Three-dimensional Transient Finite Element Research Articles

Coupled heat transfer and phase transformations of dual-phase steel in coil cooling

Dual-phase steels are generally used in the car industry due to high tensile strength and good formability, which are obtained by a mixture of bainite and ferrite phases. This microstructure is achieved through slow rate coil cooling. However, the manufacturing of dual-phase steels introduces various challenges such as the instability of the cold rolling process. An important factor affecting this is the non-uniform coil cooling of a hot rolled strip. In coil cooling the cooling rates are not controlled and there are different thermal contacts during coil conveyance causing unequal cooling of the steel coil. Unequal cooling rates lead to non-uniform coil cooling, producing irregular phase transformations on different sides of the coil, which causes periodical variations of the phase fractions in the steel strip. Varying phase fractions cause thickness deviations in the strip during the cold rolling process. A three-dimensional transient heat transfer finite element model was developed and used for modeling the complete coil conveyance chain and coil field cooling of the coil on an industrial scale. A coupled phase transformation model is implemented as a subroutine into the finite element model for calculating the resulting phase fractions. It was found that the different thermal contacts during the coil conveyance produce uneven cooling rates causing length- and widthwise variations in the phase fractions. The heat transfer model is validated by comparing temperature profiles between the simulated and measured coil edges. The phase transformation model is fitted into experimental data and verification is carried out in industrial conditions by comparing the modeled phase fractions and test samples from a cooled and unwound steel coil.

Laser-induced softening analysis of a hardened aluminum alloy by physical simulation

The study focuses on the analysis of the softening effects of the work-hardened aluminum alloy sheets EN AW 5754 H32 1.5 mm thick, through the physical simulation of thermal cycles induced in the material by laser heat treatments (LHTs). A numerical-experimental approach was implemented to define the laser thermal cycles and to subsequently reproduce them on the GleebleTM 3180 physical simulator. The obtained softening was measured by microhardness and metallographic analysis tests. For the definition of laser thermal cycles, preliminary tests with a 2.5 kW CO2 laser source have been realized, and a three-dimensional transient finite element thermal models were developed and calibrated with the experimental results. The investigated laser heat treatment parameters explored thermal cycles with different shape, interaction time, and peak temperature. Physical simulation tests were performed using laser thermal cycles that showed the maximum softening of the aluminum alloy. A three-dimensional transient finite element thermoelectric model was developed to design the shape of the Gleeble specimens, which satisfy the heating and cooling rate required by laser thermal cycles. Results obtained show that it is possible to physically simulate the investigated laser thermal cycles, reducing the cross section of the shaped part of the specimen. Softening effects depend on the thermal cycle shape. Greater softening is observed by increasing the interaction time and the peak temperature, but beyond a peak temperature threshold value, negligible effects are detected.

Finite Element Model of a Melting Terminal Debris Bed in a CANDU Calandria

Abstract Melting of the terminal debris bed at the bottom of a Canada deuterium uranium (CANDU) 6 calandria vessel during a severe accident is studied using a three-dimensional transient finite element analysis. Settling of the debris is modeled, as are the effects of changing temperature and porosity on debris material properties. The time and magnitude of maximum heat rejection from the debris bed, and the maximum mass of molten debris, are calculated as functions of the accident timing. The results are compared with those from the modular accident analysis program (MAAP)-CANDU severe accident code.

Dynamics of the heat affected zone and induced strains in laser machining below ablation threshold

The Heat Affected Zone - HAZ of a laser irradiated AISI H-13 steel workpiece, is investigated via numerical simulations and experimental measurements. A three-dimensional transient thermo-structural finite element model is developed to simulate the machining process. A Gaussian laser beam is employed as the heat source. The developed finite element material model considers the effects of plastic strain, strain rate and temperature, along with a fracture model. The experiments are carried out with a laser of 1-4 W power and with a scanning speed of 100 mm/min. Thermocouple sensors are used for the temperature measurements, while the surface roughness is measured using white light interferometry and related experimental diagnostics. A parametric numerical analysis regarding the average absorptivity of the workpiece is performed and is compared to the experimental findings. The depth and width of HAZ and the induced strains are studied for the plastic and melting regimes. The influence of the surface roughness of the metal workpiece on the dynamics of HAZ is also experimentally demonstrated. The findings of this study highlight the role of the absorption coefficient and the surface roughness on the HAZ below the ablation threshold and can be applied to related laser machining processes.

Thermal Contact Resistance between Aero Engine Compressor Blade and Flexible Fixture

In the process of two-pass micro plasma arc welding of titanium alloy sheet, based on the thermal contact resistance theory, a three-dimensional transient heat transfer finite element model of contact heat transfer between titanium alloy sheet and flexible fixture was established. The effects of contact upper surface temperature, micro-contact thermal resistance, micro-gap thermal resistance, DC and pulse welding on thermal contact resistance were investigated, and the simulation and experimental results were compared. The results show that the thermal contact resistance increases as the temperature increases when the temperature of the contact upper surface (titanium alloy sheet) is in the range of 290–350 K. The effect of micro-contact thermal resistance on the thermal contact resistance is 26.1%–46.3% larger than the micro-gap thermal resistance. The thermal contact resistance of pulse welding is 3.1%–3.5% larger than DC welding. The error of simulation and experimental results of weld pool depth is 8.6%, which verifies the reliability of the model.

Modeling and numerical simulation on launch dynamics of integrated launch package in electromagnetic railgun

This paper presents a numerical approach to modeling launch dynamics of integrated launch package in railguns. This approach was based on the three-dimensional transient finite element solutions of the multi-physical field equations. Numerical simulations were conducted for a railgun system composed of the capacitor-based pulse forming network, advanced containment launcher, and integrated launch package. Some issues about induced eddy currents, stress distributions, and projectile lateral motions were discussed. The results show that the in-bore motion of the projectile is sensitive to the launch package configuration and launcher stiffness. Moreover, the armature under a heavy current is prone to serious deformation and then leads to launch failure. The launch dynamics model provides a method to predict the in-bore processes and evaluate the in-bore survivability of the integrated launch package in a railgun.

Validation of Sinus Filter Choke Temperature Model

<span lang="EN-GB">This article discusses the relationship between the losses of a sinus filter choke. Its influence on the loaded sinus filter temperature field distribution within and on the surface, verification of these performance and temperature relationships. It includes three-dimensional transient finite element analysis (FEA) of the sinus filter choke temperature conditions based on a mathematical description of the conduction, free convection and losses and describing temperature field validation methodology. In addition, there is shown mutual evaluation of the validation measurement and FEA simulation. Finally, there are outlined further options for the future optimisation of the sinus filter choke thermal simulation.</span>

Numerical Simulation of Thermal Evolution and Solidification Behavior of Laser Cladding AlSiTiNi Composite Coatings

In order to better understand how a high energy input and a fast cooling rate affect the geometric morphology and microstructure of laser cladding aluminum composite coatings, a three-dimensional (3D) transient finite element model (FEM) has been established to study the temperature field evolution during laser cladding of AlSiTiNi coatings on a 304 stainless steel substrate. In this model, a planar Gauss heat source and a temperature selection judgment mechanism are used to simulate the melting and solidification process as well as the geometric morphology of the laser cladding coatings. The differences in physical characteristics of the cladding materials before and after melting are considered. The results of thermal simulations, including temperature history, temperature gradient, and solidification rate, of the laser cladding coatings are investigated. Corresponding experiments, conducted using an IPG-YLS-5000 fiber laser, are used to verify the simulation results. The experimental observations agree well with the theoretical predictions, which indicates that the established model is valid.

Rotor Shape Multi-Level Design Optimization for Double-Stator Permanent Magnet Synchronous Motors

This paper presents a rotor shape multi-level-objective optimization designed to reduce the mechanical stress distribution in the rotor core of a double-stator permanent magnet synchronous motor. The second objective is weight minimization performed via a response surface methodology with a uniform precision central composite design function. The optimal operation point, with a substantial population size, is reached using a Monte Carlo algorithm on the fitted model. The goodness-of-fit for the model is evaluated based on the modified Akaike information criterion and the Bayesian information criterion with a linear regression approach. To achieve these goals, a multi-level design procedure is proposed for the first time in machine design engineering. All the electromagnetic forces of the machine, such as normal, tangential, and centrifugal forces, are calculated using three-dimensional transient finite element analysis. The outcome of the proposed rotor core optimization shows that the finalized shape of the studied core has significantly smaller weight and mechanical stress, while the electromagnetic performance of the machine has remained consistent with a pre-optimized machine.

Effects of electrolytic jet plasma oxidation (EJPO) coatings on thermal behavior of engine cylinders

Aluminum engine blocks with ceramic-coated cylinder bores can effectively reduce the self-weight and largely improve the wear resistance. However, the presence of coatings to some extent also affects the heat transfer of internal combustion (IC) engine between the cylinder and the coolant due to their low thermal conductivities. In this paper, electrolytic jet plasma oxidation (EJPO) coatings were adopted to deposit on the engine cylinder bores. A three-dimensional transient finite element analysis (FEA) thermal model was developed to investigate the thermal behavior of EJPO-coated cylinders. It was found that both coating thickness and thermal conductivity could significantly influence the bore surface temperature and temperature fluctuation behaviors at the different crank angles. A possible selection of the parameter combination of coating thickness and thermal conductivity would provide a newly promising opportunity in the design of a high-quality coating for the cylinder bores to improve IC engine efficiency.

A numerical model for full and partial penetration hybrid laser welding of thick-section steels

Full and partial penetration welding using high power lasers exhibit different melt pool geometries. The main difference is that full penetration welds tend to widen at the root side. In recent years, full penetration laser welding has been modeled using sophisticated multiphase numerical models. However, less computationally-complex thermo-mechanical models that are capable of accounting for the root widening phenomenon in full penetration laser welding are lacking. In this study, hybrid laser welding was performed for full and partial penetration modes on butt joints of structural steel. A numerical model was presented that used a three-dimensional transient Finite Element (FE) analysis and thermal conduction heat transfer for calculating the temperature fields in both full and partial penetration welding modes. For this purpose, a double-conical volumetric heat source was developed based on the three-dimensional conical (TDC) heat source in the literature. The model was validated and calibrated with different experiments. The results show that the model is capable of calculating the transient temperatures for the common melt pool geometries obtainable by the full and partial penetration hybrid laser welding of thick-section steels. The model can potentially be employed as the basis for predicting e.g. microstructural properties or residual stresses for a given welding procedure.

Effect of Latent Heat Released by Freezing Droplets during Frost Wave Propagation.

Frost spreads on nonwetting surfaces during condensation frosting via an interdroplet frost wave. When a supercooled condensate water droplet freezes on a hydrophobic or superhydrophobic surface, neighboring droplets still in the liquid phase begin to evaporate. Two possible mechanisms govern the evaporation of neighboring water droplets: (1) The difference in saturation pressure of the water vapor surrounding the liquid and frozen droplets induces a vapor pressure gradient, and (2) the latent heat released by freezing droplets locally heats the substrate, leading to evaporation of nearby droplets. The relative significance of these two mechanisms is still not understood. Here, we study the significance of the latent heat released into the substrate by freezing droplets, and its effect on adjacent droplet evaporation, by studying the dynamics of individual water droplet freezing on aluminum-, copper-, and glass-based hydrophobic and superhydrophobic surfaces. The latent heat flux released into the substrate was calculated from the measured droplet sizes and the respective freezing times ( tf), defined as the time from initial ice nucleation within the droplet to complete droplet freezing. To probe the effect of latent heat release, we performed three-dimensional transient finite element simulations showing that the transfer of latent heat to neighboring droplets is insignificant and accounts for a negligible fraction of evaporation during microscale frost wave propagation. Furthermore, we studied the effect of substrate thermal conductivity on the transfer of latent heat transfer to neighboring droplets by investigating the velocity of ice bridge formation. The velocity of the ice bridge was independent of the substrate thermal conductivity, indicating that adjacent droplet evaporation during condensation frosting is governed solely by vapor pressure gradients. This study not only provides key insights into the individual droplet freezing process but also elucidates the negligible role of latent heat released into the substrate during frost wave propagation.

Analysis on the magnetic shunt structure of large power transformer

Installing magnetic shunts on the surfaces of tank and clamps of power transformer is able to reduce the eddy current losses and decrease the temperature rise effectively. Here, the three-dimensional transient finite element method and the magnetic thermal coupling method are used to calculate and analyse the effect of magnetic shunts with different structures. The non-linear magnetic property of both the transformer structural parts and the magnetic shunts are considered in the analysis. The lamination structure of the shunt is also considered, which is simulated by a thick plate with anisotropic magnetic property. A 334 MVA single-phase transformer is taken as an example in the analysis. The optimisation shunt structure is obtained. By comparing the L-shaped, the inverted L-shaped, and the U-shaped magnetic shunts for the clamps, it is proved that the U-shaped shunt is more effective in reducing the eddy current loss and temperature rise.

Microstructure prediction of selective laser melting AlSi10Mg using finite element analysis

Selective Laser Melting (SLM) technology is a complex process controlled by mass and heat transfer. It is very important to understand the microstructure of single track. This work predicted the single track's microstructure of SLMed AlSi10Mg by calculating the thermal variables and using columnar to equiaxed transition (CET) criterion. Firstly, a high accurate transient three-dimensional finite element model was established with anisotropic thermal conductivities verified by both molten pool dimensions and track surface feature. Secondly, the finite element model was used to accurately predict the thermal variables, such as temperature gradient, cooling rate and solidification rate of the molten pool. Thirdly, a columnar to equiaxed transition criterion was established by connecting the predicted thermal variables and experimental microstructure, the experimental results verified that it can predict the microstructure of SLMed AlSi10Mg very well.

A three-dimensional transient mixed hybrid finite element model for superabsorbent polymers with strain-dependent permeability.

A hydrogel is a cross-linked polymer network with water as solvent. Industrially widely used superabsorbent polymers (SAP) are partially neutralized sodium polyacrylate hydrogels. The extremely large degree of swelling is one of the most distinctive characteristics of such hydrogels, as the volume increase can be about 30 times its original volume when exposed to physiological solution. The large deformation resulting from the swelling demands careful numerical treatment. In this work, we present a biphasic continuum-level swelling model using the mixed hybrid finite element method (MHFEM) in three dimensions. The hydraulic permeability is highly dependent on the swelling ratio, resulting in values that are orders of magnitude apart from each other. The property of the local mass conservation of MHFEM contributes to a more accurate calculation of the deformation as the permeability across the swelling gel in a transient state is highly non-uniform. We show that the proposed model is able to simulate the free swelling of a random-shaped gel and the squeezing of fluid out of a swollen gel. Finally, we make use of the proposed numerical model to study the onset of surface instability in transient swelling.

Composite wall test-chamber assessment for hydrogen blast loads

Simplified energy based analytical models and close form solutions are used to evaluate the limiting quasi-static and impulsive over-pressure transient response of a composite wall test-chamber, which is validated and confirmed with experimental observations using controlled hydrogen combustion tests. Further a detail three-dimensional transient finite element simulation is presented to compare the test results with the numerical results. The effectiveness of evolved procedures is highlighted in the context of the blast resistance evaluation of experimental facilities besides the other important infrastructures that might be subjected to hydrogen blast loads. Despite the known limitations of the simplified analytical models and close form solutions, its usefulness is emphasized to develop fundamental understanding for arriving at sound engineering judgment for conducting blast experiments in a safe manner. With this background, the interpretation of the associated detail three-dimensional transient dynamic finite element analysis results is shown to be consistent and in good agreement with the test observations.

Finite element modeling of continuous induction welding of thermoplastic matrix composites

Continuous induction welding for thermoplastic matrix composites requires an accurate modeling of the temperature distribution in the laminates, depending on the electromagnetic field. In this work, a transient three-dimensional finite element (FE) model was developed in order to study the heat transfer phenomena, and melting and crystallization in the welding area during the continuous induction welding of carbon fiber reinforced Poly(ether ether ketone) (CF/PEEK) laminates. The multiphysics problem was solved by coupling electromagnetic and heat transfer equations considering matrix melting and crystallization behavior. The model was able to simulate the continuous process along a linear path at a constant speed. The computed temperatures were in good agreement with experimental measurements. Several numerical simulation were used for selecting a processing window as a function of coil speed and current, for the welding of CF/PEEK joints. The results of welding experiments were evaluated by single lap shear tests and morphology characterization of the welded interfaces and fracture surfaces.

Composite Wall Test-chamber Assessment for Hydrogen Blast Loads

Simplified energy based analytical models are used to evaluate the quasi-static and impulsive over-pressure responses of blast resistance composite wall test-chamber for different hydrogen charges, which is validated with experimental observations during hydrogen combustion tests. Further a detail three-dimensional transient finite element simulation of the test-chamber is presented to compare the test results with the finite element results. The effectiveness of evolved procedures is highlighted for the blast resistance evaluation of experimental facilities besides the other infrastructures that might be subjected to hydrogen blast loads.

A new solution method for wheel/rail rolling contact.

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit–explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit–explicit order solution method is used to solve the FE model. Results show that the explicit–explicit order solution method has faster operation speed and higher efficiency than the implicit–explicit order solution method while the solution accuracy is almost the same. Hence, the explicit–explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

Finite element simulation and experimental investigation of residual stresses in selective laser melted Ti–Ni shape memory alloy

A three-dimensional transient finite element method (FEM) model was established to predict the stress distribution of parts shaped by selective laser melting (SLM) technology, using Ti–Ni two-component powders as the raw materials. The moving heat source with a Gaussian distribution was applied in the simulation process. By simulating the laser beam scanning process, the peak values of the thermal stresses were first recorded at the onset of the first track where the first heating–cooling cycle occurred. After the whole part was cooled down, the largest residual stresses were found at the end of the first track and the last track. To verify the simulation results, the experimental investigation with the same parameters was conducted. The initial area of the first track of the fabricated part was fully dense where the residual stresses were small. The larger residual stresses obtained at the following track resulted in the formation of the cracks at the end edge of the parts, which testified that the results were in good agreement with the simulation predictions.