Energy release rate and stress field calculation for debonding crack extension at the fibre-matrix interface during single-fibre pull-out

For the micromechanical modelling of the macroscopic failure of fibre-reinforced composites the formulation of a critical parameter for initiation and extension of debonding cracks at the fibre-matrix interface is essential. This point is discussed for the 'fibre pull-out' specimen, a test commonly used to measure the adhesion quality of fibre-matrix systems. Some of the simplifying assumptions fundamental to shear lag theory-based models of the fibre pull-out test are compared with results from a detailed finite element (FE) model to examine their validity. The FE model strongly contradicts assumptions made with the shear lag theory that the axial stress gradient in the matrix can be neglected from the equilibrium equation. A critical interface shear strength is commonly used as a measure of adhesion quality. But for elastic materials the nature of the stress concentrations at the fibre end and interface crack-tip are singular. Therefore a fracture mechanic approach is better suited for a debonding criterion than a simple finite shear strength. The energy release rate shows a minimum for short crack lengths and may stabilize the moving crack.     

Weibull analysis of microbond shear strength at sisal fibre–polyester resin interfaces

An analysis has been made of the tensile strength of sisal fibres and the interfacial adhesion between fibres and polyester resin droplets. Density and microscopy methods were used to determine the cross-sectional area of the sisal fibres. The average tensile strength of treated sisal fibres decreased by a modest amount following treatment with 0.06 M NaOH. However, this treatment resulted in a substantial increase in the interfacial shear strength at the sisal fibre to polyester resin interface. Weibull analysis has been used successfully to analyse variability in tensile strengths and interfacial shear strength using probability of failure plots. Scanning electron microscopy has revealed the shape of resin droplets on the surface of treated and untreated sisal fibres and contact angles are much lower for droplets on treated fibres. Damage to the surface of fibres has been examined following shear testing. Weibull analysis is an effective tool for characterising highly variable fibre properties and evaluating the level of adhesion between polymer resin and the fibre surface.     

Effect of emulsifier content of sizing agent on the surface of carbon fibres and interface of its composites

In this work, carbon fibres were sized with different emulsifier content sizing agent in order to improve the performances of carbon fibres and the interface of carbon fibres composites. The surface characteristic changing after modification was investigated by scanning electron microscopy (SEM), atomic force microscopy (AFM). Wetting and surface energy along with contact angles were determined by the dynamic contact angle analysis test (DCAT). At the same time, the single fibre strengths and weibull distributions were also studied in order to understand the effect of the emulsifier content of sizing agent on the carbon fibres. The interfacial shear strength and hygrothermal ageing of the composites were measured which showed a different enhancement, respectively. The results revealed that sizing agent E-3 showed better interface adhesion between fibres and matrix and sizing agent E-2 sized carbon fibre has better ageing resistant properties.     

Improving the adhesion between a aqueous PU and a polyamide fibre with silane

Glycidoxypropyltrimethoxysilane (GPS) and γ-aminopropyltrimethoxysilane (APS) were used to modify the surface chemistry of polyamide fibre. The surface chemistry was characterised using X-ray photoelectron spectroscopy. The silanol functional group was designed to be introduced on the surface of polyamide fibre to increase its chemical activity by N-alkylation of GPS and hydrolysis of APS, and to improve the poor interfacial adhesion between a polyamide 66 fibre and an aqueous polyurethane polymer adhesive. The microbond test was used to measure the interfacial shear strength between the waterborne PU adhesive and the polyamide fibre. It has been found that APS hydrolysis and GPS-alkylated fibre surface can be used to improve the interfacial adhesion of polyamide fibre to PU. The IFSS can be improved by N-alkylation of GPS from 5.0 to 8.4?MPa. After water immersion at 50?°C for 48?h, then drying, the IFSS increased to 8.8?MPa due to the plasticisation of PU in water. Better interfacial adhesion was also observed by the hydrolysis of APS, but not significantly improved by this method due to the relatively weak hydrogen bond at the interface between APS and polyamide fibre.     

Observation of transcrystalline growth of PLA crystals on sisal fibre bundles and the effect of crystal structure on interfacial shear strength

Hot-stage microscopy was used to characterise crystal growth at the interface between sisal fibre bundles and a polylactic acid (PLA) matrix in order to better understand the mechanical properties of sisal fibre–PLA composites. Cooling rates and crystallisation temperatures and times were varied to influence crystalline morphology at the interface. Single sisal fibre bundles were evaluated in their as received state or treated with 6 wt.% caustic soda solution for 48?h at room temperature. A microbond shear test was used to characterise the shear strength of the interface as a function of fibre surface treatment. These tests were performed on sisal fibre bundles carefully embedded in flat films of PLA supported on card mounts. Fibre bundles in a PLA matrix were cooled from 180?°C at rates from 2 to 9?°C/min and then crystallised isothermally. For as received fibre bundles uneven growth of PLA spherulites occurred at all cooling rates and crystallisation temperatures. For caustic soda treated fibres, uneven spherulitic growth was observed at crystallisation temperatures at and above 125?°C. In contrast, transcrystalline growth was observed for samples cooled to 120?°C at cooling rates from 2 to 6?°C/min and then allowed to crystallise. The microbond shear strengths of untreated and caustic soda treated fibre bundles were evaluated using Weibull statistics and the caustic soda treated fibres exhibited higher interfacial shear strengths in comparison to untreated fibres, reflecting the development of a transcrystalline layer at the fibre to matrix interface.     

Micromechanical analysis of transverse damage of fibre-reinforced composites

The mechanical behaviour of fibre-reinforced composites under transverse tension, compression and shear is studied using computational micromechanics. The representative volume element is constructed for fibre’s random distribution. The Drucker–Prager model and cohesive zone model are used to simulate the matrix damage and interfacial debonding, respectively. The stress distribution along the interface is studied using the model with only one fibre embedded in the matrix. It is found that the interface tensile failure at the equators of fibre firstly occurs under transverse tension; the interface shear failure firstly occurs under transverse compression; both the interface tensile failure and shear failure occur under transverse shear. The direction of fracture plane is perpendicular to the loading direction under transverse tension, 52.5° with the perpendicular direction under compression and 7.5° with the perpendicular or vertical direction under shear, respectively.     

Predicting Interfacial Strengthening Behaviour of Particulate-Reinforced MMC — A Micro-mechanistic Approach

The fracture properties of particulate-reinforced metal matrix composites (MMCs) are influenced by several factors, such as particle size, inter-particle spacing and volume fraction of the reinforcement. In addition, complex microstructural mechanisms, such as precipitation hardening induced by heat treatment processing, affect the fracture toughness of MMCs. Precipitates that are formed at the particle/matrix interface region, lead to improvement of the interfacial strength, and hence enhancement of the macroscopic strength properties of the composite material. In this paper, a micro-mechanics model, based on thermodynamics principles, is proposed to determine the fracture strength of the interface at a segregated state in MMCs. This model uses energy considerations to express the fracture toughness of the interface in terms of interfacial critical strain energy release rate and elastic modulus. The interfacial fracture toughness is further expressed as a function of the macroscopic fracture toughness and mechanical properties of the composite, using a toughening mechanism model based on crack deflection and interface cracking. Mechanical testing is also performed to obtain macroscopic data, such as the fracture strength, elastic modulus and fracture toughness of the composite, which are used as input to the model. Based on the experimental data and the analysis, the interfacial strength is determined for SiC particle-reinforced aluminium matrix composites subjected to different heat treatment processing conditions.     

Stress field calculation around a particle in elastic–plastic polymer matrix under multiaxial loading as basis for the determination of adhesion strength

The stress distribution around a single particle coated with an elastic interphase embedded within an elastic–plastic polymer matrix under multiaxial load was considered. The specimen has a curved (necked) geometry, which causes multiaxial local stresses in the neighbourhood of the particle. The motivation for the calculations is to determine the maximum radial stress (debonding strength) at the particle surface as a function of applied load. The effect of the particle size on failure initiation is considered. Assuming that the normal stress at the interface is responsible for debonding, the adhesion strength can be determined from the critical load at debonding initiation. Because of the matrix yielding, the relation between the applied load and the maximum radial stress at the particle/interphase interface is a non-linear one. Using this relation, the determination of interfacial strength will be possible by a tensile test.     

An energy criterion for the initiation of interface failure ahead of a matrix crack in brittle matrix composites

The mechanism of interfacial failure occurring as a consequence of the stress concentration induced by a matrix crack located in the vicinity of the interface is analysed. For this purpose, an asymptotic analysis is carried out to assess the competition between the propagation of the matrix crack towards the interface and the nucleation of an interfacial debond. An energetic approach provides a necessary condition comparing the ratio of the interfacial toughness over the matrix toughness to a critical value depending on the elastic mismatch between the fibre and the matrix and the ratio of the interfacial nucleation length over the width of the matrix ligament. Presented results show that the interfacial debonding is enhanced if the matrix is softer than the fibre. Further, a modified condition which does not involve the crack increment ratio is established if the matrix crack lies in the stiffest material.     

Application of nano-indentation, nano-scratch and single fibre tests in investigation of interphases in composite materials

Three novel experimental techniques were employed in this work in order to investigate the influence of the interphase region in polymer–glass composites on the bulk material properties: (i) the microdroplet test is a single fibre test designed to characterize the fibre–matrix bond (interface region) and to determine the interfacial shear stress in composite material; (ii) the nano-indentation test, a novel nano-hardness technique with ability to produce an indent as low as a few nanometres was employed in order to measure nano-hardness of the fibre–matrix interphase region; and (iii) the nano-scratch test, used in conjunction with the nano-indentation test for measurement of the interphase region width. The microdroplet test (MDT) has been used to characterize the interfacial bond in fibrous composite materials. The specimen consists of a fibre with a drop of cured resin pulled while the drop is being supported by a platinum disc with a hole. A properly tested specimen fails at the droplet’s tip–fibre interface, revealing the ultimate interfacial shear strength. In this study, finite element analysis (FEA) of the MDT has been focused toward simulation of the fibre–matrix interphase region. The influence of several functional variations of the material properties across the interphase layer on the stress distribution at the droplet’s tip was analysed. The results showed that the variation of the interphase properties significantly affects the stress distribution at the fibre–droplet interface, and, therefore, the stress redistribution to composite material. These results led to further experimental investigation of the interphase region, in order to obtain the material properties essential for the interfacial stress analysis. The interphase region in dry and water aged polymer–glass composite materials was investigated by means of the nano-indentation and the nano-scratch techniques. The nano-indentation test involved indentation as small as 30 nm in depth, produced along a 14 μm path between the fibre and the matrix. The distinct properties of the interphase region were revealed by 2–3 indents in dry materials and up to 15 indents in water aged, degraded materials. These results indicated interdiffusion in water aged interphase regions. The nano-scratch test involves moving a sample while being in contact with a diamond tip. The nano-scratch test, used in conjunction with the nano-indentation test, accurately measured the width of the interphase region. The results showed that the harder interphase region dissolved into the softer interphase region (both regions being harder/stronger than the matrix) expanding its width after aging in water.     

Influence of interfacial reaction on interfacial performance of carbon fiber and polyarylacetylene resin composites

The influence of interfacial reaction on interfacial performance of carbon fiber/polyarylacetylene resin composites was studied. For this purpose, vinyltrimethoxysilane containing a double bond was grafted onto the carbon fiber surface to react with the triple bond of polyarylacetylene resin. The reaction between polyarylacetylene resin and vinyltrimethoxysilane was proved by reference to the model reaction between phenylacetylene and vinyltrimethoxysilane. Surface chemical analysis by XPS, surface energy determination from the dynamic contact angle, and the interfacial adhesion in composites was evaluated by interfacial shear strength test as well. It was found that vinyltrimethoxysilane, which can react with polyarylacetylene resin, had been grafted onto the carbon fiber surface. Furthermore, because the reaction between polyarylacetylene resin and vinyltrimethoxysilane took place at the interface, the interfacial adhesion in composites was significantly increased, and the improvement of interfacial adhesion was all attributed to the interfacial reaction.     

Growth of interfacial debonding in notched two-dimensional unidirectional composite under stress and displacement controls

A simplified calculation method for study of the growth of interfacial debonding between elastic fiber and elastic matrix ahead of the notch-tip in composites under displacement and stress controlled conditions was presented based on the shear lag approach in which the influences of residual stress and frictional shear stress at the debonded interface were incorporated. The calculation method was applied to a model two-dimensional composite. An outline is given of the difference and similarity in the growing behavior of the debonding between the displacement and stress controls, and of the influences of the residual stresses, frictional shear stress, the nature of the final cut component (fiber or matrix) and sample length on the debonding behavior.     

Improving the interfacial strength of PMMA resin composites by chemically grafting graphene oxide on UHMWPE fiber

Controlling interfacial microstructure and interactions between (ultra high molecular weight polyethylene) UHMWPE fiber and matrix is of crucial importance for the fabrication of advanced polymer composites. In this paper, (UHMWPE fiber-g-graphene oxide [GO]) was prepared. GO nanoparticles distributed onto the ?ber surface uniformly, which could increase surface polarity and roughness. Increases of interlaminar shear strength (ILSS) and interfacial shear strength (IFSS) of UHMWPE fiber-g-GO composites were achieved. These enhancements can be attributed to the existent of GO interface with providing chemical bonding and strong mechanical interlocking between the ?ber and matrix. Moreover, impact resistance of UHMWPE fiber-g-GO composites was enhanced.     

Interfacial strength in glass fibre-polypropylene composites: influence of chemical bonding and physical entanglement

For glass fibre–polypropylene (PP) composites, the non-polar nature of polypropylene presents a problem. The present investigation shows that it is necessary to introduce a functionalised PP, for example PP-g-MAH, in order to enhance the bond strength between the PP matrix and aminosilane treated glass fibre. To achieve a better bonding between the substances, three different systems (1–3) in addition to a reference system (0), have been investigated in this study. The two first are based on PP-g-MAH coupling agents, with different concentrations of acid anhydride groups, and the third is a directly reacting system. In the first system, the silane treated glass fibre is exposed to molten mixture of 95 wt% PP homopolymer and 5 wt% PP-g-MAH. In the second system, the silane treated glass fibre is covered by a thin layer of PP-g-MAH and thereafter exposed to the molten PP. The interfacial shear strength is highest for the systems with the pre-compounded graft-copolymer. The resulting influence of the selected coupling systems on the interfacial bond strength of single fibre composite is studied by fragmentation testing. The intermolecular shear strength between fibre and matrix increases with the intermolecular entanglement length of the PP-g-MAH and not by the degree of functionalisation. The PP-g-MAH mixed into the PP gave better results than the route of first covering the glass fibre with a thin layer of PP-g-MAH. This is explained in terms of the probability of generating entanglements and in terms of a weak boundary layer at the glass surface. This conclusion is also supported by the results from using the third principle, i.e. direct reaction between the PP matrix and azidosilane treated glass fibres.     

Numerical study of the single fibre push-out test: Part III. Singularity of interface stresses

The singular behaviour at the free edges of the fibre-matrix interface is analysed for the fibre push-out test geometry based on the boundary element method. The fibre push-out test has been extensively used to measure the fibre-matrix interfacial properties in polymer, ceramic and metal matrix composites. There are two free edges in the fibre push-out specimen: one is at the loaded fibre end and the other at the supported fibre end. The singular stresses can be expressed as a function of singular exponent and singular stress intensity. It is shown that the singular exponents obtained at both fibre ends are characteristic of composite constituent properties, such as Young's moduli of fibre and matrix, and does not vary with specimen dimensions. The singular exponents are real and identical for the shear and radial stress components at fibre ends where the wedge angles are the same. The singular stress intensities are also implicit in material properties, and vary with specimen dimensions, such as fibre to matrix radius ratio, fibre aspect ratio and support hole size. An interfacial failure criterion is proposed here based on the average stress concept to determine the critical singular stress intensities in mode I and mode II loads.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part II. Crack propagation: Effect of friction on force-displacement curves

In micromechanical tests for estimating fiber-matrix interfacial properties, such as the pull-out and microbond tests, fiber debonding from a matrix is often accompanied by friction in debonded areas. In the present study, force-displacement curves, which are usually recorded in these tests, were modeled with taking interfacial friction into consideration. The friction stress was assumed, as a first approximation, to be constant across the interface. Two different approaches to interfacial failure were used: the shear-lag approach with a stress-based debonding criterion (the ultimate interfacial shear strength) and the linear elastic fracture mechanics approach using the critical energy release rate as a condition for crack propagation. The force-displacement curves derived from both models are in good agreement with each other and with experimental micromechanical data. It was shown that any pull-out and microbond experiment comprises four stages: (1) linear loading up to the point where debonding starts; (2) stable crack propagation with friction-controlled debonding; (3) catastrophic debonding; and (4) post-debonding friction. Stable crack propagation was shown to be controlled by both friction and release of residual thermal stresses. An algorithm for estimating both fiber-matrix adhesion and interfacial friction from the microbond and pull-out tests data has been proposed.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

三层介质超声谐振模式随材料和界面粘接性能变化的演变规律

在用超声波谐振对粘接材料的粘接强度进行无损评估时, 不同模式对粘接强度的敏感程度受到众多因素和参数的影响, 对检测结果的可靠性至关重要. 基于多层介质中声传播和界面弱粘接边界条件的理论模型, 将一个上下非对称的金属-粘接剂-金属三层结构的平面波反射系数函数中的谐振模式看作是上下铝金属层各自的Lamb波频散模式通过夹心粘接剂层相互耦合后叠加组成. 改变影响结构粘接强度的因素, 即粘接剂的性能参数(声阻抗、密度、厚度)和界面切向劲度系数k_t来分析三层结构谐振模式耦合方式的变化,得出结论: 粘接结构粘接性能的变化基本上不改变与被粘铝层相关的固有部分的Lamb波模式, 而它们的耦合模式则在谐振频率上产生平移并会与固有模式进行交换和替代; 不同参数的变化引起的模式演变有各自的规律, 大多可彼此区分.     

Influence of the environment on equilibrium properties of Au-Pd clusters

The question of the influence of the environment on the structure and thermodynamic state of a bimetallic cluster is examined, using Metropolis Monte Carlo methods. An embedded atom model is used to estimate metal energies. The environment is modeled at a generic level as a rigid matrix which atoms interact with the atoms of an embedded Au-Pd cuboctahedral cluster via a Lennard Jones (LJ) potential. The high sensitivity of the cluster properties on its environment is demonstrated by scaling the LJ potential. It is found that the strength of the interfacial interactions completely determines surface segregation. Full segregation with either Au or Pd at the surface favors the occurrence of stable alloy phases in the cluster core while the subsurface layer acts as a buffer accommodating both the induced surface segregation and the inner composition constrained by phase stability. Cluster surface disorder induced by an amorphous matrix limits interface segregation and phase stability in the cluster core, even when the interfacial interaction strength is weak. The contrast between the epitaxial and amorphous matrix cases over a wide range of interface energies suggests the importance in the thermodynamic properties of the cluster core of the interfacial atomic arrangement in the matrix.