Numerical analysis of dynamic debonding under anti-plane shear loading

We present an efficient numerical scheme specially developed to simulate a wide variety of dynamic debonding problems under anti-plane shear loading conditions. The algorithm is based on an exact spectral representation of the elastodynamic relations between the interface stresses and displacements. It involves an explicit time stepping scheme with, for each time step, the use of FFT to link the spatial and spectral domains, and the computation of a convolution over the past displacement or velocity history. Two versions of the spectral algorithm are presented: in the first one, the elastodynamic response of each half space is investigated separately before the two solutions are linked with the aid of the interface continuity conditions. In the second approach, the interface conditions and the modulus mismatch are combined in a single bimaterial elastodynamic relation. Various problems involving stationary or rapidly moving interfacial cracks are investigated and contrasted with existing analytical results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Real-time ultrasonic monitoring of fiber-matrix debonding in ceramic-matrix composite

Real-time ultrasonic techniques were developed for monitoring damage in a unidirectional ceramic-matrix composite under longitudinal tensile loading. Specifically, shear-wave transducers producing waves polarized in the transverse to the fiber direction were used in contact with the specimen to detect the initiation and propagation of fiber—matrix debonding, and to determine the transverse shear modulus and its degradation. The ultrasonically measured transverse shear modulus and its degradation was in reasonably good agreement with a prediction based on a modified shear lag model and interpolation between available solutions for fully bonded and fully unbonded fibers.     

Delamination in composite plates: influence of shear deformability on interfacial debonding

An elastic interface model is introduced to investigate the effects of in-plane and out-plane shear stresses on interfacial debonding in laminated composite plates by means of the energy release rate concept. This is done by utilising an improved laminated plate model in which the Reissner–Mindlin kinematics type for each layers is coupled with an adhesion mechanism modelled by means of a linear interface model, acting in the opening and sliding failure mode directions. The problem is faced through an analytical solution procedure. Increasing the stiffnesses of the interface leads to restoring displacement continuity at the interface between layers and to recovering energy release rate components through the work performed by the singular stress field at the crack tip. In view of the great importance of shear deformation in laminated composite plates the effect of shear stresses on the mechanism of delamination are investigated pointing out new features which emerge from the interaction of normal and shear stresses acting on the transverse section near the crack tip. Several examples of mixed mode delamination schemes used in experimental applications are examined, showing the influence of transverse shear stresses in coupling with normal stresses on energy release rates determination.     

Toughness of interfaces from initial fiber-matrix debonding in a single fiber composite fragmentation test

We present new theoretical and experimental results which demonstrate that the degree of fiber-matrix bonding can be quantified by means of the interface energy for the initiation of debonding, rather than by using a stress-based interfacial parameter. A one-dimensional model for the energy necessary to initiate/nucleate an interfacial crack from its associated transverse fiber break during a single fiber fragmentation test is proposed. The interface energy for the initiation of debonding is shown to be a function of the fiber and matrix geometrical and material characteristics, and of the initial debonding length. The validity of the approach is demonstrated in the case of fragmentation of sized and unsized E-glass fibers embedded in an UV-cured polymeric matrix.     

Analytical solution for an interfacial crack subjected to dynamic anti-plane shear loading

Summary A closed form solution for an interfacial crack problem is obtained. The crack lies on the interface of two bonded dissimilar orthotropic strips. Its surfaces are subjected to a dynamic anti-plane shear traction. Separation of variables technique is employed, to reduce the problem to a singular system of triple series equations, then to a singular integral equation. That is solved exactly, such that the asymptotic stress field distribution and the stress intensity factor are obtained in closed form expressions. The validity of the solution is proved. Further, a parametric study is introduced to investigate the effects of elastic and geometric characteristics of the composition on the values of the dynamic stress intensity factor (DSIF).     

Elastoplastic modeling of progressive interfacial debonding for particle-reinforced metal-matrix composites

Summary The purpose of this study is to model the elastoplastic behavior of particle-reinforced metal-matrix composites with particle-matrix interfacial debonding. The partially debonding process at the interface is represented by the debonding angles. The equivalent orthotropic elastic moduli are constructed for the debonded yet isotropic particles to characterize the reduction of the load-transfer ability in the debonded directions. To simulate the debonding evolution and the transition between various debonding modes, the volume fractions of various particles are expressed in terms of the Weibull's statistical functions. Micromechanical homogenization procedures are utilized to estimate the effective moduli and the overall yield function of the resultant multi-phase composites. The associative plastic flow rule and isotropic hardening law are postulated based on the continuum plasticity theory. The effects of partially interfacial debonding on the overall yield surfaces and stress-strain relations of the composites are investigated and illustrated via numerical examples as well.     

含面芯界面缺陷的蜂窝夹芯板侧向压缩破坏模式

为了对含面芯层间脱胶缺陷的蜂窝夹芯板在侧向压缩载荷作用下的典型破坏模式进行数值预报, 建立了基于蔡-希尔破坏准则和粘结模型的计算模型。该计算模型是建立在对蜂窝夹芯板的双悬臂梁(DCB)和单臂梁(SLB) 试验中所发现的一种新的破坏模式的分析基础之上的。对蜂窝夹芯板的侧向压缩破坏行为的数值预报中, 发现一种新的破坏模式: 位于脱胶区域的面板首先发生局部屈曲失稳, 随后面板内部靠近芯子的45°/0°层间出现分层, 与此同时最靠近芯子的45°铺层发生断裂, 伴随着45°/0°层间分层的扩展, 面板发展成为对称性整体屈曲失稳。与侧向压缩试验测试结果对比发现, 计算模型模拟中所预报的破坏模式在实验测试中也得到了很好的验证。      

Effects of interfacial debonding on fatigue damage of cemented hip prostheses

Abstract

Clinical studies on retrieved cement mantles have pointed out that the cemented hip prostheses failed after long‐term use due to debonding at the cement‐stem interface and local fractures in the cement mantles. These were linked to fatigue damages of cement mantles proved by fatigue experiments. In this paper, a numerical approach based on finite element analysis and continuum damage mechanics is proposed to investigate the fatigue behavior of cement mantles during gait cycles. Results reveal that the major sites for failure initiation are at the proximal medial regions and at the distal prostheses tip. Such fatigue failures not only result in the corruption of cementstem interfaces, but also greatly affect the stress distribution and damage rate of the proximal cement mantles in subsequent loading cycles. The interfacial debonding rate increases from 2.5% to 15% with gait loadings from five to twenty million cycles. Meanwhile, owing to the partial debonding of interface, the cement stresses on the remaining regions increase by 91% to 871% when compared with those generated with a fully bonded interface, which in turn accelerates the fatigue damage accumulation rate of the cement mantle from 5.99 % to 21.5%.     

Estimation of the effects of initially closed interfacial cracks on fiber-matrix stability in compression

Effects of initially closed cracks at fiber-matrix interface on fiber-matrix stability are estimated. A linearized problem formulation, based on a theory of finite subcritical strains, is used. The formulation allows studying problems with transversely isotropic incompressible fibers. Calculations for a simple particular 3D case are carried out to illustrate the application of the theory.     

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.     

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。     

Some further considerations of the theory of fibre debonding and pull-out from an elastic matrix. Part 2: Non-constant interfacial frictional shear stress

Solutions for fibre debonding and pull-out from an elastic matrix have previously been obtained under the condition that the interfacial frictional shear stress is independent of the bond length. However, this condition is not strictly valid. In this paper, an analysis of fibre debonding and pull-out is carried out by considering the dependence of the interfacial frictional shear stress on bond length. The maximum fibre pull-out stress necessary to cause complete debonding and eventual pull-out is determined to be dependent on the fibre-to-matrix elastic modulus ratio, the interfacial shear strength, the interfacial frictional coefficient, the fibre volume fraction and the embedded fibre length. Excellent agreement between the present theoretical analyses and existing experimental results is obtained.     

On the debonding of an elastic elliptical inhomogeneity under antiplane shear

This paper presents an explicit solution to the antiplane problem of a partially debonded elliptical inhomogeneity embedded in an isotropic elastic medium. The boundary value problem is formulated through the complex variable method and is reduced to the solution of a Riemann-Hilbert problem with the aid of the conformal mapping technique and the analytical continuation principle. The complex potentials governing the problem are derived explicitly in both the elliptical inhomogeneity and the surrounding matrix and the corresponding formulae for the stress intensity factors of the interface crack are provided. Several particular solutions, resulting from the current general formulation, are considered in detail and verified by comparison with those existing in the literature. In addition, the effects of material and geometrical parameters upon the change in the stress intensity factors are discussed.     

Transverse elastic moduli of unidirectional fiber composites with fiber/matrix interfacial debonding

An elastic contact model is developed to predict the transverse Young's modulus, Poisson's ratio and shear modulus of unidirectional fiber composites with interfacial debonding. The elastic deformation formulae of the fiber under contact pressure are derived by the use of elasticity theory. These results are then used in the formulation of an analytic boundaryelement method for solving the interfacial debonding problem. The two extreme cases of perfect bonding and the fiber-like void are also studied. On the basis of this theory, the upper and lower bounds of the transverse moduli for unidirectional fiber composites with imperfect fiber/matrix interfaces are provided. Numerical calculations of parametric studies are conducted for four composites, and some basic characteristics of the transverse elastic moduli of unidirectional fiber composites with interfacial debonding are presented.     

Visualization of debonding of fully and partially embedded glass fibres in epoxy resins

Very short glass fibres have been embedded in bars of epoxy resin and the debonding process was observed under the microscope as the polymer was stressed. In addition, fibre pull-out specimens have been similarly watched while the fibre was pulled. The interfaces of the fully embedded fibres failed across the fibre ends at strains of 0·2–0·3%, and circumferential failure started at about 0·6% strain. The low values for the end failures are compatible with models involving stress concentrations at the fibre ends. The circumferential failure value is in agreement with the results of earlier pull-out studies. In the case of the pull-out specimen, the behaviour was complex. Fibres with short embedded lengths debonded first across the embedded end. Failure of the cylindrical surface was too fast for the direction of crack propagation to be determined. Longer fibres first debonded at the fibre entry point and then arrested while debonding occurred across the embedded end. Final failure was again very fast. Long fibres debonded continuously, starting at the entry point. A slow fracture process appeared to be involved at least initially, so that the average shear stress on the region still bonded increased continuously throughout the process. Fast fracture occurred only in the very last stages of the process. These observations are compatible with the traditional theory, but reverse bonding is not ruled out for the shortest embedded lengths.     

Formulation of off-axial interfacial debonding and sliding problem by constrained conditional finite element method

In ceramics matrix composites (CMCs), fiber-matrix interfacial debonding and sliding are the main toughening mechanisms. An interfacial debonding and sliding problem was formulated in this study, using the constrained conditional finite-element method (CC-FEM). In this formulation, the equivalence of nodal displacements at the interface and the equilibrium of contact forces are assumed as constrained conditions in which Coulomb’s law of friction is taken into account. As a distinguished advantage, numerical solutions are obtainable by a single calculation without an iterative algorism. We earlier treated a case in which fibers were oriented along the loading direction. In actual CMCs, however, fibers are not necessarily oriented along the loading direction. The fiber diameter also fluctuates along the axis. In this study, therefore, the off-axial interfacial debonding and sliding problem based on CC-FEM was formulated. Its validity was discussed by comparison with ANSYS. In both cases of on-axis and off-axis, the resultant fiber and matrix stress distributions agreed well with those of ANSYS. Comparison between on-axis and off-axis cases showed that the matrix stress in the latter recovered more steeply because of the higher equivalent friction coefficient.     

3D-analysis of the effect of interfacial debonding on the plastic behaviour of two-phase composites

The present paper deals with the interfacial debonding processes in Al/SiC metal matrix composites, by using 3D finite element calculations on representative cells. The reinforcements are considered as elastic, while the behaviour of the matrix is described by an elastoviscoplastic law. The debonding of the reinforcement is allowed for by using a non-linear elastic dependence between the stress vector and the separation vector at the interface. The results obtained show that the macroscopic behaviour of the composite depends to a large extent on the ratio between the the normal and tangential strength of the interface and the characteristic lengths defining the geometry of the reinforcements.     

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.