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.     

Sound transmission across orthotropic laminates with a 3D model

This investigation examines the propagation of elastic waves in orthotropic materials to explain the sound insulation of FRP (Fiber Reinforced Plastics). The mechanical characteristics of an orthotropic material generally require nine independent parameters: three Young’s moduli, three shear moduli and three Poisson’s ratios. Three-dimensional analysis is performed with the elastic wave equations of an orthotropic material. The transfer matrix method which expresses the relationship between stress and velocity is adopted to calculate the sound transmission loss across an orthotropic material. Further, the transfer matrix method can only be calculated under the continuous boundary condition in the interface of each FRP layer. The boundary conditions which are indicated above are velocity and stress. The numerical results are compared with the experimental results. Additionally, along with varying material properties such as Young’s modulus, the acoustical properties of the orthotropic material are explained and discussed later.     

Interfacial debonding and slipping of carbon fiber-reinforced ceramic-matrix composites under two-stage cyclic loading

In this paper, the interface debonding and frictional slipping of carbon fiber-reinforced ceramic-matrix composites (CMCs) under two-stage cyclic fatigue loading have been investigated using micromechanics approach. Under cyclic fatigue loading, the fiber/matrix interface shear stress degrades with increasing cycle number due to interface wear. The synergistic effect of interface wear and fatigue loading sequence on interface debonding and frictional slipping has been analyzed. Based on the fatigue damage mechanism of fiber slipping relative to matrix, in the interface debonded region, upon unloading and subsequent reloading, the interface debonded length and interface slip lengths, i.e. interface counter-slip length and interface new-slip length, are determined using the fracture mechanics approach. The relationships between interface debonding, interface slipping, interface wear, cycle number, and different loading sequences are determined. There are two types of fatigue loading sequences considered, i.e. (1) cyclic loading under low peak stress for N₁ cycles, and then high peak stress; and (2) cyclic loading under high peak stress for N₁ cycles, and then low peak stress. The effects of peak stress level, interface wear, cycle number, and loading sequence on interface debonding and frictional slipping of fiber-reinforced CMCs have been analyzed. The fatigue hysteresis loops of cross-ply carbon fiber-reinforced silicon carbide composite corresponding to different cycle number under two-stage cyclic fatigue loading have been predicted.     

Effect of interfacial debonding and matrix cracking on mechanical properties of multidirectional composites

In composites, debonding at the fiber–matrix interface and matrix cracking due to loading or residual stresses can effect the mechanical properties. Here three different architectures — 3-directional orthogonal, 3-directional 8-harness satin weave and 4-directional in-plane multidirectional composites — are investigated and their effective properties are determined for different volume fractions using unit cell modeling with appropriate periodic boundary conditions. A cohesive zone model (CZM) has been used to simulate the interfacial debonding, and an octahedral shear stress failure criterion is used for the matrix cracking. The debonding and matrix cracking have significant effect on the mechanical properties of the composite. As strain increases, debonding increases, which produces a significant reduction in all the moduli of the composite. In the presence of residual stresses, debonding and resulting deterioration in properties occurs at much lower strains. Debonding accompanied with matrix cracking leads to further deterioration in the properties. The interfacial strength has a significant effect on debonding initiation and mechanical properties in the absence of residual stresses, whereas, in the presence of residual stresses, there is no effect on mechanical properties. A comparison of predicted results with experimental results shows that, while the tensile moduli E ₁₁, E ₃₃and shear modulus G ₁₂ match well, the predicted shear modulus G ₁₃ is much lower.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

Prestressed FRP and interface slip effect on interfacial stresses analysis: the new FRP sheets rigidity model

This paper presents an improved bi-material beam theory with adhesive interface and the new prestressed-fiber reinforced polymer (FRP) – model, which has been applied to the study the problem of interfacial stresses. This work explicitly considers the interfacial slip effect on the structural performance by including both the effect of adherend shear deformations and the fiber volume fraction of the prestressed laminates. This new method needs only one differential equation to determine both shear and normal interfacial stress, which is one aspect that has not been taken into account by the previous studies in the literature. A parametrical study is carried out to show the effects of some design variables, e.g., stiffness and thickness of adhesive layer and FRP plate.     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

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.     

Influence of heat treatment on microstructure and mechanical properties of the interface in an EN AW-6082/1.4310 composite extrusion

The presented paper deals with a unidirectional steel wire reinforced aluminum matrix composite manufactured by composite extrusion. The main objective of this work was to determine the effect of heat treatment, and the influence of long solution annealing times on the composites interface regarding microstructural changes and the resulting interface strength. For evaluation of the microstructure high resolution transmission electron microscope (TEM) investigations accompanied with electron dispersive X-ray spectroscopy (EDX) were performed. It could be shown that diffusion from the steel wire into the aluminum matrix occurs and that the diffusion paths as well as particle formation is influenced by the preceded heat treatment. Diffusion paths in the range of 40–150 nm could be observed for Al, Fe, Cr and Ni. After annealing times over 5 h an extensive growth of an intermetallic reaction layer was found. The mechanical properties of the interface were determined by push-out-tests and tensile tests radial to the interface, which provided the debonding shear strength σ_deb and for the latter experiment the interfacial radial strength σ_IR. It has become apparent that debonding shear strength is highly influenced by matrix properties. In radial tensile tests the failure is predominantly controlled by the chemical bond of the interface. It was shown that interface strength of specimen with small reaction zones of about 3 μm were beneficial for the mechanical behavior in both loading conditions. Longer annealing times showed a drastic decrease of interface shear strength. It was concluded from EDX measurements and in comparison with literature that the reaction zone is dominated by the growth of Al₅Fe₂ (η-phase).     

双凹盘形解开口膜泡形状的解析法研究

随着开口膜泡在实验上的发现,对开口泡形状的数值及解析研究逐渐成为该领域的一个热点.讨论了如何由欧阳双凹盘形闭合解构造开口泡的解析解的问题.首先将开口泡要满足的三个不独立的边界条件简化为两个独立的边界条件,给出高斯测地曲率kg=-2,边界条件2可满足,然后由边界条件1得到确定膜泡边界的几何方程.进而讨论了由欧阳双凹盘解可构造的开口泡的各种可能形状,得到了三类管型拓扑解,它们是外凸管形解、类环管形解、类悬链面管形解.     

Study of shear transfer in Al/epoxy joint by digital photoelasticity

An improved six-step phase-shifting method is proposed for calculating full-field shear stress based on a four-step color phase-shifting method in digital photoelasticity. The method was verified using a disk under diametral compression and then applied to an aluminum alloy/epoxy joint for studying the shear transfer behavior. Experimental results revealed that the isochromatic fringe order and shear stress at the bonding interface are distributed continuously and increased with compression. In particular, an antisymmetric thermal residual shear stress appears at the bonding interface, because of the difference in the thermal expansion coefficients of Al and the resin. This indicates that the thermal residual shear stress at the bonding interface is self-balanced and reaches a peak at the edges of the bonding interface. The load transfer is realized by the shear band from the bonding interface to the bottom support. Basically, the bonding interfacial shear stress is balanced with the load.     

Effect of Surface Roughness, Type and Size of Model Aggregates on the Bond Strength of Aggregate/Mortar Interface

The paper reports on a two-stage study of the interface between three types of model cylindrical aggregates (sandstone, limestone and granite) and two types of mortar matrix (plain and 20% Silica Fume mortar). In the first stage, the surface roughness (R _a) of the aggregates and the interfacial bond strength using push-out specimens have been experimentally determined. In the second, aggregate push-out geometry has been modelled using two different approaches. In the first approach, the surface roughness is ignored and the cylindrical aggregates are assumed to have an ideally smooth surface with a constant radius, r ₀ over the aggregate length, L. In the second approach, the surface roughness of the aggregates is included so that the radius, r varies along the length of the cored rock aggregate. Hence, the influence of the surface roughness of the aggregates on the interfacial bond strength is obtained. It is found that the surface roughness plays a significant role in determining the interfacial bond strength, in particular of smaller size aggregates. The effect, however, diminishes as the aggregate size increases, regardless of the aggregate and mortar type.     

热应力作用降低LPE层中的位错

提出由温差造成热剪切应力,引起衬底穿线位错滑移,形成<110>界面位错,从而降低LPE层中位错的模型。稳定自然对流下的温度梯度液相外延,存在衬底厚度方向的温差,能在边缘固定的衬底中造成热剪切应力。生长了厚GaAs和Ga_1-xAl_xAs层(x<0.3),估算的热剪切应力大于产生<110>暗线缺陷的临界剪切应力。表面腐蚀坑观察表明,外延层位错密度下降,或无位错。界面蚀槽和阴极荧光观察表明,衬底穿线位错在界面弯曲成<110>界面位错。透射电子显微镜观察表明,界面位错多 关键词：     

Vacuum Boundary Effects

The Casimir effect is highly dependent on the shape and structure of space boundaries. This dependence is encoded in the variation of vacuum energy with the different types of boundary conditions. We analyze from a global perspective the properties of the Casimir energy as a function on the largest space of the consistent boundary conditions M_F\mathcal{M}_{F} for a massless scalar field confined between to homogeneous parallel plates. In particular, we analyze the analytic properties of this function and point out the existence of a third order phase transition at periodic boundary conditions. We also characterize the boundary conditions which give rise to attractive or repulsive Casimir forces. In the interface between both regimes we find a very interesting family of boundary conditions without Casimir effect, and fully characterize the boundary conditions which do not induce any type of Casimir force.     

The surface cracking behavior in air plasma sprayed thermal barrier coating system incorporating interface roughness effect

The objective of this work is to understand the effect of interface roughness on the strain energy release rate and surface cracking behavior in air plasma sprayed thermal barrier coating system. This is achieved by a parameter investigation of the interfacial shapes, in which the extended finite element method (XFEM) and periodic boundary condition are used. Predictions for the stress field and driving force of multiple surface cracks in the film/substrate system are presented. It is seen that the interface roughness has significant effects on the strain energy release rate, the interfacial stress distribution, and the crack propagation patterns. One can see the completely different distributions of stress and strain energy release rate in the regions of convex and concave asperities of the substrate. Variation of the interface asperity is responsible for the oscillatory characteristics of strain energy release rate, which can cause the local arrest of surface cracks. It is concluded that artificially created rough interface can enhance the durability of film/substrate system with multiple cracks.     

Evaluation on the interfacial fracture toughness of fiber-reinforced titanium matrix composites by push out test

The models for single-fiber push out test are developed to evaluate the fracture toughness G_IIc of the fiber/matrix interface in titanium alloys reinforced by SiC monofilaments. The models are based on fracture mechanics, taking into consideration of the free-end surface and Poisson expansion. Theoretical solutions to G_IIc are obtained, and the effects of several key factors such as the initial crack length, crack length, friction coefficient, and interfacial frictional shear stress are discussed. The predictions by the models are compared with the previous finite element analysis results for the interfacial toughness of the composites including Sigma1240/Ti-6-4, SCS/Ti-6-4, SCS/Timetal 834, and SCS/Timetal 21s. The results show that the models can reliably predict the interfacial toughness of the titanium matrix composites, in which interfacial debonding usually occurs at the bottom of the samples.     

Elastic interaction of a dislocation array with a phase boundary

The equilibrium configuration of an array of dislocations in parallel equidistant slip planes under an external shear stress near a welded boundary between two isotropic half-spaces having different elastic constants is computed. For large external stress, the dislocations are arranged into an arc concave when seen from the boundary. It is concluded that such an arc is formed at the tip of a twin or of a martensitic plate near a phase boundary. The tensile stress across the boundary due to an edge dislocation array is discussed in connection with the formation of an interfacial crack.     

An efficient coupled layerwise theory for dynamic analysis of piezoelectric composite beams

An efficient new coupled one-dimensional model is developed for the dynamics of piezoelectric composite beams. The model combines third order zigzag approximation for the displacement with layerwise approximation of the electric field as piecewise linear for sublayers. By enforcing the conditions of zero transverse shear stress at the top and bottom and its continuity at layer interfaces, the displacement field is expressed in terms of three primary displacement variables and potentials. The governing coupled equations of stress and charge equilibrium and boundary conditions are derived from Hamilton's principle. Analytical solutions are obtained, for free vibrations and forced response under harmonic load, for simply supported hybrid beams and the results are compared with the exact three-dimensional solution and uncoupled first order shear deformation theory solution. The present results show significant improvement over the first order solution and agree very well with the exact solution for both thin and thick hybrid beams. The results demonstrate the capability of the developed theory to adequately model open and closed circuit electric boundary conditions to accurately predict their influence on the response.