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This research is aimed at investigating the influence of the coal height ratio on the mechanical properties and damage behavior of rock-coal-rock combined samples (RCRCS) under coupled static and dynamic loads. For this purpose, a uniaxial cyclic dynamic loading experiment with four different coal height ratios of RCRCS was conducted. Mechanical properties, failure modes, and wave velocity evolution of RCRCS were analyzed; the process of rock burst under coupled static and dynamic loads in rock-coal-rock combined structure was discussed. The following research results are obtained. (1) The peak strength of RCRCS under static and dynamic load decreases with the increasing coal height ratio as an inverse proportional function. (2) The loading and unloading modulus remains consistent for the same levels of dynamic load; the coal height ratio of 40% may be the limit for the stable value of modulus. (3) The increase of the coal height in RCRCS leads to a gradual increase of the energy release rate; the cracks develop preferentially in coal and then extend to rock sample. The distribution of AE events and damage is consistent with the distribution of passive wave velocity. The research results provide important scientific bases for the guidance of early warning of rock burst.

Growing use of recycled asphalt materials in asphalt pavement means the current volumetric-based Superpave mixture design may not address durability concerns arising from replacement of a proportion of virgin binder with recycled ones. To address this limitation, performance-based testing is introduced to supplement conventional volumetric mixture design in assessing cracking performance of asphalt mixtures. Louisiana Department of Transportation and Development’s Specifications for Roads and Bridges specify a criterion for the critical strain energy release rate, Jc, obtained from semi-circular bend (SCB) test as a complement of current practice to evaluate cracking resistance of asphalt mixtures. Quality control/assurance practices, however, require SCB samples to be long-term aged for five days at 85°C, which is a time-consuming process. Therefore, it is beneficial to be able to estimate SCB Jc for long-term aged asphalt mixtures based on SCB Jc measured from plant-produced asphalt mixtures. Asphalt mixture aging is complex, and various variables are involved in the aging process, including volumetric properties of asphalt mixture and chemical/rheological characteristics of asphalt binder. With the capability of artificial neural network (ANN) to address complex relationships between input and output variables, this study aims to predict the fracture parameter, SCB Jc, of asphalt mixtures using ANN. A total of 34 asphalt mixtures were selected for this study. SCB fracture test and asphalt binder tests for chemical and rheological characterization were conducted. Stepwise regression analysis was used to determine the significant parameters in the correlation with SCB Jc. With determined significant parameters, ANN using the gradient descent backpropagation approach was then applied to develop and validate the predictive model. It was shown that the developed ANN model was able to predict the fracture parameter, SCB Jc, of asphalt mixtures more accurately than linear and non-linear regression models.

Double-cantilever beams (DCBs) are widely used to study mode-I fracture behavior and to measure mode-I fracture toughness under quasi-static loads. Recently, the authors have developed analytical solutions for DCBs under dynamic loads with consideration of structural vibration and wave propagation. There are two methods of beam-theory-based data reduction to determine the energy release rate: (i) using an effective built-in boundary condition at the crack tip, and (ii) employing an elastic foundation to model the uncracked interface of the DCB. In this letter, analytical corrections for a crack-tip rotation of DCBs under quasi-static and dynamic loads are presented, afforded by combining both these data-reduction methods and the authors’ recent analytical solutions for each. Convenient and easy-to-use analytical corrections for DCB tests are obtained, which avoid the complexity and difficulty of the elastic foundation approach, and the need for multiple experimental measurements of DCB compliance and crack length. The corrections are, to the best of the authors’ knowledge, completely new. Verification cases based on numerical simulation are presented to demonstrate the utility of the corrections.

Non-conventional fracture test geometries such as single cantilever bending, clamped beam bending and clamped wire bending have been developed over the years to suit the needs of micro- and nano-scale testing. The same geometries can also be used at the macro-scale if testing standards are well established. Development of length scale compatible geometries helps the materials engineer to seamlessly extract material properties across multiple length scales. This article proposes the crack driving force (or energy release rate G) criteria for the above three geometries. These geometries have found widespread use at the micro-scale and can be adapted to the macro-scale. Use of a global energy-based criterion instead of the local stress-based criteria (stress intensity factor K) has its own advantages, especially in multi-phase materials and interface-dominated structures which display an R-curve. Aspects of crack stability even under load control arising because of the geometric factors, especially the beam or wire aspect ratio, are discussed in this context. Validation of the compliance approach is carried out by comparing it to the J-integral extracted directly for a linear elastic material using extended finite element modeling and also using the analytical formulation for a double-cantilever beam specimen. Experimental evidence of the validity of the solutions in determining the fracture energy of a linear elastic brittle material, PMMA, as a homogeneous model system is shown.

Asphalt overlay or concrete overlay on existing pavements is a common strategy for pavement maintenance. Interlayer bonding performance between asphalt and concrete layers is a critical concern in achieving optimal long-term structural performance due to the possible cracking along the interface. In this study, bonding behaviors of asphalt concrete interface were characterized by employing mode I fracture tests conducted at −10 and 25°C, respectively. Two typical interface conditions were manually prepared. A tack coat material was applied on the interface with four distinct rates: 0.1, 0.2, 0.3, and 0.4 L/m2. Parameters including fracture strength, stress intensity factor (KIC), facture energy (GF), and energy release rate (J integral) were selected to evaluate the fracture performance. Results showed that optimum tack coat rates were 0.1 and 0.3 L/m2 for specimens with unmilled and milled surfaces. At the optimum tack coat rates, KIC and GF increased with the increase of interface roughness at −10°C, while, at 25°C, J integral of specimens with unmilled interface was larger than that of specimens with milled interface at the optimum tack coat rates. Analysis of variance (ANOVA) was conducted to evaluate the significance of the factors on the fracture loads and found that surface roughness is significant at −10°C and becomes nonsignificant at 25°C. Temperature and tack coat rate were significant factors considering a given interface.

Air plasma sprayed thermal barrier coatings (APS-TBCs) saw their wide application in high-temperature-related cutting-edge fields. The lamellar structure of APS-TBCs provides a significant advantage on thermal insulation. However, short life span is a major headache for APS-TBCs. This is highly related to the property changes and passive behaviors of the coatings during thermal service. Herein, a finite element model was developed to investigate the dynamic stiffening and substrate constraint on total spallation process. Results show that the stiffening accelerates the crack propagation of APS-TBCs. The driving force for crack propagation, which is characterized by strain energy release rate (SERR), is significantly enlarged. Consequently, the crack starts to propagate when the SERR exceeds the fracture toughness. In addition, the changing trends of SERR and crack propagation features are highly associated with temperatures. A higher temperature corresponds to more significant effect of stiffening on substrate constraint. In brief, temperature-dependent stiffening significantly aggravates the substrate constraint effect on APS-TBCs, which is one of the major causes for the spallation. Given that, lowering stiffening degree is essential to maintain high strain tolerance, and to further extend the life span of APS-TBCs. This understanding contributes to the development of advanced TBCs in future applications.

This paper aims to investigate the vibration characteristics of a geared rotor-bearing system (GRS) with a shaft crack. Firstly, a lateral–torsional coupling model is proposed. In the dynamic model, the rotating shafts of the GRS are modeled as Timoshenko beams; the meshing gear is modeled as a pair of rigid disks connected by a spring–damper with time-varying mesh stiffness; the opening and closing behavior of the crack is analyzed based on strain energy release rate theory and stress intensity factor theory. Then, this dynamic model is utilized to analyze the vibration characteristic of the GRS with a shaft crack. The results show that the most significant effect of a crack on the GRS is amplitude modulation of vibration signals. Not all the natural frequencies of the GRS can be affected by the crack. In addition, the feature frequencies of the GRS will also show some unique characteristics. This study provides a theoretical basis for the analysis and diagnosis of a GRS with a shaft crack.

A comparative study of electromagnetic radiation (EMR) detection from Soft PZT (SP 5A) and Hard (SP 4) PZT under impact at high temperatures has been presented. EMR is detected by applying impact load on the samples at temperatures varying from 288 to 514 K. With increase in temperature, thermal energy increases imparting molecular vibrations which reduce the net effective polarization and this in turn results in the low amplitude of EMR signals. EMR voltage amplitude and EMR energy release rate show an overall decreasing pattern with increase in temperature. Experiments conducted on samples poled at different d.c. poling fields exhibit strong dependence of EMR signals on d.c. poling field. EMR voltage amplitude is found to increase with increase in the strength of d.c. poling field. This study pertaining to the effect of poling as well as high temperatures on the EMR signal variation will be an aid towards the development of wireless sensing technique.

The adhesive bonding strength of the membrane layers between the asphalt concrete surface layers and the decks of steel bridges has a strong influence on the fatigue life of orthotropic steel deck bridges (OSDBs). The interfacial properties between the membrane and the layers bonded to it have not been extensively studied in the current orthotropic steel deck bridge system. For the adequate characterisation of the adhesive-bonding strength of various membranes and surrounding materials on OSDBs and for the collection of the necessary parameters for finite element model, details of the membrane adhesion test (MAT) are introduced and simulated by using the adhesive traction-separation interface element which was developed in a companion paper to this contribution (Liu, X., Kasbergen, C., Li, J., & Scarpas, A. (2019). Modelling of membrane bonding response: part 1 development of an adhesive contact interface element. International Journal of Pavement Engineering). Parametric studies of the adhesive contact element utilised for modelling the membrane bonding layer in the MAT test have been performed on the basis of the combination of different critical strain energy release rates and the characteristic opening length in the constitutive model. Comparison of membrane deformation profiles and the in-time debonding force distribution between experimental observations and finite element simulations have been presented.

Delamination is one of the major failure mechanisms for composites and traditionally the simulation requires high expertise in fracture mechanics and dedicated knowledge of the Finite Element Analysis (FEA) tool. Yet, the simulation cycle times are high. Geometrically nonlinear analysis approach, which is based on the Reissner-Mindlin-Von K´arm´an type shell facet model, has been implemented into the Elmer FE solver. Altair ESAComp software runs the Elmer Solver in the background. A post-processing capability, which enables the prediction of the delamination onset from the FEA output, has been implemented into the AltairESAComp software. A Virtual Crack Closure Technique (VCCT) specifically developed for shell elements defining the Strain Energy Release Rate (SERR) related to the different delamination modes at the crack front is used. The onset of delamination is predicted using the relevant delamination criteria that utilize the SERR data and material allowables in the form of fracture toughness. The modeling methodology is presented for laminates including initial through-the-width delamination. Examples include delamination in the solid laminate and debonding of the skin laminate in the sandwich structure. Rather coarse FE mesh has proved to yield good results when compared to typical approaches that utilize the standard VCCT or Cohesive Zone Elements.

A new method for obtaining energy release rate by the Double Cantilever Beam test for angle-ply laminates is proposed. Two different sequences, symmetric and anti-symmetric, have been studied. The fact that the layers are oriented at different angles and the residual stresses, causes the existence of mixed mode fracture. The analytical model presented, based on the complementary energy of a laminated beam, is an extension of a previous model for unidirectional laminates and includes hygrothermal effects. Experimental results of the energy release rate obtained by means of the area method agree with those determined by the proposed approach.

This work in on the development of an ordinary differential equation (ODE) model coupled with statistical methods for the prediction of fracture toughness of a magnetostrictive, piezoelectric smart self-sensing Fiber Reinforced Polymer (FRP) composite. The smart composite with sensing properties encompasses Terfenol-D alloy nanoparticles and Single Walled Carbon NanoTubes (SWCNT). To explore various configurations the of nanoparticle constituents’ effect on fracture toughness within the FRP composite, the ODE model developed within a finite element analysis (FEA) environment is considered to attain fracture observations across the solution space. The acquired FEA data is then used to feed the machine-learning (ML) algorithms to obtain composite fracture toughness predictions. A comparison and development of artificial neural networks (ANN), decision trees and support vector machines (SVM) models for FRP smart self-sensing composite fracture toughness prediction is done. Qualitative results stating if the sample has fractured or not and quantitative data giving the fracture toughness and strain energy release rate for the smart self-sensing FRP composites is attained. A comparison of all predictions from the developed models for both fracture toughness is corroborated with literature data.

As a man-made engineering hazard, it is widely accepted that the rockbursts are the result of energy release. Previous studies have examined the unloading of in-situ stress resulting from deep tunnel excavation as a quasi-static process but the transient stress variation during excavation has received less attention. This research discusses rockbursts that happened during the construction of a diversion tunnel at Jinping II hydropower station. The brittle-ductile-plastic (BDP) transition property of Jinping marble was numerically described by the Hoek-Brown strength criterion, and the dynamic energy release process derived from the transient unloading of in-situ stress was studied using an index, local energy release rate. Studies have shown that, due to transient unloading, the strain energy of the surrounding rock mass goes through a dynamic process of decreasing at first, increasing second, then reducing before finally stabilizing. The first decrease of strain energy results from elastic unloading waves and does not cause brittle failure in rock masses, which is consistent with the elastic condition but the secondary reduction of strain energy is because the accumulated strain energy in rock masses exceeds the storage limit, which will inevitably trigger the brittle failure in the rock mass. Thus, the shorter the distance to the tunnel wall the bigger and more intense the energy release. Finally, a relationship between the average value of the local energy release rate and the rockburst intensity was established to assess the risk of rockburst induced by the blasting excavation of a deep tunnel.

In some circumstances, the standard formulation of the virtual crack closure technique (VCCT) may yield negative values of the modal contributions to the energy release rate. To avoid such physically meaningless results, a revised formulation is available. However, the revised VCCT does not take into account possible interpenetration of the crack faces, that may be predicted by the linearly elastic solution. The present work extends the revised VCCT formulation by introducing suitable contact constraints to prevent local interpenetration of the crack-tip nodes. By considering open vs. interpenetrated cracks and tensile vs. compressive crack-tip forces, four cases emerge. For each case, a suitable two-step crack closure process is outlined with the two steps respectively corresponding to fracture modes II and I. The contact pressure force, if present, is evaluated and accounted for in the computation of the crack closure work. As a result, novel analytical expressions are derived for the modal contributions to the energy release rate accounting for contact and prevented interpenetration.

Semicircular Bending Test (SCB) is a commonly used procedure to evaluate the cracking resistance of Asphalt Concrete (AC). Ho wever, all the current procedures as described by ASTM as well as other agencies, a crack is initiated as a ‘notch’ in the vertical plane and the loading and crack propagation occurs in the horizontal direction. However, in pavements, most of the cracks in AC initiate in the horizontal plane, which propagates along the vertical direction. Therefore, there is a difference in loading and crack propagation direction between the test procedure and real pavement. This study evaluated the fracture resistance of AC in a vertical direction and compared it with the horizontal direction. Also, it is necessary to know how different material properties affect the fracture resistance of asphalt concrete. This study evaluated the fracture resistance of “X” mixes using the Semicircular Bending (SCB) test. The effect of binder grade, amount, and other mix parameters on the ultimate load, deformation to ultimate load, strain energy, and critical strain energy release rate (J-integral) was evaluated. It is observed that mix with soft binder allows a higher level of deformation before the initiation of cracking. Effective binder content in the mix affects J-integral value. The ultimate or maximum load in the SCB test shows a good correlation with the indirect tensile strength of the mix. The higher the Indirect Tensile Strength (ITS) value, the higher the SCB strength. Displacement and strain energy showed clear anisotropic behavior. Higher values for lateral cores are obtained. J-integral showed some sort of anisotropy, however further studies with more mixes is recommended. 4 out of 7 mixes showed higher J-integral value for horizontal cores, 3 mixes showed the same value in both directions.

In this paper, the evaluation procedures of the natural frequency and the stress intensity factor in the opening mode are established for the Euler–Bernoulli cracked beam by using (a) a technique in the framework of the finite element method, (b) a group method of data handling (GMDH), and (c) the software ABAQUS software. In the first one, the stiffness and mass matrices of the beam are enriched according to the depth and location of the crack for the determination of the natural frequency. A discrete spring model is used to simulate the crack in the structure based on the energy release rate. The continuity conditions in a cracked element are applied to connect two sub-elements of both sides of the crack. In the second method, the natural frequency and the stress intensity factor are determined using the GMDH algorithm. Design of experiments technique is employed to create an optimum arrangement for the application in the GMDH neural network. A few case studies are examined to investigate the results of the analysis, in addition, to identify the priority and the comparison of the three methods. The procedure of the analysis explains the advantages and limitations of the finite element-based technique, the GMDH method, and ABAQUS.

Based on the theory of linear elastic fracture mechanics, the relationships between material constants c3, c4 required in Abaqus and constants C, m in Paris formula are derived. Then extended finite element method (XFEM) of Abaqus software is used to is used to predict the crack propagation path and life of the plate with center inclined through crack and typical stiffened wing spar with initial crack under the constant amplitude fatigue load. The results show that the predicted crack propagation path is in good agreement with the experimental results, and the crack propagation life error is less than 6.3%. It also shows that this method can accurately predict the fatigue crack growth path and life of two-dimensional and three-dimensional complex structures under constant amplitude loads. This study can provide an effective way for damage tolerance analysis of structures and has certain engineering application value.

This study investigated, experimentally and numerically, the fracturing behavior of thermoset polymer structures featuring cracks and sharp u-notches. It is shown that, even for cases in which the sharpness of the notch would suggest otherwise, the failure behavior of cracked and pre-notched specimens is substantially different, the failure loads of the former configuration being about three times lower than the latter one. To capture this interesting behavior a two-scale cohesive model is proposed. The model is in excellent agreement with the experimental data and its predictions allow to conclude that (a) residual plastic stresses cannot explain the very high failure loads of notched structures; (b) the strength of the polymer at the microscale can be from six to ten times larger than the values measured from conventional tests whereas the fracture energy at the microscale can be about forty times lower; (c) the pre-notched specimens investigated in this work failed when the stress at the tip reached the microscale strength whereas the cracked specimens failed when the energy release rate reached the total fracture energy of the material. The foregoing considerations are of utmost importance for the design of microelectronic devices or polymer matrix composites for which the main damage mechanisms are governed by the strength and cohesive behavior at the microscale., 35 pages, 12 figures, 2 tables

Lifetime is a basic support for the thermal insulation function of thermal barrier coatings (TBCs). Therefore, extending the life span is essential to develop next-generation TBCs. For this objective, the columnar structure formed by vertical cracks appears to make sense. However, the underlying mechanism is still unclear. This work scrutinizes the influence of periodic vertical cracks on cracking behavior in order to tailor high strain tolerant TBCs. A finite element model was evolved to explore the crack behavior influenced by thermal mismatch strain between substrate and coating. The virtual crack closure technique (VCCT) was used to describe the propagation of crack under load. It is found clearly that the space between two vertical cracks (short for SVC) along the in-plane direction has a noteworthy influence on the strain tolerance of TBCs. Results indicate that the strain energy release rate (SERR) and stresses at the pre-crack tip increase continuously with the increase of the SVC, suggesting that the driving force for cracks is increasing. The crack is not propagated when the SVC is very small, whereas the crack grows continuously with the increase of the SVC. The growth of a crack can be prevented by reducing the SVC. A critical value for the SVC was found. When the SVC is less than the critical value, the SERR can be dramatically reduced. Thus, the SVC of periodic cracks can be tailored to obtain TBCs with high strain tolerance.

An experimental correlation showing flipchip packaged larger dies more susceptible to corner delamination is, first, established in this work. Chamfer structures have been inserted into the architecture of traditional orthogonal crackstop designs with the aim to alleviate the accumulation of strains present in the corners of larger dies. Finite element modeling (FEM) was employed to uncover the optimum chamfer structure size that minimizes both the chamfer space usage as well as chip package interaction (CPI) related risks. Die size was shown to have quantifiable impact on the corner strain. The effect of die size was shown to be enhanced with lower underfill modulus. The effect of changing the crackstop corner chamfer structure size on both corner strain and strain energy release rate was studied. While varying the crackstop corner chamfer structure size had minimal effect on strain, it did have a significant effect on the strain energy release rate. It was observed that chamfer structure significantly reduces the strain energy release rate at the edge of the die near the corner. It has been determined that the optimum location for the support structure triangle vertex is to be situated at the point where the peeling strain switches from compressive to tensile at the corner square. The effectiveness of corner chamfer support structures in reducing CPI risk at the optical attach cavity used for lateral optical fiber attach was evaluated. The simulations have determined that inclusion of crackstop corner support structures at the newly created internal cavity corners of the die result in a reduction of the average corner strain by 33% at the external corner and 21% at the internal corner of the optical cavity.

The subject of controlled interface fracture is gaining considerable attention and goes hand-in-hand with ‘smart’ and ‘on-demand’ material designs and ‘metamaterial’ approach. To further unlock the potential behind geometrical enhancements, an effective crack tip forces approach is used to derive the strain energy release rate and the critical fracture onset force for layered and laminated materials of arbitrary shapes. The analytical formulation allows prediction of delamination onset forces as a function of laminate cross-section geometry at the crack front. Here, we focus on width-varying geometries with the choice motivated by the recent use of composite, patch-alike, multilayer material systems and repairs. The theoretical model is successfully verified by comparison with experimental data from width-varying carbon fibre laminates and numerical results. The proposed theoretical and experimental approaches are beneficial for predicting and controlling fracture and can prove useful to motivate new designs for multilayer and laminated material by indicating the relationship between the material geometry and the delamination onset force.

In this paper a theoretical analysis of crack initiation and propagation conditions in a bonded specimen loaded under pure mode II condition is proposed. The end-loaded-split (ELS) test response is evaluated using a semi-analytical model where the adherends are modeled as two deformable Timoshenko beams and considering non-linear behaviour of the adhesive. Bi-linear elastic-plastic, elastic-softening and trapezoidal adhesive layer shear behaviours (ALSBs) have been implemented and studied. From the results we observed that the load–displacement curve does not permit accurate evaluation of the adhesive layer shear behaviour. An alternative procedure consisting of analyzing the strain energy release rate versus shear displacement at the crack tip is proposed for data reduction of ELS test results.

Robust and efficient predictions of buckling-driven delamination propagation , enabled by a novel analytical modelling approach, are presented. The model considers full mechanical coupling (extension-shear, extension-bend, extension-twist/shear-bend and bend-twist), contact and mode-mixity and thus significantly enhances the capabilities of current analytical approaches. A problem description in cylindrical coordinates enables the evaluation of the energy release rate along the delamination boundary. The model uses an energy formalism to determine the post-buckling deformation and a crack-tip element analysis employing force and moment resultants acting on the delamination boundary to determine the energy release rate. Composite panels with circular thin-film delaminations and various multi-directional stacking sequences are investigated for in-plane compressive loading . Predictions of applied strains causing delamination growth , i.e. threshold strain, show good agreement with published experimental data and 3D finite element analysis . A parametric study varying the ratio of delamination size to depth is performed. Based on the findings obtained, governing deformation characteristics of buckling-driven delamination growth are identified and insight into damage tolerant design of composite laminates is obtained, which is of particular interest for compression after impact (CAI) strength of composite structures.

Adhesively bonding has been increasingly used for numerous industrial applications to meet the high demand for lightweight and safer structures. Debonding of adhesively bonded joints is a typical mixed mode failure process. It is highly depended on the interactional effects of material properties and geometric definitions of the constituents, which is very complicated. The existing studies in identifying fracture modes of joints based on either experiments or finite element analysis are often prohibitively time and computational expensive. This paper proposed an innovate method by combining Finite Element Analysis (FEA), Latin Hypercube Sampling (LHS) and Genetic Programming (GP) to understand the effect of the physical attributes on the fracture modes of adhesively single lap joints. A dataset of 150 adhesive joint samples has been generated using LHS, including different combinations of adherend and adhesive’s material properties and thicknesses. The mixed mode ratios of the 150 samples are calculated using Strain Energy Release Rate (SERR) outputs embedded in Linear Elastic Fracture Mechanics (LEFM), which has been validated by experimental tests. Finally, a GP model is developed and trained to provide an extracted explicit expression used for evaluating the early-state failure modes of the adhesively bonded joints against the design variables.

For structural integrity assessment, when dealing with problems such as uncertainty quantification, real-time structural health monitoring, and reliability analysis, fracture mechanics parameters, e.g. the energy release rate, are required to be evaluated for a large amount of crack configurations. Using finite element (FE) models directly for this task is generally time consuming. This work follows a machine learning-based method aiming at a fast estimation of the fracture mechanics parameters. Towards this end, the offline data are first created by performing the FE simulations for a set of crack configurations from which these parameters can be extracted and then a machine learning algorithm (e.g. artificial neural network (ANN)) is used to build a surrogate model with the obtained data. Using this surrogate model, the above mentioned tasks can be performed with a significantly reduced computational cost while assuring accurate results.

Three different experimental methods used in fracture testing sandwich panels are studied in the context of providing an assessment of face sheet-to-core interface strength. For this reason, strain energy release rate (ERR), complex stress intensity factors (SIFs) and mode mixity phase angle are computed. The analytical models exploit both the framework of linear elastic fracture mechanics (LEFM) in a combination of analytical considerations and numerical results and one-dimensional (1D) beam theories, whereas the finite element predictions are conducted using the capabilities of the ABAQUS package and a standalone subroutine developed in MATLAB environment for post-processing the results of two-dimensional (2D) finite element analysis. The results presented in this research allow drawing conclusions on the accuracy of fracture analysis predictions for each of the three different specimens by comparing 2D numerical calculations with semi-analytical results and 1D analytical solutions.

Two state-of-the-art analytical compression after impact (CAI) modelling approaches are presented and evaluated for the problem of thin-film buckle-driven propagation of a delamination in composite laminates. Characteristic phenomena are investigated by evaluating the behaviour of the energy release rate of an anisotropic sublaminate above a 2D embedded delamination. These characteristics include extension-bend, shear-bend and bend-twist coupling as well as contact of sublaminate and base laminate. A holistic approach with the aid of a detailed analysis of deformation characteristics from artificial delamination experiments and finite element analysis provide strong validation of the modelling approaches. Suggestions are made regarding analytical methods suitable for use in the initial aerospace structural design stage. It is found that models which capture the mode-mixity and post-buckled energy terms accurately will allow for better design decisions to be made that are not overly conservative. Whereas methods, which do not account for such mixity and post-buckling, can nevertheless be used to design for damage tolerance.

The primary objective of this paper is to find the threshold size of delamination as well as critical delamination location for composite road wheel of the Armoured Fighting Vehicle (AFV) under severe loading condition to which an AFV is subjected to, during the operation. The composite material considered in the study is carbon/epoxy composite (AS4/3501-6). Finite element analysis was performed using Ansys Workbench 17.2 to predict the delamination location and to study the delamination growth behaviour. The delamination onset spot was predicted using the stress-based failure criteria developed by Puck. Various delamination sizes were modelled at the critical location and the Strain Energy Release Rate (SERR) with respect to the fracture modes, viz., mode I, mode II and mode III were found using Virtual Crack Closure Technique (VCCT). The 3D failure criterion which was developed based on Benzeggagh–Kenane (B-K) mixed-mode I and II failure criterion was employed to predict the delamination growth based on which the threshold delamination size was found.

Many failures in aircraft structures are due to fatigue cracks initiating and developing from fastener holes at which there are large stress concentrations. In a typical wing skin, in the zone of riveted joint of rib/skin, the combination of high stress concentration could potentially lead to the appearance of the crack initiation and then crack growth under cyclic loading. Stress Intensity Factor (SIF) solutions are required for the assessment of fracture strength and residual fatigue life for defects in structures. In this context, many research works focused on evaluating the residual life of various cracked aircraft structures but only a few works have been done on light transport aircraft wing skin. The material used for wing skin is AL 2024-T351. A computational model for estimating the residual fatigue life of cracked wing skin is proposed. The complete computation procedure for the crack propagation analysis using low-cycle fatigue material properties is illustrated with the damaged wing skin. Initially, stress concentration effects at the cracked wing skin rivet holes are determined by applying analytical and numerical methods. Further, residual life and the failure mechanism in the cracked rivet holes of the wing skin are estimated. The wing skin with two cracked rivet holes for a pitch of 26 mm was analyzed using MSC NASTRAN/PATRAN for different crack lengths using MVCCI (Modified Virtual Crack Closure Integral) method by which strain energy release rate as well as stress intensity factors are calculated for different crack lengths, and fatigue crack growth life for progressive cracks for different R ratios is computed using a MATLAB program. Comparisons of the stress intensity factors estimated by FE analysis were in good agreement with the analytical solutions. Further, using SIF solutions, the residual life was estimated for the cracks emanating from the two rivet holes using crack growth models. The work also investigates the first failure mechanism out of two competing mechanisms of failure; Failure due to fracture or Failure due to plastic collapse at the net section between two advancing crack tips of the rivet holes of the wing skin. It was observed that the wing skin with crack rivet holes would fail by plastic collapse due to net section yielding. Further, the study can be extended to a multi-axial stress condition.

Purpose The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded). Design/methodology/approach The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification. Findings Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments. Originality/value A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation.

Microscale techniques capable of selectively isolating and delaminating embedded multilayer interfaces in a stable manner have the potential to be powerful characterisation tools for improving the reliability of microelectronic devices. Here we propose an analytical approach to assess the steady-state strain energy release rate during the delamination of an embedded multilayer interface, initiated by our recently developed miniaturised four-point bending technique. Stable delamination of a SiN-GaAs interface was initiated via nanoindentation induced bending of microbridges that had been milled into the surface of an Al-SiN-GaAs multilayer using a focused ion beam. Analytical models quantify the strain energy released within a section of a microbridge using the load-displacement relation obtained during delamination. The models are validated by demonstrating their capacity to approximate the experimentally observed linear-elastic deformation of a reference microbridge under both three- and four-point bending. We find that deformation of the clamped-ends as well as indenter penetration of a microbridge contribute significantly to the total indenter displacement. We then show this can be accounted for through a combination of Euler–Bernoulli beam and Hertzian contact theory. A mean steady-state strain energy release rate of G ¯ S S = 2.20 ± 0.36 J m − 2 is obtained for the SiN–GaAs interface.

A problem of an inclined wedge crack in transverse isotropic piezoelectric material under electromechanical loading is analyzed. A single anti-plane mechanical and in-plane electrical loads are applied at a point either on wedge surface or on crack surface. By using Mellin transform, the problem based on the generalized displacement and stress vector is formulated. The derived equation is solved employing the Wiener-Hopf technique, from which the intensity factors and the energy release rates are obtained in closed forms. With material properties of PZT-5H, the intensity factors and energy release rate for wedge and crack surface loadings are calculated numerically and investigated. The closed form solutions can be used as a Green’s function for arbitrarily coupled anti-plane mechanical and inplane electrical loading cases.

The increasing number of thin film interfaces in modern microelectronic components makes determining fatigue delamination properties and understanding the underlying mechanisms a necessity to ensure the reliability of such devices. In this work an advanced four-point bending setup for cyclic delamination investigations of multi-layered thin film samples has been developed. The static and cyclic delamination behaviour of two types of Si/SiN/TiW/Cu/Polyimide thin film stacks has been investigated. By calculating the delamination growth rate da/dN in relation to the cyclic energy release rate range ΔG, it is shown that the cyclic delamination occurs at levels lower than those observed under static loading. The dynamic bending experiments also indicated a threshold of the energy release rate for the onset and propagation of the adhesive delamination.

To increase the confidence in the design of adhesive structures, it is necessary to accurately predict their strength and fracture properties (critical strain energy release rate in tension, GIC, and shear, GIIC). It is of great importance the perception of fracture under mixed-mode, namely in which relates to the strain energy release rate in tension, GI, and shear, GII. This allows choosing the best failure criterion to use in cohesive zone models (CZM), to predict the joints’ behaviour. This work presents an experimental and numerical study using the Single-Leg Bending (SLB) test on bonded specimens to obtain the mixed-mode fracture properties. The analysis of GI and GII obtained during the experimental phase were addressed. Framing the obtained values in several fracture envelopes enable to select which failure criterion is more appropriate for each adhesive. In the numerical simulations it was possible to reproduce the observed behaviour of the experimental tests, with a positive validation of the chosen propagation criteria.

Physical characteristics: Original contains color illustrations, Accepted: 2018-05-30, 資料番号: PA1920007000

A critical plane-based mixed-mode delamination growth model for composite materials under fatigue loadings is proposed in this study. A brief review for mixed-mode delamination is given and the special focus in the study is on a critical plane-based fracture criterion since it can automatically adapt for different local failure modes. An equivalent energy release rate range suitable for fatigue analysis is proposed for the delamination growth rate prediction under general proportional and non-proportional multiaxial loadings. The proposed methodology is validated with extensive experimental data available in the open literature. A general good agreement is observed between model predictions and experimental observations. Finally, some discussion and conclusions are drawn based on the proposed model.

This work aims at studying the mixed-mode delamination process in Moment-Loaded Double Cantilever Beam (MLDCB) specimens. The delamination problem is addressed both analytically and numerically, while considering the interfaces as an assemblage of two sublaminates partly bonded together by an elastic interface. Such interface is modeled as a continuous distribution of elastic-brittle springs acting along the normal and/or tangential direction depending on the interfacial mixed-mode condition. The Timoshenko’s beam theory is here applied to determine the governing equations of the differential problem and the associated boundary conditions, whose solution is not straightforward. The Generalized Differential Quadrature (GDQ) method is then applied as numerical tool to solve directly the differential equations of the problem in a strong form. The capability of the proposed numerical approach is first exploited through a comparative evaluation of the results with the analytical predictions resting on a suitable change of variables for delamination test specimens. The local and global response is determined, in terms of interfacial stresses, internal forces and displacements, as well as in terms of compliance, energy release rate, mode mixity angle, and moment-rotation curves. A further check of the proposed numerical method is performed with respect to a Finite Fracture Mechanics (FFM) criterion, which is able to join both stress- and energy-based approaches. A good agreement between results confirms the good feasibility of the GDQ method when studying delamination phenomena occurring within composite materials or laminated joints, usually subjected to mixed-mode conditions.

Fatigue crack growth phenomenon in concrete is complex in nature and is characterised by various parameters. Important crack growth characterizing parameters must be considered in the analysis for accurate crack propagation and fatigue life prediction. In the present work, an analytical formulation has been developed to predict the propagation of crack in plain concrete members subjected to repetitive nature of loading. Dimensional analysis approach for fatigue crack growth problems has been adopted in conjunction with the theory of intermediate asymptotic for the development of the proposed model. The model has been derived considering the effect of critical energy dissipation in fatigue called fatigue fracture energy which can capture the observed size effect in concrete fatigue. Other important crack growth characterizing parameters considered in the present formulation are, change in energy release rate, maximum energy release rate, initial crack length, tensile strength, and ratio of maximum aggregate size to characteristic size of the structure. Further, the influence of fracture process zone has been incorporated in the proposed formulation through the loading parameter. The developed closed form expression has been calibrated with the available experimental results. The applicability of the mathematical model has been verified using the existing experimental results following both deterministic and statistical approach. The dependence of various governing parameters on fatigue life has been demonstrated through sensitivity study.

Foam core polymeric sandwich structures have been widely used in structural engineering due to their advantages such as lightweight, high strength, and so on. However, the mechanical properties of face sheets and foam cores, and the interfacial bond strength of sandwich structures are affected by the combined hygrothermal conditions, which is common in the most civil engineering applications. In this study, the mechanical properties of face sheets and foam cores in the combined hygrothermal conditions were investigated. Meanwhile, a series of sandwich double cantilever beams were tested at different ageing time to evaluate the effect of ageing time on interfacial fracture of polymeric sandwich structures. Furthermore, an analytical model, considering the effect of hygrothermal ageing, was proposed to predict the strain energy release rate of mode I interfacial fracture of the polymeric sandwich structures at different ageing time. The analytical results were found to be well matched with the experimental results.

To evaluate the service life of spur gears and design high-performance gears, fracture characteristics must be examined. Since, asymmetric spur gears are not standardised, the majority of the existing literature studies of spur gear fracture behaviour are based on symmetric spur gears. The research of spur gear with asymmetric teeth is attracting attention as the industry seeks to improve load transmission capabilities and service life. This paper investigates the combined effect of pressure angle and other gear parameters suchs as module, no.of teeth and gear ratio on the fracture characteristics of asymmetric spur gears subjected to mix mode fracture. The stress intensity factor (SIF) at the fillet crack tip along the face width for each gear pair is determined based on strain energy release rate approach. An increase in pressure angle reduces the contact ratio and top land thickness which is not recommended for smooth operation of spur gears. Hence, combined effect of pressure angle with the other gear parameters such as module, number of teeth and gear ratio on SIF to improve resistance towards fracture is addressed. Further, the effective SIF and influence of mode I, mode II and mode III on effective SIF for each gear pair are explored. This study aims to provides valuable input to design asymmetric spur gears and to select the gear parameters.

Intermetallic compounds (IMC) are found in the dual-layer composite, such as Si/Cu composite in multilayer semiconductor structures, and are often ignored in simulations that aim to predict the mechanical properties. The interface model of Si/Cu composites with different thickness of IMC layer is first established by molecular dynamics simulation. Then this study analyzed the elastoplastic behavior and adhesion behavior of the Si/Cu interface and the effect of IMC on the fracture properties. The simulation results demonstrate that the Si/Cu interface fails in a quasi-brittle fracture mode. The crack propagates along the interface between Si and the IMC layer. An apparent dislocation emission and large plastic deformation are found exclusively in the Cu layer. The thickness of the IMC layer increased from 2 to 10 A, and the critical strain energy release rate increased from 14.48 J/m2 to 19.76 J/m2, while the equivalent modulus is not increase monotonically. Therefore, the IMC is of high significance for predicting the mechanical properties of the dual-layer composite.

Based on the concept of the hoop field intensity factors of an initial crack prior to any kink, an apparent hoop mechanical (strain) energy release rate (MERR) is defined to approximate the MERR of a piezoelectric crack with an infinitesimal kink at any arbitrary angle. The validity and the efficiency of the simplified approximation are examined by numerical examples using the boundary element method (BEM). The generalized crack-opening-displacements or displacement jumps are computed by the traction boundary integral equations (BIEs). By using the displacement extrapolation method, the crack-tip field intensity factors of any arbitrarily kinked crack in linear piezoelectric materials are obtained and the BEM results are validated by comparing them with the available reference analytical results. Then, the differences between the conventional field intensity factors and MERR of an infinitesimally kinked crack and the hoop field intensity factors and hoop MERR of the main crack prior to any kink are numerically analyzed. Finally, the crack propagation in an infinite linear piezoelectric material is numerically simulated. The paths of the crack growth are predicted by adopting four different fracture criteria, namely, the maximum hoop stress intensity factor (SIF) and MERR fracture criteria for the main crack-tip before the next propagation, and the maximum KI and MERR fracture criteria for the kinked tip of the main crack with an infinitesimal branch at an arbitrary kinking angle evaluated by using a trial crack extension technique. The comparisons among these results show that the present simplified approximation can efficiently provide a sufficient accuracy for numerical simulation of crack growth in linear piezoelectric materials.

This work proposes thermodynamic model for stored energy evolution in metals within the internal variable approach. It is assumed that stored energy is a function of strain-type variable (structural strain) while dissipated energy is a function of plastic strain. Constitutive equations are derived for one-dimensional case and then generalized to the three-dimensional one. The proposed model is based on the introduction of two independent dissipation potentials with the corresponding multipliers for plastic strain and structural strain. Efficiency of the proposed model is demonstrated by two numerical examples. The first example is a simulation of the energy balance in the process of quasi-static deformation of Ti-1Al-1Mn alloy. The second example is modeling of the fatigue crack growth rate in Ti-1Al-1Mn alloy on the base of the consideration of energy balance at the crack tip. Numerical results have good agreement with the original experimental data.

The aim of this paper is to provide evidence on the validation of a modified Paris relation in fatigue crack growth with fibre bridging. Energy principles were first applied to investigate energy release in fatigue delamination growth. A comparison between the Paris and the modified Paris relations was completed subsequently. The application of the Paris relation can artificially cause different resistance curves of fatigue delamination with fibre bridging, violating the hypothesis of similitude and the energy dissipation results. However, the use of the modified Paris relation can result in a master resistance curve, which is physically consistent with the law of similitude and the energy release regulations. This derives from using an appropriate similitude parameter in data reduction. It is therefore reasonable to use the strain energy release rate (SERR) actually applied on the crack front, rather than the total applied SERR, as similitude to correlate fatigue crack growth. The master resistance curve was finally employed to predict fatigue results from literature. Acceptable agreement between predictions and experiments was achieved, validating the effectiveness of the modified Paris relation in determining fatigue crack growth with fibre bridging.

This work presents a new fatigue crack growth prediction model for non-load-carrying fillet welded steel joints. For this joint configuration the fatigue cracks will emanate from the weld toe region. Due to the presence of a V-notch in this region the crack initiation point becomes a point of singularity for the stress field. This may in many cases make it difficult to determine the Stress Intensity Factor Range (SIFR) for small cracks by conventional methods based on Linear Elastic Fracture Mechanics (LEFM). The present approach solves this problem by using the Energy Release Rate (ERR) to determine the SIFR in the small crack growth regime. The model is fitted to crack growth curves from tests with cruciform steel welded joint subjected to constant stress ranges in both axial and bending loading mode. The Paris crack propagation law is adopted and the calculation of SIFR for larger cracks outside the material volume influenced by the V-notch singularity is carried out by the conventional approach. The model gives results in agreement with experimental facts and has also the potential of being extended to variable amplitude loading. The model is also well suited for taking into account the crack initiation phase that is significant for high quality welded joints

Continuum damage mechanics model with consideration of crack direction is developed for the prediction of fracture behavior in fiber reinforced polymer (FRP) composites under quasi-static load. Traditional continuum damage mechanics (CDM) models cannot well predict the crack propagation path in the development state of discrete crack. The crack direction parameter is introduced as a major factor with damage variable for damage propagation and failure analysis. The CDM model, which has the capability to reliably predict the initiation and direction of crack propagation while analysing the multi failure of FRP composites, is proposed by introducing crack direction parameter to material property degradation method. Failure criteria is set up according to the behavior of FRP composites for damage initiation, and fracture-mechanics-based energy release rate criteria is employed for damage evolution. APDL is used to simulate crack propagation, ultimate strength and complex failure behavior of FRP composite structure for this model. Results from the previous researches, when compared with those of this model, showed good agreement, thus demonstrating that proposed methodology can be used for simulation of FRP composite damage failure and strength prediction.

A computational framework is presented for the delamination propagation analysis in laminated composite strips that combines an extended high-order layerwise model and a spectral finite element with high-order spatial approximation in the plane of the structure. The extended layerwise laminate mechanics approximate the through-thickness fields using Hermite cubic splines , while the discontinuities in displacement induced by a delamination crack are treated as generalized damage degrees of freedom (DOFs). The layerwise mechanics are integrated into a novel spectral strip finite element, which involves integration points collocated with the nodes, thus providing accurate nodal predictions of the interlaminar stresses on the interface and ahead of the delamination crack tip . Strain energy release rate is predicted by adapting the VCCT method to rely exclusively on the damage DOFs. Finally, an iterative solution method is developed that takes advantage of the damaged DOFs to quickly predict the crack propagation without remeshing. The proposed numerical scheme is applied to mode I, II and mixed-mode delamination fracture problems and is validated vs. reference literature solutions, experimental results and standard 2D plane-strain FE models. The numerical results ultimately illustrate the capacity of the present method to provide accurate predictions with moderately coarse meshes and high computational speed.

The dynamic mode-II energy release rate of the end-notched flexure (ENF) test with applied time-dependent displacement is derived for the first time with the effect of vibration included. A dynamic Euler-Bernoulli beam theory is employed together with a deflection condition to simulate contact. To investigate the dynamic effect and the relative dynamic contribution from each vibration mode, a dynamic factor and a spatial factor are defined. It is found that the contribution of the ith vibration mode is dependent on the spatial factor (which is a function of the delamination length and the total length of the ENF specimen) and that certain vibration modes are dominant (depending on the delamination-length ratio). In addition, for a given spatial factor, there may be a certain vibration mode with a zero contribution to the ERR. The developed theory is verified against results from finite-element-method simulation for two cases of ENF tests and they are in excellent agreement. This work now allows the loading rate-dependent mode-II delamination toughness of layered materials to be determined using ENF tests. In addition, it provides understanding of the structural dynamic response in the presence of mode-II delamination and can guide the design of structures to mitigate the vibration-driven delamination.

Large scale fiber bridging in composite laminates is one of the most common toughening mechnisms, exerting a close-force on the crack surfaces to restrain the delamination propagation . To account for the effect of the fiber bridging in delamination simulation, a physically semi-analytical method based on the Euler-Bernoulli beam theory considering the bridging stress is presented. The mode I energy release rate for every crack length is explicitly expressed in terms of the external load and bridging-traction parameters, which are iterately identified by the proposed optimization procedure . Based on the presented method, a cohesive zone model integrating the identified bridging-tractions is established to simulate the mode I delamination of three kinds of composite laminates with different interfaces, the numerical results correspond well with the experimental ones, indicating the effectiveness and applicability of the presented method. The delamination morphologies are investigated for better interpretation of the toughening mechanism. The major advantage of the proposed method is that it is efficient and convienient since only basic material properties and experimental load–displacement data of the double cantilever beam specimens are required, without additional parameters measurement with the help of external equipments.

A hypothesis is made that delamination can be driven by pockets of energy concentration (PECs) in the form of pockets of tensile stress and shear stress on and around the interface between a thin film and a thick substrate, where PECs can be caused by thermal, chemical or other processes. Based on this hypothesis, three analytical mechanical models are developed to predict several aspects of the spallation failure of elastic brittle thin films including nucleation, stable and unstable growth, size of spallation and final kinking off. Both straight-edged and circular-edged spallations are considered. The three mechanical models are established using partition theories for mixed-mode fracture based on classical plate theory, first-order shear-deformable plate theory and full 2D elasticity. Experimental results show that all three of the models predict the initiation of unstable growth and the size of spallation very well; however, only the 2D elasticity-based model predicts final kinking off well. The energy for the nucleation and stable growth of a separation bubble comes solely from the PEC energy on and around the interface, which is ‘consumed’ by the bubble as it nucleates and grows. Unstable growth, however, is driven both by PEC energy and by buckling of the separation bubble. Final kinking off is controlled by the fracture toughness of the interface and the film and the maximum energy stored in the separation bubble. This work will be particularly useful for the study of spallation failure in thermal barrier coating material systems.