Fatigue delamination growth in woven glass/epoxy composite laminates under mixed-mode II/III loading conditions at cryogenic temperatures

We investigate the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode II/III fatigue loading. Fatigue delamination tests were conducted with six-point bending plate (6PBP) specimens at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), and the delamination growth rate data for various mixed-mode ratios of Modes II and III were obtained. The energy release rate was evaluated using the three-dimensional finite element method. In addition, the fatigue delamination growth mechanisms were characterized by scanning electron microscopic observations of the specimen fracture surfaces.     

Mode III interlaminar fracture of carbon/epoxy laminates using a four-point bending plate test

A new four-point bending plate (4PBP) test was used for characterising the mode III interlaminar fracture of carbon/epoxy laminates. The specimen has a cross-ply lay-up and two edge delaminations whose propagation becomes visible at the edges. Although the test setup is very simple, determination of the mode III critical strain energy release rate G_IIIc requires finite element analyses (FEA). The virtual crack closure technique with an assumed initiation region was first proposed for computing G_IIIc. This scheme was subsequently validated by crack growth simulations with a cohesive zone model. The results showed an average G_IIIc = 1550 J/m², which is significantly higher than the G_IIIc = 850–1100 J/m² and G_IIc = 800 J/m² measured in previous studies.     

Effect of damage on the interlaminar shear properties of hybrid composite laminates at cryogenic temperatures

This paper presents the experimental and numerical characterization of the interlaminar shear failure of hybrid composite laminates at cryogenic temperatures. Cryogenic short beam shear tests were performed on hybrid laminates consisting of woven glass fiber reinforced polymer (GFRP) composites and polyimide films to evaluate their interlaminar shear strength. Microscopic observations of damage accumulation and failure mechanisms were also made on failed specimens. In addition, a progressive damage analysis was conducted to predict the initiation and growth of damage in the specimens, and the interlaminar shear strength was determined from the maximum shear stress in the failure region. The damage effect on the interlaminar shear properties of hybrid laminates at cryogenic temperatures was examined based on the experimental and numerical results.     

Cryogenic through-thickness tensile characterization of plain woven glass/epoxy composite laminates using cross specimens: Experimental test and finite element analysis

This paper investigates the through-thickness tensile behavior of woven glass fiber reinforced polymer (GFRP) composite laminates at cryogenic temperatures. Tensile tests were carried out with cross specimens at room temperature and liquid nitrogen temperature (77 K), and the through-thickness elastic and strength properties of the woven GFRP laminates were evaluated. The failure characteristics of the woven GFRP laminates were also studied by optical and laser scanning microscopy observations. A three-dimensional finite element analysis was performed to calculate the stress distributions in the cross specimens, and the failure conditions of the specimens were examined. It is found that the cross specimen is suitable for the cryogenic through-thickness tensile characterization of laminated composite materials. In addition, the through-thickness Young's modulus of the woven GFRP composite laminates is dominated by the properties of the matrix polymer in the given temperature, while the tensile strength is characterized by both, the fiber to matrix interface energy and the cohesion energy of the matrix polymer.     

Mode III interlaminar fracture of carbon/epoxy laminates using the edge crack torsion (ECT) test

The mode III interlaminar fracture of carbon/epoxy laminates was evaluated with the edge crack torsion (ECT) test. Three-dimensional finite element analyses were performed in order to select two specimen geometries and an experimental data reduction scheme. Test results showed considerable non-linearity before the maximum load point and a significant R-curve effect. These features prevented an accurate definition of the initiation point. Nevertheless, analyses of non-linearity zones showed two likely initiation points corresponding to G_IIIc values between 850 and 1100 J/m² for both specimen geometries. Although any of these values is realistic, the range is too broad, thus showing the limitations of the ECT test and the need for further research.     

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.     

Analysis of mixed-mode interlaminar fracture and damage behavior of GFRP woven laminates at cryogenic temperatures

The objective of this work is to investigate the interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates loaded in a mixed-mode bending (MMB) apparatus at cryogenic temperatures. The finite element analysis (FEA) is used to determine the mixed-mode interlaminar fracture toughness of MMB specimen at room temperature (RT), liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). A FEA coupled with damage is also employed to study the damage distributions within the MMB specimen and to examine the effect of damage on the mixed-mode energy release rate. The technique presented can be efficiently used for characterization of mixed-mode interlaminar fracture and damage behavior of woven laminate specimens at cryogenic temperatures.     

Mixed-mode I/II wood fracture characterization using the mixed-mode bending test

In this work fracture characterization of wood under mixed-mode I/II loading is addressed. The mixed-mode bending test is used owing to its aptitude for easier alteration of mode ratio. Experimental tests were performed covering a wide range of mode ratios in order to obtain a mixed-mode fracture criterion for the maritime pine (Pinus pinaster Ait.) in the RL crack propagation system. A data reduction scheme based on beam theory and crack equivalent concept was used to overcome some difficulties inherent to the test. The method does not require crack length monitoring during propagation and provide an entire resistance curve allowing easier identification of the fracture energy. A numerical analysis using cohesive elements was also performed to validate the method. The linear energetic fracture criterion was proved to be the most adequate to describe the failure envelop of this wood species.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

Mode III interlaminar fracture of carbon/epoxy laminates using the Six-Point Edge Crack Torsion (6ECT)

The recently proposed Six-Point Edge Crack Torsion (6ECT) test was used to evaluate the mode III interlaminar fracture of carbon/epoxy laminates. Plate specimens with starter delaminations in 0/0, 0/90 and 0/45 interfaces were tested. Data reduction was performed with an effective crack scheme validated in a previous numerical study. The tests allowed the evaluation of fairly unambiguous initiation G_IIIC values and of subsequent R-curves. Examinations of specimen cross-section showed considerable lengths of pure interlaminar propagation in specimens with starter delaminations in 0/90 and 0/45 interfaces. The latter specimens had the lowest initiation G_IIIC values.     

Discrete cohesive zone model for mixed-mode fracture using finite element analysis

The discrete cohesive zone model (DCZM) is implemented using the finite element (FE) method to simulate fracture initiation and subsequent growth when material non-linear effects are significant. Different from the widely used continuum cohesive zone model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses rod type elements and applies the cohesive law as the rod internal force vs. nodal separation (or rod elongation). These rod elements have the provision of being represented as spring type elements and this is what is considered in the present paper. A series of 1D interface elements was placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes were introduced within the interface element to extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations were examined. For pure mode I, the double cantilever beam configuration, using both uniform and biased meshes were analyzed and the results show that the DCZM is not sensitive to the mesh size. Results also show that DCZM is not sensitive to the loading increment, either. Next, the end notched flexure for pure mode II and, the mixed-mode bending were studied to further investigate the approach. No convergence difficulty was encountered during the crack growth analyses. Therefore, the proposed DCZM approach is a simple but promising tool in analyzing very general two-dimensional crack growth problems. This approach has been implemented in the commercial FEA software ABAQUS^® using a user defined subroutine and should be very useful in performing structural integrity analysis of cracked structures by engineers using ABAQUS^®.     

Mixed Bending-Tension (MBT) test for mode I interlaminar and intralaminar fracture

A new Mixed Bending-Tension (MBT) test is proposed for mode I fracture of laminated composites. The MBT specimen consists of a relatively small pre-cracked laminate adhesively bonded to pin-loaded steel beams. This design reduces significantly the bending stresses that prevent successful application of DCB tests to certain laminates. The MBT was here applied to carbon/epoxy unidirectional [0°]₂₆ and [90°]₂₆ laminates with starter delaminations. Interlaminar initiation G_IC values of [0°]₂₆ laminates agreed well with previous DCB test results, while [90°]₂₆ laminates exhibited 50% higher values. Significant lengths of fairly planar intralaminar crack propagation were seen in the latter laminates. The results showed a fibre bridging related R-curve, which was more pronounced in [0°]₂₆ laminates. The consistency of the present results indicates that the MBT opens new possibilities for the interlaminar and intralaminar mode I fracture.     

CF/EP composite laminates with carbon black and copper chloride for improved electrical conductivity and interlaminar fracture toughness

An experimental study was conducted to improve the electrical conductivity of continuous carbon fibre/epoxy (CF/EP) composite laminate, with simultaneous improvement in mechanical performance, by incorporating nano-scale carbon black (CB) particles and copper chloride (CC) electrolyte into the epoxy matrix. CF/EP laminates of 65 vol.% of carbon fibres were manufactured using a vacuum-assisted resin infusion (VARI) technique. The effects of CB and the synergy of CB/CC on electrical resistivity, tensile strength and elastic modulus and fracture toughness (K_IC) of the epoxy matrix were experimentally characterised, as well as the transverse tensile modulus and strength, Mode I and Mode II interlaminar fracture toughness of the CF/EP laminates. The results showed that the addition of up to 3.0 wt.% CB in the epoxy matrix, with the assistance of CC, noticeably improved the electrical conductivity of the epoxy and the CF/EP laminates, with mechanical performance also enhanced to a certain extent.     

Analysis of mode II interlaminar fracture and damage behavior in end notched flexure testing of GFRP woven laminates at cryogenic temperatures

Summary Interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures is investigated for end notched flexure (ENF) pure Mode II configuration. The corrected beam theory (CBT) and finite element analysis (FEA) are used to calculate the Mode II interlaminar fracture toughness of ENF specimen at room temperature (RT), liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). A FEA coupled with damage is also employed to study the damage distributions within the specimen and to examine the effect of damage on the Mode II energy release rate. The numerical results show that damage occurs at the matrix and causes a decrease in the energy release rate. The technique presented can be efficiently used for the characterization of cryogenic Mode II interlaminar fracture and damage behavior of woven laminate ENF specimens.     

Combination of finite element and reliability methods in nonlinear fracture mechanics

This paper presents a probabilistic methodology for nonlinear fracture analysis in order to get decisive help for the reparation and functioning optimization of general cracked structures. It involves nonlinear finite element analysis. Two methods are studied for the coupling of finite element with reliability software: the direct method and the quadratic response surface method. To ensure the response surface efficiency, we introduce new quality measures in the convergence scheme. An example of a cracked pipe is presented to illustrate the proposed methodology. The results show that the methodology is able to give accurate probabilistic characterization of the J-integral in elastic–plastic fracture mechanics without obvious time consumption. By introducing an “analysis re-using” technique, we show how the response surface method becomes cost attractive in case of incremental finite element analysis.     

Linear and nonlinear finite element analyses of unidirectional, symmetric single leg four-point bending tests

Geometrically linear and nonlinear finite element analyses are used to determine the energy release rate and mode ratio in simulated tests of unidirectional, symmetric, single leg bending specimens under four-point bending. It is shown that the finite diameter loading rollers that are typically used in practical test set-ups cause this test to be inherently nonlinear. The differences between the linear and nonlinear results are presented parametrically as a function of material properties, specimen thickness, roller diameter, crack length, and inner and outer span length. The perceived advantages and disadvantages of this test are compared to those of the more commonly used three-point single leg bending test. It is concluded that the four-point test provides an attractive alternative, as it can use the same type of test specimens and will produce toughnesses with essentially the same accuracy. Moreover, it allows non-precracked and precracked toughnesses, as well as R-curve data, to be obtained from each specimen tested.     

Compressive response of Z-pinned woven glass fiber textile composite laminates: Modeling and computations

3D multi-layer and multi-representative unit cell (RUC) models are presented in order to capture the failure mechanisms of Z-pinned laminated textile composites presented in part 1 [Huang H, Waas A. Compressive response of Z-pinned woven glass fiber textile composite laminates: experiments, this issue] of this two part sequel. Simulations of 1, 9, 16, and 25-RUC models are compared to establish cell number effects in representing the textile composites for strength predictions. Further, simulations using multi-layer representations of the textile laminate are conducted to account for unintended stacking effects that occur during the manufacturing cycle. From the results of these simulations, the 3-layer model that has 16-RUCs in each layer is found to be the most adequate representation of the 3D multi-layer and multi-RUC models. Simulations show that stacking effects (layers not compacting and consolidating exactly as intended, resulting in a phase shift) during the manufacturing of the laminates, influence the outcome of the predicted compression strength.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

Finite element simulation and experimental study on mechanical behavior of 3D woven glass fiber composite sandwich panels

The results of finite element simulation followed by an experimental study are presented in order to investigate the mechanical behavior of three-dimensional woven glass-fiber sandwich composites using FE method. Experimental load–displacement curves were obtained for flatwise compressive, edgewise compressive, shear, three-point bending and four-point bending loads on the specimens with three different core thicknesses in two principal directions of the sandwich panels, called warp and weft. A 3D finite element model is employed consisting of glass fabric and surrounding epoxy resin matrix in order to predict the mechanical behavior of such complex structures. Comparison between the finite element predictions and experimental data showed good agreement which implies that the FE simulation can be used instead of time-consuming experimental procedures to study the effect of different parameters on mechanical properties of the 3D woven sandwich composites.     

Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method

This paper presents a new fractal finite element based method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and two-dimensional linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predicts the first-order sensitivity of J-integral or mode-I and mode-II stress-intensity factors, K_I and K_II, more efficiently and accurately than the finite-difference methods. Unlike the integral based methods such as J-integral or M-integral no special finite elements and post-processing are needed to determine the first-order sensitivity of J-integral or K_I and K_II. Also a parametric study is carried out to examine the effects of the similarity ratio, the number of transformation terms, and the integration order on the quality of the numerical solutions. Four numerical examples which include both mode-I and mixed-mode problems, are presented to calculate the first-order derivative of the J-integral or stress-intensity factors. The results show that first-order sensitivities of J-integral or stress-intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.