Compliant Inclusions Research Articles

Microstructural, Mechanical and Corrosion Characteristics of Degradable PM Biomaterials Made from Copper-Coated Iron Powders.

Copper-containing iron-based materials have recently been recognized as potential biomaterials possessing antimicrobial ability. Since then, iron-copper systems have been prepared by different methods and investigated. This article is focused on PM materials made from composite powders. The powders, each particle of which consisted of an iron core and a copper shell, were prepared by electroplating. Test-pieces with copper contents of 0, 3.2, and 8 wt.% were fabricated by pressing and sintering from iron and composite powders. Some microstructural, mechanical, and corrosion characteristics of test-pieces were examined. Microstructures were composed of pores and iron grains with alloyed peripheral regions and copper-free cores. As the copper content in test-pieces was increased, their density and Young’s modulus decreased, and macrohardness, corrosion potential and corrosion current density increased. Likely causes of density and Young’s modulus reduction were higher porosity, low enough copper content, and compliant inclusions in stiff matrix. The increase in macrohardness was attributed to the precipitation hardening which prevailed over softening induced by pores. The increase in corrosion potential and corrosion current density was most likely due to the presence of more noble phase providing surfaces for a faster cathodic reaction.

Effect of Carbon Nanofiber Clustering on the Micromechanical Properties of a Cement Paste.

The use of carbon nanofibers (CNFs) in cement systems has received significant interest over the last decade due to their nanoscale reinforcing potential. However, despite many reports on the formation of localized CNF clusters, their effect on the cement paste micromechanical properties and relation to the mechanical response at the macroscopic scale are still not fully understood. In this study, grid nanoindentation coupled with scanning electron microscopy and energy dispersive spectroscopy was used to determine the local elastic indentation modulus and hardness of a portland cement paste containing 0.2% CNFs with sub-micro and microscale CNF clusters. The presence of low stiffness and porous assemblage of phases (modulus of 15–25 GPa) was identified in the cement paste with CNFs and was attributed primarily to the interfacial zone surrounding the CNF clusters. The CNFs favored the formation of higher modulus C–S–H phases (>30 GPa) in the bulk paste at the expense of the lower stiffness C–S–H. Nanoindentation results combined with a microscale–macroscale upscaling homogenization method further revealed an elastic modulus of the CNF clusters in the range from 18 to 21 GPa, indicating that the CNF clusters acted as compliant inclusions relative to the cement paste.

Dynamic Stresses in the Elastic Matrix with One-Periodic Array of Compliant Penny-Shaped Inclusions

We consider a symmetric problem of harmonic wave loading of an infinite elastic matrix with a oneperiodic array of penny-shaped compliant inclusions. By using the periodic Green function, we reduce this problem to a boundary integral equation for a function characterizing a jump of displacements on one representative inclusion. The Green function used to describe the interaction of inclusions is adapted for the efficient determination of its representation in the form of exponentially convergent Fourier integrals. To solve the boundary integral equation, we use the method of collocations. The numerical results are obtained and analyzed for the mode I dynamic stress intensity factor in the vicinity of points of the contour of an inclusion depending on the wave number and the distance between the inclusions.

Guiding and Trapping Cracks With Compliant Inclusions for Enhancing Toughness of Brittle Composite Materials

Abstract The problem of toughening heterogeneous materials with a stiff matrix and compliant inclusions is investigated through numerical simulations and experiments. Specifically, the problem of optimizing a combination of effective toughness and effective elastic modulus in the context of a square array of compliant inclusions in a stiff matrix is explored. Crack propagation in the heterogeneous material is simulated using a variational phase-field approach. It is found that the crack can meander between or get attracted to and trapped in the inclusions. Composite specimens with a stiff matrix and compliant circular inclusions were 3D printed, and their fracture toughness was measured using a specially designed loading fixture. The experimental results show agreement with the numerical predictions by demonstrating the attraction and trapping of cracks in the inclusions. This study demonstrates the potential for significant enhancement of toughness through elastic compliance contrast between the matrix and the inclusion without notably compromising the effective elastic modulus of the composite material.

Effect of patterned inclusions on the fracture behavior of ceramic composites

Developments in additive manufacturing have enabled the reinforcement of ceramic composites across the scales. Understanding the fracture behavior of such composites is critical for structural design and engineering. However, systematic investigations on the relationship between the patterning characteristics and the effective fracture properties have been scarce. This work proposes a mixed-mode phase field model to investigate the effects of elastic modulus and pattern characteristics of circular inclusions on the fracture behavior of a ceramic composite beam. The modeling results have shown that the stiff and compliant inclusions can either repel or attract the crack. The extent of repelling and attraction can be controlled by altering the pattern characteristics. In addition, utilizing the relationship between the pattern characteristics and resulting fracture path, fracture growth can be controlled with appropriate inclusion properties. The targeted enhancement in fracture toughness can also be predicted using an effective fracture model linked with the underlying fracture path computed by the proposed mixed-mode phase field model.

Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Guided by theoretical predictions, we have demonstrated experimentally the existence of negative refraction on the two lowest acoustic-branch passbands (shear and longitudinal modes) of a simple two-dimensional phononic crystal consisting of an isotropic stiff (aluminum) matrix and square-patterned isotropic compliant (PMMA) circular inclusions. We experimentally distinguished the shear and longitudinal modes to ensure that there are no couplings between the two modes and that the shear-mode negative refraction is an inherent property of periodic composites with stiff matrix and compliant inclusions. We have also discovered that a composite with compliant (PMMA) matrix and stiff (aluminum) inclusions does not display negative shear-mode refraction on its first branch. At frequencies and wave vectors where the refraction on the acoustic-branch passbands is negative, the effective mass-density and the effective stiffness tensors of the crystal are positive-definite, and this is an inherent property of such phononic crystals.The equi-frequency contours and energy flux vectors as functions of the phase-vector components, reveal a rich body of refractive properties that can be exploited to realize, for example, beam splitting, focusing, and frequency filtration on the lowest passbands of the crystal where the dissipation is minimum. By proper selection of material and geometric parameters these phenomena can be realized at remarkably low frequencies (large wave lengths) using rather small simple two-phase unit cells.

Digital Image Correlation for Improved Detection of Basal Cell Carcinoma

Border detection is a critical aspect during removal of a basal cell carcinoma tumor. Since the tumor is only 3% to 50% as stiff as the healthy skin surrounding it, strain concentrates in the tumor during deformation. Here we develop a digital image correlation (DIC) technique for improved lateral border detection based upon the strain concentrations associated with the stiffness difference of healthy and cancerous skin. Gelatin skin phantoms and pigskin specimens are prepared with compliant inclusions of varying shapes, sizes, and stiffnesses. The specimens with inclusions as well as several control specimens are loaded under tension, and the full-field strain and displacement fields measured by DIC. Significant strain concentrations develop around the compliant inclusions in gelatin skin phantoms, enabling detection of the tumor border to within 2% of the actual border. At a lower magnification, the lateral border between a pigskin/inclusion interface is determined within 23% of the border. Strain concentrations are identified by DIC measurements and associated with the lateral edges of the compliant inclusions. The experimental DIC protocol developed for model specimens has potential as a tool to aid in more accurate detection of basal cell carcinoma borders.

Numerical modelling of regular structures with randomly perturbed structural elements

The problem of the effective elastic properties of regular composites with randomly perturbed geometric and mechanical parameters is formulated and solved numerically. Mean sample values and standard deviations of compliances are used to characterize the elastic properties. Compliance data are obtained by solving reduction problems for each of a set of realizations of random perturbations, and here the number of realizations is increased until the values of the statistical means become stable (within a given tolerance). Calculations for each realization are carried out by numerical solution of the complex hypersingular boundary integral equations obtained for a doubly periodic structure. The principal cell of this structure, containing a fairly large number of perturbed elements, is identified with a representative volume when a further increase in the number of perturbed elements do not alter the statistical means (again, within a given tolerance). Calculations are carried out for square and triangular grids with different densities of circular inclusions or holes, the centre coordinates of which are given random perturbations (weak, medium and strong). The results of the calculations are summed up in tables showing the effective compliances with an accuracy to at least three significant digits. An analysis of the values obtained for the holes shows’ that, with a tolerance of 5%, the principal cell of a square grid with four holes determines the representative volume for all the geometric parameter combinations investigated. For rigid inclusions this cell is the representative volume at a considerably greater tolerance than for compliant inclusions (4% as against 0.9%). Data on the effective properties of perturbed structures indicate that the difference between their compliance and that of the initial regular structures depends substantially on the relative stiffness of the inclusions. It is most marked for holes and rigid inclusions (9.5 and 12.6% respectively). It is established that, for a square grid, random perturbations have a stronger effect on the normal components of the compliance than on the shear component, and the opposite for a regular triangular grid – perturbations have a greater effect on the shear compliance. Calculations also show that symmetrical perturbations of holes (rigid inclusions) along one of the coordinates lead to a marked increase (reduction) in compliance in the orthogonal direction. The established dependence of the additional effective compliance on the amplitude of the perturbation enables the inverse problem to be solved: to find the parameters of the perturbed structure using data on its effective statistical properties.

Controlled crack arrest in brittle thin films: The effect of embedded voids

Controlled crack arrest is useful for controlling self-assembled crack paths in micro-fabrication, as well as limiting crack length in toughening composites. Compliant inclusions and voids can effectively attract and arrest cracks, thereby controlling the crack pattern. Analytical stress solution indicates that when the inclusion is about 10 times more compliant than its matrix, it may be effectively modeled as a void. The crack arrest capability is expressed in terms of the critical angle of the initial crack path, as the inclusion size, shape, crack origin and film properties are varied. Simple criteria are established to maximize the crack arrest ability and to determine the critical crack angle. The effectiveness of using different void patterns to arrest cracks is also explored. The results are useful for both controlling and restricting cracks in brittle thin films, through the utilization of compliant or void-like inclusions as crack arrestors.

Couple-stress moduli of a trabecular bone idealized as a 3D periodic cellular network

Trabecular bone is modeled as a cellular material with an idealized periodic structure made of open cubic cells, which is effectively orthotropic. We evaluate apparent couple-stress moduli of such a periodic material; apparent moduli refer to the moduli obtained using a domain smaller than a Representative Volume Element and they depend on boundary conditions. We conduct this analysis computationally (using ANSYS) by subjecting a unit cell of this periodic cellular material to either displacement or traction boundary conditions. Cell walls, representing bone tissue, and void space, representing bone marrow, are both modeled and they are assumed to be linear elastic. The applied loadings include a uniaxial extension (or uniaxial stress), a hydrostatic deformation (or hydrostatic stress) and a shear deformation (or shear stress) to evaluate the first stiffness (or compliance) tensor, and an applied curvature (or bending moment), a uniaxial twist (or torsion), and a triaxial twist (or triaxial torsion) to evaluate the second couple-stress stiffness (or compliance) tensor. Apparent couple-stress moduli are computed by equating the total strain energy stored in the unit cell with the energy of an equivalent homogeneous orthotropic couple-stress material for each applied loading. The moduli computed using displacement boundary conditions give upper bound, while those obtained using traction boundary conditions give lower bound on effective couple-stress moduli. These bounds are very wide due to a large mismatch in elastic moduli of bone tissue and bone marrow. These results are in agreement with our studies on composite materials with very stiff or very compliant inclusions.

The effective elastic moduli of microcracked composite materials

The self-consistent mechanics method has been widely used to estimate the macroscopic elastic moduli of solids containing microvoids and inclusions. Another method based on the crack energy release and potential energy balance has also been used to estimate the overall elastic moduli of a microcracked solid. It is shown here that these two approaches are equivalent for microcracked solids, thus one can take advantage of both methods to estimate the elastic moduli of inclusion-crack-matrix composites i.e. microcracked composite material. A solid containing spherical inclusions and randomly distributed penny-shaped cracks is then studied. The effective elastic moduli of a solid with spherical inclusions and parallel-distributed penny-shaped cracks are also studied. It is established that the effects of inclusions and microcracks on overall moduli are approximately decoupled for stiff inclusions, which are in most metal matrix composites. This conclusion is particularly useful since one may then obtain the moduli of composites by a simple two-step estimation. For compliant inclusions, including the limiting case of voids, the decoupling does not hold.

Impedance-Transforming Wave Systems with Spatially Varying Density or Elasticity

Acoustic impedance can be transformed either with an acoustic horn that controls the variation of wavefront area as the wave progresses, or by transmitting the waves through a medium in which there is a gradient of density or elasticity. Analysis shows that for plane waves a medium in which density varies as (B+mx)−2 or elastic modulus as (B−mx)2, where x is distance and B and m are constants, is analogous to the ideal exponential horn. Furthermore, radial variations of density and elasticity can readily be found which transform the behavior of sectoral and conical horns into the acoustic equivalents of exponential horns. Since the wave equation is separable in both cylindrical and spherical coordinates, these solutions are exact. In practice, the effective density of a fluid medium can be increased by introducing suitable arrays of obstacles, and the bulk modulus of a liquid decreased by compliant inclusions. The relationships between array size, bandwidth, and damping are discussed, and three artificial fluid structures are suggested.

Acoustic Horns with Spatially Varying Density or Elasticity

The transformation of acoustic impedance can be accomplished either by a controlled variation of wavefront area as the wave progresses, or by transmission of the waves through a medium in which there is a gradient of density or elasticity. The second concept does not seem to have been exploited despite the fact that the effective density of a fluid medium can be increased by introducing suitable arrays of obstacles, and the bulk modulus of a liquid decreased by compliant inclusions. The present analysis shows that for plane waves a medium in which density varies as (B + mx)−2 or elastic modulus as (B − mx)2, where x is distance and B and m are constants, is analogous to the familiar exponential horn. Simple analytical solutions are also found for radial variations of density or elasticity which transform the behavior of sectoral and conical horns into the acoustic equivalents of exponential horns. Since the wave equation is separable in both cylindrical and spherical coordinates, these solutions are exact. Three examples of artificial fluid structure are given and the relationships between array size, bandwidth, and damping are discussed.

Acoustic Horns with Spatially Varying Elasticity or Density

The transformation of acoustic impedance can be accomplished either by a controlled variation of wavefront area as the wave progresses, or by transmission of the waves through a medium in which there is a gradient of elasticity or density. The second concept does not seem to have been exploited despite the fact that the effective density of a fluid medium can be increased by introducing suitable arrays of obstacles, and the bulk modulus of a liquid decreased by compliant inclusions. Analysis shows that, for plane waves, a medium in which density varies as (C+mx)−2 or elastic modulus as (C−mx)2, where x is distance and C and m are constants, is analogous to the familiar exponential horn. Simple analytical solutions have also been found for radial variations of density of elasticity which transform the behavior of sectoral and conical horns into acoustic equivalents of exponential horns. Since the wave equation is separable in both cylindrical and spherical coordinates, these solutions are exact.