Strain Energy Release Rate In Mode Research Articles

Study of the Fracture Behavior under the Effect of Cross-ply and Angle-ply Arrangement of FRP Composite Laminate Subjected to Central Circular Cut-out with Mechanical and Thermal Loading Conditions

In advance composite material the propagation of crack is a regular failure problem in various engineering applications especially in aircrafts body. The aircraft body components are subjected to various thermal and mechanical loading conditions. It is very difficult, time-consuming and costly process of testing the aircrafts components failure due to various thermal and mechanical conditions. Strain energy release rate (SERR) is the significant parameter for the composite materials and quality of composite materials depends in SERR values.The present investigation is based on ANSYS analysis for finding the strain energy release rate (SERR) value using Virtual Crack Closure Technique (VCCT) to understand the fracture behavior of the composite lamina. The circular crack present in the middle of the composite plate and subjected to Pressure and temperature loading for different angle (cross-ply& and angle-ply) composite structure laminas. The angle-ply shows less SERR in mode I & II while cross-ply shows less SERR in mode III under the constant Pressure loading conditions. Mode II shows the maximum SERR in cross-ply compared to mode I and III for temperatures 30ºC,80ºC, 130 ºC & 180ºC. SERR for mixed-mode was found by considering the total mode of fracture and validation based on published literature for SERR due to the Thermal load of mode I (GI) for different fiber layup configurations of the circular cut-out.

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.

Delamination propagation analyses of spar wingskin joints made with curved laminated FRP composite panels

Initiation and propagation of inter-laminar delamination in adhesive bonded spar wingskin joint (SWJ) made with laminated fibre-reinforced plastic (FRP) composite curved panels have been studied employing three-dimensional finite element analyses. In-plane and out-of-plane normal and shear stress distributions are seen to be highly three-dimensional in nature. Tsai-Wu coupled stress failure criteria have been employed to identify critical locations of onset of delamination-induced damage. This occurs underneath the toe-end of the spar overlap and at the inter-laminar surface between the first and second plies of the curved FRP wingskin panel. Significant edge effects on the joint strength have been observed due to the curvature geometry of the composite wingskin panels. Non-linear finite element analyses have been carried out for study of delamination propagation using contact and multi point constraint (MPC) elements. The use of contact elements prevents inter-penetration of delaminated surfaces. Whereas, sequential release of MPC elements facilitates computation of opening, sliding and cross-sliding modes of delamination-induced strain energy release rates (SERR) by using virtual crack closure technique. Variation in delamination lengths significantly effects the variation of peel and inter-laminar shear stresses and different modes of SERRs. Variations on the two delamination fronts are seen to be quite different indicating dis-similar propagation rates. The Mode I SERR (GI) predominantly governs the delamination propagation in the SWJ.

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.

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.

Fracture in foam core composite sandwich beams under mixed-mode I/II/III loading conditions

Static fracture in foam core composite sandwich beams under mixed-mode I/II/III crack loading conditions is studied theoretically by the Mixed Mode Flexure (MMF) beam configuration. The basic idea of this paper is that mixed-mode I/II/III crack loading conditions can be generated by loading the MMF sandwich beam by an inclined force (usually, the MMF beam, loaded by a vertical force, is used for investigating mixed-mode I/II fracture in continuously fiber reinforced polymer com- posites). Three-dimensional finite element simulations of the MMF sandwich beam are performed using the ANSYS program system. The methods of linear-elastic fracture mechanics are applied. The fracture behavior is studied in terms of the strain energy release rate. The virtual crack closure technique is applied to analyze the strain energy release rate mode components distribution along the crack front in the MMF beam at the force inclination varying from 0 ◦ (force parallel to the crack front) to 90 ◦ (vertical force). The analysis revealed that the MMF beam loaded by an inclined force can be used to study the mixed-mode

Mixed-mode I/II fracture study of polymer composites using Single Edge Notched Bend specimens

Fracture behavior of polymer composites was investigated using Single Edge Notched Bending (SENB) specimens. The basic idea of this research was to check the ability of the SENB test method for generating mixed-mode I/II loading conditions by introducing an inclined notch as initial crack. For this purpose, SENB specimens containing a notch inclined at different angles were tested under static loading at room temperature. Three-dimensional finite element models were developed for simulating the mechanical response of the SENB test specimens. The test data were analyzed using methods of linear-elastic fracture mechanics. In order to validate the models, the predicted load–displacement responses were compared to the measured ones at different inclinations of the notch. From the experimentally measured crack growth initiation loads critical strain energy release rates at various mixed-mode I/II loading conditions were computed using the virtual crack closure technique. Non-uniform distribution of the critical strain energy release rate mode components along the crack front was obtained. It was found that besides modes I and II, there was also insignificant mode III component of the critical strain energy release rate. The simulations revealed that the relative amount of mode II component of the critical strain energy release decreased with increasing the notch inclination. It was shown that SENB specimens with inclined notch can be used for investigating fracture behavior of fiber reinforced polymer composites under various mixed-mode I/II crack loading conditions.

3D FE delamination induced damage analyses of adhesive bonded lap shear joints made with curved laminated FRP composite panels

This paper deals with the evaluation of inter-laminar stresses in the adhesive layer existing between the lap and the strap adherends of lap shear joints (LSJ) made with curved laminated fibre reinforced plastic (FRP) composite panels for varied embedded delaminations between the first and second plies of the strap adherend. Non-linear finite element analyses have been carried out using contact and multi point constraint (MPC) elements. The use of contact elements ensures avoidance of inter-penetration of delaminated surfaces. Sequential release of MPC elements facilitates computation of individual modes of Strain Energy Release Rates (SERR). The effects of varied delamination lengths on variations of peel and inter-laminar shear stresses and different modes of SERR are seen to be very significant. Their variations on both the delamination fronts, for each size of the delamination, are found to be much different from each other indicating different propagation rates at the two delamination fronts. The structural integrity of the LSJ in the presence of delaminations, thus, can be predicted with adaptive finite element (FE) simulations. It is further seen that the peak stress magnitudes and SERRs are higher in the LSJs made with curved FRP composite panels as compared to the flat laminates. This may be due to the stiffening effects induced by the curvature geometry of the curved composite panels.

Fracture study of rigid foam using single edge notched bend specimens with inclined notch

This paper presents results from a study of fracture behavior of rigid foam. Various mixed-modes I/II loading condi- tions were generated by the aid of single edge notched three point bending (SENB) test specimens containing an inclined notch as an initial crack. Three-dimensional finite element models of the SENB specimens were developed for analyzing the fracture test data. From the experimentally measured crack growth initiation loads various mixed-mode I/II critical strain energy release rates were computed by the virtual crack closure technique. The analysis revealed that besides mode I and mode II, there was also insignificant mode III component of the critical strain energy release rate. The variation of the critical strain energy release rate mode components with increase of the notch inclination was studied. It was found that the relative amount of the mode II component progressively decreases with increasing the notch inclination. It was concluded that the considered version of the SENB test specimen can be used for investigating fracture behavior of rigid foams in a function of the mixed-mode ratio over an interval of 0 G a/G a 0.413. It was found also that the theory of Sih can be applied successfully for analysis of

Validation and enhancements for the localised experimental–numerical technique

Over many years the use of composite structures in aerospace and automobile applications has been expanding. Thus, the study of weaknesses associated with composite materials has become paramount. Delamination is a fundamental concern with these structures, and mixed mode strain energy release rates are valuable information for analysing delamination cracks. The localised experimental–numerical technique (LENT), which measures local test displacement data and combines this with local finite element analysis to evaluate the mixed mode strain energy release rates, is examined via extensive experimental testing and analysis to provide validation for the technique. Additionally, a sensitivity analysis is presented to assess the influence of pixel size on the strain energy release rate results determined using LENT. Enhancements to the method are presented focusing on reducing the pixel size and improving post-processing techniques for increased accuracy. Variations in the local area analysed with LENT are also investigated. The results demonstrate that the localised experimental–numerical technique has potential for the evaluation of mixed mode strain energy release rates using localised test data.

A localised experimental–numerical technique for determining mixed mode strain energy release rates

Composite structures are being used increasingly in the aerospace industry due to their superior specific stiffness and strength. One key issue associated with such structures is delamination, and how to effectively predict this. A new method which is derived from localised test displacement data is presented to determine the mixed mode strain energy release rates of layered structures with a pre-existing crack. Images taken during experimentation of the vicinity of the crack tip are analysed at low load and high load to determine the displacement changes across the load variation. These displacements are applied as boundary conditions to a simple local numerical model including a constraint at the crack tip. The forces and displacements at the crack tip are taken as output data and combined with the Virtual Crack Closure Technique to predict strain energy release rates. Initial validation of the localised experimental–numerical technique (LENT) shows that applying experimental data to a numerical model does give reasonable agreement thus far in the established trends, and hence LENT is promising for use in determining mixed mode strain energy release rates and mode mixity ratios.

Influence of SiC Electron Acceptor–Donor Modification on Thermal and Physical Properties of Carbon Fiber/SiC/Epoxy Composites

In this work, the effects of electron acceptor–donor modification on the surface properties of SiC were investigated in the mechanical interfacial properties of carbon fibers-reinforced SiC-impregnated epoxy matrix composites. The surface properties of the SiC were determined according to acid/base values and FT-IR, and contact angle measurements. The thermal and mechanical interfacial properties of the composites were evaluated using a thermogravimetric analysis, critical strain energy release rate mode II (G IIC), and impact strength testing. As a result, the electron acceptor-treated SiC had a higher acid value and polar component in surface free energy than did the untreated SiC or the electron donor-treated SiC. The G IIC and impact strength mechanical interfacial properties of the composites had been improved in the specimens treated by acidic solutions due to the good wetting and a high degree of adhesion with electron donor characteristic epoxy resins.

Three Dimensional Failure Analysis and Damage Propagation Behavior of Adhesively Bonded Single Lap Joints in Laminated FRP Composites

A three-dimensional finite element analysis has been developed to compute the out-of-plane normal (known as peel stress) and shear stresses in an adhesively bonded single lap joint (SLJ) with laminated FRP composite plates which, in comparison to other analytical methods for bonded joint analysis, is capable of handling more general situations related to initiation of damages and its growth. Other analytical methods, such as Hart-Smith’s (Hart-Smith, L. J. (1973). Adhesive-Bonded Single Lap Joints, NASA-CR-112236.), are 1-D and mainly focus on obtaining adhesive stresses, while generally ignoring stresses in laminated adherends, particularly interlaminar stresses which are known to be the key contributors to the failure. Unlike the Volkersen’s (Volkersen, O. (1938). Die Niektraftverteilung in Zugbeanspruchten mit Konstanten Laschenquerschritten. Luftfahrtforschung, 15: 41-47.) and Goland-Reissener’s (Goland, M. and Reissner, E. (1944). The Stresses in Cemented Joints, Journal of Applied Mechanics, 11: 17-27.) analysis, the free rotation of the overlap region and adherends are considered in the present analysis. Joining of composite structures using adhesive bonding has always been a concern to the designers because the performance of the joint is severely influenced by the characteristics of the laminated composite adherends, which usually have low inter-laminar strengths. The present method computes local 3D stress fields in the most critical region, which vary along the overlap length. Adhesive layer is a linearly elastic material whereas the adherend materials are orthotropic. Thus an accurate evaluation of 3D local stress fields will enable the failure criterion to be employed effectively to predict joint strength and initiation/propagation of damages. The analysis consists of four steps. In the first step a complete three dimensional stress analysis is carried out with a special importance for the evaluation of out-of-plane stresses. Failure indices at different surfaces are calculated in the second step. The third step identifies the location of damage initiation based on the value of the failure indices. The failure index for the adhesive layer is calculated using quadratic failure criterion (QFC), whereas the Tsai-Wu’s coupled stress quadratic failure criterion is used for the interface of adherend and adhesive. Subsequently, damage propagation is analyzed by fracture mechanics based strain energy release rate (SERR) approach using virtual crack closure technique (VCCT). It is seen that the three-dimensional effects exist in the joint. The stress distributions in the joint overlap region near the free surface are quite different from those occurring in the interior. Also, it is found that the peel stresses are extremely sensitive to this three-dimensional effect, but the shear stresses are not. The value of the failure index at the interface of the loaded adherend (top) and adhesive along the free edge is the highest which indicates the location of the possibility of damage initiation. Such type of damage is considered as an adhesive failure. The propagation of such damage is governed by SERR. It is observed that the individual mode of SERR remains constant over the damage front irrespective of the damage length except at the free edge. Moreover, it is found that contribution of SERR in mode II is prominent compared to the mode I and mode III for the damage propagation due to the adhesive failure in the SLJ.

A shell/3D modeling technique for the analysis of delaminated composite laminates

A shell/3D modeling technique was developed for which a local solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local 3D model and the global structural model which has been meshed with shell finite elements. Double Cantilever Beam, End Notched Flexure, and Single Leg Bending specimens were analyzed first using full 3D finite element models to obtain reference solutions. Mixed mode strain energy release rate distributions were computed using the virtual crack closure technique. The analyses were repeated using the shell/3D technique to study the feasibility for pure mode I, mode II and mixed mode I/II cases. Specimens with a unidirectional layup and with a multidirectional layup were simulated. For a local 3D model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Delamination in Thickness Tapered Composite Laminates

The structural performance of thickness-tapered laminates has been investigated using an energy-based damage tolerance methodology. The geometry studied is a thin laminate with discontinuous internal plies and a through-width delamination embedded at the interface between continuous and discontinuous sublaminates. An analytic model, based on shear deformation plate theory and linear-elastic fracture mechanics is employed to determine the Mode I and Mode II components of strain energy release rate. A two-dimensional plane strain finite element analysis is conducted to confirm the accuracy of the analytic predictions. The resulting pure mode strain energy release rates are combined with a mixed-mode growth criterion to predict the axial load required to induce delamination growth. Finally, the analytic and numerical model were used to predict failure in a delamination critical test specimen. Reasonable agreement of the actual and predicted failure loads was observed.

The components of energy release rate for interfacial cracks

Interfacial crack growth is inherently mixed mode in nature and mode-mixity must be defined clearly in order to characterize it. Mode and mode strain energy release rates for an interfacial crack in bimaterial system were analytically derived by the virtual crack closure technique. It is shown that the energy release rate for mode and mode do not converge due to the presence of violent oscillatory near tip behavior. However, the total energy release rate is well-defined.

Strain Energy Release Rates in Finite Graphite/Epoxy Plates with a Crack under Mixed Mode Deformation

This paper investigates the mixed mode problem numerically and experi mentally for the finite orthotropic plate where an inclined crack parallel to the fiber direc tion is centrally placed. The mixed mode correction factors of strain energy release rate are calculated by using the modified mapping collocation method and those of graphite/ epoxy plates are presented as functions of the crack length for various aspect ratios, crack angles and boundary conditions. To confirm the validity of these results, the mixed mode fracture test for graphite/epoxy specimens is performed for selected combinations of crack length and angle. Mixed mode strain energy release rates for various crack angles and crack lengths are obtained.