Application of finite anisotropic elasticity to the behavior of natural rubbers
Anisotropic strain energy function describing mechanical behavior of rubber
RUBBER↗
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Experimental and Computational Studies on Superhard Material Rhenium Diboride under Ultrahigh Pressures
An emerging class of superhard materials for extreme environment applications are compounds formed by heavy transition metals with light elements. In this work, ultrahigh pressure experiments on transition metal rhenium diboride (ReB 2 ) were carried out in a diamond anvil cell under isothermal and non-hydrostatic compression. Two independent high-pressure experiments were carried out on ReB 2 for the first time up to a pressure of 241 GPa (volume compression V/V 0 = 0.731 ± 0.004), with platinum as an internal pressure standard in X-ray diffraction studies. The hexagonal phase of ReB 2 was stable under highest pressure, and the anisotropy between the a-axis and c-axis compression increases with pressure to 241 GPa. The measured equation of state (EOS) above the yield stress of ReB 2 is well represented by the bulk modulus K 0 = 364 GPa and its first pressure derivative K 0 ´ = 3.53. Corresponding density-functional-theory (DFT) simulations of the EOS and elastic constants agreed well with the experimental data. DFT results indicated that ReB 2 becomes more ductile with enhanced tendency towards metallic bonding under compression. The DFT results also showed strong crystal anisotropy up to the maximum pressure under study. The pressure-enhanced electron density distribution along the Re and B bond direction renders the material highly incompressible along the c-axis. Our study helps to establish the fundamental basis for anisotropic compression of ReB 2 under ultrahigh pressures
36 MATERIALS SCIENCE↗
Effect of damage on elastically tailored composite laminates
A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.
Armanios, Erian↗
Tuning energy barriers by doping 2D group-IV monochalcogenides
Structural degeneracies underpin the ferroic behavior of anisotropic next-generation two-dimensional materials and lead to peculiar two-dimensional structural transformations under external fields, charge doping, and/or temperature. The most direct indicator of the ease of these transformations is an elastic energy barrier, defined as the energy difference between the (degenerate) structural ground state unit cell and a unit cell with an increased structural symmetry. Proximity of a two-dimensional material to a bulk substrate can affect the magnitude of the critical fields and/or temperature at which these transformations occur, with the first effect being a relative charge transfer, which could trigger a structural quantum phase transition. With this physical picture in mind, we report the effect of modest charge doping (within -0.2 and +0.2 electrons per unit cell) on the elastic energy barrier J s of ferroelastic black phosphorene and nine ferroelectric/ferroelastic monochalcogenide monolayers. J s is the energy needed to create a Pnm2 1 →P4/nmm two-dimensional structural transformation, and it is sensitive to the orbital character of the electronic charge added or removed. Similar to the effect on the elastic energy barrier of ferroelastic SnO monolayers, group-IV monochalcogenide monolayers show a tunable elastic energy barrier for similar amounts of doping, and a decrease (increase) of J s can be engineered under a modest hole (electron) doping of not more than one-tenth of an electron or a hole per atom.
36 MATERIALS SCIENCE↗
Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response
Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these microstructural tunings can be done throughout a part to achieve functional gradation and optimization at a structural level. To predict the performance of particular microstructural configuration and thereby overall performance, constitutive models of materials with microstructure are needed. In this work we provide neural network architectures that provide effective homogenization models of materials with anisotropic components. These models satisfy equivariance and material symmetry principles inherently through a combination of equivariant and tensor basis operations. We demonstrate them on datasets of stochastic volume elements with different textures and phases where the material undergoes elastic and plastic deformation, and show that the these network architectures provide significant performance improvements.
anisotropy↗
Graph neural networks for mechanical property prediction of 2D fiber composites
This work investigates the ability of graph neural networks (GNNs) to homogenize 2D fiber composite microstructures. We use different inhomogeneity and anisotropy indices to motivate and show that the Volume Elements (VEs) used in ML methods should ideally be far from their Representative Volume Element (RVE) size limit and, consequently, are notably anisotropic. Hence, training only the isotropic limit properties may not be acceptable. Another aspect is the need to normalize elastic stiffness values for ML, especially when high elastic contrast ratios are encountered between composite phases or in the material set. We introduce a normalization technique based on the mean-field method (MFM) to handle such high contrast ratios and train for the entire stiffness tensor. We show that the proposed GNN approaches exhibit high accuracy and efficiency compared to traditional methods and convolutional neural networks, utilizing unstructured graphs constructed from microstructure topology. Our model successfully predicts the stiffness tensor, peak strength under bulk damage, and brittle fracture initiation strength across diverse microstructure configurations while maintaining high accuracy even for extreme material contrasts and volume fractions. We also present a method to improve prediction accuracy for small dataset sizes using Voronoi partitioning.
Brittle strength↗
Anisotropy of machine building materials
The results of experimental studies of the anisotropy of elastic and strength characteristics of various structural materials, including pressure worked metals and alloys, laminated fiberglass plastics, and laminated wood plastics, are correlated and classified. Strength criteria under simple and complex stresses are considered as applied to anisotropic materials. Practical application to determining the strength of machine parts and structural materials is discussed.
Ashkenazi, Y. K.↗
Cell Model Of A Disordered Solid
Elastic properties predicted from first principles. Paper discusses generalization of cell theory of disordered (non-crystaline) solid to include anisotropic stresses. Study part of continuing effort to understand macroscopic stress-and-strain properties of solid materials in terms of microscopic physical phenomena. Emphasis on derivation, from first principles, of bulk, shear, and Young's moduli of glassy material at zero absolute temperature.
Peng, Steven T. J.↗
Composite laminated shells under internal pressure
A theoretical study is conducted of the response of filament-wound composite shells under internal pressure; a system of sixth-order ordinary differential equations is obtained by means of the cylindrically anisotropic elasticity field equations and Lekhnitskii's (1963) stress functions. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Attention is given to the influence of the degree of material anisotropy and fiber orientation on the axial and induced twisting deformation.
Yuan, F. G.↗
New insights on carbon black suspension rheology—Anisotropic thixotropy and antithixotropy
We report a detailed experimental study of peculiar thixotropic dynamics of carbon black (CB, Vulcan XC-72) suspensions in mineral oil, specifically the observation of sequential stress increase then decrease at a fixed shear rate in a step-down test. We verify that such dynamics, though peculiar, come from a true material response rather than experimental artifacts. We also reveal how this long-time stress decay is associated with antithixotropic structural change rather than viscoelastic stress relaxation by using orthogonal superposition (OSP) rheometry to probe viscoelastic moduli during the step-down tests. The orthogonal storage and loss moduli are present, showing this two-timescale recovery then decay response, which demonstrates that this response is antithixotropic, and it involves shear-induced structuring. We further show a mechanical anisotropy in the CB suspension under shear using OSP. Based on the rheological results, a microstructural schematic is proposed, considering qualitatively thixotropic structure build-up, antithixotropic densification, and anisotropic structure evolution. Our observation for these CB suspensions is outside the standard paradigm of thixotropic structure-parameter models, and the elastic response provides us with new insight into the transient dynamics of CB suspensions.
Mechanics↗
Dynamic crystallography reveals spontaneous anisotropy in cubic GeTe
Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered. In GeTe and related IV–VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the <100> c direction. We show that this anisotropy naturally emerges from a Ginzburg–Landau model that couples polarization fluctuations through long-range elastic interactions. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes and show that spontaneous anisotropy is ubiquitous in cubic IV–VI materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
An analytical and experimental study of crack extension in center-notched composites
The normal stress ratio theory for crack extension in anisotropic materials is studied analytically and experimentally. The theory is applied within a microscopic-level analysis of a single center notch of arbitrary orientation in a unidirectional composite material. The bulk of the analytical work of this study applies an elasticity solution for an infinite plate with a center line to obtain critical stress and crack growth direction predictions. An elasticity solution for an infinite plate with a center elliptical flaw is also used to obtain qualitative predictions of the location of crack initiation on the border of a rounded notch tip. The analytical portion of the study includes the formulation of a new crack growth theory that includes local shear stress. Normal stress ratio theory predictions are obtained for notched unidirectional tensile coupons and unidirectional Iosipescu shear specimens. These predictions are subsequently compared to experimental results.
Beuth, Jack L., Jr.↗
Ultrasonic and micromechanical study of damage and elastic properties of SiC/RBSN ceramic composites
Ultrasonic techniques are employed to develop methods for nondestructive evaluation of elastic properties and damage in SiC/RBSN composites. To incorporate imperfect boundary conditions between fibers and matrix into a micromechanical model, a model of fibers having effective anisotropic properties is introduced. By inverting Hashin's (1979) microstructural model for a composite material with microscopic constituents the effective fiber properties were found from ultrasonic measurements. Ultrasonic measurements indicate that damage due to thermal shock is located near the surface, so the surface wave is most appropriate for estimation of the ultimate strength reduction and critical temperature of thermal shock. It is concluded that bonding between laminates of SiC/RBSN composites is severely weakened by thermal oxidation. Generally, nondestructive evaluation of thermal oxidation effects and thermal shock shows good correlation with measurements previously performed by destructive methods.
Chu, Y. C.↗
The impact of anisotropic thermal expansion on the isothermal annealing of polycrystalline α -uranium
Although grain growth impacts microstructural evolution in a wide variety of materials systems, the effect of anisotropic thermal expansion on grain boundary mobility and texture evolution has not been widely studied. Anisotropic thermal expansion occurs in multiple non-cubic metals, and the thermomechanical processing behavior of these materials can be better understood with further study into the impact of thermal expansion on grain boundary mobility and texture evolution. In this work, we develop a mesoscale phase field model of grain growth that includes the effect of anisotropic thermal expansion, which is applied to study polycrystalline α-uranium, a highly anisotropic metal. Three-dimensional simulations on polycrystalline a-uranium with and without thermal expansion eigenstrains are performed to study the grain boundary mobility and texture evolution as a function of temperature. A strain-free temperature of 933 K is selected, and the system is studied at within the range of 873 – 933 K at intervals of ten degrees, resulting in increasing thermal eigenstrain with decreasing temperature. We also estimate a grain boundary mobility prefactor and activation energy based on existing experimental data of isothermal annealing of α-uranium. The grain boundary mobility is found to display significant deviation from Arrhenius behavior with the inclusion of thermal expansion eigenstrain as the amount of thermal eigenstrain (and thus elastic strain energy within the system) increases. This result explains an experimentally observed grain boundary mobility deviation from Arrhenius behavior. Furthermore, the texture evolution is affected, such that the grain orientations become less random with increasing thermal eigenstrain, which could explain experimentally observed texture behavior. These results indicate that the effect of thermal expansion should be considered when predicting the thermomechanical processing behavior of α-uranium and other materials with anisotropic thermal expansion.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Elasticity solutions for a class of composite laminate problems with stress singularities
A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.
Wang, S. S.↗
Friction and wear of ceramics
The adhesion, friction, wear and lubricated behaviors of both oxide and non-oxide ceramics are reviewed. Ceramics are examined in contact with themselves, other harder materials and metals. Elastic, plastic and fracture behavior of ceramics in solid state contact is discussed. The contact load necessary to initiate fracture in ceramics is shown to be appreciably reduced with tangential motion. Both friction and wear of ceramics are anisotropic and relate to crystal structure as with metals. Grit size effects in two- and three-body abrasive wear are observed for ceramics. Both free energy of oxide formation and the d valence bond character of metals are related to the friction and wear characteristics for metals in contact with ceramics. Surface contaminants affect friction and adhesive wear. For example, carbon on silicon carbide and chlorine on aluminum oxide reduce friction while oxygen on metal surfaces in contact with ceramics increases friction. Lubrication increases the critical load necessary to initiate fracture of ceramics both in indentation and with sliding or rubbing.
Buckley, D. H.↗
Tribological properties of structural ceramics
The tribological and lubricated behavior of both oxide and nonoxide ceramics are reviewed in this chapter. Ceramics are examined in contact with themselves, other harder materials and metals. Elastic, plastic and fracture behavior of ceramics in solid state contact is discussed. The contact load necessary to initiate fracture in ceramics is shown to be appreciably reduced with tangential motion. Both friction and wear of ceramics are anisotropic and relate to crystal structure as has been observed with metals. Grit size effects in two and three body abrasive wear are observed for ceramics. Both free energy of oxide formation and the d valence bond character of metals are related to the friction and wear characteristics for metals in contact with ceramics. Surface contaminants affect friction and adhesive wear. For example, carbon on silicon carbide and chlorine on aluminum oxide reduce friction while oxygen on metal surfaces in contact with ceramics increases friction. Lubrication increases the critical load necessary to initiate fracture of ceramics both in indentation and with sliding or rubbing. Ceramics compositions both as coatings and in composites are described for the high temperature lubrication of both alloys and ceramics.
Buckley, D. H.↗
Friction and wear of ceramics
The adhesion, friction, wear, and lubricated behaviors of both oxide and non-oxide ceramics are reviewed. Ceramics are examined in contact with themselves, other harder materials, and metals. Elastic, plastic, and fracture behavior of ceramics in solid state contact is discussed. The contact load necessary to initiate fracture in ceramics is shown to be appreciably reduced with tangential motion. Both friction and wear of ceramics are anisotropic and relate to crystal structure as with metals. Grit size effects in two and three body abrasive wear are observed for ceramics. Both the free energy of oxide formation and the d valence bond character of metals are related to the friction and wear characteristics for metals in contact with ceramics. Surface contaminants affect friction and adhesive wear. For example, carbon on silicon carbide and chlorine on aluminum oxide reduce friction while oxygen on metal surfaces in contact with ceramics increases friction. Lubrication increases the critical load necessary to initiate fracture of ceramics both in indentation and with sliding or rubbing.
Buckley, Donald H.↗