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The axisymmetric one-dimensional line (radius) element from the domain, on the cylindrical chromium steel bar which had been heated and then submerged in sea water.
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The modelling of an axisymmetric industrial quenched chromium steel bar AISI-SAE 8650H based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-dimensional line (radius) element axisymmetric model has been adopted to predict temperature histor...
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The modelling of an axisymmetric industrial quenched chromium steel bar AISI-SAE 5147H, sea water cooled based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-Dimensional line (radius) element axisymmetric model has been adopted to predict...
Mathematical modelling of axisymmetric transient industrial quenched chromium steel bar AISI-SAE 8650H, water cooled based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-D line (radius) element axisymmetric model has been adopted to predic...
The modelling of an axisymmetric industrial quenched molybdenum steel bar AISI-SAE 4037H quenched in sea water based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-dimensional line (radius) element axisymmetric model has been adopted to pr...
The modeling of an axisymmetric industrial quenched alloy steel SCM440 based on the finite element method (FEM) has been produced to investigate the impact of process history on material properties and metallurgical. Mathematical modeling of the 1-Dimensional element axisymmetric model has been adopted to determine the temperature history and conse...
Citations
... however, another solution is possible by finite element software analysis called numerical solution [2]. Heat transfer during quenching operation of steel specimen is in an unsteady state, where the temperature variation with time [3]. Analysis heat transfer of a 3dimensional model could be simplified to a 2-dimensional axisymmetric analysis to reduce cost and computing time limit [2], [4], [5], [12], [17]. ...
Simulation of hardness distribution in quenched specimens has been investigated using three-dimensional finite-element (FE) analyses which reduced into a 2-dimensional axisymmetric analysis based on Ansys Software capable of predicting temperature history; evolution hardness of four different types of Molybdenum steel bars during thermal processing of materials in quenching process is presented. The Jominy test results are used to estimate specimen hardness. specimen points hardness used to be determined through conversion of evaluated characteristic cooling time for phase transformation t8/5 into hardness. The lowest hardness point (LHP) of each quenched Molybdenum steel bar has been determined to be in mid its length in the center. Experimentally, it is quite impossible to determine this hardness value, and earlier approaches could only assess surface hardness. Normally, this value of hardness at the surface is greater than (LHP), that, under certain conditions might lead to component failure and deformation. The model can be employed to establish a cooling method to attain the required microstructure as well as mechanical properties, which include hardness.
... From the derived heat conduction equation, the Galerkin residual for 1-Dimensional line (radius) element in an unsteady state heat transfer by integration the shape functions times the residual which minimize the residual to zero becomes; (16) where, [S] T = the transpose of the shape function matrix {ℜ} ( ) = the residual contributed by element (e) to the final system of equations. ...
... Two point recurrence formulas will allow us to compute the nodal temperatures as a function of time. In this paper, Euler's method which is known as the backward difference scheme (FDS) will be used to determine the rate of change in temperature, the temperature history at any point (node) of the steel bar [5,[14][15][16][17]. ...
The modelling of an axisymmetric industrial quenched chromium steel bar AISI-SAE 5147H, sea water cooled based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-Dimensional line (radius) element axisymmetric model has been adopted to predict temperature history and consequently the hardness of the quenched steel bar at any point (node). The lowest hardness point (LHP) is determined. In this paper hardness in specimen points was calculated by the conversion of calculated characteristic cooling time for phase transformation t8/5 to hardness. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical properties such as hardness. The developed mathematical model converted to a computer program. This program can be used independently or incorporated into a temperature history calculator to continuously calculate and display temperature history of the industrial quenched steel bar and thereby calculate LHP. The developed program from the mathematical model has been verified and validated by comparing its hardness results with commercial finite element software results. The comparison indicates reliability of the proposed model.
... Because of the complexity and non-linear nature of the problem, no analytical solution exists. However, numerical solution is possible by finite difference method, finite volume method, and the most popular one -finite element method (FEM) [1,5] . During the quenching process of a steel bar, the heat transfer is in an unsteady state as there is a variation of temperature with time [1,6] . ...
... However, numerical solution is possible by finite difference method, finite volume method, and the most popular one -finite element method (FEM) [1,5] . During the quenching process of a steel bar, the heat transfer is in an unsteady state as there is a variation of temperature with time [1,6] . ...
... In this paper the heat transfer analysis is carried out in three dimensions (3D). The (3D) analysis is reduced to a 1-D axisymmetric analysis to save cost and computer time [1,5,[7][8][9][10][11] . This is achievable because in axisymmetric conditions, the temperature deviations is only along radius (R) while there is no temperature variation in the (Ɵ) and (Z) directions as indicated in Fig. 1, Fig. 2 and Fig. 3 [1,[36][37][38][39][40][41] . ...
One-dimensional (1D) model of an axisymmetric industrial quenched carbon steel-1045 bar based on finite element method (FEM) has been applied to investigate the influence of process history on its material properties. The lowest hardness point (LHP) and the effect of the radius of the bar on its temperature history and the LHP is determined. In this paper hardness in specimen points was obtained by calculated characteristic cooling time for phase transformation t 8/5 to hardness. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical properties such as hardness. A computer program of the model is developed, which can be used independently or incorporated into a temperature history software named LHP-software to continuously calculate and display temperature history of the industrial quenched steel bar and thereby calculate LHP and to study the effect of radius on temperature history and LHP. The developed program based on 1D FEM model has been verified by comparing its hardness results with experimental results. The comparison indicates its validity and reliability.
... Because of the complexity and non-linear nature of the problem, no analytical solution exists. However, numerical solution is possible by finite difference method, finite volume method, and the most popular one -finite element method (FEM) [1,5] . During the quenching process of a steel bar, the heat transfer is in an unsteady state as there is a variation of temperature with time [1,6] . ...
... However, numerical solution is possible by finite difference method, finite volume method, and the most popular one -finite element method (FEM) [1,5] . During the quenching process of a steel bar, the heat transfer is in an unsteady state as there is a variation of temperature with time [1,6] . ...
... In this paper the heat transfer analysis is carried out in three dimensions (3D). The (3D) analysis is reduced to a 1-D axisymmetric analysis to save cost and computer time [1,5,[7][8][9][10][11] . This is achievable because in axisymmetric conditions, the temperature deviations is only along radius (R) while there is no temperature variation in the (Ɵ) and (Z) directions as indicated in Fig. 1, Fig. 2 and Fig. 3 [1,[36][37][38][39][40][41] . ...
One-dimensional (1D) model of an axisymmetric industrial quenched carbon steel-1045 bar based on finite element
method (FEM) has been applied to investigate the influence of process history on its material properties. The lowest
hardness point (LHP) and the effect of the radius of the bar on its temperature history and the LHP is determined. In
this paper hardness in specimen points was obtained by calculated characteristic cooling time for phase
transformation t8/5 to hardness. The model can be employed as a guideline to design cooling approach to achieve
desired microstructure and mechanical properties such as hardness. A computer program of the model is developed,
which can be used independently or incorporated into a temperature history software named LHP-software to
continuously calculate and display temperature history of the industrial quenched steel bar and thereby calculate LHP
and to study the effect of radius on temperature history and LHP. The developed program based on 1D FEM model has
been verified by comparing its hardness results with experimental results. The comparison indicates its validity and
reliability.
... Quench process involves raising the steel temperature above a certain critical value, holding it at that temperature for a specified time and then rapidly cooling it in a suitable medium to room temperature [4]. Mackerle [5] and Elmaryami and Omar [6] define quenching as a common manufacturing process, aiming to produce components with desirable properties such as low residual stresses and distortions, avoidance of cracks, specific hardness, and achievement of improved properties. It has also been described as one of the most common heat treatment processes used to impart the desire mechanical properties such as high strength, hardness and near resistance to metal parts using quenchants such as air, water and polymer solution [7,8]. ...
... The response surface methodology was first developed by Box and Wilson [10] in the statistical field during the 1950s and is now broadly used in a lot of fields, such as chemical, agriculture, biological, and manufactures [11] and [12]. Elmaryami and Omar [6] investigated the effect of process history on metallurgical and material properties of an industrial quenched chromium steel bar AISI-SAE 8650 H. A mathematical model based on Finite Element Method was developed to predict temperature history and consequently the hardness of the quenched steel bar at any point to determine the Lowest Hardness Point (LHP). ...
... In this paper the heat transfer analysis will be carried out in 3-dimensions. The three dimensional analysis will be reduced into a 1-dimensional axisymmetric analysis to save cost and computer time [1,5,[7][8][9][10][11]. This is achievable because in axisymmetric conditions, the temperature deviations is only in (R) while there is no temperature variation in the theta (θ ) and (Z) direction as it is clear in Fig. 1, Fig. 2 and Fig. 3. ...
... The heat transfer across the steel bar is uniform. As known during quenching, there are two important temperatures [800 o C and 500 o C] to calculate the cooling time [12,[21][22][23][24][25][26][27], because the characteristic cooling time, relevant for structure transformation for most structural steels, is the time of cooling from 800 to 500°C (time t 8/5 ) [8][9][10][11][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Then important mechanical properties such as hardness can be computed. ...
Mathematical modeling of an axisymmetric transient industrial quenched chromium steel bar AISI-SAE 5147H, water cooled based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-D line (radius) element axisymmetric model has been adopted to predict temperature history of the quenched chromium steel bar at any point (node). The temperature history of four different radii cylindrical geometry chromium steel 5147H is determined. The temperature history needs to be properly understood in order to efficiently produce high quality components. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical properties such as hardness. The developed mathematical model converted to a computer program. This program can be used independently or incorporated into a temperature history calculator to continuously calculate and display temperature history of the industrial quenched chromium steel bar and thereby calculate the mechanical properties. The developed program from the mathematical model has been verified and validated by comparing its temperature simulation results with commercial finite element software results. The comparison indicates reliability of the proposed model.
... Quenching is a heat treatment usually employed in industrial processes in order to control mechanical properties of steels such as hardness [1,2]. The process consists of raising the steel temperature above a certain critical value, holding it at that temperature for a specified time and then rapidly cooling it in a suitable medium to room temperature [1,3]. ...
... Quenching is a heat treatment usually employed in industrial processes in order to control mechanical properties of steels such as hardness [1,2]. The process consists of raising the steel temperature above a certain critical value, holding it at that temperature for a specified time and then rapidly cooling it in a suitable medium to room temperature [1,3]. The resulting microstructures formed from quenching (ferrite, cementite, pearlite, upper bainite, lower bainite and martensite) depend on cooling rate and on chemical composition of the steel [1,4]. ...
... The process consists of raising the steel temperature above a certain critical value, holding it at that temperature for a specified time and then rapidly cooling it in a suitable medium to room temperature [1,3]. The resulting microstructures formed from quenching (ferrite, cementite, pearlite, upper bainite, lower bainite and martensite) depend on cooling rate and on chemical composition of the steel [1,4]. Quenching of steels is a multi-physics process involving a complicated pattern of couplings among heat transfer. ...
Mathematical modelling of axisymmetric transient industrial quenched chromium steel bar AISI-SAE 8650H, water cooled based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-D line (radius) element axisymmetric model has been adopted to predict temperature history of the quenched chromium steel bar at any point (node). The temperature history of four different radii cylindrical geometry chromium steel 8650H is determined. The temperature history needs to be properly understood in order to efficiently produce high quality components. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical properties such as hardness. The developed mathematical model converted to a computer program. This program can be used independently or incorporated into a temperature history calculator to continuously calculate and display temperature history of the industrial quenched chromium steel bar and thereby calculate the mechanical properties. The developed program from the mathematical model has been verified and validated by comparing its temperature simulation results with commercial finite element software results. The comparison indicates reliability of the proposed model.
... Quenching is physically one of the most complex processes in engineering, and very difficult to understand. Simulation of steel quenching is thus a complex problem [2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Quenching is a heat treatment usually employed in industrial processes in order to control mechanical properties of steels such as toughness and hardness [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. ...
... Simulation of steel quenching is thus a complex problem [2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Quenching is a heat treatment usually employed in industrial processes in order to control mechanical properties of steels such as toughness and hardness [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The process consists of raising the steel temperature above a certain critical value, holding it at that temperature for a specified time and then rapidly cooling it in a suitable medium to room temperature [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. ...
... Quenching is a heat treatment usually employed in industrial processes in order to control mechanical properties of steels such as toughness and hardness [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The process consists of raising the steel temperature above a certain critical value, holding it at that temperature for a specified time and then rapidly cooling it in a suitable medium to room temperature [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The resulting microstructures formed from quenching (ferrite, cementite, pearlite, upper bainite, lower bainite and martensite) depend on cooling rate and on chemical composition of the steel [3,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. ...
... 1-3. [34][35][36][37][38][39]. ...
... The shape functions were to represent the variation of the field variable over the element. The shape function of axisymmetric 1-dimensional line (radius) element expressed in terms of the r coordinate and its coordinate are shown in Fig. 4; [34][35][36][37][38][39]. ...
The modelling of an axisymmetric industrial quenched molybdenum steel bar AISI-SAE 4037H quenched in sea water based on finite element method has been produced to investigate the impact of process history on metallurgical and material properties. Mathematical modelling of 1-dimensional line (radius) element axisymmetric model has been adopted to predict temperature history and consequently the hardness of the quenched steel bar at any point (node). The lowest hardness point (LHP) is determined. In this paper hardness in specimen points was calculated by the conversion of calculated characteristic cooling time for phase transformation t8/5 to hardness. The model can be employed as a guideline to design cooling approach to achieve desired microstructure and mechanical properties such as hardness. The developed mathematical model was converted to a computer program. This program can be used independently or incorporated into a temperature history calculator to continuously calculate and display temperature history of the industrially quenched steel bar and thereby calculate LHP. The developed program from the mathematical model has been verified and validated by comparing its hardness results with commercial finite element software results. The comparison indicates reliability of the proposed model.
A Novel 2-D mathematical modeling to determine LHP to ... ZASTITA MATERIJALA 64 (2023) broj 3 ABSTRACT 2-dimensional mathematical model of axisymmetric transient industrial quenched low carbon steel bar, to examine the influence of process history on metallurgical and material characteristics, a water-cooled model based on the finite element technique was adopted. A 2-dimensional axisymmetric mathematical model was utilized to predict temperature history and, as a result, the hardness of the quenched steel bar at any node (point). The LHP (lowest hardness point) is evaluated. In this paper, specimen points' hardness was evaluated by the transformation of determined characteristic cooling time for phase conversion t8/5 to hardness. The model can be used as a guideline to design a cooling approach to attain the desired microstructure and mechanical properties, such as hardness. The mathematical model was verified and validated by comparing its hardness results to commercial finite element software results. The comparison demonstrates that the proposed model is reliable.
