Search

Motivated by the existence of a universal singular stress field at bimaterial interface corners, a fair amount of work has been performed to support the use of the corresponding critical stress intensities to correlate fracture initiation. The approach is in the spirit of interface fracture mechanics but applicable to a different class of problems, specifically, when a crack does not previously exist (or cannot be detected, at least economically), and when subsequent crack propagation does not necessarily occur along the interface. Here we further progress toward the development, understanding, and application of the approach, both experimentally and theoretically, for a series of silicon/glass anodically bonded structures. To this end we designed and fabricated two series of silicon/glass anodically bonded bimaterial specimens with different interface corner geometries that commonly arise from different silicon etching technologies. Offset three-point flexure tests were performed that resulted in brittle fracture that initiated at the interface corner. From a rigorous stress analysis at the interface corner, we determined the order of the stress singularities and the angular variation of the stress fields. We computed the corresponding stress intensities via full-field finite element analyses of the silicon/glass specimens loaded in offset three-point flexure. Measured fracture data show that although the failure stress varies significantly with bond size, the corresponding critical stress intensity of the dominant mode is constant, thus providing support for its use as a fracture initiation criterion. In the light of both the stress analysis and the measured fracture data, we discuss the effect of mode mixity (loosely shearing versus opening) and show that it has little influence on the results for the specimens and loading considered in this study. Via an idealized model of a small crack, either interfacial or extending into one of the adherends, we study the effects of geometrical perturbations at the interface corner on the stress state, and discuss implications for fracture analysis and interpretation of fracture data. We also explore the prediction of the crack initiation angle and achieve reasonable success with a simple criterion based on the maximum circumferential stress near the uncracked interface corner.

Ceramics and polymers are attractive candidate materials for MEMS applications because of the wide range of properties that can be obtained, and the promise of improved performance as compared to the existing materials set for MEMS. A challenge in the fabrication of ceramic MEMS is prohibiting cracking that can occur during processing. For example, this is significant in the development of a microcasting fabrication technique from a polymer precursor for silicon carbonitride (SiCN) MEMS. In this case, shrinkage mismatch between the SiCN structure and the microfabricated mold during thermal processes leads to significant stresses that can crack the ceramic structure. Here, we propose an approach to overcome this problem that relies on demolding prior to the large shrinkage mismatch thermal processes, which itself is a nontrivial challenge. To this end, we propose and describe a microforging process that facilitates demolding and show representative results for numerous SiCN ceramic microstructures.

This paper describes the use of photopolymerization of a liquid polysilazane as a novel, versatile and cost-effective means of fabricating SiCN ceramic MEMS. SiCN is a new class of polymer-derived ceramics whose starting material is a liquid-phase polymer. By adding a photo initiator to the precursor, photolithographical patterning of the pre-ceramic polymer can be accomplished by UV exposure. The resulting solid polymer structures are then crosslinked under isostatic pressure, and pyrolyzed to form an amorphous ceramic capable of withstanding over 1500°C. By adding and curing successive layers of liquid polymer on top of one another, multi-layered ceramic MEMS can be easily fabricated. The use of photopolymerization can also be used to make thin, membrane-like ceramic structures. Key issues concerning the fabrication process are discussed. By combining photopolymerization with other in-house developed techniques such as polymer-based bonding and flip-chip bonding, three SiCN MEMS devices for high-temperature applications have been fabricated: an electrostatic actuator, a pressure transducer, and a combustion chamber. These represent a wide range of MEMS, demonstrating the versatility of this technique.

This paper studies a novel method to fabricate three-dimensional (3D) structure from 2D thermo-responsive shape memory polymer (SMP)/elastomer bilayer laminate. In this method, the shape change is actuated by the thermal mismatch strain between the SMP and the elastomer layers upon heating. However, the glass transition behavior of the SMP locks the material into a new 3D shape that is stable even upon cooling. Therefore, the second shape becomes a new permanent shape of the laminate. A theoretical model that accounts for the temperature-dependent thermomechanical behavior of the SMP material and thermal mismatch strain between the two layers is developed to better understand the underlying physics. Model predictions and experiments show good agreement and indicate that the theoretical model can well predict the bending behavior of the bilayer laminate. The model is then used in the optimal design of geometrical configuration and material selection. The latter also illustrates the requirement of thermomechanical behaviors of the SMP to lock the shape. Based on the fundamental understandings, several self-folding structures are demonstrated by the bilayer laminate design.

Recent developments in soft materials and 3D printing are promoting the rapid development of novel technologies and concepts, such as 4D printing and soft machines, that in turn require new methods for fabricating conductive materials. Despite the ubiquity of silver nanoparticles (NPs) in the conducting electrodes of printed electronic devices, their potential use in stretchable conductors has not been fully explored in 4D printing and soft machines. This paper studies the effect of thermal cure conditions on conductivity and electro-mechanical behaviors of silver ink by the direct ink write (DIW) printing approach. We found that the electro-mechanical properties of silver wires can be tailored by controlling cure time and cure temperature to achieve conductivity as well as stretchability. For the silver NP ink we used in the experiments, silver wires cured at 80 °C for 10–30 min have conductivity >1% bulk silver, Young's modulus

Variational bounds for the eŒective moduli of heterogeneous piezoelectric solids are developed by generalizing the Hashin± Shtrikman variational principles. Narrower bounds than Voigt± Reuss-type bounds are obtained by taking into account both the inclusion shape and the volume fraction. The proposed bounds for the eŒective electroelastic moduli are applicable to statistically homogeneous multiphase composites of any microgeometry and anisotropy and are self-consistent. A prescription for the calculation of the bounds is presented that takes advantage of existing, often closed-form expressions for the piezoelectric Eshelby tensor for ellipsoidal inclusions. Numerical results are presented and compared with measurements for four composite materials with diŒerent microstructures.The Hashin± Shtrikman-type bounds are much narrower than the Voigt± Reuss-type bounds. In many but not all cases they are suc ciently narrow to serve as good estimates of various elastic, dielectric and piezoelectric moduli, as assessed by comparison with measurements. Furthermore, the average of the Voigt- and Reuss-type bounds (which is often used for elastic polycrystals and composites) does not in general accurately describe the eŒective moduli of the heterogeneous solid either quantitatively or qualitatively.

We study the viscoelectroelastic behavior of heterogeneous piezoelectric solids, focusing on the connection between heterogeneity and coupled mechanical and electrical relaxations. Our approach is based on the existence of a correspondence between quasistatic viscoelectroelasticity and static piezoelectricity when linear constitutive response exists. We couple this correspondence principle with micromechanics models to predict the overall behavior of heterogeneous piezoelectric solids in terms of microstructural details. We devote specific attention to a class of two-phase materials consisting of a lossless piezoelectric phase embedded in a lossy (mechanically and electrically) matrix and obtain closed form expressions for the effective complex electroelastic moduli. Numerical results are presented and discussed, and qualitative agreement with experiment is observed.

In this paper, a novel and cost-effective technology for the fabrication of high-temperature MEMS based on injectable polymer-derived ceramics is described. Micro-molds are fabricated out of SU-8 photoresist using standard UV-photolithographic processes. Liquid-phase polymers are then cast into the molds and converted into monolithic, fully-dense ceramics by thermal decomposition. The resultant ceramic, based on the amorphous alloys of silicon, carbon and nitrogen, possess excellent mechanical and physical properties for high-temperature applications. This capability for micro-casting is demonstrated in the fabrication of simple single-layered, high aspect ratio SiCN microstructures. A polymer-based bonding technique for creating more complex three-dimensional structures is also presented.

We propose an approach to correlate fracture initiation at three-dimensional bimaterial interface corners based on the existence of a universal singular stress field in the context of linear elasticity. The idea is to correlate fracture initiation with critical values of the stress intensities of the singular fields calculated from a linear elastic stress analysis. The approach is in the spirit of interface fracture mechanics but applicable to a different class of problems, specifically, situations without a preexisting crack and situations where subsequent crack propagation does not necessarily occur along the interface. In order to validate the proposed approach, we designed and fabricated a series of aluminum/epoxy bimaterial specimens that possess well-defined three-dimensional interface corners. They consist of two perfectly bonded square prisms with varying interface dimensions and surface finishes. The specimens were loaded in four-point flexure until fracture initiated at the three-dimensional interface corner. The nominal stress at failure varied significantly with interface dimensions, thus invalidating its use as a fracture criterion. From a rigorous asymptotic analysis of the three-dimensional interface corner stress state, we determined the order of the singularity and the angular variation of the stress and displacement fields. We determined the corresponding stress intensities via full-field finite element analyses of the aluminum/epoxy specimens. Although the measured failure stress varied significantly with interface dimensions, the corresponding critical stress intensity did not, although as expected it varied with interface surface finish. These findings support the use of critical stress intensities to correlate fracture initiation at three-dimensional bimaterial interface corners.

We consider the role of small scale geometric and material features at geometric discontinuities other than a crack and study their relevance to fracture analysis. We are motivated by relatively recent experiments that show that under certain circumstances fracture initiation from geometric (sharp notches) and material (bimaterial interface corners) discontinuities can be successfully correlated with critical values of stress intensities that arise from a linear elastic analysis of the corresponding singular stress state. Implicit to such an approach is the idea that perturbations of the elastic fields near the discontinuity, which of course destroy the singular stresses, occur over a scale that is sufficiently small so that the complex behavior in this region is correlated by the elastic stress intensity. While the fracture mechanician will recognize these ideas as extensions of classical linear elastic fracture mechanics, significant differences exist and these are discussed in detail. We motivate the ideas through the use of a series of model problems in antiplane shear that are mostly amenable to exact analyses. We expect that the ideas carry through, albeit at the expense of far more complicated analysis, to planar and even three-dimensional situations.

Using dynamic methods, we measured the elastic constants of a composite comprising alumina platelets (0.2 volume fraction) in a 3:2 mullite matrix. Instead of the expected elastic stiffening, we found an elastic softening. For example, the Young modulus was 222 GPa, below mullite’s value of 228 GPa, and far below the value predicted by a solid-mechanics model assuming good alumina–mullite interfaces: 256 GPa. As possible softening sources, we considered voids, cracks, poor particle–matrix-interface bonding, and an enveloping third phase, either around the platelets or around the mullite particles. We concluded that the mullite particles must be enveloped by silica, an elastically soft phase. Solid-mechanics modeling considering a three-phase composite supports our conjecture. Our conjecture received further confirmation from careful SEM and STEM observations.

In this paper, dispersion of guided waves in a three-layered sandwich plate is considered. The focus here is on a configuration consisting of a thin anisotropic layer sandwiched between two identical isotropic layers. This configuration could model, for example, a superconducting tape where the middle layer is a brittle superconductor and the surrounding layers are isotropic and ductile. An approximate dispersion relation correct to O(h) governing the guided waves is obtained by expanding the field inside the thin middle layer in powers of the small thickness h of the layer. Numerical examples are given for two specific systems with superconducting middle layers. Some characteristic features, particularly at low frequencies, are investigated. Comparison between the exact and approximate dispersion relations are made to show that the approximation works well in the frequency interval of interest. The characteristic features may be useful for ultrasonic measurements of the anisotropic elastic constants of the thin layer.

We consider the relationship of the Eshelby inclusion theory to the Wechsler–Lieberman–Read, Bowles–Mackenzie (WLR–BM) theories of martensite crystallography. The WLR–BM theories proceed by solving for an invariant plane strain and by assuming a lattice invariant deformation, often (110) twinning or its equivalent. Eshelby’s theory estimates the strain, stress, and minimum strain energy of an ellipsoidal inclusion (or inhomogeneity) transforming in a constraining matrix. We use a Lagrangean finite-strain definition for the eigenstrain. We pay special attention to the crystallographic twinning plane and to twin coherency, specifically how they affect the eigenstrain. Focusing on many crystallographic features, including the habit plane and shape change, we find identical (within numerical accuracy) predictions of the crystallographic and energy-minimization theories for the Fe–31Ni f.c.c.–b.c.c. steel transformation, which shows enormous principal strains (0.13, 0.13, 0.20). The identity surprises us because we substitute finite strains into the infinitesimal strain inclusion theory. The inclusion-model contains all crystallographic features and, thus, is complete. This approach to martensite crystallography offers enormous new research possibilities. We enumerate twelve.

We apply our recently-developed acoustic approach to characterize the fiber orientation distribution function (ODF) of short fiber composites to predict relevant anisotropic thermomechanical properties of such composites. The acoustic approach consists of a tight coupling of acoustic velocity measurements and micromechanics modeling. It can not completely characterize the ODF, but delivers information regarding lower-order terms of the ODF when expanded in a series of generalized spherical harmonics. We apply the approach to two composite material systems (SiC/Al and glass/polyphenylene sulfide) with different overall symmetry (transversely istropic and orthotropic). For the two composites, we predict the overall anisotropic elastic moduli, thermal expansion coefficients, elastic–plastic constitutive behavior, and thermal conductivity. The predictions agree well with measurements in all cases; this demonstrates that the lower-order terms of the ODF expansion are sufficient to characterize a large number of other physical and mechanical properties of the composite, when coupled with the appropiate models. As a result, we conclude that the combination of acoustic velocity measurements and micromechanics modeling provides a powerful approach to characterize the fiber ODF, and its effect on overall composite properties.

Ogi H., Dunn M., Takashima K., et al. "Elastic properties of a unidirectional SiCf/Ti composite: Acoustic-resonance measurements and micromechanics predictions", Journal of Applied Physics, 87(6), 2769-2774 (2000) https://doi.org/10.1063/1.372254., Using the mode-selective contactless resonance ultrasound spectroscopy, we measured the complete elastic-stiffness tensor Cij and the corresponding internal-friction tensor Q-1ij of a silicon-carbide fiber unidirectionally reinforced Ti-6Al-4V-matrix composite. This material shows orthorhombic symmetry and possesses nine independent Cij and Q-1ij. We independently excited and detected an unique vibration-mode group among the eight vibration groups of a orthorhombic rectangular parallelepiped. This provides a great advantage in identifying the vibration modes of the observed resonance peaks, whose frequencies yield the Cij by solving an inverse problem. To verify the resultant Cij, we also determined Cij by point-contact resonance ultrasound spectroscopy and pulse-echo methods. Then, using the composite Cij, we inversely calculated the transverse-isotropic fiber elastic stiffnesses with micromechanics theory. With the fiber Cij and the isotropic matrix Cij, we reconstructed the composite Cij as a function of fiber-volume fraction. © 2000 American Institute of Physics.

We describe an approach to characterize the initiation toughness (resistance to fracture initiation) of silicon/glass anodic bonds based on the universal stress state that exists at the most common site of fracture initiation: the silicon/glass interface corner. The framework is universal in that it is independent of the bond size (area). It can be applied to rank bond initiation toughness as a function of processing parameters, and also used to design reliable bonds. In order to validate the theory we designed and fabricated relatively simple anodic bond test specimens and carried out a mechanical test program to characterize bond initiation toughness. We find that while failure stresses vary significantly with bond area, the inferred initiation toughness is invariant with respect to bond area. We emphasize that the primary objective of this paper is not to develop the simplest, perhaps nondestructive, test possible. Instead it is to provide a rigorous mechanics-based framework to assess the initiation toughness of anodic bonds that can be used both to evaluate bond quality and to design reliable anodic bonds.

This study follows a previous one by the authors, who calculated martensite habit planes by two methods: (1) invariant-plane strain based on a theory proposed by Wechsler–Lieberman–Read (WLR) and Bowles–Mackenzie (BM) and (2) elastic-strain energy minimization of a thin-disc inclusion based on a theory similar to those described by Eshelby, Mura, Khachaturyan, and others. Our previous study considered three example materials (In–Tl, Au–Cd, Fe–Ni) but neglected twins. The present study introduces twins. Our model contains specifically the twinning plane, often (011)A, and the WLR angle φ, the relative rigid-body rotation to ensure twin-interface coherency. We focused on the much-studied f.c.c.–b.c.c. transition in Fe–31Ni. Using inclusion theory, we found that the two-Bain strain (twinned) theory gives much better agreement with invariant-plane-strain theory calculations and with observation than did the twin-free theory.

Conditions are given for the existence of exact solutions for the effective thermal and electroelastic moduli of polycrystals exhibiting fiber texture. The exact solutions are then developed through the consideration of a class of uniform fields in a polycrystal acted upon by various external thermal and electroelastic loadings. These exact results are verified by direct orientational averaging that shows the coincidence of the Voigt and Reuss bounds on the overall moduli.

We obtain explicit closed-form solutions for the half-space Green’s functions for a transversely isotropic piezoelectric solid. The boundary of the half-space is taken to be a plane normal to the unique material axis. The Green’s functions are obtained using a formulation where general solutions in transversely isotropic piezoelectricity are expressed in terms of two potential functions; one satisfying a weighted triharmonic equation and the other satisfying a weighted harmonic equation. By assuming a series solution for the potentials we derive explicit expressions for the Green’s functions.

The complete elastic-constant tensor C[sub if] and the corresponding internal friction Q[sub ij][sup [minus]1] for a cross-ply composite are measured. It consists of silicon-carbide fibers in a Ti-6Al-4V matrix; it contained 35 vol.% fibers. With tetragonal symmetry, this composite possesses six independent C[sub ij] and Q[sub ij][sup [minus]1]. Principally, two measurement methods were used: noncontacting and point-contact resonance-ultrasound spectroscopy. Specimens were rectangular parallelepipeds measuring a few to several millimeters. By changing the magnetic-field direction, which is needed for the Lorentz-force coupling, a particular macroscopic-vibration-mode group among the eight groups for free vibration of a rectangular parallelepiped could be independently excited and detected. This provides a big advantage in identifying the vibration modes of the observed resonance peaks, whose frequencies yield the C[sub if] by solving an inverse problem. Contactless coupling allowed the measurement of intrinsic internal friction, avoiding the energy loss associated with contact coupling. The internal-friction tensor was determined by a free-decay method. Theoretical calculations were made using an extended Mori-Tanaka mean-field theory and good theory-measurement agreement was found.

A theory is developed to analyze the internal fields in heterogeneous piezoelectric solids. It is used to derive expressions for mean values and variations of the internal fields due to external loading and eigenfields. The general theory is applicable to both polycrystalline ceramics as well as matrix-based composites. After the general development, the theory is applied to multiphase matrix-based piezoelectric composites, and explicit relations are obtained for two-phase composites. Exact connections are established between the effective thermal properties and the effective electroelastic moduli, and these agree with previous results of Benveniste [3] and Dunn [15] obtained by two different approaches. The stored enthalpy of the heterogeneous solid is also expressed as an explicit function of the effective thermoelectroelastic properties. Finally, to demonstrate the applicability of the theory, numerical results for average fields and field variations are presented for a two-phase composite consisting of continuous piezoelectric fibers embedded in a polymer matrix.

We designed and fabricated a series of micromechanical test structures for microtensile testing by anisotropically etching epitaxial silicon. Specimens were fabricated to study Young’s moduli, the uniaxial tensile strength, and the strength of T-structures which are tensile bars with an abrupt reduced cross section that have a 90° corner at the point of reduction. They are a generic mimic of actual transitions that occur in micromechanical structures due to anisotropic etching. The test structures were loaded in uniaxial tension in a piezoactuated microtensile test apparatus. The applied force and crosshead displacement were recorded and displacements in the specimen gage section were directly measured using a speckle interferometry technique. During tensile loading of the T-structures, fracture always initiates at the sharp 90° corners. This results in an interesting apparent strength scaling where the nominal strength of the structures increases as their width decreases. In order to understand the fract...

Asymptotic stress and displacement fields near the tip of a sharp anisotropic bimaterial interface corner are computed using a combination of the Stroh formalism and the Williams eigenfunction expansion method. From the asymptotic fields, the path independent H-integral is developed and implemented to calculate anisotropic interface corner stress intensities. The calculation procedure is demonstrated for two glass–silicon interface corner configurations that commonly arise in practice in the microsensor industry. In each case, the bimaterial interface corner experiences mixed mode I and II loading, and accurate estimates of both stress intensities are obtained.

We studied, both experimentally and theoretically, the thermoelastic response of short-fiber composites with a preferred orientation of the short fibers, i.e., a morphological texture. Our theoretical efforts are general, being applicable to any composite system with constituents that exhibit linear thermoelastic response. We propose a relatively simple micromechanics model to predict the thermal expansion coefficient (CTE), and give simple, easily used, results for orientation distributions of practical significance. We also present a convenient approach to represent the effects of texture on thermal expansion of short fiber composites, namely, a texture map. Our experimental efforts focus on a series of extruded SiC/Al short-fiber composites that we have fully characterized. This includes measurement of the complete set of elastic constants, the volume fraction, and the fiber orientation distribution function (ODF) using neutron diffraction. We measured the axial and transverse components of the overall CTEs of these composites using a quartz-rod dilatometer. Predictions are in good agreement with measurements.

We present a procedure to calculate mode I and II notch stress intensities in anisotropic media using the path-independent H-integral. The method is based on coupling the analysis of asymptotic stress and displacement fields near a sharp notch with a path independent integral that results from the application of Betti's reciprocal theorem to the notched solid. The approach is demonstrated for two loading/geometry combinations that arise naturally in etched single crystal silicon: mode I loading of a 70.53° notch and mixed mode I and II loading of a T-structure with a 90° notch. Results agree well with those obtained by correlating computed notch-flank displacements with the asymptotic solution.

A micromechanics approach is developed to analyze the average fields and effective moduli of heterogeneous media that exhibit full coupling between stationary elastic, electric, and magnetic fields. Exact relations regarding the internal field distribution inside a heterogeneous magnetoelectroelastic solid are first established, followed by exact connections between the effective magnetoelectroelastic and thermal moduli of two-phase composites. The Mori-Tanaka mean field approach is then applied to obtain closed form expressions for the effective moduli of fibrous and laminated composites. Finally, numerical results for BaTiO3-CoFe2O4 composites are presented and discussed.

We study the fields in and around inclusions and inhomogeneities in anisotropic solids exhibiting full coupled-field behaviour using Eshelby's pioneering approach. Explicit expressions are obtained for the generalized Eshelby tensors, as are a class of shape-independent relations for the Eshelby tensors. These can be used in the same manner as Eshelby's tensor for elastic inclusions.

We present an easily understood, one-dimensional development of composite micromechanics that bridges the gap between the state of the art in composites research and composites education. By developing the general framework in a one-dimensional setting, a clear exposition of the basic ideas evolves. Exact analysis is carried out as far as possible, until one arrives at a natural point where assumptions must be introduced. The nature of the necessary assumptions is then clear and they have a simple physical interpretation. The connection between the framework presented here and traditional mechanics of materials analyses is discussed at length, as is a method by which the approach can be used in conjunction with an experimental programme to assess the validity of various assumptions. The general approach in one dimension leads naturally to the extension to two and three dimensions, along with the extension to analogous physical and thermomechanical properties.

We analyse the electroelastic fields in and around inclusions and inhomogeneities in transversely isotropic piezoelectric solids using Eshelby’s pioneering approach. Following a brief review of the general theory, we obtain explicit, closed-form expressions for the four tensors that are the piezoelectric analog of Eshelby’s tensor for spheroidal inclusions in a transversely isotropic piezoelectric medium. We focus on no specific problem pertaining to piezoelectric inclusions and inhomogeneities, but instead provide an easily-used general solution. The explicit expressions for the four tensors can be used, in the same manner as Eshelby’s tensor for elastic inclusions, to solve a wide range of problems in the mechanics and physics of heterogeneous piezoelectrics.

We propose a relatively simple micromechanics model to predict the elastic-plastic response of short-fiber composites with a preferred orientation of the reinforcement, i.e. a texture. Our theoretical efforts are directed toward a composite system with an elastic-plastic matrix containing elastic reinforcement, but the extension to allow elastic-plastic response of the reinforcement is straightforward. The theory is based on the combination of our recent model for textured elasticity of short-fiber composites and the often-used idea of a linear comparison composite to simulate the nonlinear behavior of the actual composite as proposed by Hill ( J. Mech. Phys. Solids , 1965, 13, 89) and Hutchinson ( Proc. R. Soc. London , 1970, A319, 247). We compute the effective stress of the heterogeneously deforming matrix from the distortional energy of the matrix using the approach recently proposed by Qiu and Weng ( J. appl. Mech. , 1992, 59, 261; J. appl. Mech. , 1995, 62, 1039). We give simple, easily used, results for orientation distributions of practical significance. We compare our predictions with measured stress-strain curves for an extruded SiC/6061-A1 short-fiber composite with a fiber orientation distribution that is axially symmetric about the extrusion axis. The predictions are in excellent agreement with measurements for the axial and transverse Young's moduli and the 0.2% yield stress. Good agreement is obtained between the predicted and measured flow stress over the entire range of deformation.

We present simple, closed-form expressions for stress intensity factors for cracked I-beams subjected to a bending moment. The estimates are based on the elementary strength theory for cracked beams forwarded by Herrmann and co-workers, coupled with dimensional considerations and a finite element calibration. The expressions given here are valid for the case when the crack has propagated through the flange and into the web of the beam. The simple expressions are accurate to within 5% of detailed finite element calculations for the range of practical applicability. To further demonstrate the validity of the stress intensity factor expression, we measured fracture loads for cracked polymethyl methacrylate (PMMA) I-beams in four-point flexure. Using the failure loads and our expression for the stress intensity factor, we deduce the fracture toughness. The fracture toughness so-obtained results in excellent fracture correlation for the cracked I-beams.

In the context of linear elasticity, a stress singularity of the type Knrδ(δ

We created graphene blisters that cover and seal an annular cylinder-shaped microcavity in a SiO2 substrate filled with a gas. By controlling the pressure difference between the gas inside and outside of the microcavity, we switch the graphene membrane between multiple stable equilibrium configurations. We carried out experiments starting from the situation where the pressure of the gas inside and outside of the microcavity is set equal to a prescribed charging pressure, p0 and the graphene membrane covers the cavity like an annular drum, adhered to the central post and the surrounding substrate due to van der Waals forces. We decrease the outside pressure to a value, pe which causes it to bulge into an annular blister. We systematically increase the charging pressure by repeating this procedure causing the annular blister to continue to bulge until a critical charging pressure pc(i) is reached. At this point the graphene membrane delaminates from the post in an unstable manner, resulting in a switch of graphene membrane shape from an annular to a spherical blister. Continued increase of the charging pressure results in the spherical blister growing with its height increasing, but maintaining a constant radius until a second critical charging pressure pc(o) is reached at which point the blister begins to delaminate from the periphery of the cavity in a stable manner. Here, we report a series of experiments as well as a mechanics and thermodynamic model that demonstrate how the interplay among system parameters (geometry, graphene stiffness (number of layers), pressure, and adhesion energy) results in the ability to controllably switch graphene blisters among different shapes. Arrays of these blisters can be envisioned to create pressure-switchable surface properties where the difference between patterns of annular versus spherical blisters will impact functionalities such as wettability, friction, adhesion, and surface wave characteristics.

Large arrays of 3-terminal nanoelectromechanical graphene switches are fabricated. The switch is designed with a novel geometry that leads to low actuation voltages and improved mechanical integrity, while reducing adhesion forces, which improves the reliability of the switch. A finite element model including non-linear electromechanics is used to simulate the switching behavior and to deduce a scaling relation between the switching voltage and device dimensions.

Reconfigurable multifunctional structures, which allow combined changes of shape, functionality and mechanical properties on demand, require new adaptive materials and novel chemistry that permit reversible modulation of mechanical properties in effective manner. They also demand the development of robust modeling and design tools based on a fundamental understanding of the complex and time-variant properties of the material and mechanization structure in diverse environments. In this research, we: 1) developed two new classes of two-way shape memory polymers (SMPs); 2) fostered these two SMPs to free-standing SMP composites with enhanced reversible modulation through novel composite design; 3) pursued a fundamental understanding of underlying physics of the proposed two-way SMPs and composites; 4) established modeling and simulation-design tools for applications of these novel materials for reconfigurable aerospace structures; and 5) explored design, fabrication and testing of novel SMP devices enabling for Air Force applications.

Closed-form expressions are obtained for the infinite-body Green's functions for a transversely isotropic piezoelectric medium. The four Green's functions represent the coupled elastic and electric response to an applied point force or point charge. The Green's functions are obtained using a formulation where the three displacements and the electric potential are derivable from two potential functions. When piezoelectric coupling is absent, the results reduce to those for uncoupled elasticity and electrostatics.

We studied the transversely isotropic elastic response of a series of textured short-fiber SiC/Al metal-matrix composites. By texture we mean the preferred orientation of the short fibers. We fully characterized the microstructure of the extruded SiC/Al short-fiber composites through a combination of mass-density measurements, optical and scanning electron microscopy, and neutron diffraction. We measured all components of the overall elastic-stiffness tensor of the composites using two methods: MHz-frequency pulse-echo ultrasonics and kHz-frequency acoustic-resonance spectroscopy, the latter being the first application of the method to short-fiber or particle-reinforced composites. We propose a relatively simple micro-mechanics model to predict the entire set of elastic constants, and give simple results for orientation distributions of practical significance. The predictions are in excellent agreement with measurements.

The first steps toward measuring the elastic and piezoelectric constants of piezoelectric solids using resonant ultrasound spectroscopy (RUS) have been undertaken. Specifically, free‐vibration frequencies of a piezoelectric LiNbO3 crystal were measured up to 1 MHz. The vibration frequencies of the piezoelectric parallelepiped were also predicted using the finite element method with published values of the elastic, piezoelectric, and dielectric constants of LiNbO3. Published values of these constants from different sources using different methods are in reasonably good agreement. They also agree well with measurements of some of the constants performed in this study using a pulse‐echo technique. Predicted piezoelectric vibration frequencies agree well with measured frequencies. Predictions from an elastic vibration analysis underestimate those from a piezoelectric vibration analysis by up to 12%. The results presented here suggest the feasibility of developing an inversion method to extract both the elasti...

A method for estimating the orientation distribution function (ODF) of short‐fiber composites using measured ultrasonic velocities is presented. The method is based on the coupling of (i) a forward micromechanics model of the effective ultrasonic velocities of the textured composite in terms of the coefficients in an expansion of the ODF in generalized spherical harmonics, (ii) ultrasonic measurements of the velocities, and (iii) an inversion algorithm to obtain the coefficients of the ODF from the measured velocities and the forward model. The approach is used to determine the ODF coefficients for a transversely isotropic short‐fiber SiC/Al metal‐matrix composite. The ODF coefficients obtained by inversion of ultrasonic velocities agree reasonably with those obtained from neutron‐diffraction pole figures. Corresponding elastic constants predicted with these coefficients also agree well with independently measured elastic constants.

We examine the storage and release of internal stresses in shape memory polymers reinforced with a dispersion of nanometer-scale SiC particles. A quantitative Rietveld analysis of diffraction peaks was used to measure changes in the lattice parameter of the SiC particles after permanent deformation at 25 °C, and subsequent shape recovery induced by heating to 120 °C. Under 50% compression of the composite material, the nanoparticles store a finite compressive stress, which is almost completely released during heated strain recovery. The values of the stored internal stresses in the particles are compared to values based on micromechanic calculations.

We study the mechanics of pressurized graphene membranes using an experimental configuration that allows the determination of the elasticity of graphene and the adhesion energy between a substrate and a graphene (or other two-dimensional solid) membrane. The test consists of a monolayer graphene membrane adhered to a substrate by surface forces. The substrate is patterned with etched microcavities of a prescribed volume and when they are covered with the graphene monolayer it traps a fixed number (N) of gas molecules in the microchamber. By lowering the ambient pressure, and thus changing the pressure difference across the graphene membrane, the membrane can be made to bulge and delaminate in a stable manner from the substrate. Here we describe the analysis of the membrane/substrate as a thermodynamic system and explore the behavior of the system over representative experimentally-accessible geometry and loading parameters. We carry out companion experiments and compare them to the theoretical predictions and then use the theory and experiments together to determine the adhesion energy of graphene/SiO2 interfaces. We find an average adhesion energy of 0.24 J/m2 which is lower, but in line with our previously reported values. We assert that this test, which we call the constant N blister test, is a valuable approach to determine the adhesion energy between two-dimensional solid membranes and a substrate, which is an important, but not well-understood aspect of behavior. The test also provides valuable information that can serve as the basis for subsequent research to understand the mechanisms contributing to the observed adhesion energy. Finally, we show how in the limit of a large microcavity, the constant N test approaches the behavior observed in a constant pressure blister test and we provide an experimental observation that suggests this behavior., Comment: To appear in Journal of Applied Mechanics

A theoretical approach is proposed to estimate the elastic moduli of three-phase composites consisting of a matrix phase reinforced by two-phase particles. The theoretical predictions are based on a simple extension to nondilute concentrations of the mechanical concentration factors obtained from the recent analysis of the average elastic fields in a double inclusion by Hori and Nemat-Nasser (1993). The proposed micromechanics theory can account for the effects of shapes and concentrations of both the particles and the dispersed phase in the particles. Theoretical estimates of the concentration factors and the effective elastic moduli are obtained in closed form and are diagonally symmetric and fall within the Hashin-Shtrikman-Walpole bounds for all cases considered. The theoretical predictions are in excellent agreement with experimental results obtained from pulse-echo and rod-resonance measurements of the elastic moduli of a three-phase composite consisting of an aluminum matrix reinforced by mullite/alumina particles.

An analytical model is proposed for the analysis of viscoelastic damping in two‐phase composite materials. The model is based on the coupling of the Mori–Tanaka [Acta Metall. 21, 571–574 (1973)] mean‐field approach for the elastic behavior of composite materials with the viscoelastic correspondence principle to yield predictions for the complex viscoelastic moduli. Predictions are obtained for composites containing viscoelastic reinforcement that is either aligned, randomly oriented, or planar randomly oriented. Explicit expressions for the real and imaginary components of the effective moduli are presented for the technologically important case of an isotropic viscoelastic matrix containing elastic reinforcement. The analytical predictions for the complex bulk modulus of isotropic composites and the plane‐strain bulk modulus of transversely isotropic composites are shown to lie on or within the bounds of Gibiansky and Milton [Proc. R. Soc. London Ser. A 440, 163–188 (1993)] for all reinforcement shapes a...

We present a theoretical study of the effective Poisson's ratio of elastic solids weakened by porosity and microcracks. Explicit expressions of the effective Poisson's ratio are obtained using the Mori-Tanaka mean-field approach as applied to macroscopically isotropic solids containing randomly distributed and randomly oriented spheroidal pores. We focus on the influence of pore shape and concentration and devote special attention to the limiting cases of spherical, penny-shape, and needle-shape pores. A key result of this study is that the effective Poisson's ratio depends only on pore concentration, pore shape, and Poisson's ratio of the bulk solid. In other words, it is independent of any other elastic constants of the bulk solid. Also, theratioof the shear and bulk moduli behaves similarly. Unlike other elastic constants which monotonically decrease with pore concentration, Poisson's ratio may increase, decrease, or remain unchanged as a function of pore concentration, depending on the pore shape and Poisson's ratio of the bulk solid. We discuss ramifications of these findings with regard to the elastic constants of oxide superconductors, especially the bismuth cuprates, which show unusually low Poisson's ratios. We also discuss these low Poisson's ratios, including the possibility of negative Poisson's ratios.

The authors review some of their recent studies on the effective elastic constants of composites where the occluded phase is spherical or spheroidal (oblate or prolate). From constituent properties and phase geometry, they estimated the composites` effective macroscopic elastic constants using two models: the Ledbetter-Datta scattered-plane-wave ensemble-average model and the Mori-Tanaka effective-field model. The authors measured elastic constants by three principal methods: resonance, pulse-echo, and acoustic-resonance spectroscopy. They show microstructures, measurements, and model calculations for five representative composites: SiC{sub p}/Al, Al{sub 2}O{sub 3}-mullite{sub p}/Al, Al{sub 2}O{sub 3p}/mullite, graphite{sub p}/ferrite (cast iron), voids/Ti.

A theoretical approach is proposed to estimate the effects of grain shape anisotropy on the overall response of polycrystalline piezoelectric ceramics. The self‐consistent approach is applicable to a polycrystal with arbitrary grain shapes, orientations, and anisotropy, but emphasis is placed on the effective bulk and shear moduli and the dielectric constant of a polycrystal consisting of randomly oriented piezoelectric grains. Because typical piezoelectric ceramics often contain substantial porosity, the effects of randomly oriented pores of various shapes on the overall electroelastic properties are considered. Analytical predictions are compared to simplified predictions which ignore the effects of piezoelectricity at the grain level and the effects of grain shape. Analytical predictions are in good agreement with measurements for unpoled, porous BaTiO3 polycrystals. A FORTRAN computer program developed to implement the theory is available upon request from the author.

We examine thermal expansion of textured polycrystalline aggregates and focus on polycrystals containing hexagonal monocrystals. Our analysis is based on the coupling of the Voigt–Reuss–Hill averaging procedures for elastic constants, Roe’s [R. J. Roe, J. Appl. Phys. 36, 2024 (1965)] framework for the mathematical description of the crystallite orientation‐distribution function (ODF), and the exact connections of Hashin [Z. Hashin, J. Mech. Phys. Solids 32, 149 (1984)] and Schulgasser [K. Schulgasser, J. Mech. Phys. Solids 35, 35 (1987)] between the thermal‐expansion coefficients of a polycrystalline aggregate and the corresponding polycrystal elastic constants, monocrystal elastic constants, and monocrystal thermal‐expansion coefficients. The results are simple expressions for the polycrystal thermal‐expansion coefficient in terms of the monocrystal elastic constants, thermal‐expansion coefficients, and the coefficients in the expansion of the crystallite ODF in a series of generalized spherical harmonic...

A hybrid experimental-numerical approach has been used to measure the fracture resistance of a sandwich structure consisting of a 304 stainless steel/partially stabilized zirconia ceramic-matrix composite crack-arresting layer embedded in a partially stabilized zirconia ceramic specimen. The mode 1 fracture toughness increases significantly when the crack propagates from the ceramic into the ceramic-matrix composite region. The increased toughening due to the stainless steel particles is explained reasonably well by a toughening model based on processing-induced thermal residual stresses. In addition, several experimental modifications were made to the chevron-notch wedge-loaded double cantilever beam specimen to overcome numerous problems encountered in generating a precrack in the small, brittle specimens used in this study.

A rigorous theoretical framework is presented for the analysis of thermoelectroelastic heterogeneous media. These materials include, among others, piezoelectric composite media which exhibit pyroelectricity. Formal definitions of a representative volume element, phase constitutive behavior, and numerous averaging theorems are presented. Expression for the average fields in the constituent phases in terms of thermal and electroelastic concentration factors are presented as are exact expressions for the effective moduli in terms of the concentration factors. An approach is presented to estimate the phase concentration factors which is based on the rigorous solution for the auxiliary problem of a single piezoelectric inhomogeneity embedded in an infinite matrix (which is also outlined). The theoretical principles are presented in the framework of a convenient 9 x 9 and 9 x 1 matrix formulation which greatly simplifies their numerical implementation. The framework presented here allows for the clean delineation between exact and assumed relations and allows a clear interpretation of all assumptions. Applications are made to polycrystalline piezoelectric ceramics, cracked piezoelectric solids, and two-phase piezoelectric composites.