•Interfacial energy storage and dissipation computed by incremental energy minimization.•Multiscale modelling of interfacial energy effects in SMA polycrystals.•Interfacial energy strongly affects ...the shape and width of the stress strain hysteresis loop.•Non monotonic nonlinear stress strain response predicted for the material.•Stress plateau predicted for the tensile specimen deforming nonuniformly.
The effect of formation and evolution of stress-induced martensitic microstructures on macroscopic mechanical properties of shape memory alloys in the pseudoelastic regime is investigated with account for size-dependent energy of interfaces. A quantitative relationship is established between the changes in free energy and dissipation on the interfaces at three microstructural scales and the overall mechanical characteristic of the material under tensile loading. The multiscale analysis carried out for a polycrystalline NiTi shape memory alloy has revealed that the interfacial energy storage and dissipation can strongly affect the shape and width of the stress–strain hysteresis loop. The predicted non-monotonic stress–strain response for the material of a selected grain size shows a remarkable similarity to the experimental one extracted from a tensile test of a laminate by Hallai and Kyriakides (2013). By the classical Maxwell construction, the non-monotonic response for a material element results in a commonly observed stress plateau for a tensile specimen, which is associated with the propagation of phase transformation fronts. This behaviour is confirmed with striking accuracy by 3D finite-element computations performed for a macroscopic tensile specimen, in which propagating instability bands are treated explicitly.
A recently developed gradient-enhanced crystal-plasticity model is applied to predict the size effects in wedge indentation. In the model, the internal length scale is defined through standard ...quantities that appear in the underlying non-gradient hardening law. A careful calibration of the non-gradient hardening law is thus performed, and the model is validated against published experimental results. To this end, a comprehensive computational study of wedge indentation into a nickel single crystal is performed, and the obtained results show a good agreement with the experiment in terms of the load–penetration depth curves for three wedge angles, as well as in terms of the distributions of lattice rotation, GND density, and net Burgers vector. For the indentation depth of about 200 μm, as employed in the experiment, the predicted size effects are insignificant. Accordingly, the size effects are next studied for the indentation depth varied between 200 μm and 1 μm. As an intermediate result, apparently not published to date, the general 3D crystal plasticity model with anisotropic hardening is consistently reduced to a 2D plane-strain model in which plastic deformation is realized by three effective in-plane slip systems, each representing two crystallographic slip systems.
•Crystal plasticity model employing the `minimal' gradient enhancement of the hardening law.•Consistent derivation of a 2D plane-strain CP model with three effective in-plane slip systems.•Comprehensive study of wedge indentation into a nickel single crystal for three wedge angles.•Load-depth curves, lattice rotations and GND distribution validated against experiment.•Prediction of the size effect on hardness, residual imprint, lattice rotation and GND distribution.
•Enhanced contact model with non-standard contact conditions for a Cosserat continuum.•Contact occurs through rigid microblocks that rotate according to the Cosserat kinematics.•Consistent coupling ...of displacements and microrotations at the contact interface.•Analytical solution for the boundary layers induced by the non-standard contact conditions.•New qualitative features and size effects observed in a 2D Hertz-like contact problem.
Generalized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or for the respective generalized tractions. In this paper, we address several related open problems, namely, how to enhance the classic contact conditions to include the effects of the additional kinematic variables, how to link the enhanced contact model to the underlying microstructure of the solid, and how to do it in a consistent manner. As a first step towards a new class of contact models for generalized continua, a microblock contact model is derived for a Cosserat solid based on simple micromechanical considerations. To illustrate the non-trivial effects introduced by the non-standard boundary conditions, the problem of compression of an infinite strip with nonaligned microblocks is considered, and the analytical solution is derived for the corresponding boundary layers. A Hertz-like contact problem is also solved numerically with the focus on non-standard features of the solution and on the related size effects.
This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among ...the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.
Display omitted
•Modelling of and experiment on the evolution of contact area between soft solids under shear.•Computational finite-deformation model combining non-adhesive contact and non-linear ...elasticity.•Anisotropic area reduction quantitatively reproduced by the model with no adjustable parameter.•Three elementary mechanisms revealed: local contact lifting (main contributor), contact laying and in-plane deformation.•The findings are supported by an original experiment employing particle-tracking analysis.
Display omitted
Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models. Here we show that quantitative agreement with recent high-load experiments can be obtained, with no adjustable parameter, using a non-adhesive model, provided that finite deformations are taken into account. Analysis of the model uncovers the basic mechanisms underlying anisotropic shear-induced area reduction, local contact lifting being the dominant one. We confirm experimentally the relevance of all those mechanisms, by tracking the shear-induced evolution of tracers inserted close to the surface of a smooth elastomer sphere in contact with a smooth glass plate. Our results suggest that finite deformations are an alternative to adhesion, when interpreting a variety of sheared contact experiments involving soft materials.
•We find hardening exponent in crystal plasticity from spherical indentation test.•The procedure is based on finite element study of deformed surface topography.•Hardening exponent is strongly ...correlated with anisotropic pile-up/sink-in pattern.•New hardening exponent indicator is defined as ring-based pile-up/sink-in volume.•Experimental verification by compression of Cu single crystal is satisfactory.
A novel methodology is proposed for estimating the strain hardening exponent of a metal single crystal directly from the spherical indentation test, without the need of solving the relevant inverse problem. The attention is focused on anisotropic piling-up and sinking-in that occur simultaneously in different directions, in contrast to the standard case of axial symmetry for isotropic materials. To correlate surface topography parameters with the value of material hardening exponent, a finite-element study of spherical indentation has been performed within a selected penetration depth range using a finite-strain crystal plasticity model. It is shown how the power-law hardening exponent can be estimated from the measured pile-up/sink-in pattern around the residual impression after indentation in a (001)-oriented fcc single crystal of a small initial yield stress. For this purpose, a new parameter of surface topography is defined as the normalized material volume displaced around the nominal contact zone, calculated by integration of the local residual height (positive or negative) over a centered circular ring. That indicator can be easily determined from an experimental topography map available in a digital form. Comparison is made with the estimates based on measurements of the contact area and the slope of the load–penetration depth curve in logarithmic coordinates. The proposed methodology is extended to estimation of the hardening exponent simultaneously with the initial yield stress when the latter is not negligible. Experimental verification for a Cu single crystal leads to promising conclusions.
Display omitted
In this paper, rate-independent dissipation is introduced into the phase-field framework for modelling of displacive transformations, such as martensitic phase transformation and ...twinning. The finite-strain phase-field model developed recently by the present authors is here extended beyond the limitations of purely viscous dissipation. The variational formulation, in which the evolution problem is formulated as a constrained minimization problem for a global rate-potential, is enhanced by including a mixed-type dissipation potential that combines viscous and rate-independent contributions. Effective computational treatment of the resulting incremental problem of non-smooth optimization is developed by employing the augmented Lagrangian method. It is demonstrated that a single Lagrange multiplier field suffices to handle the dissipation potential vertex and simultaneously to enforce physical constraints on the order parameter. In this way, the initially non-smooth problem of evolution is converted into a smooth stationarity problem. The model is implemented in a finite-element code and applied to solve two- and three-dimensional boundary value problems representative for shape memory alloys.
The Reynolds equation, which describes the lubrication effect arising through the interaction of two physical surfaces that are separated by a thin fluid film, is formulated with respect to a ...continuously evolving third surface that is described by a time-dependent curvilinear coordinate system. The proposed formulation essentially addresses lubrication mechanics at interfaces undergoing large deformations and a priori satisfies all objectivity requirements, neither of which are features of the classical Reynolds equation. As such, this formulation may be particularly suitable for non-stationary elastohydrodynamic lubrication problems associated with soft interfaces. The ability of the formulation to capture finite-deformation effects and the influence of the choice of the third surface are illustrated through analytical examples.
We show that the logarithmic (Hencky) strain and its derivatives can be approximated, in a straightforward manner and with a high accuracy, using Padé approximants of the tensor (matrix) logarithm. ...Accuracy and computational efficiency of the Padé approximants are favourably compared to an alternative approximation method employing the truncated Taylor series. As an application, Hencky-type hyperelasticity models are considered, in which the elastic strain energy is expressed in terms of the Hencky strain, and of our particular interest is the anisotropic energy quadratic in the Hencky strain. Finite-element computations are carried out to examine performance of the Padé approximants of tensor logarithm in Hencky-type hyperelasticity problems. A discussion is also provided on computation of the stress tensor conjugate to the Hencky strain in a general anisotropic case.
PDF
