Huajian Gao

Indentation size effects in crystalline materials: A law for strain gradient plasticity

Abstract We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].

Materials become insensitive to flaws at nanoscale: Lessons from nature

Natural materials such as bone, tooth, and nacre are nanocomposites of proteins and minerals with superior strength. Why is the nanometer scale so important to such materials? Can we learn from this to produce superior nanomaterials in the laboratory? These questions motivate the present study where we show that the nanocomposites in nature exhibit a generic mechanical structure in which the nanometer size of mineral particles is selected to ensure optimum strength and maximum tolerance of flaws (robustness). We further show that the widely used engineering concept of stress concentration at flaws is no longer valid for nanomaterial design.

Mechanism-based strain gradient plasticity : I. Theory

Abstract A mechanism-based theory of strain gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of strain gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of strain gradient plasticity in which the Taylor model is adopted as a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.

Dislocation nucleation governed softening and maximum strength in nano-twinned metals

In conventional metals, there is plenty of space for dislocations—line defects whose motion results in permanent material deformation—to multiply, so that the metal strengths are controlled by dislocation interactions with grain boundaries and other obstacles. For nanostructured materials, in contrast, dislocation multiplication is severely confined by the nanometre-scale geometries so that continued plasticity can be expected to be source-controlled. Nano-grained polycrystalline materials were found to be strong but brittle, because both nucleation and motion of dislocations are effectively suppressed by the nanoscale crystallites. Here we report a dislocation-nucleation-controlled mechanism in nano-twinned metals in which there are plenty of dislocation nucleation sites but dislocation motion is not confined. We show that dislocation nucleation governs the strength of such materials, resulting in their softening below a critical twin thickness. Large-scale molecular dynamics simulations and a kinetic theory of dislocation nucleation in nano-twinned metals show that there exists a transition in deformation mechanism, occurring at a critical twin-boundary spacing for which strength is maximized. At this point, the classical Hall–Petch type of strengthening due to dislocation pile-up and cutting through twin planes switches to a dislocation-nucleation-controlled softening mechanism with twin-boundary migration resulting from nucleation and motion of partial dislocations parallel to the twin planes. Most previous studies did not consider a sufficient range of twin thickness and therefore missed this strength-softening regime. The simulations indicate that the critical twin-boundary spacing for the onset of softening in nano-twinned copper and the maximum strength depend on the grain size: the smaller the grain size, the smaller the critical twin-boundary spacing, and the higher the maximum strength of the material.

Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic

Abstract Structural reliability concerns of various electromechanical devices call for a better understanding of the mechanisms of fracture in piezoelectric ceramics subjected to combined mechanical and electrical loading. For these materials, due to unexplained discrepancies between theory and experiments, even the basic criterion of fracture remains a point of controversy. A viewpoint adopted in this paper is to model piezoelectric ceramics as a class of mechanically brittle and electrically ductile solids. As a first step toward understanding the effects of electric yielding, a strip saturation model is developed for a finite crack perpendicular or parallel to the poling axis of an infinite poled piezoelectric ceramics medium with electrical polarization reaching a saturation limit along a line segment in front of the crack. This model may be considered as a generalization of the classical Dugdale model for plastic yielding near cracks in thin metal sheets. The essential features of the strip saturation model are analyzed via a simplified electroelasticity formulation. Two energy release rates emerge from this analysis. An “apparent” or global energy release rate appears when evaluating J-integral along a contour surrounding both the electrical yielding strip and the crack tip. Under small scale yielding conditions, this energy release rate is equal to that of a linear piezoelectric crack without electrical yielding. A “local” energy release rate is obtained by evaluating J along an infinitesimal contour near the crack tip. The local energy release rate gives predictions which seem to be in broad agreement with experimental observations. It is also interesting that the local energy release rate is independent of the strength and size of electrical yielding.

Mechanism-based strain gradient plasticity—II. Analysis

A mechanism-based theory of strain gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. Such a linear dependence is consistent with the Taylor plastic work hardening model relating the flow stress to dislocation density. This part of this paper provides a detailed analysis of the new theory, including equilibrium equations and boundary conditions, constitutive equations for the mechanism-based strain gradient plasticity, and kinematic relations among strains, strain gradients and displacements. The theory is used to investigate several phenomena that are influenced by plastic strain gradients. In bending of thin beams and torsion of thin wires, mechanism-based strain gradient plasticity gives a significant increase in scaled bending moment and scaled torque due to strain gradient effects. For the growth of microvoids and cavitation instabilities, however, it is found that strain gradients have little effect on micron-sized voids, but submicron-sized voids can have a larger resistance against void growth. Finally, it is shown from the study of bimaterials in shear that the mesoscale cell size has little effect on global physical quantities (e.g. applied stresses), but may affect the local deformation field significantly.

Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model

An analytical model based on a molecular mechanics approach is presented to relate the elastic properties of a single-walled carbon nanotube to its atomic structure. We derive closed-form expressions for elastic modulus and Poissons ratio as a function of the nanotube diameter. Properties at different length scales are directly connected via these expressions. The analytically calculated elastic properties for achiral nanotubes using force constants obtained from experimental data of graphite are compared to those based on tight binding numerical calculations. This study represents a preliminary effort to develop analytical methods of molecular mechanics for applications in nanostructure modeling.

The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites

Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the stiffening effect of carbon nanotubes is quantitatively investigated by micromechanics methods. Especially, the effects of the extensively observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight nanotubes. Then, a novel micromechanics model is developed to consider the waviness or curviness effect of nanotubes, which are assumed to have a helical shape. Finally, the influence of nanotube agglomeration on the effective stiffness is analyzed. Analytical expressions are derived for the effective elastic stiffness of carbon nanotube-reinforced composites with the effects of waviness and agglomeration. It is found that these two mechanisms may reduce the stiffening effect of nanotubes significantly. The present study not only provides the relationship between the effective properties and the morphology of carbon nanotubereinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites. @DOI: 10.1115/1.1751182#

Graphene microsheets enter cells through spontaneous membrane penetration at edge asperities and corner sites

Understanding and controlling the interaction of graphene-based materials with cell membranes is key to the development of graphene-enabled biomedical technologies and to the management of graphene health and safety issues. Very little is known about the fundamental behavior of cell membranes exposed to ultrathin 2D synthetic materials. Here we investigate the interactions of graphene and few-layer graphene (FLG) microsheets with three cell types and with model lipid bilayers by combining coarse-grained molecular dynamics (MD), all-atom MD, analytical modeling, confocal fluorescence imaging, and electron microscopic imaging. The imaging experiments show edge-first uptake and complete internalization for a range of FLG samples of 0.5- to 10-μm lateral dimension. In contrast, the simulations show large energy barriers relative to kBT for membrane penetration by model graphene or FLG microsheets of similar size. More detailed simulations resolve this paradox by showing that entry is initiated at corners or asperities that are abundant along the irregular edges of fabricated graphene materials. Local piercing by these sharp protrusions initiates membrane propagation along the extended graphene edge and thus avoids the high energy barrier calculated in simple idealized MD simulations. We propose that this mechanism allows cellular uptake of even large multilayer sheets of micrometer-scale lateral dimension, which is consistent with our multimodal bioimaging results for primary human keratinocytes, human lung epithelial cells, and murine macrophages.

Cell entry of one-dimensional nanomaterials occurs by tip recognition and rotation

Materials with high aspect ratio, such as carbon nanotubes and asbestos fibres, have been shown to cause length-dependent toxicity in certain cells because these long materials prevent complete ingestion and this frustrates the cell. Biophysical models have been proposed to explain how spheres and elliptical nanostructures enter cells, but one-dimensional nanomaterials have not been examined. Here, we show experimentally and theoretically that cylindrical one-dimensional nanomaterials such as carbon nanotubes enter cells through the tip first. For nanotubes with end caps or carbon shells at their tips, uptake involves tip recognition through receptor binding, rotation that is driven by asymmetric elastic strain at the tube-bilayer interface, and near-vertical entry. The precise angle of entry is governed by the relative timescales for tube rotation and receptor diffusion. Nanotubes without caps or shells on their tips show a different mode of membrane interaction, posing an interesting question as to whether modifying the tips of tubes may help avoid frustrated uptake by cells.