Concept Of Average Stress Research Articles

A Meso-Mechanical Constitutive Model of Particle-Reinforced Titanium Matrix Composites at High Temperatures

The elastoplastic properties of TiC particle-reinforced titanium matrix composites (TiC/TMCs) at high temperatures were examined by quasi-static tensile experiments. The specimens were stretched at 300 °C, 560 °C, and 650 °C, respectively at a strain rate of 0.001/s. scanning electron microscope (SEM) observation was carried out to reveal the microstructure of each specimen tested at different temperatures. The mechanical behavior of TiC/TMCs was analyzed by considering interfacial debonding afterwards. Based on Eshelby’s equivalent inclusion theory and Mori-Tanaka’s concept of average stress in the matrix, the stress or strain of the matrix, the particles, and the effective stiffness tensor of the composite were derived under prescribed traction boundary conditions at high temperatures. The plastic strains due to the thermal mismatch between the matrix and the reinforced particles were considered as eigenstrains. The interfacial debonding was calculated by the tensile strength of the particles and debonding probability was described by Weibull distribution. Finally, a meso-mechanical constitutive model was presented to explore the high-temperature elastoplastic properties of the spherical particle-reinforced titanium matrix composites by using a secant modulus method for the interfacial debonding.

The Effect of Initial Void on the Elasto-Plastic Properties of Particle-Reinforced Composite Coating

Many defects such as micro-voids, micro-cracks are introduced during the preparation of particle reinforced composite coating, which significantly change the mechanical properties of the coating. Based on Mori-Tanaka’s concept of average stress in the matrix and Eshelby’s equivalent inclusions microscopic theory, an incremental theory coupled with ABAQUS subroutine UMAT, is developed to study the influence of initial void and void growth on elasto-plastic properties of composite coating. In the composite containing hard spherical particles, debonding of particle-matrix interface is a significant damage process, and the effect of initial void on particle damage is also considered.

Fracture characteristics of concrete subjected to impact loading

This paper takes concrete as a four-phase composite made of the intact matrix and three mutually perpendicular groups of penny-shaped micro-cracks. The intact matrix is assumed to be elastic, homogeneous and isotropic, and the micro-cracks are penny-shaped. Combined with the failure mechanism of concrete subjected to impact loading, a dynamic constitutive model for concrete is developed based on Mori-Tanaka’s average stress concept and Eshelby’s equivalent inclusion theory. Experimental results show that concrete is rate-dependent. The model predictions are in good agreement with the experimental results. The model may be used to simulate the mechanical behavior of concrete under impact loadings.

Elastoplastic Behavior of Particle Reinforced Composites Considering the Effect of Interfacial Debonding

Based on Mori-Tanaka’s concept of average stress in the matrix and Eshelby’s equivalent inclusions theory, the stress or strain of the matrix, the reinforced particles and the composite are derived under a prescribed traction boundary conditions. The plastic strains and strains due to thermal mismatch between matrix and reinforced phase are considered as eigenstrains. The matrix and composite are postulated isotropic and the matrix satisfies isotropic hardening law. The interface debonding is decided by the tensile strength of the particles whose debonding probability is described by Weibull distribution function. Then the overall elastoplastic constitutive relation of spherical particle-reinforced metal matrix composite is derived by secant modulus method considering the interface debonding. The theoretical uniaxial stress-strain bebavior of the composite agrees well with the experimental curves.

Modulus prediction and discussion of reinforced syntactic foams with coated hollow spherical inclusions

The elastic properties of syntactic foams with coated hollow spherical inclusions have been studied by means of Mori and Tanaka’s concept of average stress in the matrix and Eshelby’s equivalent inclusion theories. Some formulae to predict the effective modulus of this material have been derived theoretically. Based on these formulae, the influences of coating parameters such as the thickness and Poisson’s ratio on the modulus of the syntactic foams have been discussed at the same time.

Numerical study of the single fibre push-out test: Part III. Singularity of interface stresses

The singular behaviour at the free edges of the fibre-matrix interface is analysed for the fibre push-out test geometry based on the boundary element method. The fibre push-out test has been extensively used to measure the fibre-matrix interfacial properties in polymer, ceramic and metal matrix composites. There are two free edges in the fibre push-out specimen: one is at the loaded fibre end and the other at the supported fibre end. The singular stresses can be expressed as a function of singular exponent and singular stress intensity. It is shown that the singular exponents obtained at both fibre ends are characteristic of composite constituent properties, such as Young's moduli of fibre and matrix, and does not vary with specimen dimensions. The singular exponents are real and identical for the shear and radial stress components at fibre ends where the wedge angles are the same. The singular stress intensities are also implicit in material properties, and vary with specimen dimensions, such as fibre to matrix radius ratio, fibre aspect ratio and support hole size. An interfacial failure criterion is proposed here based on the average stress concept to determine the critical singular stress intensities in mode I and mode II loads.

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.

Stress fields in composites reinforced by coated cylindrically orthotropic fibers

Local fields and effective thermoelastic properties are derived for coated fiber composites with cylindrically orthotropic fibers and transversely isotropic coating and matrix phases. Thermomechanical loading situations are considered in which a uniform stress and a uniform temperature change are applied to the boundary of the composite aggregate. A micromechanical model, based on the Mori and Tanaka's concept of average stress in the matrix, is used to account for phase interaction. It is found that a special treatment is needed in formulation of effective properties of composites reinforced by constituents which are curvilinearly anisotropic. Results are presented for a pitch precursor carbon fiber, carbon coating and titanium aluminate matrix system.

Delamination of tapered composite structures

The delamination of tapered composite laminates with multiple internal ply drop steps is investigated. Both experimental testing of glass-epoxy coupon specimens and finite element modeling of the tapered region are conducted. The average stress concept is applied to out-of-plane stresses from a three-dimensional finite element model. Delamination failure criteria are then used to predict strength based on ply failure and interply resin failure. Strength predictions based on interply resin failure using a stress averaging distance of one ply thickness are found to correlate well with the experimental results. Delamination in the tapered laminates is due to interlaminar shear failure of the interply resin surrounding the last ply drop step.

A Theory of Particle-Reinforced Plasticity

A simple, albeit approximate, theory is developed to determine the elastoplastic behavior of particle-reinforced materials. The elastic, spherical particles are uniformly dispersed in the ductile, work-hardening matrix. The method proposed combines Mori-Tanaka’s concept of average stress in elasticity and Hill’s discovery of a decreasing constraint power of the matrix in polycrystal plasticity. Under a monotonic, proportional loading the latter was characterized, approximately, by the secant moduli of the matrix. The theory is established for both traction and displacement-prescribed boundary conditions, under which, the average stress and strain of the constituents and the effective secant moduli of the composite are explicitly given in terms of the secant moduli of the matrix and the volume fraction of particles. In particular, the yield stress and work-hardening modulus of the composite are shown to be inversely proportional to the deviatoric part of average stress concentration factors of the matrix, and therefore will increase (or decrease) with increasing hard (or soft) particle concentration. It is also found that, even if the matrix is plastically incompressible, the composite as a whole is not. Comparison between the theory and the experiment for a silica/epoxy system shows a reasonable agreement. The theory is also compared with a recently developed one by Arsenault and Taya; while both give the same initial yield stress for the composite, the work-hardening modulus predicted by their theory is found to be higher.

Stress Distribution in and Around Spheroidal Inclusions and Voids at Finite Concentration

A simple, albeit approximate, close-form solution is developed to study the elastic stress and energy distribution in and around spheroidal inclusions and voids at finite concentration. This theory combines Eshelby’s solution of an ellipsoidal inclusion and Mori- Tanaka’s concept of average stress in the matrix. The inclusions are taken to be homogeneously dispersed and undirectionally aligned. The analytical results are obtained for the general three-dimensional loading, and further simplified for uniaxial tension applied parallel to the axis of inclusions. The ensuing stress and energy fields under tensile loading are illustrated for both hard inclusions and voids, ranging from prolate to oblate shapes, at several concentrations.