Energy Release Rate In Mode Research Articles

A simple procedure for the determination of the cohesive law in 4-ENF test with consideration of the friction and R-curve effect

The measurement of initiation and propagation fracture toughness is important for characterizing the delamination behavior of composite laminates, especially in the case with distinct R-curve behavior which can be caused by fiber bridging, shear deformation of matrix, etc. Four-Point End Notched Flexure (4-ENF) is one of the widely adopted tests to measure the mode II toughness values, while the friction between the crack surfaces may have a significant impact on the results. In this paper, a simple procedure to determine the cohesive law in 4-ENF test with consideration of the friction and R-curve effect is proposed. Firstly, determining the equivalent crack advance according to the compliance variation of the specimen is performed, without the need for monitoring the crack length during the test. Next, the Energy Release Rate in mode II (GII) and crack sliding displacement (δt) are derived based on the point-friction assumption and beam theory. Finally, the cohesive law is obtained via the J-integral approach. To obtain suitable values of the penalty stiffness and interface strength, the influence of these parameters on the prediction of 4-ENF test is studied. Comparisons of the numerical results and the experimental data show a good correlation. The effect of variation of friction coefficients on derived cohesive stress and initiate energy release rate is discussed as well.

Investigation of energy release rate under mode II loading in a rectangular orthotropic plate with a band crack using 3D finite element analysis

A rectangular plate containing a band crack and made of orthotropic elastic material is considered and the energy release rate (ERR) component in mode II at this crack front is investigated. It is assumed that the crack’s edge planes are parallel to the upper and lower face planes of the plate and the edge planes of the crack are loaded with uniformly distributed sliding forces. The corresponding boundary value problem is formulated within the scope of the three-dimensional linear theory of elasticity and the solution to this problem is found by employing 3D finite element method (3D FEM) modeling. Numerical results on the ERR for mode II and on the influence of the mechanical-orthotropic properties of the plate material are presented and discussed. In particular, it is established that the influence of the shear modulus in a plane which is simultaneously perpendicular to the crack’s front and crack’s plane on the ERR is more significant than that caused by the change of another modulus of the orthotropic material.

Characterization of cohesive model and bridging laws in mode I and II fracture in nano composite laminates

The cohesive model and traction-separation curves have brought a considerable possibility for researchers and fracture engineers to assess and simulate failure in composite laminates. Reliable determination of the traction–separation laws is very pivotal to the success of this approach in finite element methods. The objective of this paper is assessment of nanoparticles effect on bridging laws, cohesive mechanism and traction-separation parameters of nanocomposites mode I and II fracture. To do this analyzing of the experimental data from double cantilever beam, and end notched flexure tests including construction of the R-curves (energy release rate versus crack length), reconstruction of these curves in terms of the pre-crack tip opening and sliding displacement, and calculation of the corresponding bridging and traction-separation laws through the J-integral approach were carried out. For the calculation of the energy release rate in Mode I, three corresponding data reduction schemes namely Corrected Beam Theory, Experimental Compliance Method and Modified Compliance Calibration are utilized, while Compliance Calibration Method, Corrected Beam Theory and Compliance-Based Beam and II fracture are applied for that of mode II. The main concern of this research is introduction of critical parameters of two modified models to simulate mode I and II fracture. Adding 0.43 wt% nanoparticles to composite DCB samples leads to increase of 116%, 68% and 70% in GI,0 calculated by CBT, ECM and MCC respectively, and a 72% increase in GI,ss is measured by CBT, while this value for ECM and MCC is 110% and 48%. Adding 0.2 wt% nanoparticles to the composite samples results in 86% (50 MPa) increase in critical stress in mode II fracture calculated by method CBBM. This method presented the lowest value for critical displacement, fluctuated between 0.08-.11 mm in mode II.

Fracture Toughness and Shear Strength of the Bonded Interface Between an Aluminium Alloy Skin and a FRP Patch

The existing techniques to determine the fracture properties such as critical energy release rate in mode I (GIc) and mode II (GIIc) of an interface between two sheets of same material were modified to determine these properties between the sheets of dissimilar materials and thickness. In addition, the interface shear strength (ISS) was also determined. Experiments were carried out on the specimens made of a pre-cracked thin aluminium alloy skin and a Fiber reinforced polymer (FRP) patch. Two kinds of surface preparation of the aluminium skin were employed; (i) emery-paper roughened surface (ERS) and (ii) Sodium Hydroxide (NaOH) treated surface (NTS). GIc of ERS specimen was found to be 36.1 J/m2, while it was found to be much higher for NTS specimens, that is, 87.3 J/m2. GIIc was found to be 282.4 J/m2 for ERS specimens and much higher as 734.5 J/m2 for NTS specimens. ISS was determined as 32.6 MPa for ERS specimen and significantly higher for NTS specimen, that is, 44.5 MPa. The micrographs obtained from a field emission-scanning electron microscope (FE-SEM) and the surface roughness test showed that the NTS was significantly rougher than the ERS, explaining the higher values of all the three kinds of NTS specimens.

Trapezoidal traction–separation laws in mode II fracture in nano-composite and nano-adhesive joints

The main focus of this paper is on the experimental investigation and comparison between different bridging laws. For mode II fracture in the presence of nano-particles, these laws are calculated from three data reduction schemes for describing the bridging zone and trapezoidal traction–separation law parameters. For the calculation of the energy release rate in mode II fracture, three corresponding data reduction schemes, compliance calibration method, corrected beam theory and compliance-based beam method, have been utilized for different percentages of nano-particles in the adhesives and the adherents.

An Out-of-plane Loaded Double Cantilever Beam (ODCB) test to measure the critical energy release rate in mode III of adhesive joints

A novel fracture mechanical test for adhesive joints subjected to pure mode III loading is presented. The experiment uses a modified double cantilever beam specimen, which is loaded out of the plane of crack propagation. The paper presents and discusses first experimental results, applying the new test method on adhesively bonded joints of an elastic-plastic structural adhesive. The tests have been performed under quasi-static load conditions. Beside the critical energy release rate, the test gives information about the total shape of the corresponding Traction-Separation-Law at the location of the initial crack tip. The calculation of the critical energy release rate is done by two different analytical approaches. Firstly, an evaluation method based on the Irwin-Kies equation is proposed, which is strictly valid for Linear-Elastic Fracture Mechanics conditions only and which is commonly used in case of classical Double Cantilever Beam tests. The second approach deals with a calculation of the J-integral, which holds for non-linear fracture behavior as well. The two evaluation methods are applied to experimental results of the new test method; the differences between both methods are pointed out and discussed. Additionally, the obtained test results in mode III are compared to equivalent results from mode II tests, which are taken from literature to proof a possible correlation between the shear crack opening modes II and III.

Hygrothermal ageing of polymeric sandwich structures used in structural engineering

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.

Evaluation of the energy release rate in mode I of asymmetrical bonded composite/metal assembly

Composite structures assembled by bonding are widely found in different areas of high performance applications such as aeronautics. The energy release rate (G) is mainly used to predict fracture. However, in some special cases, this parameter serves to investigate the propagation, the rate or the stability of a crack. The main issue resides in the calculation of this energy release rate because it strongly depends on the crack geometry and the loading mode. An energetic criterion based on the compliance method was chosen, assuming that the release of potential energy is transformed in surface energy due to the creation of wider cracks (new surfaces). To investigate the properties of an asymmetrical composite/metal bonded structure, modified Double Cantilever Beam (DCB) specimens were tested in mode I. The fracture toughness and the fatigue behavior were evaluated by experimental means, finite elements modeling (FEM) and linear elastic fracture mechanics (LEFM) theories. Timoshenko and Kanninen theories, experimental and FEM results were compared on an R-curve. A modified Kanninen theory was then proposed, to take into account the specific assembly design. As a result, the Paris’ law was built for that situation. The objective of this work was to adapt and validate a non-standard fatigue compliance methodology which calculates the energy release rates in mode I, for asymmetrical bonded structures.

Synchrotron X-ray characterization of crack strain fields in polygranular graphite

The strain field of a crack in polygranular isotropic nuclear graphite, a quasi-brittle material, has been studied during stable fracture propagation. Synchrotron X-ray computed tomography and strain mapping by diffraction were combined with digital volume correlation and phase congruency image analysis to extract the full field displacements and elastic crystal strains. The measured displacement fields have been analysed using a Finite Element method to extract the elastic strain energy release rate as a J-integral. Non-linear properties described the effect of microcracking on the elastic modulus in the fracture process zone. The analysis was verified by the good agreement of the predicted and measured elastic strain fields when using the non-linear model. The intrinsic critical elastic strain energy release rate for mode I crack propagation is approximately 200 J m−2.

A string-based cohesive zone model for interlaminar delamination

The objective of this paper is to develop a string-based cohesive zone model (CZM) for interlaminar delamination, whose associated cohesive elements behave reliably and consistently when deformed along complex separation paths and can display experimental critical energy release rate–mode mixture ratio relationships. Each cohesive element is idealized as a deformable string exhibiting path dependent damage behavior, and the thermodynamic equations are formulated in a generalized standard manner. A damage model having a path dependence function is developed. The rate form of the cohesive law is subsequently derived. The path dependence function is constructed such that each cohesive element can exhibit designated, possibly sophisticated mixed-mode behavior. The interface parameters associated with the present CZM are calibrated from experimental data. The present CZM is validated through simulating a series of flexural tests using Abaqus/Explicit. It is found to be capable of producing reliable simulation results. The interfacial strength is found to affect the predicted applied load–load point displacement curves. The present CZM may be amended to handle other types of fracture or interfacial debonding.

Mode I interfacial fracture characterization of foam core sandwich materials at elevated temperatures

Foam core sandwich materials are being widely used in structural engineering due to their advantages such as lightweight, high strength, and corrosion resistance. But the interfacial bond strength of foam core sandwich materials is weakened at elevated temperatures. In practice, the influence of high temperature cannot be ignored since the composites with foam are sensitive to the change in the environment. In this study, a series of sandwich double cantilever beams were tested at different temperatures to evaluate the effect of high temperatures on the interfacial fracture of the foam core sandwich materials. The temperature range studied was from 30 to 90℃, noting the glass transition temperatures are 85.7℃ for the composites and 72.1℃ for the foam core, respectively. In the meantime, the mode I interfacial crack propagation and its corresponding interfacial strain energy release rate were analyzed. Furthermore, an analytical model, considering the change in temperature, was proposed to predict the strain energy release rate of mode I interfacial facture of the foam core sandwich materials. The analytical results were found to be well matched with the experimental results.

Effects of strain rate on fracture toughness and energy release rate of gas shales

Understanding the aspect of enhanced energy extraction through an approach of rock mechanics requires a detailed interpretation of rock fracture mechanism. Common examples are hydraulic fracturing of gas shales and geothermal energy systems. Resolving rock fracture behavioural patterns and its properties such as fracture toughness and energy-release rate during fracturing is important for the successful implementation of such projects. These properties are a function of different environmental factors such as temperature, humidity, water vapour, pressure, and strain rate. In this study, the effects of various strain rates on the fracture toughness as well as the energy-release rate of gas shales were investigated. The three-point bending method was applied using notched semicircular bending shale specimens that were prepared as per the international standards. The fracture toughness and the energy-release rates were measured for three different modes, namely, mode I, mixed mode (I–II) and mode II. In addition, X-ray diffraction analysis was carried out to identify the composition of the selected shales. Finally, scanning electron microscope (SEM) analyses were performed in order to acquire an insight into the effects of strain rate on fractures at microstructural scales. The experimental results indicate that the fracture toughness and the energy-release rate for all the three modes are a function of strain rate. At lower strain rates, the fracture toughness and the strain-energy-release rates for all the modes are comparable but vary significantly at higher strain rates. At high strain rates, the strength and stiffness of the shale increases, which in turn increases the fracture toughness and, eventually, the energy-release rate of the shale. For all the strain rates, mode I requires the minimum application of energy, while mode II requires maximum energy for the onset of crack growth. The energy-release rate in mode I is maximum, in comparison with the two other modes. The findings of this investigation will be useful in achieving a better and comprehensive understanding of some aspects such as initiation, propagation and failure of shales during hydraulic fracturing for the extraction of hydrocarbons.

Fibre Type Effect on Mixed-Mode I/II Interlaminar Fracture in Polymer Composites

The fibre type effect on mixed-mode I/II interlaminar fracture in unidirectional fibre reinforced polymer composite beams is studied. Linear-elastic fracture mechanics is applied. Three composite systems (with three different types of reinforcing fibres) are investigated. The fracture behaviour is studied in terms of the strain energy release rate using a three-dimensional virtual crack closure technique. For this purpose, a three-dimensional linear-elastic finite element model of the composite beam is developed. The distribution of the strain energy release rate mode components along the crack front is analyzed. The findings are verified by the crack closure technique. The calculations reveal that the strain energy release rate decreases with increase of the modulus of elasticity of the reinforcing fibres. This finding is attributed to the increase of the beam stiffness with the composite modulus of elasticity.

Analysis of Mixed Mode I/II/III Fracture in Foam Core Sandwich Structures Using Imposed Displacement Split Cantilever Beams

Abstract Static fracture in foam core sandwich structures under mixed mode I/II/III loading conditions was studied theoretically. In order to generate such loading conditions, a thread guide was used to impose in- plane displacements of the lower crack arm of a sandwich Split Cantilever Beam (SCB). The upper crack arm was loaded by a transverse force. A three-dimensional finite element model of the imposed displacement sandwich SCB configuration was developed. The fracture was studied applying the concepts of linear-elastic fracture mechanics. The strain energy release rate mode components distribution along the crack front was analyzed using the virtual crack closure technique. The influence of the imposed displacement magnitude and the crack length on the fracture was evaluated. The effect of the sandwich core material on the mixed-mode I/II/III fracture was studied. For this purpose, finite element simulations were carried-out assuming that the core is made by different rigid cellular foams. It was found that the strain energy release rate decreases when the foam density increases.

Analysis of mixed-mode II/III fracture in sandwich beams

Purpose– The purpose of this paper is to study theoretically the ability of the prestressed foam core composite sandwich Split Cantilever Beam (SCB) for generating mixed-mode II/III crack loading conditions (the mode II fracture was provided by prestressing the beam using imposed transverse displacements).Design/methodology/approach– The concepts of linear-elastic fracture mechanics were used. The fracture behavior was studied in terms of the strain energy release rate. For this purpose, a three-dimensional finite element model of the prestressed sandwich SCB was developed. The virtual crack closure technique was applied in order to analyze the strain energy release rate mode components distribution along the crack front.Findings– It was found that the distribution is non-symmetric. The analysis revealed that a wide mixed-mode II/III ratios range can be generated by varying the magnitude of the imposed transverse displacement. The influence of the sandwich core material on the mixed-mode II/III fracture behavior was investigated. For this purpose, three sandwich beam configurations with different rigid cellular foam core were simulated. It was found that the strain energy release rate decreases when the foam core density increases.Originality/value– For the first time, a mixed-mode II/III fracture study of foam core composite sandwich beam is performed.

Mixed-mode I/III fracture study of sandwich beams

AbstractThe capacity of prestressed split-cantilever beam (SCB) for investigation of mixed-mode I/III fracture in foam core sandwich constructions was evaluated theoretically. The fracture was studied in terms of the strain energy release rate. In this relation, a three-dimensional finite-element model was developed. The strain energy release rate mode components were analyzed by the virtual crack closure technique. The analysis revealed that the mode I and the mode III components have maximum at the center of the crack front and gradually decrease toward the edges. Different mixed-mode ratios were generated by varying the mutual transverse displacement at the end of the sandwich SCB crack arms (in this way, the use of steel rollers with different diameters for prestressing the SCB to provide the mode-I part of the loading was modeled). The effect of the sandwich core material on the mixed-mode I/III fracture was investigated. For this purpose, three sandwich SCB configurations with different rigid cellul...

Impact Fracture Study of Laminated Composite Using Single Edge Notched Bend Specimens

The results of an investigation of impact fracture in laminated composite material are presented in this paper. Low velocity impact fracture tests were carried out on single edge notched three-point bending (SENB) specimens using a drop-weight rig. An inclined notch was introduced in the SENB specimen in order to generate mixed-mode I/II crack loading conditions. Different mixed-mode ratios were obtained by varying the notch inclination from 10° to 90° with a step of 10°. The SENB specimens were subjected to various impact potential energies by varying the drop-height in order to determine the critical impact potential energy at which the crack growth initiates from the initial notch tip position for each of the considered notch inclinations. The mechanical response of the SENB specimen to impact loading was analyzed using a two-dimensional linear-elastic finite element model. Good agreement was obtained between the predicted contact force – time curve and the measured one at various impact potential energy levels and notch inclinations. The strain energy release rate mode components were computed by the virtual crack closure technique. The composite fracture toughness under impact loading was characterized in terms of the critical dynamic strain energy release rate at the onset of crack growth. It was found that the fracture toughness under impact loading increases with decreasing the notch inclination. This finding was attributed to the increase of mode II component of crack loading. A comparison of the fracture behaviour under impact and static loading was performed. It was found that the fracture toughness under impact loading was between 19% and 23% lower than the static one for the different notch inclinations. Therefore, it was concluded that static fracture toughness should not be used in the fracture mechanics based design of composite structures which are subjected to impact loading during their lifetime.

Determining mode I cohesive law of Pinus pinaster by coupling double cantilever beam test with digital image correlation

The direct identification of the cohesive law in pure mode I of Pinus pinaster is addressed. The approach couples the double cantilever beam (DCB) test with digital image correlation (DIC). Wooden beam specimens loaded in the radial-longitudinal (RL) fracture propagation system are used. The strain energy release rate in mode I (GI ) is uniquely determined from the load-displacement ( P ?? ) curve by means of the compliance-based beam method (CBBM). This method relies on the concept of equivalent elastic crack length ( eq a ) and therefore does not require the monitoring of crack propagation during test. The crack tip opening displacement in mode I ? ? I w is determined from the displacement field at the initial crack tip. The cohesive law in mode I I I (? ? w ) is then identified by numerical differentiation of the I I G ? w relationship. Moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. It is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode I of P. pinaster.

Mixed-Mode II/III Fracture in Foam Core Sandwich Beams

This paper is motivated by the fact that no mixed-mode II/III fracture studies of foam core composite sandwich beams were found in the literature available. In order to generate mixed-mode II/III crack loading conditions, it is proposed here to load an End-Loaded Split (ELS) foam core composite sandwich beam in torsion and bending by applying a transversal load at one of the beam corners. The fracture behavior was studied theoretically using the methods of linear-elastic fracture mechanics. The strain energy release rate mode components distribution along the crack front was analyzed by the virtual crack closure technique. For this purpose, three-dimensional linear-elastic finite element simulations of the ELS foam core sandwich beam configuration were performed. The analysis yielded non-uniform distribution of the strain energy release rate mode components along the crack front. The influence of the sandwich beam core material on the mixed-mode II/III fracture was studied assuming that the core is made by three different rigid cellular foams. The mixed-mode I/II/III fracture was analyzed too. The results obtained indicate that the mixed-mode II/III and the mixed-mode I/ II/III fracture performance of the sandwich beam can be improved using a foam core with higher density.

Determining mode II cohesive law of Pinus pinaster by combining the end-notched flexure test with digital image correlation

This work addresses the direct identification of cohesive law of Pinus pinaster in mode II. The end-notched flexure (ENF) test is selected for mode II loading. The strain energy release rate in mode II (GII) is determined according to the compliance-based beam method (CBBM) by processing the global load–displacement curve, without requirements to monitor the crack length during test. The fracture test is coupled with digital image correlation (DIC) for the local measurement of the crack tip opening displacement in mode II (wII). Using a direct method, the cohesive law in mode II (σII–wII) is determined by differentiating the GII–wII relationship. The procedure is validated from both numerical, using finite element analyses including cohesive zone modelling, and experimental approaches. The methodology and accuracy on this reconstruction is discussed. It is concluded that the proposed data reduction scheme is suitable for assessing the cohesive law of P.pinaster in mode II.