Heat Source Model Research Articles

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.

A Gaussian Process-Based extended Goldak heat source model for finite element simulation of laser powder bed fusion additive manufacturing process

Laser powder bed fusion (L-PBF) additive manufacturing (AM) is a key enabling technology to manufacture highly complex and integrated metallic structures. In L-PBF AM process, the melting of the metal powders and the layers underneath can be governed by either “conduction mode” or “keyhole mode”, with the keyhole mode reportedly leading to porosity and decreased strength and ductility by many studies. In part scale simulations, finite element (FE) model is often used to study the temperature distribution during printing and to predict the residual stress, where a volumetric heat flux with a Gaussian or a double ellipsoidal (Goldak) distribution is often applied as the laser heat source. However, the above heat source models can only capture the melt pool shape in the conduction mode, and fail to capture the transition to keyhole melting mode when the process parameters change. To overcome this inaccuracy, an extended Goldak heat source model is proposed by introducing a laser penetration term as a function of laser parameters obtained from a Gaussian-Process (GP) model. The model is validated by “2D pad” AlSi10Mg L-PBF experiments under a wide range of laser power, scan speed, and laser focus offset, and the results show the model successfully captures the measured melt pool shape in all conditions.

Comparative Study between Thermo-Mechanical and Inherent Strain Method in Analysing Part Distortion of WAAM Component Using Numerical Simulation

This research investigates the part distortion of WAAM process by utilizing advanced numerical simulation. The WAAM component is made of a stainless steel SS316L deposition layer that is deposited on top of a mild steel S235 substrate plate to create a hollow, rectangular structure with a thin wall. In this study, Goldak's double-ellipsoid was used as the heat source model, and an isotropic hardening rule based on the von-Mises yield criterion was used. MSC Marc/Mentat is utilized as the numerical FE software for this research. The commercial S235 mild steel for substrate and the evolved SS316L was scanned by JMATPRO as the input for material modelling. In order to reduce the computational time of the numerical WAAM process, an Inherent Strain Method (ISM) is proposed for a numerical WAAM simulation in Marc. There are two ISM methods proposed for this study, the first is the analytical ISM based on the calculations and second is the calibration-based ISM using Virtual Calibration Test (VCT). On obtaining the ISM value based on the result of VCT, the mathematical software MATLAB were utilized to find the optimized ISM value. This research has a final purpose to determine which numerical simulation model that has a clear advantage on predicting the component deformation result in term of result accuracy as well as computational time. The expected final outcome of this study is the implementation of ISM method on numerical WAAM simulation is able to predict a part distortion in an accurate manner similar to TMM model with significantly faster computational time. Keywords: WAAM, Part Distortion, Numerical Simulation, Inherent Strain Method, Computational Time.

Model-Based Sensitivity Analysis of the Temperature in Laser Powder Bed Fusion.

To quantitatively evaluate the effect of the process parameters and the material properties on the temperature in laser powder bed fusion (LPBF), this paper proposed a sensitivity analysis of the temperature based on the validated prediction model. First, three different heat source modes-point heat source, Gaussian surface heat source, and Gaussian body heat source-were introduced. Then, a case study of Ti6Al4V is conducted to determine the suitable range of heat source density for the three different heat source models. Based on this, the effects of laser processing parameters and material thermophysical parameters on the temperature field and molten pool size are quantitatively discussed based on the Gaussian surface heat source. The results indicate that the Gaussian surface heat source and the Gaussian body heat source offer higher prediction accuracy for molten pool width compared to the point heat source under similar processing parameters. When the laser energy density is between 40 and 70 J/mm3, the prediction accuracy of the Gaussian surface heat source and the body heat source is similar, and the average prediction errors are 4.427% and 2.613%, respectively. When the laser energy density is between 70 and 90 J/mm3, the prediction accuracy of the Gaussian body heat source is superior to that of the Gaussian surface heat source. Among the influencing factors, laser power exerts the greatest influence on the temperature field and molten pool size, followed by scanning speed. In particular, laser power and scan speed contribute 38.9% and 23.5% to the width of the molten pool, 39.1% and 19.6% to the depth of the molten pool, and 38.9% and 21.5% to the maximum temperature, respectively.

Investigation of the Effect of Heat Transfer during Friction Stir Welding (FSW) of AZ80A Mg Alloy Plates using a Pin Tool by Conducting Finite Elements Analysis

Friction stir welding (FSW) is an innovative solid-state welding process that has attracted substantial attention due to its potential for combining problematic materials such magnesium alloys, such as AZ80A. In order to better understand the impact of heat transport during FSW of AZ80A magnesium alloy plates using a pin tool, this study used finite element analysis (FEA). The welding process's thermal features, such as temperature distribution, thermal stresses, and material flow patterns, are the major focus of this analysis. The first step of the study is to conduct a comprehensive literature evaluation to lay a firm groundwork and pinpoint knowledge gaps. The thermal conductivity, specific heat, density, and mechanical characteristics of AZ80A magnesium alloy are measured and recorded as part of the material characterisation process. To ensure an exact simulation of real-world welding circumstances, a comprehensive 3D model of the welding setup is built, including the AZ80A magnesium alloy plates and the pin tool. In order to accurately record temperature variations, a tiny mesh is used, particularly in the welding zone. By include boundary conditions that mimic the real-world welding characteristics, such as the rotation of the pin tool and the clamping or fixturing of the plates, finite element analysis is used to model the FSW procedure. To simulate the heat input produced by FSW, a heat source or heat production model is used.

Modeling of Yb:YAG Laser Beam Caustics and Thermal Phenomena in Laser-Arc Hybrid Welding Process with Phase Transformations in the Solid State.

This paper focuses on the mathematical and numerical modeling of the electric arc + laser beam welding (HLAW) process using an innovative model of the Yb:YAG laser heat source. Laser energy distribution is measured experimentally using a UFF100 analyzer. The results of experimental research, including the beam profile and energetic characteristics of an electric arc, are used in the model. The laser beam description is based on geostatistical kriging interpolation, whereas the electric arc is modeled using Goldak's distribution. Hybrid heat source models are used in numerical algorithms to analyze physical phenomena occurring in the laser-arc hybrid welding process. Thermal phenomena with fluid flow in the fusion zone (FZ) are described by continuum conservation equations. The kinetics of phase transformations in the solid state are determined using Johnson-Mehl-Avrami (JMA) and Koistinen-Marburger (KM) equations. A continuous cooling transformation (CCT) diagram is determined using interpolation functions and experimental research. An experimental dilatometric analysis for the chosen cooling rates is performed to define the start and final temperatures as well as the start and final times of phase transformations. Computer simulations of butt-welding of S355 steel are executed to describe temperature and melted material velocity profiles. The predicted FZ and heat-affected zone (HAZ) are compared to cross-sections of hybrid welded joints, performed using different laser beam focusing. The obtained results confirm the significant influence of the power distribution of the heat source and the laser beam focusing point on the temperature distribution and the characteristic zones of the joint.

An ANN Hardness Prediction Tool Based on a Finite Element Implementation of a Thermal–Metallurgical Model for Mild Steel Produced by WAAM

WAAM has emerged as a promising technique for manufacturing medium- and large-scale metal parts due to its high material deposition efficiency and automation level. However, its high heat accumulation and complex thermal evolution strongly affect the resulting microstructures and mechanical properties. The heterogeneous and unpredictable nature of these properties hinder the widespread application of WAAM in the steel construction industry. In this study, an artificial neural network (ANN) hardness model is developed, based on a thermal–metallurgical model for mild steel. The objective is to establish non-linear relationships between the input process parameters and the desired output, i.e., hardness. The thermal–metallurgical model utilizes a well-distributed heat source model, a death-and-birth algorithm, and a metallurgical model to simulate the temperature field and to calculate the microstructure phase fraction. The temperature prediction errors at four thermocouple positions are mostly below 20%. Because of the limited experimental data, twenty-five simulation experiments are performed using the L25 orthogonal array based on the Taguchi method. The analysis of variance (ANOVA) reveals that the travel speed has the greatest impact on hardness. With the dataset from the thermal–metallurgical model, an ANN model to predict hardness is developed. A comparison to experimental data shows excellent performance and accuracy, with the Mean Absolute Percentage Error (MAPE) of ANN predictions within 10% of the targeted hardness.

Study on thermal penetration process of oil casing in shallow water environment by plasma arc based on heat source simulation and experiments

Abandoned offshore oil wellheads must be removed and plugged to protect the marine environment. Underwater plasma arc cutting holds the promise of playing a significant role in this work. However, much remains unknown about the thermal burn-off process of underwater plasma arcs for oil well casing. This work investigated the thermal penetration process of oil casing in a shallow water environment through experiments and heat source modeling simulations. A workpiece made of mild steel plate and cement block was considered as a small segment of the oil casing to be penetrated. The hole diameters, depths, and removal volumes of the workpieces were investigated experimentally. A combined heat source consisting of an elliptical cone heat source and a semi-ellipsoidal heat source was established based on the hole shape. The simulated and experimental hole profiles matched well. The results showed that the evolution of the hole shape of the workpiece was related to the motion state of the plasma arc and could be reflected by the variation of the arc voltage. Compared to steel plates, cement materials were easily removed by heat. These findings are favorable to promote the development of underwater plasma arc cutting in oil casing removal.

Numerical analysis of static and dynamic heat source model approaches in laser micro spot welding

Numerical analysis of static and dynamic heat source model approaches in laser micro spot welding

Heat transfer in Z-scan experiments

In this study, we present the results of theoretical calculations concerning heat exchange in materials subjected to laser irradiation, with particular emphasis on Z-scan experiments. Using explicit difference methods, we model the temperature distribution in three-dimensional samples of various sizes, such as [4 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 4 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 2] mm, [5 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 5 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 2] mm, and [6 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 6 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 2] mm. The simulations encompass two different types of pulsed lasers with durations of 10 (ns) and 100 (ps), adjusting laser parameters to achieve a peak irradiance intensity of 5 GW/cm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${^2}$$\\end{document}. The temperature distribution in samples, denoted as T(x, y, z, t), is computed using a novel laser heat source model specifically designed for this problem. The computational program Z-lambda enables not only the simulation of thermal processes during the Z-scan experiment but also post-experiment analysis. The development of this software was one of the main objectives of this study. The results indicate that the thermal analysis of Z-scan experiments requires consideration of factors such as laser pulse duration, laser repetition time, sample geometry, and heat exchange between the studied material and the surroundings. Especially in the Z-scan technique, controlling thermal parameters before the experiment is crucial for obtaining precise and reproducible results. It is noteworthy that sample heating during the experiment can significantly influence charge carrier density, subsequently affecting the parameters of nonlinear optics (NLO). Tools like the Z-lambda program allow for the optimization of laser parameters, minimizing sample heating, and reducing the thermal impact on NLO parameters.

A Physically Motivated Heat Source Model for Laser Beam Welding

In this contribution, we present a physically motivated heat source model for the numerical modeling of laser beam welding processes. Since the calibration of existing heat source models, such as the conic or Goldak model, is difficult, the representation of the heat source using so-called Lamé curves has been established, relying on prior Computational Fluid Dynamics (CFD) simulations. Lamé curves, which describe the melting isotherm, are used in a subsequent finite-element (FE) simulation to define a moving Dirichlet boundary condition, which prescribes a constant temperature in the melt pool. As an alternative to this approach, we developed a physically motivated heat source model, which prescribes the heat input as a body load directly. The new model also relies on prior CFD simulations to identify the melting isotherm. We demonstrate numerical results of the new heat source model on boundary-value problems from the field of laser beam welding and compare it with the prior CFD simulation and the results of the Lamé curve model and experimental data.

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.

Research on Computer Aided Deformation Control Strategy for Welding of Large Long Straight Beams

<p>Long straight string beams are often used as supporting structures in large equipment. Due to the large size of string beams, welding technology is generally used to complete their production. This article first constructs the finite element model and heat source model of the chord beam based on the structure of the long straight beam, and then obtains the distribution and evolution law of the temperature field, as well as the temperature rise law of the temperature field under dynamic simulation. Based on this law data, an improved BP neural network model is used to predict the deformation of the beam. In order to verify the authenticity of the prediction results, the article finally builds a Matlab simulation experimental environment and conducts simulation experiments on the welding deformation prediction of the beam.</p> <p> </p>

Mechanical properties of CO2 laser beam butt-welded plates of Hastelloy c-276

In the current investigation, thermo-mechanical analysis is carried out for Hastelloy C-276 using laser beam welded butt joints. The Gaussian heat source model is used for transient thermal analysis, and the maximum temperature at the weld area resulted in residual stresses within safe limits. To validate, the experimentation was carried out with CO2 Laser beam welding using an L4 orthogonal array. Sample 2 had the least-residual stresses in the weldment, and the mechanical and metallurgical properties studies were carried out. The residual stress distribution was measured using X-ray diffraction and was acceptable within the yield limits of the material. Finite Element Analysis (FEA) and experimental residual stresses were compared; the FOS was 2.088, and the remaining samples were more than 2.0 compared to the base material tensile strength. Tensile tests confirmed that the strength of the weld zone is higher than that of the parent metals.

Study on the ablative characteristics of steel target irradiated by nanosecond pulsed pseudo spark electron beams: Experiment and molecular dynamics simulation

A combination of simulation and experimentation is employed to explore the influence of the non-uniformity of energy distribution in nanosecond PSEB on the target ablation. Firstly, A spatiotemporally distributed heat source model is built using Monte Carlo computational method and an ablation phase transition model is established using molecular dynamics method. The results reveal the time evolution of multiple cavities in the sub-surface region, as well as the temperature and stress field distributions with electron beam irradiation. Phase explosion formation and lattice structure changes in the steel target during the ablation process is found for the first time. The PSEB modified AISI1045 steel samples is experimentally conducted. The characterization results show the changes in the crystal structure within AISI1045 steel, which is attributed to the formation of an amorphous layer resulting from grain refinement and structural defects, as well as the combined effects of thermal elastic stress waves, shock thermal stress waves and temperature gradient distribution. The experimentally obtained crystal phase changes are consistent with the simulation results, confirming the accuracy and validity of the modelling. The findings of this study provide a molecular-scale explanation for the formation of unique morphology and micro-structures during the PSEB ablated metal target.

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.

Research and process optimization of crankshaft grinding parameters based on Gaussian heat source model

Research and process optimization of crankshaft grinding parameters based on Gaussian heat source model

Numerical simulations and mathematical models in laser welding: a review based on physics and heat source models

The dominant phenomenon in laser welding processes is heat transfer by conduction, making it crucial to gain insights into energy distribution within the heat-affected region, including the melt pool. Thermal analysis enables the description of thermo-mechanical, metallurgical aspects, and also addresses studies related to fluid flow and energy transfer. As research in welding processes has advanced, these models have evolved. This is why it is now efficient to use computational modeling techniques as it allows us to analyze the behavior of laser welding during the process. This underlines the importance of this work which has carried out an exhaustive theoretical literature review with the objective of classifying and describing the numerical simulations of laser welding based on the physics involved. In that sense, the mathematical models and strategies used in laser welding are explored in a general way. Therefore, two types of laser welding by conduction and deep penetration are defined from this point and they are categorized according to the phenomena involved in Model Heat Conduction and Model Integral Multiphysics. This comprehensive review article serves as a valuable resource for higher education students by providing a structured and detailed exploration of laser welding and its mathematical modeling. By classifying and describing numerical simulations based on the physics involved, it offers a framework for students to understand the complexities of this field. Additionally, this innovative approach to organizing and presenting research contributes to educational innovation by facilitating a more efficient and effective learning experience, helping students acquire the knowledge and research skills necessary for advancements in the laser welding domain.

Temperature field simulation and microstructure study of WAAM fabricated Mg-Gd-Y-Zn-Zr alloy

A new combined heat source model was established to more accurately simulate the shape and temperature distribution of the molten pool in additive manufacturing. The model was verified by comparing experimental and simulated results. Experimental and simulation studies have ascertained that the cooling rate of the liquid phase directly impacts the microstructure, thereby significantly affecting the performance of the fabricated parts. When the inter-layer cooling time is controlled at 400 seconds to maintain a thermal accumulation temperature below 246°C, the liquid phase cooling rate is between 2295 °C/s and 1395 °C/s. Under these manufacturing conditions, a profusion of networked secondary phases precipitate along the grain boundaries, primarily composed of rod-like LPSO structures and Mg5(Gd,Y,Zn). Employing this process can notably enhance the performance across different regions of the formed parts, with the hardness reaching up to 110.4 HV, yield strength up to 223 MPa, and compressive strength up to 498 MPa.