Strain Rate Sensitivity Index Research Articles

Quantitative Evaluation for the Effect of Tableting Speed on Compression Behavior of Pharmaceutical Powders using a Rotary Tablet Press

The purpose of this study is to evaluate the effect of tableting speed on the compression behavior of pharmaceutical powders using an R&D rotary tablet press. Cilostazol, probucol and ibuprofen were selected as model drugs, and they were mixed at a mass concentration of 20% into two base formulations composed of different excipients. The tablets were prepared at two levels of turret rotation speeds of 20 rpm and 60 rpm, and the physical properties of the tablets were evaluated. As a result, placebo tablets and cilostazol tablets had no effect on the tableting speed. However, the compressibility of probucol and ibuprofen tablets decreased and the capping tendency was observed, although the compactibility was not affected. The strain rate sensitivity (SRS) index was obtained from an out-of-die Heckel analysis, which was used to quantitatively evaluate the effect of tableting speed on the compressibility. It was found that the R&D rotary tablet press was possible to evaluate the compressibility and capping tendency by the SRS index.

Understanding Fiber-Matrix Integrity in Fiber-Reinforced Polymer Composites from Strain Rate Sensitivity Concept

The understanding of fiber-matrix integrity in fiber-reinforced polymer composites from strain rate sensitivity concept was considered from interfacial energetics point-of-view. The methodology involved the preparation of plantain fibers, treatment of fibers with nine different liquids to render their surfaces hydrophobic, molding of fiber reinforced composites, measurement of contact angles on fibers and composites, composites tensile strength determination, and fiber pullout tests. The results showed that Methyl Ethyl Ketone Peroxide (MEKP) and mercerization (NaOH) rendered the fibers most hydrophobic. MEKP and NaOH treated fibers gave the lowest surface energies, maximum works of adhesion and hence better fiber-matrix bonding (increased fiber-matrix integrity) when compared with other treatments. The strain-rate sensitivity index, m, obtained ranged from 0.2264 for phosphoric acid-treated fiber in the composite to 0.2385 MEKP treatment fiber with an overall average value of m of 0.2341, while the value of m, for untreated fiber reinforced composite was 0.2321. MEKP and NaOH treated fibers were most hydrophobic gave the highest m values and therefore most desired for treatment of fibers for composite formation. The pullout tests result showed that increase in work of adhesion led to an increase in the tensile energy, showing that stronger bonding will guarantee fiber-matrix composite stability and integrity. MEKP and NaOH with maximum free energies of adhesion also exhibit maximum pullout forces which implied that the bonding between fiber and matrix was stronger for these treatments and hence higher fiber-matrix integrity in the composite. It was also shown that the pull-out force increased with the strain rate sensitivity index confirming that one would need composites with higher m-values for stronger fiber/matrix composites. The results of this work are very important in structures that are made with fiber reinforced composite materials, such as, airplane and car bodies. This work shows that the use of the adhesive energy-stress concept to determine the strain rate is valid since the values of strain rate sensitivity indices calculated are comparable with values reported in the literature and that fiber-matrix integrity can be understood from interfacial free energies and strain rate sensitivity concepts.

The simple hyperbolic-sine equation for superplastic deformation and parameters optimization

The flow behavior of Ti-6Al-4V alloy in superplastic forming (SPF) is studied, and a simple constitutive model is established based on the hyperbolic-sine equation. The constant strain rate high temperature tensile tests were performed at 890, 920, and 950℃, the selected strain rates are 10-2, 10-3, and 10-4/s. The calculation results of strain rate sensitivity index (m) indicates there are two dominant mechanisms of deformation: (i) grain boundary sliding (GBS) when the temperature is below 920℃ or strain rate is above 10-3/s; (ii) GBS and diffusion creep if the temperature is above 920℃ and strain rate is below 10-3/s. Besides, the higher temperatures or the lower strain rates, the smaller void volume fraction. The genetic algorithm (GA) is applied to optimize the parameters in the constitutive model, the average absolute relative error (AARE) between the prediction results and experimental data of stress is reduced from 11.10% to 5.52%. A new modeling method of strain compensation is provided, which is based on stress hardening and softening. The term K is introduced to describe the effects of strain on flow behavior in SPF, and a good agreement between the predicted results and experimental data can be obtained. In summary, the simple hyperbolic-sine constitutive model established in this work with parameter optimization can achieve high prediction accuracy.

Dynamic Mechanical Response and Damage Mechanism of HTPB Propellant under Impact Loading.

The dynamic mechanical behaviors of Hydroxyl-terminated polybutadiene (HTPB) propellant was studied by a split Hopkinson pressure bar apparatus (SHPB) at strain rates ranging from 103 to 104 s−1. The obtained stress–strain curves indicated that the mechanical features, such as ultimate stress and strain energy, were strongly dependent on the strain rate. The real time deformation and fracture evolution of HTPB propellant were captured by a high-speed digital camera accompanied with an SHPB setup. Furthermore, microscopic observation for the post-test specimen was conducted to explore the different damage mechanisms under various conditions of impact loading. The dominated damage characteristics of HTPB propellant were changed from debonding and matrix tearing to multiple cracking modes of ammonium perchlorate (AP) particles, along with the increase of the strain rate. For the first time, the influence of AP particle density on the dynamic response of HTPB propellant was studied by analyzing the strain-rate sensitivity (SRS) index of HTPB propellant with two different filler content (80 wt.% and 85 wt.%), which deduced from a power function of ultimate stress and strain energy density. The result of this study is of significance for evaluating the structural integrity and security of HTPB propellant.

Theoretical predication of dislocation-included high-temperature deformation mechanism maps for GH4742 alloy

ABSTRACT Based on high-temperature compression tests and focusing on the mechanical behaviour characteristics and microstructure evolution laws during high-temperature compression, laws relating to the strain-rate sensitivity index m and the activation energy of deformation Q-value at varying strain rates and deformation temperatures are clarified. Deformation mechanism maps involving dislocation quantity are plotted. Dislocation evolution laws and deformation mechanisms of the grain size with Burgers vector compensation, and the flow stress with modulus compensation during high-temperature deformation are predicted using the deformation mechanism maps.

Evolutions of mechanical properties of AISI 304L stainless steel under shear loading

The evolutions of microstructure and mechanical properties during shear punch testing (SPT) of an AISI 304L metastable austenitic stainless steel were studied at deformation temperatures ranging from 0 °C to 550 °C and strain rates in the range of 10-3 s-1 to 1 s-1. Based on the X-ray diffraction (XRD) phase analysis and metallographic observations, it was inferred that by increasing the deformation temperature from 0 °C to 200 °C, the amount of transformed strain-induced martensite decreases at all strain rates, leading to the weakening of the transformation-induced plasticity (TRIP) effect. However, depending on the strain rate, at temperatures higher than 200 °C, an anomalous trend in shear strength was observed, i.e. the shear strength rose by increasing the deformation temperature at low strain rates, due to the dynamic strain aging (DSA) phenomenon. Strain rate sensitivity studies in conjunction with the microstructural evolutions revealed four temperature-dependent regimes: 0–200 °C, 200–300 °C, 300–500 °C and higher than 500 °C, where the respective strain rate sensitivity index (m) becomes positive, zero, negative, and then positive again. These regimes were rationalized based on the TRIP effect, DSA phenomenon, and thermally-activated dislocation glide.

Kinetic analysis and strain-compensated constitutive models of Ti-42.9Al-4.6Nb–2Cr during isothermal compression

The hot deformation behavior of Ti-42.9Al-4.6Nb–2Cr (at. %) was investigated by isothermal compression tests at the deformation temperature range of 1373–1573 K, strain rate range of 0.001–1.0 s−1, up to the strain of 0.69. The flow stress test results of Ti-42.9Al-4.6Nb–2Cr showed negative temperature and positive strain rate sensitivity. Besides, strain had a great effect on the hot deformation behavior of Ti-42.9Al-4.6Nb–2Cr. Kinetic analysis was adopted to assess the hot workability of Ti-42.9Al-4.6Nb–2Cr via apparent activation energy (Q) of hot deformation, strain-rate sensitivity index (m) and strain hardening index (n). The Q value varied from 607.1 ± 0.7 kJ·mol−1 to 512.6 ± 10.8 kJ mol−1 with the increasing of strain from 0.1 to 0.6. The effect of strain on the Q value at the deformation temperatures below 1473 K was mainly related to dynamic recrystallization of γ phase and kinking of γ lamellae, while the Q value at the deformation temperature above 1473 K might be linked to γ→α phase transformation and DRV of α phase. Based on the kinetic analysis, strain-compensated Arrhenius model and Hensel-Spittel model were successfully established to predict the hot workability (flow stress). Average absolute relative errors of established strain-compensated Arrhenius model and Hensel-Spittel model were 7.52% and 11.95%, respectively. Moreover, both established constitutive models can be extrapolated for predicting the flow stress of Ti-42.9Al-4.6Nb–2Cr to larger strain levels.

Forming Limit Evaluation for AA5182 Aluminum Alloy at Warm Temperatures Based on M–K Model

The M–K method is used to predict the forming limit of AA5182 aluminum alloy to study the effect of temperature, strain rate sensitivity index and strain hardening exponent. Three kinds of yield criterion Yld2000, Barlat’s 1989 and Hill’s 1948 are introduced into the model, respectively, to find which one is most suitable for predicting the forming limit of AA5182 at different temperatures. The forming limit experiment of AA5182 aluminum alloy under different temperatures is carried out to verify the accuracy of the prediction. As results show that both Barlat’s 1989 and Yld2000 can get the ideal prediction results for the forming limit of AA5182. However, since Barlat’s 1989 can be implemented with fewer parameters, it is considered to be more convenient and suitable for predicting forming limit of AA5182 than the other two yield criteria. Then, influence of parameters in the flow stress model is analyzed. It indicates that strain rate sensitivity index has great influence on the material forming limit and the effect of strain hardening exponent is negligible.

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.

Study on constitutive model and dynamic recrystallization softening behavior of AZ80A magnesium alloy

The microstructures of as-cast AZ80A magnesium alloy before and after homogenization treatment were studied. The flow behaviors of the homogenized alloy under different deformation conditions were studied by isothermal compression tests. Based on the flow stress-strain curves of the homogenized alloy, the constitutive model was established by the strain compensation method. The strain rate sensitivity index maps with different strains were constructed to quantify the dynamic recrystallization softening behavior of the homogenized alloy. Based on this, the influence of deformation temperature and strain rate on strain rate sensitivity index and dynamic recrystallization microstructure evolution were studied. The results show that both increasing homogenization temperature and holding time are beneficial for the β-phases to dissolve and alloying elements to diffuse. It is concluded that the proper homogenizing parameter of as-cast AZ80A magnesium alloy is 683 K for 20 h. Both the increase of deformation temperature and the decrease of strain rate are beneficial to the increase of strain rate sensitivity index. The region with an index greater than 0.22 corresponds to dynamic recrystallization softening zone and has good deformation properties.

Study on Strain Rate–Dependent Deformation Mechanism of WC–10 wt% Ni3Al Cemented Carbide by Micropillar Compression

Herein, the strain rate–dependent deformation mechanism of WC–10 wt% Ni3Al cermet micropillars is studied by in situ uniaxial compression. The results show that compression at high strain rates exhibits a relatively smooth stress–strain response compared with that at low strain rates. Microstructural characterization suggests that at high strain rates, grain boundary sliding is the dominant mechanism of deformation, whereas at low strain rates, dislocation annihilation plays the dominant role. The strain rate sensitivity index also varies with the strain rate from 1 × 10−2 to 5 × 10−3 s−1, confirming that the dominant deformation mechanisms change in this range.

Rheological Law and Mechanism for Superplastic Deformation of Ti-6Al-4V.

The behaviors of and mechanisms acting in Ti–6Al–4V alloy during low-temperature superplastic deformation were systematically studied by using a Gleeble-3800 thermocompression simulation machine. Focusing on the mechanical behaviors and microstructure evolution laws during low-temperature superplastic compression tests, we clarified the changing laws of the strain rate sensitivity index, activation energy of deformation, and grain index at varying strain rates and temperatures. Hot working images based on the dynamic material model and the deformation mechanism maps involving dislocation quantity were plotted on the basis of PRASAD instability criteria. The low-temperature superplastic compression-forming technique zone and the rheological instability zone of Ti–6Al–4V were analyzed by using hot processing theories. The dislocation evolution laws and deformation mechanisms of the grain size with Burgers vector compensation and the rheological stress with modulus compensation during the low-temperature superplastic compression of Ti–6Al–4V were predicted by using deformation mechanism maps.

Inducing superplasticity in extruded pure Mg by Zr addition

Addition of 0.7 wt% Zr to pure Mg resulted in a bimodal structure, consisting of both coarse and fine recrystallized grains with a mean grain size of 2.8 μm, and a large fraction of high angle grain boundaries after extrusion. A maximum strain rate sensitivity index of 0.42, obtained by shear punch test (SPT) at 673 K, together with activation energy of 96 kJ mol–1 indicated that grain boundary sliding controlled by grain boundary diffusion is the dominant mechanism in superplastic regime.

Treatment of Concurrent Microstructure Evolution and Deviation from Steady-State Flow in Constitutive Relationship for Superplastic Deformation

Abstract Superplasticity is the ability of certain polycrystalline materials to exhibit exceptionally large elongations by grain boundary sliding and its accommodation by diffusion, dislocation slip, or both. One of the critical requirements for this phenomenon to occur is the fine equiaxed grains, which should be stable during deformation at elevated temperature. Under this condition, there exists a unique relationship between stress and strain rate as a function of temperature and grain size, with the high values of strain rate sensitivity index m of greater than 0.3. However, there is ample evidence of the variation in flow stress with strain along with concurrent microstructural evolution. Often the microstructures are known not to be equiaxed yet exhibit superplasticity by rapid change in morphology and size during early stage of deformation. This leads to flow softening and hardening with strain as a result of the dominance of one type of change over the other. Mechanistically, accommodation of grain boundary sliding by grain boundary migration leads to grain growth, resulting in flow hardening, whereas the absence of the same may cause the formation of cavities because of stress concentration at triple points and at two-phase or particle–matrix interphase boundaries. In view of this, the constitutive relationship needs to be modified by incorporating the dependence of stress on strain and concurrent microstructure changes. The present work critically examines the nature of stress–strain curves and microstructure evolution in an attempt to account for the non–steady-state flow and attain a generalized form of constitutive relationship for superplastic deformation. An attempt is made to quantify the variations in flow stress and microstructures interdependently as well as with strain by exploring the suitable trend lines. These equations can numerically and physically help in correlating the microscopic and macroscopic properties to the mechanisms for superplastic deformation.

Superplasticity of fine-grained Mg–xGd alloys processed by multi-directional forging

Microstructural development and superplastic behavior of Mg–xGd (x = 1, 2, 3 wt%) alloys were investigated after the multi-directional forging (MDF) process. Microstructural observations of the extruded materials revealed non-homogeneous structures with bimodal grain sizes, consisting of coarse elongated grains resulting from deformation, surrounded by fine grains formed by partial dynamic recrystallization. The grain sizes of the recrystallized regions in the Mg–1Gd, Mg–2Gd and Mg–3Gd alloys were 5.6, 3.9 and 3.1 μm, respectively. After six passes of the MDF process, the bimodal grain structure disappeared as a result of complete dynamic recrystallization and almost homogeneous microstructures with the grain sizes of 2.5, 2.2 and 1.9 μm were obtained in the Mg–1Gd, Mg–2Gd and Mg–3Gd alloys, respectively. The smaller fraction of the recrystallized region in the extruded Mg–3Gd alloy and the smaller grain size in the MDF processed condition imply that more pronounced recrystallization retardation occurs through solute drag mechanism at the highest Gd content. Superplasticity was assessed by measuring the strain rate sensitivity index (m-value), through shear punch testing (SPT) in a temperature range of 623–698 K at various strain rates. After six passes of MDF, peak m-values of 0.45 and 0.46 were obtained at 648 K for Mg–1Gd and Mg–2Gd alloys, respectively, while for the Mg–3Gd alloy the peak m-value of 0.48 was achieved at a lower temperature of 623 K. According to the m-value of about 0.5 and the corresponding activation energies of 101–114 kJ/mol, the governing superplastic deformation mechanism was determined as grain boundary sliding (GBS) controlled by grain boundary diffusion.

Superplasticity in a multi-directionally forged Mg–Li–Zn alloy

Superplastic behavior of the Mg–8Li–1Zn alloy, processed by extrusion at 573 K followed by multi-directional forging (MDF) at 423 K, was studied using shear punch testing (SPT) of miniature specimens at various temperatures and strain rates. Microstructural analysis indicated moderate grain refinement, reducing the gran size from 8 μm in the initial as-extruded condition to 4 μm after 8 passes of MDF. Processing by MDF not only refined the grain structure but also provided a more homogeneous microstructure and a larger fraction of high-angle grain boundaries. SPT was performed at shear strain rates in the range of 3.3 × 10−3–1.3 × 10−1 s−1 and temperatures in the range of 498–573 K. The strain rate sensitivity (SRS) index (m-value), obtained from the slope of the central region of the sigmoidal shear stress–shear strain rate curves, was as high as 0.51 for the MDF processed material at 548 K. This is in contrast to the as-extruded material that exhibited a linear behavior with a maximum m-value of only 0.29 at the same temperature. For the MDF processed material, the activation energy of 61 kJ mol−1, which is close to 67 kJ mol−1 for the grain boundary diffusion in β-Li, and the high m-value of 0.51 suggest that the prevailing deformation mechanism is grain boundary sliding (GBS) controlled by grain boundary diffusion.

Evaluating the high temperature superplastic behavior of a thermomechanically processed Al–Cu aluminum alloy through miniaturized testing method

The high temperature superplastic behavior of ultrafine grain A206 aluminum alloy was examined employing miniaturized shear punch jump test method. To achieve a fine-grained microstructure, accumulative back extrusion were applied at 200 °C up to 1, 3 and 5 passes on the as-annealed microstructure. The high temperature mechanical properties of the products were assesses at 100, 200 and 300 °C. The strain rate sensitivity indices (m) of the processed specimens were evaluated under the base strain rate of 0.004 s−1 with the incremental jump to 0.01 s−1, and various temperatures. The temperature of 300 °C was found as the optimum temperature for superplastic deformation of the experimented material, and a considerable increase in the m value was observed after 3 and 5 passes. The highest elongation to fracture value was observed in 5-passes processed specimen at 300 °C where the m value was obtained about 0.35. In this condition, grain boundary sliding was announced to be the dominant deformation mechanism. Lastly, TEM and XRD characterization exposed that the fine Al2Cu precipitates are rarely observed in 1-pass processed microstructure while a high fraction of fine precipitates (7–10 nm) were found in 5-passes processed material. These fine precipitates were thermally stable and coherent with the aluminum matrix, and thus were able to pin the grain boundaries and at the high temperatures and decrease grain growth rate.

Properties of self-compacting concrete (SCC) with recycled tire rubber aggregate: A comprehensive study

Abstract Disposal of massive scrap tires in an eco-friendly way has become a worldwide concern due to the booming automobile industry. The introduction of waste tire rubber particles into concrete as an alternative aggregate provides a promising way to solve the problem. It is noteworthy that the substitute of natural aggregates with rubber particles can mitigate environmental destruction and resource consumption caused by mining activities of natural aggregates. In this study, a series of experiments were conducted to evaluate both fresh and hardened properties of self-compacting concrete (SCC) with recycled tire rubber aggregate (RA), aiming at providing fundamental insight of its performance for the potential large-scale applications. Results show that the addition of RA leads to a slight decline in workability and an increase in air content of fresh SCC. Increasing RA content results in the improvement of the damping ratio, fracture energy and ductility index while a loss of compressive strength and dynamic modulus. SCC with RA also presents high strain rate sensitivity and toughness index under impact load, indicating improved impact resistance. In addition, use of RA enables SCC to achieve low water absorption and high resistance to chloride ion penetration. From the above, this study provides a comprehensive investigation of the clean and effective utilization of recycled tire rubber in concrete.

Hot tensile test for determining the material constant on superplastic 5083Al alloy sheet

Abstract The superplastic alloys are characterized by strain rate sensitivity index (m). Actual values of m depend on temperature, strain rate and grain size. This experiment aims to attain maximum formability by superplastic forming processes in AA 5083 alloy using uniaxial hot tensile test method. To optimize the different material parameters such as maximum elongation, yield stress, temperature, strain rate and strain rate sensitivity index with the help of the uniaxial hot tensile method. An experimental and Finite Element method are adopted, to attain the permeability by achieving the material properties, at various temperatures and various initial strain rate conditions.

Indentation creep and tribological characterization of AISI 321, AISI 431 and FDMA borided and non-borided steels

In this paper, the mechanical properties, the creep and the tribological behaviours of three borided and non-borided steel materials were analysed. The alloy steel substrates were borided by a powder-pack boriding process during 8 h at 950 °C. The creep process during the holding stage of nanoindentation test was analysed using various mathematical models. The tribological properties of the studied materials were investigated by wear experiments on a ball disc test wearing. It was found that the corresponding indentation creep behaviour can be correctly described by a power-law relationship. Furthermore, based on the selected power-law creep function, the stress exponents and the corresponding strain rate sensitivity (SRS) indices were also determined. In particular, boride layers showed excellent mechanical properties and they were found to be more creep and wear resistant compared to base steel substrates. Furthermore, with an increase in applied load, the wear tests revealed an increase in wear loss and a decrease in the friction coefficient.