properties associated with the fracture toughness, critical strain energy release rates, brittleness indices, and machinability indices; and ultrasonic vibration amplitudes. Pre-crystallized LS with more glass matrix and lithium metasilicate crystals yielded respective 1.8 and 1.6 times greater damage depths and specific damage areas than crystallized LS with less glass matrix and tri-crystal phases in conventional machining. Ultrasonic machining at optimized amplitudes diminished such damages by over 50 % in pre-crystallized LS and up to 13 % in crystallized LS. This research highlights that ultrasonic vibration assistance at optimized conditions may advance current dental CAD/CAM machining techniques by significant suppression of edge chipping damage in pre-crystallized LS.