Delamination Fracture Behaviour Research Articles

Experimental study on effects of asymmetrical stacking sequence on carbon fiber/epoxy filament wound specimens in DCB, ENF, and MMB tests

This study focused on the delamination fracture behavior of asymmetrical stacking sequences of CFRP laminates subjected to different loading directions in double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode bending (MMB) tests. CFRP laminates with three different stacking sequences mimicking the winding angles of filament wound structures were considered. As the stacking sequences were asymmetrical, flipped and non-flipped specimens were tested to examine the effects on different test loading conditions. According to the results, each stacking sequence provided a different load–displacement response and fracture toughness. The flipped and non-flipped specimens did not appear to affect the fracture toughness in the DCB test. However, significant effects were observed in the ENF and MMB tests. Observations at the edges of the specimens indicated the dependency of the delamination behavior on the specimen stacking sequence. The delamination surfaces were further analyzed using a scanning electron microscope (SEM). SEM images revealed several delamination mechanisms that contributed to the load–displacement response and fracture toughness of the laminates.

Analyses of delaminations in non-linear elastic multilayered inhomogeneous beam configurations

This paper presents investigation of delamination fracture behavior of multilayered non-linear elastic beam configurations by using the Ramberg-Osgood stress-strain relation. It is assumed that each layer exhibits continuous material inhomogeneity along the width as well as along thickness of the layer. An approach for determination of the strain energy release rate is developed for a delamination crack located arbitrary along the multilayered beam height. The approach can be applied for multilayered beams of arbitrary cross-section under combination of axial force and bending moments. The layers may have different thickness and material properties. The number of layers is arbitrary. The approach is applied for analyzing the delamination fracture behavior of a multilayered beam configuration subjected to four-point bending. The beam has a rectangular cross-section. The delamination crack is located symmetrically with respect to the beam midspan. The strain energy release rate is derived assuming that the modulus of elasticity varies continuously in the cross-section of each layer according to a hyperbolic law. In order to verify the solution to the strain energy release rate, the delamination fracture behavior of the multilayered non-linear elastic four-point bending beam configuration is studied also by applying the method of the J-integral. The solution to the strain energy release rate derived in the present paper is used in order to perform a parametric study of delamination.

Influence of the viscoelastic material behaviour on the delamination in multilayered beam

An analysis of the influence of the viscoelastic behaviour of the material on the delamination fracture in multilayered beam structures subjected to creep is carried-out. The fracture is studied in terms of the strain energy release rate. For this purpose, an approach for calculation of the strain energy release rate by analyzing the energy balance in the beams is developed. Four viscoelastic models consisting of combinations of linear dashpots and springs for a constant applied stress are used for treating the creep behaviour. The approach is applied to analyze the strain energy release rate in a multilayered cantilever beam with a delamination crack subjected to creep. The analysis indicates that the creep leads to increase of the strain energy release rate. The effects of the ratios of coefficients of viscosity and the moduli of elasticity in the beam layers on the delamination fracture behaviour are evaluated by using the four viscoelastic models.

Influence of sine material gradients on delamination in multilayered beams

The present paper deals with delamination fracture analyses of the multilayered functionally graded non-linear elastic Symmetric Split Beam (SSB) configurations. The material is functionally graded in both width and height directions in each layer. It is assumed that the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section. Sine laws are used to describe the continuous variation of the material properties in the cross-sections of the layers. The delamination fracture is analyzed in terms of the strain energy release rate by considering the balance of the energy. A comparison with the J-integral is performed for verification. The solution derived is used for parametric analyses of the delamination fracture behavior of the multilayered functionally graded SSB in order to evaluate the effects of the sine gradients of the three material properties in the width and height directions of the layers and the location of the crack along the beam width on the strain energy release rate. The solution obtained is valid for two-dimensional functionally graded non-linear elastic SSB configurations which are made of an arbitrary number of lengthwise vertical layers. A delamination crack is located arbitrary between layers. Thus, the two crack arms have different widths. Besides, the layers have individual widths and material properties.

Influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams

The delamination fracture in four-point bending beams made of adhesively bonded lengthwise vertical layers is studied assuming that each layer exhibits smooth material inhomogeneity along the width and length of the layer. The study aims at determining the strain energy release rate with applying the Ramberg-Osgood equation for modeling the non-linear mechanical behavior of the material in each layer. Cosine laws are used to describe the continuous variation of the modulus of elasticity in width and length directions of layers. Beams made of an arbitrary number of vertical layers which have individual widths and material properties are considered. Besides, the delamination crack is located arbitrary between layers, i.e. the two crack arms have different widths. The J-integral is applied for verification of the non-linear solution to the strain energy release rate derived in the present paper. The solution is used to investigate the influence of material inhomogeneity in width and length directions of layers, the crack location along the beam width, the non-linear mechanical behavior of the material and the crack length on the delamination fracture behavior. The approach developed is expected to be useful in structural design of multilayered inhomogeneous beams with considering the delamination fracture behavior.

Non-linear delamination in two-dimensional functionally graded multilayered beam

PurposeA delamination fracture analysis of two-dimensional functionally graded multilayered end-loaded split beam configuration with non-linear mechanical behaviour of material is conducted. The beam is made of an arbitrary number of longitudinal layers. Perfect adhesion between layers is assumed. The material is two-dimensional functionally graded in the cross-section of each layer. Also, each layer has individual thickness and material properties. A delamination crack is located arbitrary along the beam height. The paper aims to discuss these issues.Design/methodology/approachThe delamination fracture behaviour is investigated analytically in terms of the strain energy release rate by analysing the balance of the energy. An additional analysis of the delamination fracture is performed by applying the J-integral approach for verification.FindingsThe solutions derived are used to evaluate the effects of crack location, material gradients and material non-linearity on the delamination fracture behaviour of end-loaded split beam. The effect of material gradient on the distribution of the J-integral value along the crack front is elucidated too.Originality/valueDelamination in the multilayered functionally graded end-loaded split beam exhibiting non-linear mechanical behaviour of the material is analysed assuming that the material property is distributed non-linearly in both thickness and width directions in each layer.

Fracture Analysis of a Three-Dimensional Functionally Graded Multilayered Beam

Delamination fracture behavior of the three-dimensional functionally graded multilayered crack lap shear (CLS) beam configuration was studied analytically in terms of the strain energy release rate with linear-elastic fracture mechanics methods. The CLS under consideration can consist of an arbitrary number of layers, each having different thickness and material properties. The material of each layer is functionally graded along its width, thickness, and length. A delamination crack is arbitrarily located along the beam height. The strain energy release rate was derived by analyzing its density in the beam cross section ahead and behind the crack front. It was additionally analyzed using the strain energy release rate was performed by using the beam strain energy for verification. The effect of the material gradient and crack location along the beam height on the delamination fracture behavior was evaluated.

Delamination of Multilayered Functionally Graded Beams with Material Nonlinearity

Delamination fracture in multilayered functionally graded, split cantilever beams is analyzed with account taken of the nonlinear behavior of the material. The fracture is studied analytically in terms of the strain energy release rate. The mechanical behavior of the material is described by a power-law stress–strain relation that is not symmetric for tension and compression. The beam can have an arbitrary number of vertical layers of different thickness. Each layer can have different material properties. Besides, the material in each layer is functionally graded along the layer thickness. Also, the delamination fracture can occur at any interface. The strain energy release rate is derived by analyzing the complementary strain energy of the beam. The solution obtained is applied to elucidating the effects of crack location, material gradient and material nonlinearity on the delamination fracture behavior of multilayered functionally graded beam configuration. It is found that the material nonlinearity leads to increase of the strain energy release rate, which implies that the material nonlinearity should be taken into account in the fracture mechanics based safety design of multilayered functionally graded structural members and components.

Non-linear fracture analysis of multilayered two-dimensional graded beams

PurposeThe purpose of this paper is to present an analytical study of the delamination fracture behaviour of a multilayered two-dimensional functionally graded cantilever beam configuration. A delamination crack is located arbitrary along the height of the beam cross-section. The layers have different thicknesses and material properties. Perfect adhesion is assumed between layers. The material is functionally graded in both thickness and width directions in each layer. Besides, the material of the beam exhibits non-linear-elastic behaviour.Design/methodology/approachThe delamination fracture behaviour is analysed in terms of the strain energy release rate. The J-integral approach is applied in order to verify the analysis of the strain energy release rate developed in the present paper.FindingsThe influence of material properties, the crack location along the height of the beam cross-section and the non-linear behaviour of the material on the delamination fracture is examined.Originality/valueA non-linear delamination fracture analysis of multilayered two-dimensional non-symmetric functionally graded beam configuration is developed.

Elastic-plastic delamination of multilayered graded four-point bending beam

PurposeThis paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.Design/methodology/approachThe mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness.FindingsThe analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions.Originality/valueDelamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

Fracture analysis of a three-dimensional functionally graded beam

PurposeThe purpose of this paper is to carry out a delamination fracture analysis of the three-dimensional functionally graded split cantilever beam (SCB) configuration.Design/methodology/approachThe fracture behaviour was studied analytically in terms of the strain energy release rate by applying methods of linear elastic fracture mechanics. It was assumed that the material is functionally graded along the beam width, height and length. The strain energy release rate was derived by analysing the stress and strain state in the beam cross-sections ahead and behind the crack front. An additional analysis of the strain energy release rate was performed by considering the beam strain energy for verification.FindingsThe influence of material gradient along the beam width, height and length on the delamination fracture behaviour was investigated. The effect of crack length was analysed too. The analytical approach developed is very useful for parametric fracture investigations. The results obtained in the present study can be applied for optimisation of three-dimensional functionally graded beam systems in their design with respect to delamination fracture behaviour.Originality/valueAn analytical approach for studying the delamination fracture in the SCB configuration that is functionally graded along the beam width, height and length was developed.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.

Delamination Analysis of a Multilayered Two-Dimensional Functionally Graded Cantilever Beam

Delamination fracture behaviour of a multilayered two-dimensional functionally graded cantilever beam is analyzed in terms of the strain energy release rate. The beam is made of an arbitrary number of layers. Perfect adhesion is assumed between layers. Each layer has individual thickness and material properties. Besides, the material is two-dimensional functionally graded in the cross-section of each layer. There is a delamination crack located arbitrary between layers. The beam is loaded by a bending moment applied at the free end of the lower crack arm. The upper crack arm is free of stresses. The solution to strain energy release rate derived is applied to investigate the influence of the crack location and the material gradient on the delamination fracture. The results obtained can be used to optimize the multilayered two-dimensional functionally graded beam structure with respect to the delamination fracture behaviour.

Delamination analysis of a layered elastic-plastic beam

PurposeThe purpose of this paper is to perform a theoretical analysis of delamination fracture behaviour of the Crack Lap Shear layered beam configuration taking into account the material non-linearity. A delamination crack located arbitrarily along the beam height was considered in this study.Design/methodology/approachThe beam mechanical behaviour was described by using the Ramberg-Osgood stress-strain relation. Fracture was analysed by applying the J-integral approach. Besides by using symmetric Ramberg-Osgood stress-strain curve, fracture was investigated also by Ramberg-Osgood stress-strain curve that is not symmetric with respect to tension and compression. The J-integral solutions were verified by performing elastic-plastic analyses of the strain energy release rate.FindingsThe effects of crack location and material properties on the non-linear fracture behaviour were evaluated. It was found that the material non-linearity leads to increase of the J-integral values. Therefore, the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members composed by layered materials. The analytical solutions derived are very useful for parametric investigations of delamination fracture with considering the material non-linearity. The results obtained can be applied for optimisation of the beam structure with respect to fracture performance.Originality/valueThe present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

An analytical solution to the stain energy release rate of a crack in functionally graded nonlinear elastic beams

An analytical approach was developed for studying the delamination fracture behaviour of functionally graded beam configurations with considering the material non-linearity. It was assumed that the mechanical response of functionally graded beams can be described by a non-linear stress-strain curve that is not symmetric for tension and compression (different stress-strain relations were used for tension and compression). The material is functionally graded along the beam height. Fracture behaviour was analyzed in terms of the strain energy release rate. A delamination crack located arbitrarily along the beam height was considered. The strain energy release rate was expressed in a function of the bending moments and axial forces in the cross-sections ahead and behind the crack front. The approach developed was applied to analyze the strain energy release rate in the functionally graded Double Cantilever Beam (DCB) configuration with material non-linearity. The strain energy release rate derived was compared with fracture analysis by the J-integral for verification. The effects of material properties and crack location on the fracture in the DCB were evaluated. It was shown that the approach developed is very useful for studying the fracture in functionally graded beam structures that exhibit material non-linearity.

Non-linear study of mode II delamination fracture in functionally graded beams

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the <i>J</i>-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the <i>J</i>-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The <i>J</i>-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

Bimodularity of interface layer and curing stress coupling effects on mixed mode fracture behaviour of functionally graded tee joint

Adhesive bonded tee joints are being used excessively in civil, military aircraft and ship building industries to join light weight Fiber reinforced Polymeric (FRP) laminates to other metal or composite structures. The mismatch of thermo-mechanical properties between adherend and adhesive bond line induces residual curing stresses even during manufacturing stages resulting in unaccounted failure and fracture behaviour of adhesive joints. The present work investigates the influence of bimodulus behaviour of adhesive and curing stresses on interface delamination fracture behaviour of tee joints by conducting a sequential thermal and geometrically non-linear finite element analysis (FEA) iteratively for evaluating strain energy release rate along the delamination front. The stress dependent elasticity problem of interface fracture has been studied based on the concepts of Modified Crack Closure Integral (MCCI) for different numerical specimens with tension compression modulus ratio R varying from 1 to 5 along the bond line for the respective functionally graded bimodular adhesively bonded tee joint. It is illustrated that the variation of bimodularity index has a strong influence on the interface delamination crack propagation characteristics apart from the other aspects of functionally grading and thermo-elastic anisotropy. The influence of bimodularity in comparison to functionally grading is found to be much more significant on mixed-mode fracture behaviour depicting dissimilar variation of GI, GII and GIII along the interface failure front indicating retardation of the interfacial failure propagation rate over certain zones of adherend.

Delamination fracture in a functionally graded multilayered beam with material nonlinearity

The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress–strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity.

Non-linear study of delamination cracks in multilayered beams

Purpose The purpose of this paper is to deal with an analytical investigation of delamination fracture in the mixed-mode bending (MMB) multilayer beam configurations taking into account the material non-linearity. Design/methodology/approach The J-integral approach was applied in fracture analysis. The beam layers non-linear mechanical response was described by using a power-law stress-strain relation with four material constants. Analytical solutions of the J-integral were derived by using the technical beam theory. The fracture analysis developed is valid for MMB beams whose layers may have different thicknesses. Also, the values of material constants in the non-linear stress-strain equation may be different for each layer. Findings The effect of material constants, crack location and layer thicknesses on the non-linear fracture was evaluated. The analytical solutions obtained are very suitable for parametric studies of non-linear fracture behaviour. The approach developed here can be used for optimization of multilayered beam structures with respect to the delamination fracture performance. The present study can also be useful for the understanding of fracture in multilayered beams exhibiting material non-linearity. Originality/value For the first time, an analytical study was performed of the delamination fracture behaviour of the MMB multilayered beam configuration taking into account the material non-linearity.

AE analysis of delamination crack propagation in carbon fiber-reinforced polymer materials

Delamination fracture behavior was investigated using acoustic emission (AE) analysis on carbon fiber-reinforced polymer (CFRP) samples manufactured using vacuum-assisted resin transfer molding (VARTM). CFRP plate was fabricated using unidirectional carbon fiber fabric with a lay-up of six plies [+30/−30]6, and a Teflon film was inserted as a starter crack. Test pieces were sectioned from the inlet and vent of the mold, and packed between two rectangular epoxy plates to load using a universal testing machine. The AE signals were monitored during tensile loading using two sensors. The average tensile load of the inlet specimens was slightly larger than that of the vent specimens; however, the data exhibited significant scattering due to non-uniform resin distribution, and there was no statistically significant different between the strength of the samples sectioned from the inlet or outlet of the mold. Each of the specimens exhibited similar AE characteristics, regardless of whether they were from the inlet or vent of the mold. Four kinds of damage mechanism were observed: micro-cracking, fiber-resin matrix debonding, fiber pull-out, and fiber failure; and three stages of the crack propagation process were identified.