Elastic interaction of partially debonded circular inclusions. II. Application to fibrous composite

A complete analytical solution has been obtained of the elasticity problem for a plane containing periodically distributed, partially debonded circular inclusions, regarded as the representative unit cell model of fibrous composite with interface damage. The displacement solution is written in terms of periodic complex potentials and extends the approach recently developed by Kushch et al. (2010) to the cell type models. By analytical averaging the local strain and stress fields, the exact formulas for the effective transverse elastic moduli have been derived. A series of the test problems have been solved to check an accuracy and numerical efficiency of the method. An effect of interface crack density on the effective elastic moduli of periodic and random structure FRC with interface damage has been evaluated. The developed approach provides a detailed analysis of the progressive debonding phenomenon including the interface cracks cluster formation, overall stiffness reduction and damage-induced anisotropy of the effective elastic moduli of composite.     

An elastoplastic multi-level damage model for ductile matrix composites considering evolutionary weakened interface

An elastoplastic multi-level damage model considering evolutionary weakened interface is developed in this work to predict the effective elastoplastic behavior and multi-level damage evolution in particle reinforced ductile matrix composites (PRDMCs). The elastoplastic multi-level damage model is micromechanically derived on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. The Eshelby’s tensor for an ellipsoidal inclusion with slightly weakened interface [Qu, J., 1993a. Eshelby tensor for an elastic inclusion with slightly weakened interfaces. Journal of Applied Mechanics 60 (4), 1048–1050; Qu, J., 1993b. The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mechanics of Materials, 14, 269–281] is adopted to model particles having mildly or severely weakened interface, and a multi-level damage model [Lee, H.K., Pyo, S.H., in press. Multi-level modeling of effective elastic behavior and progressive weakened interface in particulate composites. Composites Science and Technology] in accordance with the Weibull’s probabilistic function is employed to describe the sequential, progressive weakened interface in the composites. Numerical examples corresponding to uniaxial, biaxial and triaxial tension loadings are solved to illustrate the potential of the proposed micromechanical framework. A series of parametric analysis are carried out to investigate the influence of model parameters on the progression of weakened interface in the composites. Furthermore, the present prediction is compared with available experimental data in the literature to verify the proposed elastoplastic multi-level damage model.     

Plasticity of isotropic composites with randomly oriented and packeted inclusions

Based on an energy approach, the nonlinear elastoplastic behavior of a two-phase, isotropic composite with two kinds of inclusion morphologies are determined as a function of inclusion shape at the low concentration range. Both types of morphology involve the three-dimensional randomly oriented spheroidal inclusions, but one is homogeneously dispersed, resulting in an ordinary two-phase composite, and the other possesses a packeted structure in a form similar to a polycrystalline arrangement. The overall elastoplastic response of these two kinds of composite is found to be strongly dependent upon the inclusion shape and their morphological arrangement. Disc-shaped inclusions generally give a superior reinforcing effect, but when the inclusions become very stiff or totally rigid, needle-shaped inclusions tend to be more effective. In line with the known elastic behavior, the overall elastoplastic response of an ordinary two-phase composite is markedly stiffer than that of the packeted composite at a given inclusion shape and concentration. The theory is finally compared with the finite-element calculations of a particle-reinforced composite and of a packeted one with oblate and prolate inclusions, and also with some experimental data for a silicon-carbide/aluminium system. In both cases, reasonable agreement is found in the comparison.     

Interfacial debonding of two-phase composite with periodic structure

A mixed analytical-numerical (boundary element method) procedure is presented for estimating the effective elastic moduli of a two-phase periodic composite by application of a unit cell. The two-phase composite consists of a metal/polymer matrix and one/three circular ceramic inclusions with adhesive and partial debonding of the interface. The results are displayed numerically with special attention given to development of plastic zones as debonding occurs. Dependence of load-time history is exhibited.     

Influence of skin/core debonding on free vibration behavior of foam and honeycomb cored sandwich plates

The dynamic behavior of partially delaminated at the skin/core interface sandwich plates with flexible cores is studied. The commercial finite element code ABAQUS is used to calculate natural frequencies and mode shapes of the sandwich plates containing a debonding zone. The influence of the debonding size, debonding location and types of debonding on the modal parameters of damaged sandwich plates with various boundary conditions is investigated. The results of dynamic analysis illustrated that they can be useful for analyzing practical problems related to the non-destructive damage detection of partially debonded sandwich plates.     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

Constitutive equations for elastoplastic composites with imperfect bonding

Closed-form constitutive relations are given for the prediction of the overall response of unidirectional fiber-reinforced composites having constituents that are elastoplastic materials. In these equations the damage mode of imperfect bonding between the fiber and matrix phases is incorporated. The interface decohesion is represented by two parameters that completely determine the degree of adhession at the interfaces in thenormal and tangential directions. Perfect contact, perfectly lubricated contact, and complete debonding are obtained as special cases. In the elastic region, the average stress-strain relations are given in terms of the effective elastic moduli of the damaged composite, all of which are given by closed-form expressions. The derived constitutive equations can be readily implemented for the analysis of metal matrix composites.     

Influences of reinforcing particle and interface bonding strength on material properties of Mg/nano-particle composites

In the present study, an effective model is proposed to predict the effective elastic behavior of the three-phase composite containing spherical inclusions, each of which is surrounded by an interphase layer. The constitutive equations are derived for the stress and strain of each phase of the composite subjected to a far-field tension. Based on these constitutive laws, the effective bulk, shear and Young’s modulus are obtained. A statistical debonding criterion is adopted to characterize the varying probability of the evolution of interphase debonding. Influences of debonding damage, particle volume fraction, interphase properties and bonding strength on overall mechanical behavior of composites are also discussed. Numerical analyses are carried out on particle-reinforced composites and the predictions have a good agreement with the experimental results.     

Effective thermoelastic properties of discrete-fiber reinforced materials with transversally-isotropic components

In the present paper, we will illustrate the application of the method of conditional moments by constructing the algorithm for determination of the effective elastic properties of composites from the given elastic constants of the components and geometrical parameters of inclusions. A special case of two-component matrix composite with randomly distributed unidirectional spheroidal inclusions is considered. To this end it is assumed that the components of the composite show transversally isotropic symmetry of thermoelastic properties and that the axes of symmetry of the thermoelastic properties of the matrix and inclusions coincide with the coordinate axis x ₃. As a numerical example a composite based on carbon inclusions and epoxide matrix is investigated. The dependencies of Young’s moduli, Poisson’s ratios and shear modulus from the concentration of inclusions and for certain values which characterize the shape of inclusions are analyzed. The results are compared and discussed in context with other theoretical predictions and experimental data.      

Elastic interaction of partially debonded circular inclusions. I. Theoretical solution

A complete solution has been obtained of the elasticity problem for a plane containing a finite array of partially debonded circular inclusions, regarded as the open-crack model of fibrous composite with interface damage. A general displacement solution of the single-inclusion problem has been derived by combining the complex potentials technique with the newly derived series expansions. This solution is valid for any non-uniform far load and is finite and exact in the case of polynomial far field. Applying the superposition principle expands this theory to the multiple inclusion problem and provides a simple and rapidly convergent iterative algorithm. The presented numerical data show an accuracy and numerical efficiency of the proposed method and discover the way and extent to which the elastic interaction between the partially debonded inclusions affects the local fields, stress intensity factors and the energy release rate at the interface crack tips.     

Analysis of a partially debonded elliptic inhomogeneity in piezoelectric materials

A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method. It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface. The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems. This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions. The resulting solution was then used to obtain the electroeiastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface. The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity , totally debonded elliptic inhomogeneity, partially debonded rigid and conducting elliptic inhomogeneity, and partially debonded circular inhomogeneity.     

Plastic deformation anisotropy and work-hardening of composite materials

An energy-balance method is applied to discuss plastic anisotropy and work-hardening rate of a composite material. It is found that aligned fibers introduce a strongly anisotropic mode of plastic deformation while randomly-oriented inclusions produce isotropic plastic deformation. The hardening rate due to randomly-oriented inclusions is shown to be independent of the inclusion shape, and to be equal to that due to spherical inclusions when the elastic constants of the inclusions are the same as those of the matrix.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

Analysis of hollow inclusion–matrix debonding in particulate composites

This work aims at understanding the effect of particle–matrix interfacial debonding on the tensile response of syntactic foams. The problem of a single hollow inclusion with spherical-cap cracks embedded in a dissimilar matrix material is studied. Degradation of elastic modulus, cavity formation in the proximity of debonded regions, stress localization phenomena in the inclusion, debonding energetics, and crack kinking are studied for a broad range of inclusion wall thickness and debonding extent. A series solution based on the Galerkin method is proposed and validated through comparison with findings from boundary element and finite element methods. Results are specialized to glass particle-vinyl ester matrix systems widely used in marine structural applications. The insight gained into the role of particle–matrix debonding extent and inclusion wall thickness is useful in understanding the possible failure mechanisms of syntactic foams under tensile and flexural loading conditions and in tailoring their parameters for specific applications.     

Étude de la décohésion fibre-matrice dans les arcs composites circulairesA study of fiber debonding in circular composite arches

In the framework of linear elasticity, we consider a composite arch constituted by a matrix and a fiber reinforcing the structure. This arch is clamped at one extremity, while at the other the fibre is subject to either prescribed displacements or forces. By making an asymptotic analysis based on the slenderness and loading parameters, we study by means of an energy criterion the fiber-matrix debonding, resulting from the inextensional displacements of the medium line. We show in particular that for these specific loading types, the debonding occurs brutally and the critical length of initiation is of order 1. To cite this article: K. Madani, C. R. Mecanique 330 (2002) 535–541.     

内聚力模型的形状对胶接结构断裂过程的影响

内聚力模型被广泛应用于粘接结构的断裂数值模拟过程中,为深入分析不同形状内聚力模型与胶黏剂性质和粘接结构断裂之间的关系,本文分别采用脆性和延展性两种类型胶黏剂,对其粘接的对接试件进行了单轴拉伸、剪切实验,以及其粘接的双臂梁试件进行了断裂实验.3种类型的内聚力模型(抛物线型、双线型和三线型)分别模拟了以上粘接结构的断裂过程,并与实验结果进行对比.结果发现:双线型的内聚力模型适用计算脆性胶黏剂的拉伸与剪切的断裂过程;指数型内聚力模型较适合计算延展性胶黏剂的拉伸和剪切的断裂过程,临界应力、断裂能和模型的形状参数是分析拉伸和剪切的重要参数;双臂梁试件的断裂过程模拟结果发现,断裂曲线与胶黏剂性质有关,内聚力模型形状参数也有影响.通过实验与计算结果分析,双线型内聚力模型更适合脆性胶黏剂粘接的双臂梁断裂计算,而三线型更适合计算延展性胶黏剂粘接的双臂梁断裂过程,此研究结果对胶黏剂的使用和粘接结构的断裂分析有很重要意义.     

Effect of debonding in active constrained layer damping patches on hybrid control of smart beams

A new model for a smart beam with a partially debonded active constrained layer damping (ACLD) patch is presented, and the effects of the debonding of the ACLD patch on both passive and hybrid control are investigated. In this model, both shear and compressional vibrations of the viscoelastic material (VEM) layer are considered. The moment inertia and the transverse shear effect are also taken into account based on the Timoshenko’s beam theory. The adhesive layer between the host beam and the piezoelectric sensor patch is modeled as an elastic load transferring media. The debonding of the ACLD patch is approximated by removing the VEM between the constraining layer and the host beam in the debonding region, and the continuity conditions are imposed based on displacement continuity and force balance. A modal velocity observer-based modal control scheme is also given to perform the active modal control of the beam. In order to examine the effects of part debonding of the ACLD patch, the characteristic equation of the beam treated with an ACLD patch is derived. The simulation example results show that an edge debonding of the ACLD patch can significantly affect both passive and hybrid control. It is also found that the additional mode induced by the debonding has unique effects on the modal damping ratios and frequencies of both open-loop and closed-loop system.     

Effective pressure-sensitive elastoplastic behavior of particle-reinforced composites and porous media under isotropic loading

The composite under investigation consists of an elastoplastic matrix reinforced by elastic particles or weakened by pores. The material forming the matrix is pressure-sensitive. The Drucker–Prager yield criterion and a one-parameter non-associated flow rule are employed to formulate the yield behavior of the matrix. The objective of this work is to estimate the effective elastoplastic behavior of the composite under isotropic tensile and compressive loadings. To achieve this objective, the composite sphere assemblage model of Hashin [Z. Hashin, The elastic moduli of heterogeneous materials, ASME J. Appl. Mech. 29 (1962) 143–150] is used. Exact solutions are thus derived as estimations for the effective secant and tangent bulk moduli of the composite. The effects of the loading modes and phase properties on the effective elastoplastic behavior of the composite are analytically and numerically evaluated.     

A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial

The present study is devoted to the development and validation of a nonlinear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modeled as an heterogeneous composite composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill [Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101]. The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase. Due to the matrix/inclusion morphology of the microstructure of the argillite, a Mori–Tanaka scheme is considered for the localization step. The developed model is first compared to Finite Element calculations and then validated and applied for the prediction of the macroscopic stress–strain responses of argillites.