On microstructural mechanisms causing non-linear stress-strain behavior of porous ceramics under tension

Possible micromechanisms that explain experimental data on stress-strain behavior of porous ceramics (such as cordierite) under tensile cyclic loading are discussed. The data show that, in the first cycle, the stress-strain curve exhibits non-linear behavior, with sharply higher incremental stiffness at the beginning of unloading and noticeable hysteresis. In subsequent cycles, the curves are almost perfectly linear. Whereas the underlying micromechanisms of such behavior are presently not fully clear, we suggest possible mechanisms that involve frictional sliding on microcracks. Such sliding may take place under tensile loads provided the cracks have complex non-flat geometries (such as zigzag ones).     

Fracture behavior dependence on load-bearing capacity of filler in nano- and microcomposites of polypropylene containing calcium carbonate

The fracture toughness and deformation mechanism of PP/CaCO₃ (15 wt.%) composites were studied and related to load-bearing capacity of the particles. To alter the load-bearing capacity of the particles, different particle sizes (0.07–7 μm) with or without stearic acid coating were incorporated. The fracture toughness of the composites was determined using J-Integral method and the deformation mechanism was studied by transmission optical microscopy of the crack tip damage zone. It was observed that the load-bearing capacity of the particles decreased by reduction of particle size and application of coating. A linear relationship between normalized fracture toughness and inverse of load-bearing capacity of particles was found. The crack tip damage zone in composites, which consists in massive crazing, further grows by reduction in load-bearing capacity.     

界面效应对功能复合材料热传导行为的影响

界面是复合材料内部连接不同两相的桥梁,极大地影响着复合材料的热学、电学、力学等各项性能.作为复合材料领域中的一个新的分支,导热复合材料近年来因电子电器的高速发展的需求而受到越来越多的关注.然而,研究发现,即使采用了高填料填充方案,复合材料的导热系数也很难达到导热填料的百分之几,其中界面热阻是影响复合材料导热系数提升的关...     

Fracture statistics in the three-dimensional random fuse model

We present numerical simulations for the fracture of the three dimensional random fuse model. The damage accumulated prior to fracture follows a Gaussian distribution, suggesting the absence of long-range correlations. The strength distribution is found to be Lognormal with a logarithmic size effect for the average strength. We relate this result with the distribution of damage clusters.     

Fracture parameters for interfacial cracks: an experimental-finite element study of crack tip fields and crack initiation toughness

Crack tip measurements and analysis of interfacial parameters for PMMA-aluminum bimaterial system are presented. A variety of crack tip mode-mixities are obtained by subjecting asymmetric four-point-bend specimens to different boundary loads. The crack tip fields are mapped using the optical method of Coherent Gradient Sensing (CGS). The complex stress intensity factors and the associated crack tip mixities () are measured from CGS fringe patterns. The asymptotic expansion field for interface cracks is used for extracting fracture parameters by accounting for higher order contributions to the experimental data. The measurements are compared with complementary finite element computations. A linear relationship between crack tip mixity and the applied load mixity is experimentally demonstrated in this large elastic mismatch system. The fracture load and hence the energy release rate G _cr () at crack initiation is measured as applied load mixities are varied. Limited discussion on the influence of surface roughness prior to bonding on the fracture toughness is included. Positive and negative shear on the crack plane produce different failure responses in this bimaterial system and the observed asymmetry is akin to the one predicted by the T&H model that includes crack tip nonlinearty.     

Stochastic finite element method applied to non-linear analysis of embankments

The deterministic Finite Element Method (FEM) is a valuable tool for understanding and predicting the mechanical behaviour of earth structures. The main difficulty in the application of this technique generally arises from the large uncertainties affecting the mechanical properties of materials to be introduced in the analysis. In many instances, these parameters should actually be considered as random variables or random fields. The Stochastic Finite Element Method (SFEM) should then be used to assess the results of the analyses in probabilistic terms.In this paper, the usefulness of the SFEM approach for engineering purposes is discussed and illustrated by analyses of embankments constructed by placing successive lifts of compacted soil. Construction materials are assumed to follow a simple non-linear constitutive law (Duncan JM, Chang CY. Non-linear analysis of stress and strain in soils, Journal of the Soils Mechanics and Foundation Division, ASCE 1970;96(5):1629–1653). Stochastic finite element analyses are performed using both the First Order-Second Moment method (FOSM) and Monte Carlo simulations (MC). A simple example shows that SFEM analyses can be useful to evaluate the relative influence of each of the parameters of the constitutive model on the results. Uncertainties affecting displacements, strains and stresses predictions for a large earth dam are also presented.     

Influence of fiber/matrix interfacial adhesion on composite fracture behavior

A systematic study has been conducted to identify the effect of fiber/matrix interface strength on various composite properties. A new fiber treatment technique was developed to allow fibers to be treated and then made into prepregs and composites of acceptable quality. T500 carbon fibers were treated with release agent to establish the extreme case of poor fiber/matrix interface. Composite systems made of toughened epoxy R6376 and T500 fibers with and without such a treatment were subjected to a number of fracture and impact tests. For tests involving propagating pre-existing delamination cracks, such as double cantilever beam (DCB), end notched flexural (ENF) and crack lap shear (CLS) methods, the material properties were not appreciably affected by the release agent-treated fiber surfaces. For tests that had to initiate cracks in specimens without pre-introduced cracks, such as impact and edge delamination, the material variables and failure modes were highly sensitive to the fiber/matrix interface. The critical role of the fiber/matrix interface in crack initiation was demonstrated in this study.     

Fracture statistics of torsion in glass cylinders

This paper has adopted a theoretical viewpoint for studying fracture statistics in round bars subjected to torsion, and for determining the cumulative probabilities of fracture using Weibull's and Kies-Kittl's specific-risk functions for materials that exhibit volume and surface brittleness. The use of the integral equations method has allowed us to obtain the specific-risk-of-fracture function and, in addition, to carry out a separation between the volume part and surface part for materials which show both types of brittleness at the same time. Diagrams of the cumulative probability of fracture for commercial glass samples are plotted as a practical application. The parameters of Kies-Kittl's functions regarding torsion as well as those of Weibull's functions regarding bending are appraised employing nomograms and minimizing the chi-square, respectively. Dispersion of the same is determined resorting to Fisher's information matrix. The different forms of the statistical functions followed by the same material in the two tests are due to form and size influences of the crack originating the fracture.     

On the modelling of interfacial transition behaviour in composite materials

Here, the development of two types of models for describing the transition behaviours of interfacial regions such as interlayers in laminated composites has been presented. The first model is defined based on physical considerations, using a spatial function continuously varying/describing the graded properties of the interlayer, for example, in the case of epoxy laminates, it depends on resin enrichment and fibre specific distribution. The second kind of model is proposed using interface laws defined on material surfaces (with no thickness). These laws, obtained by asymptotic analysis, are equivalent to the evolutive behaviour model primarily developed for the interlayer. Depending on the flexible or rigid nature of the interlayer, two types of interface laws have been suggested. Finally, these models are employed in a numerical analysis for studying the stress concentration due to free-edge effects in a multilayered symmetric cross-ply (0°/90°)s laminate having different kinds of interlayers. The present results are compared with those of classical/ideal perfect interface model to show the significance of the proposed models, incorporating the influence of the interlayer transition behaviour on the free-edge effect evaluation.     

The quasi-linear method of fundamental solution applied to non-linear wave equations

This paper presents a new meshless method developed by combining the quasi-linear method of fundamental solution (QMFS) and the finite difference method to analyze wave equations. The method of fundamental solution (MFS) is an efficient numerical method for solution Laplace equation for both two- and three-dimensional problems. The method has also been applied for the solution of Poisson equations and transient Poisson-type equations by finding the particular solution to the non-homogeneous terms. In general, approximate particular solutions are constructed using the interpolation of the non-homogeneous terms by the radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. The current work suggests a linearization scheme for the non-homogeneous term in terms of the dependent variable and finite differencing in time resulting in Helmholtz-type equations whose fundamental solutions are available. Consequently, the particular solution is no longer needed and the MFS can be directly applied to the new linearized equation. The numerical examples illustrate the effectiveness of the presented method.     

Reproducing kernel collocation method applied to the non-linear dynamics of pipe whip in a plane

A windowed collocation method, based on a moving least squares reproducing kernel particle approximation of functions, is explored for spatial discretization of the strongly non-linear system of partial differential equations governing large, planar whipping motion of a cantilever pipe subjected to a follower force pulse (the blow-down force) normal to the deflected centreline at its tip. This problem was discussed by Reid et al. [An elastic–plastic hardening–softening cantilever beam subjected to a force pulse at its tip: a model for pipe whip. Proc R Soc London A1998;454:997–1029] where a space–time finite difference discretization was employed to solve the governing partial differential equation of motion. It was shown that, despite the deflected shape predictions being accurate, numerical solutions of these equations might exhibit problematic (possibly spurious) steep localized gradients. The resolution of this problem in the context of structural mechanics is novel and is the subject of this paper. In particular, it is demonstrated that it is possible to reduce significantly such spurious and localized numerical instabilities through a windowed collocation approach with a suitable choice of the window size. The collocation procedure presently adopted is based on the moving least squares reproducing kernel particle method. Material and structural non-linearity in the beam (pipe) model is incorporated via an elastic–plastic-hardening–softening moment–curvature relationship. The projected ordinary differential equations are then integrated in time through a fifth order, explicit Runge–Kutta method with adaptive step sizes.     

The non-conservatism of the Weibull function when applied to the statistics of fracture toughness

It has become very clear that in many cases fracture toughness for a given material is variable; for example a quenched and tempered, high-strength low-alloyed steel such as might be used for the construction of pressure vessels for nuclear-power plants or off-shore platforms. Indeed for these materials fracture toughness can no longer be looked upon as a single-valued property at any given temperature but must rather be seen as a property with an inherent distribution of its values. The present paper shows that recent models for the distribution of toughness which are based on the two-parameter Weibull function are potentially dangerously non-conservative both for the estimation of low and medium values of toughness and for the estimation of the sizes of defects present in proof-tested parts.

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Résumé Il est devenu très clair que, dans de nombreux cas, la ténacité à la rupture d'un matériau est variable. Ainsi en est-il d'un acier à haute résistante faiblement allié, trempé et revenu, de la nuance utilisée pour la fabrication des capacités sous pression des centrales nucléaires, ou des composants de plateforme offshore.Pour ces matériaux, en effet, la ténacité à la rupture ne peut plus guère être considérée comme une propriété à valeur unique pour une température déterminée, mais doit plutôt être envisagée comme une propriété dont les valeurs répondent à une distribution qui lui est caractéristique.Le mémoire montre que les modèles récemment proposés pour décrire la distribution de la ténacité, qui sont basés sur une fonction de Weibull à deux paramètres, sont potentiellement empreints d'une dangereuse insécurité, pour l'estimation des valeurs inférieures et moyennes de la ténacité et pour l'estimation de la dimension des défauts présents dans les pièces soumises à essais.

     

Time-interval statistics applied to the analysis of low-polydispersity samples for low light-intensity levels

A time-interval-statistics method that is based on the measurement of the Laplace transform of the probability function of the time intervals between two successive photoelectrons has been applied to experiments of light diffusion from low-polydispersity samples from which the scattered intensity is weak (less than 1 photoelectron/characteristic fluctuation time). Computer-simulation methods have been used to simulate intensity fluctuations and positions of individual photoelectrons for different experimental situations. The parameters characterizing the diffusion-coefficient distribution function of the sample (mean and index of polydispersity) and their corresponding errors are obtained and analyzed as a function of the mean intensity and the polydispersity index.     

Cost function analysis applied to the determination of aorta parameters

It has been shown by Fich and Welkowitz that a model of the aorta which is tapered in area and elastic constant and is essentially reflectionless is a good representation for the calculation of pressure and flow wave propagation in the aorta. If one then measures a steady state pressure transfer function in the aorta and relates it to the steady state pressure transfer function of the model, it is possible to adjust the physical parameter values that appear in the model until the transfer functions coincide. By this means it is possible to determine the physical parameters of the aorta.

Both analog and digital data techniques were developed for efficient handling of the data. Matching of the transfer functions was accomplished by finding the ‘best’ set of parameters that minimized a weighted error cost function derived from the magnitude and phase of the transfer functions.     

The quasi-linear method of fundamental solution applied to transient non-linear Poisson problems

This paper proposes the use of a quasi-linear method of fundamental solution(QMFS) and explicit Euler method to treat the transient non-linear Poisson-type equations. The MFS, which is a fully meshless method, often deals with the linear and non-linear poisson equations by approximating a particular solution via employing radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. The current work suggests a linearization scheme for the nonhomogeneous term in terms of the dependent variable and finite differencing in time resulting in Helmholtz-type equations whose fundamental solutions are available. Consequently, the particular solution is no longer needed and the MFS can be directly applied to the new linearized equation. The numerical examples illustrate the effectiveness of the presented method.     

Fracture of crazes by the propagation of interfacial stress waves

Fracture of crazes in glassy polymers can occur by a quasi-brittle separation at the interface between the craze and the adjacent bulk. In some grades of polystyrene this type of fracture can take the form of a very regular pattern, the so-called mackerel pattern, of parallel or concentric craze strips as fracture alternates from one side of the craze layer to the other. The alternating pattern of fracture is determined by the coupling between stress waves propagating along the craze—bulk boundaries.     

Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration

This paper presents a new module towards the development of efficient computational stochastic mechanics. Specifically, the possibility of an adaptive polynomial chaos expansion is investigated. Adaptivity in this context refers to retaining, through an iterative procedure, only those terms in a representation of the solution process that are significant to the numerical evaluation of the solution. The technique can be applied to the calculation of statistics of extremes for nongaussian processes. The only assumption involved is that these processes be the response of a nonlinear oscillator excited by a general stochastic process. The proposed technique is an extension of a technique developed by the second author for the solution of general nonlinear random vibration problems. Accordingly, the response process is represented using its Karhunen-Loeve expansion. This expansion allows for the optimal encapsulation of the information contained in the stochastic process into a set of discrete random variables. The response process is then expanded using the polynomial chaos basis, which is a complete orthogonal set in the space of second-order random variables. The time dependent coefficients in this expansion are then computed by using a Galerkin projection scheme which minimizes the approximation error involved in using a finite-dimensional subspace. These coefficients completely characterize the solution process, and the accuracy of the approximation can be assessed by comparing the contribution of successive coefficients. A significant contribution of this paper is the development and implimentation of adaptive schemes for the polynomial chaos expansion. These schemes permit the inclusion of only those terms in the expansion that have a significant contribution.     

Thermochemical modelling of interfacial reactions in molybdenum disilicide matrix composites

The thermal and environmental stabilities of molybdenum disilicide have been evaluated using thermochemical modelling. The chemical reactivity of molybdenum disilicide with oxygen indicates that various molybdenum compounds and silica are formed, depending on oxygen pressures. The structure and properties of the silica films play an important role in the oxidation reaction and the reactions of water vapour (moisture) with molybdenum disilicide at high temperatures. The thermodynamic stabilities of various potential reinforcements, e.g. carbon, silicon carbide, silicon nitride, alumina, and some refractory compounds (borides, carbides, and oxides of titanium, zirconium and hafnium) in molybdenum disilicide matrix have been evaluated. Based on the results of thermochemical computations, SiC, Si₃N₄, TiC, ZrC, HfC, TiB, TiB₂, ZrB₂, HfB₂, ZrO₂ and HfO₂ were found to be stable, but carbon and TiO₂ were found to be unstable in MoSi₂.The Al₂O₃/MoSi₂ system was found to be stable below 1800 K. At temperatures above 1800 K, significant mass losses could occur due to the high vapour pressures of gaseous species (Al₂O, SiO). These thermodynamic predictions are in agreement with available experimental data.