Effects of higher-order interface stresses on the elastic states of two-dimensional composites

We propose a simple model to simulate higher-order interface stresses along the interface between two neighboring media in two dimensions. The interface behavior is modeled from a thin interphase of constant thickness by taking a proper limit process. In the formulation the deformation of the thin interphase is approximated by the Kirchhoff-Love assumption of thin shell. To incorporate the higher-order interface stresses, we consider the bending effects resulting from the non-uniform surface stress across the layer thickness. The stress equilibrium conditions is fulfilled by consideration of balance for forces as well as stress couples. Depending on the difference in stiffness and length scales of the interphase, we show that the interfaces can be classified into four different types. This findings, upon suitable definitions of material parameters, agree with a rigorous asymptotic analysis proposed by Benveniste and Miloh [Benveniste, Y., Miloh, T., 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33 309-323]. To illustrate the higher-order effects, we derive analytically the stress concentration factor of an infinite plate containing a circular cavity with interface stresses of different orders subjected to a remote transverse shear loading. The closed-form expressions show how the orders of interface stresses influence the concentration factor in a successive manner. In addition, we examine the effective shear modulus of composites with circular inclusions with higher-order interface effects. The effective transverse shear modulus is derived based on the generalized self-consistent method.     

A J-integral method for calculating steady-state matrix cracking stresses in composites

A general expression for the steady-state matrix cracking stress in reinforced brittle matrix composites is derived using a J-integral analysis. The result is expressed in terms of the stress-displacement relation that characterizes the stretching of crack bridging ligaments. The influence of residual stress is assessed and a condition for spontaneous matrix cracking due to residual tensile stress in the matrix is evaluated. Results of the analysis are compared with independent solutions for composites containing unbonded reinforcing fibers.     

On the development of fatigue failure maps for titanium matrix composites

The purpose of the present article is to demonstrate how fatigue failure maps can be constructed for fiber-reinforced titanium alloys. The maps are constructed using a combination of micromechanical models and experimental measurements of fatigue cracking and fracture. The maps are used to identify the regimes in which various failure mechanisms dominate. Moreover, they provide information about the fatigue life and the critical amount of crack extension at failure. Examples of such maps for a well-characterized titanium matrix composite are presented and used to illustrate the sensitivity of fatigue life and critical crack extension to both the applied stress and the length of pre-existing cracks or notches.     

Mesh-independent modeling of both distributed and discrete matrix cracking in interaction with delamination in composites

A finite element model is presented for failure analysis of composite laminates with the phantom node method for matrix cracking and interface elements for delamination. The phantom node method allows for mesh-independent representation of straight intraply cracks in laminates. In laminates two different phenomena that both involve such cracks are distinguished, namely distributed matrix cracking and discrete splitting, where the transition between the two is related to delamination. It is investigated how both phenomena and their transition can be represented in a single computational framework. Objectivity of the results with respect to element size and the introduced crack spacing parameter is examined.     

Aspects of residual thermal stresses in continuous-fibre-reinforced ceramic matrix composites

An analytical model is presented that predicts the thermal stresses which arise from mismatch in coefficients of thermal expansion between a fibre and the surrounding matrix in a continuous fibre composite. The model consists of two coaxial isotropic cylinders. Stress transfer between the fibre and the matrix near an unstressed free surface has been modelled by means of a shear-lag analysis. Away from the free surface the theoretical approach satisfies exactly the conditions for equilibrium and continuity of stress at the fibre-matrix interface. Application of the model to a composite consisting of a glass-ceramic calcium alumino-silicate (CAS) matrix containing unidirectional Nicalon fibres points to a strong dependence of stress on fibre volume fraction. Surface effects are significant for depths of the order of one fibre diameter. Near-surface shear stresses resulting from cooling from the stress-free temperature are sufficiently high to suggest that a portion of fibre close to the surface is debonded at room temperature. Experimental results acquired with a scanning electron microscope (SEM) equipped with a heating stage are consistent with this prediction. Consequently, the model has been modified in a simple way to incorporate frictional slip at the interface, according to the Coulomb friction law. Although detailed measurements are limited by the resolution of the technique, experimental evidence suggests that the transfer length is within an order of magnitude of the model prediction.     

On the mechanical behaviour under cyclic loading of ceramic matrix composites

In this paper, a constitutive law is presented to model the mechanical behaviour of ceramic matrix composites. It allows matrix-cracking, interfacial debonding, sliding and wear to be accounted for in the framework of continuum mechanics. Based upon micromechanical studies, a 1D and 2D model was derived. An application was performed on a [0,90] SiC/SiC composite.     

Evolution of internal strain during plastic deformation in magnesium matrix composites

Synchrotron radiation diffraction during in situ tensile tests has been used to evaluate the internal elastic strains within the grains of magnesium alloy, AZ31, unreinforced and reinforced with 5 and 10% volume of SiC particles. Composites present initial thermal residual stresses, which are positive (tensile) in the matrix and negative (compressive) in the reinforcing particles. Internal elastic strains evolve in a similar behaviour in the unreinforced AZ31 and in both composites. However, the accumulated elastic strains are reduced in the case of the composite because a part of the applied load is borne by the ceramic particles.     

Coulomb friction controlled bridging stresses and crack resistance of ceramic matrix composites

Bridging stresses in ceramic matrix composites (CMC) are calculated taking into account the effect of Poisson contraction of fibre and matrix during loading and a two parameter Weibull distribution of fibre strength. A parameter study is performed in order to assess the influence of the constituent properties. The bridging stress curve provides the link from the micromechanical analysis to the prediction of macroscopic composite behaviour. The load–deflection behaviour of pre-notched CMC specimens is derived by application of the method of weight functions. The predictions are compared with experimental results giving information about the actual properties of the material.     

Effects of nonuniformity of fiber distribution on thermally-induced residual stresses and cracking in ceramic matrix composites

A three-dimensional finite element analysis is conducted to estimate stresses induced by thermal cooldown in unidirectionally fiber-reinforced ceramic matrix composites. Various configurations of nonuniform fiber distributions are considered. Both cases of thermal expansion mismatch between isotropic, linearly thermoelastic fibers and matrix are studied. Significant effects of nonuniformity of fiber distributions on the local stress states are found. The initiation of various possible cracking modes is discussed in the light of these results.     

Buffered internal stresses in diamond-like carbon films reinforced with single-walled carbon nanotubes

Diamond-like carbon (DLC) films reinforced with single-walled carbon nanotubes (SWCNTs) were fabricated by sputter-deposition of DLC onto a few monolayers of spray-coated SWCNTs on glass substrates. The thickness-averaged internal stress was reduced by 1.5 GPa by incorporation of SWCNTs into 10-nm-thick DLC films. Stress analysis indicates that the internal stress is reduced by 1.8 GPa at the SWCNT-DLC nanocomposite layer and decreases exponentially as a function of film thickness. Microscopy reveals significant cracking and delamination in 150-nm-thick DLC films, while the SWCNT-reinforced films remain essentially intact. The results demonstrate that SWCNTs in DLC films influence the early stage of DLC film growth and act as an effective stress-buffering layer near the boundary between the film and substrate.     

Analysis and simulation of cracking patterns in coating under biaxial tensile or thermal stress using analysis/FEM strain-accommodation method

The cracking patterns in coatings under biaxial tensile or thermal stress are analyzed by the “analysis/FEM strain-accommodation method” that combines the strain of the substrate with a coating obtained from thermo-elastic analysis with the strain of the substrate calculated by a finite element method. The simulation using this method is effective not only for expressing the cracking patterns observed in punch press tests of disk specimens with WC-Co cermet and Al₂O₃-TiO₂ ceramic coatings but also predicting the cracking process for the coating deposited on a part with a complex shape under thermal stress.     

Phase-stress partition and residual stress in metal matrix composites

Finite element (FE) modeling based on axisymmetrical cells was performed for relating the phase-stress partition and residual phase stress in metal matrix composites (MMCs) to the reinforcement volume fraction and shape, matrix hardening behavior and applied strain levels. The phase stress is defined as mean effective stresses in the constituent phases. The elastic, plastic phase-stress partition behavior during loading, and the resultant residual stress in matrix followed unloading are delineated. A set of formulas is given for predicting the value of the phase stress in each phase, and residual stress in matrix from the inclusion volume fraction and aspect ratio, as well as matrix hardening exponent and applied strain level.     

Statistical issues in the fracture of brittle-matrix fibrous composites

This paper reviews recent work and presents new results on statistical aspects of the failure of composites consisting of brittle fibers aligned in a brittle matrix. The failure process involves quasi-periodic matrix cracking in planes perpendicular to the fiber, frictional sliding of the fibers in fiber break zones, and fiber bridging of cracks in a load-sharing framework that may vary from global to fairly local. First, we review the overall statistical features of the failure process, and identify certain issues in terms of critical geometric, statistical and mechanical parameters. This leads to two interesting cases, one where the spacing of matrix cracks is small relative to the length scale of load transfer in the fibers, and one where it is larger. Next we consider ‘characteristic’ bundles in the composite which capture essential features of the statistics of the failure process, and develop their distributions for strength in terms of certain characteristic stress and length scales. We then model the composite as a chain arrangement of such bundles both longitudinally and laterally, as the scale of load transfer among fibers in a bundle may be smaller than the full composite cross-section. This scale, though not precisely quantified, depends on such things as the stiffness of the matrix relative to the fibers, the volume fraction of the matrix and the spacing of periodic cracks. We then consider the strength distribution for the composite on the basis of the failure of the weakest characteristic bundle. We also consider issues related to fiber pull-out and the work of fracture as well as the possibility of severe strain localization especially within the bundle triggering overall failure. Substantial reductions in strength are predicted for smaller bundle sizes, but composite reliability is typically very high and the size effect very mild. Finally, we mention limited comparisons with Monte Carlo simulations and experimental results.     

Residual stress generation in metal matrix composites after cooling

Effects of reinforcements’ shapes, sizes and contents on (a) von-Mises stress along a horizontal line in MMCs, (b) directions and distributions of principal stresses inside particles, matrix and interface, and (c) distribution of thermal residual stress in MMCs were analysed in this investigation. It was found that the matrix–particle interfaces experience a sudden change of von-Mises stress which depends on the reinforcement shape. The smoothest change of stress occurred in triangle particle-reinforced MMCs. However, the highest stress was concentrated at the corners of the triangular particles. The directions of stress vectors depend on the shape of the particles. The extent of the von-Mises stress increases with the increase in reinforcement content and a decrease in particles size at constant content.     

Fabrication of hybrid ceramic matrix composites

The desire to improve the transverse properties and microcracking stress of unidirectional continuous fiber reinforced ceramic matrix composites has led to development of the hybrid ceramic matrix composite (HCMC). This paper discusses the techniques we used in the fabrication of HCMC specimens used for mechanical characterization.     

On the analysis of the causes of cracking in a wind tower

This paper presents an analysis of the cracking causes in a wind tower of a wind farm. The cracks were detected in several towers of the farm, in the welded joint between the lower ring of the towers and the flange connecting the towers to their corresponding foundation. In the extreme case, here analysed, the crack was a through thickness crack.In order to clarify the cracking causes, the component was inspected in situ, non-destructive tests were performed on the base material, the weld bead and the Heat Affected Zone (HAZ), and a Finite Elements (FE) simulation was carried out to determine the stress state in the welded joints and to develop the corresponding fatigue analysis following the Fatigue Module (Chapter 7) of the FITNET FFS Procedure.The analysis has demonstrated that the main cause of the cracking process is an inadequate design of the joint, with high stress concentrations and an insufficient resistant section on the flange.Finally, two tentative solutions (grinding and grinding plus soft transition) have been analysed but none of them have provided satisfactory results.     

On the calculation of boundary stresses with the Somigliana stress identity

The computation of boundary stresses by Boundary Element Method (BEM) is usually performed either by expressing the boundary tractions in a local co-ordinate system, calculating the remaining stresses by shape function differentiation and inserting into Hooke's law or recently also by solving the hypersingular integral equation for the stresses. While direct solution of the hypersingular integral equation, the so-called Somigliana stress identity, has been shown to be more reliable, the interpretation and numerical treatment of the hypersingularity causes a number of problems. In this paper, the limiting procedure in taking the load point to the boundary is carried out by leaving the boundary smooth and the contributions of all different types of singularities to the boundary integral equation are studied in detail. The hypersingular integral in the arising boundary integral equation is then reduced to a strongly singular one by considering a traction free rigid body motion. For the numerical treatment, an algorithm for multidimensional Cauchy Principal Value (CPV) integrals is extended that is applicable for the calculation of boundary stresses. Moreover, the shape of the surrounding of the singular point is studied in detail. A numerical example of elastostatics confirms the validity of the proposed method.     

Deformation of extreme viscoelastic metals and composites

The figure of merit for structural damping and damping layer applications is the product of stiffness E and damping tan δ. For most materials, even practical polymer damping layers, E tan δ is less than 0.6 GPa. We consider several methods to achieve high values of this figure of merit: high damping metals, metal matrix composites and composites containing constituents of negative stiffness. As for high damping metals, damping of polycrystalline zinc was determined and compared with InSn studied earlier. Damping of Zn is less dependent on frequency than that of InSn, so Zn is superior at high frequency. High damping and large stiffness anomalies are possible in viscoelastic composites with inclusions of negative stiffness. Negative stiffness entails a reversal of the usual directional relationship between force and displacement in deformed objects. An isolated object with negative stiffness is unstable, but an inclusion embedded in a composite matrix can be stabilized under some circumstances. Ferroelastic domains in the vicinity of a phase transition can exhibit a region of negative stiffness. Metal matrix composites containing vanadium dioxide were prepared and studied. The concentration of embedded particles was sensitive to the processing method.     

Microstructure and abrasive wear characteristics of in situ vanadium carbide particulate-reinforced iron matrix composites

In this work, in situ synthesis with infiltration casting and subsequent heat treatment was applied to fabricate vanadium carbide (V₈C₇) particulate-reinforced iron matrix composites. The microstructure and wear-resistance of V₈C₇ particulate-reinforced iron matrix composites with different volume fraction were studied using scanning electron microscopy, X-ray diffraction, and wear testing. The V₈C₇ particles were uniformly distributed in the matrix, and the size of the V₈C₇ reinforcement was 2–12 μm. The relative wear resistance of the composites initially increases decreases with higher V₈C₇ volume fractions. The best wear resistance of the composites was 21.2 times higher than that of gray cast iron under a 20 N load. This was achieved at 24% V₈C₇ volume fraction. Wear of the composites manifests as grooves, broken carbide particles, and re-embedment of wear debris.