Double Differential Method Research Articles

A novel method for measuring electrolytic conductivity with a polarization impedance control function

The article presents an idealized model of the differential method utilized in conductometry to measure electrolytic conductivity (EC). It identifies the main drawback of the widely used differential method: the inability to control the influence of polarization impedance on EC measurement results. A criterion for the absence of error caused by polarization effects is proposed, involving equality between the ratios of resistance differences and cell constant differences. A novel method for EC measurement, termed the double differential method, is introduced. This method relies on repeated differential impedance measurements and incorporates an additional third impedance measurement of a virtual liquid column. The new approach enables the identification of polarization impedance influence on EC measurements and the calculation of measurement errors for correction. A 3 times lower type A measurement uncertainty value can be achieved by averaging the corrected results.

Investigation on hot deformation behavior and microstructure evolution of superaustenitic stainless steel S31254 during elevated temperature compression testing

The study thoroughly investigated the hot deformation behavior and microstructure evolution of superaustenitic stainless steel S31254. Hot compression tests were conducted at temperatures ranging from 950 °C to 1200 °C and strain rates of 0.01–10 s−1. The flow behavior of S31254 is influenced by adiabatic heating, particularly at high strain rates. The critical conditions of dynamic recrystallization for various deformation conditions were calculated based on the “double differential method.” An rise in deformation temperature or a reduction in strain rate reduces critical stress. Using the Arrhenius equation and Zener-Hollomon parameter to represent the deformation parameters, a linear connection between peak stress and dynamic recrystallization critical conditions was determined. Electron backscattering diffraction and transmission electron microscopy were used to characterize the microstructure under various deformation conditions. The dynamic softening of superaustenitic stainless steel is mainly achieved through dynamic recrystallization. The recrystallized grains are driven by distorted energy to nucleate preferentially at high-angle grain boundaries and grow towards high misorientations. Discontinuous dynamic recrystallization characterized by grain boundary bowing out is the main recrystallization mechanism in S31254. However, at high temperatures and low strain rates (1200 °C, 0.01 s−1), the dynamic recrystallization process shifts from discontinuous to continuous, with subgrain coalescence serving as the nucleating mode.

Thermal deformation behavior and microstructure evolution of Fe−8.5Mn−1.5Al light−weight medium manganese steel

In this paper, Fe−8.5Mn−1.5Al light−weight medium Mn steel is used as the research object, and the hot compression test is conducted by Gleeble−3500 thermal simulation tester. The dynamic reversion and dynamic recrystallization (DRX) processes are analyzed according to the true stress−strain curve; the θ−σ work−hardening rate curve is plotted by P−J double differential method to analyze the influence law between work−hardening and dynamic reversion and recrystallization softening effect of the material; the DRX critical strain model is established to analyze the influence law of deformation parameters on DRX; Based on the dynamic material model theory, the hot working diagram and three−dimensional power dissipation diagram are constructed, and the best hot working area is determined by combining the microstructure of the material. Finally, based on the above research content, a systematic overview of the dynamic softening effects of DRX and dynamic recovery (DRV) will be provided.

Effect of hot isostatic pressing on microstructural and micromechanical properties of additively manufactured 17–4PH steel

Microstructural and mechanical characterization techniques were utilized to establish the effect of the combined hot isostatic pressing (HIP) and standard H1025 heat treatment schedule on the properties of 17–4PH steel manufactured by means of laser powder bed fusion (LPBF). The as-printed (AP) sample initially consists of a dual-phase microstructure, with 78% martensite and 22% retained austenite. Then, the combined HIP and H1025 applied to the AP sample resulted in lower retained austenite of 7%. The microstructural analysis indicates that the post-processing after printing alleviated the process-induced defects reducing the overall defect content from 0.37% to 0.01%. Moreover, it is observed that the characteristic melt pools are dissolved, resulting in a homogeneous microstructure with reduced grain sizes. A room-temperature compression testing was then applied to the sample before and after post-processing treatment. It has been identified that, in both samples, the retained austenite transforms into martensite, a characteristic of the transformation-induced plasticity effect. The critical stress to initiate the dynamic transformation was then determined to be lower in the HIP sample than that of the AP sample. Based on the results, it can be concluded that the combined HIP+H1025 processing employed in this work effectively increased the mechanical properties of LPBF-fabricated 17–4PH steel. • 17–4Ph steel was fabricated via laser powder bed fusion. • Characterization of the samples was done by the means of EBSD analysis. • Using double differential method, the critical stresses for initiation of dynamic transformation of HIP sample was higher.

Magnetic and Plasmonic Composite Nanostructures for Creating Optical Filters at Substance and Material Diagnostics Systems

Introduction. Porous silicon (PS) and materials on its basis are of interest for application in nanoelectronics, targeted drug delivery and advanced gas sensors. In addition, PS-based nanostructures are promising as filters in fibre-optic communication systems, since conventional thin-film deposition filters possess sidebands in their operating range thus requiring high vacuum for nanometer-thick coatings.Aim. To develop optical band-stop filter prototypes based on composite magnetic nanoparticles and the effect of localized surface plasmon resonance (LSPR) in an array of silver nanoparticles located on the PS surface. Materials and methods. The development and synthesis of nanostructures for the creation of filter prototypes. The double differentiation method in conjunction with Mie absorption theory was used for processing and analyzing the prototypes attenuation characteristics.Results. Two prototypes were developed. An analysis of the attenuation characteristics of a prototype based on SiO2 matrix functionalized by FemOn indicated that the parameters of the detected absorption bands depend on the size of FemOn nanoparticles. The attenuation characteristics of the LSPR-based prototype contain two absorption bands. The center wavelength value in the band caused by LSPR in the array of silver nanoparticles, close to spherical, is 367.5 nm. Excitation of LSPR in silver quantum clusters, manifested by the appearance of the corresponding band, occurs at a wavelength of 265.5 nm. The suppression in each of the bands can be controlled by changing the parameters of the PS matrix synthesis.Conclusion. Despite the disadvantages, e.g. a relatively low accuracy in setting the center wavelength, as well as certain difficulties concerned with reducing the unevenness in the absorption band, the obtained prototypes surpass existing analogues and are prospective for the development of compact analysis and diagnostics systems in a wide energy range.

Effect of Double Hit Hot Deformation on the Evolution of Dynamically Transformed Ferrite

Double-hit hot compression tests were carried on medium-carbon low-alloy steels using Gleeble 3800® thermomechanical simulator. The experiments were performed at strain rates of 0.25 and 0.5 s−1 and temperatures of 1150 and 1200 °C with interpass times of 5, 15, and 25 s. The onset of critical stresses for dynamic transformation (DT) for both first and second hit were detected using the double-differentiation method. It was found that the critical stress for DT increased with a decrease in temperature and an increase in strain rate. The presence of dynamically transformed ferrite was observed and quantified using electron-backscatter diffraction, kernal average misorientation, and grain boundary maps. Then, a thermodynamic analysis was carried out using JmatPro software. A method of determining the change in Gibbs energy during DT phenomenon is proposed for double hit deformation.

Microstructure Evolution, Mechanical Properties and Deformation Behavior of an Additively Manufactured Maraging Steel.

In this work, the microstructure and mechanical properties of an additively manufactured X3NiCoMoTi18-9-5 maraging steel were determined. Optical and electron microscopies revealed the formation of melt pool boundaries and epitaxial grain growth with cellular dendritic structures after the laser powder bed fusion (LPBF) process. The cooling rate is estimated to be around 106 °C/s during solidification, which eliminates the nucleation of any precipitates. However, it allows the formation of austenite with a volume fraction of about 5% and dendritic structures with primary arm spacing of 0.41 ± 0.23 µm. The electron backscatter diffraction analysis showed the formation of elongated grains with significant low-angle grain boundaries (LAGBs). Then, a solutionizing treatment was applied to the as-printed samples to dissolve all the secondary phases, followed by aging treatment. The reverted austenite was evident after heat treatment, which transformed into martensite after tensile testing. The critical plastic stresses for this transformation were determined using the double differentiation method. The tensile strength of the alloy increased from 1214 MPa to 2106 MPa after the aging process due to the formation of eta phase. The experimental data were complemented with thermodynamic and mechanical properties simulations, which showed a discrepancy of less than 3%.

Strain-Induced Ferrite Formation During Steckel Mill Simulations with Varying Roughing Pass Schedules

It has been previously demonstrated that austenite may undergo partial dynamic transformation (DT) during the plate rolling process. Austenite dynamically transforms into unstable ferrite during hot deformation even at very high temperatures. In this work, the plate rolling simulations, with emphasis on Steckel mill operations, through torsion testing under isothermal conditions were performed on an X70 steel. Four different roughing schedules were tested followed by five finishing passes with pass strains of 0.3 applied at 900 °C. The roughing schedules had zero, one, two and three roughing passes at a temperature of 1100 °C, strain of 0.4 and strain rate of 1 s−1. The stress–strain curves as well as the mean flow stress (MFS) behaviors indicated that both dynamic transformation (DT) and dynamic recrystallization (DRX) occurred during straining. The critical strains for the onset of DT and DRX were determined by means of the double differentiation method and the critical strain values decreased with the number of roughing and finishing strains from the first going to the last pass. It was observed that the volume fraction of the dynamically formed ferrite increased sharply during the finishing stage as the number of previous roughing passes increased, which can be attributed to higher strain accumulation. The results presented here indicate that improved models are needed to control the microstructure of the material during subsequent cooling.

Velocity Measuring Tool of Projectile in the Barrel: Experimental Research Results of the Valid Layout

The work is devoted to the consideration of the methodology of experimental research of velocity measuring tool of the projectile in the barrel. The content of individual stages of conducting research is outlined. The research of the optical quality of the reflective coating is carried out. It is shown that the use of reflective paint and envelope in the coating of the front part of the projectile provides an effect of retroreflection, sufficient for the Doppler frequency shift. The influence of the retroreflective coating on the ballistic characteristics of the projectile has been investigated. It is defined that the relative increase of the mass and dimensions of the projectile, wich caused by the planted of the retroreflective coating on its front part, does not exceed, in accordance 0,10% and 0,025% of its output mass and length, therefore, the effect of these projectile parameters is too small and unable to exert a noticeable effect on its ballistic characteristics during of movement in barrel. The velocity projectile curves were carried by experimentally on an valid layout of the measuring tool , and their analysis was carried out. The possibility of using the double differential method of laser Doppler anemometry to measure the velocity of the projectile in barrel has been confirmed. Found that form the experimental curves velocity corresponds to the expected nature of the increase velocity of the projectile in the barrel of velocity measuring tool. The adequacy of the mathematical model of the measurement tool which obtained theoretically is confirmed.

The Avrami Kinetics of Dynamic Recrystallization in Nickel-Niobium Alloys

The flow curves determined on a series of Ni-Nb alloys are analysed. Six alloys containing Ni–0.01, 0.1, 1, 2, 5 and 10 wt. % Nb with pure Ni were tested in torsion at various strain rates within the hot forging temperature range. Under these conditions, large strains were attained, which permitted steady state flow to take place. The double-differentiation method is employed to define the critical strain for the initiation of DRX, leading to the evaluation of the strain hardening and dynamic recovery parameters. The relations obtained are compared to ones determined earlier using a least squares approach. It is shown that the two sets of relations do not differ appreciably. These results are employed to predict the Avrami kinetics of a range of Ni-Nb alloys strained at different temperatures and strain rates. The Avrami time exponents all fall in the range 1.0 to 5.0. The dependence of the time of half-softening, t50, on Nb content, strain rate and temperature is also derived under the same conditions.

A Two-Stage Physical-Based Model for Predicting Flow Stress of As-cast TiAl Alloy Under Hot Deformation Conditions

The hot deformation behavior of Ti-30Al-4.2Mn-4.5Nb-0.2B alloy was investigated using the isothermal compression experiment at temperatures of 1020-1200 °C and strain rates of 0.001-1 s−1. The flow stress was sensitive to the deformation parameters like temperature and strain rate, which decreases with the increase in temperature and decrease in strain rates. Based on the true stress-true strain data, a two-stage physical-based model was proposed to describe the flow stress curve of as-cast TiAl alloy during hot deformation process. For establishing the model, at first, the flow curves of dynamic recovery (DRV) were modeled by employing stress-dislocation relation and adjusting dislocation annihilation coefficient Ω. Then, the flow curves of dynamic recrystallization (DRX) were modeled by considering the dynamic softening behavior into Avrami equation. Finally, the flow curves in the entire deformation stages could be described by embedding the predicted data of DRV model (i.e., flow stress before the critical strain) into the predicted data by DRX model (i.e., flow stress after the critical strain). The critical strain for initiation of DRX was determined by the double-differentiation method. To evaluate the applicability and effectiveness of DRX kinetics equation, the DRX curves were calculated and were consistent with the microstructure observation. Comparison between the experimental and predicted data shows that the proposed physical-based model can well forecast the flow stress under a wide working domain.

Twinning, dynamic recrystallization, and crack in AZ31 magnesium alloy during high strain rate plane strain compression across a wide temperature

Plane strain compression (PSC) tests were carried out on as-cast AZ31 magnesium alloy samples at temperatures from 250 to 400 °C with different strain rates (≥ 10 s−1). The microstructures along the crack boundaries and secondary cracks were detected. The electron backscatter diffraction (EBSD) results indicated that twin induced dynamic recrystallization (DRX). The flow curves were analyzed using the double differentiation method and two or three minima were detected. The first set of minima is shown to identify the critical strain for twinning, while the second set indicates the critical strain for the initiation of DRX or micro-cracks, and the third set is related to the onset of micro-cracks. Twinning affects the nucleation and propagation of crack. The crack in the matrix grain is inhibited due to the preferred initiation of twinning to impede competitive crack extension. With increasing temperature, the competitive relationship between crack and DRX exists on the twin boundaries. The nucleation, growth and coalescence of voids on the grain boundaries and at grain triple junctions contributes to the formation of cracks in the fine-grained area.

Real Time Detection of R – Peak in QRS Complex of ECG using Microcontroller

<p>Real-time detection of R peaks in QRS complex of ECG signal is the first step in the processing of ECG waveform. Based on this, various other ECG parameters can be extracted. These parameters provide substantial information about various heart diseases. In this paper, we are proposing a method to detect R – peaks of ECG signal dynamically. The most prominent role in the R – peak detector is executed by the microcontroller. This method originates by acquiring signal from the subject and necessary pre-processing is carried out on the signal in order to achieve the denoised signal. Subsequently, this filtered signal is handed over to microcontroller where a pulse is generated for each R – peak that is found in the QRS complex of ECG signal. The microcontroller is embedded with a signal processing algorithm. The algorithm used to determine the R – peaks is double differentiation method which is straightforward and robust. </p>

Determination of the Critical Stress Associated with Dynamic Phase Transformation in Steels by Means of Free Energy Method

The double differentiation method overestimates the critical stress associated with the initiation of dynamic transformation (DT) because significant amounts of the dynamic phase must be present in order for its effect on the work hardening rate to be detectable. In this work, an alternative method (referred to here as the free energy method) is presented based on the thermodynamic condition that the driving force is equal to the total energy obstacle during the exact moment of transformation. The driving force is defined as the difference between the DT critical stress (measured in the single-phase austenite region) and the yield stress of the fresh ferrite that takes its place. On the other hand, the energy obstacle consists of the free energy difference between austenite and ferrite, and the work of shear accommodation and dilatation associated with the phase transformation. Here, the DT critical stresses in a C-Mn steel were calculated using the free energy method at temperatures ranging from 870 °C to 1070 °C. The results show that the calculated critical stress using the present approach appears to be more accurate than the values measured by the double differentiation method.

Deformation Behavior of a Coarse-Grained Mg-8Al-1.5Ca-0.2Sr Magnesium Alloy at Elevated Temperatures

The compression tests were carried out on a coarse-grained Mg-8Al-1.5Ca-0.2Sr magnesium alloy samples at temperatures from 300 to 450 °C and strain rates from 0.001 to 10 s−1. The flow stress curves were analyzed using the double-differentiation method, and double minima were detected on the flow curves. The first set of minima is shown to identify the critical strain for twinning, while the second set indicates the critical strain for the initiation of dynamic recrystallization (DRX). Twin variant selection was numerically identified by comprehensive analysis of the Schmid factors for different deformation modes and the accommodation strains imposed on neighboring grains. It was found that twinning is initiated before DRX. Dynamic recrystallization volume increases with strain rate at a given deformation temperature. At high strain rate, various twin variants are activated to accommodate deformation, leading to the formation of twin intersections and high DRX volume. Fully dynamic recrystallized structure can be obtained at both high and low strain rates due to the high mobility of the grain and twin boundaries at the temperature of 400 °C.

Flow softening of 253 MA austenitic stainless steel during hot compression at higher strain rates

The flow softening of 253 MA austenitic stainless steel was investigated by means of hot compression tests performed over the temperature range of 900–1150°C. Constant true strain rates of 0.01s−1, 0.1s−1, 1s−1, 10s−1 and 20s−1 were used. The effect of deformation temperature and strain rate on the flow softening and the flow softening mechanisms in the high strain-rate regime (1–20s−1) was examined. The flow curves at higher strain rates, i.e. 10s−1 and 20s−1, were characterized by a single peak followed by continuous stress softening at higher strain levels. The degree of flow softening increased with increasing strain rate and increasing temperature. The flow softening was attributed to thermal softening due to deformation heating, microstructural softening by dynamic recrystallization (DRX) and flow instability. Deformation heating produced by plastic work resulted in significant temperature rise in the steel. The thermal softening due to deformation heating was more pronounced at higher strain rates and lower temperatures. DRX was found to take place at higher deformation temperatures and higher strain rates; this was confirmed by the double-differentiation method proposed by Poliak and Jonas. Flow instability in the form of localized deformation bands occurred at the temperatures of 900°C and 950°C. The processing map developed as per Murty–Rao's instability criterion was found to yield an overestimate of the unstable flow region. Based on the flow behavior and microstructure analysis, it is concluded that this steel is suitable to be hot worked at higher strain rates and higher temperatures in order to reduce the flow stress and to refine grain size.

Flow Softening-based Formation of Widmanstätten Ferrite in a 0.06%C Steel Deformed Above the Ae<sub>3</sub>

Compression tests were carried out at a strain rate of 1 s(-1) on a 0.06%C-0.3%Mn-0.01%Si steel over two temperature ranges: i) 920 degrees C to 980 degrees C, and ii) 500 to 750 degrees C. Optical and scanning electron microscopy images indicCompression tests were carried out at a strain rate of 1 s(-1) on a 0.06%C-0.3%Mn-0.01%Si steel over two temperature ranges: i) 920 degrees C to 980 degrees C, and ii) 500 to 750 degrees C. Optical and scanning electron microscopy images indicated that significant volume fractions of Widmanstatten ferrite were formed dynamically above the Ae(3) temperature. The ferrite plates coalesced into polygonal grains during straining. The double differentiation method was applied to the stress-strain curves, providing average values for the dynamic transformation (DT) and dynamic recrystallization (DRX) critical strains of 0.12 and 0.20, respectively. These results are interpreted in terms of the flow softening-based transformation model by calculating both the driving forces promoting the transformation as well as the energy barriers that oppose it. The model predicts the temperature range over which DT can occur as well as the observed critical strains.ated that significant volume fractions of Widmanstatten ferrite were formed dynamically above the Ae(3) temperature. The ferrite plates coalesced into polygonal grains during straining. The double differentiation method was applied to the stress-strain curves, providing average values for the dynamic transformation (DT) and dynamic recrystallization (DRX) critical strains of 0.12 and 0.20, respectively. These results are interpreted in terms of the flow softening-based transformation model by calculating both the driving forces promoting the transformation as well as the energy barriers that oppose it. The model predicts the temperature range over which DT can occur as well as the observed critical strains.

Initiation and accommodation of primary twins in high-purity titanium

Uniaxial compression tests were carried out at room temperature and at strain rates of 0.001, 0.01, 0.1 and 1s−1 on samples of high-purity titanium. The initial texture was favorably oriented for contraction twinning. The double-differentiation method was employed to detect the initiation of twinning as well as of dynamic recrystallization. Critical strains of about −0.24 and −0.65 were determined, respectively, for these two mechanisms. The relevant mechanisms were identified by means of electron backscatter diffraction (EBSD) techniques. At a true strain of ε=−0.3, two main kinds of primary twins, {112¯2} contraction and {101¯2} extension, were observed and second-generation twins were also identified by means of the EBSD analysis. The presence of low Schmid factor (SF) (<0.2) twins was established as well as the absence of potential high SF (>0.4) twins. The appearance of the low SF twins is explained in terms of the low accommodation work required in the neighboring grains; this involves prismatic glide in the present case. The absence of the potential high SF twins, on the other hand, is justified as requiring the operation of a combination of several difficult deformation modes: basal glide, pyramidal glide, and twinning.

Flow softening, twinning and dynamic recrystallization in AZ31 magnesium

The compression tests were carried out on AZ31 magnesium alloy samples at temperatures from 300 to 450°C and strain rates of 0.03–0.3s−1. The evolution of the microstructure and texture was followed and the volume fractions recrystallized were determined as a function of strain and temperature. The flow curves were analyzed using the double differentiation method and double minima were detected on all the curves. The first set of minima is shown to identify the critical strain for twinning, while the second set indicates the critical strain for the initiation of dynamic recrystallization. The texture analysis and EBSD results indicate that flow softening is mainly caused by the grain reorientations brought about by twinning. The remainder of the flow softening is associated with the volume fraction recrystallized. The microstructure analysis shows that the volume fraction recrystallized does not approach its asymptotic value of one even during steady state flow.

Dynamic Transformation during Simulated Hot Rolling

High temperature flow curves were evaluated on two Nb steels in both compression and torsion and at a series of temperatures and strain rates. The critical strains for the initiation of dynamic transformation (DT) were determined by the double differentiation method. These are shown to be distinctly lower than those associated with dynamic recrystallization (DRX). It is also evident that the compression critical strains for both DT and DRX are lower than the equivalent torsion critical strains. Mean flow stresses (MFSs) were calculated by integration from the flow curves. When plotted against inverse temperature, stress drops were observed about 30 degrees above the Ae3. These drops are shown to be caused by the dynamic transformation of austenite to ferrite, a softer phase. The characteristics of the ferrite produced dynamically are described and the transformation is shown to be displacive in nature, leading to the appearance fine Widmanstatten plates.