Numerical modeling of strain rate hardening effects on viscoplastic behavior of metallic materials

The main goal of the present work is to provide a finite strain elasticviscoplastic framework to numerically account for strain, strain rate hardening, and viscous effects in cold deformation of metallic materials. The aim is to provide a simple and robust numerical framework capable of modeling the main macroscopic behavior associated with high strain rate plastic deformation of metals. In order to account for strain rate hardening effects at finite strains, the hardening rule involves a rate dependent saturation hardening, and it accounts for linear hardening prevailing at latter deformation stages. The numerical formulation, finite element implementation, and constitutive modeling capabilities are assessed by means of decremental strain rate testing and constant strain rate loading followed by stress relaxation. The numerical results have demonstrated the overall framework can be an efficient numerical tool for simulation of plastic deformation processes where strain rate history effects have to be accounted for

Crystal plasticity model calibration for 316l stainless steel single crystals during deformation

Type 316L austenitic stainless steel is an important structural material used for the in-core components and pressure boundaries of light water reactors. In order to study degradation mechanisms in such a steel, like crack initiation and propagation, it is crucial to develop reliable crystal plasticity models at microscale that would account for anisotropic nature of the material and realistic modelling of grain topology. In this work we present a procedure for calibrating material properties of a slip-based crystal plasticity finite element model and investigate its suitability as a constitutive model for single-crystal tensile test simulations. The material properties include the anisotropic elastic and crystal plasticity material parameters that are calibrated against experimental tensile test curves for 316L stainless steel single crystals at selected crystallographic orientations. For the crystal plasticity material parameters a systematic sensitivity study using Bassani and Wu hardening law is performed

Modular elliptic curves over real abelian fields and the generalized Fermat equation x2ℓ+y2m=zpx^{2\ell}+y^{2m}=z^p

Using a combination of several powerful modularity theorems and class field theory we derive a new modularity theorem for semistable elliptic curves over certain real abelian fields. We deduce that if $K$ is a real abelian field of conductor $n<100$, with $5 \nmid n$ and $n \ne 29$, $87$, $89$, then every semistable elliptic curve $E$ over $K$ is modular. Let $\ell$, $m$, $p$ be prime, with $\ell$, $m \ge 5$ and $p \ge 3$.To a putative non-trivial primitive solution of the generalized Fermat $x^{2\ell}+y^{2m}=z^p$ we associate a Frey elliptic curve defined over $\mathbb{Q}(\zeta_p)^+$, and study its mod $\ell$ representation with the help of level lowering and our modularity result. We deduce the non-existence of non-trivial primitive solutions if $p \le 11$, or if $p=13$ and $\ell$, $m \ne 7$.Comment: Introduction rewritten to emphasise the new modularity theorem. Paper revised in the light of referees' comment

Testing the Limits of Anaphoric Distance in Classical Arabic: a Corpus-Based Study

One of the central aims in research on anaphora is to discover the factors that determine the choice of referential expressions in discourse. Ariel (1988; 2001) offers an Accessibility Scale where referential expressions, including demonstratives, are categorized according to the values of anaphoric (i.e. textual) distance that each of these has in relation to its antecedent. The aim of this paper is to test Ariel’s (1988; 1990; 2001) claim that the choice to use proximal or distal anaphors is mainly determined by anaphoric distance. This claim is investigated in relation to singular demonstratives in a corpus of Classical Arabic (CA) prose texts by using word count to measure anaphoric distance. Results indicate that anaphoric distance cannot be taken as a consistent or reliable determinant of how anaphors are used in CA, and so Ariel’s claim is not supported by the results of this study. This also indicates that the universality of anaphoric distance, as a criterion of accessibility, is defied

On Rigidity of Generalized Conformal Structures

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity of conformal transformations, that is such a transformation is fully determined by its 2-jet at any point. We prove here a similar rigidity for generalized conformal structures defined by giving a one parameter family of metrics (instead of scalar multiples of a given one) on each tangent space

Elliptic Curves over Real Quadratic Fields are Modular

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio