Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

Triaxial tension–compression tests for multiaxial cyclic plasticity

The aim of this paper is to present triaxial tension–compression tests and a new triaxial specimen devoted to the study of cyclic plasticity under non-proportional loadings. Because the stress state in the central part of the specimen is not homogeneous, the analysis of the tests need a 3D finite element computation. The constitutive equations used in the simulations have been deduced from complex tension–torsion tests. The comparison between the structural analysis and the experimental results allows to determine the accuracy of the set of constitutive equations and if needed to optimize this set by modifying some hardening rules.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

Analysis of phase transformation from austenite to martensite in NiTi alloy strips under uniaxial tension

Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation.This work presents an analysis using the theory of phase transfor- mation.The jump of deformation gradient across the interface between two phases and the Maxwell relation are considered.Governing equations for the phase transformation are derived.The analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique,real and physically acceptable solution.The equa- tions are solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress,the stresses and strains inside both anstenite and martensite phases, and the transformation-front orientation angle are determined to be in reasonably good agreement with experimental observations.     

Superelastic behavior in tension–torsion of an initially-textured Ti–Ni shape-memory alloy

A recently-developed crystal-mechanics-based constitutive model for polycrystalline shape-memory alloys [J. Mech. Phys. Solids 49 (2001) 909] is shown to quantitatively predict the superelastic response of an initially-textured Ti–Ni alloy in (i) a proportional-loading, combined tension–torsion experiment, as well as (ii) a path-change, tension–torsion experiment.     

The effect of viscosity,surface tension and non-linearity on Richtmyer–Meshkov instability

A weakly non-linear theoretical model of the Richtmyer–Meshkov instability between two viscous fluids with surface tension is proposed. The model is based on the application of singular perturbations techniques to the incompressible Navier–Stokes equations written for two superposed immiscible fluids. A simple analytical law of interface deformation is obtained, in which the effects of viscosity, surface tension and non-linearities appear under the form of independent terms. The model gives also access to the velocity and pressure distribution in the fluids, which can be of interest for estimating vorticity diffusion in the fluids. A comparison with accurate direct numerical simulations confirms the validity of the proposed theory. The interface deformation law is then applied to typical experimental configurations in order to estimate the relative influence of surface tension, viscosity and non-linearities on the growth of perturbations for each of the chosen cases.     

Micromechanical modeling of the elastic–viscoplastic behavior of polycrystalline steels

A self-consistent model developed to describe the elastic–viscoplastic behavior of heterogeneous materials is applied to low carbon steels to simulate tensile tests at various strain rates in the low temperature range. The choice of crystalline laws implemented in the model is discussed through the viscoplastic flow rule and several strain-hardening laws. Comparisons between three work-hardening models show that the account of dislocation annihilation improves the results on simulations at large strains. The evolution of the Lankford coefficients and texture development are also successfully simulated. Some microstructural aspects of deformation such as the stored energy and the evolution of the flow rates are discussed. By including the dislocation density on each slip system as internal variable, intragranular heterogeneities are underscored.     

Dual-phase steel sheets under cyclic tension–compression to large strains: Experiments and crystal plasticity modeling

In this work, we develop a physically-based crystal plasticity model for the prediction of cyclic tension–compression deformation of multi-phase materials, specifically dual-phase (DP) steels. The model is elasto–plastic in nature and integrates a hardening law based on statistically stored dislocation density, localized hardening due to geometrically necessary dislocations (GNDs), slip-system-level kinematic backstresses, and annihilation of dislocations. The model further features a two level homogenization scheme where the first level is the overall response of a two-phase polycrystalline aggregate and the second level is the homogenized response of the martensite polycrystalline regions. The model is applied to simulate a cyclic tension–compression–tension deformation behavior of DP590 steel sheets. From experiments, we observe that the material exhibits a typical decreasing hardening rate during forward loading, followed by a linear and then a non-linear unloading upon the load reversal, the Bauschinger effect, and changes in hardening rate during strain reversals. To predict these effects, we identify the model parameters using a portion of the measured data and validate and verify them using the remaining data. The developed model is capable of predicting all the particular features of the cyclic deformation of DP590 steel, with great accuracy. From the predictions, we infer and discuss the effects of GNDs, the backstresses, dislocation annihilation, and the two-level homogenization scheme on capturing the cyclic deformation behavior of the material.     

The Onset of Prandtl–Darcy–Prats Convection in a Horizontal Porous Layer

We consider the effect of finite Prandtl–Darcy numbers of the onset of convection in a porous layer heated isothermally from below and which is subject to a horizontal pressure gradient. A dispersion relation is found which relates the critical Darcy–Rayleigh number and the induced phase speed of the cells to the wavenumber and the imposed Péclet and Prandtl–Darcy numbers. Exact numerical solutions are given and these are supplemented by asymptotic solutions for both large and small values of the governing nondimensional parameters. The classical value of the critical Darcy–Rayleigh number is $4\pi ^2$ 4 π 2 , and we show that this value increases whenever the Péclet number is nonzero and the Prandtl–Darcy number is finite simultaneously. The corresponding wavenumber is always less than $\pi $ π and the phase speed of the convection cells is always smaller than the background flux velocity.     

Modeling of particle–resin suspension impregnation in compression resin transfer molding of particle-filled,continuous fiber reinforced composites

A particle–resin suspension impregnation model is used for analyzing the mold filling process in compression resin transfer molding (CRTM) of particle-filled, continuous fiber composites. The model is based on Darcy flow coupled with particle filtration and is applicable to two-dimensional impregnation through isotropic/anisotropic fiber preforms. Comparisons with simple analytical solutions and experimental results from the literature were made to validate the numerical solution. Simulations showed that CRTM was advantageous over resin transfer molding (RTM) for smaller non-homogeneity in composite microstructure, when particle filtration was high. Limits on certain process parameters were observed beyond which molding pressures in CRTM became comparable with those in RTM. The preform anisotropy was effective in the particle distribution profile. The choice of inlet gate configuration in CRTM was found influential in the particle distribution homogeneity and molding pressures. The developed modeling tool can be extended to analyze any composite liquid molding process involving particle fillers.     

The homogenization method of Bakhvalov–Pobedrya in the composite mechanics

The role of Professor Pobedrya in the development of the homogenization method in the mechanics of composite materials with periodic structure is discussed. A generalization of the homogenization method is proposed to the case of heterogeneous bodies whose structure is not periodic.     

Grain–boundary interactions and orientation effects on crack behavior in polycrystalline aggregates

A dislocation-density grain–boundary interaction scheme has been developed to account for the interrelated dislocation-density interactions of emission, absorption and transmission in GB regions. The GB scheme is based on slip-system compatibility, local resolved shear stresses, and immobile and mobile dislocation-density accumulation at critical GB locations. To accurately represent dislocation-density evolution, a conservation law for dislocation-densities is used to balance dislocation-density absorption, transmission and emission from the GB. The behavior of f.c.c. polycrystalline copper, with different random low and high angle GBs, are investigated for different crack lengths. For aggregates with random low angle GBs, dislocation-density transmission dominates at the GBs, which can indicate that the low angle GB will not significantly change crack growth directions. For aggregates with random high angle GBs, extensive dislocation-density absorption and pile-ups occur. The high stresses associated with this behavior, along the GBs, can result in intergranular crack growth due to potential crack nucleation sites in the GB.     

The Dielectric Permittivity of Crystals in the Reduced Hartree–Fock Approximation

In a recent article (Cancès et al. in Commun Math Phys 281:129–177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree–Fock model, the ground state electronic density matrix is decomposed as ${\gamma = \gamma^0_{\rm per} + Q_{\nu,\varepsilon_{\rm F}}}$ , where ${\gamma^0_{\rm per}}$ is the ground state density matrix of the host crystal and ${Q_{\nu,\varepsilon_{\rm F}}}$ the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ε _F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix ${Q_{\nu,\varepsilon_{\rm F}}}$ (which is known to be a self-adjoint Hilbert–Schmidt operator on ${L^2(\mathbb{R}^3)}$ ). We show in particular that if ${\int_{\mathbb{R}^3}\,\nu \neq 0, Q_{\nu,\varepsilon_{\rm F}}}$ is not trace-class. Moreover, the associated density of charge is not in ${L^1(\mathbb{R}^3)}$ if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of ${Q_{\nu,\varepsilon_{\rm F}}}$ . Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler–Wiser formula.     

The effects of chain conformation in the microfluidic entry flow of polymer–surfactant systems

An associative polymer–surfactant system has been used to observe the effects of chain conformation in the entry flow through a microfabricated planar 16:1:16 contraction–expansion geometry. The well-studied system of the flexible polymer poly(ethylene oxide) (PEO) and anionic surfactant sodium dodecyl sulfate (SDS) was used. Dilute polymer solutions with increasing SDS concentration were characterized in steady and dynamic shear, as well as capillary breakup extensional rheology. Based on this characterization, the primary quantitative difference is an increase in zero-shear viscosity as a result of the PEO chain expansion brought on by association of SDS surfactant micelles. However, these quantitatively similar solutions were observed to exhibit much more qualitatively different flow patterns via fluorescent streak imaging in the entry flow. In contrast to previous work on PEO solutions, the PEO–SDS systems were observed to transition to a steady viscoelastic flow regime characterized by stable lip vortices at much lower elasticity and Weissenberg numbers. The resulting insight gained regarding the utility of microfluidic flows in elucidating effects of subtle conformational changes further illustrates the potential for using microfabricated devices as rheometric tools for measuring the properties of dilute and weakly viscoelastic fluids.     

Mechanical and microstructural investigations of an austenitic stainless steel under non-proportional loadings in tension–torsion-internal and external pressure

This paper is concerned with the experimental behaviour of a 316 austenitic stainless steel at room temperature and under non-proportional cyclic and ratchet strainings in tension–torsion-internal and external pressures. The main investigations deal with the over-strengthening due to the multiaxiality of the loadings. A classification of the different kinds of cyclic tests can be established with respect to the increasing maximum over-strengthening. Concerning the ratchetting effect, from tests performed under in or out-of-phase cyclic tension–torsion plus a static stress due to internal pressure, it is shown that the rate of the diametrical ratchetting is an increasing function of the phase lag between the cyclic components. Dislocation substructures resulting from cyclic and ratchetting tests are investigated and various kinds of microstructures are reported. An analysis of these microstructures shows that the over-strengthening is not solely related to the slip multiplicity but also to the development of heterogeneous substructures. It has been also possible to evaluate the intra- and inter-granular back stresses and the effective stress as a function of the strengthening.     

The Horton–Rogers–Lapwood Problem Revisited: The Effect of Pressure Work

The problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows that, while the contribution of viscous dissipation is ineffective, the contribution of the pressure work may be important. The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical value of the Darcy– Rayleigh number may be considerably affected by the pressure work contribution, the critical value of the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh number.