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.     

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.     

Stress transfer in the fibre fragmentation test

The micromechanics of stress transfer has been analysed in a multiple-fibre composite which was subjected to uniaxial tension. The model composite was treated as a three-cylinder assemblage, which consisted of a central fibre, a matrix annulus and a composite medium. Analytical solutions have been derived for all major stress components for the composite with fully bonded fibre-matrix interface. A parametric study was performed on a carbon fibre-epoxy matrix composite. The result suggests that the principal effect of a stiff composite medium surrounding a discontinuous isolated fibre due to the high fibre volume fraction and stiff matrix, is to reduce the efficiency of stress transfer over the central potion of the fibre, while promoting the fibre-matrix interface shear stress concentration at the fibre end region. Practical implications of this observation with respect to fibre fragmentation and interfacial debonding are discussed.     

Stress transfer in the fibre fragmentation test

An improved micromechanics model has been developed of the stress transfer for a single fibre embedded in a matrix subjected to uniaxial loading. Debond crack growth is analysed based on the shear strength criterion such that when the interfacial shear stress reaches the shear bond strength, debonding occurs; and the average strength concept based on Weibull statistics is considered for fibre fragmentation. The influences of the interfacial shear bond strength and the fibre strength on the stress distributions in the composite constituents are evaluated. Depending on the relative magnitudes of these two strength parameters and given the elastic constants and geometric factors, three distinct conditions of the fibre-matrix interface are properly identified which include full bonding, partial debonding and full frictional bonding. Also quantified are the necessary criteria which must be satisfied in order for each interface condition to be valid. Finally, the mean fibre fragment length is predicted as a function of applied strain using a model composite of carbon fibre-epoxy matrix. The parametric study suggests that the critical transfer length predicted when the applied strain (or stress) required for further fibre fragmentation approaches infinity, can be regarded as a material constant, which is the sum of the bonded and the debonded lengths for the model composite.     

Single-fibre Broutman test: fibre–matrix interface transverse debonding

The single-fibre Broutman test was used to study the fibre–matrix interface debonding behaviour when subjected to a transverse tensile stress. During testing, damage was detected using both visual observation under polarized light and acoustic emission (AE) monitoring. Separation of failure mechanisms, based on AE events, was performed using time domain parameters (amplitude and event width) and fast Fourier transform (FFT) frequency spectra of the AE waveforms. The latter can be considered as a fingerprint allowing to discriminate fibre failure, matrix cracking, fibre–matrix interface debonding, friction and ‘parasite noise’. Stresses in the specimens were evaluated using a two-dimensional finite element model (FEM) and monochromatic photoelasticity was used to verify the simulated stress distribution.Two failure mechanisms appeared to be in competition in the Broutman test: fibre failure under compressive stresses and fibre–matrix interface debonding under transverse tensile stresses. For systems in which the interfacial adhesion is not so ‘good’, like glass fibre–polyester systems for instance, fibre–matrix debonding was observed, and the progression of the debonding front with the interfacial transverse stress was recorded. Thermal stresses are also discussed, and a FEM simulation shows that they encourage fibre failure under compressive stresses.     

界面脱粘对正交铺设SiC/CAS复合材料基体开裂的影响

采用细观力学方法研究了正交铺设SiC/CAS复合材料在单轴拉伸载荷作用下界面脱粘对基体开裂的影响。采用断裂力学界面脱粘准则确定了0°铺层纤维/基体界面脱粘长度, 结合能量平衡法得到了主裂纹且纤维/基体界面发生脱粘(即模式3)和次裂纹且纤维/基体界面发生脱粘(即模式5)的临界开裂应力, 讨论了纤维/基体界面剪应力、 界面脱粘能对基体开裂应力的影响。结果表明, 模式3和模式5的基体开裂应力随纤维/基体界面剪应力、 界面脱粘能的增加而增加。将这一结果与Chiang考虑界面脱粘对单向纤维增强陶瓷基复合材料初始基体开裂影响的试验研究结果进行对比表明, 该变化趋势与单向SiC增强玻璃陶瓷基复合材料的试验研究结果一致。     

Matrix cracking and interface debonding in fiber-reinforced cement-matrix composites

The processes of matrix cracking and interface debonding were studied using the high sensitivity Moire interferometry technique. The experiments were conducted with continuous steel fiber reinforced cementitious composites subjected to uniaxial tension. The initiation and propagation of cracking and debonding were observed during the tests with the specimens of different fiber-volume ratios. Based on the experiments, the fiber stress, the interface slip, the interface shear stress, and the matrix strain distribution were calculated. It was shown that interfacial frictional shear stresses were not constant either along the whole interface or at different loading levels. The strain localization was observed in the matrix where it was bonded to the fiber. The average contribution of the matrix was greater for the composites with the higher fiber-volume ratio.     

Data reduction methodologies for single fibre fragmentation test: Role of the interface and interphase

The single fibre fragmentation test (SFFT) is commonly used to characterise the fibre/matrix adhesion. In order to quantify the fibre/matrix adhesion the cumulative stress transfer function (CSTF) methodology was developed so that the elastoplasticity of the matrix could be included in the analysis through the plasticity-effect model [Tripathi D, Chen F, Jones FR. A comprehensive model to predict the stress fields in a single fibre composite. J Comp Mater 1996;30;1514–38., Tripathi D, Jones FR. Measurement of the load-bearing capability of the fibre/matrix interface by single fibre fragmentation. Comp Sci Technol 1997;57:925–35.] The limitations of this technique for the data reduction have been addressed by the use of the Plasticity Model to input the non-linearity of the matrix into methodology for fragmentation of a fibre in a matrix. An improved methodology, known as the revised cumulative stress transfer function (RCSTF) is described. The adhesion of a nanoscale plasma copolymer coated glass/epoxy system has been used to examine this approach to the fragmentation process. This methodology is also extended to account for the presence of an interphase. To validate the three phase model, carbon fibre coated with high and medium modulus epoxy resin were used to simulate fibre/interphase/matrix.     

Single fibre transverse debonding: stress analysis of the Broutman test

The paper presents an extended analytical approach for the interfacial transverse stress that is generated by the Broutman test specimen under compression. The analysis is based on the division of the specimen into a bulk region and a near fibre region. Treating separately each region a compound equation for the interfacial stress can be derived. The equation also includes residual thermal stress and fibre anisotropy. A 3D finite element model was used to validate the approach. The calculations are performed for two commonly used material systems (carbon/glass fibre, epoxy resin). A comparison between the finite element results and the analytical solutions indicates that the accuracy of the analytical approach is very good.     

Modelling of critical fibre length and interfacial debonding in the fragmentation testing of polymer composites

Micro-mechanical models based on a unidimensional load transfer approximation are used to predict the critical fibre length as a function of applied strain in the fragmentation testing of polymer matrix composites. Conditions of perfect adhesion, partial debonding, and total debonding are considered in turn. Situations are identified where the critical length cannot be viewed as a material constant, i.e. where it remains strain dependent as the applied strain increases. Numerical results based on the partial debonding model are given for the critical fibre length and the extent of the debonding zone as a function of applied strain. The prediction of the total debonding model is recovered asymptotically for large strains. We find, however, that the critical length predicted by the partial debonding model can be lower than the one predicted by the total debonding model if the interfacial bond strength is sufficiently larger than the frictional shear stress. These theoretical results show that both bond strength and frictional shear stress must be taken into account in the interpretation of the fragmentation test data.     

Characterizing the fibre/matrix interface of carbon fibre-reinforced composites using a single fibre pull-out test

A single fibre pull-out technique has been used to determine the interfacial bond strength of carbon fibres embedded in epoxy resin. A method is presented whereby the maximum interfacial bond shear stress may be evaluated from the simple measurement of the pull-out force and fibre dimensions. Additional information may also be obtained concerning the interface morphology. The results obtained demonstrate the feasibility of the method and good agreement between theory and experiment.     

纤维增强复合材料界面脱层和基体裂纹的模拟分析

基于Ghosh提出的Voronoi单元有限元方法,构造能同时反映纤维增强复合材料界面脱层和基体裂纹扩展的单元(X-VCFEM单元);应用界面力学理论和断裂力学理论,建立界面脱层、界面裂纹扩展方向和基体裂纹扩展的判断准则;结合网格重划分技术,模拟分析了只含有一个夹杂时界面脱层和基体裂纹扩展的过程,并通过与传统有限元计算结果的比较,验证X-VCFEM单元的可靠性和有效性;同时,模拟分析含任意随机分布夹杂的纤维增强复合材料界面脱层和基体裂纹的产生和扩展过程。结果表明：应用该方法模拟复杂多相复合材料裂纹问题具有计算速度快和精度高的优越性。     

Effect of interface debonding on the thermal conductivity of microencapsulated-paraffin filled epoxy matrix composites

Microcapsules containing phase change materials (microPCMs) can be filled in polymeric matrix forming smart temperature-controlling composites. The aim of this study was to investigate the effect of interface debonding on the thermal conductivity of microPCMs containing paraffin/epoxy composites. The shell thickness and average size of microPCMs were controlled by regulating the core/shell ratios and emulsion stirring rates. Test results indicated that the thermal conductivity (K_e) of all composites decreased after a thermal shock treatment. SEM and thermography measurements were applied to observe the interface behaviors of composites after a violent thermal treatment process. It was proved that the interface debonding was generated because of the mismatch of expansion coefficient between shell and epoxy. A modeling analysis of the relative thermal conductivity (K_r) indicated that the effective approach to decrease the debonding is to enhance the molecule tangling degree between shell and matrix.     

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.     

The interface in carbon-magnesium composites: fibre and matrix effects

Two types of carbon fibres were incorporated into magnesium alloy matrices by squeeze casting. Mechanical testing showed that surface treatment of the fibres led to a marked increase in the interfacial shear strength and a corresponding decrease in the longitudinal tensile strength. A small amount of fine AI₄C₃ forms at the fibre matrix interface in simple binary Mg-AI matrices. Mg₁₇AI₁₂ and Mg₂Si form at the interface in the Mg-AI-Si matrix: precipitation is greatly enhanced by residual stresses at the interface and many fibres are surrounded by a brittle layer leading to inferior mechanical properties.     

Analysis of the effect of embedded fibre length on fibre debonding and pull-out from an elastic matrix

Experimental results obtained from single fibre pull-out tests on specimens with different fibre embedment lengths, consisting of a brass-coated steel wire as fibre and a cementitious mortar as matrix, are analysed using the appropriate theories reviewed in the first part of this paper. The analyses indicate that both adhesional bonding and frictional resistance to slipping along the portion of the interface over which the adhesional bond has failed contribute significantly to the total resistance to completion of fibre debonding and initiation of fibre pull-out in these specimens. Estimated values of the adhesional (maximum) interfacial bond shear strength and the frictional resistance to slipping obtained from the apparent variation of maximum pull-out load with embedded fibre length are compared and found, for theories which are similar, to be generally in agreement.     

Analysis of the effect of embedded fibre length on fibre debonding and pull-out from an elastic matrix

The nature and properties of the resistance to fibre-matrix interfacial debonding in composites composed of ductile fibres in a brittle or elastic matrix can be determined using the single-fibre pull-out test. The results of such tests on cementitious matrix specimens indicate a non-linear relationship between the debonding and/or pull-out load and the embedded length of the fibre. Several of the theories developed to explain the debonding process and enable estimation of the parameters representing the debonding resistance through an analysis of pull-out test results are reviewed in this first of a two-part paper. The application of these theories to experimental data for steel fibre-cementitious matrix pull-out specimens is examined in the second part.Nomenclature b _i effective thickness of the fibre—matrix interface - d _f diameter of the fibre - l _c embedded fibre length at which fibre fracture rather than pull-out occurs - l _d debonded fibre length - l _e embedded length of the fibre in a pull-out specimen - l _{e, min} a minimum embedded fibre length which equals (1/₂cosh^–1 (_ib,max/_ib,f)^1/2 - l _k minimum embedded fibre length required to support the debonding stress in the fibre - l _p maximum embedded fibre length at which complete debonding occurs instantaneously - q _{ib, max} elastic shear flow resistance to fibre-matrix interfacial debonding - q _{ib, f} frictional shear flow resistance to slipping at the fibre-matrix interface after the elastic bond has broken - r _f radius of the fibre - r _m effective radius of the matrix block in a pull-out test specimen - A _f cross-sectional area of the fibre - A _m cross-sectional area of the matrix block in a pull-out test specimen - C ₁ a constant representing the normal compressive stress at the fibre-matrix interface - C ₂ a constant representing the coefficient of friction between the fibre and the matrix at the interface - D length of the debonding plateau (see Fig. 5a) - E _m modulus of elasticity of the matrix - E _f modulus of elasticity of the fibre - G _i shear modulus of the fibre-matrix interface - G _m shear modulus of the matrix - P _f load applied to the fibre in a pull-out test - P _{f, max} maximum load applied to the fibre in a pull-out test - P _{f, ult} applied load at which fibre fracture occurs - P _{f, edb} load required to break the adhesional or elastic fibre-matrix interfacial bond in a pull-out test specimen - P _{f, edb} maximum value of P _{f, edb} (see Fig. 7) - P _{f, d} instantaneous decrease in applied fibre load when debonding is complete - P _f,r residual fibre load required to overcome initial frictional resistance to fibre pull-out - P _f, applied fibre load required to debond an infinitely long fibre with no frictional resistance to slipping at the fibre-matrix interface - an elastic constant ₁ = (2G _i/b _i r _f E _f)^1/2 ₂ = [(2 G _m/ln(r _m r _f))(1/A _f E _f–1/A _m E _m)]^1/2 ₃=[4 G _m/ln(r _m/r _f)r _f E _f]^1/2 ₄=[G _m(A _f E _f + A _m E _m/A _f E _f A _m E _m)]^1/2 - _i surface energy of the fibre-matrix interface - _f fibre extension or displacement in a pull-out test - slope of the linear portion of the P _{f, max} against ₂ l _e curve and is equal to _ib,fd _f/₂ - fibre-matrix misfit - coefficient of friction between the fibre and matrix at the interface - _f Poisson's ratio of the fibre - _m Poisson's ratio of the matrix - _{f, max} stress in the fibre at which interfacial debonding occurs in a pull-out test specimen, i.e. debonding stress - _{f, max} plateau debonding stress (see Fig. 5b) - _{f, po} stress in the fibre when fibre pull-out begins, i.e. immediately following the completion of interfacial debonding - _{f, ult} ultimate tensile strength of the fibre - _{i, n} normal compressive stress exerted by the matrix on the fibre across the interface - _{i, av} average shear stress at the fibre-matrix interface - _{i, max} maximum shear stress at the fibre-matrix interface - _{ib, av} average shear strength of the fibre-matrix interfacial bond - _{ib, max} maximum or adhesional shear strength of the fibre-matrix interfacial bond - _{ib, f} frictional resistance to slipping at the fibre-matrix interface after the elastic bond has broken     

3D in situ observations of glass fibre/matrix interfacial debonding

X-ray microtomography was used for 3D in situ observations of the evolution of fibre/matrix interfacial debonding. A specimen with a single fibre oriented perpendicular to the tensile direction was tested at a synchrotron facility using a special loading rig which allowed for applying a load transverse to the fibre. Three distinguishable damage stages were observed: (i) interfacial debond initiation at the free surface, (ii) debond propagation from the surface into the specimen and (iii) unstable debonding along the full length of the scanned volume. The high resolution microtomography provides both qualitative and quantitative 3D data of the debonding initiation and propagation. Thus, microtomography is demonstrated as a promising technique which can assist micromechanical model development.