Investigation on the thickness distribution of highly customized titanium biomedical implants manufactured by superplastic forming
Mechanical performances of titanium biomedical implants manufactured by superplastic forming are strongly related to the process parameters: the thickness distribution along the formed sheet has a key role in the evaluation of post-forming characteristics of the prosthesis. In this work, a finite element model able to reliably predict the thickness distribution after the superplastic forming operation was developed and validated in a case study. The material model was built for the investigated titanium alloy (Ti6Al4V-ELI) upon results achieved through free inflation tests in different pressure regimes. Thus, a strain and strain rate dependent material behaviour was implemented in the numerical model. It was found that, especially for relatively low strain rates, the strain rate sensitivity index of the investigated titanium alloy significantly decreases during the deformation process. Results on the case study highlighted that the strain rate has a strong influence on the thickness profile, both on its minimum value and on the position in which such a minimum is found.
We consider the time-dependent 1D Schrödinger equation on the half-axis with variable coefficients becoming constant for large x. We study a two-level symmetric in time (i.e. the Crank-Nicolson) and any order finite element in space numerical method to solve it. The method is coupled to an approximate transparent boundary condition (TBC). We prove uniform in time stability with respect to initial data and a free term in two norms, under suitable conditions on an operator in the approximate TBC. We also consider the corresponding method on an infinite mesh on the half-axis. We derive explicitly the discrete TBC allowing us to restrict the latter method to a finite mesh. The operator in the discrete TBC is a discrete convolution in time; in turn its kernel is a multiple discrete convolution. The stability conditions are justified for it. The accomplished computations confirm that high order finite elements coupled to the discrete TBC are effective even in the case of highly oscillating solutions and discontinuous potentials.
The study is carried out by the first author within The National Research University Higher School of Economics' Academic Fund Program in 2012-2013, research grant No. 11-01-0051.
We deal with an initial-boundary value problem for the generalized time-dependent Schrödinger equation with variable coefficients in an unbounded $n$-dimensional parallelepiped ($n\geq 1$). To solve it, the Crank-Nicolson in time and the polylinear finite element in space method with the discrete transparent boundary conditions is considered. We present its stability properties and derive new error estimates $O(\tau^2+|h|^2)$ uniformly in time in $L^2$ space norm, for $n\geq 1$, and mesh $H^1$ space norm, for $1\leq n\leq 3$ (a superconvergence result), under the Sobolev-type assumptions on the initial function. Such estimates are proved for methods with the discrete TBCs for the first time.
This paper is devoted to the simple methodic for determining the rheological characteristics approbation. Methodic is based on the free bulge experiments. In this work methodic is applied for determining rheological characteristics of АА5083 aluminum alloy at 450 Celsium degree. These characteristics were verified by using finite element modelling and compared with characteristics obtained from literature.
The volume contains articles of scientific staff and faculty of the Department of Computer Science and Applied Mathematics and Scientific-Educational Center of computer modeling of unique buildings and complexes of Moscow State University of Civil Engineering (National Research University), devoted to actual problems of applied mathematics and computational mechanics.
The paper presents a simple technique for the characterization of materials superplasticity by free bulging tests, which is based on inverse analysis. The main idea of this technique is a semianalytical solution of the direct problem instead of finite element simulation which allows one to reduce the calculation time significantly. Presented method use experimental time-thickness and time-dome height of the workpiece dependancies as initial experimental data. Presented method has been applied for AZ31 magnesium alloy at 520. Received properties have been veracity via simulation by finite element method. Obtained time-height relations were comparison with the data presented in the literature.
This study proposes a method for determination of material characteristics by inverse analysis of free bulging tests results. The blow-forming tests were carried out at the temperature of 415 °C using aluminum alloy (AMg-6) sheets of a 0.92 mm thickness. Each test was performed at constant pressure. For each fixed value of pressure, a series of experiments was carried out with different forming times to obtain evolutions of dome height H and thickness s. Two different constitutive equations were used to describe the dependence of flow stress on the effective strain rate: the Backofen power equation and the Smirnov one taking into account an s-shape of stress-strain rate curve in the logarithmic scale. The constants of these equations were obtained by least squares minimization of deviations between the experimental variations of H and s and ones predicted by a simplified engineering model formulated for this purpose. Using the Smirnov constitutive model to describe the dependence of flow stress on strain rate, unlike the classical power law, makes it possible to analyze the variation of strain rate sensitivity index m with strain rate. On the basis of the obtained data, the optimum strain rate for AMg-6 processing was estimated as one corresponding to the maximum of strain rate sensitivity index. The validity of the proposed method was examined by finite element simulation of free bulging process.
The application of mathematical modeling methods (with subsequent computer sales) to determine the parameters of accuracy geometry bands obtained with the new equipment and process the step deformation bands of hard alloys based on copper
The paper provides a number of proposed draft operational guidelines for technology measurement and includes a number of tentative technology definitions to be used for statistical purposes, principles for identification and classification of potentially growing technology areas, suggestions on the survey strategies and indicators. These are the key components of an internationally harmonized framework for collecting and interpreting technology data that would need to be further developed through a broader consultation process. A summary of definitions of technology already available in OECD manuals and the stocktaking results are provided in the Annex section.