Thermo-mechanical Finite Element Model Research Articles

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.

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.

Thermally induced mechanical interactions of energy pile groups subjected to cyclic nonsymmetrical thermal loading

Prior to this study, the long-term thermally-induced mechanical interactions of cyclic nonsymmetrical thermally loaded energy pile groups in soft clay have not been systematically elucidated, particularly with a limited understanding of the interactions among operating and non-operating energy piles, soil, and caps. Observing such a challenge, this paper presents a three-dimensional (3D) thermomechanical finite-element model (FEM), which considers the thermal-dependent behavior at the pile-soil interface and is validated using typical centrifuge tests reported in the literature. Special attention is given to the influence of soil-pile thermal expansion coefficient ratio, pile-soil stiffness ratio, and slab-soil stiffness ratio on the abovementioned interaction. The results indicate that a larger soil-pile thermal expansion coefficient ratio intensifies the interaction between energy piles and the surrounding soil, causing cyclic variations in thermally mobilized friction. With increasing pile-soil stiffness ratios, the differential thermomechanical responses among different piles within a group are enhanced because the toe and shaft resistances mobilized by the cap through nonoperating energy piles are weakened in the interaction process among energy piles, nonoperating energy piles, and the cap. Moreover, the increase in the slab-soil stiffness ratio exacerbates this interaction, strengthening the integrity of the pile groups.

Multi-scale modelling of the microstructure evolution during friction stir welding of 2195 Al–Li alloy

Al–Li alloy has a wide range of application prospects in aerospace and rail transportation fields. Friction stir welding (FSW) is suitable for joining of Al–Li alloy. The microstructure evolution in FSW of Al–Li alloy determines the final joint properties. However, it is difficult to directly observe the microstructure evolution in FSW of Al–Li alloy only by experimental methods. Therefore, a Monte Carlo model in cooperation with a thermomechanical finite element model was proposed to study the microstructure evolution in FSW of 2195 Al–Li alloy. The validated thermomechanical finite element model was first used to calculate the temperature field, strain rate and strain evolution during the FSW process. Then, the achieved thermomechanical history was used in the Monte Carlo model to predict the transient microstructure evolution and the final morphology of the grain structure. It is found that the plastic materials on the advancing side experience a higher strain compared with that on the retreating side with the same distance from the joint line. The plastic material in the middle of the weld nugget zone (WNZ) experiences a relatively high temperature with more severe plastic deformation. Therefore, fully dynamic recrystallization takes place for the material at this region as it flows across the tool during FSW, which results in a fine recrystallization grain in the middle of WNZ. However, the material on the advancing side at 2 mm away from the joint line experiences a lower strain rate, which results in partial recrystallization with some relatively large grains of the base materials. The simulated average grain size and grain morphology were in good agreement with the measured results by EBSD method.

Compact modelling of a thermo-mechanical finite element model of a microelectronic package

Thermo-mechanical behaviour of microelectronic components, when subjected to thermal cycling, plays a vital role in reliability assessments. This motivates the use of accurate numerical simulation tools. However, numerical simulations are time-consuming and thus, model order reduction methodologies are required. Most literature so far, focuses on single-domain model reduction approaches, that is, the reduction of only thermal or structural domain models. This paper extends existing work to order reduction of coupled linearized thermo-mechanical finite element models. Three thermo-mechanical reduction approaches are studied within the framework of the Krylov-basis reduction technique. This enables the examination of the most efficient approach to reduce the one-way coupled problem. The reduced order model is verified through the comparison with the full order model. The results show that the reduced model significantly decreases the computational costs while providing highly accurate results for temperature and deformation. This paper also emphasizes the potential of model order reduction in enabling system-level simulation of microelectronic components.

Experimental study on thermo-mechanical behaviour of beam string structures

Beam string structures (BSS) have been widely employed in large-span spatial structures, while the experimental study on BSS in fire conditions is limited. This paper presents experimental investigation on thermo-mechanical behaviour of BSS with different load ratio. ISO834 standard fire and large space fire are adopted as fire conditions, respectively. The strain of BSS at high temperatures is measured by advanced strain gauges. The test results show that the prestressed string is the most vulnerable component of BSS in fire. The temperature distribution is non-uniform, and the temperature difference between the top flag and string can be up to 396.3 °C. The critical string temperature is in a range of approximate 350 °C–450 °C. Load ratio has little effect on the critical string temperature, and fire conditions with higher heating rate can increase the critical string temperature. Furthermore, the drop of residual prestress causes the rapid increase of mid-span vertical displacement and horizontal displacement. The direction of horizontal displacement of BSS without external load is outward, due to the thermal expansion. The strain distribution along the cross section indicates the additional bending moment induced by temperature. In addition, three behaviour modes of BSS at elevated temperatures are proposed according to the contribution of prestress. The behaviour modes illustrate the working mechanism of BSS as the temperature increases. Finally, a thermo-mechanical finite element model of BSS in fire conditions is established by assembly load method. The numerically predicted temperature distribution, displacement and residual prestress have a good agreement with the experimental results.

Finite element based 3-D modelling of residual stress in high vacuum actively brazed diamond/Ni-Cr filler/C45 steel joint

In active brazing of diamonds, high brazing temperature and difference in the thermo-mechanical properties of the diamond grain, filler alloy, and substrate lead to the development of unfavorable residual stresses in the bonding region. This residual stress can potentially cause initiation of cracks within the interfacial reaction layer formed between diamond and filler-alloy, weakening the joint. Since the diamond particles used in diamond grinding tools are micro-sized and complex in shape, it is experimentally difficult to measure residual stress at the grit-filler interface. In the present investigation, a coupled thermo-mechanical three-dimensional finite element model has been developed to predict, map, and analyse the formation of residual stresses in diamond-bond-substrate systems. The presented model uniquely differs from those in literature, which are mostly 2-D type and did not consider the presence of interfacial reaction layer between diamond and filler. A Ni-Cr-Fe-B active brazing alloy has been selected as the filler and C45 steel as the substrate in the current simulation. Chromium carbide has been considered to be the interfacial compound. The numerical simulation suggests that the maximum value of residual stresses, predominantly tensile in nature, gets shifted from the diamond to the intermetallic zone at the bond level when the interfacial reaction compound is introduced between the diamond and filler. It also establishes that orientations of diamond during its placement on substrate for brazing have significant influence on the magnitude of induced residual stress. Approximately 40 % reduction has been observed in case of hexagon-base brazed diamonds when compared to that (1620 MPa) developed on square-base brazed diamonds. Raman spectral analysis of brazed specimen was conducted to experimentally validate the numerical simulation results. Residual stress was estimated from the peak shift of D-band in the spectra. The numerically computed residual stresses were found to deviate within the range of 3–15 % of the experimentally determined values.

Smart-substrate: a novel structural design to avert residual stress accretion in directed energy deposition additive manufacturing

ABSTRACT Residual stresses, related distortions and cracks are detrimental in metallic Additive Manufacturing (AM). Previously developed stress-control strategies based on reducing thermal gradients hardly diminish the stress concentrations at the built basement and easily affect other physical phenomena involved in AM. To overcome this, a novel strategy, named as Smart-Substrate, consisting of optimising the inner structure and local stiffness of the substrate is proposed to avert stress accretion and related part deformations. To demonstrate its advantages, a coupled thermomechanical finite element model for AM, experimentally calibrated with in-situ temperature and displacement measurements, is employed to analyse the thermal and mechanical behaviour of three groups of different structures with increasing geometrical complexity (single-wall, rectangular and block parts) fabricated by Directed Energy Deposit (DED) on the standard and smart substrates, respectively. Through using Smart-Substrate, the generation of residual stresses, especially the stress concentrations at the bottom corner of DED-builds being highly sensitive to cracks, and the induced deflections, are fundamentally throttled, and contrariwise for the standard substrate. More importantly, the use of Smart-Substrate is almost without prejudice to the temperature field, metallurgy and resulting mechanical hardness. This provides a possibility for addressing different physical problems individually, enlarging the AM process window.

Coupled thermomechanical FE model of a railway disc brake for friction material wear calculations

The article presents a fully coupled 3D thermomechanical model of a railway vehicle disc brake for calculations of temperature, stress, contact pressure and wear distributions. Five specially designed composite organic friction materials associated with a cast-iron ventilated brake disc were analyzed. The performed computer simulations correspond to the operational parameters of braking carried out on a full scale dynamometer test stand at constant braking power and constant vehicle velocity. These conditions were obtained by correcting the clamping force in relation to changes in the coefficient of friction. In the finite element (FE) model of the disc brake, the pad wear depth distribution was determined on the basis of the Archard's law taking into account the specific wear rate, contact pressure and sliding velocity. To create the numerical model with the geometry deformation allowing for friction material loss due to wear, advanced techniques were adapted. The geometric model of the brake includes the complex shapes of the brake pad holder, brake pad and ventilated disc. The wear constants of the tested friction material were obtained by means of the FE simulation and the measurement of the pad weight loss before and after the test on a full scale dynamometer test stand. The distributions of temperature, stresses, contact pressure and accumulated wear depth, obtained from the finite element analysis, in combination with the measured changes in the clamping force and coefficient of friction during braking, enabled to establish relationships between the properties of materials, operational parameters of braking and geometrical features of the brake components.

Modeling the evolution of representative dislocation structures under high thermo-mechanical conditions during Additive Manufacturing of Alloys

Mesoscale simulations of discrete defects in metals provide an ideal framework to investigate the micro-scale mechanisms governing the plastic deformation under high thermal and mechanical loading conditions. To bridge size and time-scale while limiting computational effort, typically the concept of representative volume elements (RVEs) is employed. This approach considers the microstructure evolution in a volume that is representative of the overall material behavior. However, in settings with complex thermal and mechanical loading histories careful consideration of the impact of modeling constraints in terms of time scale and simulation domain on predicted results is required. We address the representation of heterogeneous dislocation structure formation in simulation volumes using the example of residual stress formation during cool-down of laser powder-bed fusion (LPBF) of AISI 316L stainless steel. This is achieved by a series of large-scale three-dimensional discrete dislocation dynamics (DDD) simulations assisted by thermo-mechanical finite element modeling of the LPBF process. Our results show that insufficient size of periodic simulation domains can result in dislocation patterns that reflect the boundaries of the primary cell. More pronounced dislocation interaction observed for larger domains highlight the significance of simulation domain constraints for predicting mechanical properties. We formulate criteria that characterize representative volume elements by capturing the conformity of the dislocation structure to the bulk material. This work provides a basis for future investigations of heterogeneous microstructure formation in mesoscale simulations of bulk material behavior.

Determination of cohesion and friction angle of a MgO-C refractory at room and elevated temperatures

The use of constitutive models in thermomechanical finite element modelling of refractory linings requires knowing the temperature-dependent material parameters. The mechanical testing of carbon-containing refractory materials at elevated temperatures necessitates the protection of samples from oxidation. Therefore, the test concept of the modified shear test (MST) was further developed and a setup was designed to protect the carbon-containing materials from oxidation. A carbon-containing magnesia refractory (MgO–C), which is usually applied in secondary metallurgy for steel ladle refractory linings, was selected as the material of interest. The setup allows the determination of cohesion and friction angle of MgO–C refractories under reducing conditions at temperatures up to 1500 °C. The procedure allows a material parameters determination from uniaxial loading. While coked and as-delivered samples showed different behaviours, a significantly higher cohesion was noted in the as-delivered material. The results showed that the cohesion is highly temperature-dependent, whereas the friction angle remains nearly unaffected.