Modeling and numerical issues in hyperelasto-plasticity with anisotropy

In the paper we discuss modeling and numerical issues that arise in conjunction with anisotropic hyperelastic–plastic response. Both elastic and plastic anisotropy are included. A particular kinematic hardening rule is proposed and its predictive capability is investigated. From the numerical viewpoint, we are concerned with the algorithmic consequences of the loss of coaxiality that arises from anisotropy. The numerical investigation shows that significant truncation errors are introduced if commonly used linearizations of the (classical) exponential Backward Euler rule are utilized in the presence of non-coaxiality.     

On the stability of elastic-plastic systems with hardening

This paper discusses the stability of quasi-static paths for a continuous elastic-plastic system with hardening in a one-dimensional (bar) domain. Mathematical formulations, as well as existence and uniqueness results for dynamic and quasi-static problems involving elastic-plastic systems with linear kinematic hardening are recalled in the paper. The concept of stability of quasi-static paths used here is essentially a continuity property of the system dynamic solutions relatively to the quasi-static ones, when (as in Lyapunov stability) the size of initial perturbations is decreased and the rate of application of the forces (which plays the role of the small parameter in singular perturbation problems) is also decreased to 0. The stability of the quasi-static paths of these elastic-plastic systems is the main result proved in the paper.     

Discrete dislocation plasticity analysis of the wedge indentation of films

The plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter is analyzed using discrete dislocation plasticity. The crystals have three slip systems at ±35.3^° and 90^° with respect to the indentation direction. The analyses are carried out for three values of the film thickness, 2, 10 and , and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and thick films decreases with increasing contact size and attains a contact size-independent value for contact lengths . On the other hand, for the films, the indentation pressure first decreases with increasing contact size and subsequently increases as the plastic zone reaches the rigid substrate. For the 10 and thick films sink-in occurs around the indenter, while pile-up occurs in the film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact size-independent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 43, 411-423]; and (iii) the computed contact area is compared with that obtained from the estimation procedure of Oliver and Pharr [1992. An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7, 1564-1583].     

Capillary Adhesion Between Elastically Hard Rough Surfaces

The adhesion versus vapor pressure (p/p _s) trend between two elastically hard rough surfaces is modeled and compared with experimental results. The experimental samples were hydrophilic surface-micromachined cantilevers, in which the nanometer-scale surface roughness is on the order of the Kelvin radius. The experimental results indicated that adhesion increases exponentially from p/p _s=0.3 to 0.95, with values from 1 mJ/m² to 50 mJ/m². Using the Kelvin equation to determine the force-displacement curves, the mechanics of a wetted rough interface are treated in two ways. First, the characteristics of a surface with rigid asperities of uniform height are derived. At low p/p _s, menisci surrounding individual asperities do not interact. Beyond a transition value, [p/p _s]_tr, a given meniscus grows beyond the asperity it is associated with, and liquid fills the interface. Capillary adhesion in each realm is found according to the integrated work of adhesion. Second, a more general approach allowing an arbitrary height distribution of Hertzian asperities subject to capillary forces is justified and developed. To compare with experimental results, a Gaussian height distribution is first assumed but significantly underestimates the measured adhesion. This is because equilibrium is found far into the Gaussian tail, where asperities likely do not exist. It is shown that by bounding the tail to more likely limits, the measured adhesion trend is more closely followed but is still not satisfactorily matched by the model. The uniform summit height model fits the data very well with a single free parameter. These results can be rationalized if the upper and lower surfaces are geometrically correlated.     

Reproduction of solutions of bidimensional ideal plasticity

The symmetries of a system of differential equations allowed the transformation of its solutions to a solution of this system. New analytical exact solutions of a system of two-dimensional ideal plasticity equations were constructed from two well-known solutions, that for a circular cavity stressed by normal pressure, and Prandtl's solution for a block compressed between perfectly rough plates, for the case where the thickness of the block was rather small. A mechanical sense of new solutions was discussed.     

On an elastic-plastic transition zone in cellular metals

Summary A theory of plasticity is proposed for cellular metals to describe their elastic-plastic transition zone at small strain. Under certain conditions, only a plane strain test is necessary to determine the yield surface. The method to derive the elastic–plastic behaviour [14, 15] was originally proposed for classical metals. A simple cubic model of a cellular metal is used to demonstrate the method by the finite element method. Recommendations for the numerical simulation are given. The influence of the relative density and the hardening behaviour of the cell wall material is investigated.     

The role of electron shells in kinetic electron emission and luminescence under ion bombardment

Abstract

PRODUCTION ET RESTAURATION DES DEFAUTS PRODUITS PAR DES ELECTRONS A BASSE TEMPERATURE DANS LE CADMIUM On a irradié du cadmium par des électrons de 3 MeV à 20°K et étudié la restauration des défauts cristallins par des mesures de résistivité électrique. On compare nos résultats à ceux obtenus auparavant par R. R. Coltman concernant du cadmium irradié par des neutrons thermiques. Les différentes hypothèses pour expliquer ?important stade III sont discutées à la lumière des résultats connus sur les défauts ?irradiation et les défauts de trempe dans le cadmium.

Cadmium samples were irradiated with 3 MeV electrons at 20°K. The defect production and subsequent recovery up to 20°K were studied by means of electrical resistivity measurements. Our results are compared with those obtained earlier by R. R. Coltman relating to irradiated cadmium with thermal neutrons. The different hypotheses, in order to explain the important stage III, are discussed in the light of the existing experimental data on irradiation defects and quenched defects in cadmium.     

Wave attenuation in microcrystal copper at irradiation by a powerful electron beam

The numerical study of high-rate plasticity of Cu target with different grain sizes under the action of nanosecond relativistic high-current electron beam has been carried out in the paper. The model of microcrystal material plasticity includes dislocation kinetics and dynamics as well as the stress relief in the grain boundaries of the polycrystal. This model has only two adjustable parameters. The presented results demonstrate a strong dependence of the shock wave attenuation coefficient on the grain size. At the grain size of about 70 nm, the plasticity mechanism of the dislocation glide inside grains changes to plasticity mechanism along grain boundaries.