Total Energy Release Rate Research Articles

Finite Element solution of the fiber/matrix interface crack problem: Convergence properties and mode mixity of the Virtual Crack Closure Technique

The bi-material interface arc crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix interface crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix interface crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the crack tip neighborhood, while the total ERR is independent of element size.

Effect of the aspect ratio of the pre-existing rectangular adhesion failure on the structural integrity of the adhesively bonded single lap joint

Non-linear three dimensional (3-D) finite element analyses (FEA) of the single lap joints (SLJs) having pre-existing rectangular adhesion failure in the interface of the strap adherend and the adhesive have been carried out. The effect of the size, the shape and the aspect ratio of the pre-existing rectangular adhesion failure on (i) the strength, (ii) the interfacial stresses and (iii) the strain energy release rates (SERRs) in the vicinity of the adhesion failure front have been presented in this research work. The SLJ is subjected to uniformly applied tensile load. The adherends are made with very high strength steels and the adhesive is a commercially available AV119. The analyses of the adhesion failure propagation have been carried out by sequentially releasing the constraints of the nodes ahead of the pre-existing adhesion failure front in finite element model. The SERR values in the vicinity of the adhesion failure fronts are computed using the virtual crack closure technique (VCCT) for assessment of the structural integrity of the SLJ. The strength of the SLJ, the interfacial stresses, and the three modes of strain energy release rates (SERRs) have been found to be significantly affected by the shape and size of adhesion failures. The SERRs and interfacial stresses along the rectangular adhesion failure front are compared with the corresponding values around the circular adhesion failure front of same area, pre-existing in the SLJ. It is observed that the circular and rectangular adhesion failures of the same area will have dissimilar growth rate and the mode II is the dominant failure mode. The total strain energy release rate and the failure strength, computed from the 3-D FEA of the SLJ is in good agreement with the experimental fracture toughness of the AV119 adhesive and the experimentally obtained failure loads, respectively.

Numerically-based method for fracture characterization of Mode I-dominated two-dimensional delamination in FRP laminates

A new numerically-based method suitable for determining the total strain energy release rate (SERR) involved in two-dimensional (2D) Mode I-dominated delamination under opening loads in FRP laminates is presented. The method is based on the mutual dependence of the load vs opening displacement curves slope exhibited after the full development of the fracture process zone (FPZ) and the total SERR involved in the delamination process. The equation relating these parameters is derived from three-dimensional finite element analyses performed using simple linear-softening cohesive zone models. Considering that the load-displacement curve reflects the overall fracture behavior, the above-mentioned slope correlates with the mean total SERR required to propagate the total 2D crack, independently of any local total SERR’s variation along the crack front. Thus, the same mean cohesive zone model is used in all directions. By substituting the corresponding experimental slope of the load-displacement curves in the derived equation the total SERR is obtained. The method was validated using the experimental results from three types of GFRP/epoxy laminates with different fiber architectures. The measurement of the crack front is not required and the method is valid for any fiber architecture, crack shape and boundary conditions in Mode I-dominated and opening loading cases.

A Comparative Study of the Behavior of CFRP and GFRP Laminates in a Plate Specimen Using Modified Virtual Crack Closure Technique (MVCCT)

The applications of polymer composites in aircraft industry have exponentially increased in the recent years due to their high strength to weight ratio. Presence of delaminations in composites is inevitable which affects the structural stability due to reduction in structural stiffness and strength. The degradation of a structural component depends on the geometric characteristics of delamination, nature of loading and material characteristics. Damage tolerance study is thus essential to determine the extent of degradation of the structure due to the presence of delamination. The present paper brings about a comparision between the behaviour of a standard plate specimen made up of Carbon Fibre Reinforced Polymer (CFRP) and Glass Fibre Reinforced Polymer (GFRP) laminates with circular delaminations of varying diameters and subject to compressive load.A constant compressive load in terms of initial displacements was applied on a quasi-isotropic square plate specimen of dimensions 200 mm x 200 mm with a thickness of 2.88 mm of both CFRP and GFRP configurations. A circular delamination was introduced at the centre of the plate and its diameter and position along the thickness direction were varied and studied. Using ABAQUS codes of practice, Strain Energy Release Rate (SERR) was computed. The principles of Modified Virtual Crack Closure Technique (MVCCT) was used to compute SERR. Delamination propagates when the computed mixed mode energy release rate exceeds the critical value, GC. Depending on the external loading and material properties, Total strain energy release rate, GT (GT=GI+GII+GIII) was used to predict growth of delamination. The onset of delamination growth was determined by plotting the values of (GT/GC) across various delamination sizes along the thickness of the plate and reported.

A finite element study of fatigue crack propagation in single lap bonded joint with process-induced disbond

This paper presents a method for predicting fatigue crack propagation in adhesive bonded composite joints with an initial full-width disbond using finite element analysis and numerical integration of the material's fatigue crack growth rate law. Fatigue tests were conducted on single lap joints. Crack lengths were monitored from four runout corners. In-situ crack growth measurements were performed by ink injection to identify the crack front profile during fatigue loading. The crack growth was modelled using a fracture mechanics criterion considering two different crack propagation patterns. The material's fatigue crack growth rate law was determined experimentally using the standard double cantilever beam and end notch flexure specimens. Using the total strain energy release rate and the two crack scenarios, the numerical model predicted the lower and upper bounds of the measured fatigue crack growth rates of the lap joint.

Numerical simulation of two-dimensional in-plane crack propagation in FRP laminates

A numerical investigation was carried out in order to simulate experimental results previously obtained concerning two-dimensional (2D) in-plane crack propagation in laminated glass fiber-reinforced polymer (GFRP) plates. The laminated plates were designed with an embedded circular pre-crack and subjected to quasi-static out-of-plane loads. In order to study the transition from standard fracture mechanics tests, where the crack propagates only in one dimension (1D), to 2D scenarios, additional double cantilever beam (DCB) experiments were carried out on the same material system. Three-dimensional finite element models were developed for the simulation of the experimental fracture responses and cohesive elements were used to take into account the fracture mechanisms acting on the fracture process zone. Compared to the 1D DCB specimens, a much higher value of the total strain energy release rate (SERR) was obtained for the 2D plates, which was correlated to their higher flexural stiffness and to the stress stiffening effect caused by the stretching of their deformed part. Furthermore, and based on the numerical results, it was proved that the area of the fully developed fiber-bridging in the plates can be directly obtained from the experimental compliance vs crack area curves.

Asymptotic solution for interface crack between two materials governed by dipolar gradient elasticity

An asymptotic solution for interface crack between mismatched materials that obey a special form of linear isotropic strain gradient elasticity under conditions of plane strain is developed. It is shown that the asymptotic solution depends in a complicated manner both on a mismatch of elastic properties and a mismatch of the internal length scale parameter. Numerical analysis shows that the mismatch of elastic moduli and the gradient coefficient c respectively lift the degeneracy of the exponent p that is characteristic for a crack in homogeneous material. The total energy release rate Gint due to a crack extension along the interface is derived generalizing the classical virtual crack closure method. The reciprocal work contour integral method for the evaluation of amplitude factors in the asymptotic expansion is extended to interface crack in the linear isotropic strain gradient elasticity.

The effect of explosive percentage on underwater explosion energy release of hexanitrohexaazaisowurtzitane and octogen based aluminized explosives

To control the explosion energy output by optimizing explosive components is a key requirement in a number of different application areas. The effect of different Al/O Ratio on underwater explosion of aluminized explosives has been studied detailedly. However, the effect of explosive percentage in the same Al/O Ratio is rarely researched, especially for Hexanitrohexaazaisowurtzitane (CL-20) based aluminized explosives. In this study, we performed the underwater explosion experiments with 1.2-kilogram explosives in order to investigate the explosion energy released from CL-20 and Octogen (HMX) based aluminized explosives. The percentage of the explosive varied from 5% to 30% and it is shown that: the shockwave peak pressure (pm) grows gradually; shock wave energy (Es) continues increasing, bubble energy (Eb) increases then decreases peaking at 15% for both formulas, and the total energy (E) and energy release rate (η) peak at 20% for CL-20 and 15% for HMX. This paper outlines the physical mechanism of Eb change under the influence of an aluminium initial reaction temperature and reaction active detonation product percentage coupling. The result shows that CL-20 is superior as a new high explosive and has promising application prospects in the regulation of explosive energy output for underwater explosives.

Numerical simulation of the deflagration-to-detonation transition of iso-octane vapor in an obstacle-filled tube

Flame acceleration and deflagration-to-detonation transition of an iso-octane vapor–air mixture in an obstacle-filled detonation tube were simulated by solving Navier–Stokes equations with a single-step reaction mechanism. A variable specific heat ratio was used in these simulations. Detonation cell size was successfully simulated for the iso-octane vapor–air mixture. Two methods for initiating detonation waves were revealed in a detonation tube with obstacles. Pressure and flame parameters, such as the temporal variation of total energy release rate, flame front location, propagation velocity of the flame front, and flame front area, were investigated during the flame acceleration and deflagration-to-detonation transition process. According to the variation of these parameters, flame acceleration and deflagration-to-detonation transition processes could be divided into four stages, i.e. the early stage of flame acceleration, the middle stage of flame acceleration, the end stage of flame acceleration, and the detonation transition stage. The effects of activation energy and pre-exponential factor on deflagration-to-detonation transition processes were examined. The results indicate that the pre-exponential factor and activation energy influence the flame parameters, but not the development law of flame acceleration or deflagration-to-detonation transition processes. For lower reactants activity, detonation wave is easy to fail in couple while bypassing obstacles in the obstacle-filled detonation tube, which causes a large fluctuation in flame propagation velocity and total energy release rate. The length of detonation tube filled by obstacles should not be more than deflagration-to-detonation transition distance. These investigations are conducive to understanding the flame acceleration and deflagration-to-detonation transition and developing detonation combustion chamber of pulse detonation engine.

Delamination in a Two-Dimensional Functionally Graded Beam

An analytical study of delamination in the crack lap shear beam is performed. It is assumed that the material is functionally graded along the width and height of the beam. Delamination is studied in terms of the total strain energy release rate by applying methods of linear-elastic fracture mechanics. An additional analysis of the total strain energy release rate is performed by considering the strain energies in the beam cross sections ahead of and behind the crack front for verification. The effects of the crack location and material gradient on delamination are evaluated.

Fracture Toughness Analysis of Delamineted Composites under Variable Temperatures

Abstract The main goal of the present paper is to approach the modeling of one of the most important and critical failure modes for composite laminates which is known as interlaminar delamination in the aeronautical structures. The analytical model is based on a fracture mechanics approach; it’s used to estimate the total mixed mode energy release rate for composite laminates. A finite element simulation has been achieved in combination with the virtual crack closure technique (VCCT) to analyze the effect of temperature on the interlaminar fracture toughness growth of a delaminated carbon/epoxy material, namely IM7/8552 subjected to mechanical loading at variable temperatures. The developed model may serve as the basis for treating different types of thermal and mechanical loading, different stacking sequences and thickness of lamina in order to build safe working conditions for composite laminates.

Dynamic interfacial fracture of a thin-layered structure

To calculate the dynamic energy release rate of a crack is important for understanding a structure’s fracture behavior under transient or varying loads, such as impact and cyclic loads, when the inertial effect can be significant. In this work, a method is proposed to derive an analytic expression for the dynamic energy release rate of a stationary crack under general applied displacement. An asymmetric double cantilever beam with one very thin layer is considered as a special case, with vibration superimposed onto a constant displacement rate applied to the free end. The resulting expression for dynamic energy release rate is verified using the finite-element method (FEM) in conjunction with the virtual crack closure technique. The mode-mixity of the dynamic energy release rate is also calculated. The predicted total dynamic energy release rate and its components, GI and GII, are both in close agreement with results from FEM simulations.

Influence of matrix ductility and toughness on strain energy release rate and failure behavior of woven-ply reinforced thermoplastic structures at high temperature

Abstract The purpose of the present work is to investigate damage evolution in 5-harness satin weave carbon fabric reinforced PolyPhenylene Sulphide (PPS) structures with an initial edge notch. To understand how the physical properties of the constituents (e.g. matrix toughness and ductility) and the architecture of reinforcement (woven-ply) affect the fracture behavior of C/PPS laminates, it is useful to have analytical representation of the translaminar failure modes based on fracture mechanics concepts, the strain energy release rate G especially. Translaminar failure is determined by the combination of loading, location of defect and material heterogeneity (presence of matrix-rich regions at the crimp area in woven-ply laminates). When translaminar failure is initiated from an existing notch, a sequence of energy-absorbing events (fiber breakage, matrix cracking, fibers pull-out, fiber/matrix debonding) occurs in a region surrounding the notch tip. The knowledge of energy-absorbing processes is therefore important since they are responsible for the toughness of the composite. Depending on laminates' stacking sequence, the contribution of matrix behavior to strain energy release rate can be evaluated during damage in both brittle and ductile composite laminates subjected to high temperature conditions (T > T g ) when matrix ductility and toughness are enhanced. Depending on the initial notch orientation (0 or 45°), the failure mode is either a mode I or a mixed mode (I + II). The acoustic energy associated with translaminar failure was correlated with the strain energy release rate during translaminar failure. The total strain energy release rate in quasi-isotropic (QI) laminates is 6 times as low as in angle-ply (AP) laminates, suggesting that large plastic deformation (due to a matrix-driven behavior and an enhanced matrix ductility at T > Tg) are instrumental in dissipating a great portion of the mechanical energy brought to the specimen in AP laminates. The “material” effect is combined with a structural one (rotation of the fibers) at the crack tip, and leads to ductile failure. Both effects contribute to high fracture toughness in AP laminates.

Effect of hygrothermal conditioning on the energy release rate and failure mechanism of metal only adherend-glass fibre prepreg co-cured single lap joints

Fibre-reinforced composite materials are extensively used in repair and rehabilitation of oil and gas metal infrastructures which are largely exposed to water and hydrocarbon. An important aspect to this is applying adequate surface preparation to the metal to ensure a durable bond between the composite and metal substrate. In this paper, mild steel surface was prepared using grit blasting and single lap joint (SLJ) test specimens were manufactured and tested to investigate the adhesion in terms of total energy release rate (GT) of the interface between mild steel adherend and glass fibre prepreg. An out-of-water usable epoxy resin primer was incorporated to join mild steel adherend with glass fibre prepreg by curing at a temperature of 55 °C for 48 h. Upon durability testing of the SLJ specimens using hygrothermal conditioning at a temperature of 55 °C for 1000 h, the experimental GT values were seen to reduce significantly. Comparatively lower amount of cohesive failure and increased amount of swelling or delamination of the adhesive was observed for conditioned SLJ specimens when compared to controlled SLJ specimens. Furthermore, the experimental GT values were found to correlate well with an analytical adhesive interface model.

Experimental study on ceiling gas temperature and flame performances of two buoyancy-controlled propane burners located in a tunnel

Multiple energy sources in a tunnel might lead to merge of flames with small enough spacings, releasing more heat and pollutant emissions than a single energy release source in tunnel and thus posing a great threat to tunnel structure, facilities and trapped people. As the heat detection, controlling and cooling systems are originally designed for the single energy release source, while the spacing between energy sources in tunnel is changeable and unpredictable. Then it is important and helpful to research on the much different characteristics of multiple energy sources with interacting ceiling flames for effective control the high risk scenarios. This paper aims to study the ceiling gas temperature profile and flame properties induced by two interacting energy sources in tunnel so as to improve the understanding of the arrangement of heat detectors and water sprinklers in tunnel. Two identical propane burners were used as energy sources located in a longitudinal array in tunnel. The total energy release rate and burner spacing were varied. The flame merging probability, ceiling gas temperature, vertical flame height and longitudinal flame extension were measured. The criteria of beginning merging and fully merging of flames are respectively proposed for two energy sources in tunnel. Results showed that the area of ceiling flame region increases with higher energy release rate. Models for predicting the ceiling gas temperature profiles induced by two energy sources in tunnel are established respectively for weak and strong plumes impinging on the ceiling. A modified model for predicting the combined vertical and longitudinal flame lengths from two burners in tunnel is proposed involving the normalized energy release rate, burner size and spacing. Finally, the comparison between models proposed for ceiling gas temperatures and flame lengths in tunnel and other configurations identifies the high risk of multiple energy sources in tunnel.

Energy release rate of beam-type fracture specimens with hygrothermal influence

Three interface joint models for calculating energy release rate are extended to include hygrothermal effect with consideration of uniform or nonuniform changes of temperature or moisture through layer thickness in a cracked bilayer beam system using both J-integral and correction methods. The method of J-integral leads to a general expression of total energy release rate in terms of the crack-tip moments and forces, while the correction method gives explicit formulas of total energy release rate with inclusion of a separate energy release rate term subjected to only mechanical loads. Several bilayer beam fracture specimens subjected to transverse load or equivalent bending moment and thermal load are considered to validate accuracy of two methods in connection with three interface joint models, and the results show that the flexible joint model produces the best predictions for all the specimens. A parameter study is conducted to evaluate influences of thickness ratio, modulus ratio of upper and lower layers, change of temperature, and temperature gradient on the energy release rate. All the factors show a pronounced influence on the energy release rate, and a special attention is paid to evaluate effect of temperature change and temperature gradient on the energy release rate of bilayer beams. The moisture change and its gradient have the same effect and formulations on the energy release rate of bilayer beams as those of temperature, and the moisture portion of derivations and its effect are thus not given in detail.

Effect of Poisson’s ratio mismatch on brittle interfacial cracking between two dissimilar elastic layers

Previous work by the authors (Harvey et al., 2015) on brittle interfacial cracking between two dissimilar elastic layers is extended to accommodate Poisson’s ratio mismatch in addition to the existing capability for elastic modulus mismatch. Under crack tip bending moments and axial forces, it is now possible to use a completely analytical 2D elasticity-based theory to calculate the complex stress intensity factor (SIF) and the crack extension size-dependent energy release rates (ERRs). To achieve this, it is noted that for a given geometry and loading condition, the total ERR and bimaterial mismatch coefficient are the two main factors affecting the partitions of ERR. Based on this, equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson’s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be ‘transformed’ into cases for which the analytical solution does exist. The approach is verified against results from 2D finite element method simulations in which excellent agreement is observed for cases of plane stress and plane strain with a variety of loading conditions.

Analysis of the damage mechanisms in mixed-mode delamination of laminated composites using acoustic emission data clustering

In this study, acoustic emission (AE) technique is used to investigate different time-to-failure mechanisms of delamination in glass/epoxy composite laminates. Woven and unidirectional layups were subjected to the double cantilever beam, end notch flexure, and mixed-mode bending tests and the generated AE signals were captured. Discrimination of the AE events, caused by different types of the damage mechanisms, was performed using wavelet packet transform (WPT) and fuzzy clustering method (FCM) associated with a principal component analysis (PCA). The FCM and WPT analyses identified three dominant damage mechanisms. Furthermore, different interface layups and different GII/GT modal ratio values (ratio of mode II strain energy release rate per total strain energy release rate) indicated different time-to-failure mechanisms incidence. Additionally, the damaged mechanisms were observed using scanning electron microscopic (SEM) analysis. The results showed that the dominant damage mechanisms in all the specimens are matrix cracking and fiber–matrix debonding. Besides, some fiber breakage appeared during the tests, and the percentage of this damage mechanism in the unidirectional specimens and mode I condition was higher than those in the woven specimens and mode II. SEM observations were also in good agreement with the obtained results. It was found that the presented methods can be utilized to improve the characterization and discrimination of damage mechanisms in the actual occurring modes of delamination in composite structures.

Calculation of total energy release rate in post-local buckling delamination of composite laminates

In the present article, the variational energy principle is used to derive the expression for energy release rate in buckled composite laminate containing through-the-width delamination, subjected to in-plane strains. Boundary conditions are clamped at both edges. Buckling and post-buckling solutions are obtained and expressions for critical buckling load and post-buckling deflection have been developed. A through-the-width delamination model has been considered and formulations are based on higher order shear deformation theory. The effects of considering the higher order shear deformation theory on equivalent bending rigidity, buckling load, and energy release rate have been investigated. Finally, the results of current study have been compared with the results of finite element method analysis by Abaqus/CAE and those available in the literature.

On the total electro-mechanical potential energy and energy release rate at the interface crack tips in an initially stressed sandwich plate-strip with piezoelectric face and elastic core layers

An investigation into the values of the total electro-mechanical potential energy and energy release rate (ERR) at the interface crack tips in an initially stressed sandwich plate-strip is carried out for the opening crack mode. It is assumed that the face layers of the considered sandwich plate are made from piezoelectric materials but that the core is made of elastic material, and that this sandwich plate has initial stresses caused by the uniformly distributed normal forces acting on the planes of the two parallel grounded ends of the plate. The plate has two parallel interface cracks symmetrically located with respect to the middle planes and additional uniformly distributed normal opening mechanical forces acting on the cracks’ edges. Moreover, the face planes of the face layers and the cracks’ edges are unelectroded with vanishing normal electric displacement and are free of electrical charge. The investigations are made by utilizing the three-dimensional linearized theory of electro-elasticity in a plane-strain state within the framework of the piecewise homogeneous body model. The solution to the corresponding boundary value problems are found numerically by employing the finite element method. Numerical results, which are presented and analyzed, illustrate the influences of the geometrical parameters and the initial stresses, as well as the coupling effects between the electro-mechanical fields, on the values of the total electro-mechanical potential energy and of the ERR.