A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels)

Coret, Michel; Combescure, Alain

doi:10.1016/s0020-7403(02)00053-x

Cited by 43 publications

(55 citation statements)

References 11 publications

(12 reference statements)

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“…• the initial temperature (T 0 ) in the whole area is equal to 293 K, • the thermophysical properties such as: heat transfer coefficient, thermal capacity, Young's modulus and yield point for the appropriate phase depends on the temperature and phase composition [6], Determination of stresses in the steel pipe during the superficial heat treatment process with helical path 83…”

Section: Numerical Simulationmentioning

confidence: 99%

Determination of stresses in the steel pipe during the superficial heat treatment process with helical path

Kulawik

Sczygiol

Wróbel

2016

J. Appl. Math. Comput. Mech.

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Abstract. In the paper a numerical model for the quench hardening process with the moving heat source of steel pipe made of medium carbon steel have been presented. The constant speed rotation and moving of the pipe was assumed to obtain the path of the heat source in the shape of the helical line. In this model the relationship occurring between thermal phenomena, phase transformation in the solid state and mechanical phenomena have been taken into account. The temperature and stress fields are determined using the copyright software based on the finite element method (three-dimensional tasks). To calculate the phase content in the solid state, the macroscopic model based on the analysis of the CTP diagrams is used. The range of the martensite transformations depends on the value of stresses. In the model the tempering phenomena is also taken into account. In the model of mechanical phenomena the elastic, thermal, structural, plastic strains and transformations plasticity are considered.

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Section: Numerical Simulationmentioning

confidence: 99%

Determination of stresses in the steel pipe during the superficial heat treatment process with helical path

Kulawik

Sczygiol

Wróbel

2016

J. Appl. Math. Comput. Mech.

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“…Udział austenitu powstającego w procesie nagrzewania wyznaczano korzystając z formuły Avramiego [1,9,10]. Udziały faz powstałych z austenitu w procesie chłodzenia są determinowane temperaturą i szybkością chłodzenia w przedziale temperatury T8/5.…”

Section: Przemiany Fazowe W Stanie Stałymunclassified

“…Granice plastyczności (Y0(T0,ηк)) przyjęto równe: 150, 500, 230, 1100 i 230 MPa odpowiednio dla austenitu, bainitu, ferrytu, martenzytu i perlitu, natomiast, Y0(TSol,ηк)=5 MPa. Wielkości te ustalono na podstawie danych w pracach [7,9]. W przedziale temperatury [T0,(TSol+TLik)/2] moduły Younga i styczny oraz granice plastyczności aproksymowano sklejanymi funkcjami kwadratowymi (stycznymi dla temperatury 900 K, rys.…”

Section: Przykłady Obliczeńunclassified

Analityczno-numeryczna analiza spawania laserowego płaskowników smukłych

Wróbel

Kulawik

Bokota

2016

Przegląd Spawalnictwa

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StreszczenieW pracy przedstawiono model analityczno-numeryczny oraz analizę zjawisk cieplnych, przemian fazowych i zjawisk mechanicznych towarzyszących spawaniu techniką laserową smukłych elementów płaskich. Do rozwiązania zagadnienia przewodzenia ciepła zastosowano metodę funkcji Greena. Model szacowania udziału faz oraz ich kinetyki oparto na wykresie spawalniczym ciągłego chłodze-nia (CTPc-S). Udziały faz metalurgicznych powstających podczas ciągłego nagrzewania i chłodzenia (austenit, perlit lub bainit) wyznaczano równaniem Johnsona-Mehla i Avramiego. Do wyznaczania tworzącego się martenzytu wykorzystano zmodyfikowane równanie Koistinena i Marburgera. Naprężenia i odkształcenia wyznaczono z rozwiązania metodą elementów skończonych równań równowagi w formie prędkościowej. Uwzględniono odkształcenia cieplne, strukturalne, plastyczne oraz odkształcenia indukowane przemianami fazowymi. Do wyznaczania odkształceń plastycznych zastosowano warunek plastyczności Hubera-Misesa ze wzmocnieniem izotropowym, natomiast odkształcenia plastyczne indukowane przemianami fazowymi obliczano formułą Leblonda. Dokonano analizy składu fazowego i naprężeń towarzyszących spawaniu doczołowemu elementów wykonanych z niskowęglowej spawalnej stali (S235). Analizę przeprowadzono dla dwóch wersji spawania: pojedynczą wiązką laserową oraz podwójnymi wiązkami, z których jedna została użyta do podgrzewania wstępnego, a druga do spawania.Słowa kluczowe: spawanie laserowe; przemiany fazowe; zjawiska cieplne i mechaniczne AbstractIn the paper an analytical-numerical model and the analysis of thermal phenomena, phase transformations and mechanical phenomena occur in laser welding of thin flat bars were presented. To solve the heat transfer equation, the method of Green's function was used. To calculate the phase fractions and their kinetics the model based on the analysis of the continuous cooling diagram for the welding (CCT) is used. Phase fractions which occur during the continuous heating and cooling (austenite, pearlite or bainite) are described by Johnson-Mehl-Avrami (JMA) formula. To determine the formed martensite the modified KoistinenMarburger (KM) equation is used. The stress and strain are determined by the solution of the equilibrium equations in the rate form using finite element method. In the model the thermal, structural, plastic strains and induced plasticity are taken into account. To calculate the plastic strains the Huber-Mises plasticity condition with isotropic hardening is used. Whereas to determine transformations induced plasticity the modified Leblond model is applied. The analysis of the phase content and stress state which occur during the butt welding of elements made of low carbon steel (S235) were performed. The calculations were carried out for the two cases of welding: a single laser beam and a double laser beam, where first was a preheating source and the second the main welding source.

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“…Young's modulus and tangential modulus (E and E t ) in the simulation of mechanical phenomena are temperature dependent, whereas yield strength (Y) depends on temperature and phase composition. based on work presented in [39,40] young's modulus and tangential modulus are set to 2×10 5 MPa and 2×10 4 MPa, yield strength 200 MPa, 320 MPa, 600 MPa, 1200 MPa and 320 MPa for austenite, ferrite, bainite, martensite and pearlite respectively in temperature 300 K. In temperatures T≥1700 K Young's modulus and tangential modulus equal 100 MPa and 10 MPa, whereas yield strength equals 5 MPa. These values are approximated using square functions (Fig.7).…”

Section: Examples Of Numerical Prediction Of Structure Composition Inmentioning

confidence: 99%

Modelling and Analysis of Phase Transformations and Stresses in Laser Welding Process / Modelowanie I Analiza Przemian Fazowych I Naprężeń W Procesie Spawania Laserowego

Piekarska¹

2015

Archives of Metallurgy and Materials

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The work concerns the numerical modelling of structural composition and stress state in steel elements welded by a laser beam. The temperature field in butt welded joint is obtained from the solution of heat transfer equation with convective term. The heat source model is developed. Latent heat of solid-liquid and liquid-gas transformations as well as latent heats of phase transformations in solid state are taken into account in the algorithm of thermal phenomena. The kinetics of phase transformations in the solid state and volume fractions of formed structures are determined using classical formulas as well as Continuous-Heating-Transformation (CHT) diagram and Continuous-Cooling-Transformation (CCT) diagram during welding. Models of phase transformations take into account the influence of thermal cycle parameters on the kinetics of phase transformations during welding. Temporary and residual stress is obtained on the basis of the solution of mechanical equilibrium equations in a rate form. Plastic strain is determined using non-isothermal plastic flow with isotropic reinforcement, obeying Huber-Misses plasticity condition. In addition to thermal and plastic strains, the model takes into account structural strain and transformation plasticity. Changing with temperature and structural composition thermophysical parameters are included into constitutive relations. Results of the prediction of structural composition and stress state in laser butt weld joint are presented.

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A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels)

Cited by 43 publications

References 11 publications

Determination of stresses in the steel pipe during the superficial heat treatment process with helical path

Determination of stresses in the steel pipe during the superficial heat treatment process with helical path

Analityczno-numeryczna analiza spawania laserowego płaskowników smukłych

Modelling and Analysis of Phase Transformations and Stresses in Laser Welding Process / Modelowanie I Analiza Przemian Fazowych I Naprężeń W Procesie Spawania Laserowego

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