Superplastic Deformation Regime Research Articles

Общие свойства показателя скоростной чувствительности диаграмм деформирования, порождаемых линейной теорией вязкоупругости и существование максимума у его зависимости от скорости

Анализируется скоростная чувствительность семейства диаграмм деформирования, порождаемых физически линейным определяющим соотношением вязкоупругости Больцмана-Вольтерры с произвольной функцией релаксации в одноосных испытаниях с постоянными скоростями деформации. Выведено общее выражение для показателя скоростной чувствительности (скоростного упрочнения) и аналитически исследованы его общие качественные свойства: зависимость от деформации, скорости деформации и характеристик функции релаксации, диапазон значений, интервалы монотонности и существование точек экстремума, предельные значения при стремлении скорости деформации к нулю или бесконечности, способы определения по диаграммам деформирования или по кривым релаксации. Установлено, что (в рамках линейной теории вязкоупругости) этот показатель зависит не от двух независимых аргументов (деформации и скорости деформации), а только от их отношения, что он выражается через отношение касательного модуля к секущему и может быть вычислен по одной диаграмме деформирования с произвольной скоростью деформации, и что по заданной (или измеренной в испытаниях) функции скоростной чувствительности можно однозначно восстановить функцию релаксации. Доказано, что значения показателя скоростной чувствительности всегда лежат в интервале от нуля до единицы (т.е. линейное определяющее соотношение описывает только псевдопластические среды и не может описывать дилатантные) и могут быть сколь угодно близки к единице (верхней границе для псевдопластических сред), что как функция скорости он не только может монотонно возрастать или убывать, но может иметь точки экстремума, в частности точку максимума (при малообременительных ограничениях на функцию релаксации). Тем самым обнаружена неожиданная способность линейной теории вязкоупругости не только порождать семейство диаграмм деформирования с выраженными участками течения при практически постоянном напряжении, но и качественно описывать «сигмоидальную» форму зависимости напряжения от скорости деформации (в логарифмических осях) и очень высокую скоростную чувствительность, характерные для режима сверхпластического деформирования материалов. Установленные свойства показателя скоростной чувствительности и его характерные особенности проиллюстрированы на примерах классических регулярных, сингулярных и фрактальных моделей вязкоупругости (Максвелла, Фойгта, Кельвина, Зенера, Бюргерса, Скотт-Блэра) и их параллельных соединений.

Effect of the Strain and Strain Rate on Microstructure Evolution and Superplastic Deformation Mechanisms

Parameters of superplasticity of the Al–7.6% Mg–0.6% Mn–0.25% Cr alloy have been studied in the range of 490–520°C, and the optimum temperature of deformation has been determined. The evolution of the grain structure in the bulk and on the surface of samples during the superplastic deformation at a temperature of 510°C has been analyzed. The contribution of grain-boundary sliding has been estimated in the strain-rate regime of superplastic deformation according to the results of the analysis of changes in the structure of the surface with preliminarily applied marker scratches. The contribution of grain-boundary sliding to the total deformation is 20–30%; the contribution of diffusion creep decreases from 40 to 20% with an increase in the deformation rate by an order of magnitude, from 1 × 10–3 to 1 × 10–2 s–1. The intragranular deformation is localized in the peripheral regions of grains and in the region of striated zones.

ХАРАКТЕРИСТИКА СКОРОСТНОЙ ЧУВСТВИТЕЛЬНОСТИ ДИАГРАММ ДЕФОРМИРОВАНИЯ В ЛИНЕЙНОЙ ТЕОРИИ ВЯЗКОУПРУГОСТИ И ПОСТРОЕНИЕ ПО НЕЙ ФУНКЦИИ РЕЛАКСАЦИИ

Properties of the stress-strain curves family generated by the Boltzmann-Volterra linear viscoelasticity constitutive equation under uni-axial loadings at constant strain rates are studied analytically. Assuming relaxation modulus is arbitrary, the general expression for strain rate sensitivity index as the function of strain and strain rate is derived and analyzed. It is found out (within the framework of the linear viscoelasticity theory) that the strain rate sensitivity index depends only on the single argument that is the ratio of strain to strain rate. So defined function of one real variable is termed “the strain rate sensitivity function” and it may be regarded as a material function since it is interconvertible with relaxation modulus. It is found out that this function can be increasing or decreasing or non-monotone or can have local maximum or minimum without any complex restrictions imposed on the relaxation modulus. It is proved that the strain rate sensitivity value is confined in the interval from zero to unity (the upper bound of strain rate sensitivity index for pseudoplastic media) whatever strain and strain rate magnitudes are and its values may be close to unity (even for the standard linear solid model). It means that the linear viscoelasticity theory is able to produce high values of strain rate sensitivity index and to provide existence of the strain rate sensitivity index local maximum with respect to strain rate (for any fixed strain). These properties are the most distinctive features of superplastic deformation regime observed in numerous materials tests. The explicit integral expression for relaxation modulus via the strain rate sensitivity function is derived. It enables one to restore relaxation modulus assuming a strain rate sensitivity function is given. The restrictions on the strain rate sensitivity function are obtained to provide decrease and convexity down of the resulting relaxation modulus as a function of time, i.e. to provide necessary properties of a relaxation modulus in the linear viscoelasticity. Thus, the technique is developed to evaluate relaxation modulus using test data for strain rate sensitivity, in particular, using piecewise smooth approximations (by splines, for example) of an experimental strain rate sensitivity function.

ХАРАКТЕРИСТИКА СКОРОСТНОЙ ЧУВСТВИТЕЛЬНОСТИ ДИАГРАММ ДЕФОРМИРОВАНИЯ В ЛИНЕЙНОЙ ТЕОРИИ ВЯЗКОУПРУГОСТИ И ПОСТРОЕНИЕ ПО НЕЙ ФУНКЦИИ РЕЛАКСАЦИИ

Properties of the stress-strain curves family generated by the Boltzmann-Volterra linear viscoelasticity constitutive equation under uni-axial loadings at constant strain rates are studied analytically. Assuming relaxation modulus is arbitrary, the general expression for strain rate sensitivity index as the function of strain and strain rate is derived and analyzed. It is found out (within the framework of the linear viscoelasticity theory) that the strain rate sensitivity index depends only on the single argument that is the ratio of strain to strain rate. So defined function of one real variable is termed “the strain rate sensitivity function” and it may be regarded as a material function since it is interconvertible with relaxation modulus. It is found out that this function can be increasing or decreasing or non-monotone or can have local maximum or minimum without any complex restrictions imposed on the relaxation modulus. It is proved that the strain rate sensitivity value is confined in the interval from zero to unity (the upper bound of strain rate sensitivity index for pseudoplastic media) whatever strain and strain rate magnitudes are and its values may be close to unity (even for the standard linear solid model). It means that the linear viscoelasticity theory is able to produce high values of strain rate sensitivity index and to provide existence of the strain rate sensitivity index local maximum with respect to strain rate (for any fixed strain). These properties are the most distinctive features of superplastic deformation regime observed in numerous materials tests. The explicit integral expression for relaxation modulus via the strain rate sensitivity function is derived. It enables one to restore relaxation modulus assuming a strain rate sensitivity function is given. The restrictions on the strain rate sensitivity function are obtained to provide decrease and convexity down of the resulting relaxation modulus as a function of time, i.e. to provide necessary properties of a relaxation modulus in the linear viscoelasticity. Thus, the technique is developed to evaluate relaxation modulus using test data for strain rate sensitivity, in particular, using piecewise smooth approximations (by splines, for example) of an experimental strain rate sensitivity function.

On the microstructural behavior of titanium alloy during nonoptimal regime of superplastic deformation

In industrial superplastic forming, maintenance of the narrow ranges of condition required for optimal superplastic flow from beginning to end is a very difficult and challenging task. When these conditions required for optimal superplastic flow lie beyond a certain limit during deformation process, non-optimal process of superplastic deformation is observed during which the microstructure of the material changes very significantly. As the microstructure changes, the stress required to deform the material changes accordingly and the response of the material becomes dependent on the history of loading in this regime of superplastic deformation. A near alpha titanium alloy has been used in this study to find out those parameters of microstructure, which are varying significantly during non-optimal regime of superplastic deformation. Superplasticity tests have been carried out on tensile specimens at 930°C with a constant strain rate of 1×10−4 s−1 successfully stopped at two different percentages of elongation. Results indicated that percentage of alpha phase, number of alpha grains per unit area, size of alpha grain, parameter of non-uniaxiality of alpha grain and grain boundary area of alpha grain, etc. varied significantly during non-optimal regime of superplastic deformation.

Superplastic deformation and energy dissipation mechanism in surface-bonded carbon nanofibers

Molecular dynamics simulations are used to understand the role of surface C–C bonds formed by heat treatment on plastic deformation and fracture mechanisms in cone-stacked carbon nanofibers. The simulations predict that the surface bond density linearly relates to the heat treatment temperature. As the surface bond density increases, it is found that tensile strength and ductile fracture energy in carbon nanofibers rise dramatically by more than 65% and 622%, respectively; hence unveiling a regime of superplastic deformation that is unmatched by standard carbon nanotubes and graphitic nanofibers. We demonstrate that both strengthening and superplasticity effects are enabled by the occurrence of surface bond-induced fiber splaying processes that can effectively resist interlayer sliding and crack propagation during deformation. The findings of this computational study have important implications for designing flaw-tolerant nanocomposite systems.

Graininess variation research of steel 20 welding joints at deformation-thermal treatment

It is known that the metal grains’ size affect on the metal physical-and-mechanical properties. At the fusion welding the metal grains irregular growth takes place, graininess is increasing. It affects negatively on physical-and-mechanical properties on the welding joint metal. For decreasing graininess variation thermal and thermoplastic treatment of welding joints (annealing, thermoplastic treatment) is used. In was carried out the comparative analysis of the results of steel 20 welding joints structure research after deformation at the temperature-rate regime of super plastic deformation and after annealing and after thermo cyclical treatment. At superplastic deformation during hot deformation, became possible processes of dislocation redistribution, including vacancy creeping, forming recrystallization nuclei and their growth, migration of the large angular boundaries. In this research a thermo mechanical treatment at super plasticity regime deformation is studied. In this case the effect of super plasticity deformation is not revealed in full, because for that there must present fine grain structure. The results of the research showed the positive effect of the thermoplastic treatment at super plasticity regime deformation. Slow rate of deformation in combination with definite temperature affects on the thermal activated processes of thermal loss of strength. Microstructure research was carried out on Neophot-30 microscope. For studying the graininess structure variation changing the parameters of grains dimensions distribution were calculated by using the industry system of images analysis SIAMS 600. It was determined that in the zone of the welding joint thermal effect the increasing of graininess variation in metal took place. After annealing of the welding joint the graininess variation in the zone of thermal effect almost had not changed. After isothermal rolling with heated rollers at the regime of super plastic deformation and thermo cyclical treatment the graininess variation in the zone of thermal effect decreased and approached to the value of the basic metal graininess variation.

Influence of deformation on mechanical properties of 20 and 30HGSA steel welded joints in superplasticity regime

It may prove to be promising to use hot plastic deformation of welded joints in temperature/velocity regimes of metal superplacticity effect revealed, in order to get structural homogeneity and combination of high strength and plasticity. Isothermal rolling with hot rolls of 20 and 30HGSA steel weld joint specimens was carried out at 10, 20 and 40% deformation degrees at a temperature of 730 ± 5 oС being the optimal temperature of superplastic deformation for constructional steels, at a constant strain rate of 0.003 s-1. The rolling was performed in the laboratory six-high LIS-6/200 mill of the Institute for Metals Superplasticity Problems, Russian Academy of Sciences, with isothermal deformation conditions being provided by heating the working rolls and regulating their temperature. The minimum difference in the weld joint base metal ultimate strength values compared to the initial state is observed at 20% deformation degree and is equal to 6.3% for 20 steel and 5.2% for 30HGSA steel. The minimum difference in the weld joint base metal yield point values compared to the initial state is also observed at 20% deformation degree and is equal to 6.0% for 20 steel and 4.6% for 30HGSA steel. It is shown that isothermal rolling with hot rolls in superplastic deformation regime results in reduction of scattering of mechanical properties in different zones of 20 and 30HGSA constructional steel welded joint compared to the initial state. The comparative analysis of micro hardness and hardness values of the welded 20 and 30HGSA steel specimens after different kinds of welding treatment with equal time spent on the treatment showed that the rolling with isothermal rolls in superplastic deformation regime with 20% degree of strain has an advantage in achieving homogeneity of mechanical properties compared to annealing and thermal cycling treatment.

Experimental study on microstructural variation in near alpha titanium alloy during non-optimal regime of superplastic deformation

Superplasticity is generally achieved in titanium alloys with a fine grained microstructure when deformation is carried out under narrow ranges of strain rate and temperature. Under these conditions, titanium alloys show large elongation with a relatively stable microstructure. When the aforesaid conditions lie beyond a certain limit during deformation process, non-optimal process of superplastic deformation is observed. The microstructure changes actively during the non-optimal process of superplastic deformation. Near alpha titanium alloy has been used in the present study to find out those parameters of microstructure, which are varying significantly during non-optimal process of superplastic deformation. Superplasticity tests have been carried out at 930°C with constant strain rates of 1×10−4 and 5×10−4 s−1 and jump wise varying strain rates between 1×10−4 and 5×10−4 s−1. Results indicated that microstructural parameters, i.e. percentage of alpha phase, number of alpha grains per unit area, average size of alpha grain, parameter of non-uniaxiality of alpha grain and grain boundary area of alpha grain, varied significantly during non-optimal process of superplastic deformation. Strain induced grain growth and deformation induced phase transformation are also observed in near alpha titanium alloy during non-optimal process of superplastic deformation. Optical microscope, micro-Vickers hardness test and X-ray diffraction have been used to characterise the microstructure of the near alpha titanium alloy.

Superplastic behavior of magnesium-based Mg-10 wt % Gd alloy after severe plastic deformation by torsion

Characteristic features of superplastic behavior of Mg-10 wt % Gd alloy with an ultrafine-grained structure produced by severe plastic deformation by high-pressure torsion have been considered. The ultrafine-grained structure has been studied by transmission electron microscopy and X-ray diffraction. The optimum temperature-strain-rate regime of superplastic deformation of the ultrafine-grained alloy and the magnitudes of the strain-rate sensitivity parameter of the flow stress have been determined.

Deformation processing in superplasticity regime-production of aircraft engine compressor discs out of titanium alloys

Superplastic deformation (SPD) that utilizes the inherent superplasticity in suitable alloys has been employed for developing compressor discs for a jet engine in a titanium alloy equivalent to IMI-685. Deformation in the SPD regime by appropriate modification of the microstructure of the workpiece has enabled forming to near-net shape at comparatively lower forming loads. The equipment used for the deformation processing includes an electric furnace with robotic handling of heated billets, a 2000 ton isothermal forging press with numerical controls for speed and load, and a cooling station for controlled cooling of forged discs. The starting microstructure of the forging stock consisting of mainly α laths within prior β boundaries was refined to fine equiaxed α grains by appropriate deformation in the α+ β regime. The refined structure enabled isothermal forging in the α+ β phase field at low deformation loads. The effect of SPD and subsequent thermal treatment on the isotropy of properties in discs has been studied. The forging characteristics, and the microstructure and mechanical properties realized in the discs are presented. It is seen that SPD is a practical method which enables high quality items to be made that are unique in form and reliable in use. The process can be used in a serial production of parts of specified metallurgical properties.

Superplasticity of fine-grained 7475 Al alloy and a proposed new deformation mechanism

A study has been made to investigate the superplastic deformation mechanisms of 7475 Al alloy in relation to the variation of grain size ranging between 5.5 μm and 13 μm. The strain-rate sensitivity ( m) was increased with decreasing grain size in the superplastic deformation regime. Microstructural investigation after tension tests revealed that the dispersoid free zones were produced mostly at the grain boundaries normal to the tensile direction. A new model for describing the deformation behavior of the 7475 Al alloy has been proposed based on the assumption that the grain boundary sliding was accommodated by both diffusional flow and slip. This new model well predicts many aspects of experimental results.

The high strain rate superplastic deformation mechanisms of mechanically alloyed aluminum IN90211

The tensile behavior of mechanically alloyed (dispersion strengthened) IN90211 was investigated at strain rates between 0.0001 and 340 s −1 at temperatures between 425 and 475 °C. At strain rates above 0.1 s −1, superplastic elongations were obtained (maximum elongation of 525% at 475 °C and 2.5 s −1). Superplastic elongations were found to result from grain boundary sliding. The data were analyzed assuming that a threshold stress resists dislocation motion. The threshold stresses were obtained assuming n = 2 (grain boundary sliding) or n = 3 (solute drag) for the stress exponent. Both assumptions provided equally credible values for a temperature-dependent threshold stress between 1% and 20% of the Orowan looping stress. The n = 3 threshold stresses agreed with load relaxation data, but the n = 2 values corresponded to the lower limit of the superplastic deformation regime, as indicated by creep tests at lower strain rates. Based upon the threshold stress theories in the literature, the threshold stresses are suggested to arise from a combination of local and general climb of lattice dislocations over particles. Consideration of the activation energies, details of flow behavior, and stress relaxation experiments provided strong evidence for the n = 3 solute drag mechanism to be the rate-limiting process in the superplastic deformation regime.