K. C. Hwang

Thermal Expansion of Single Wall Carbon Nanotubes

We have developed an analytical method to determine the coefficient of thermal expansion (CTE) for single wall carbon nanotubes (CNTs). We have found that all CTEs are negative at low and room temperature and become positive at high temperature. As the CNT diameter decreases, the range of negative CTE shrinks. The CTE in radial direction of the CNT is less than that in the axial direction for armchair CNTs, but the opposite holds for zigzag CNTs. The radial CTE is independent of the CNT helicity, while the axial CTE shows a strong helicity dependence.

A micromechanics constitutive model of transformation plasticity with shear and dilatation effect

Abstract B ased on micromechanics, thermodynamics and microscale t → m transformation mechanism considerations a micromechanics constitutive model which takes into account both the dilatation and shear effects of the transformation is proposed to describe the plastic, pseudoelastic and shape memory behaviors of structural ceramics during transformation under different temperatures. In the derivation, a constitutive element (representative material sample) was used which contains many of the transformed m-ZrO2 grains or precipitates as the second phase inclusions embedded in an elastic matrix. Under some basic assumptions, analytic expressions for the Helmholtz and complementary free energy of the constitutive element are derived in a self-consistent manner by using the Mori-Tanaka method which takes into account the interaction between the transformed inclusions. The derived free energy is a function of externally applied macroscopic stress (or strain), temperature, volume fraction of transformed phase and the averaged stressfree transformation strain (eigenstrain) of all the transformed inclusions in the constitutive element, the latter two quantities being considered to be the internal variables describing the micro-structural rearrangement in the constitutive element. In the framework of the Hill-Rice internal variable constitutive theory, the transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for proportional and non-proportional loading histories are derived, respectively. The theoretical predictions are compared with the available experimental data of Mg-PSZ and Ce-TZP polycrystalline toughening ceramics.

The Influence of Indenter Tip Radius on the Micro-Indentation Hardness

The micro-indentation experiments have shown that the indentation hardness depends not only on the indentation depth hut also on the indenter tip radius. In fact, the indentation hardness displays opposite dependence on the indentation depth h for a sharp, conical indenter and for a spherical indenter, decreasing and increasing, respectively, with increasing h. We have developed an indentation model based on the theory of mechanism-based strain gradient plasticity to study the effect of indenter tip radius. The same indentation model captures this opposite depth dependence of indentation hardness, and shows the opposite depth dependence resulting from the different distributions of strain and strain gradient underneath a conical indenter and a spherical indenter. We have also used the finite element method to study the indentation hardness for a spherical indenter as well as for a conical indenter with a spherical tip. It is established that the effect of indenter tip radius disappears once the contact radius exceeds one half of the indenter tip radius.

Stiffness and thickness of boron-nitride nanotubes

Some of the main experimental observations related to the occurrence of exchange bias in magnetic systems are reviewed, focusing the attention on the peculiar phenomenology associated to nanoparticles with core/shell structure as compared to thin film bilayers. The main open questions posed by the experimental observations are presented and contrasted to existing theories and models for exchange bias formulated up to date. We also present results of simulations based on a simple model of a core/shell nanoparticle in which the values of microscopic parameters such as anisotropy and exchange constants can be tuned in the core, shell and at the interfacial regions, offering new insight on the microscopic origin of the experimental phenomenology. A detailed study of the magnetic order of the interfacial spins shows compelling evidence that most of the experimentally observed effects can be qualitatively accounted within the context of this model and allows also to quantify the magnitude of the loop shifts in striking agreement with the macroscopic observed values.We establish an analytic approach to determine the tensile and bending stiffness of a hexagonal boron-nitride (h-BN) monolayer and single- and multi-wall boron-nitride nanotubes (BNNTs) directly from the interatomic potential. Such an approach enables one to bypass atomistic simulations and to give the tensile and bending stiffness in terms of the parameters in the potential. For single- and multi-wall BNNTs, the stiffness also depends on the (inner most or outer most) wall radius and the number of the walls. The thickness of h-BN monolayer is also discussed.

Mechanics of noncoplanar mesh design for stretchable electronic circuits

A noncoplanar mesh design that enables electronic systems to achieve large, reversible levels stretchability (>100%) is studied theoretically and experimentally. The design uses semiconductor device islands and buckled thin interconnects on elastometric substrates. A mechanics model is established to understand the underlying physics and to guide the design of such systems. The predicted buckle amplitude agrees well with experiments within 5.5% error without any parameter fitting. The results also give the maximum strains in the interconnects and the islands, as well as the overall system stretchability and compressibility.

The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses

An investigation of asymptotic crack tip singular fields and their domain of validity is carried out for mode I cracks in solids characterized by the phenomenological strain gradient plasticity theory proposed by Fleck NA, Hutchinson JW. (Strain gradient plasticity. In: Hutchinson JW, Wu TY, editors. Advances in applied mechanics, vol. 33. New York: Academic Press, 1997. pp. 295‐361.) Separable near-tip singular fields are determined where fields quantities depend on the radial and circumferential coordinatesOr, yU according to r p fOyU. The singular field is completely dominated by the strain gradient contributions to the constitutive law. In addition to the asymptotic analysis, full field numerical solutions are obtained by a finite element method using elements especially suited to the higher order theory. It is found that the singular field provides a numerically accurate representation of the full field solution only within a distance from the tip that is a tiny fraction of the constitutive length parameter. The constitutive theory itself is not expected to be valid in this domain. Curiously, the normal traction acting across the extended crack line ahead of the crack tip is found to be compressive in the singular field. The conclusion which must be drawn is that the singular field has a tiny domain of mathematical validity (neglecting crack face interaction), but no domain of physical validity. The significant elevation of tractions ahead of the crack tip due to strain gradient hardening occurs at distances from the crack tip which are well outside this tiny domain in a region where the plasticity theory is expected to be applicable. The asymptotic singular fields are incapable of capturing the eAect of traction elevation. # 1999 Elsevier Science Ltd. All rights reserved.

The size effect on void growth in ductile materials

We have extended the Rice–Tracey model (J. Mech. Phys. Solids 17 (1969) 201) of void growth to account for the void size effect based on the Taylor dislocation model, and have found that small voids tend to grow slower than large voids. For a perfectly plastic solid, the void size effect comes into play through the ratio el/R0, where l is the intrinsic material length on the order of microns, e the remote effective strain, and R0 the void size. For micron-sized voids and small remote effective strain such that el/R0⩽0.02, the void size influences the void growth rate only at high stress triaxialities. However, for sub-micron-sized voids and relatively large effective strain such that el/R0>0.2, the void size has a significant effect on the void growth rate at all levels of stress triaxiality. We have also obtained the asymptotic solutions of void growth rate at high stress triaxialities accounting for the void size effect. For el/R0>0.2, the void growth rate scales with the square of mean stress, rather than the exponential function in the Rice–Tracey model (1969). The void size effect in a power-law hardening solid has also been studied.

Analytic and numerical studies on mode I and mode II fracture in elastic-plastic materials with strain gradient effects

This paper presents a study on fracture of materials at microscale (∼1 µm) by the strain gradient theory (Fleck and Hutchinson, 1993; Fleck et al., 1994). For remotely imposed classical K fields, the full-field solutions are obtained analytically or numerically for elastic and elastic-plastic materials with strain gradient effects. The analytical elastic full-field solution shows that stresses ahead of a crack tip are significantly higher than their counterparts in the classical K fields. The sizes of dominance zones for mode I and mode II near-tip asymptotic fields are 0.3l and 0.5l,while strain gradient effects are observed within land 2l to the crack tip, respectively, where l is the intrinsic material length in strain gradient theory and is on the order of microns in strain gradient plasticity (Fleck et al., 1994; Nix and Gao, 1998; Stolken and Evans, 1997). The Dugdale–Barenblatt type plasticity model is obtained to provide an estimation of plastic zone size for mode II fracture in materials with strain grain effects. The finite element method is used to investigate the small-scale-yielding solution for an elastic-power law hardening solid. It is found that the size of the dominance zone for the near-tip asymptotic field is the intrinsic material lengthl. For mode II fracture under the small-scale-yielding condition, transition from the remote classical KIIfield to the near-tip asymptotic field in strain gradient plasticity goes through the HRR field only when KIIis relatively large such that the plastic zone size is much larger than the intrinsic material length l. For mode I fracture under small-scale-yielding condition, however, transition from the remote classical KI field to the near-tip asymptotic field in strain gradient plasticity does not go through the HRR field, but via a plastic zone.

A Finite-Temperature Continuum Theory Based on Interatomic Potentials

There are significant efforts to develop continuum theories based on atomistic models. These atomistic-based continuum theories are limited to zero temperature (T=0 K). We have developed a finite-temperature continuum theory based on interatomic potentials. The effect of finite temperature is accounted for via the local harmonic approximation, which relates the entropy to the vibration frequencies of the system, and the latter are determined from the interatomic potential. The focus of this theory is to establish the continuum constitutive model in terms of the interatomic potential and temperature. We have studied the temperature dependence of specific heat and coefficient of thermal expansion of graphene and diamond, and have found good agreements with the experimental data without any parameter fitting. We have also studied the temperature dependence of Youngs modulus and bifurcation strain of single-wall carbon nanotube.

Mechanical properties of functionalized carbon nanotubes

Carbon nanotubes (CNTs) used to reinforce polymer matrix composites are functionalized to form covalent bonds with the polymer in order to enhance the CNT/polymer interfaces. These bonds destroy the perfect atomic structures of a CNT and degrade its mechanical properties. We use atomistic simulations to study the effect of hydrogenization on the mechanical properties of single-wall carbon nanotubes. The elastic modulus of CNTs gradually decreases with the increasing functionalization (percentage of C-H bonds). However, both the strength and ductility drop sharply at a small percentage of functionalization, reflecting their sensitivity to C-H bonds. The cluster C-H bonds forming two rings leads to a significant reduction in the strength and ductility. The effect of carbonization has essentially the same effect as hydrogenization.