Elastic Properties Of Inclusions Research Articles

Impact of la on steel inclusions: a first-principles investigation into elastic properties and anisotropy

This study employed first-principles calculations based on density functional theory to explore the La-induced modifications in the elastic properties of inclusions at the microscopic level. Initially, through formation energy calculations, stable La2O3, La2O2S, and LaAlO3 inclusions were identified after the treatment with the rare earth element La. Subsequently, the elastic moduli and anisotropy of both the steel matrix and the inclusions were computed. The results revealed a substantial difference in the average elastic moduli between the common inclusions MnS, Al2O3 and the steel matrix, indicating their non-ductile nature. Conversely, La-modified inclusions, such as La2O2S and LaAlO3, exhibited closer average elastic moduli to the steel matrix with reduced anisotropy, mitigating stress concentration. This elucidates one of the reasons behind the enhanced fatigue performance of La-doped steel.

Efficient homogenization techniques for elastic composites: Maxwell scheme vs. effective field method

The work is devoted to the comparative analysis of four homogenization techniques (the original and generalized Maxwell schemes and the one-particle and multi-particle effective field methods) in application to the problem of calculation of the effective elastic stiffness tensor of matrix composites. The generalized Maxwell scheme and multi-particle effective field method reduce the problem to calculation of elastic fields in a finite volume of the composite embedded in the infinite homogeneous matrix medium and subjected to a constant external stress or strain field. For the solution of this problem, an efficient numerical method based on Gaussian approximating functions and fast Fourier transform technique is used. The results of the methods are compared for composites with ellipsoidal inclusions which elastic moduli are much smaller or much larger than the moduli of the matrix. The case of hybrid composites with two different families of ellipsoidal inclusion is also considered. It is shown that for various shapes and elastic properties of inclusions, the generalized Maxwell scheme and multi-particle effective field method give close results. But in the case of hard inclusions of large volume fractions the results of these methods deviate substantially from the original Maxwell scheme that does not take into account interactions between inclusions.

EHL Modeling for Nonhomogeneous Materials: The Effect of Material Inclusions

Inclusions are common in bearing materials and are a primary site for subsurface fatigue crack initiation in rolling element bearings. This paper presents a new approach for computing the pressure, film thickness, and subsurface stresses in an elastohydrodynamic lubrication (EHL) contact when inclusions are present in the elastic half-space. The approach is based on using the discrete element method to determine the surface elastic deformation in the EHL film thickness equation. The model is validated through comparison with the smooth EHL line contact results generated using linear elasticity. Studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the EHL pressure and film thickness profiles. Both inclusions that are stiffer than and/or softer than the base material are seen to have effects on the pressure distribution within the lubricant film and to give rise to stress concentrations. For inclusions that are stiffer than the base material (hard inclusions), the pressure distribution within the lubricant film behaves as though there is a bump on the surface, whereas for inclusions that are less stiff than the base material (soft inclusions), the pressure distribution behaves in a manner similar to that of a dented surface. Inclusions close to the surface cause significant changes in the contact stresses that are very significant considering the stress life relationship. For inclusions that are located deep within the surface, there is little change in the EHL pressure and film thickness.

Evaluation of Stresses Around Inclusions in Hertzian Contacts Using the Discrete Element Method

Inclusions are the primary sites for subsurface fatigue crack initiation in bearing contacts. To understand the mechanisms of subsurface crack nucleation under contact loading, a detailed description of the stress field around these inclusions is necessary. This paper presents a new approach to computing stresses in an inhomogeneous medium where inclusions are treated as inhomogeneities in a homogeneous material matrix. The approach is based on the Discrete Element (DE) Method in which the material continuum is replaced by a set of rigid discrete interacting elements. The elements are connected to each other along their sides through springs and dampers to form the macro-continuum and undergo relative displacements in accordance with Newton’s laws of motion under the action of external loading. The spring properties are derived in terms of the overall elastic properties of the continuum. The relative motion between elements gives rise to contact forces due to stretching or compression of the inter-element springs. These forces are evaluated at each time-step and the corresponding equations of motion are solved for each element. Stresses are calculated from the inter-element joint forces. A Hertzian line contact case, with and without the presence of subsurface inclusions, is analyzed using the DE model. The DE model was used to determine stresses for an inclusion-free medium that compares well with that obtained from the continuum elasticity models. Parametric studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the subsurface stress field. Both inclusions that are stiffer and/or softer than the base material are seen to give rise to stress concentrations. For inclusions that are stiffer than the base material (semi-infinite domain), the stress concentration effect increases with their elastic modulus. The stress concentration effect of a softer inclusion is higher than that of a stiffer inclusion. Inclusions that are oriented perpendicular to the surface give rise to much higher von Mises stresses than the ones that are oriented parallel to the surface. There is little change in the maximum von Mises stress for inclusions that are located deep within the surface.

Experiments and analysis of laminates with artificial damage

Quasi-isotropic carbon/epoxy laminates with holes, polymer plugs and cut fibres are studied experimentally and analytically. Strain fields are measured using digital speckle photography. The results are used to validate an inverse method, where elastic properties of inclusions are determined by matching computed and measured displacements. Tensile and compressive strength is measured and the applicability of notch failure criteria to soft inclusions is examined. Available closed form solutions agree well with measured strains. The elastic properties predicted by the inverse method are in fairly good agreement with data from coupon tests although predictions are sensitive to measuring errors. The laminate toughness in compression was higher than in tension, as expected from the different failure mechanisms (fibre kinking versus fibre tearing). Laminates with inclusions were tougher than laminates with holes, which may indicate that inclusions restrain in-plane fibre kinking. Higher toughness was reflected in larger characteristic lengths.

Polydisperse structures of composites with random elastic properties of inclusions

A generalized self-consistent method [1, 2] is developed and applied to the boundary-value problems of composites with random elastic properties of inclusions. The approach suggested makes it possible to allow for a random mutual arrangement, statistical dispersion of elastic properties and sizes of the inclusions, and their mutual correlation in terms of special homogenized indicator functions. For comparison, the analytical solutions and those obtained from a corresponding sequence of H+1 (H=0,1,…) linked homogenized problems of the self-consistent method for the strain distribution in the inclusions and for the tensor of effective elastic properties of the composite are given. A numerical calculation of the effective transversely isotropic elastic characteristics for a unidirectional polydisperse fibrous composite is also presented.

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].

Elastic circular inclusion in an infinite plane containing two cracks

The elastic fields in an elastic circular inclusion and surrounding infinite matrix containing two cracks symmetrically situated, are determined when the matrix is subjected to loads at infinity. In this problem, the elastic properties of inclusion could differ from those of the matrix. The Muskhelishvili's technique is used. The solution depends upon two sets of suitable complex potentials Φ m ( z), Ψ m ( z), Φ i ( z), Ψ i ( z) for matrix and inclusion respectively, which solves the problem.