Double Ellipsoidal Heat Source Model Research Articles

Numerical simulation and experimental analysis of thermal conduction and stress in laser cladding repair of thin-walled parts

To minimize the deformation of thin-walled parts during the laser cladding process and enhance the quality of the repaired parts, the Finite Element Abaqus software was used to develop a thermal conduction and 3D stress model, the heat source used in the experiments was a double ellipsoid heat source model. This model simulates the thermal process and the deformation resulting from residual stresses in the laser cladding process on a titanium alloy substrate with a thickness of 2 mm. Through the simulation, the temperature field of the substrate at the end of each pass was obtained, and the cladding sequence with the smallest temperature gradient during the multi-pass laser melting process was determined. By combining simulation and practice, the multilayer stacking pattern was optimized to achieve deformation control. Analog simulation experiments indicate that the optimized single-layer multi-pass laser cladding method results in less heat accumulation and thermal stress compared to the unidirectional sequential scanning method. The flatness test results show that the specimens have less deformation with the optimized multilayer stacking method. In addition, the metallographic organisation of the two cladding specimens is analysed in this paper, and the results show that the optimised specimens exhibit excellent microstructures and properties.

Influence of welding sequences and boundary conditions on residual stress and residual deformation in DH36 steel T-joint fillet welds

This paper aims to investigate the influence of welding sequences and boundary conditions on welding-induced residual stress and residual deformation of DH36 steel T-joint fillet welds through experimental and numerical methods. A series of typical experiments of successive and simultaneous double-sided welding conditions are conducted to explore both the magnitude and distribution of temperature field, residual stress and residual deformation. Meanwhile, thermal elastic-plastic finite element analysis based on a double ellipsoidal heat source model is performed to investigate the heat transfer and deformation mechanism during the welding process. The influencing factors are further explored to determine and quantify the residual stress and residual deformation induced by different welding sequences and boundary conditions. There is generally well agreement between the experimental and numerical results in terms of temperature field, residual stress, residual deformation and molten pool morphology. The results show that the welding sequences have an important influence on the magnitude and distribution of residual stress and residual deformation. Continuous simultaneous double-sided welding can significantly reduce residual stress and residual deformation to obtain better-quality welds. Boundary conditions have a significant effect on the distribution and magnitude of residual deformation and little effects on residual stress. Tightening the ends of the flange plate with bolts during the welding process can significantly reduce the deformation.

Determination of residual stress field in laser cladding using finite element updating method driven by contour deformation

Laser cladding is a cutting-edge technology widely used in additive manufacturing and surface modification. This process entails rapid melting and solidification driven by laser heating, which induces residual stress within the material. This study presents a data-driven approach to refine the numerical model of laser cladding, simultaneously emphasizing both the temperature characteristics and residual stress distribution within the thermomechanical coupling process. After integrating the residual stress distribution data obtained through the contour method with the molten pool morphology shaped by the thermal effects of laser cladding, a Levenberg-Marquardt optimization algorithm based finite element model updating scheme is proposed to efficiently identify the parameters of double ellipsoid heat source model, which employs parallel computing to reduce the computational time for iterations. The effectiveness of the proposed method is validated using experimental data. Moreover, this approach is adaptable, unaffected by the specimen size and shape, and can accurately predict the residual stress distribution characteristics. Therefore, it offers a robust framework for simulating the mechanisms of residual stress generation in titanium alloy laser cladding.

Experimental and numerical investigation on optimization of welding parameters and prediction of temperature distribution during shielded metal arc welding of ultra high hard armor steel joints

In this investigation, Ultra-high Hard Armor (UHA) steel plate by Shielded Metal Arc Welding (SMAW) process using the Austenitic Stainless Steel (ASS) electrode. In the first part of this investigation, using the finite element method (FEM), thermal analysis parameters were optimized using bead on plate welds in software code, known as SYSWELD. In the second part, using optimized parameters, a coupled thermo-mechanical analysis on multipass welded fabrication was carried out. Weld thermal cycles were analyzed by simulation and compared with experimentally measured temperature profiles. A double ellipsoidal heat source model was used to simulate the SMAW process. The heating rate and cooling rate were calculated along with residual stresses. This range of heating and cooling rate resulted in untempered martensite in the heat-affected zone (HAZ), confirmed by microstructure analysis and hardness mapping. Good validation was found between the measured and simulated 2D model with a 4–10% variation. This study suggests that numerical simulation is the capable technique in understanding the thermal and mechanical properties that influence the welding of ultra-high hard armor steels joints.

Numerical study of full penetration single- and double-sided U-rib welding in orthotropic bridge decks

Under the repeated action of residual stress and wheel load caused by welding, fatigue cracks easily occur on the top plate-U rib welding of an orthotropic bridge deck (OBD). These affect the service life. To study the influence of different full-penetration welding methods on the residual stress and fatigue of OBD, this study compared the residual stress, welding deformation, and fatigue performance of full-penetration single- and double-sided welding through finite element analysis. The welding temperature and residual stress fields were simulated based on Goldak's double ellipsoid heat source model using the thermal elastic-plastic method. The numerical results were verified using measured data from relevant literature, and the two were in good agreement. The results showed that the longitudinal residual stress of the double-sided welded U-rib was larger than that of the single-sided welded U-rib, primarily in the compressive stress range, and the maximum deviation reached 99.44 MPa. The longitudinal displacement of single-sided welding along the weld direction was 0.060 mm lesser than that of double-sided welding, and the maximum vertical displacement perpendicular to the weld direction was 2.457 mm lesser than that of double-sided welding. For the same frequency of fatigue load (wheel load), the fatigue strength of single-sided welding was larger than that of double-sided welding, and the fatigue life increased by 29.7%. In this study, analysis models of the full-penetration single-sided and full-penetration double-sided welding were established, which could provide a reference for structural fatigue assessment using the two full-penetration welding techniques under the influence of residual stress.

Multi-field coupling numerical simulation and experimental research of submerged arc surfacing process on the descaling rolls with different wall thickness

Iron and steel industry descale rolls long-term high-pressure water erosion, high temperature, easy to wear, corrosion failure and other problems, the continuous production of steel rolling impact, descale rolls base wall thickness is the main cause of cracking of the surfacing gradient lap organization. This article combines numerical simulation and experimental testing, the use of CALPHAD method to calculate the surfacing material temperature change physical parameters, based on the double ellipsoid heat source model, the establishment of the descale roller submerged arc surfacing process of multi-field coupling three-dimensional numerical model, calculations and reveal the descale roller submerged arc surfacing process of the temperature field, the stress field, the phase change field and the flow field of the transient evolution of the law, and further analyze the descale roller wall thickness of the surfacing process of the influence of the mechanism. Calculation results show that the depth of melting of the surfacing matrix is positively correlated with the width of the double ellipsoid heat source, and the larger the wall thickness, the faster the cooling rate, the greater the formation of residual stress. The austenite and martensite phase transformation of the overlay welding process is greatly influenced by the wall thickness. At the same time, SEM, EDS, XRD material science microcharacterization experiments were carried out to observe the micro-morphology, phase and elemental composition of the cladding layer. This study lays an important theoretical foundation for optimizing the submerged arc surfacing process of descale roller.

Temperature Field Simulation and Experimental Confirmation of Laser Cladding High-Entropy Alloy Coating on Cr12MoV

In order to meet the mechanical property of the die steel, this study used laser cladding to prepare a high-entropy alloy coating on Cr12MoV. A finite element method using a double ellipsoidal heat source model is proposed to simulate the evolution of the temperature field in laser cladding. The simulation results showed that with the increase in the power, the peak temperature of the molten pool increased from 2005.5 °C to 2357.4 °C, and the depth of the molten pool increased from 1.60 mm to 2.04 mm. The coating with the laser power of 1600 W had a good macroscopic quality and high lattice distortion (2.43 × 10−2). Due to the increase in laser energy density, the size of equiaxed crystals gradually increased from 1400 W to 1700 W. Under the comprehensive effect of the solution and fine grain strengthening, the coating with the power of 1600 W had a higher average microhardness (600 HV), which is 150% higher than that of the substrate. The experiment results further confirmed the accuracy of the simulation.

Analysis of the sequentially coupled thermal–mechanical and cladding geometry of a Ni60A-25 %WC laser cladding composite coating

In this research, a three-dimensional (3D) transient finite element model based on a sequentially coupled thermal–mechanical analysis (SCTMA) is proposed to simulate the evolution of the temperature field and stress field as well as the cladding geometry of the Ni60A-25 % WC laser cladding composite coating. Based on the thermo-physical properties of Ni60A-25 % WC powder and the design of the double ellipsoidal heat source model, a 3D finite element model of double-layer laser cladding with two channels is established. The evolution of the temperature field and the residual stress field at different laser process parameters are investigated to evaluate the quality of the cladding layer. The impact of different laser cladding process parameters on the cladding dimensions is investigated. The dimensions of the simulated molten pool are analyzed by fitting a polynomial curve. The simulation results show that the laser power is proportional to the temperature, and the temperature growth rate of the coating is significantly higher than that of the substrate. The scanning speed is inversely proportional to the temperature. The maximum temperature of the cladding is 1.5 times the maximum temperature of the substrate. The temperature growth rate of the cladding layer is twice that of the substrate. Due to the asymmetry of the heat source in the multi-pass cladding process, the laser energy absorption rate is not the same on both sides of the melted layer. The double ellipsoidal heat source model has a larger diffusion range in the un-melted powder, resulting in asymmetry in the width direction of the cladding layer. The analysis of the residual stresses in the cladding layer shows that the residual compressive stresses in all paths increase with the increasing laser power. The normal x residual compressive stress in the coating and the maximum residual compressive stress occur at the end of the laser beam scan. The residual compressive stress in all paths decreases as the scanning speed increases. The results show that the dimensions of the molten pool are proportional to the laser power and inversely proportional to the scanning speed. The cladding geometry can be calculated with polynomial fitting equations at a selected laser power (500 W–2800 W) and scanning speed (1 mm/s–8 mm/s). The error analysis of the simulation and the experimental results can validate the proposed finite element simulation model. The error in the molten pool size is less than 20 % for the simulation and experimental results.

Inverse analysis method of molten shape by deep learning

Most structural damage occurs in welds, and transient stress analysis corresponding to the welding procedure is performed to investigate the cause. To accurately reproduce the stress generated in the welds, it is necessary to accurately reproduce the transient heat input in the welding procedure. Thus, traditionally, inverse analysis on the transient heat input is conducted by focusing on the molten shape of the actual components; i.e., try and error work performing transient temperature distribution analysis assuming heat input until the molten shape is reproduced. Goldak's double-ellipsoidal heat source model was used by most of the researchers. In this case, heat source parameters from experience are assumed, and transient temperature distribution analysis is repeated by changing the parameters until the obtained region above the melting point matches the target molten shape. Recently, machine learning methods have been become effective to improve inverse analysis in structural integrity issues to straight-forward analysis. In this work, a model using the deep learning has been developed that can directly determine the parameters of the heat source model from the welding records and the molten shape, which can omit the inverse analysis of the heat source parameters, which has been a bottleneck in the past. This deep learning model can reduce the time required determining parameters used in FEA for failure analysis of welded components.

Influence of heat input on temperature and stress field of X80 steel pipeline cirumferential weld using type-B sleeve repairing

Abstract The multi-pass fillet welds of casing pipe were welded onto the in-service pipeline, which is widely used in pipeline repairs. However, the influence of welding heat input of B-type sleeve circumferential fillet weld on the temperature and stress field at the pipe circumferential weld is still unclear. In this paper, a double ellipsoid heat source model is developed to investigate the weld temperature field, residual stress field, and deformation field of the repair welding in service. The results show that the increase of weld heat input can effectively increase the size of the weld pool and the size of the high-temperature zone of the B-type sleeve circumferential fillet weld. And the peak temperature of the inner wall of the pipe girth weld increases with the increase of welding heat input of the sleeve circumferential fillet weld. The axial stress peak of the inner wall of the pipe girth weld reduces with the increase of welding heat input of sleeve circumferential fillet weld, and the axial deformation peak of the inner wall of the pipe girth weld increases first and then decreases with the increase of welding heat input of sleeve circumferential fillet weld.

Experimental and numerical study on the distribution of temperature field and residual stress in a multi-pass welded tube joint of Inconel 617 alloy

The purpose of this study is to compare the residual stress generation during hot wire gas tungsten arc welding (HW-GTAW) welding and conventional gas tungsten arc welding (GTAW) in a multi-pass pipe weld of a nickel-based superalloy. HW-GTAW yields better mechanical properties at low heat input than conventional GTAW, and decreases the accumulation of residual stress significantly. The distribution of residual stress developed in the through-thickness direction is determined experimentally using the Deep hole drilling method. As a result of the analysis, it was observed that the highest residual stress arises in Fusion Zone (FZ) and Heat Affected Zone (HAZ). In the case of conventional GTAW the hoop stress was observed to be tensile and distributed over 70% of the weld whereas only 20% of the weld is found to be under tensile hoop stress in the case of HW-GTAW along the weld center. The results show that shrinkage at the weld HAZ region affects the stresses produced at the cylinder's outer surface. The bending effect created during the welding process is primarily responsible for the distribution of residual stresses in the weld zone. A comprehensive numerical analysis has been carried out using ABAQUS software to predict the level of thermal and residual stresses in the weld zone, FZ, and HAZ in the case of both welding process. A 2D finite element models have been developed to simulate the welding process using the ABAQUS FE tool based on coupled thermal-mechanical analysis. A double ellipsoidal heat source model has been developed using a DFLUX subroutine file to simulate the welding process during the numerical analysis. The predicted residual stresses were validated with the experimentally obtained results.

Impact of process parameters on temperature and residual stress distribution of X80 pipe girth welds

This paper studies the impact of process parameters on the temperature field and residual stress distribution of X80 pipe girth welds. The process parameters investigated were welding power, pre-heating temperature, inter-pass temperature, welding speed, diameter-to-thickness ratio (D/t) and restraint. 2D axisymmetric finite element models with a 8-pass girth weld in the middle were established. The thermal analysis was carried out by using the double ellipsoid heat source model. This was followed by mechanical analysis to study the residual stress distributions. The results revealed that the distribution of axial and hoop residual stresses along the center of the weld was generally symmetrical. The welding power had the greatest impact on the maximum temperature of the molten pool. The other parameters had the following sequence in terms of their influence on the maximum temperature of the molten pool: D/t, welding speed, inter-pass temperature and pre-heat temperature. The sequence from large to small that the process parameters affecting the maximum axial residual stress is: restraint > power > inter-pass temperature > pre-heat temperature > D/t > welding speed. However, the sequence changed for the maximum hoop residual stress as: welding speed > inter-pass temperature > power > pre-heat temperature > D/t > Restraint. In general, all process parameters had a greater influence on the axial residual stress than the hoop residual stress.

Welding Penetration Research on the Effect of Various Welding Torch Tilt Angles in All-Position Metal Active Gas Arc Welding

An all-position welding experimental platform for pipelines was conducted, and metal active gas arc welding (MAG) was used to study the effect of various welding torch tilt angles on the welding quality. Under the same MAG welding parameters, the single-factor experimental method was adopted, and different welding torch tilt angles were selected in the welding experiment based on a grade X80 pipeline. In this study, a double ellipsoid heat source model was built, considering different welding torch tilt angles. Based on the model, the effect of various welding torch tilt angles on the depth and width of the molten pool was investigated in the welding process. The experimental results show that the forward-tilt welding torch had a wider and shallower molten pool compared to the welding torch with backward tilt and perpendicular postures. The research results suggest that appropriate welding torch tilt angles should be adopted according to the welding technology selected in all-position welding for pipelines, which has important guiding significance for getting better quality weld beads, reducing welding defects, and improving the welding technology.

Numerical Simulation of Temperature Field and Melt Pool Characteristics of CP-Ti Manufactured by Laser Powder Bed Fusion

A coupled heat source model that combined a Gauss surface heat source with a Gauss cylindrical volumetric heat source was introduced to simulate temperature field distribution and melt pool characteristics using a finite element simulation (FEM) method for the deep and narrow melt pools formed in laser powder bed fusion (L-PBF) aiming at commercial pure titanium (CP-Ti). For comparison, the same simulations using the Gauss surface heat source model and the double ellipsoid heat source model were also performed. The simulated melt pool geometries using the coupled heat source model match well with the measurements, with an average error of 1% for the melt pool depth and 7% for the width. Based on the single-track experimental results, it was found by comparing the simulated results from the three heat source models that the coupled heat source model had better accuracy than the other two. Then, the temperature field and the melt pool geometries of CP-Ti fabricated at different laser power levels from 300 W to 500 W and scanning speeds from 600 mm/s to 4000 mm/s were simulated. According to the simulated maximum temperature and geometries of the melt pool, a suitable process parameters map for CP-Ti was obtained. The reported experimental results agree well with the simulated map. The coupled heat source model is more accurate and applicable for the deep and narrow melt pools formed during L-PBF.

Investigation on the microstructure and mechanical properties analysis of 304L stainless steel multi-pass filler welding joint for pipeline

The multi-pass welding of 45 mm thick 304 L stainless steel is carried out by flux-cored wire arc welding. The mechanical property of the welded joint is characterized. Residual stress measurement on the surface of welded joints is carried out by blind hole method. The finite element model of multi-pass welding joint is established based on actual weld morphology. The temperature and stress field have been investigated by the double ellipsoid heat source model during the welding process. The microstructure analysis results show that the upper surface is consist of austenite and ferrite phase, which is larger than the lower weld zone. And the microhardness distribution is shown as welded metal < heat affected zone < base metal. After welding, the maximum longitudinal residual stress is 398 MPa, and the maximum transverse residual stress is 441 MPa.

Cover plate welding sequence and shape rationality simulation analysis on wall cracks of stainless steel spent fuel pool

The wall of spent fuel pools is prone to pitting or electrochemical corrosion owing to a long-term service in acidic media, where a penetrating cracking may occur in severe cases. Moreover, totally replacing the spent fuel pool causes huge economic losses. Thus, cover plate welding is used to repair the cracked region of spent fuel pools using the ‘fitness for service’ principle. The finite element method is used to simulate and analyse the temperature and stress fields during the repair process of cover plate welding to guarantee that the repair process does not cause new dangerous effects on the cracked region. In this study, we used self-fusion gas tungsten arc welding (GTAW) to cover defects with square and circular patch plates. The modified double-ellipsoid heat source model is derived for cure welding. The effects of two patch plate shapes and different welding sequences on the temperature and stress fields during the welding process were compared using numerical analyses. Finally, a reasonable patch board shape and welding sequence were determined.

Molten pool behavior and solidification characterization in steady magnetic field assisted laser-MIG hybrid welding of aluminum alloy

Microstructure evolution is highly correlated with the melt flow characterization in welding. In this study, a 3D heat flow model with consideration of magnetic field was constructed to describe the temperature field, the flow and keyhole behaviors in the molten pool during the laser-MIG hybrid welding. The role of magnetic flux density in the molten pool dynamics and microstructure evolution was explored. A moving hybrid heat source model including Gaussian surface heat source model and Gaussian rotary body heat source model as well as double ellipsoidal heat source model was carried out to elucidate the laser and MIG arc energy distribution. Decent agreement is realized between the measured weld geometry and predicted weld pool dimension. Numerical results indicate that an expanded molten pool is clearly observed under magnetic field. As the magnetic flux density increases, the downward flow velocity of the molten pool is enhanced. Moreover, visible difference of oscillation growth period for keyhole depth is produced and this leads to a variation in the time it takes for the molten pool to stabilize. Significant grain refinement appearing in both arc-affected zone at the weld upper part and laser-affected zone at the weld lower part is documented although the refinement degree varies at different zones. This is attributed to the formation of many initial nuclei or crystallites, originated from the enhanced flow of the molten pool with the assistance of magnetic field. This study provides a perspective in understanding the physical phenomena involved in magnetic field assisted laser-MIG hybrid welding and lays the foundation for weld microstructure optimization.

Residual Stress Simulation of Heterogeneous Cladding Layer Between SiC/Ti6Al4V

SiC cladding on the alloy surface can significantly improve the high temperature resistance and oxidation resistance of the material. However, heterogeneous cladding usually produces large residual stress and affects the service life of the material. In the process of laser cladding simulated by finite element method, the mechanism of residual stress during SiC deposition on alloy surface is studied by using moving double ellipsoid heat source model. The simulation results show that the residual stress is unevenly distributed near the cladding layer, and the residual stress presents a compression-tension-compression distribution in the thickness direction due to the mixing law of material properties, which provides a reliable numerical prediction method for the residual stress of SiC cladding layer cladding on the alloy base.

Numerical simulation for determination of temperature field and residual stress of stainless steel butt joints with and without clamping

Many welded structures are fabricated from stainless steels because these steels have good mechanical properties and good corrosion resistance. It is necessary to predict the residual stress after welding in order to evaluate the performance of the welded joint. In this paper, the butt welded joint of AISI 316L stainless steel plates is studied. The Metal Inert Gas (MIG) welding process is selected for this material. A SYSWELD software based on the Finite Element Method (FEM) is used to determine the temperature field and residual stresses of two stainless steel plates. The welding simulation includes a sequential coupled thermomechanical analysis. The elemental generation and death technique is utilized to simulate metal deposition in welding. The double ellipsoidal heat source model is used for the heat input of the MIG welding process. The temperature distribution for various time steps at some important points is presented. Cooling times and cooling rates over a temperature range of 800 oC to 500 oC at these points are determined. The residual stress distribution in the longitudinal and transverse direction in two cases with and without clamping is obtained and compared. Obtained results show that: the temperature field in the case of clamping is the same as in the case of no clamping; only the longitudinal stress and transverse stress components are important, the other stress components are not important; the longitudinal stress at the middle of weld line is very high; the transverse stress in the case of clamping is greatly increased, so it is necessary to limit clamping to reduce residual stress after welding

Effect of Residual Stress on Hydrogen Diffusion in Thick Butt-Welded High-Strength Steel Plates

Thick high-strength steel plates are increasingly being used for ship structures. Moreover, hydrogen enters the process of manufacturing and service, and large residual tensile stress occurs near the weld. Such stress can facilitate the diffusion and accumulation of hydrogen in the material, leading to hydrogen embrittlement fracture of the shell. Therefore, residual-stress-induced diffusion and accumulation of hydrogen in the stress concentration region of thick butt-welded high-strength steel plate structures need to be studied. In this study, manual metal arc welding was realized by numerical simulation of residual stress in a thick butt-welded high-strength steel plate model using the thermoelastic–plastic theory and a double ellipsoidal heat source model. To analyze residual stress, a set of numerical simulation methods was obtained through comparative analysis of the test results of relevant literature. Residual and hydrostatic stress distributions were determined based on these methods. Then, hydrogen diffusion parameters in each region of the model were obtained through experimental tests. Finally, the results of the residual stress field were used as the predefined field of hydrogen diffusion to conduct a numerical simulation analysis. The distribution of hydrogen diffusion under the influence of residual stress was obtained based on the theory of stress-induced hydrogen diffusion. The weak area of the welding joint was found to be near the weld toe, which exhibited high hydrostatic stress and hydrogen concentration. Further, the maximum hydrogen concentration value of the vertical weld path was approximately 6.1 ppm, and the maximum value of the path parallel to the weld centerline and 31 mm away from the weld centerline was approximately 6.22 ppm. Finally, the hydrostatic tensile stress in the vertical weld path was maximized (~345 MPa), degrading the material properties and causing hydrogen-related cracking. Hence, a reliable method for the analysis of hydrogen diffusion according to residual stress in thick high-strength steel plates was obtained. This work could provide a research basis for controlling and eliminating the adverse effects of hydrogen on the mechanical properties of ship structures and ensuring the safe service of marine equipment.