Total Strain Energy Release Rate Research Articles

Application of a hierarchical quadrature element method to interface crack analysis in bi-material systems

This paper presents an extension of the hierarchical quadrature element method (HQEM) with p-convergence to evaluating fracture mechanical parameters of bi-material interface cracks. The numerical implementation of HQEM in combination with the virtual crack closure method (VCCM) is comprehensively illustrated, and the formulas for calculating the strain energy release rate (SERR) are rederived. The relationship between components of SERR and the complex stress intensity factors (SIFs) is established. In addition, the effectiveness of an auxiliary parameter related to the dual energy release rates in measuring the accuracy of the present method is examined.The feasibility of applying HQEM to the interface crack problems is demonstrated by investigating the benchmark problem of an infinite bi-material plate with a central interface crack. Two loading cases are considered, including pure tensile loading and mixed tensile-shear loading. The influence of the crack tip element size Δa on the convergence characteristics and computational accuracy of fracture parameters is quantitatively investigated to provide guidance for choosing the most reasonable value of Δa. Numerical results show that even with very coarse meshes, together with a virtual crack extension consisting of only one element, HQEM yields highly accurate results for the total SERR and the complex SIFs, making it suitable for complex, large-scale interface crack problems in dissimilar media.

An Analytical Solution of the Total Strain Energy Release Rate and Mode Partitioning of a Beam Type Delamination Specimen under High Speed Mixed-Mode Loading

In this work an analytical solution for the calculation of the total Stain Energy Release Rate and mode partitioning of beam type delamination specimen, at crack initiation, under high speed, mixed-mode loading is obtained for the first time. The analytical model is based on the dynamic response of a Mixed-Mode End Load Split type specimen subjected to loading with a constant velocity. The Timoshenko beam theory is used to model the specimen's kinematics and the mode partitioning method used is based on the Virtual Crack Closure Technique. To model the bonded region a method based on Lagrangian multipliers is utilized. The specimen is considered as a waveguide and the waves that are allowed to propagate are analytically obtained. Due to the complexity of the analytical form of the wavenumbers for the bonded region of the specimen, which makes the calculation of eigenfrequencies intractable, a series approximation method is used. The results of the proposed analytical solution are verified using a 2D Finite Element Model. The results show the dependency of the Strain Energy Release Rate and the mode mixity on the eigenfrequencies and the eigenmodes of the specimen rendering the value of the mode mixity highly inconsistent through time.

Mixed-mode I+II fatigue/fracture characterisation of bi-material Aluminium/CFRP bonded joints

The fatigue/fracture behaviour of bi-material Aluminium/CFRP (Carbon-Fibre Reinforced Polymer) bonded joints was addressed in this work using the modified Paris law. Five types of tests were employed to cover appropriately the entire mode I – mode II range. Data reduction schemes based on equivalent crack length concept were developed for all types of tests. Following this methodology, the compliance versus number of cycles relation becomes sufficient to perform post-processing fatigue data analysis. The coefficients of the modified Paris law for each type of test were obtained by fitting a power law to the crack growth rate versus the ratio of total strain energy release rate and its critical value. The objective was to obtain relations representative of the evolution of those coefficients as function of mode ratio. These relations were subsequently input in a cohesive zone model at the local level, i.e., at each integration point. It was verified that the compliance versus number of cycles curves and the fatigue lives predicted numerically are in agreement with the experimental values.

Mixed-mode thermo elastic delamination fracture behavior of composite skin stiffener containing interface delamination

This paper presents the thermo-elastic effect on materials having anisotropic behavior and stresses developed due to residual temperature on interlaminar delamination fracture characteristics of composite skin stiffener. For the preexisting interlaminar delaminations subjected to uniaxial loading and three-point bending of three-dimensional coupled field thermo-elastic finite element analyses have been accomplished. The individual mode of strain energy release rate along the delamination front has been evaluated by modified crack-closure integral method based on the concept of mechanics of linear elastic fracture. Qualitative comparison has been illustrated for the individual modes of energy release rate along the delamination front of skin stiffener for both the loadings. The influence of coupled field thermo-elastic material anisotropy of the constituting laminae has been reasoned for the asymmetric variation of total strain energy release rate along delamination front. This was found to be significantly higher for the case of residual thermal stresses compared to mechanical loading.

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.

Extend the thermal cyclic lifetime of La2Zr2O7/YSZ DCL TBCs by reducing modulus design on a toughening ceramic surface

La2Zr2O7 (LZO), a potential thermal barrier coating material, is extensively used for components bearing remarkably higher temperatures due to its phase stability up to 2300 °C, but the lifetime of the pure LZO coatings is generally limited by the low toughness due to the cracking driving force. In this study, to decrease the driving force facilitating the failure of LZO layer and then extend the durability of thermal barrier coatings (TBCs), reducing modulus design on a toughening ceramic surface is introduced into the system. Three groups of LZO/YSZ double ceramic layers (DCL) TBCs with different low/high modulus (E) combination are used to satisfy the design. The crack driving force is evaluated by the strain energy release rate (SERR) at the tip of the LZO/YSZ interface crack. The total SERR G decreases from 28.2 N/m to 20.6 N/m when the thickness of low E LZO layer increases from 0 to 2 units (1 unit = 48 μm low E LZO), which reduces the cracking driving force of TBCs. After subjected to the gradient thermal cyclic tests with the surface temperature of 1300 °C. The TBCs system with 2 low E LZO shows the longest lifetime, which is 50% higher than that of pure YSZ TBCs. Thereby, reducing modulus design on a toughening ceramic surface may provide an alternative approach to improve the durability of TBCs.

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.

Adhesion failure propagation analyses of Spar Wingskin Joints made with curved laminated FRP composite and FGM panels

Spar Wingskin Joint (SWJ) comprises of a thin spar which overlaps and is co-cured to a thick wingskin by suitable adhesive materials. These joints are mostly used in integral modular fabrication of aircraft and fuselage wing structures usually made with curved laminated Fibre Reinforced Polymeric (FRP) composite panels. This paper deals with the analyses of initiation of adhesion failure and its propagation in SWJs subjected to transverse loadings using Finite Element Analyses (FEA) and fracture mechanics approach. Normal and shear stress distributions at different interfacial locations between the adherends and the adhesive have been evaluated. Tsai-Wu coupled stress failure criteria have been used to identify the location of onset of adhesion failure. The critical location for onset of adhesion failure has been found to be at the toe-end of the spar wingskin overlap region. Pre-embedded adhesion failure has been simulated at this location and Strain Energy Release Rate (SERR) components corresponding to Mode I, Mode II and Mode III of adhesion failure have been determined using the principle of Virtual Crack Closure Technique (VCCT). Rate of propagation of adhesion failure has been evaluated by sequential release of Multi-Point Constraint (MPC) and contact finite elements provided at the pre-embedded failure front. It has been observed that Mode I component of SERR primarily governs the process of adhesion failure propagation. The appropriate spar overlap length on the wingskin has been determined in order to prevent adhesion failure. Further, an attempt has been made to improve the structural integrity of the SWJ by reducing the stress concentration at the ends of spar and wingskin overlap. This has been achieved by obtaining a favourable stress distribution over the entire joint structure by using Functionally Graded Materials (FGM) in the spar and wingskin adherend instead of FRP composite panels. Exponential gradation indices have been used for material grading of the spar and wingskin adherends. It has been seen that peel and shear stresses and values of SERR components as well as total SERR reduce significantly by use of FGMs with suitable exponential material grading index.

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.

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.

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.

Dependence of the interlaminar fracture toughness of E-Glass/Polyester woven fabric composites laminates on ply orientation

Delamination is one of the most important defects in fiber reinforced composite laminates. This paper presents the delamination resistance of thick woven glass fiber reinforced polyester specimens and experimentally examines the effect of ply orientations in terms of the critical strain energy release rate. Specimens with different ply orientations (0°, 30°, 45° and 70°) are fabricated with plain woven (taffetas) fabrics. The tests used for the experiments are Double Cantilever Beam (DCB) for pure mode I, End Load Split (ELS) for pure mode II and Mixed Mode Flexure (MMF) for mixed mode I/II under static conditions. The experimental results have been expressed in terms of total strain energy release rate and R-curves. Results show that fiber bridging for woven fabrics occurred due to non-midplane crack propagation. The fracture toughness results show that the delamination resistance increase with ply angle until 45° then it decrease.

Mixed-Mode I/II fracture behavior of asymmetric composite joints

The partitioning of the total strain energy release rate, Gtot, into the Mode I, GI, and Mode II, GII, components is challenging, especially in asymmetric cracks. Although many researchers have studied the fracture behavior of composite materials under mixed-mode loading using symmetric and/or asymmetric mixed-mode bending (MMB) specimens, few studies exist in the literature regarding the experimental investigation and analysis of the fracture behavior of asymmetric MMB specimens comprised of orthotropic layered adherends.In this study, a new approach, designated as the “extended global method”, was established the fracture mode partitioning. The “extended global method” was applied for the analysis of the experimental data. The mixed-mode fracture behavior of adhesively-bonded composite joints was experimentally investigated using asymmetric mixed-mode bending specimens. Finite element models were developed in order to validate the approach. The virtual crack closure technique was used for the calculation of the fracture components at the crack tip and an exponential traction-separation cohesive law was used to simulate the fiber bridging zone. The crack propagated along paths outside the symmetry plane and, therefore, mode partition could not be performed in commonly accepted ways followed for symmetric specimens. In addition, the experimental compliance method was used for calculating the fracture energy of the examined asymmetric mixed-mode bending specimens. Results obtained using the “extended global method” and the experimental compliance method were in good agreement with the results from FE models. The outcome of this study combined with the results obtained from pure Mode I and Mode II experiments can be used to establish failure criteria for the examined joints, that can be eventually be used for designing structural joints with the same adherends and adhesives.

Quasi-Three-Dimensional Crack Tip Element Analysis for Evaluation of Total Energy Release Rate in Composite Laminates

An analytical quasi-three-dimensional crack tip element model is developed to provide a quick assessment of the delamination behavior for composite laminates. A closed-form solution for the average total strain energy release rate is obtained by taking into consideration of all the displacement components defined in the classical laminated plate theory. By means of numerical experiments, it is shown that the presented method can predict the average total strain energy release rates with satisfactory accuracy for a relatively large variety of composite layups under opening and in-plane-shearing loading conditions. It indicates that the influence of out-of-plane transverse displacements on the total energy release rate can be significant for certain type of layups even under in-plane loading conditions. Furthermore, an orthotropic parameter is introduced to represent the influence of out-of-plane transverse effects.

Thermoelastic analysis of nonhomogeneous structural materials with an interface crack under uniform heat flow

Many modern materials are layered material systems. Interfaces are inherent to these materials because they are heterogeneities, such as thermal and residual stresses in the elastic properties. In this paper, we study a partially insulated interface crack between two different functionally graded materials bonded to a homogeneous material subjected to a steady-state heat flux away from the crack region as well as mechanical crack surface stresses. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The properties of the functionally graded materials vary as exponential function in the thickness direction. Using the Fourier transform and a superposition technique, the singular integral equations for the temperature and the displacement fields are derived. The total strain energy release rate and strain energy density are obtained. Critical parametric studies are conducted for non-homogeneity parameter, the thermal stress intensity factors and minimum strain energy density.

Test Development and Materials Characterization Capability for High-Strength Aluminum Alloy Fatigue Crack Growth Response Under Mixed-Mode Loading Conditions

Abstract To meet operational efficiency and productivity demands of the 21st century marketplace, aerospace and transportation sector platforms are being driven to incorporate increasingly larger and more highly stressed unitized structural components. This recent trend has prompted the need for improved fatigue crack growth characterization methodologies to understand impact of relevant mixed-mode loading conditions on crack growth direction and life estimation. This paper describes the development of an Alcoa capability to study and model fatigue crack growth behavior under combined mode I and mode II loading in high-strength aluminum products. The objective is to demonstrate the experimental capability necessary to improve the basic understanding of the roles and synergistic effects of mixed-mode loading (modes I and II) and microstructural resistance, as they relate to fatigue crack growth direction and life estimation. The particular alloy selected for this study is aluminum alloy (AA) 7050-T7651 thick plate taken to be representative of a widely used material for aircraft thick structural parts. The specimens chosen for this capability study are based on the compact tension shear (CTS) specimen documented in the literature. Results are presented to demonstrate the development of stress-intensity factor and compliance solutions to automate the fatigue precracking step. Full-field strain measurements for a notched specimen are used to further validate the finite element analysis. In addition, preliminary results are presented to explore the feasibility of a Keq approach based on total strain-energy release rate to evaluate similitude in the fatigue crack growth rate relationship for the mixed-mode loading case. Preliminary fatigue crack growth test results show that under combined modes I and II loading, the fatigue crack growth rate and direction depend strongly on the competition between the mixed-mode crack-tip driving force and microstructural planes offering the weakest crack growth resistance.

Interfacial failure analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates

This paper deals with three-dimensional non-linear finite element analyses to assess the structural behavior of adhesively-bonded double supported tee joint of laminated FRP composites having embedded interfacial failures. The onset of interfacial failures is predicted by using Tsai–Wu coupled stress failure criterion with pre-determined stress values. The concept of fracture mechanics principle is utilized to study the sustainability of the tee joint having interfacial failures pre-existed at the critical locations. Individual modes of the strain energy release rates (SERR) GI, GII and GIII, are considered as the damage growth parameters and, are evaluated using the Modified crack closure integral (MCCI) technique based on the concept of linear elastic fracture mechanics (LEFM). Based on the stress analyses, it has been observed that the interfacial failures in tee joint structure trigger at the interface of base plate and adhesive layer from both ends of base plate. Depending on the SERR magnitudes, it has been noticed that the interfacial failure propagates under mixed mode condition. Therefore total SERR (GT) is considered as the governing parameter for damage propagation. Furthermore, efforts have been made to retard damage propagation rate by employing functionally graded adhesive (FGA) instead of monolithic adhesive material. Series of numerical simulations have been performed for varied interfacial failure length in functionally graded adhesively bonded double supported tee joint structure in order to achieve the significant effect of FGA with various modulus ratios on SERR. Material gradation of adhesive indicates significant SERR reduction at the incipient stage of failure which necessitates the use of functionally graded adhesive for the tee joint and prolong the service life of the structure.