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.     

Analysis of extension propagation process of interface crack between belts of a radial tire using a finite element method

A radial tire is a very complex structure made from rubber elastomers and fiber–rubber composite materials. During its use, extension propagation of interface crack between belts can occur, which obviously affects its durability and life. In the present paper, a new mathematical model of extension propagation of interface crack in complex composite structures is presented. The model can reveal the extension propagation dependence of interface crack on the relative size of energy release rates at the left and right crack tips and on the interfacial material properties. The extension propagation model of interface crack, Irwin’s virtual crack close technique and the finite element analysis method are used together in simulating numerically the extension propagation process of a interface crack between belts of a radial tire. The present study numerical results show that the extension propagation model of interface crack proposed in this paper can more realistically characterize the complexity of the extension propagation process of interface crack in complex composite structures.     

A combined finite/discrete element algorithm for delamination analysis of composites

A combined finite/discrete element method is developed to model delamination behaviour in laminated composites. A penalty based algorithm is employed to evaluate the interlaminar stress state. The failure surface for delamination is defined by a Chang-Springer criterion, and the interlaminar crack propagation is achieved by a standard discrete element contact/release algorithm. The ability of the method for simulation of this behaviour is assessed by solving standard test cases available from the literature.     

Three-Dimensional Variational Analysis of Composite Structures Using Bernstein Polynomial Approximations. Report 2

The application of the previously developed 3D varionational analysis approach to the investigation of crack propagation in composite bonded joints is presented. In this application, the propagation of three different types of a 2D planar crack (adhesive, cohesive, and interfacial) is modeled by relaxing the respective continuity conditions for displacements between adjacent bricks in the mosaic structure. The crack propagation process is then characterized by the release rate of the total potential energy between two consecutive states of the mosaic body with different crack lengths. Numerical examples illustrate the 3D analysis of double-lap adhesively bonded joints with unidirectional and cross-ply laminated composite adherends. The numerical results provide an illustration of various characteristics of the crack propagation process. The values of the ultimate failure load predicted by analyzing the initial stage of crack propagation are found to be in a good agreement with experimental data.     

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.     

Mode I,mode II,and mixed-mode I/II interlaminar fracture toughness of GFRP influenced by fiber surface treatment

The interlaminar fracture behavior of unidirectional glass fiber reinforced composites with fiber surface treatment has been investigated in modes I and II and for fixed mode I to mode II ratio of 1.33. The data obtained from these tests have been analyzed by using different analytical approaches. The present investigation is focused on the influence of the glass fiber surface treatment on the interlaminar fracture toughness of unidirectional laminates. Glass fibers with two different fiber surface treatments have been investigated. fiber surface treatment was carried out by using a polyethylene or silane coupling agent in combination with modifying agents. The glass fibers were embedded in the brittle epoxy matrix. Mode I, mode II, and mixed-mode I/II tests were performed in order to determine critical strain energy release rates. Double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode flexure (MMF) specimens were used. For both types of fiber surface treatment about the same values of mode I initiation fracture toughness G_IC ^init were obtained. It was observed that in mode I interlaminar crack growth in the DCB test for the composite sized by polyethylene, the crack propagation is accompanied by extensive fiber bridging. For both fiber surface treatments interlaminar fracture toughness increases considerably with increasing of crack length. For the fiber surface treatment with the silane coupling agent, the value of mode II initiation fracture toughness G_IIC ^init was about 2.5-times higher in comparison with that of a composite sized by polyethylene. For both types of fiber surface treatments the mixed-mode I/II test has shown a similar behavior to the mode I DCB test.     

Degradation modeling of 2 fatigue‐crack growth characteristics based on inverse Gaussian processes: A case study

Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue‐crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time‐scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device.     

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.     

On a numerical scheme for curved crack propagation based on configurational forces and maximum dissipation

A numerical scheme is presented to predict crack trajectories in two dimensional components. First a relation between the curvature in mixed–mode crack propagation and the corresponding configurational forces is derived, based on the principle of maximum dissipation. With the help of this, a numerical scheme is presented which is based on a predictor–corrector method using the configurational forces acting on the crack together with their derivatives along real and test paths. With the help of this scheme it is possible to take bigger than usual propagation steps, represented by splines. Essential for this approach is the correct numerical determination of the configurational forces acting on the crack tip. The methods used by other authors are shortly reviewed and an approach valid for arbitrary non–homogenous and non–linear materials with mixed–mode cracks is presented. Numerical examples show, that the method is a able to predict the crack paths in components with holes, stiffeners etc. with good accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model and extended Kuhn–Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation

When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this bilevel multi-follower issue is where these followers are uncooperatively making their decisions while having cross reference to decision information of the other followers. This situation is called a referential-uncooperative situation in this paper. The well-known Kuhn–Tucker approach has been previously successfully applied to a one-leader-and-one-follower linear bilevel decision problem. This paper extends this approach to deal with the above-mentioned linear referential-uncooperative bilevel multi-follower decision problem. The paper first presents a decision model for this problem. It then proposes an extended Kuhn–Tucker approach to solve this problem. Finally, a numerical example illustrates the application of the extended Kuhn–Tucker approach.     

Interfacial fracture of layered magnetoelectroelastic materials

A problem for an interface crack located in a layered magnetoelectroelastic material strip of semi-infinite length is solved. A closed-form solution is obtained for anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for stresses and electric and magnetic fields, together with their intensity factors and the energy release rate, are obtained. The extreme cases of impermeable and permeable cracks are discussed. Using the basic solution for a single crack, solutions for two collinear interface cracks in an infinitely long layered magnetoelectroelastic medium, an interface crack in an infinitely long layered magnetoelectroelastic medium, and an edge crack at the interface of a semi-infinitely long layered magnetoelectroelastic medium are also obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 145–164, March–April, 2008.     

Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements

This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given.     

Initiation of Cracks in Griffith’s Theory: An Argument of Continuity in Favor of Global Minimization

The initiation of a crack in a sound body is a real issue in the setting of Griffith’s theory of brittle fracture. If one uses the concept of critical energy release rate (Griffith’s criterion), it is in general impossible to initiate a crack. On the other hand, if we replace it by a least energy principle (Francfort–Marigo’s criterion), it becomes possible to predict the onset of cracking in any circumstance. However this latter criterion can appear too strong. We propose here to reinforce its interest by an argument of continuity. Specifically, we consider the issue of the initiation of a crack at a notch whose angle ω is considered as a parameter. The result predicted by the Griffith criterion is not continuous with respect to ω, since no initiation occurs when ω>0 while a crack initiates when ω=0. In contrast, the Francfort–Marigo’s criterion delivers a response which is continuous with respect to ω, even though the onset of cracking is necessarily brutal when ω>0. The theoretical analysis is illustrated by numerical computations.     

Mathematical model of an internal crack in an elastoplastic cylindrical shell

We propose a mathematical model that makes it possible to reduce the problem of the stressed state and limit equilibrium of a cylindrical anisotropic elastoplastic shell with internal crack to a system of nonlinear singular integral equations with discontinuous functions on the right-hand sides. We construct an algorithm for numerical solution of such systems together with the conditions of plasticity and boundedness of stresses near the crack. For a transversally isotropic shell, we carry out a numerical analysis of the dependence of the opening of the internal crack front on the load and geometric and mechanical parameters. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 111–116, April–June, 1998     

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.     

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.     

Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

The problem of interaction of a plane time-harmonic SH-wave with an elastic fiber of quasi-square or quasi-triangular cross section, when an interface crack is present between an infinite elastic matrix and the fiber, is considered. The modified null-field method taking into account the asymptotic behavior of the solution at crack tips is exploited for obtaining numerical results. The effects of fiber shape, fiber/matrix material combination, debonding (crack size), and direction of wave incidence on the scattering amplitude in the far zone are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 245–254, March–April, 2008.     

Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.     

An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations

This study aims to reduce the computational cost in the simulation of fatigue crack growth process. Extended finite element method and combined approximations (CA) are integrated to form an efficient algorithm for such analysis. In the CA approach, binomial series are used as high quality basis vectors for the reduced basis expression and then crack propagation path can be predicted without solving the complete set of system equations. The validity of presented algorithm is fully investigated through several numerical examples. From these results, it is shown that the presented algorithm is very accurate and can save huge amounts of computational effort.     

Dynamics of a bridged crack in a discrete lattice

The paper addresses a problem of partial fracture of a latticeby a propagating fault modelling a crack bridged by elasticfibres. It is assumed that the strength of bonds within thelattice alternates periodically, so that during the dynamiccrack propagation only weaker bonds break, whereas the strongerbonds remain intact. The mathematical problem is reduced tothe functional equation of the Wiener–Hopf type, whichis solved analytically. The load–crack speed dependenceis presented, which also has implications on the stability analysisfor the bridged crack propagating within the lattice. In particular,we address the evaluation of the dissipation rate, which isfound to be strongly dependent on the crack speed. In this latticemodel, our results also cover the case of the supercriticalcrack speed.