Investigations of interlaminar fracture toughness of laminated polymeric composites

The behavior of interlaminar fracture of fiber reinforced laminated polymeric composites has been investigated in modes I, II, and different mixed mode I/II ratios. The experimental investigations were carried out by using conventional beam specimens and the compound version of the CTS (compact tension shear) specimen. In this study, a compound version of the CTS specimen is used for the first time to determine the interlaminar fracture toughness of composites. In order to verify the results obtained by the CTS tests, conventional beam tests were also carried out. In the beam tests, specimens of double cantilever beam (DCB) and end notched flexure (ENF) were used to obtain the critical rates of the energy release for failure modes I and II. The CTS specimen is used to obtain different mixed mode ratios, from pure mode I to pure mode II, by varying the loading conditions. The highest mixed mode ratio obtained in the experiment was G _I /G _II =60. The data obtained from these tests were analyzed by the finite element method. The separated critical rates G _I and G _II of the energy release were calculated by using the modified virtual crack closure integral (MVCCI) method. The experimental investigations were performed on a unidirectional glass/epoxy composite. The results obtained by the beam and CTS tests were compared. It was found that the interlaminar fracture toughness G _IC ^init of mode I at crack initiation and the corresponding value G _II ^Cinit of mode II obtained by the conventional beam and the CTS tests were in rather good agreement. The experimental results of interlaminar fracture of mixed mode were used to obtain the parameters required for the failure criterion. The two different failure criteria were compared. The best correlation with the experimental data was obtained by using the failure criterion proposed by Wu in 1967 containing linear and quadratic terms of the rates of the energy release.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 307–322, May–June, 1998.     

Interlaminar fracture of multidirectional glass/epoxy laminates under mixed-mode I + II loading

The mixed-mode I + II interlaminar fracture of multidirectional glass/epoxy laminates is investigated. Mixed-mode bending (MMB) tests were performed on specimens with delaminations in 0/θ-type interfaces, with θ varying from 0 to 90°. Preliminary three-dimensional finite-element analyses validated the beam theory model (BTM) used for analysing experimental data. The compliances measured are in a good agreement with BTM predictions. The total critical energy release rate G_c varies linearly with the mode II ratio G_II/G, although some discrepancies are observed in the high-mode II results for the 0/45 and 0/90 specimens. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 349–366, May–June, 2007.     

The onset of mixed-mode intralaminar cracking in a cross-ply composite laminate

The intralaminar fracture toughness of a unidirectionally reinforced glass/epoxy composite is determined experimentally at several mode I and mode II loading ratios. The crack propagation criterion, expressed as a quadratic form in terms of single-mode stress intensity factors (alternatively, linear in terms of energy release rates), approximates the test results reasonably well. The mixed-mode cracking criterion obtained is used to predict the intralaminar crack on set in a cross-ply glass/epoxy composite under off-axis tensile loading. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 785–794, November–December, 2008.     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

An evaluation of the interlaminar fracture toughness of a thermoplastic composite with offset centre flies

Conclusion The offset DCB specimen has been used to characterize the influence of cooling rate and loading rate on the interlaminar fracture properties of carbon fibre reinforced PEEK. By offsetting the mid-plane fibres by several degrees, the amount of fibre bridging occurring during fracture has been reduced considerably. It has been shown that IM6 carbon fibre PEEK is quite sensitive to the cooling conditions employed after consolidation at 380 °C. Low rates of cooling yield a high level of crystallinity and a reduced fracture toughness. The modified DCB specimen has been successfully applied to highlight a distinct interlaminar fracture rate sensitivity. The high rate properties of this material still leave cause for concern and more work is required before these materials will find widespread use.Published in Mekhanika Kompozitnykh Materialov, No. 4, pp. 476–483, July–August, 1992.     

An efficient procedure for determining mixed-mode energy release rates in practical problems of delamination

A computationally efficient procedure is presented for the prediction of mixed-mode strain energy release rates in practical problems of delamination. In this procedure, an analytical crack tip element analysis is used for the determination of all singular field quantities. By comparison with two- and three-dimensional finite element results, the procedure is shown to be accurate for mixed-mode problems where mode I, mode II and/or mode III crack tip singularities are present. The procedure is applicable for those cases where a near-tip inverse-square-root singularity exists, as well as those where an oscillatory singularity exists. For these latter cases, an alternative approach to using oscillatory field quantities to characterize crack advance is suggested.     

Carbon-Fiber-Reinforced Plastics Based on an Imide Polymerizing Oligomer Binder with a Semi-Interpenetrating Structure

Semi-interpenetrating polymer networks (SIPNs) are synthesized based on a polyimide binder (imide polymerizing oligomer) with addition of polyamide acid. As acylating agents, they include derivatives of benzophenone-tetracarboxylic and diphenyloxide-tetracarboxylic acids and as aminocomponents - diaminodiphenylmethane, diaminodiphenyloxide, and metaphenylene diamine. It is shown that these systems form SIPNs of the snake-in-the-cage type. Uncured compositions forming melts at 300-330°C are used as binders for carbon-fiber-reinforced plastics (CFRP). The homophase structure of the SIPNs in CFRP is shown by dynamic mechanical tests. The interlaminar fracture toughness (G _1c) is measured by the method of a double cantilever beam. It is found that G _1c, as a function of the content (wt.%) of polyamid acid (PAA) in the initial composition used for obtaining CFRP, is of linear character, which is another confirmation of the homophase structure of the SIPNs. The interlaminar fracture toughness achieved for CFRP is 340 J/m² at a 30% PAA content in the initial composition, and the glass transition temperature, which determines the thermal stability of the composites, reaches 320°C. The prospects of employing these plastics in tribotechnics are discussed.     

Mode II Delamination of a Unidirectional Carbon Fiber/Epoxy Composite in Four-Point Bend End-Notched Flexure Tests

Results from an experimental study on the delamination of a unidirectional carbon fiber/epoxy composite by using the four-point bend end-notched flexure (4ENF) test are presented. It was found that the compliance data obtained in load-unload-reload and continuous loading tests were very similar. The R-curves for specimens of different thickness were also found experimentally. These curves showed an appreciable toughening with crack advance, which can be explained by the presence of fiber bridging. The finite-element method with cohesive elements allowing us to model the progressive delamination was used to analyze the 4ENF test. __________ Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 573–584, September–October, 2005.     

Simulation of crack growth using cohesive crack method

We present an effective cohesive discrete crack method in the context of the Reproducing Kernel Particle Method (RKPM) in order to study fracture of concrete structures. The discrete crack approach is based on the visibility method and a simple node splitting scheme. We also present an effective implementation of the visibility method and an iteration free algorithm by including the cohesive force term directly into the stiffness equations. The crack is represented by straight-line segments and the cohesive zone model is employed to model the post-localization behavior of concrete. The method is applied to several examples involving mode I and mixed-mode fracture. These results are compared to experimental data and show good agreement.     

Fracture toughness characteristics of laminated composites

Parameters characterizing the resistance of laminated composites to interlaminar fracture are discussed. The properties of the specific interlaminar fracture work, i.e., the amount of work spent on the formation of a unit of new surface of interlaminar crack, were examined. Taking account of the anisotropy of the material, this work may be characterized using a matrix. Upon change in the direction of crack growth, the matrix elements are transformed similarly to the components of a symmetrical second rank tensor. An interpretation is offered for the matrix elements. The proposed theoretical model was in accord with our experimental results.Moscow Engineering Institute. Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 21–31, January–February, 1996.     

复合材料平面断裂中的J积分

本文采用复变函数方法,首先将裂纹尖端应力和位移代入J积分的一般公式得到了线弹性正交异性复合材料单向板复合型裂纹尖端的J积分的复形式,其次证明了该J积分的路径无关性,最后推出了该J积分的计算公式.作为特例,给出了线弹性正交异性复合材料单向板Ⅰ,Ⅱ型裂纹尖端的J积分的复形式,路径无关性和计算公式.     

Numerical crack path prediction considering orthotropic effects and experimental verification

For a reliable prediction of crack paths, on the one hand the accurate calculation of crack tip loading quantities is inevitable, on the other hand orthotropic features of the fracture toughness need to be taken into account. The interplay of crack tip loading and material response due to fracture is still unclear and seems to have a crucial effect on crack path predictions. Numerical tools for the accurate calculation of crack tip loading quantities using path-invariant J-integrals and interaction integrals (I-integral) are presented. Here, global approaches are beneficial when considering crack tips approaching other crack faces or internal boundaries. Curved crack faces have to be taken into account and special treatment regarding crack face integrals is necessary. Experimental investigations are carried out at standard CT-specimens of rolled aluminum alloy Al-7075 exhibiting a directional orthotropy of the fracture toughness. Considering that property, the numerically predicted crack paths based on FE calculations show very good agreement with subcritically grown paths obtained from experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Simple Model for the Simulation of Delamination in Fiber-ReinforcedComposite Laminates under Mixed-Mode Loading Conditions

For a reliable prediction of the mechanical behavior of unidirectional fiber-reinforced composite laminates (FRCL), it is inevitable to take into account various damage and fracture mechanisms. In this work, delamination under arbitrary mixedmode loading conditions is examined in the framework of the finite element method. Delamination is assumed to be caused by failure of the resin-rich area in the interface between two layers of FRCL's. In this work, a cohesive interface elementin terms of natural stress-strain relationships which allows to describe the interlaminar mechanical behavior of FRCL's is introduced. The proposed model prevents the restoration of cohesion in the interface. The interpenetration of the crack faces is avoided by incorporating a simple contact algorithm. A representative numerical example shows the applicability of the proposed concept. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Experimental study of fracture toughness and energy in composite materials

The paper presents an experimental investigation of fracture characteristics of composite materials. The post-peak response of the load-crack opening displacement of notched specimens is used to evaluate the fracture energy associated with progressive matrix damage and crack growth. Effects of fiber orientation and other geometric characteristics on fracture parameters are studied. The load versus crack opening displacement as well as crack length, fracture toughness, and energy versus the number of loading cycles are obtained for different specimens. Based on the experimental results of this study, concepts of the fracture mechanics are applied to evaluate the evolution of fracture toughness and energy.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Department of Mechanical & Industrial Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 323–332, May–June, 1998.     

The Effect of an Active Diluent on the Properties of Epoxy Resin and Unidirectional Carbon-Fiber-Reinforced Plastics

The influence of an active diluent on the properties of an epoxy matrix and carbon-fiber-reinforced plastics (CFRP) is investigated. The physicomechanical properties of an ED-20 epoxy resin modified with diglycidyl ether of diethylene glycol (DEG-1), the adhesion strength at the epoxy matrix–steel wire interface, and the mechanical properties of unidirectional CFRP are determined. The concentration of DEG-1 was varied from 0 to 50 wt.%. The properties of the matrix, the interface, and the composites are compared. It is stated that the matrix strength affects the strength of unidirectional CFRP in bending and not their strength in tension, compression, and shear. The latter fact seems somewhat unexpected. The interlaminar fracture toughness of the composites investigated correlates with the ultimate elongation of the binder. A comparison between the concentration dependences of adhesion strength and the strength of CFRP shows that the matrices utilized provide such a high interfacial strength that the strength of CFRP no longer depends on the adhesion of its constituents.     

Fracture mechanics analysis of debond growth in a single-fiber composite under cyclic loading

A model is developed to analyze the growth of a fiber/matrix debond along a broken fiber interface in a single-fiber composite subjected to tension-tension fatigue. The Paris law expressed in terms of debond growth and strain energy release rates is used. An analytical solution for the Mode II energy release rate G _II is obtained for long debonds, where the interface crack growth is self-similar. For short debonds, the interface crack interacts with the fiber break, and therefore a FEM modeling in combination with the virtual crack closure technique was performed to calculate the increase in G _II . Finally, the calculated G _II dependences are summarized in simple expressions that are used to simulate the debond growth in fatigue. A parametric study of the effect of Paris law parameters on the debond growth is performed.     

Design of a new fracture specimen by 3D singularity analyses

A new design of a fracture mechanics specimen is presented. It ensures a valid square‐root singularity along the whole threedimensional crack front under mode‐I conditions. Within the proposed concept it is possible to adjust the angle between the crack front and the free surface in advance. Therefore, the shape of the whole crack front can be influenced in a desired manner. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)