Characterization of stress-strain behavior of superplastic titanium alloy by free bulging tests with pressure jumps
The work is dedicated to determination of stress-strain behavior of Ti6Al4V alloy deformed in conditions of biaxial tension provided by free bulging testing. The dome height during each test was continuously measured and recorded using a magnetostrictive position transducer. All the tests were performed using stepped pressure regime with jump pressure changing between two values at evenly spaced time moments. This experimental technique provides the possibility to study strain rate sensitivity index variation during the test and subsequently construct strain and strain rate dependent material model. The output data of each test include the evolution of dome height, subsequent pressure regime and final thickness of the specimen at the dome pole. In the framework of this study the processing of such data in order to evaluate the material behavior is discussed. Inverse analysis with different material models was implemented as well as special direct technique allowing one to construct stress-strain curves based on the results of free bulging tests with pressure jumps. The obtained material model was verified by finite element simulation.
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.
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.
The purpose of this study is to find out the characteristics of hot forming of Ti-6Al-4V titanium alloy in order to determine the conditions of its superplastic behavior. The experiments were performed in two stages: the stepped tensile-tests series (temperature range 700 – 925 °С) and the constant strain rate tensile-test series (temperature range 775 – 925 °С). By the results of stepped tensile tests the constitutive equations which describe relationship between stress and strain rate for each temperature were constructed. On the base of obtained data, the temperature and strain-rate ranges which ensure the realization of superplasticity at forming of Ti-6Al-4V alloy as well as optimal strain rates which corresponds to the maximum value of strain rate sensitivity exponent were determined. In was shown that at low temperatures (700 – 775C) the Ti-6Al-4V alloy shows all signs of superplasticity, however at these temperatures the optimal strain rates are too slow for industrial technological procedures. The dependence between optimum strain rate and reciprocal temperature appears to be well fitted by exponential low. At the second stage of the experimental research, the tensile-tests with a constant, optimum for each temperature strain-rate were carried in order, to estimate the real initial flow stress and the character of strain hardening of the material during the deformation with optimum strain rate. In was found that flow stress values obtained by stepped tensile tests matches the values form constant-strain-rate tests with effective strain value equal to 0,2 and the strain hardening during the deformation with optimal strain rates is significant.
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
This volume presents new results in the study and optimization of information transmission models in telecommunication networks using different approaches, mainly based on theiries of queueing systems and queueing networks .
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.