Thermo-mechanical Finite Element Model Research Articles

Thermomechanical finite element modeling of extruded polyvinylchloride tubes for temperature and warpage prediction

AbstractIn this study, a thermomechanical finite element process simulation model for rigid polyvinylchloride extruded products with a tubular cross‐section is developed and validated. The goal is to predict the warpage of the extruded tubes with varying levels of (a)symmetry (wall thickness ratios ranging from 1/1 to 1/5), utilizing the temperature distribution developed during the cooling phase of the process. The material undergoes significant temperature variation (from melt to room temperature), potentially leading to significant changes in material properties during the process. Therefore, temperature‐dependent material properties are determined experimentally and implemented into commercial simulation software. Boundary conditions in the model are changed depending on the different process settings and the location of the product in the process. The model is validated by comparing measured temperatures and warpages with simulated ones for six levels of wall thickness ratios and varying process settings. The model is shown to predict warpages within 86% of accuracy and temperatures within 90% of accuracy.Highlights Measurement and implementation of temperature‐dependent material properties. Development of extrusion process model with varying boundary conditions. Thermal and mechanical (warp) prediction for six levels of wall thickness ratios.

Porosity control and properties improvement of Al-Cu alloys via solidification condition optimisation in wire and arc additive manufacturing

ABSTRACT This study presents an innovative liquid-nitrogen cooling (LNC) strategy to address hydrogen porosity in Wire and Arc Additive Manufactured (WAAM) Al-Cu alloys, which negatively affects part properties. A coupled thermo-mechanical finite element model, calibrated with in-situ measurements, is used to analyse the thermal, mechanical and metallurgical evolutions of two single-walls fabricated with conventional gas cooling (CGC) and LNC, respectively. A hydrogen solute coupling model evaluates hydrogen supersaturation during solidification. The LNC strategy significantly reduces porosity by optimising the solidification process: (i) Grain size is reduced, lowering hydrogen concentration at the solid/liquid interface; (ii) The length and duration of the hydrogen supersaturation region are shortened due to higher temperature gradients; (iii) Enhanced Marangoni convection and reduced molten pool depth facilitate hydrogen bubble escape. Compared to the CGC part, the LNC part shows a 63.8% reduction in pore density and a 59.4% reduction in overall porosity, achieving a final porosity of 0.39%. This improves mechanical properties, with the LNC component displaying a yield strength of 100.3 MPa, ultimate tensile strength of 250.1 MPa and elongation to failure of 19.4%. Despite a slight increase in residual stresses, the LNC strategy prevents cracking in Al-Cu alloys with high cracking susceptibility.

Influence of Scanning Strategy on Residual Stresses in Laser-Based Powder Bed Fusion Manufactured Alloy 718: Modeling and Experiments.

In additive manufacturing, the presence of residual stresses in produced parts is a well-recognized phenomenon. These residual stresses not only elevate the risk of crack formation but also impose limitations on in-service performance. Moreover, it can distort printed parts if released, or in the worst case even cause a build to fail due to collision with the powder scraper. This study introduces a thermo-mechanical finite element model designed to predict the impact of various scanning strategies in order to mitigate the aforementioned unwanted outcomes. The investigation focuses on the deformation and residual stresses of two geometries manufactured by laser-based powder bed fusion (PBF-LB). To account for relaxation effects during the process, a mechanism-based material model has been implemented and used. Additionally, a purely mechanical model, based on the inherent strain method, has been calibrated to account for different scanning strategies. To assess the predicted residual stresses, high-energy synchrotron measurements have been used to obtain values for comparison. The predictions of the models are evaluated, and their accuracy is discussed in terms of the physical aspects of the PBF-LB process. Both the thermo-mechanical models and the inherent strain method capture the trend of experimentally measured residual stress fields. While deformations are also adequately captured, there is an overall underprediction of their magnitude. This work contributes to advancing our understanding of the thermo-mechanical behavior in PBF-LB and provides valuable insights for optimizing scanning strategies in additive manufacturing processes.

Comparative analysis of wheel‒rail frictional temperature rise using moving heat source and thermo-mechanical coupling methods at various wheel‒rail creepages

A finite element (FE) model of wheel‒rail frictional heating with moving heat source is proposed in this paper for estimating the wheel‒rail contact temperature distributions under repeated long-term operation. To calculate the temperature rise in wheel‒rail friction, this study compares the computational accuracy and efficiency of the temperature field generated by the moving heat source method and the thermo-mechanical coupling method. A three-dimensional transient wheel‒rail rolling contact thermo-mechanical coupling finite element model is established using ANSYS/LSDYNA software. The moving heat source method is conducted through ANSYS transient thermal analysis with a time step of 2.57 × 10−5 s, meeting the thermal analysis requirements. Taking into account the influence of complex operating conditions and the third medium between the wheel and rail, this study compares and analyzes the two methods under different wheel–rail creepage conditions. The following conclusions were drawn: as creepages increase, the wheel tread surface temperature increases approximately linearly, with the temperature calculated by the moving heat source method being larger. The temperature difference between the two methods gradually increases, and the maximum temperature value difference is 4.9%, which is less than 5%. The moving heat source approach can save approximately 20 times the computational time. Considering both calculation time and efficiency, the moving heat source method can be employed as an alternative to the three-dimensional transient wheel‒rail rolling contact thermo-mechanical coupling finite element method. This study provides theoretical support and a finite element model reference for the calculation of wheel‒rail friction temperature rise.

Effect of considering thermoplasticity of gun steel on thermomechanical coupling response of barrel

Abstract To explore the effect of considering thermoplasticity of gun steel on the thermomechanical coupling of the barrel during artillery firing, the thermoplastic coupling behavior of the barrel under transient thermal and mechanical loads is investigated. A thermomechanical coupling finite element model of the barrel was established. The transient temperature field and stress field of the barrel during the gun firing process were analyzed. By comparing the results of the thermoelastic model with that of thermoplasticity model, the effect of considering thermoplastic of gun steel on thermomechanical coupling response of barrel was investigated. The results show that the peak of Mises stress evolution considering thermoplasticity of material in the bore of the barrel is significantly reduced during the gun firing process, and the hoop stress evolution appears double-peak phenomenon. In addition, at the peak moment of bore pressure, the peak values that the hoop and Mises stress distributions along the radial direction at the midpoint of the land are reduced by 14.5 % and 20.9 %, respectively. This paper can provide a reference for the design of a large-caliber barrel.

A multi-scale modeling framework for solidification cracking during welding

A multi-scale multi-physics modeling framework has been developed to predict solidification cracking susceptibility (SCS) during welding. The framework integrates a thermo-mechanical finite element model to simulate temperature and strain rate profiles during welding, a cellular automata model to simulate the solidified microstructure in the weld pool, and a granular model to calculate the pressure drop in the mushy zone. Verification was achieved by comparing the model’s predictions with welding experiments on two steels, demonstrating its capability to accurately capture the effects of process parameters, grain refinement, and alloy composition on SCS. Results indicate that increasing welding velocity, while maintaining a constant power-to-velocity ratio, extends the size of the mushy zone and increases the maximum pressure drop in the mushy zone, leading to higher SCS. Grain refinement decreases separation velocities and the permeability of liquid channels, which increases SCS, but it also raises the coalescence temperature, resulting in an overall reduction in SCS. Alloy composition impacts SCS through thermal diffusivity and segregation. Lower thermal diffusivity or stronger segregation tends to elongate the mushy zone, resulting in an increase in SCS. This framework provides a robust tool for understanding the mechanisms of solidification cracking, optimizing welding parameters to prevent its occurrence, and comparing SCS of different compositions during alloy design.

КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ТЕМПЕРАТУРНЫХ ПОЛЕЙ В СВАРНОМ ШВЕ ПРИ ИЗМЕНЕНИИ ТЕХНОЛОГИЧЕСКИХ ПАРАМЕТРОВ СВАРКИ ТРЕНИЕМ С ПЕРЕМЕШИВАНИЕМ АЛЮМИНИЯ И МЕДИ

This paper discusses numerical modeling of temperature fields in friction stir welding (FSW) of aluminum (AD1) and copper (M1). A three-dimensional thermomechanical finite element model based on the coupled Euler-Lagrange (CEL) approach is used. The paper models and experimentally confirms the influence of FSW parameters on the distribution and peak temperature values in weld zones. The maximum temperature values are observed on the copper side. This is due to the high thermophysical properties of copper compared to aluminum. Changing the rotation speed of the welding tool from 800 rpm to 1000 rpm leads to an increase in the peak temperature from 492 °C (800 rpm) to 692 °C on the side of the copper plate (1000 rpm). The maximum discrepancy between the calculated and experimental temperature curves does not exceed 9%, which is quite acceptable for assessing the temperature field.

Computational modeling of multi-track multi-layer laser directed energy deposition process

This study presents the development of a 3D fully coupled thermomechanical finite element model to evaluate the melt pool geometry, defects, and micro-hardness of multi-track multi-layer deposition in the powder feed laser-directed energy deposition (LDED) technique. Fabrication strategies can significantly affect the melt pool geometry and material behavior of the manufactured components. Understanding the effect of process parameters in a multi-track multi-layer LDED is important. Optimal process parameters are crucial for achieving high-quality deposition in terms of deposition geometry and integrity. The model can aid in mitigating issues such as inadequate inter-track or track-substrate fusion, porosity, cracks, and other defects. A multi-track multi-layer finite element model (FEM) can realistically predict melt pool evolution, mechanical properties, and defects in laser-LDED. This work focuses on the development of a fully coupled thermomechanical model for multi-track multi-layer deposition processes using ABAQUS®. The finite element framework employs Johnson-Cook’s flow stress model for constitutive behavior and the Koistein-Marburger equation for predicting hardness. Two tracks and two layers of SS316L powder are deposited on an SS304 substrate in finite element simulations and experiments. The model has been validated for the melt-pool depth in the substrate, deposition geometry, heat-affected zone, and hardness. It has been observed that there is a ∼10 % error in the prediction of melt pool geometry characterization and a ∼12 % error in hardness as compared to experimental results. The melt-pool width, depth, substrate dilution, and hardness have been characterized as a function of process parameters via simulations and experiments. The model is capable of predicting inter-track and interface defects. In addition, the effect of interlayer cooling on the melt-pool geometry and hardness has been studied.

Mechanism of initiation and propagation of surface cracks in gun bore under thermomechanical coupling impact

Surface cracks in gun bore may exacerbate rifling ablation and wear and in turn shorten barrel life. Thermomechanical coupling finite element (FE) models of bore are established and the dynamic responses of the bore under high-temperature and high-pressure are numerically simulated. The stress distribution characteristics on the inner surface are analyzed and the effects of autofrettage, number of firings and harden layer on the stress distribution are discussed. Based on the stress distribution characteristics, FE models with two initial cracks on the ledge of land surface are set up and the propagation, interaction and intersection of the cracks are numerically simulated, considering the effect of the distance between the two cracks. Based on simulation results, the initiation and propagation pattern and mechanism of the cracks on the inner surface are analyzed. An ablation test system was designed and produced, and used to experimentally verify the initiation and propagation mechanism of the cracks. The observed crack patterns on the inner surface of a real gun bore are also used to illustrate the mechanism obtained in this work. Understanding of the initiation and propagation mechanism of cracks in gun bore can be applied to improve and optimize the design of barrels.

Prediction of residual stresses in additively manufactured parts using lumped capacitance and classical lamination theory

Several industries are interested in Laser Powder Bed Fusion (L-PBF) Additively Manufactured (AM) metal parts because their designs can be made arbitrarily complex while retaining bulk-type material properties. However, the residual stresses (RS) and distortions caused by the heat gradients inherent to L-PBF processes are detrimental to the structural integrity of the parts and must be taken into consideration during the part design cycle. Predicting the state of stresses in as-built 3D printed parts is a difficult problem that is typically approached with the use of transient thermomechanical Finite Element Models (FEMs). However, the nonlinearities associated with AM processes are difficult to capture in these FEMs without increasing the computational cost of the simulation, limiting their ability to be incorporated into practical design cycles. This work presents a novel analytical framework that combines lumped capacitance nonlinear heat transfer with time dependent classical lamination theory to efficiently and accurately predict RS in as-built L-PBF parts without the need of FEMs. The simulation was compared to Neutron Diffraction (ND) residual strain measurements taken at Oak Ridge National Laboratories (ORNL) as well as Synchrotron X-ray Diffraction (XRD) strain data published by the National Institute of Standards and Technology (NIST). The simulation predictions and the experimental data showed excellent agreement for the in-plane strain directions, and general agreement for the out of plane strain component, highlighting an area where further development can be implemented.

Thermomechanical modelling of residual stresses and distortion in laser powder bed fusion: Assessment of the effect of build plate preheating on the behaviour of Inconel 718

The fabrication of complex metallic parts via laser powder bed fusion (L–PBF) is becoming more mainstream to overcome the limitations of traditional manufacturing methods. However, L–PBF induces undesirable residual stresses (RS) and possible geometric distortion of the component. This study aims to show the capabilities of build plate preheating in mitigating both defects. A thermomechanical finite element model is developed to investigate the outcomes of various preheating conditions when producing Inconel 718 samples consisting in a base and an overhanging beam restricted with support structures. Initially, the model is calibrated against the deflection result of an academic work employing a resemblant geometry. Our study is then performed. The as–built von Mises stress evolution along two paths as well as part distortion are assessed at 100, 300, and 500°C, then compared to the reference “no preheating” case results. A peak top surface RS of 803MPa was reached without preheating and reduced by 48.69% at 500°C. Along the vertical path, the mean stress value went from 897MPa at 20°C to 474MPa at 500°C. Distortion of the as–built part is essentially a non–uniform contraction of the beam along the x–direction due to progressive bending of the supports about y–axis. Once the beam is unrestricted from the substrate, it deforms as a cantilever structure. Increasing the preheating temperature decreases the maximum build direction deflection by 14.56% at 100°C, up to 76.94% at 500°C in comparison to the 4.12mm reached at 20°C. In conclusion, preheating the substrate is a very effective way to mitigate RS and distortion in L–PBF of Inconel 718. Even the relatively low 100°C showed a notable improvement in this regard.

Equal heat flux loading optimization approach for uniform wear of the wet brake

Due to their exceptional ability to endure heavy loads, cam-lobe radial-piston hydraulic motors are extensively utilized in heavy machinery. The wet brake is a key part capable of providing highly braking torque, which has numerous friction pairs and a compact structure. However, there exists a challenge in solving the issue of irrational pressure distribution which leads to non-uniform heat flux distribution and severe wear failure of the brake discs. For this, an innovative method to optimize the wet brake's loading structure has been developed to address the issue of non-uniform heat flux distribution. A thermomechanical coupling finite element (FE) model was established to establish a clear correlation between loading structure parameters and contact pressure distribution on the brake disc. An innovative equal heat flux criterion was introduced to guide the optimization process. Simulation results confirmed that the optimized loading structure achieved a brake disc contact pressure distribution aligned with the ideal heat flux density criteria. Experimental validation further demonstrated a notable reduction of up to 44.39 % in maximum wear depth (hmax) across different radii of the brake disc compared to the unoptimized structure. These findings underscore the efficacy of our approach in reducing wear rates and enhancing durability of the wet brakes.

Finite element simulation for Si3N4 heating and sintering

The fabrication of large silicon nitride ceramic components is intricate and demands expertise in gas pressure liquid phase sintering (GPS-LPS). The forefront technology of finite element (FEM) thermo-mechanical modeling plays a key role in sizing aerospace components that necessitate high precision and mechanical strength. A comprehensive sintering simulation should encompass not only densification and grain growth models but also consider the heating environment, accounting for gas convection, conduction, and surface-to-surface radiation. Moreover, silicon nitride sintering simulation addresses the intricate behavior, including the swelling phenomenon during the transitions from intermediate to final stage sintering. The challenge of significant slumping in hollow parts, resulting in costly rejection, is a primary concern for industrial companies when dealing with low-viscosity liquid phase sintering. Validation of the model is achieved through the computation of simple cylindrical cases, while a meticulous comparison between simulations and sintering experiments on complex hollow bodies and deflection bars facilitates precise adjustment of the shear viscosity theoretical parameter derived from the Skorohod-Olevsky continuum theory of sintering. The findings from these simple cases guide the simulation of a complex geometry representative of typical aerospace components, determining the ideal sintering configuration to mitigate slumping issues.

Coupled thermomechanical finite element analysis of ultrasonic hot embossing process

Ultrasonic Hot Embossing of polymers is one of the most attractive manufacturing methods of high-quality and complex microparts needed for biological and chemical processes. A little simulation work has been done to study the deformation mechanism and the required load in the Ultrasonic Hot Embossing of polymethyl methacrylate (PMMA). This paper developed a 2D coupled thermo-mechanical finite element model to simulate the forming behavior of the ultrasonic embossing process of PMMA, optimize the mold microfeature corner, and predict the embossing load as well. VDISP ABAQUS subroutine has been used to describe the downward motion of the mold assisted with ultrasonic vibration. The Arbitrary Eulerian-Lagrangian re-meshing technique has been implemented to refine the deformation zone during simulation to avoid divergence due to localized excessive deformation. Embossing load, temperature, stresses, strains, and energy dissipation have been recorded and analyzed. Simulation results revealed that the coupled thermo-mechanical FE Model efficiently captures the deformation behavior and Embossing load. It also proved that a Mold microfeature corner of 20 μm filet radius is recommended to adequately fill out the area around the mold and maintain uniform temperature and strain distributions.

A coupled data-physics computational framework for temperature, residual stress, and distortion modeling in autoclave process of composite materials

It is challenging to obtain the full-field temperature profile during autoclave processes to control the temperature uniformity and minimize the residual stress and distortion of cured composite structures. This paper proposes a coupled data-physics computational framework for full-field temperature reconstruction and the subsequent residual stress/distortion modeling by using limited monitoring temperature data. Firstly, a Long Short-Term Memory (LSTM) model is developed for full field temperature reconstruction. In this LSTM model, a cross-recombination method is proposed to maximize the value of monitored temperature data. The method effectively cuts through the bottleneck of neural network training with limited labeled data. The LSTM model’s prediction stability is enhanced based on the mean-teacher and ensemble learning strategy. To train and validate the proposed method, we perform experiments using an autoclave at the National Institute for Aviation Research (NIAR). The LSTM model’s accuracy is assessed by comparing its predicted results with the thermocouple (TC) data from measurements and high-fidelity simulation data from computational fluid dynamics (CFD). The study shows that the proposed LSTM model can effectively reconstruct the full-field temperature using limited monitoring data and significantly improve accuracy and efficiency compared with the CFD-based counterpart. Then, we create a coupled data-physics computational framework by embedding the data-driven LSTM model into a physics-based thermo-mechanical finite element model to predict residual stress and distortion. The simulation results show that the coupled data-physics framework provides an effective way for process-to-performance modeling and simulation of autoclave curing processes.

Numerical simulation of friction extrusion: process characteristics and material deformation due to friction

This study employs a finite element thermo-mechanical model, using a Lagrangian incremental setting to investigate friction extrusion (FE) under varying process conditions. The incorporation of rotation in FE generates substantial frictional heat, leading to significantly reduced process forces in comparison to conventional extrusion (CE). The model reveals the interplay between temperature, strain, and strain rate across different microstructural zones of the resulting wire. Specifically, the sticking friction condition in FE enhances initial shear deformation, aligning with a homogeneous spatial strain distribution and predicting complete grain refinement in the extruded wire, as per Zener-Hollomon calculations. On the other hand, under the sliding friction condition in FE, the shear deformation is reduced which results in an inhomogeneous microstructure in the extruded wire. The analysis of material flow in the workpiece reveals distinct transitions from the base material to the thermo-mechanically affected zones. The simulated process force, thermal history, and microstructure during sliding friction conditions align well with the findings from performed friction extrusion experiments.

A finite element thermomechanical analysis of the development of wheel polygonal wear

Polygonal wear is a type of damage commonly observed on the railway wheel tread. It induces wheel-rail impacts and consequent train/track components failure. This study presents a finite element (FE) thermomechanical wheel-rail contact model, which is able to cope with the three possible generation and development mechanisms of polygonal wear: initial defects, thermal effect, and structural dynamics. The polygonal wear-induced impact contact and further development of wear are simulated. The simulated elastic contact solutions are verified against the program CONTACT. Different material properties (elastic, elasto-plastic and elasto-plastic-thermo, i.e. with thermal softening) and initial polygonal profiles are then applied to the FE model to investigate the influence of wheel/rail material and wear amplitude on wheel-rail contact stress and wear development. The simulations indicate that the wheel-rail impact-induced temperature may reach up to 362 ℃ at the contact interface, and the high temperature at the contact area influences wheel-rail contact stress and wear depth.

3-D FE modelling of residual stress distribution in 3003 aluminium alloy overlapped joints by ARM laser with beam oscillations

Adjustable Ring Mode (ARM) laser technology combined with Beam Oscillation optics module was introduced to effectively enhance weld quality in joining aluminium alloys. This study developed a three-dimensional (3-D) thermo-mechanical finite element (FE) model to analyze the distribution of thermally induced residual stresses in laser-welded 3003 aluminium alloy. The accuracy of model was validated through comparisons with experimental weld cross-sections and further reinforced by X-ray diffraction residual stress measurements. The transient temperature field and stress distribution during the welding process were investigated using the verified model. Additionally, the hardness and microstructure of the welded samples were examined through micro-hardness tests and scanning electron microscopy. Results showed that welding with beam oscillation resulted in less penetration but higher hardness and finer columnar grain size in the fusion zone. Additionally, the influence of varying standoff distances between two sequential weld beads on residual stress distribution was investigated. Numerical findings revealed that higher residual stress concentrations were located at the weld seam and dominated by tensile longitudinal residual stress and compressive transverse residual stress. As the distance between weld beads increased, transverse and equivalent residual stresses decreased, while longitudinal residual stress away from the bead increased.

A new variant of the inherent strain method for the prediction of distortion in powder bed fusion additive manufacturing processes

A new variant of the inherent strain (IS) method is proposed to predict component distortion in powder bed fusion additive manufacturing (AM) that addresses some of the shortcomings of the previous work by accounting for both the compressive plastic strain formed adjacent to the melt pool and the thermal strain associated with the changing macroscale thermal field in the component during fabrication. A 3D thermomechanical finite element (FE) model using the new approach is presented and applied to predict the distortion of a component fabricated in an electron beam powder bed fusion (EB-PBF) machine. To improve computational efficiency, each computational layer is comprised of six powder layers. A time-averaged volumetric heat input based on beam voltage and current data obtained from the EB-PBF system was calculated and applied to each computational layer, consistent with the process timing. The inherent strains were applied per computational layer as an initial anisotropic contribution to the thermal strain at the time of activation of each computational layer, resulting in the sequential establishment of static equilibrium during component fabrication, which accounts for the variation in the local macroscale thermal field. The thermal field and distortion predicted by the thermomechanical model were verified using experimentally derived data. The model predicts in-plane compressive strains in the order of 10−3. Differences in the inherent strain were found at different locations in the component, consistent with differences in the macroscale thermal field. The proposed method is general and may also be applied to the laser powder bed fusion (L-PBF) process.

Numerical and experimental study of underwater friction stir welding of 1Cr11Ni2W2MoV heat-resistant stainless steel

Due to the benefits of solid-state joining, friction stir welding (FSW) has seen an increase in applications in the aircraft and automotive industries. However, short tool life and heat-affected zone (HAZ) softening are the two main issues with the FSW of advanced high-strength steel. In this study, the underwater friction stir welding (UFSW) of 1Cr11Ni2W2MoV steel was investigated and compared to the Normal friction stir welding (NFSW). Besides, a 3-D thermo-mechanical finite element model was developed to understand the effect of the different cooling mediums and tool rotation rates on the thermal cycles, plastic deformation, tool wear, and microstructure evolution. The simulation results revealed that the stir zone (SZ) of the UFSW exhibits lower peak temperatures and smaller plastic strain compared to the NFSW. The experimental results showed that a high tool rotation rate can be used during UFSW without causing overheating of the workpiece and tool materials resulting in high joint quality and low tool wear. The M23C6 and Fe3C carbide fractions in the HAZ at UFSW are lower than that at NFSW. The UFSW reduces the soft HAZ's width and increases its hardness. The ultimate tensile strength was increased by 17 %, and the HAZ width was decreased by 35 % at UFSW compared to that at NFSW.