Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test, the end notch flexure test, the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.     

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.     

Intralaminar fracture mechanism in unidirectional CFRP composites: Part I: Intralaminar toughness and AE characteristics

Three types of representative carbon fiber reinforced unidirectional composite materials were used and their intralaminar fracture behavior was investigated using the double-cantilever beam specimen with a simultaneous acoustic emission measurement. The intralaminar fracture toughness was evaluated by both the compliance method and energy area method. As a result, it was found that the intralaminar fracture toughness without bridging fibers had a constant value during crack propagation but it increased greatly when bridging fibers were present. The effect of bridging fibers on the intralaminar fracture toughness was estimated quantitatively by cutting the bridging fibers. Distinct differences in load–displacement curves, compliance, crack propagating behavior and acoustic emission signal characteristics between these three types of unidirectional composite materials were observed. It was also found that bridging fiber failure generated relatively large power spectra and contributed to the peak frequencies of 600–700 kHz in the spectrum analysis of acoustic emission (AE) signals. This suggested that the bridging fibers were also an important source of AE signals. Furthermore, a linear relationship between crack length and normalized cumulative AE event count rate was obtained.     

Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing and numerical analysis

Bridging by intact fibers in composite materials is one of the most important toughening mechanisms. However, a direct experimental assessment of its contribution is not easy to achieve. In this work a semi-experimental method is proposed to quantify its contribution to fracture of unidirectional carbon fiber/epoxy double cantilever beam (DCB) specimens in mode I delamination under monotonic and 1 Hz fatigue loads. In each specimen, an embedded optical fiber with an array of eight wavelength-multiplexed fiber Bragg gratings is used to measure local strains close to the crack plane. The measured strain distribution serves in an inverse identification procedure to determine the tractions in the bridging zone in monotonic and fatigue loads. These tractions are used to calculate the energy release rate (ERR) associated with bridging fibers. The results indicate that the ERR due to bridging is about 40% higher in fatigue. The bridging tractions are further included in a cohesive element model which allows to predict precisely the complete load displacement curve of monotonic DCB tests. Using the principle of superposition and the identified tractions, the total stress intensity factor (SIF) is calculated. The results show that the SIF, at initiation, is very close to the one calculated at crack propagation and bridging by intact fibers is responsible for the entire increase in toughness seen in the DCB specimens used herein.     

Panel stiffener debonding analysis using a shell/3D modeling technique

A shear loaded, stringer reinforced composite panel is analyzed to evaluate the fidelity of computational fracture mechanics analyses of complex structures. Shear loading causes the panel to buckle. The resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. The panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot, web and noodle as well as the panel skin near the delamination front were modeled with a local 3D solid model. Across the width of the stringer foot, the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with a mixed-mode failure criterion of the graphite/epoxy material. The objective was to study the effect of the fidelity of the local 3D finite element model on the computed mixed-mode strain energy release rates and the failure index.     

Assessment of energy dissipation during mixed-mode delamination growth using cohesive zone models

The use of cohesive elements to simulate delamination growth involves modeling the inelastic region existing ahead of the crack tip. Recent numerical and experimental findings indicate that the mixed-mode ratio varies at each material point within the inelastic region ahead of the crack tip during crack propagation, even for those specimens whose mixed-mode ratio is expected to be constant. Although the local variation of the mode mixity may adversely affect the predicted numerical results, most existing formulations do not take it into account. In this work, the mode-decomposed J-integral is implemented as a finite element post-processing tool to obtain the strain energy release rates and the mixed-mode ratio of the inelastic region as a whole, allowing the assessment of crack propagation in terms of energy dissipation and mixed-mode ratio computation. Different cohesive elements are assessed with this method.     

Mixed-mode interlaminar fracture and damage characterization in woven fabric-reinforced glass/epoxy composite laminates at cryogenic temperatures using the finite element and improved test methods

The present research examines experimentally and analytically the mixed-mode interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures. The mixed-mode bending (MMB) tests were performed with the improved test apparatus, at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). The energy release rates at the onset of delamination crack propagation were evaluated for the woven GFRP specimens using both beam theory and finite element analysis. The fracture surfaces were also examined to verify the fracture mechanisms. In addition, the initiation and growth of damage in the specimens were predicted by a damage analysis, and the damage effect on the mixed-mode interlaminar fracture properties at cryogenic temperatures was explored.     

On damage accumulations in the cyclic cohesive zone model for XFEM analysis of mixed-mode fatigue crack growth

Predicting mixed-mode fatigue crack propagation is an important and troublesome issue in structure assessment for decades. In the present paper an extended finite element method (XFEM) combined with a new cyclic cohesive zone model (CCZM) is introduced for simulating fatigue crack propagation under mixed-mode loading conditions, which has been implemented in the commercial general purpose software ABAQUS. The algorithm allows introducing a new crack surface at arbitrary locations and directions in a finite element mesh, without re-meshing. The cyclic cohesive zone model is based on the known S–N curves and Goodman diagram for metallic materials and validated by uniaxial tension results. Furthermore, the sensitivity of the model parameter is investigated for mixed-mode fatigue. The virtual crack closure technique has been extended to the cohesive zone model and proposed to calculate the energy release rate for the generalized Paris’ law. Finally, the crack propagation rate and direction under mixed-mode fatigue loading conditions are studied.     

Unusual Characteristics of Mixed-Mode Delamination Fracture in the Presence of Large-Scale Bridging

The unusual characteristics of mixed-mode delamination fracture in the presence of large bridging zones of through-thickness reinforcement are explained through an idealization of the mixed-mode bending specimen. With simple but realistic constitutive laws assumed for the bridging mechanisms, beam theory offers insightful analytical solutions and illuminates the length scales that control the crack characteristics. Of particular significance is that the mode I energy release rate can vanish after a period of crack growth, due to the bridging effect of the through-thickness reinforcement. This crack tip closure phenomenon is one manifestation of bridging-induced spatial oscillations that sometimes appears in the crack displacement function, which can be understood qualitatively through the similarity of the fracture problem to the classical problem of a beam on a Winkler foundation. The possibility of crack closure and consequent crack arrest has important consequences for designing certifying tests for laminates with through-thickness reinforcement and predicting strength and lifetime.     

Computational modeling of mixed-mode fatigue crack growth using extended finite element methods

The extended finite element method (XFEM) combined with a cyclic cohesive zone model (CCZM) is discussed and implemented for analysis of fatigue crack propagation under mixed-mode loading conditions. Fatigue damage in elastic-plastic materials is described by a damage evolution equation in the cohesive zone model. Both the computational implementation and the CCZM are investigated based on the modified boundary layer formulation under mixed-mode loading conditions. Computational results confirm that the maximum principal stress criterion gives accurate predictions of crack direction in comparison with known experiments. Further popular multi-axial fatigue criteria are compared and discussed. Computations show that the Findley criterion agrees with tensile stress dominant failure and deviates from experiments for shear failure. Furthermore, the crack propagation rate under mixed mode loading has been investigated systematically. It is confirmed that the CCZM can agree with experiments.     

Crack – fiber sensor interaction and characterization of the bridging tractions in mode I delamination

Fiber bridging is regularly encountered in mode I delamination tests of unidirectional fiber reinforced composites. However, characterization of the bridging tractions is rather difficult. One way to indirectly evaluate the bridging traction distribution is to embed a fiber Bragg grating (FBG) sensor close to the crack tip and to measure the distributed strain along this FBG. The strain measurements from the FBG sensor are used to characterize the fiber bridging tractions by an identification method. In this work, the sensor is embedded in a unidirectional carbon/epoxy composite. Firstly, it is treated as an inclusion near the crack plane and a numerical analysis is performed to study its effect on the measured strain field and energy release rate. The results demonstrate that the sensor, located at about two fiber diameters from the crack plane, has a negligible effect on the fracture process. Secondly, among the identified linear, bilinear, and exponential bridging traction distributions, the exponential one is found to be a suitable model. Characterization of the bridging tractions allows to calculate the energy release due to the bridging fibers which is similar to the difference between the initiation energy release and the propagation value . The results also agree with the bridging tractions evaluated from the conventional energy release rate – crack opening displacement method.     

Delamination of multidirectional composite laminates at 0°/θ° ply interfaces

The main objective of this study is to develop a methodology for establishing mixed-mode delamination propagation criteria of non-unidirectional laminates. The crack interface was chosen to be 0°/45° and the effort was mainly focused on obtaining the mode I fracture toughness (G_IC). The widely used DCB test was avoided due to anticipated problems with intralaminar damage developing at the ply interface of interest. The ADCB and AMMF methods were used to determine the mixed-mode fracture toughness with the largest amount of mode I. The selected stacking sequence resulted in desirable crack propagation behavior; there was no change of delamination plane, an acceptable crack front profile, no initial specimen curvature, and no energy dissipation through global specimen damage. Finite element simulation was found to be the only tool capable of analyzing the experimental data.     

A phenomenological analysis of Mode I fracture of adhesively-bonded pultruded GFRP joints

The fracture behavior of adhesively-bonded pultruded joints was experimentally investigated under Mode I loading using double cantilever beam specimens. The pultruded adherends comprised two mat layers on each side with a roving layer in the middle. An epoxy adhesive was used to form the double cantilever beam specimen. The pre-crack was introduced in three different depths in the adherend in order to induce crack initiation and propagation between different layers and thus investigate the effect of these different crack paths on the strain energy release rate. Short-fiber and roving bridging increased the fracture resistance during crack propagation. Specific levels of critical strain energy release rates could be attributed to each of the crack paths, with their levels depending on the amount of short-fiber bridging and the presence of a roving bridge. The different levels of critical strain energy release rate could be correlated to the morphology of the fracture surface and the strain energy release rate can thus be determined visually without any measurement.     

Simulation of crack propagation of fiber reinforced cementitious composite under direct tension

Mode I crack propagation in fiber reinforced cementitious composite is simulated based on fracture mechanics criteria. To analyze crack propagation, a superposition method is employed to calculate the stress intensity factor at the crack tip resulted from both the applied load and the crack bridging stress. Using the model, the effects of various material parameters on the tensile performance are investigated. The requirements for tensile strain-hardening and multiple cracking are analyzed and possible methods for material performance optimization are discussed. Finally, predicted behavior is verified by tensile and bending tests performed on two fiber reinforced cementitious composite beams.     

Crack onset and propagation at fibre–matrix elastic interfaces under biaxial loading using finite fracture mechanics

A new fracture criterion able to predict crack onset and propagation at interfaces between solids is formulated, implemented in a computational code and applied to a particular problem in composites on a microscale. More specifically, this criterion is used to study the debond onset and propagation in mixed mode in the case of a single fibre subjected to a biaxial remote loading. The fracture criterion formulation is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Each of these criteria is a necessary but not sufficient condition for crack onset and propagation. Two empirical mixed-mode fracture criteria are considered and tested: the interface fracture toughness law by Hutchinson and Suo and the quadratic stress criterion. The FFM + LEBIM approach developed offers an adequate characterization of the interface stiffness in contrast to the too restrictive, original LEBIM formulation.     

Influence of mixed-mode loading on fatigue-crack propagation

The subject of fatigue which comprises crack nucleation, crack propagation and final failure or fracture has, over the years, been the subject of numerous theoretical and experimental studies. These studies have highlighted the extrinsic influence of mixed-mode loading in governing the fatigue behavior of a wide spectrum of engineering materials and structures. In this paper we review the basic criteria and models that have been proposed and used to predict crack behavior and response for structures containing large cracks and subject to mixed-mode loading. Since the aspect of crack growth is the focus of this review, the effects or contributions from intrinsic microstructural effects are largely excluded. Specific criteria discussed are the maximum tangential stress, minimum strain-energy density and the maximum energy-release rate criteria. The use of these criteria to predict the behavior of structures is examined based on results published in the open literature. The characteristics and implications of each criterion are examined and discussed with particular relevance to threshold conditions on crack growth, direction of crack growth and crack-growth rate. The limitations of each criterion are highlighted.     

Analytical and numerical modeling of R curves for cracks with bridging zones

At the onset of fracture in materials with process zones, the fracture resistance, or R curve, rises as the process zone develops. After process zone development, crack propagation proceeds by steady state growth. By considering J integral contours inside and outside the process zone, the available energy can be partitioned into crack tip energy release rate and process zone energy. To model the rising R curve, however, required assumptions about damage mechanisms in the process zone and partitioning of its energy into released and recoverable energy. By considering process zones that are elastic fiber-bridging zones with softening regions caused by fiber breakage or damage, equations for rising R curves were derived as a function of crack tip toughness and bridging zone mechanics. The new methods were implemented into the Material Point Method for generalized numerical crack propagation simulations with bridging zones. The simulation method includes pure fracture mechanics and pure cohesive zone models as extreme special cases. The most realistic simulations for many materials will likely fall between these two extremes. The results guided comments on interpretation of experimental R curves.     

Application of the biaxial Iosipescu method to mixed-mode fracture of unidirectional composites

In this paper the biaxial Iosipescu test method has been used, employing specimens with a central precrack placed along the notch-root axis, to study the intralaminar failure properties of a unidirectional carbon/epoxy composite under mixed-mode (dominated by shear) loadings. A linear finite element analysis has been performed to determine the energy release rates and stress intensity factors for the central crack under various biaxial loading conditions. In addition, a series of simple and biaxial fracture experiments have been performed on the composite material. Numerical results indicate that the method is capable of generating a wide range of mixed-mode loading conditions at the crack tip for various loading angles and crack lengths. Using the numerical results, in conjunction with experimental data, the biaxial intralaminar failure process in the cracked Iosipescu specimens has been explained.     

超高分子量聚乙烯架桥纤维与裂缝的交互微观力学

使用拉曼光谱研究了架桥纤维与裂缝微观力学,以超高分子量聚乙烯(UHMWPE)纤维为例,将纤维搭桥试样进行微拉伸试验,着重分析架桥纤维的止裂作用和架桥纤维/环氧树脂界面的应力分布,并对不同位置架桥试样的裂缝扩展速度和应力分布进行分析,并进一步运用剪切滞后模型,对架桥纤维在不同拉伸载荷下的应力分布进行了拟合分析,结果表明:架桥纤维能够分散部分外载应力,对于裂纹扩展具有显著的止裂作用。在低于UHMWPE纤维最大应变拉伸时,发现在裂缝中心位置处架桥纤维所承受的应力最大,其应力不超过2GPa,而基体树脂的应力可达到12GPa,架桥纤维/基体界面的应力传递达不到100%。以UHMWPE为架桥的应力传递模型呈"正抛物线"型,应力分布存在于粘结区、脱粘区和架桥区。     

Mechanical interactions between fiber and cracked coating layer and their influences on fiber strength

The mechanical interactions between the elastic fiber and cracked elastic coating layer and their influences on fiber strength for strong and weak interfaces were studied. In the case of a strong interface, the energy release rate for the propagation of the crack in the coating layer into fiber increases and, therefore, the fiber strength decreases with increasing elastic modulus and thickness of the coating layer. When multiple cracking occurs in the coating layer, the energy release rate becomes low because of the reduced crack-spacing, resulting in a higher strength of the fiber, the double and graded coatings reduce the energy release rate and, therefore, raise the fiber strength in comparison with that for a single coating with high elastic modulus if the material with low elastic modulus is used as the inner layer adjacent to the fiber. In the case of weak interface, when the critical energy release rate for the interfacial debonding is lower than 0.3 times the critical one for the crack propagation into fiber, the debonding occurs prior to the crack propagation, resulting in higher fiber strength than that for strong interface because of the blunting at crack-tip.