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Khanh Chau Le

Publications and source records attributed to Khanh Chau Le.

36 records · Page 2Linked to original sources
arXiv2020

Thermodynamic dislocation theory for polycrystals under tension/compression

Starting from the assumption that all possible orientations of grains are equally probable, we prove that the geometric factor of thermodynamic dislocation theory for polycrystals subjected to axially symmetric tension or compression must be equal to 2. We then use large-scale least-square analysis to identify the physics based parameters of this theory and show that the simulated stress-strain curves for OFHC copper, ARMCO iron and 4340 steel agree well with the experiments of Johnson and Cook.

cond-mat.mtrl-sci↗
arXiv2020

Asymptotically exact theory of fiber-reinforced composite beams

An asymptotic analysis of the energy functional of a fiber-reinforced composite beam with a periodic microstructure in its cross section is performed. From this analysis the asymptotically exact energy as well as the 1-D beam theory of first order is derived. The effective stiffnesses of the beam are calculated in the most general case from the numerical solution of the cell and homogenized cross-sectional problems.

physics.class-ph↗
arXiv2019

Thermodynamic dislocation theory: Finite deformations

The present paper extends the thermodynamic dislocation theory initiated by Langer, Bouchbinder and Lookman [2010] to non-uniform finite plastic deformations. The equations of motion are derived from the variational equation involving the free energy density and the positive definite dissipation function. We also consider the simplified theory by neglecting the excess dislocations. For illustration, the problem of finite strain constrained shear of single crystals with one active slip system is solved within the proposed theory.

cond-mat.mtrl-sci↗
arXiv2018

Thermal softening during high-temperature torsional deformation of aluminum bars

A simple extension of the thermodynamic dislocation theory to non-uniform plastic deformations is proposed for an analysis of high-temperature torsion of aluminum bars. Employing a small set of physics-based parameters, which we expect to be approximately independent of strain rate and temperature, we are able to fit experimental torque-twist curves for five different twist rates and at one fixed ambient temperature. We find that thermal softening due to temperature rise is significant at high twist rates.

cond-mat.soft↗
arXiv2018

Thermodynamic dislocation theory: Size effect in torsion

The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here for the analysis of twisted copper wires. With a small set of physical parameters that we expect to be independent of strain rate and temperature, we can simulate the torque-twist curves that match the experimental ones of Liu et al. (2012). It is shown that the size effect results from the accumulation and pile-up of excess dislocations.

cond-mat.mtrl-sci↗
arXiv2018

Thermodynamic dislocation theory: Bauschinger effect

The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here to simulate the stress-strain curves for crystals subjected to anti-plane shear-controlled load reversal. We show that the presence of the positive back stress during the load reversal reduces the magnitude of shear stress required to pull excess dislocations back to the center of the specimen. There, the excess dislocations of opposite signs meet and annihilate each other leading to the Bauschinger effect.

cond-mat.mtrl-sci↗
arXiv2018

Non-uniform plastic deformations of crystals undergoing anti-plane constrained shear

The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. By incorporating the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict the stress-strain curves and the dislocation densities.

cond-mat.mtrl-sci↗
arXiv2017

Thermodynamic dislocation theory of adiabatic shear banding in steel

The statistical-thermodynamic dislocation theory developed in our earlier studies is used here in an analysis of the experimental observations of adiabatic shear banding in steel by Marchand and Duffy (1988). Employing a small set of physics-based parameters, which we expect to be approximately independent of strain rate and temperature, we are able to explain experimental stress-strain curves at six different temperatures and four different strain rates. We make a simple model of a weak notch-like disturbance that, when driven hard enough, triggers shear banding instabilities that are quantitatively comparable with those seen in the experiments.

cond-mat.mtrl-sci↗
arXiv2016

Optimal parameters uncoupling vibration modes of oscillators

A novel optimization concept for an oscillator with two degrees of freedom is proposed. By using specially defined motion ratios, we control the action of springs and dampers to each degree of freedom of the oscillator. If the potential action of the springs in one period of vibration, used as the payoff function for the conservative oscillator, is maximized, then the optimal motion ratios uncouple vibration modes. The same result holds true for the dissipative oscillator. The application to optimal design of vehicle suspension is discussed.

physics.class-ph↗
arXiv2016

An asymptotically exact theory of smart sandwich shells

An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.

physics.class-ph↗
arXiv2016

Distribution of dislocations in twisted bars

An asymptotically exact continuum dislocation theory of single crystal bars under torsion is proposed. The dislocation distribution minimizing energy of the bar with zero torque is shown to be uniform. If the applied torque is non-zero, the minimizer exhibits a dislocation-free zone at the outer ring of the bar's cross-section. The non-uniform distribution of dislocations in equilibrium as well as the twist angle per unit length are found in terms of the given torque. With the energy dissipation being taken into account, there exists an elastic core region, while dislocation are concentrated in a ring between two dislocation-free zones. This leads to the change of the stress distribution increasing the critical threshold of the torque.

cond-mat.mtrl-sci↗
arXiv2015

A single crystal beam bent in double slip

The theory of plastic bending of single crystal beam having two active slip systems is proposed. Applying the variational-asymptotic method we reduce the energy functional of the beam to the one-dimensional energy functional which admits analytical solutions for the symmetric slip systems. The threshold value at the onset of plastic yielding, the dislocation density, as well as the moment-curvature curve are found. We solve also a similar problem that takes the energy dissipation into account.

cond-mat.mtrl-sci↗
arXiv2015

Stress and dislocation distributions near a crack tip in ductile single crystals

Within the continuum dislocation theory the asymptotic analysis of the plane strain crack problem for a single crystal having only one active slip system on each half-plane is provided. The results of this asymptotic analysis show that the square root stress singularity remains valid during the plastic deformation, while the dislocation density is proportional to the stress intensity factor and distributed as the square root of the distance from the crack tip. The analytical solution for the angular distribution of the dislocation density is found.

cond-mat.mtrl-sci↗
arXiv2015

Three-dimensional continuum dislocation theory

A three-dimensional continuum dislocation theory for single crystals containing curved dislocations is proposed. A set of governing equations and boundary conditions is derived for the true placement, plastic slips, and loop functions in equilibrium that minimize the free energy of crystal among all admissible functions, provided the resistance to the dislocation motion is negligible. For the non-vanishing resistance to dislocation motion the governing equations are derived from the variational equation that includes the dissipation function. A simplified theory for small strains is also provided. An asymptotic solution is found for the two-dimensional problem of a single crystal beam deforming in single slip and simple shear.

cond-mat.mtrl-sci↗
arXiv2015

Self-energy of dislocations and dislocation pileups

A continuum model of dislocation pileups that takes the self-energy of dislocations into account is proposed. An analytical solution describing the distribution of dislocations in equilibrium is found from the energy minimization. Based on this solution we show (i) the existence of a critical threshold stress for the equilibrium of dislocations within a double pileup, and (ii) the existence of a non-linear regime in which the number of dislocations in a double pileup does not scale linearly with the resolved external shear stress, contrary to the classical double pileup model.

cond-mat.mtrl-sci↗
arXiv2015

Formation of grains and dislocation structure of geometrically necessary boundaries

A continuum dislocation model of formation of grains whose boundaries have a non-vanishing thickness is proposed. For a single crystal deforming in simple shear the lamellar structure of grains with thin layers containing dislocations as the geometrically necessary boundaries turns out to be energetically preferable. The thickness and the energy of this type of grain boundary are computed as functions of the misorientation angle.

cond-mat.mtrl-sci↗
arXiv2015

Continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening

This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal deforming in single slip is solved within the proposed theory. The distribution of geometrically necessary dislocations in the final state of equilibrium as well as the stress-strain curve exhibiting the Bauschinger translational work hardening and the size effect are found. Comparison with the stress-strain curve obtained from the continuum dislocation theory without statistically stored dislocations and Taylor hardening is provided.

cond-mat.mtrl-sci↗