Element Temperature Field Research Articles

In-situ elimination of β-flecks in additively manufactured Ti-3.5 wt% Fe alloy

Meta-stable β titanium alloys that feature excellent mechanical properties are of great interest for a range of engineering applications. In particular, Fe containing titanium alloy is one of the most promising alloy systems because Fe is the most economic β stabilizer. However, Fe solute is highly prone to segregation during casting, which leads to the formation of “β flecks” in the subsequent thermo-mechanical treatment and deteriorates the fatigue properties. This paper aims to eliminate β flecks in Ti-3.5 wt%Fe alloy fabricated by Laser Directed Energy Deposition (L-DED), that utilises the high cooling rate during solidification and multiple thermal cycles after solidification. SEM and EDS analysis established that a large β-fleck free zone can be achieved in as-fabricated Ti-3.5 wt%Fe thin-walled samples. Combining the finite element temperature field simulation results and the one-dimensional dynamic diffusion model, the elimination of β flecks is well rationalized. The current work provides a paradigm to evaluate the segregation elimination in the additively manufactured alloy components.

Infrared laser heating of GFRP bars and finite element temperature field simulation

Glass fiber-reinforced polymer (GFRP) composites were prepared with ortho-phthalic unsaturated polyester resin as the matrix. Mass productions were carried out on a production line using infrared laser radiation and tunnel-kiln heating. Infrared laser radiation heating can realize internal and external collaborative curing by utilizing the deep penetration of the infrared laser, whereas, the curing of tunnel kilns mainly depends on heat conduction and heat convection. The tensile strength of the bar cured by laser radiation was approximately 25% higher than that of the bar cured by the tunnel kiln. The temperature field of the GFRP bars under the two curing modes was simulated using the finite element method, and The fiber at the fracture of reinforcement was analyzed using scanning electron microscopy and FTIR spectrum. The results showed that there was more fiber adhesion resin in the GFRP bars heated by infrared laser radiation, whereas the adhesion resin on the fibers was less scattered in the tunnel–kiln-heated GFRP bars.

Comparative study on fire resistance and zero strength layer thickness of CLT floor under natural fire and standard fire

A study of the fire resistance of cross-laminated timber (CLT) flooring material exposed to different fire conditions (ISO 834 standard fire and natural fire) is described, along with the value of the zero strength layer (ZSL) thickness. Experimental studies of the flexural performance of four groups of CLT floor at ambient temperature and the fire resistance of six groups of CLT floor under the action of fire were conducted. The influence of different laminate compositions (three-ply and five-ply) and different load ratios (10%, 20%, 30%) on the internal temperature field distribution, fire resistance and carbonization of the six groups of CLT floors were compared and analyzed. Subsequently, Abaqus software was used to establish a finite element temperature field heat transfer model of the shedding of the charred layer to analyze the fire resistance of the CLT floor, and to compare the key parameters in the test (charring rate, depth of charring, and shedding of the charred layer), to verify the validity of the model. Finally, the effective residual section method was used to develop a theoretical calculation model for determining the thickness of the ZSL of the CLT floor throughout the fire process. The theoretical calculated charred depth at different times during the fire resistance tests are compared and analyzed to verify the accuracy of the theoretical method.

Effect of parameters on microstructure and mechanical property of dissimilar joints between 316L stainless steel and GH909 alloy by laser welding

Abstract This paper mainly studied the effects of high-power high-welding speed and low-power low-welding speed on 316 L/GH909 dissimilar metals laser welding joints under the same linear energy. The weld morphology, microstructure and mechanical property were compared and analyzed. The different dimensions of the molten pool between the two welds were verified by the finite element temperature field simulation, and the reason was discussed. From the results, the weld with low-power low-welding speed had a smaller temperature gradient and a lower cooling rate at the edge of the molten pool. The condition of small temperature gradient effectively made the element distribution smoother, relieved the microstructure heterogeneity of the interface layer and alleviated the liquefaction of grain boundaries at the HAZ, thus improving the tensile strength of the welded joint. Since both alloys were based on austenite, there was no common intermetallic compound in this type dissimilar joints. The detailed and systematic elemental analysis of the different phases in the 316 L/GH909 dissimilar metal weld was carried out. Especially, we found that a small amount of Cr element was solid solutioned in γ/Laves low melting phases, and the granular phases distributed at the HAZ of GH909 side were analyzed. This study mainly revealed the nuances between the two welds under the same linear energy, which can provide guidance for this type of GH909/316 L dissimilar metal welding.

Tribological Performance of Micro-Groove Tools of Improving Tool Wear Resistance in Turning AISI 304 Process.

AISI 304 has good physical and chemical properties and thus is widely used. However, due to the low thermal diffusivity, the cutting temperature of AISI 304 is high accelerating the wear of the tool. Therefore, tool wear is a major problem in machining hard cutting materials. In this study, we developed a new type of micro-groove tool whose rake surface was distributed with micro-groove by powder metallurgy based on the finite element temperature field morphology. We compared the wear of the proposed micro-groove tool with an untreated one by using a scanning electron microscope (SEM) and an X-ray energy spectrum. The abrasive, adhesive, and oxidation wear of the rake and the flank face of the micro-groove tool were lower than that of the untreated one. Due to the micro-groove on the rake face of the tool, the contact length between the tool and chip was reduced, leaving more extension space. Furthermore, chip extrusion deformation was avoided, and the energy caused by chip deformation was reduced. After 70 min of cutting, the counterpart reached the specified wear amount while the main cutting force, the feed resistance, and the cutting depth resistance of the proposed micro-groove tool were reduced by 16.1%, 33.9%, and 40.1%, respectively. With regard to steady state, the cutting temperature was reduced by 17.2% and the wear width of the flank face was reduced by 36.7%.

INVESTIGATION OF TEMPERATURE MODES IN THERMOSENSITIVE NON-UNIFORM ELEMENTS OF RADIOELECTRONIC DEVICES

Context. The non-linear boundary value problem of heat conduction for a thermosensitive non-homogeneous strip-shaped element of a radio-electronic system with a through inclusion has been solved whose analytical-numerical solution enables us to analyze temperature regimes in the element. Objective. Is to develop such a method of linearization of mathematical model of heat conduction which enables us to obtain analytical numerical solution of the corresponding non-linear boundary value problem for determination of temperature field in elements of radio electronic devices, which are geometrically represented by a thermosensitive plate with a through inclusion. Method. A linearizing function which enables us to partially linearize the initial non-linear mathematical model of heat conduction for a thermosensitive non-homogeneous element of a radio electronic system in the form of “plate-inclusion” structure has been suggested. The introduced piece-wise linear approximation of temperature on plate-inclusion interfaces has enabled us to completely linearize the corresponding partially linearized boundary value problem relative to the linearizing function. After this, it became possible to apply Fourier’s integral transformation to the obtained linear problem with respect to one of the spatial coordinates, as well as to determine the linearizing function. The linear dependence of the coefficient of heat conductivity on temperature for structure materials with the use of the linearizing function has been considered. By solving the boundary value problem, the formulae for determination of temperature field in the “plate-inclusion” thermosensetive structure have been obtained. Results. The obtained formulae for determination of temperature field in a thermosensitive non-homogeneous element of radio electronic system were used to create the software which enables us to obtain distribution of value of temperature and to analyze temperature regimes. Conclusions. A mathematical model for the calculation for the temperature field in a “plate-inclusion” thermosensitive structure is adequate to the actual physical process, because no jump of temperature at “plate-inclusion” interfaces is observed. The numerical results for the chosen materials under linear dependence of the coefficient of thermoconductivity on temperature differ by 7% from the results which are obtained for constant coefficient of heat conductivity. Prospect of further investigation will consider more complicated geometric representation of elements of radio electronic systems.

Numerical Simulation of Temperature Distribution Field in Beam Bulk in the Simultaneous Presence of Heat Insulation, Heat Flux and Heat Exchange

Most of the bearing elements of electric power installations operate in the presence of local cold insulator, heat flow, and heat transfer. To ensure the smooth operation of these elements it is necessary to develop appropriate computational algorithms and methods that allow to investigate numerically the thermomechanical condition of bearing elements. Besides, obtained numerical results should have different precision and respectively describe such a complex exceptional nonlinear process under study. Under the established process for the length of the test rod bearing element temperature field, displacement field, elastic, thermal and thermoelastic stress components field will arise. To determine these decisions, taking into account natural conditions and maintenance, we should use the techniques oriented on the basic laws of conservation of energy [1, 2].

An On-line Finite Element Temperature Field Model for Plate Ultra Fast Cooling Process

Taking the element specific-heat interpolation function into account, a one-dimensional (1-D) finite element temperature field model for the on-line control of the ultra fast cooling process was developed based on the heat transfer theory. This 1-D model was successfully implemented in one 4300 mm plate production line. To improve the calculation accuracy of this model, the temperature-dependent material properties inside an element were considered during the modeling process. Furthermore, in order to satisfy the real-time requirements of the on-line model, the variable bandwidth storage method and the Cholesky decomposition method were used in the programming to storage the data and carry out the numerical solution. The on-line application of the proposed model indicated that the deviation between the calculated cooling stop temperature and the measured one was less than ±15 °C.

Research and Application of Automation Controlling System for Plate Ultra Fast Cooling Process

To implement the new generation thermo mechanical control process (NG-TMCP), the automatic control system of ultra fast cooling (UFC) was developed by combined with the renovation project of controlled cooling system in one plate production line. This system was composed of basic automation subsystem and process automation subsystem. As the main control unit of the basic automatic control system, a S7400 PLC system is used to control the UFC device and to achieve the chain control between the UFC system and the mill system. While the process control system is to realize the automatical setting of the cooling schedule by the developed finite element temperature field model and the temperature homogeneity model. The industry application shows that the NG-TMCP which is based on the UFC can reduce the alloy content effectively and implement the low-cost reduction produce of high-grade products.

3D finite element temperature field modelling for direct laser fabrication

In order to describe the thermal dynamics behaviour in direct laser fabrication (DLF), a 3D finite element temperature field model is proposed to be built/developed based on global model and sub-model pattern. The global model exhibits the heat conduction characteristics of parts in the whole thermal history according to scanning path planning. Contact pairs and gap elements, which consider the effect of the temperature and porosity-dependent thermal conduction, are designed in the model to explain powder-to-solid intrinsic transition. In addition, the elements removed and reactivated technology is applied in the model so as to embody the material stepwise increasing feature. A laser-repairing case developed by ABAQUS demonstrates the global model’s thermal history, and the influence of non-linear behaviour of thermal properties in pure nickel on the temperature distribution is estimated as well. Adopting the thermal physical parameters with solid–liquid phase change will make the melted pool temperature higher than that where the solid–liquid phase change parameters are not considered.

Completely hierarchical p-version axisymmetric shell element for nonlinear heat conduction in laminated composites

This paper presents a completely hierarchical p-version finite element formulation for an axisymmetric shell element for nonlinear conduction in laminated composites where the element temperature field can be of arbitrary polynomial orders p ξ and P η in the longitudinal (ξ) and the transverse (η) directions of the shell element. The approximation functions and the corresponding nodal variables for the axisymmetric shell element are derived by first, constructing the one-dimensional hierarchical approximation functions of orders p ξ and p η and the corresponding hierarchical nodal variable operators for each of the two directions ξ and η and then taking their product. This procedure gives the approximation functions and the nodal variables for the axisymmetric shell element that correspond to the polynomial orders p ξ and p η . The element approximation functions as well as the nodal variables are hierarchical and therefore the element matrices and the vectors corresponding to orders p ξ and p η are a subset of those corresponding to the polynomial orders ( p ξ + 1) and ( p η + 1). The formulation ensures C 0 continuity across the interelement boundaries. A weak formulation of the Fourier heat conduction equation with temperature dependent thermal conductivities, internal heat generation, film coefficients and radiation effects for globally orthotropic material is constructed. The element properties are derived using the weak formulation and the hierarchical element approximation. This formulation is extended for generally orthotropic material behavior where the material directions are not necessarily parallel to the global axes. Further extension of the formulation for laminated composites is accomplished by incorporating the material properties of each layer through numerical integration of the element matrix for each layer. The element matrices and the equivalent heat vectors (due to convection, distributed heat flux, radiation and internal heat generation) are all hierarchical. The formulation permits any desired order temperature distribution in the shell thickness direction without remodelling. There is no restriction on the number of layers and the lay up pattern of the layers. Each layer can be generally orthotropic. The material directions and the layer thicknesses may vary from point to point within each layer. Because of the temperature dependence of thermal conductivities, internal heat generation, film coefficients and radiation boundaries; the resulting discretized equations of equilibrium are nonlinear. These equations are solved using modified Newton-Raphson method. The tangent matrix is derived using the nonlinear equations of equilibrium. The modified tangent matrix is symmetric and provides excellent convergence during the equilibrium iteration process. Numerical examples are presented to demonstrate the accuracy, efficiency and overall superiority of the present formulation and the extremely good and fast convergence of the iteration process. Comparisons are made with available results in the literature.

P-VERSION HIERARCHICAL AXISYMMETRIC SHELL ELEMENT FOR HEAT CONDUCTION

This paper presents a completely hierarchical, axisymmetric shell finite element for heat conduction. The element temperature field can be of arbitrary polynomial orders p: and Pq in the longitudinal (ξ) and the transverse (η) directions of the shell element. The approximation functions and the corresponding nodal variables for the axisymmetric shell element are derived by, first, constructing the one-dimensional hierarchical approximation functions of orders pξ;and pηand the corresponding hierarchical nodal operators for each of the two directions ξ and ηand then taking their product. Both the element approximation functions and the nodal variables are hierarchical. The formulation ensures C0 continuity across the interetemenl boundaries. The weak formulation of the Fourier heat conduction equation is constructed, and the element properties are derived using the weak formulation and the hierarchical element approximation. Numerical examples are presented to demonstrate the accuracy, efficiency, and advan...

Completely hierarchical axisymmetric shell element based on p-version for heat conduction in laminated composites

A completely hierarchical p-version finite element formulation is presented for an axisymmetric shell element for heat conduction in laminated composites, where the element temperature field can be of arbitrary polynomial orders p ξ and p η in the longitudinal (ξ) and the transverse (η) directions of the shell element. The approximation functions and the corresponding nodal variables for the axisymmetric shell element are derived by first constructing the one-dimensional hierarchical approximation functions of orders p ξ and p η and the corresponding hierarchical nodal variable operators for each of the two directions ξ and η and then taking their product (sometimes called the tensor product). This procedure gives the approximation functions and the nodal variables for the axisymmetric shell element that correspond to the polynomial orders p ξ and p η . The element approximation functions and the nodal variables are both hierarchical and therefore the element matrices and the vectors corresponding to orders p ξ and p η are a subset of those corresponding to the polynomial orders ( p ξ + 1) and ( p η + 1). The formulation ensures C 0 continuity across the interelement boundaries. The geometry of the element is described in the usual way by the Cartesian coordinates of the nodes located at the middle surface ( η = 0) of the element and the nodal vectors representing nodal values of the lamina thicknesses. Weak formulation of the Fourier heat conduction equation for globally orthotropic material is constructed in the cylindrical coordinate system rz. The element properties are derived using the weak formulation (or the associated quadratic functional) and the hierarchical element approximation. This formulation is extended for generally orthotropic material behavior where the material directions are not necessarily parallel to the global axes. Further extension of the formulation for laminated composites is accomplished by incorporating the material properties of each layer through numerical integration of the element matrix for each layer. The element matrices and the equivalent heat vectors (due to convection, distributed heat flux and internal heat generation) are all hierarchical. The formulation permits any desired order temperature distribution in the ξ and η directions without remodeling. There is no restriction on the number of layers and the lay up pattern of the layers. Each layer can be generally orthotropic. The material directions and the layer thicknesses may vary from point to point within each layer. Numerical examples are presented to demonstrate the accuracy, efficiency and overall superiority of the present formulation. For all examples, h-model results using isoparametric elements are also presented. Comparisons are made with analytical solutions wherever possible.

Curved shell elements for heat conduction with p-approximation in the shell thickness direction

A finite element formulation is presented for the curved shell elements for heat conduction where the element temperature approximation in the shell thickness direction can be of an arbitrary polynomial order p. This is accomplished by introducing additional nodal variables in the element approximation corresponding to the complete Lagrange interpolating polynomials in the shell thickness direction. This family of elements has the important hierarchical property, i.e. the element properties corresponding to an approximation order p are a subset of the element properties corresponding to an approximation order p + 1. The formulation also enforces continuity or smoothness of temperature across the inter-element boundaries, i.e. C 0 continuity is guaranteed. The curved shell geometry is constructed using the co-ordinates of the nodes lying on the middle surface of the shell and the nodal point normals to the middle surface. The element temperature field is defined in terms of hierarchical element approximation functions, nodal temperatures and the derivatives of the nodal temperatures in the element thickness direction corresponding to the complete Lagrange interpolating polynomials. The weak formulation (or the quadratic functional) of the three-dimensional Fourier heat conduction equation is constructed in the Cartesian co-ordinate space. The element properties of the curved shell elements are then derived using the weak formulation (or the quadratic functional) and the hierarchical element approximation. The element matrices and the equivalent heat vectors (resulting from distributed heat flux, convective boundaries and internal heat generation) are all of hierarchical nature. The element formulation permits any desired order of temperature distribution through the shell thickness. A number of numerical examples are presented to demonstrate the superiority, efficiency and accuracy of the present formulation and the results are also compared with the analytical solutions. For the first three examples, the h-approximation results are also presented for comparison purposes.

Three dimensional curved shell finite elements for heat conduction

This paper presents a finite element formulation for three dimensional curved shell heat conduction where nodal temperatures and nodal temperature gradients through the shell thickness are retained as primary variables. The three dimensional curved shell geometry is constructed using the coordinates of the nodes lying on the middle surface of the shell and the nodal point normals. The element temperature field is defined in terms of the element approximation functions, nodal temperatures and nodal temperature gradients. The weak formulation of the three dimensional Fourier heat conduction equation is constructed in the Cartesian coordinate system. The properties of the curved shell elements are then derived using the weak formulation and the element temperature approximation. The element formulation permits linear temperature distribution through the element thickness. Distributed heat flux as well as convective boundaries are permitted on all six faces of the element. The element also has internal heat generation as well as orthotropic material capability. The superiority of the formulation in terms of applications, efficiency and accuracy is demonstrated. Numerical examples are presented and comparisons are made with theoretical solutions.

Transition finite elements with temperature and temperature gradients as primary variables for axisymmetric heat conduction

This paper presents finite element formulation for a special class of elements referred to as “transition finite elements” for axisymmetric heat conduction. The transition elements are necessary in applications requiring the use of both axisymmetric solid elements and axisymmetric shell elements. The elements permit transition from the solid portion of the structure to the shell portion of the structure. A novel feature of the formulation presented here is that nodal temperatures as well as nodal temperature gradients are retained as primary variables. The weak formulation of the Fourier heat conduction equation is constructed in the cylindrical co-ordinate system ( r, z). The element geometry is defined in terms of the co-ordinates of the nodes as well as the nodal point normals for the nodes lying on the middle surface of the element. The element temperature field is approximated in terms of element approximation functions, nodal temperatures and the nodal temperature gradients. The properties of the transition elements are then derived using the weak formulation and the element temperature approximation. The formulation presented here permits linear temperature distribution through the element thickness. Convective boundaries as well as distributed heat flux is permitted on all four faces of the element. Furthermore, the element formulation also permits distributed heat flux and orthotropic material behaviour. Numerical examples are presented, first to illustrate the accuracy of the formulation and second to demonstrate its usefulness in practical applications. Numerical results are also compared with the theoretical solutions.

Isoparametric axisymmetric shell elements with temperature gradients for heat conduction

This paper presents a finite element formulation for axisymmetric shell heat conduction where temperature gradients through the shell thickness are retained as primary nodal variables. The element geometry is constructed using the coordinates of the nodes lying on the middle surface of the shell and the middle surface nodal point normals. The element temperature field is approximated in terms of element approximation functions, the nodal temperature, and the nodal temperature gradients. The weak formulation of the two-dimensional Fourier heat conduction equation in cylindrical coordinate system is constructed. The finite element properties of the shell element are then derived using the weak formulation and the element temperature field approximation. The formulation permits linear temperature gradients through the shell thickness. Distributed heat flux as well as convective boundaries are permitted on all four faces of the element. Furthermore, the element can also have internal heat generation as well as orthotropic material properties. The superiority of the formulation in terms of efficiency and accuracy is demonstrated. Numerical examples are presented and a comparison is made with the theoretical results.

A Radiation method of studying thermal regimes in elements of semiconductor radioelectronics

A brief description is provided of the measuring installation by means of which it is possible to analyze the temperature fields of elements 5×5 mm2 in size, with a resolution on the order of 50μ m in the temperature interval 50–120° C. The measurement results carried out on transistors are given.