Finite Element Analysis of the Competition Between Crack Deflection and Penetration of Fiber-Reinforced Composites Using Virtual Crack Closure Technique

Crack deflection along the fiber/matrix interface for fiber-reinforced composites is an important condition upon which the toughening mechanisms depend. Sound control for the interface debonding of composites contributes to improving the fracture toughness of composites. Combined with the virtual crack closure technique, a finite element model of composites is proposed to predict the competition between the matrix crack deflection along the interface and the matrix crack penetration into the fibers under the thermomechanical coupling fields. For C/C composites, the effects of the geometry size, fiber volume fraction, fiber coating materials and thermal mismatch on the energy release rate and the crack deflection mechanisms are studied. Results show the fiber coating increases the ability to deflect at large thermal mismatch and small crack sizes, and the TaC coating shows larger effect than the SiC coating. The research provides fundamental method for promoting the toughening design of C/C composites.     

The influence of the interphase and associated interfaces on the deflection of matrix cracks in ceramic matrix composites

A model is proposed to determine the influence of an interphase on the deflection of a matrix crack in ceramic matrix composites. Then, a finite element analysis is performed for a microcomposite geometry with an annular crack which initiates in the matrix and propagates in the interphase. It is applied to a SiC/C/SiC microcomposite with a pyrocarbon interphase. Criteria for penetration and deflection of the matrix crack are expressed in terms of toughness of the interphase and of the various interfaces (matrix/interphase and interphase/fibre interfaces). The predictions are found to agree with crack deflections observed in practical SiC/SiC composites and with the available interphase toughness data. Results also suggest that the real crack deflection mechanism involves debonding ahead of the propagating matrix crack.     

Stress transfer in the fibre fragmentation test: Part III Effect of matrix cracking and interface debonding

A theoretical stress analysis has been developed for the fibre fragmentation test in the presence of matrix cracks at sites of fibre breaks. The strain energy release rates for both matrix cracking and interface debonding are calculated for a carbon fibre/epoxy matrix composite. By comparing these strain energy release rates with the corresponding specific fracture resistances, the competition between matrix crack growth and interface debonding has been studied. The distributions of fibre axial stress and interfacial shear stress obtained from the present analysis show that the matrix crack substantially reduces the efficiency of stress transfer from the matrix to the fibre. This revised version was published online in November 2006 with corrections to the Cover Date.     

Conditions for matrix crack deflection at an interface in ceramic matrix composites

This paper describes a numerical approach developed to simulate the mechanism of matrix crack deflection at the fibre/matrix interface in brittle matrix composites. For this purpose, the fracture behaviour of a unit cell (microcomposite) consisting of a single fibre surrounded by a cylindrical tube of matrix was studied with the help of a finite element model. A fracture mechanics approach was used to design a criterion for deflection at the fibre/matrix interface of an annular crack present in the matrix. The analysis of the fracture behaviour of SiC/SiC and SiC/glass ceramics microcomposites shows that the introduction of a low modulus and low toughness interfacial layer at the fibre/matrix interface (e.g. a carbon coating) greatly favours matrix crack deflection at the interphase/fibre interface.     

The role of matrix cracks and fibre/matrix debonding on the stress transfer between fibre and matrix in a single fibre fragmentation test

The single fibre fragmentation test is commonly used to characterise the fibre/matrix interface. During fragmentation, the stored energy is released resulting in matrix cracking and/or fibre/matrix debonding.Axisymmetric finite element models were formulated to study the impact of matrix cracks and fibre/matrix debonding on the effective stress transfer efficiency (EST) and stress transfer length (STL). At high strains, plastic deformation in the matrix dominated the stress transfer mechanism. The combination of matrix cracking and plasticity reduced the EST and increased STL.For experimental validation, three resins were formulated and the fragmentation of an unsized and uncoupled E-glass fibre examined as a function of matrix properties. Fibre failure was always accompanied by matrix cracking and debonding. With the stiff resin, debonding, transverse matrix cracking and conical crack initiation were observed. With a lower modulus and lower yield strength resin the transverse matrix crack length decreased while that of the conical crack increased.     

Improving fracture toughness of dental nanocomposites by interface engineering and micromechanics

The fracture toughness of dental nanocomposites fabricated by various methods of mixing, silanization, and loadings of nanoparticles had been characterized using fatigue-precracked compact-tension specimens. The fracture mechanisms near the crack tip were characterized using atomic force microscopy (AFM), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). The near-tip fracture processes in the nanocomposties were identified to involve several sequences of fracture events, including: (1) particle bridging, (2) debonding at the poles of particle/matrix interface, and (3) crack deflection around the particles. Analytical and finite-element methods were utilized to model the observed sequences of fracture events to identify the source of fracture toughness in the dental nanocomposites. Theoretical results indicated that silanization and nanoparticle loadings improved the fracture toughness of dental nanocomposites by a factor of 2-3 through a combination of enhanced interface toughness by silanization, crack deflection, as well as crack bridging. A further increase in the fracture toughness of the nanocomposites can be achieved by increasing the fracture toughness of the matrix, nanofilled particles, or the interface.     

Film cracking and debonding in a coated fiber

A fracture mechanics based methodology for the determination of interface fracture toughness from crack spacing in a thin coated fiber is presented. The coating (film) may be regarded as the matrix material in typical experiments employing this configuration. Matrix crack spacing is considered to be the result of a competitive process between matrix segmentation and interface debonding which are assumed to be governed by critical energy release rate criteria. Matrix cracks are assumed to form by the process of channeling in the circumferential direction and steady state conditions are assumed at the matrix crack front in the channeling direction. Energy release rates are determined using domain integral procedures in conjunction with the finite element method. The minimum crack spacing is obtained as a function of applied stress for different values of interface fracture toughness. A methodology to relate the saturated crack spacing to interface fracture toughness is developed. Interfaces are classified into three categories: weak, intermediate and strong. It is shown that in experiments of this type, quantitative information about the interface fracture toughness can be obtained for intermediate interfaces while qualitative information may be obtained for weak and strong interfaces.     

Damage tolerance assessment by bend and shear tests of two multilayer composites: Glass fibre reinforced metal laminate and aluminium roll-bonded laminate

The damage tolerance of an aluminium roll-bonded laminate (ALH19) and a glass fibre reinforced laminate (GLARE) (both based on Al 2024-T3) has been studied. The composite laminates have been tested under 3-point bend and shear tests on the interfaces to analyze their fracture behaviour. During the bend tests different fracture mechanisms were activated for both laminates, which depend on the constituent materials and their interfaces. The high intrinsic toughness of the pure Al 1050 layers present in the aluminium roll-bonded laminate (ALH19), together with extrinsic toughening mechanisms such as crack bridging and interface delamination were responsible for the enhanced toughness of this composite laminate. On the other hand, crack deflection by debonding between the glass fibres and the plastic resin in GLARE was the main extrinsic toughening mechanism present in this composite laminate.     

Investigation of the mechanical behaviour of magnesium composites

Stress/strain and fracture toughness behaviour of a commercial heat-treatable magnesium alloy reinforced with up to 20 volume% short alumina fibres was studied at room and elevated temperatures. Microscopic examination of the composites, which were prepared by conventional squeeze casting, revealed damage of a small portion of the fibres during the infiltration process. Sufficient chemical reaction between the matrix alloy and alumina reinforcement tends to produce a good bond at the fibre/matrix interface. The tensile-related properties of the composites increased at room and elevated temperatures with increasing content of the reinforcement. The ductility and fracture toughness of the composites decreased at room temperature with increasing reinforcement content. While failure strains of the composites were slightly improved at higher testing temperatures, the fracture toughness decreased significantly as the testing temperature exceeded 100°C. Examination of the fracture surfaces of specimens tested at room temperature showed a mixed mode fracture appearance with predominantly brittle cleavage fracture. The fracture surfaces of specimens tested at temperatures above 100°C revealed increasing fibre/matrix interface debonding and fibre pull-out with increasing testing temperature. Micromechanism examinations of crack initiation and propagation indicated that the fracture process of the composites may be matrix controlled.     

Prediction of failure modes in unidirectional short-fibre composites

In short-fibre reinforced composites, penny-shaped cracks often initiate from fibre-ends and propagate into the matrix until they are arrested by the neighbouring fibres. A theoretical study on the prediction of failure modes after the arrest, that is, either the penetration of the crack into the fibres or the debonding of the matrix-fibre interface, is performed. The analytical method used in this study is the extension of the two-dimensional model of Kendall to the three-dimensional crack problem. Strain energy release rates for the initiation of the cracks of the penetration and debonding types are calculated. Also computed are the total potential energy required for a complete penetration of the crack through the fibre diameter and a complete debonding of the matrix-fibre interface. Based on these computations, the failure modes of the crack arrested by the neighbouring fibres are discussed.This research was supported by the National Science Foundation under Grant No. CME-7918249.On leave from Department of Mechanical Engineering, University of Electro-Communications, Tokyo, Japan.     

Fracture mechanisms in glass-reinforced plastics

Model glass fibre/polyester resin composites have been made in the form of double cantilever beams and the effect of a small number of fibres on quasi-static crack propagation has been studied by simultaneous plotting of load/deflection curves, measurements of crack length, and observation of the progress of fibre/resin debonding and fibre pull-out. By varying the condition of the fibre surface and the arrangement of the fibres to a limited extent and carrying out subsidiary experiments on single-fibre samples of identical character it has been possible to make direct measurements of all of the important parameters required for an analysis of the macroscopic behaviour in terms of established models of fibre/matrix interaction. Agreement between experimental and calculated fracture energies for these model composites is not highly satisfactory, but it seems clear that the fracture energy of grp is likely to be determined very largely by work done against friction between fibres and matrix after the debonding process has occurred. This conclusion opposes the currently-held view which attributes the largeγ _F values of grp to the fibre/resin debonding mechanism.     

Fracture mechanics of single-fibre pull-out test

Pull-out of an elastic fibre from an elastic matrix was investigated. A simple pull-out mechanics has been developed, based on the fracture energy criterion, to describe the debonding process, including friction. Experiments were carried out using polytetrafluoroethylene (PTFE) fibres embedded in a polypropylene (PP) matrix. It was found that growth of an interfacial crack was stable after the initiation of a debond at the loaded fibre end. At first, the debonding force increased linearly with the crack length due to friction in the debonded region. However, the crack accelerated after reaching a critical length, dependent on the embedded fibre length. At this point, the force required to propagate the debond levelled off. Thus, further increase in the debonding force was not necessary to further complete the debonding process. The debonding force was found to be in good agreement with that predicted by the present theory. Techniques for determining the interfacial properties, including adhesive fracture energy, compressive residual stress and coefficient of friction, were considered. In addition, a simple criterion has been derived to predict which fibre end, either embedded end or loaded end, will debond first when the specimen is subjected to an axial load.     

The full-cell cracking mode in unidirectional brittle-matrix composites

In this work we consider the issues associated with predicting the initiation of matrix cracking within a unidirectional brittle-matrix composite (BMC). The analysis is accomplished as a case study for a restrictive, though important, class of composites consisting of silicon carbide fibres and a glass-ceramic matrix. A newly-derived axisymmetric variational model is employed to predict the stress field and energy release rates in a composite having a single damaged cell (or randomly located non-interacting cells) in which an annular matrix crack is introduced. Propagation of this crack to the fibre/matrix interface generates what we call the full-cell cracking mode. Strength and toughness properties of the matrix material are assumed to infer the potential for growth of the annular crack as well as its influence on the interface stresses and plausible scenarios governing the behaviour of secondary flaws. In turn, the synergistic influence of the latter flaws on the original annular crack is predicted. Since fibre spacing seems to be of paramount importance in real composites, a model of a composite having a non-uniform fibre distribution is also developed. The work includes a study of crack deflection at the fibre/matrix interface and comments are made regarding the perceived need for poor bonding in these materials. Also noted are the key parameters that need to be determined by experiment to quantify the failure prediction.     

Simulation of fracture in heterogeneous elastic materials with cohesive zone models

In brittle composite materials, failure mechanisms like debonding of the matrix-fiber interface or fiber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material. Our aim is to investigate the influence of material parameters and geometrical aspects of fibers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations. We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the fibers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parameters of the interface and geometrical aspects of the fiber. In conclusion, our results can help to guide the manufacturing process of materials with a high fracture toughness.     

Stress transfer in the fibre fragmentation test: Part III Effects of interface debonding and matrix yielding

The micromechanics of stress transfer is presented for the fibre fragmentation test of microcomposites containing debonded fibre–matrix interface and yielded matrix at the interface region. Results from the parametric study are discussed for carbon fibre composites containing epoxy and polyetheretherketone (PEEK) matrices, representing respectively typical brittle debonding and matrix yielding behaviour at the interface region. The stress transfer phenomena are characterized for the two interface failure processes. The sequence of interface failure and fibre fracture as a function of applied stress are also identified. Maximum debonded and yielded interface lengths are obtained above which a fibre will fracture into smaller lengths. There are also threshold fibre fragment lengths above which fibre will fracture without interface debonding or matrix yielding. The applied stresses for these conditions are governed by three strength properties of the composite constituents, namely interface shear bond strength, matrix shear yield strength and fibre tensile strength for given elastic constants of the fibre and matrix, and the geometric factors of the microcomposite. The ineffective length, a measure of the efficiency of stress transfer across the fibre–matrix interface, is shown to strongly depend on the extent to which these failure mechanisms take place at the interface region. This revised version was published online in November 2006 with corrections to the Cover Date.     

碳酸钙增强聚丙烯复合材料的断裂韧性

介绍了J积分方法的概念、理论和方法,并应用参考国外文献建立的,积分测试方法,结合扫描电镜形态分析研究了碳酸钙增强聚丙烯复合材料的断裂韧性。结果表明,碳酸钙的加入使复合材料对裂纹起始和增长过程的阻力都有大幅度提高,聚丙烯基体发生较大幅度塑性形变屈服后取向牵伸吸收塑性能。刚性填料加入时所导致的基体应力集中及界面脱粘后的基体应力集中促进聚丙烯基体产生局部区域微观塑性牵伸被认为是断裂韧性提高的原因。     

Feasibility study of a tungsten wire-reinforced tungsten matrix composite with ZrOx interfacial coatings

Brittleness problem imposes a severe restriction on the potential application of tungsten as high-temperature structural material. In this paper, a novel toughening method for tungsten is proposed based on reinforcement by tungsten wires. The underlying toughening mechanism is analogous to that of fiber-reinforced ceramic matrix composites. Strain energy is dissipated by debonding and frictional sliding at engineered fiber/matrix interfaces. To achieve maximum composite toughness fracture mechanical properties have to be optimized by interface coating. In this work, we evaluated six kinds of ZrO_x-based interface coatings. Interfacial parameters such as shear strength and fracture energy were determined by means of fiber push-out tests. The parameter values of the six coatings were comparable to each other and satisfied the criterion for crack deflection. Microscopic analysis showed that debonding occurred mostly between the W filament and the ZrO_x coating. Feasibility of interfacial crack deflection was also demonstrated by a three-point bending test.     

Effect of physical and geometrical factors on interfacial debonding in the fibre push-out test: A new strength-based model

A strength-based model for the single-fibre push-out test has been developed. Using this model, the matrix stress, fibre stress and interfacial shear stress in a single fibre specimen subjected to push-out loading was considered. The effect of physical and geometrical factors on the stress distribution were evaluated in terms of the influence of relative moduli and sizes of the matrix and fibre, respectively. The propensity for debonding crack initiation at the interface arising from matrix yielding (due to normal stress) and interfacial yielding (due to shear stress) has been determined. The influence of these on the location of debonding crack initiation and the maximum debond force has also been studied.     

Fracture toughness of short-fibre reinforced thermoplastics

The failure process of short-fibre reinforced thermoplastics is characterized by different energy dissipation mechanisms, especially by mode II debonding along the fibre/matrix interface, sliding of debonded regions, brittle or ductile matrix fracture and pull-out. It is assumed that these failure processes are acting within a certain zone ahead of the notch tip— the dissipation zone. The modes of energy dissipation are mainly affected by the matrix fracture mode (brittle or ductile) which is mainly determined by the loading rate or temperature conditions. On the basis of an energy principle and relationships for the different energy dissipation mechanisms, we propose theoretical expressions for the static and dynamic fracture toughness and we compare these with experimental results.     

The impact strength of fibre composites

Two models have been developed which predict the crack initiation energy, notched impact strength and unnotched impact strength of fibre composites. One is applicable to composites containing short fibres and the other to composites containing long fibres. Data obtained with randomly oriented short fibre composites were consistent with the one model. The other model has been verified using composites containing uniaxially oriented long fibres and long fibres oriented randomly in a plane. The success of the model demonstrates that the high notched impact strength with long fibres is due to the redistribution of stress away from the stress concentrating notch, the extra stress that can be held by the fibre relative to the matrix and the work required to pull fibres out of the matrix during crack propagation. The parameters which have been shown to control the fracture energy are composite modulus, fibre length, fibre volume fraction, effective fibre diameter, fibre tensile strength and the coefficient of friction during fibre pull-out from the matrix. The matrix toughness on the other hand usually has no effect at all for composites containing fibres randomly oriented in two dimensions and only a minor effect in exceptional cases. The shear strength of the fibre-matrix bond has only an indirect effect in that it controls the number of fibres which pull out rather than fracture.