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.     

Experimental and Numerical Investigation of Mixed-Mode Interlaminar Fracture of Carbon-Polyester Laminated Woven Composite by Using Arcan Set-up

Composite materials are widely used in marine, aerospace and automobile industries. These materials are often subjected to defects and damages from both in-service and manufacturing process. Delamination is the most important of these defects. This paper reports investigation of mixed-mode fracture toughness in carbon–polyester composite by using numerical and experimental methods. All tests were performed by Arcan set-up. By changing the loading angle, α, from 0° to 90° at 15° intervals, mode-I, mixed-mode and mode-II fracture data were obtained. Correction factors for various conditions were obtained by using ABAQUS software. Effects of the crack length and the loading angle on fracture were also studied. The interaction j-integral method was used to separate the mixed–mode stress intensity factors at the crack tip under different loading conditions. As the result, it can be seen that the shearing mode interlaminar fracture toughness is larger than the opening mode interlaminar fracture toughness. This means that interlaminar cracked specimen is tougher in shear loading condition and weaker in tensile loading condition.     

Connecting the essential work of fracture, stress intensity factor, Hill’s criterion in mixed mode I/II loading

Ductile sheet structures are frequently subjected to mixed mode loading, resulting that the structure is under the influence of a mixed mode stress field. Instances of interest are when stable crack growth occurs and when the crack-tip is propagating in this complex mixed-mode condition, prior to final fracture. Purposely designed apparatus was built to test thin-sheets of steel (Grade: DX51D) under mixed-mode I/II. These tests, under plane stress conditions, also investigated the effect of thickness on the specific essential work of fracture or the fracture toughness of the material under quasi-static cracking conditions. The fracture toughness is evaluated under incremental mixed-mode loading conditions. The direction of the propagating crack path and fracture type were observed and discussed as the loading mixity was varied. Whilst the specific essential work of fracture or fracture toughness was obtained using the energy approach, the theoretical analysis of the fracture type and direction of crack path were based on the crack tip stresses and fracture criterions of maximum hoop stress and maximum shear stress along with the utilisation of Hill’s theory. For mixed-mode I/II loading, the variation in the fracture toughness contributions ratios are evaluated and used predicatively using the established energy criterion approach to the crack tip stress intensity approach. The comparison between the theoretical directions of the crack path, failure mode propagation are in good agreement with those obtained from experimental testing indicating the definite link between both approaches.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Analysis of the effect of biaxial loading on the fracture toughness of reactor pressure-vessel steels

The stress-strain state at the crack tip and its relation to the crack opening displacement and the J-integral under biaxial loading have been studied by solving elastoplastic problems in a geometrically nonlinear formulation by the finite-element method. Numerical investigations have been performed for various cracks and two modes of biaxial loading (tension and bending) under conditions of both small-scale and large-scale yielding. For prediction of the influence of biaxial loading on fracture toughness (at brittle fracture) a procedure has been developed that is based on established laws of stress-strain state formation at the crack tip under biaxial loading and a criterion of brittle fracture proposed earlier. The effect of biaxial loading on fracture toughness is predicted as applied to reactor pressure-vessel steels. Calculated results are compared with avilable experimental data. Alternative approaches to prediction of the effect of biaxial loading on fracture toughness are discussed. TsNII KM “Prometei,” St. Petersburg, Russia. Translated from Problemy Prochnosti, No. 5, pp. 5–26, September–October, 1999.     

Mixed-mode cohesive fracture of adhesive joints: Experimental and numerical studies

A broad experimental and analytical effort using fracture mechanics as the prime tool was conducted to investigate and improve the understanding of the mixed-mode cohesive fracture behavior of bonded joints. As a part of experimental efforts, mixed-mode fracture tests were performed using modified Arcan specimens consisting of several combinations of adhesive, composite and metallic adherends with a special loading fixture, in which by varying the loading angle, from 0° to 90°, mode-I, mixed-mode and mode-II fracture data were obtained. Finite element analyses were also carried out on specimens with different adherends. The main objective of this study was to determine the fracture toughness K_IC and K_IIC for a range of substrates under mixed-mode loading conditions. Another goal was to study the relationship between the stress intensity factors and the fracture toughness. Based on those analyses, mixed mode fracture criterion for the adhesively bonded systems under consideration determined. Fracture surfaces obtained at different mixed-mode loading conditions for various adherends were finally discussed.     

On mixed-mode fracture of PVC foam

This paper reports on mixed-mode fracture in rigid cellular PVC foam based on experimental and numerical analyses. Experiments were performed on sharp-cracked specimens using the compact-tension-shear (CTS) test loading device. Foams of three different densities were tested. The CTS specimen was, in association with a special loading device, an appropriate apparatus for experimental mixed-mode fracture analysis. Experimentally-obtained fracture toughness results show good consistency. K_IC fracture toughness was marginally different in different directions. The ratio K_{II C}/K_{I C} was found to be between 0.4 and 0.65 depending on the foam density. For mixed-mode loading, Richard's criterion – using experimentally obtained K_{I C} and K_{II C} – was the best in predicting accurately fracture locus and fracture angle. When no experimental data were used, the maximum hoop stress criterion predicted best kinking angle. The principal strain criterion predicted the best fracture locus. Fracture boundary curve and kinking angle were best predicted for low mode II contribution. This revised version was published online in August 2006 with corrections to the Cover Date.     

铺层方向和裂纹混合比对复合材料层压板混合型断裂韧性影响的试验研究

试验研究了复合材料层压板的铺层方向以及裂纹混合比对层间裂纹分层扩展的影响规律。试验结果显示: 在非0°单向板的 Ⅰ 型层间裂纹分层扩展过程中, 会出现层间裂纹穿过分层开裂面的铺层而偏离到相邻铺层间扩展的现象, 而0°铺层具有阻止该裂纹偏离扩展的作用; 在不同裂纹混合比的层压板分层开裂试验中, 相应的0°单向板的断裂韧性均可以作为下限值而偏安全; 混合断裂韧性( Ⅰ 型断裂韧性+ Ⅱ 型断裂韧性)随着裂纹混合比的变化呈现类似正弦曲线的变化规律。      

Analysis of fracture and delamination in laminates using 3D numerical modelling

The static failure behaviour of the fibre-metal laminate GLARE is examined using 3D finite element simulations. The configuration analysed is a centre-cracked tensile specimen composed of two aluminium layers sandwiching a cross-plied, fibre-epoxy layer. The crack and delamination growths are simulated by means of interface elements equipped with a mixed-mode damage model. The mode-mixity is derived from an energy criterion typically used in linear elastic fracture mechanics studies. The damage kinetic law is rate-dependent, in order to simulate rate effects during interfacial delamination and to avoid numerical convergence problems due to crack bifurcations. The numerical implementation of the interface damage model is based on a backward Euler approach. In the boundary value problem studied, the failure responses of GLARE specimens containing elastic aluminium layers and elasto-plastic aluminium layers are compared. The development of plastic deformations in the aluminium layers stabilizes the effective failure response, and increases the residual strength of the laminate. For a ‘quasi-brittle’ GLARE specimen with elastic aluminium layers, the residual strength is governed by the toughness for interfacial delamination, and is in close correspondence with the residual strength obtained from a closed-form expression derived from energy considerations. Conversely, for a ‘ductile’ GLARE specimen with elasto-plastic aluminium layers, the residual strength is also determined by the relation between the fracture strength and the yield strength of the aluminium. The amount of constraint by the horizontal displacements at the vertical specimen edges has a moderate to small influence on the residual strength. Furthermore, the ultimate laminate strength is lower for a larger initial crack length, and shows to be in good correspondence with experimental values.     

Fracture behaviour of uPVC thin tubes at high loading rates

Impact tests and fracture toughness tests were carried out using thin cylindrical specimens of unplasticized poly (vinyl chloride). The specimens, both pre-notched and unnotched, were internally pressurized to fracture at high loading rates, using a conventional shock tube. Over the wide range of the applied loading rates, failure of the pre-notched specimens occurred in a completely brittle mode, while in the case of unnotched specimens, a transition from “semi-brittle” to brittle fracture occurred over the same range of loading rate. Adopting standard linear elastic fracture mechanics (LEFM) analysis, a validity criterion is suggested based on the variation of the extent of crack tip plasticity with the loading rate, as calculated by Dugdale and Irwin models. It is suggested that the decrease in the plastic zone size with increasing rate, affects the size requirement for a valid (plane strain) fracture toughness value.     

Finite element calculation of stress intensity factors for interfacial crack using virtual crack closure integral

This paper presents a successful implementation of the virtual crack closure integral method to calculate the stress intensity factors of an interfacial crack. The present method would compute the mixed-mode stress intensity factors from the mixed-mode energy release rates of the interfacial crack, which are easily obtained from the crack opening displacements and the nodal forces at and ahead of the crack tip, in a finite element model. The simple formulae which relate the stress intensity factors to the energy release rates are given in three separate categories: an isotropic bimaterial continuum, an orthotropic bimaterial continuum, and an anisotropic bimaterial continuum. In the example of a central crack in a bimaterial block under the plane strain condition, comparisons are made with the exact solution to determine the accuracy and efficiency of the numerical method. It was found that the virtual crack closure integral method does lead to very accurate results with a relatively coarse finite element mesh. It has also been shown that for an anisotropic interfacial crack under the generalized plane strain condition, the computed stress intensity factors using the virtual crack closure method compared favorably with the results using the J integral method applied to two interacting crack tip solutions. In order for the stress intensity factors to be used as physical variables, the characteristic length for the stress intensity factors must be properly defined. A study was carried out to determine the effects of the characteristic length on the fracture criterion based the mixed-mode stress intensity factors. It was found that the fracture criterion based on the quadratic mixture of the normalized stress intensity factors is less sensitive to the changes in characteristic length than the fracture criterion based on the total energy release rate along with the phase angle.This work has been supported by ONR, with Dr. Y. Rajapakse as the program official.     

Effects of Stitching on Delamination of Satin Weave Carbon-Epoxy Laminates Under Mode I,Mode II and Mixed-Mode I/II Loadings

The objective of the present study is to characterize the effect of modified chain stitching on the delamination growth under mixed-mode I/II loading conditions. Delamination toughness under mode I is experimentally determined, for unstitched and stitched laminates, by using untabbed and tabbed double cantilever beam (TDCB) tests. The effect of the reinforcing tabs on mode I toughness is investigated. Stitching improves the energy release rate (ERR) up to 4 times in mode I. Mode II delamination toughness is evaluated in end-notched flexure (ENF) tests. Different geometries of stitched specimens are tested. Crack propagation occurs without any failure of stitching yarns. The final crack length attains the mid-span or it stops before and the specimen breaks in bending. The ERR is initially low and gradually increases with crack length to very high values. The mixed-mode delamination behaviour is investigated using a mixed-mode bending (MMB) test. For unstitched specimens, a simple mixed-mode criterion is identified. For stitched specimens, stitching yarns do not break during 25% of mode I ratio tests and the ERR increase is relatively small compared to unstitched values. For 70% and 50% of mode I ratios, failures of yarns are observed during crack propagation and tests are able to capture correctly the effect of the stitching: it clearly improves the ERR for these two mixed modes, as much as threefold.     

Influence of silane coupling agents on interlaminar fracture in glass fibre fabric reinforced unsaturated polyester laminates

The relationship between the adhesive properties of the interphase of glass fibre/resin and the resultant composite Mode I delamination fracture toughness in glass fibre fabric laminate (GFFL) was studied. The Mode I interlaminar fracture toughness of GFFL was obtained by using a double cantilever beam (DCB) specimen. The delamination resistance of GFFLs which have two silane coupling agents and three concentration finishes is discussed on the basis of interlaminar fracture toughness. The crack propagation behaviour of DCB testing was mainly divided into stable and unstable manners. The fracture toughness and the crack propagation behaviour were dependent on the types and concentration of silane coupling agents.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Mechanical and statistical analyses of fracture of whisker-reinforced ceramic-matrix composites

This paper analyzes the fracture toughness of short-fiber reinforced ceramic-matrix composites (CMC). The effects of crack deflection and fiber pullout on matrix cracking are examined using a combination of mechanical and statistical models. First, the stress intensity factors of a deflected crack subjected to closure stress due to fiber pullout are analyzed based upon the mechanical model. Distributed dislocation method is used for the elastic analysis. Since the deflected crack is subjected to biaxial loading, a mixed mode fracture criterion in linear elastic fracture mechanics is applied to calculate the fracture toughness. Secondly, the number of pullout fibers on the fracture surface is treated as a random variable, and the statistical distribution of these fibers has been determined. The pullout force acting on a deflected crack is also obtained as a random variable by assuming a simple mechanism of fiber pullout. The probability of failure of CMC can thus be estimated from the strength characteristics of the fiber and matrix as well as the interface between these two.     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

Influence of the matrix constituent on mode I and mode II delamination toughness in fiber-reinforced polymer composites under cyclic fatigue

Mode I and mode II fracture behaviour under static and dynamic loading was analyzed in two composites made up of the same reinforcement though embedded in two different matrices. Specifically, the delamination energy under static and dynamic loading was obtained for both materials and both fracture modes, i.e. the number of cycles necessary for the onset of fatigue delamination. Subsequently, the crack growth rate (delamination rate) was obtained for different percentages of the critical energy rate. The main goal of the study was to ascertain the influence of the matrix on the behaviour of the laminate under fatigue loading.From the experimental results for the onset of delamination, similar fatigue behaviour was observed at a low number of cycles for both matrices and both fracture modes, while in fatigue at a high number of cycles, a higher fatigue limit was obtained in the composite with the modified resin (higher toughness) for both fracture modes. From the point of view of crack growth rate, both materials behaved similarly for different levels of stress under fatigue and the two fracture modes for small crack lengths (initial growth zone < 5 mm), although the growth rate increased for large crack lengths. This behaviour was the same in both loading modes.     

Fracture toughness diagrams of a notched body

To describe fracture toughness diagrams of notched bodies, a model of the cohesion zone near the notch root and an averaging criterion of stresses in this zone were employed. The geometric stress concentration factor and biaxiality coefficient affect greatly the shape of fracture toughness diagram. The notch root critical stress intensity factor is a decreasing function of geometric stress concentration factor. __________ Translated from Problemy Prochnosti, No. 5, pp. 142–148, September–October, 2006. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2006, Kiev, Ukraine).     

A new M-integral parameter for mixed-mode crack growth in orthotropic viscoelastic material

This paper deals with a new independent path integral which provides the mixed-mode during a creep crack growth process in viscoelastic orthotropic media. The developments are based on an energetic approach using conservative laws. The mixed-mode fracture separation is introduced according to the generalization of the virtual work principle. The fracture algorithm is implemented in a finite element software and coupled with an incremental viscoelastic formulation and an automatic crack growth simulation. This M-integral provides the computation of stress intensity factors and energy release rate for each fracture mode. A numerical validation, in terms of energy release rate and stress intensity factors, is carried out on a CTS specimen under mixed-mode loading for different crack growth speeds.