Analytical and numerical modeling of composite-to-brick bond

In masonry components strengthened with externally bonded composites, good bonding is one of the most important aspects governing structural behavior, since failure usually takes place with detachment between reinforcement and substrate. This type of event is a brittle, sudden and therefore undesirable failure mechanism; nor does it allow the full strength of the reinforcement to be exploited. Many experimental data on bonding have recently become available from a Round Robin Test carried out within the framework of RILEM TC-223. In the present paper, experimental tests were simulated at increasing levels of complexity; bond behavior was first studied with an analytical model based on bi-linear representation of bond law. Two-dimensional and three-dimensional finite element analyses were then performed, according to various bond-slip laws. In particular, a number of bi-linear and non-linear interface laws were used, calibrated according to several strategies but with the same experimental population. Lastly, several commercial codes and types of finite elements were examined. This work may be said to represent a numerical Round Robin Test, with various simulations and modeling approaches. Analytical and numerical results are compared with experimental ones, in terms of both overall behavior (load to displacement curve) and local behavior (strain profiles on reinforcements at increasing load values), showing the importance of both types of information in order to obtain reliable predictions of experimental results.     

碳-高硅氧纤维增强C-SiC防热隔热一体化材料

制备了一种新型的防热隔热一体化材料碳高硅氧纤维增强C-SiC复合材料，沿厚度方向从抗烧蚀层渐次过渡到隔热层，其组成依次是致密C／C—SiC，致密C／C，多孔C／C，通过界面处过渡到变密度多孔HSF／C．这种材料既具有抗烧蚀性能又具有隔热性能．C／CSiC复合材料的烧蚀表面平滑，线烧蚀率只有0．028mm／s．烧蚀性能的提高得益于SiC颗粒原位氧化生成SiO2黏附在碳材料表面，对氧气有一定的阻挡遮蔽作用。密度为0．80g／cm^3的HSF／C材料，热导率为0．59W／mK．在碳纤维与高硅氧织物的界面处，针刺纤维与热解碳的结合良好，密度为1．69g／cm^3的C—HSF／C复合材料界面处的剪切强度达到16．7MPa．     

Determination of adhesion strength between a coated particle and polymer matrix

The aim of the paper is to provide the theoretical basis for a test to determine the interfacial adhesion strength between a coated particle and a polymer matrix material. The specimen has a notched (neck-like) geometry and contains a single coated particle in the centre. A non-linear relation between the true stress and logarithmic strain is considered for the interphase. Tensile axial loading of such a necked sample concentrates stresses in the smallest cross-section and causes a multiaxial loading situation in the centre of the specimen, i.e., in the vicinity of the enclosed particle. By variation of sample curvature the distribution of normal tensile stresses at the interface between particle and coating can be changed. This enables the variation of the interface area which is under tensile stress. A finite-element analysis provides the stress field within the whole specimen and especially in the vicinity of the coated particle. The motivation for the calculations is to determine the maximum radial stress at the particle surface as a function of applied load. Assuming that normal stresses at the interface are responsible for debonding, the adhesion strength can be obtained from the experimentally determined critical load at debonding initiation.     

Micromechanical modeling of imperfect textile composites

After fabrication the carbon-carbon (C/C) plain weave textile composites often show a certain degree of geometrical or material disorder including yarn waviness and misalignment or nesting of individual fiber tows together with intrinsic material porosity observed at all relevant scales. A brief survey of recently developed approaches for estimating overall elastic stiffnesses or thermal conductivities of such composite systems is presented in this paper. Depending on the source and type of available geometrical data the homogenization scheme usually relies either on finite element (FEM) simulations performed for a suitable Periodic Unit Cell (PUC) or employs one of the popular averaging techniques such as the Mori-Tanaka (MT) method. While existing applications of both methodologies are encouraging, there still exists a number of steps to be completed in the course of the future research.     

Analytical modeling of damping at micromechanical level in particulate-reinforced metal matrix composites

A new model for calculating the damping capacity of particulate-reinforced metal matrix composites (PMMCs) is proposed based on the assumption that the energy loss mainly results from the anelasticity of the particulate and matrix and the micro-plasticity of the matrix under small strain amplitude. Finite element method (FEM) with a multi particle model has been adopted. The results show that the energy loss in the loading direction can represent the total energies consumed in the composites. Moreover, the results calculated with the new model show good coincidence to the Granato–Lücke theory, which demonstrates the feasibility of damping calculation with the method.     

Evolution of interfacial nanostructures and stress states in Mg matrix composites reinforced with coated continuous carbon fibers

Magnesium (Mg) matrix composites reinforced with 45 vol.% continuous carbon fibers (C_f) were fabricated using a pressureless infiltration process in vacuum. In order to modify the interface between the C_f and the Mg matrix, the C_f were coated with 5.0 mol.% yttria stabilized zirconia (YSZ) in sol–gel route. The C_f/Mg composite exhibited a tensile strength of 1.08 GPa which reached 90% of the theoretical prediction by means of the rule of mixture. Microstructural examinations revealed the occurrence of interfacial reaction between the YSZ coating and the Mg matrix, producing a ∼20 nm thick interfacial reaction layer consisting of nanocrystalline particles, which include MgO particles, remaining ZrO₂ particles and a small quantity of ZrC particles. Interfacial reaction could induce a large compressive stress in the interfacial layer. As a result, some nanostructured defects, such as edge dislocations, were formed in interfacial layer due to the compressive stress. In the cooling process of fabricating the composite, the phase transformation of the remaining ZrO₂ from tetragonal to monoclinic could relax the thermal residual stress of interfacial layer.     

Analytical modeling of the bending behavior of textile reinforced mineral matrix composite beams

The object of this paper is to propose an analytical model for the interpretation of the overall bending behavior of textile reinforced mineral matrix composite beams. The composite material is made from inorganic phosphate cement (IPC) and E-glass fiber reinforcements (unidirectional rovings and chopped strand mat). Experimental results related to the mechanical characterization of the composite material in tension and shear, as well as the analysis in four-point bending tests of different beams, were presented in a previous paper where it was noted that the shear characteristics of the composite material define the load-bearing capacity of the beams. In order to use the full potential of the composite material, it was necessary to strengthen the beams with braiding and wrapping. The analytical modeling approach, based on composite and classical beam theories, is used to reconstruct the overall behavior of beams, taking into account the mechanical characteristics of the different materials constituting the beams. The assessment of shear load-bearing capacity is therefore based on the contribution of each component of the beam: the composite material itself and the applied strengthening. The comparison of experimental results and analytical results shows that the proposed models fit well with the actual behavior.     

Analytical modeling of material flow in equal channel angular extrusion (ECAE)

We provide analytical forms for the plastic deformation and velocity gradients associated with a single pass of equal channel angular extrusion (ECAE). Three cases of plastic deformation are considered: ideal simple shear, a plastic deformation zone (PDZ) in the shape of a central fan of angle β_m, and a two-part PDZ consisting of a central fan in the ‘upper’ region and a low intensity shear deformation in the ‘lower’ region. The analysis for simple shear considers a general die angle Φ, whereas the other two cases only consider Φ=90°. The tensors for deformation and velocity gradients completely describe the deformation, such as the directions and magnitudes of material stretching and rotations. From this analysis, one can calculate deformation and texture evolution. Texture evolution during flow through the central fan zone involves continuous rotation of the texture components causing the texture developed at the end of the extrusion to be rotated relative to the ideal simple shear case. The analysis of the two-part zone suggests inhomogeneity in texture evolution, in which features of the initial texture are retained and rotated in the lower region, while they are nearly erased in the upper region. These analytical flow patterns for a single pass can be repeatedly applied for any number of passes of any ECAE route.     

Fabrication and thermal conductivity of copper matrix composites reinforced with Mo2C or TiC coated graphite fibers

Graphite fiber reinforced Cu-based composites have good thermal conductivity, low coefficient of thermal expansion for heat sink applications. In these composites, the quality of interfacial bonding between the copper matrix and the graphite fibers has significant influence on the thermal properties of composites. In this study, two different carbide coatings (Mo₂C or TiC) were synthesized on graphite fiber to promote the interfacial bonding in composites. Fibers/Cu composites had been produced by spark plasma sintering process. The results showed that the densification, interfacial bonding and thermal conductivity of coated composites were improved distinctly compared to that of uncoated ones. The enhanced composites present 16–44% increase of thermal conductivity in X–Y plane. An original theoretical model was proposed to estimate the interface thermal resistance. The result showed that the interfacial thermal resistance was largely reduced by one order of magnitude with the introduction of carbide interlayer.     

埋置深度对黄麻纤维束与水泥基体粘结性能的影响

为了探究埋置深度对黄麻纤维束与水泥基体粘结性能的影响,利用C43电子式万能试验机进行了水泥基中黄麻纤维束的拔出试验,获得了拔出刚度、最大拔出力、等效粘结强度和拔出功随埋置深度的变化规律。试验在6 mm/min恒定试验速率下进行,测试了4组不同埋置深度（20 mm、40 mm、60 mm和80 mm）的试件。试验结果表明：随着埋置深度的增大,拔出刚度整体呈减小趋势但局部有波动;最大拔出力持续增大,并在埋置深度为60 mm时趋于稳定;等效粘结强度持续减小;拔出功初始增大,在埋置深度为60 mm处出现转折,而后迅速减小。为了进一步分析这种变化产生的具体作用机制,对不同埋置深度的破坏试件进行了观察,获得了试件破坏模式随埋置深度的变化规律。     

PAN基炭纤维中sp2杂化的C-C原子键距与结构参数之间关系

利用Raman散射及X射线衍射方法，对不同炭化温度下制备的PAN基炭纤维样品进行了测试。根据Raman散射的测试结果，从Fitzer碳键键距出发，给出了PAN基炭纤维中sp^2杂化的C—C原子键距a0随炭化温度的变化规律。由各样品的X射线衍射测试结果，得到了各样品的结构参数（La、Lc、d002）。分析了sp^杂化的C—C原子键距a0随结构参数（La、Lc、d002）变化的原因。结果表明，C—C原子键距a0与石墨化程度有关，且随La、lc的增大及d002的减小C—C原子键距增大。     

Analytical relations between effective material properties and microporosity: Application to bone mechanics

This work deals with the problem of reconstruction of microstructural parameters of viscoelastic composite material from measurements of its effective properties. The Stieltjes representation of the effective shear complex modulus of two-component composite material is exploited to recover information about structural parameters. This representation is derived from problem of torsion of a heterogeneous cylinder using asymptotic expansions method. The microstructural information is contained in the spectral measure in this analytical representation. The spectral function can be recovered from the measurements over a range of frequencies. The problem of reconstruction of the spectral measure is very ill-posed. Regularized algorithm is derived to ensure stability of the results. We apply the proposed method to recovery of porosity of cancellous bone from measurements of its effective shear modulus. Bone is modeled as a medium with a microstructure composed of two viscoelastic isotropic or/and transversely isotropic materials, with the components representing trabeculae (elastic component) and bone marrow (viscoelastic component). Porosity is understood as volume fraction of bone marrow. To verify the approach we apply it to analytically and numerically simulated response of a cylinder filled with a composite material with hexagonal microstructure. The proposed method does not use any specific assumptions about the microgeometry of the composite and is applicable to any two-phase composite medium.     

Analytical investigation of thermomechanical stresses in graded interphase between the fiber and the matrix

In this article, the thermomechanical stresses in the graded interphase between the fiber and the matrix in fiber-reinforced composites are investigated. First, the general theoretical analysis of two-dimensional steady-state mechanical and thermal stresses in a graded cylinder along the radial direction with the Power Law and Exponential Law distribution of the material properties is developed. Then the theoretical solution is applied to investigate the mechanical stresses and the thermal stresses of the fiber-matrix interphase, and the effects of material graded constant on the mechanical stresses and thermal stresses are discussed. Finally, the stress transfer mechanisms in the graded interphase are investigated which indicates that the total stresses in the fiber-matrix interphase increased with the increasing of the interphase thickness if the material graded constant varied with the radius in Power Law, but decreased in Exponential Law.     

Generalized stress intensity factors in the interaction between two fibers in matrix

To evaluate the mechanical strength of fiber reinforced composites it is necessary to consider singular stresses at the end of fibers because they cause crack initiation, propagation, and final failure. The singular stress is expressed by generalized stress intensity factors defined at the corner of fibers. As a 2D model an interaction between rectangular inclusions under longitudinal tension is treated in this paper. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. In order to analyze the problem accurately, the unknown functions are expressed as piecewize smooth functions using two types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity of 1/r ^1– ₁ and the skew-symmetric stress singularity of 1/r ^1– ₂. Then, generalized stress intensity factors at the end of inclusions are systematically calculated for various locations, spacings and elastic modulus of two rectangular inclusions in a plate subjected to longitudinal tension.     

Evaluation of interfacial strength between fiber and matrix based on cohesive zone modeling

This paper presents a measurement technique of interfacial strength considering non-rigid bonding on a fiber/matrix interface modeled as a cohesive surface. By focusing on the stress concentration near a fiber crack obtained from a single-fiber fragmentation test, the stress contours in matrix observed by photoelasticity can be related to the interfacial strength by defining a characteristic length. An equation expressing the relationship between the characteristic length on the stress contour and the interfacial strength was derived, and validated using finite element analysis. The primary advantage of proposed measurement technique is that only a single fiber crack, which usually occurs within elastic deformation of matrix, is required for the evaluation of interfacial strength, whereas saturated fiber fragmentation is necessary in the conventional method. Herein, a sample application was demonstrated using a single carbon fiber and epoxy specimen, and an average interfacial strength of 23.8 MPa was successfully obtained.     

Analytical modeling of the white-light fringe

An analytical technique for extracting phase, visibility, and amplitude information as needed for interferometric astrometry for the Space Interferometry Mission (SIM) is presented. This model accounts for a number of physical and instrumental effects and is valid for the general case of a bandpass filter. I was able to obtain a general solution for polychromatic phasors and to address the properties of unbiased fringe estimators in the presence of noise. For demonstration purposes I studied a rectangular bandpass filter with two different methods of optical path difference (OPD) modulation: stepping and ramping OPD modulation. A number of areas for further studies relevant to instrument design and simulations are outlined and discussed.     

Numerical and analytical modeling of aligned short fiber composites including imperfect interfaces

Finite element calculations were used to bound the modulus of aligned, short-fiber composites with randomly arranged fibers, including high fiber to matrix modulus ratios and high fiber aspect ratios. The bounds were narrow for low modulus ratio, but far apart for high ratio. These numerical experiments were used to evaluate prior numerical and analytical methods for modeling short-fiber composites. Prior numerical methods based on periodic boundary conditions were revealed as acceptable for low modulus ratio, but degenerate to lower bound modulus at high ratio. Numerical experiments were also compared to an Eshelby analysis and to an new, enhanced shear lag model. Both models could predict modulus for low modulus ratio, but also degenerated to lower bound modulus at high ratio. The new shear lag model accounts for stress transfer on fiber ends and includes imperfect interface effects; it was confirmed as accurate by comparison to finite element calculations.