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- Corrosion (30)
- Laser beam welding (20)
- Wear (19)
- Additive manufacturing (18)
- Friction (16)
- Additive Manufacturing (13)
- Niobium carbide (13)
- Fatigue (12)
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Organisationseinheit der BAM
- 9 Komponentensicherheit (108)
- 7 Bauwerkssicherheit (69)
- 5 Werkstofftechnik (45)
- 9.3 Schweißtechnische Fertigungsverfahren (45)
- 8 Zerstörungsfreie Prüfung (41)
- 7.6 Korrosion und Korrosionsschutz (29)
- 5.1 Mikrostruktur Design und Degradation (24)
- 9.5 Tribologie und Verschleißschutz (24)
- 7.1 Baustoffe (22)
- 6 Materialchemie (19)
- 8.0 Abteilungsleitung und andere (19)
- 9.4 Integrität von Schweißverbindungen (19)
- 9.6 Additive Fertigung metallischer Komponenten (15)
- 3 Gefahrgutumschließungen; Energiespeicher (13)
- 4 Material und Umwelt (13)
- 7.4 Baustofftechnologie (13)
- 5.2 Metallische Hochtemperaturwerkstoffe (11)
- 8.5 Röntgenbildgebung (9)
- 9.2 Versuchsanlagen und Prüftechnik (9)
- 6.2 Material- und Oberflächentechnologien (8)
- 8.4 Akustische und elektromagnetische Verfahren (8)
- 9.0 Abteilungsleitung und andere (8)
- 2 Prozess- und Anlagensicherheit (7)
- 3.4 Sicherheit von Lagerbehältern (7)
- 5.3 Polymere Verbundwerkstoffe (6)
- 1 Analytische Chemie; Referenzmaterialien (5)
- 4.2 Material-Mikrobiom Wechselwirkungen (5)
- 6.6 Physik und chemische Analytik der Polymere (5)
- 1.2 Biophotonik (4)
- 4.1 Biologische Materialschädigung und Referenzorganismen (4)
- 5.5 Materialmodellierung (4)
- 6.1 Oberflächen- und Dünnschichtanalyse (4)
- 7.5 Technische Eigenschaften von Polymerwerkstoffen (4)
- 8.1 Sensorik, mess- und prüftechnische Verfahren (4)
- 4.5 Kunst- und Kulturgutanalyse (3)
- 5.4 Multimateriale Fertigungsprozesse (3)
- 7.2 Ingenieurbau (3)
- 7.7 Modellierung und Simulation (3)
- 8.6 Faseroptische Sensorik (3)
- 2.1 Sicherheit von Energieträgern (2)
- 2.2 Prozesssimulation (2)
- 3.0 Abteilungsleitung und andere (2)
- 3.1 Sicherheit von Gefahrgutverpackungen und Batterien (2)
- 3.2 Gefahrguttanks und Unfallmechanik (2)
- 5.0 Abteilungsleitung und andere (2)
- 6.3 Strukturanalytik (2)
- 6.5 Synthese und Streuverfahren nanostrukturierter Materialien (2)
- 7.0 Abteilungsleitung und andere (2)
- 8.2 Zerstörungsfreie Prüfmethoden für das Bauwesen (2)
- 1.4 Prozessanalytik (1)
- 2.0 Abteilungsleitung und andere (1)
- 2.4 Prüfung und Bewertung von Explosivstoffen/Pyrotechnik (1)
- 2.5 Konformitätsbewertung Explosivstoffe/Pyrotechnik (1)
- 3.5 Sicherheit von Gasspeichern (1)
- 4.3 Schadstofftransfer und Umwelttechnologien (1)
- 5.6 Glas (1)
- 7.3 Brandingenieurwesen (1)
- 8.3 Thermografische Verfahren (1)
A damaging action of HNO3-55% only occurs in combination with its decomposition into nitrous gases, which can be caused by UV radiation. In a laboratory test, transparent HDPE jerrycans have been exposed to both UV radiation and 55 wt-% nitric acid solution at (41 ± 2)°C, for up to 20 days. For comparison, UV radiant exposure (21 days) and nitric acid exposure (up to 6 weeks) were performed separately, at nearly equal temperatures. The respective damages are compared with FTIR spectroscopy in ATR and HT-gel permeation chromatography (GPC) on a molecular level and with hydraulic internal pressure testing as a component test. For the used jerrycans, relevant oxidation can only be found after the combined exposure. The gradual increase in oxidative damage shows the good reproducibility of the lab exposure. The decomposition of nitric acid into nitrous gases by UV radiation – as well as the jerrycan oxidation – is also observed at lower HNO3 concentration (28 wt- %). Similar results are obtained after outdoor tests. Again, the damage occurs only after combined exposure, in contrast to the exposures to UV only and to HNO3 only, which were conducted in parallel. Outdoor exposures are most readily accepted as they represent possible end-use conditions. However, the reproducibility of these exposures is poor due to the large temporal variations in weather. There are also several safety risks, which is why the number of replicates remains limited. Since the outdoor and lab exposure tests show the same qualitative results, it is appropriate to conduct systematic studies in the laboratory. After 6 days of lab exposure, the oxidation damage is rated as critical, which corresponds to about 1/10 year in Central Europe, according to the UV radiant exposure. It should be noted that this amount can also occur in two sunny weeks.
Various software products for the simulation of industrial X-ray radiography have been developed in recent years (e.g., aRTist 2, CIVA CT, Scorpius XLab, SimCT, Wilcore) and their application potential has been shown in numerous works. However, full systematic approaches to characterise a specific CT system for these simulation software products to obtain a truthful digital twin are still missing. In this contribution, we want to present two approaches to obtain realistic grey values in X-ray projections in aRTist 2 simulations based on measured projections. In aRTist 2, the displayed grey value of a pixel is based on the energy density incident on that pixel.
The energy density is calculated based on the X-ray tube spectrum, the attenuation between source and detector as well as an energy-dependent sensitivity curve of the detector. The first approach presented in this contribution uses the sensitivity curve as a free modelling parameter. We measured the signal response at different thicknesses of Al EN-AW6082 at different tube voltages (i.e., different tube spectra). We then regarded the grey values displayed by these projections as a data regression respectively an optimisation problem and obtained the sensitivity curve that is best able to reproduce the measured behaviour in aRTist 2. The resulting sensitivity curve does not necessarily hold physical meaning but is able to simulate the real system behaviour in the simulation software.
The second approach presented in this contribution is to estimate the sensitivity curve based on assumptions about the characteristics of the scintillation detector (e.g., scintillator material, scintillator thickness and signal processing characteristics). For this approach, a linear response function (linear relationship between the deposited energy per pixel and the resulting grey value) is assumed. If the detector characteristics, which affect the simulated deposited energy, are properly modelled, the slope and offset of the response function to match the measured grey values should be the same for different tube spectra. As the offset is constant and given by the grey values measured at no incident radiation, the slope is the remaining parameter to evaluate the success of the detector modelling. We therefore adapted the detector characteristics by changing the detector setup until the slope was nearly the same for all measured tube spectra. We are aware that the resulting parameters of the scintillator material and thickness might not be the real ones, but with those modelling parameters we are able to simulate realistic grey values in aRTist 2. Both of those approaches could potentially be a step forward to a full systematic approach for a digital twin of a real CT system in aRTist 2.
Early detection of fatigue cracks and accurate measurements of the crack growth play an important role in the maintenance and repair strategies of steel structures exposed to cyclic loads during their service life. Observation of welded connections is especially of high relevance due to their higher susceptibility to fatigue damage. The aim of this contribution was to monitor fatigue crack growth in thick welded specimens during fatigue tests as holistically as possible, by implementing multiple NDT methods simultaneously in order to record the crack initiation and propagation until the final fracture. In addition to well-known methods such as strain gauges, thermography, and ultrasound, the crack luminescence method developed at the Bundesanstalt für Materialforschung und -prüfung (BAM), which makes cracks on the surface particularly visible, was also used. For data acquisition, a first data fusion concept was developed and applied in order to synchronize the data of the different methods and to evaluate them to a large extent automatically. The resulting database can ultimately also be used to access, view, and analyze the experimental data for various NDT methods. During the conducted fatigue tests, the simultaneous measurements of the same cracking process enabled a comprehensive comparison of the methods, highlighting their individual strengths and limitations. More importantly, they showed how a synergetic combination of different NDT methods can be beneficial for implementation in large-scale fatigue testing but also in monitoring and inspection programs of in-service structures - such as the support structures of offshore wind turbines.
This research deals with the development of the Vickers hardness knowledge graph, mapping the example dataset in them, and exporting the data-mapped knowledge graph as a machine-readable Resource Description Framework (RDF). Modeling the knowledge graph according to the standardized test procedure and using the appropriate upper-level ontologies were taken into consideration to develop the highly standardized, incorporable, and industrial applicable models. Furthermore, the Ontopanel approach was utilized for mapping the real experimental data in the developed knowledge graphs and the resulting RDF files were successfully evaluated through the SPARQL queries.
Since 2016 ISO Technical Committee (TC) 265 is working on standardization the whole CCS-process chain. Around 30 countries are working together to provide international guidelines. As ISO 27913 was the first standard finished within these activities it is already in the stage of first revision.
The objective of ISO 27913 is “to provide specific requirements and recommendations on certain aspects of safe and reliable design, construction and operation of pipelines intended for the large-scale transportation of CO2 that are not already covered in existing pipeline standards such as ISO 13623, ASME B31.8, EN 1594, AS 2885 or other standards. Existing pipeline standards cover many of the issues related to the design and construction of CO2 pipelines; however, there are some CO2 specific issues that are not adequately covered in these standards. The purpose of this document is to cover these issues consistently. Hence, this document is not a standalone standard, but is written to be a supplement to other existing pipeline standards for natural gas or liquids for both onshore and offshore pipelines.”
This contribution shall provide information on the content, the current stage of the revision process, encourage to contribute to this standard and make listeners aware to consider the influence of ISO standard on documents currently in draft.
The European Commission has identified Advanced Manufacturing and Advanced Materials as two of six Key Enabling Technologies (KETs). It is considered that Metrology is a key enabler for the advancement of these KETs. Consequently, EURAMET, the association of metrology institutes in Europe, has strengthened the role of Metrology for these KETs by enabling the creation of a European Metrology Network (EMN) for Advanced Manufacturing. The EMN is comprised of National Metrology Institutes (NMIs) and Designated Institutes (DIs) from across Europe and was formally established in October 2021. The aim of the EMN is to provide a high-level coordination of European metrology activities for the Advanced Manufacturing community.
The EMN itself is organized in three sections representing the major stages of the manufacturing chain: 1) Advanced Materials, 2) Smart Manufacturing Systems, and 3) Manufactured Components & Products. The EMN for Advanced Manufacturing is engaging with stakeholders in the field of Advanced Manufacturing (large companies & SMEs, industry organisations, existing networks, and academia), as well as the wider Metrology community, including Technical Committees, to provide input for the Strategic Research Agenda (SRA) on Metrology for Advanced Manufacturing.
This contribution will give an overview about the first version of the SRA prepared by the EMN for Advanced Manufacturing
Even after autoclaving for 2 weeks in the temperature range of 120 to 200 °C, CEM I paste with a water-to-cement ratio of 0.5 still contains some low-crystalline C-S-H. The conversion of low-crystalline C-S-H to crystalline is faster with increasing temperature. The observed low-crystalline and crystalline C-S-H phases (reinhardbraunsite, jaffeite) indicate that the sampleshave not reached equilibrium yet under these experimental conditions. However, there is a good agreement between experiment and thermodynamic modelling for the other solids indicating that the used datasets are suitable for this application.
The effect of the oscillating metal vapor plume on the keyhole and molten pool behavior during the laser beam welding of AlMg3 aluminum alloys is investigated by the experimental and numerical method. The real-time height of the metal vapor plume is measured by high-speed camera observation. The obtained experimental results are used to evaluate the additional heating source and laser beam attenuation caused by the scattering and absorption based on the Beer-Lambert theory. Furthermore, the dynamic behavior of the metal vapor plume is incorporated into a 3D transient heat transfer and fluid flow model, coupled with the ray tracing method, for the laser beam welding of the AlMg3 alloy. It is found that the additional heating resulting from the scattered and absorbed laser beam energy by the metal vapor plume significantly expands the shape of the molten pool on the top region. Moreover, the oscillating metal vapor plume caused the fluctuation of the molten pool shape. The probability of keyhole collapse at the bottom increases significantly to 72% due to the oscillating laser power induced by the laser beam attenuation. The internal interplay between the metal vapor plume, molten pool shape, and the keyhole collapse are obtained. The developed model has been validated by the experiments, which shows a good agreement.
Through experimental observation and auxiliary numerical simulation, this investigation studies the different types of grain refinement of 5754 aluminum alloy laser beam welding by applying a transverse oscillating magnetic field. Scanning electron microscope results have proved that the application of a magnetic field can reduce the average crystal branch width and increase its number. The interaction between the induced eddy current generated by the Seebeck effect and the applied external magnetic field produces a Lorentz force, which is important for the increase of the number of crystal branches. Based on the theory of dendrite fragmentation and the magnetic field-induced branches increment, the grain size reduction caused by the magnetic field is studied. Furthermore, the effects of the magnetic field are analyzed by combining a phase field method model and simulations of nucleation and grain growth. The grain distribution and average grain size after welding verifies the reliability of the model. In addition, the introduction of a magnetic field can increase the number of periodic three-dimensional solidification patterns. In the intersection of two periods of solidification patterns, the metal can be re-melted and then re-solidified, which prevents the grains that have been solidified and formed previously from further growth and generates some small cellular grains in the new fusion line. The magnetic field increases the building frequency of these solidification structures and thus promotes this kind of grain refinement.
The weld quality and the possible defect formation are directly determined by the weld pool shape and the thermo-fluid dynamics therein. In this paper, an untypical weld pool profile, i.e., elongated at its top and bottom but narrowed at the middle, is found experimentally and numerically in the wire feed laser beam welding. The detrimental influence of the weld pool narrowing on the element transport is analyzed and discussed. A magnetohydrodynamic technique is utilized to suppress the narrowing, aiming at a more homogenous element distribution. It is found that a low-temperature region is formed in the middle of the weld pool due to the interaction of the two dominant circulations from the top and bottom regions. The weld pool is significantly narrowed due to the untypical growth of the mushy zone in the low-temperature region, which results in a direct blocking effect on the downward flow and the premature solidification in the middle region. The Lorentz force produced by a transverse oscillating magnetic field shows the potential to change the flow pattern into a single-circulation type and the low-temperature-gradient region is mitigated.
Therefore, the downward transfer channel is widened, and its premature solidification is prevented. The numerical results are well validated by experimental measurements of metal/glass observation and X-ray fluorescence element mapping.
Numerical analysis of ultrasonic vibration enhanced friction stir welding of dissimilar Al/Mg alloys
(2023)
The ultrasonic vibration enhanced friction stir welding (UVeFSW) process has unique advantages in joining dissimilar Al/Mg alloys. While there are complex coupling mechanisms of multi-fields in the process, it is of great significance to model this process, to reveal the influence mechanism of ultrasonic vibration on the formation of Al/Mg joints.
In this study, the acoustic-plastic constitutive equation was established by considering the influence of both ultrasonic softening and residual hardening on the flow stress at different temperatures and strain rates. And the ultrasonic induced friction reduction (UiFR) effect on friction coefficient in different relative directions at the FSW tool-workpiece interface was quantitatively calculated and analyzed.
The Al/Mg UVeFSW process model was developed through introducing the above acoustic effects into the model of Al/Mg friction stir welding (FSW). The ultrasonic energy is stronger on the aluminum alloy side. In the stirred zone, there is the pattern distribution of ultrasonic sound pressure and energy. The heat generation at the tool-workpiece contact interface and viscous dissipation were reduced after applying ultrasonic vibra-tion. Due to the UiFR effect, the projection of friction coefficient and heat flux distributions at the tool-workpiece interface present a "deformed" butterfly shape. The calculated results show that ultrasonic vibra-tion enhanced the material flow and promoted the mixing of dissimilar materials.
The contactless magnetohydrodynamic technology has been considered as a potential and promising method to improve the weld qualities of deep penetration laser beam welding. In this paper, numerical investigations are conducted to study the influence of the auxiliary oscillating magnetic field on the porosity suppression in laser beam welding of 5754 aluminum alloy. To obtain a deeper insight into the suppression mechanism, a three-dimensional transient multi-physical model is developed to calculate the heat transfer, fluid flow, keyhole dynamic, and magnetohydrodynamics. A ray tracing algorithm is employed to calculate the laser energy distribution on the keyhole wall. A time-averaged downward Lorentz force is produced by an oscillating magnetic field. This force acts in the molten pool, leading to a dominant downward flow motion in the longitudinal section, which blocks the bubble migration from the keyhole tip to the rear part of the molten pool. Therefore, the possibility for the bubbles to be captured by the solidification front is reduced. The electromagnetic expulsive force provides an additional upward escaping speed for the bubbles of 1 m/s ~ 5 m/s in the lower and middle region of the molten pool. The simulation results are in a good agreement with experimental measurements. Based on the results obtained in this study, a better understanding of the underlying physics in laser beam welding enhanced by an auxiliary oscillating magnetic field can be provided and thus the welding process can be further optimized reducing the porosity formation.
A three-dimensional numerical model was developed to accurately predict the steady-state weld pool shape in full penetration laser beam welding. The model accounts for the coupling between the heat transfer and the fluid dynamics by considering the effects of solid/liquid phase transition, thermo-capillary convection, natural convection, and phase-specific and temperature-dependent material properties up to the evaporation temperature. A fixed right circular cone was utilized as a keyhole geometry to consider the heat absorbed from the laser beam. The model was used to analyze the influence of the thermodynamic activity of solutes and turbulence on the weld pool shape. A mesh sensitivity analysis was performed on a hybrid mesh combining hexahedral and tetrahedral elements. For the case of full penetration laser beam welding of 8 mm thick unalloyed steel sheets, the dependence of the weld pool shape on the surface-active element sulfur was found to be negligible. The analysis of the results showed that a laminar formulation is sufficient for accurately predicting the weld pool shape since the turbulence has a minor impact on the flow dynamics in the weld pool. The validity of the numerical results was backed up by experimental measurements and observations, including weld pool length, local temperature history, and a range of metallographic crosssections.
Numerical study on the formation of a bulging region in partial penetration laser beam welding
(2023)
A transient three-dimensional thermo-fluid dynamics numerical model was developed to study the formation of a bulging region in partial penetration laser beam welding. The model accounts for the coupling between the fluid flow, the heat transfer, and the keyhole dynamics by considering the effects of multiple reflections and Fresnel absorption of the laser beam in the keyhole, the phase transitions during melting and evaporating, the thermo-capillary convection, the natural convection, and the phase-specific and temperature-dependent material properties up to the evaporation temperature. The validity of the model was backed up by experimentally obtained data, including the drilling time, the weld pool length, the local temperature history outside the weld pool, the process efficiency, and a range of metallographic crosssections.
The model was applied for the cases of partial penetration laser beam welding of 8 mm and 12 mm thick unalloyed steel sheets. The obtained experimental and numerical results reveal that the bulging region forms transiently depending on the penetration depth of the weld, showing a tendency to transition from a slight bulging to a fully developed bulging region between penetration depths of 6 mm and 9 mm, respectively.
The spatial laser energy absorption inside the keyhole is decisive for the dynamic molten pool behaviors and the resultant weld properties in high-power laser beam welding (LBW). In this paper, a numerical simulation of the LBW process, considering the 3D transient heat transfer, fluid flow, and keyhole dynamics, is implemented, in which the free surface is tracked by the volume-of-fluid algorithm. The underlying laser-material interactions i.e., the multiple reflections and Fresnel absorption, are considered by an advanced ray-tracing method based on a localized Level-Set strategy and a temperature-dependent absorption coefficient. The laser energy absorption is analyzed from a time-averaged point of view for a better statistical representation. It is found for the first time that a noticeable drop of the time-averaged laser energy absorption occurs at the focus position of the laser beam, and the rest region of the keyhole has relatively homogenous absorbed energy. This unique absorption pattern may lead to a certain keyhole instability and have a strong correlation with the detrimental bulging and narrowing phenomena in the molten pool. The influence of the different focus positions of the laser beam on the keyhole dynamics and molten pool profile is also analyzed and compared. The obtained numerical results are compared with experimental measurements to assure the validity of the proposed model.
Monitoring and maintenance of civil infrastructure are of great importance, as any undetected damage can cause high repair costs, unintended deadtime, or endanger structural integrity. The inspection of large concrete structures such as bridges and parking lots is particularly challenging and time-consuming. Traditional methods are mostly manual and involve mapping a grid of measurement lines to record the position of each measurement. Current semi-automated methods, on the other hand, use GPS or tachymeters for localization but still require trained personnel to operate. An entirely automated approach using mobile robots would be more cost- and time-efficient. While there have been developments in using GPS-enabled mobile robots for bridge inspection, the weak signal strength in indoor areas poses a challenge for the automated inspection of structures such as parking lots. This paper aims to develop a solution for the automated inspection of large indoor concrete structures by addressing the problem of robot localization in indoor spaces and the automated measurement of concrete cover and rebar detection.
The performance of titanium alloy (Ti6Al4V) surfaces was investigated in lubricated reciprocating sliding tribological tests (RSTT). Special emphasis was laid on the effect of surface nanostructures in area of contact on the respective friction and wear behaviour. These so-called laser-induced periodic surface structures (LIPSS, ripples) were produced on the titanium alloy surface upon scan processing in air by an ultrashort pulsed femtosecond (fs) laser. As lubricant served two types of base oils, a pure polyalcylene-glycol, and an SAE 0W30 oil containing only antioxidants and temperature stabilizers. Tribological tests were carried out on polished as well as LIPSS covered areas using both types of base oil. A test metrics was established, combining the additive 2-ethylhexyl-zincdithiophosphate (ZDDP) or the ionic liquid [P6,6,6,14] [DEHP] (98% purity) with the respective base oils. The test metrics also considered the orientation of motion with respect to the orientation of the structures formed on the surface. Results are presented which show that the interplay between LIPSS and the local chemistry formed by the respective additives is beneficial for the tribological behaviour of the titanium alloy. Certain combinations of base oil, additive and LIPSS reduced friction and wear significantly in the tribological contact.
Rapidly advancing technologies and progressive digitisation are posing challenges to the established quality infrastructure (QI). In response, the key stakeholders of the German QI established the initiative QI-Digital aimed at developing new solutions for modern quality assurance. One of the central use cases herein is quality assurance for additive manufacturing, in which a fully interlinked additive manufacturing process chain is established. The intention is to collect and process data from each production step, allowing for a comprehensive digital view of the physical material flow. Within this process chain, prototypes of digital QI tools like machine readable standards and digital quality certificates are being demonstrated, tested, and evolved. This is complemented by research on the process level, comprising the evaluation and refinement of methods for in-situ and ex-situ quality assurance, as well as algorithms for registration, reduction, and analysis of process data. This paper presents the status, goals, and vision for the QI-Digital use case additive manufacturing.
The amount of absorbed energy in the keyhole as well as its spatial and temporal distribution is essential to model the laser beam welding process. The recoil pressure, which develops because of the evaporation process induced by the absorbed laser energy at the keyhole wall, is a key determining factor for the macroscopic flow of the molten metal in the weld pool during high-power laser beam welding. Consequently, a realistic implementation of the effect of the laser radiation on the weld metal is crucial to obtain reliable and accurate simulation results.
In this paper, we discuss manyfold different improvements on the laser-material interaction, namely the ray-tracing method, in the numerical simulation of the laser beam welding process. The first improvement relates to locating the exact reflection points in the ray tracing method using a so-called cosine condition in the determination algorithm for the intersection of the reflected rays and the keyhole surface. A second correction refers to the numerical treatment of the Gaussian distribution of the laser beam, whose beam width is defined by a decay of the laser intensity by a factor of 1/e2 thus ignoring around 14 % of the total laser beam energy. In a third step, the changes in the laser radiation distribution in the vertical direction were adapted by using different approximations for the converging and the diverging regions of the laser beam thus mimicking the beam caustic. Finally, a virtual mesh refinement was adopted in the ray tracing routine. The obtained numerical results were validated with experimental measurements.
New developments in nickel-based superalloys and production methods, such as the use of additive manufacturing (AM), can result in innovative designs for turbines. It is crucial to understand how the material behaves during the AM process to advance industrial use of these techniques. An analytical model based on reaction-diffusion formalism is developed to better explain the solidification behavior of the material during laser metal deposition (LMD). The well-known Scheil-Gulliver theory has some drawbacks, such as the assumption of equilibrium at the solid-liquid interface, which is addressed by this method. The solidified fractions under the Scheil model and the pure equilibrium model are calculated using CALPHAD simulations. Differential scanning calorimeter is used to measure the heat flow during the solid-liquid phase transformation, the result of which is further converted to solidified fractions. The analytical model is compared with all the other models for validation.