Modeling of bainitic phase transformation

In this work, we present a macroscopic material model for simulation of austenite to bainite and of austenite to martensite transformations accompanied by transformation-induced plasticity (TRIP), which is an important phenomenon in metal forming processes. In order to account for the incubation time the model considers nucleation of the bainite phase. When this quantity attains a barrier term, growth of bainite volume fraction is started. The model formulation allows for individual evolutions of upper and lower bainite. Furthermore, the numerical implementation of the constitutive equations into a finite element program is described. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence of phase field to phase relaxation models with memory

The qualitative properties of solutions to linear elliptic systems of any order, in an exterior domain of a space of arbitrary dimension, are analyzed to the aim of giving the weakest conditions at infinity ensuring the uniqueness of solutions to Dirichlet and Neumann problems.     

Models of elastic media with stress relaxation

The stress relaxation process is linked to the change with time of the metric stress tensor of the medium. Possible types of thermodynamically justified relaxation equations are discussed.     

Discrete transformation hypergroups and transformation hypergroups with phase tolerance space

Tolerance spaces and algebraic structures with compatible tolerances play an important role in contemporary algebra and its applications. In this contribution we present transformation hyperstructures, namely semihypergroups and hypergroups, acting on tolerance spaces. Some basic concepts concerning the mentioned structures are introduced and their fundamental properties are examined on suitable constructions.     

Investigation of stress relaxation in polypyromellitimide

A study was made of stress relaxation in polypyromellitimide film at degrees of stretching from 0.5 to 50% over a wide temperature range (below T_c). The applicability of the time-temperature superposition principle is shown at all degrees of stretching. It is shown that the Arrhenius equation for the temperature dependence of the displacement factora _T is valid only at small deformations (up to 1%). The extreme course of the relaxation rate from the level of deformations is attributed to the variations in the polypyromellitimide structure in this deformation region.Scientific-Research Institute of Plastic Compounds, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 45–50, January–February, 1972.     

On oscillatory integral Hilbert transformation with trigonometric polynomial phase

Let $ \mathcal{P}_n $ denote the set of algebraic polynomials of degree n with the real coefficients. Stein and Wpainger [1] proved that $$ \mathop {\sup }\limits_{p( \cdot ) \in \mathcal{P}_n } \left| {p.v.\int_\mathbb{R} {\frac{{e^{ip(x)} }} {x}dx} } \right| \leqslant C_n , $$ where C _n depends only on n. Later A. Carbery, S. Wainger and J. Wright (according to a communication obtained from I. R. Parissis), and Parissis [3] obtained the following sharp order estimate $$ \mathop {\sup }\limits_{p( \cdot ) \in \mathcal{P}_n } \left| {p.v.\int_\mathbb{R} {\frac{{e^{ip(x)} }} {x}dx} } \right| \sim \ln n. $$ . Now let $ \mathcal{T}_n $ denote the set of trigonometric polynomials $$ t(x) = \frac{{a_0 }} {2} + \sum\limits_{k = 1}^n {(a_k coskx + b_k sinkx)} $$ with real coefficients a _k , b _k . The main result of the paper is that $$ \mathop {\sup }\limits_{t( \cdot ) \in \mathcal{T}_n } \left| {p.v.\int_\mathbb{R} {\frac{{e^{it(x)} }} {x}dx} } \right| \leqslant C_n , $$ with an effective bound on C _n . Besides, an analog of a lemma, due to I. M. Vinogradov, is established, concerning the estimate of the measure of the set, where a polynomial is small, via the coefficients of the polynomial.     

Modelling an anomalous stress relaxation in glassy polymers (the Kitagawa effect)

Constitutive relations are derived for the nonlinear viscoelastic response of glassy polymers. The model is based on the concept of adaptive links (a version of the theory of transient networks), where the rates of annihilation of active links are determined by the Eyring formula. Adjustable parameters in the constitutive equations are found by using experimental data for a polyester resin in standard relaxation tests. The stress-strain relations are applied to describe an anomalous stress relaxation in solid polymers observed in tensile test after strain reversal (the Kitagawa effect). Qualitative agreement is demonstrated between results of numerical simulation and observations.     

Micromechanical modeling of bainitic phase transformation

We develop a micromechanical material model for phase transformation from austenite to bainite for a polycrystalline low alloys steel. In this material (e.g. 51CrV4) the phase changes from austenite to perlite-ferrite, bainite or martensite, respectively. This work is concerned with phase transformation between austenite and n-bainite variants in differently orientated grains. The characteristic features of bainite formation are the combination of time-dependent transformation kinetics and lattice shearing in the microstructure. These effects are considered on the microscale and transferred to the polycrystalline macroscale by means of homogenisation of stochastically orientated grains. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of deformation-induced phase transformation during very high cycle fatigue (VHCF) using the boundary element method

A microstructural simulation model is proposed which accounts for damage accumulation in shear bands and deformation-induced martensite formation in a metastable austenitic stainless steel (AISI304). The model is numerically solved using the two-dimensional (2-D) boundary element method. By using this method, sliding displacements can be directly evaluated in shear bands and austenite grains as well as generated martensite domains with their individual mechanical properties and shape deformation can be considered. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Darboux transformation associated with two-parameter lattice soliton equation

A new discrete matrix spectral problem with two arbitrary constants is introduced. The corresponding two-parameter integrable lattice soliton equation is obtained through the discrete zero curvature representation, and the resulting integrable lattice equation reduce to the Toda lattice in rational form for a special choice of the parameters. A Darboux transformation (DT) for the lattice soliton equation is constructed. As an application, an explicit solution of the two-parameter lattice soliton equation is presented.     

Effect of long-term storage of polycarbonates on stress relaxation

The effect of long-term storage (three-five years) on the mechanical properties of polycarbonates and Makrolon has been experimentally investigated under conditions of stress relaxation at normal and elevated temperatures.Scientific-Research Institute of Mechanics, Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 149–151, January–February, 1973.     

A new linear spectral transformation associated with derivatives of Dirac linear functionals

In this contribution, we analyze the regularity conditions of a perturbation on a quasi-definite linear functional by the addition of Dirac delta functionals supported on N points of the unit circle or on its complement. We also deal with a new example of linear spectral transformation. We introduce a perturbation of a quasi-definite linear functional by the addition of the first derivative of the Dirac linear functional when its support is a point on the unit circle or two points symmetric with respect to the unit circle. Necessary and sufficient conditions for the quasi-definiteness of the new linear functional are obtained. Outer relative asymptotics for the new sequence of monic orthogonal polynomials in terms of the original ones are obtained. Finally, we prove that this linear spectral transform can be decomposed as an iteration of Christoffel and Geronimus linear transformations.