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.     

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.     

Interfacial Debonding Around Rectangular Features in Multilayer Structures

This article describes a numerical approach for predicting debonding in multi-layers comprised of rectangular features of different sizes. A single global meshing strategy for finite element analysis is described that includes focused radial meshes at every material junction to accurately capture crack tip and material junction singularities. The strategy is designed to allow straightforward yet accurate calculations of energy release rates for steady-state interfacial debonding in complex architectures. Guidelines for meshing parameters (such as element density and distribution) are discussed on the basis of convergence studies of stress distributions along interface junctions, crack opening displacements and crack driving forces along interfaces. The utility of the approach is demonstrated via a study of debonding around rectangular inclusions, which illustrates relationships between energy release rates, inclusion aspect ratio and elastic mismatch. The paper concludes with an illustration of how interfacial debonding along finite-sized features can promote cracking in adjacent layers.     

固体间界面的物理模型和界面对声波的反射

简要描述了模拟两固体间界面特性的弹簧模型，该模型最早是根据静力学方法提出的，后来用固体间界面薄层的声波反射方法加以改进，从界面弹簧模型可以方便地得到界面外近似边界条件，其中包含界面“弹簧”振子的劲度常数和质量，文章还给出了两相间固体中界面声反射系数的表达式，介绍了测量界面劲度常数的超声反射谱方法。最后讨论了仍关声波与界面相互作用研究领域中最近的一些研究进展。     

Determination of interfacial parameters in fiber-polymer systems from pull-out test data using a bilinear bond law

We propose a new model for characterization of strength properties of fiber-polymer interfaces by means of a single fiber pull-out test. Our model is based on shear-lag analysis using a bilinear bond law (stress–slip relationship) which, in turn, is a simplified representation of the true stress behavior as a function of strain for cold-drawing polymers. According to this law, the fiber-polymer interface is subjected to the following successive processes: (1) linear loading within the elastic region; (2) yielding and subsequent bond strengthening with increasing strain; (3) local debonding and interfacial crack propagation along the interface; (4) post-debonding friction. Both crack propagation and extension of the yielded zone can be stable and unstable, depending on the values of interfacial parameters and the load applied to the free fiber end. The procedure of construction of theoretical force–displacement curves for a pull-out test is described in detail. Theoretical curves exhibit such features as multiple kinks and non-linear regions, whose positions and shape are related to interfacial parameters. By fitting experimental curves with theoretical ones, these parameters can be determined for each separate pull-out specimen. Practical examples are provided for basalt fiber–polypropylene and glass fiber–polypropylene specimens.     

Oxide nanoparticles in an Al-alloyed oxide dispersion strengthened steel: crystallographic structure and interface with ferrite matrix

Abstract

Oxide nanoparticles are quintessential for ensuring the extraordinary properties of oxide dispersion strengthened (ODS) steels. In this study, the crystallographic structure of oxide nanoparticles, and their interface with the ferritic steel matrix in an Al-alloyed ODS steel, i.e. PM2000, were systematically investigated by high-resolution transmission electron microscopy. The majority of oxide nanoparticles were identified to be orthorhombic YAlO₃. During hot consolidation and extrusion, they develop a coherent interface and a near cuboid-on-cube orientation relationship with the ferrite matrix in the material. After annealing at 1200 °C for 1 h, however, the orientation relationship between the oxide nanoparticles and the matrix becomes arbitrary, and their interface mostly incoherent. Annealing at 1300 °C leads to considerable coarsening of oxide nanoparticles, and a new orientation relationship of pseudo-cube-on-cube between oxide nanoparticles and ferrite matrix develops. The reason for the developing interfaces and orientation relationships between oxide nanoparticles and ferrite matrix under different conditions is discussed.     

Effect of inclusions on heterogeneous crack nucleation in nanocomposites

A two-dimensional theoretical model is proposed for the heterogeneous nucleation of a grain-boundary nanocrack in a nanocomposite consisting of a nanocrystalline matrix and nanoinclusions whose elastic moduli are identical to those of the matrix. The inclusions have the form of rods with a rectangular cross section and undergo dilatation eigenstrain induced by the differences in the lattice parameters and thermal expansion coefficients of the matrix and inclusions. In terms of the model, a mode-I–II nanocrack nucleates at the negative disclination of a biaxial dipole consisting of wedge grain-boundary (or junction) disclinations; then, the nanocrack opens along a grain boundary and reaches an inclusion boundary. Depending on the relative positions and orientations of the initial segment of the nanocrack and the inclusion, the nanocrack can either penetrate into the inclusion or bypass it along the matrix-inclusion interface. The nanocrack nucleation probability increases near an inclusion with negative (compressive) dilatation eigenstrain. A decrease in the inclusion size decreases (increases) the probability of a crack opening along the interface if the dilatation eigenstrain is negative (positive).     

Atomic-Scale Structure and Chemistry of Segregation at Matrix/Precipitate Heterophase Interfaces

We study experimentally the local chemistry and atomic structure of heterophase interfaces on an atomic scale. In this work, the heterophase precipitate/matrix interfaces of small molybdenum nitride precipitates in an -iron matrix are investigated on a subnanometer scale by 1-dimensional atom-probe field-ion microscopy (1D-APFIM) and 3-dimensional atom-probe microscopy (3DAPM). Molybdenum nitride precipitates are generated by annealing Fe- 2 at.% Mo- X, where X = 0.4 at.% Sb or 0.5 at.% Sn, at 550°C, in an ammonia/hydrogen atmosphere. Internal nitridation at this temperature produces thin, coherent platelet-shaped molybdenum nitride precipitates. 1D-APFIM selected area analyses are efficient in determining the composition of the precipitates and it is found that a possible Sn or Sb segregation at coherent matrix/precipitate interfaces is either nonexistent or below the detection limit of 1D-APFIM. 3DAPM analyses, however, provide significantly better counting statistics and detect a small, but significant segregation of Sb at the matrix/precipitate interface with a Gibbsian interfacial excess of 0.30 ± 0.15 nm^–2. This is in distinct contrast to the segregation behavior of Sn or Sb at the interfaces of semicoherent coarse precipitates produced by internal nitridation at 600°C, for which much larger Gibbsian interfacial excesses of Sn or Sb, up to 7 ± 3 nm^–2, have been measured. In contrast, the thin platelets are either coherent or have significantly fewer misfit dislocations than is geometrically necessary for a full compensation of the lattice parameter misfit between precipitate and matrix. This demonstrates that Sn or Sb segregation with an appreciable Gibbsian interfacial excess is related to the presence of misfit dislocations at the interfaces of the coarse precipitates.     

Relationship between fibre-matrix adhesion and the interfacial shear strength in polymer-based composites

A model is proposed to correlate the interfacial shear strength at the fibre-matrix interface, measured by means of a fragmentation test on single fibre composites, to the reversible work of adhesion between both solids, this quantity being defined as the sum of the dispersive and the acid-base interactions (physical interactions) between the fibre and the matrix. Whatever the nature of the fibres and the matrices, a linear relationship, passing through the origin, is established between the interfacial shear strength and the reversible work of adhesion. However, the slope of this straight line depends on the elastic properties and, more precisely, on the elastic moduli of both the fibre and the matrix. This leads us to express the reversible work of adhesion as the product of a mean intermolecular distance at the interface and an adhesive pressure related to the interfacial shear strength. The limits of the theoretical and experimental approaches leading to the establishment of such a model, as well as its domain of validity, are discussed.     

Stress analysis of multiple anisotropic elliptical inclusions in composites

A volume integral equation method is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple anisotropic elliptical inclusions subject to uniform remote tension or remote in-plane shear. This method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central elliptical inclusion is carried out for square and hexagonal packing of anisotropic inclusions. The effects of the number of anisotropic inclusions and various inclusion volume fractions on the stress field at the interface between the isotropic matrix and the central elliptical cylindrical inclusion are investigated in detail. The stress field at the interface between the isotropic matrix and the central elliptical inclusion is also compared with that between the isotropic matrix and the central circular inclusion.     

Analysis of stress field in a single anisotropic diamond/square shaped inclusion using the volume integral equation method and the numerical equivalent inclusion method

A volume integral equation method (VIEM) is used to study elastostatic problems in an unbounded elastic solid containing a single diamond/square shaped inclusion subject to uniform tensile stress at infinity. The inclusion is assumed to be a long parallel diamond/square cylinder composed of isotropic or anisotropic elastic materials and perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinder. A detailed analysis of the stress field at the interface between the isotropic matrix and the single isotropic/orthotropic diamond/square shaped inclusion is carried out. The effects of a single isotropic/orthotropic diamond/square shaped inclusion on the stress field at the interface between the matrix and the inclusion are investigated in detail. The accuracy of the volume integral equation method for the interfacial stress field is validated and compared by the numerical equivalent inclusion method (NEIM) and the finite element method (FEM) using ADINA. Through detailed analysis of plane elastostatic problems using the parallel volume integral equation method (PVIEM) in an unbounded isotropic matrix with multiple isotropic diamond shaped inclusions under uniform remote tensile loading, it is demonstrated that the volume integral equation method can also be applied to solve general two- and three-dimensional elastostatic problems involving multiple isotropic/anisotropic inclusions whose shape and number are arbitrary.     

Effect of matrix yield properties on fragmentation behavior of single fiber composites

Experimental and theoretical investigations have been conducted to study the dependence of fiber fragmentation behavior on matrix yielding properties. The cured Epikote 828 resins with two types of curing agents have almost similar elastic moduli, but different tensile yield strengths. The interfacial chemistry between fiber and epoxy resin is unchanged due to the same constituent of the epoxy resin. The experimental results indicate that the fragmentation behavior of the fibers embedded in the matrix is significantly different for the tested glass fiber treated by γ-glycidoxypropyltrimethoxysilane. The average fragment length decreased with increasing tensile yield strength of resin, which suggests that the interfacial shear strength determined in the fragmentation test should be different depending on the tensile yield strength of resin used. The important phenomenon observed is the transition of the micro-damage mode from matrix crack to interfacial debonding. An elastoplastic shear-lag model was used to calculate the shear stress and fiber tensile stress distributions considering different plastic behaviors of the matrices. The theoretical results indicate that the plastic behavior of the matrix has a large influence on stress transfer. Based on elastic and plastic properties of the matrix, the fiber fragmentation behavior in the matrix is predicted. Experimental and theoretical results are favorably compared.     

Mechanical characteristics approach on W/Cr nano-interface structure

The objective of this article is to provide an experimental test and evaluation on mechanical characteristics of the W/Cr interface. The elastic modulus and hardness of the sample are measured by a nanoindentation tester. The test results show that the elastic modulus and hardness of the sample are nonlinear with respect to the depth h of the interface structure, unlike the usual approximate horizontal linear relationship as expected. To understand the bonding characteristics between W and Cr in nanoscale, the nano-scratch test is conducted considering the influence of thermal cycling load on the sample. The test results show that interfacial bonding strengths are different between samples under different thermal cycling loading conditions. It implies that the thermal loading has the potential probability to reduce the bonding reliability of the W/Cr interface. It builds a basis for future work of further investigations on mechanical properties of W/Cr interface structure.     

Singular invariant integrals for elastic bodies with thin elastic inclusions and cracks

Equilibrium problems for an elastic body with partially delaminated thin elastic inclusions are considered. The inclusions are modeled within the framework of the Euler–Bernoulli and Timoshenko models of elastic beams. The presence of delamination means the existence of a crack between the inclusion and the elastic matrix. Displacements of the opposite crack faces are constrained with nonpenetration conditions. Formulas of the Griffith type giving the first derivatives of energy functionals with respect to the crack length are established. It is shown that the formulas for the derivatives admit representation in the form of invariant integrals independent of the smooth closed curve surrounding the crack tip. The obtained invariant integrals consist of the sum of regular and singular parts and are analogues of the classical Eshelby–Cherepanov–Rice J-integral.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

Assessment of interface deformation and fracture in metal matrix composites under transverse loading conditions

The transverse properties of unidirectional metal matrix composites (MMCs) are dominated by the fiber/matrix interfacial properties, residual stresses and matrix mechanical response. In order to monitor and study, in situ, the failure of interfaces in titanium-based composites subjected to transverse loading conditions, an ultrasonic imaging technique has been developed. The interface was imaged ultrasonically and the change in ultrasonic amplitude with the transverse loading was monitored, indicating the sensitivity of the technique to fracture and deformation of interfaces. This change in amplitude has been explained in terms of the multiple reflection theory of ultrasonic waves. The multiple reflection theory enabled estimation of the interfacial deformation and debonding as a function of loading. The ultrasonic technique was also used in conjunction with finite element modeling in order to quantify the fiber/matrix interfacial transverse strength in situ in MMCs.     

Limitations of interface sharpness in a-Si:H/a-SiC:H multilayers

The goal of this work is to study the sharpness of interfaces in amorphous silicon based compositional multilayers (superlattices) by a number of different techniques and to discuss their limitations. From monitoring plasma transients during glow discharge deposition of a-Si:H/a-SiC:H multilayers, a lower limit of 3 Å for interface sharpness is estimated. Transmission electron microscopy (TEM) images yield an upper limit of 5–10 Å. These images directly show the increase in undulation from the substrate towards the film surface. From the comparison of simulated X-ray diffraction (XRD) spectra with measurements the interface sharpness is found to be between 5 and 8 Å. Using a series of multilayers with increasing number of interfaces, structural characteristics of the interfacial region can be extracted. For example, infrared absorption spectroscopy (FTIR) and elastic recoil detection (ERD) lead to an estimate of 1.1 × 10¹⁴ cm^-2 additional hydrogen atoms per single interface.     

金属-砷化镓界面的电调制反射光谱与Franz-Keldysh效应研究

通过调制光谱这种基础的光学方法来研究Au-GaAs,Al-GaAs,Ni-GaAs的金属半导体界面的一些电学性质,并且加以比较,其中包括电场、费米能级扎钉和界面态密度等情况。这些界面是通过在SIN+ GaAs样品上沉积金属(Au,Al,Ni)生长成的。通过观察电反射谱来研究金属GaAs的界面电场和费米能级扎钉的情况,然后通过傅里叶变换这些所取得的电反射谱来分析这些材料的界面性质。通过测量氦氖激光器诱导产生的光电压和激光器光强之间的关系来得到这些材料的界面态密度情况,从而进行进一步的研究。