Thermo-mechanical Finite Element Method Research Articles

Coupled thermo-mechanical field-enriched finite element method for simulating the thermal failure process of quasi-brittle solids

Thermal loads and temperature changes significantly impact the deformation and fracture of quasi-brittle solids, and the computational simulation of such a process is challenging. In this paper, a coupled thermo-mechanical field-enriched finite element method (TM-FE-FEM) is proposed to simulate the thermal fracture process of quasi-brittle solids. The accuracy and correctness of the proposed coupled TM-FE-FEM are validated by four benchmark examples, and the ability to simulate thermal induced crack is validated by the plate containing single edge flaw under coupled thermo-mechanical loading. Finally, the thermal fracture process of the Lac du Bonnet (LdB) granite specimen is reproduced by the proposed method. It can be concluded from the numerical results that the proposed coupled TM-FE-FEM has the ability to simulate the processes of heat conduction, thermal deformation and thermal fracture in quasi-brittle solids.

Design and Optimization of Interface Morphology of Thermal Barrier Coatings Based on Regulation of Residual Stress: A Finite Element Simulation Study

Laser surface texture (LST) technology can be used to increase the adherence of thermal barrier coating (TBC). The primary research method is to conduct a large number of laser experiments to determine the optimal texture parameters. To minimize costs and enhance efficiency, in the current work, five types of circular pit textures were summarized; the plane strain model was established using the transient thermomechanical coupling finite element method; the residual stress field after spraying was used as the prestress field; the influence of different textures on the distribution of the residual stress field after a thermal cycling was analyzed; and the propagation law of cracks in the coating was predicted. The current work focuses on: (1) The two-dimensional cross-sectional morphology of texture; (2) the principal stress s22 perpendicular to the interface (resulting in mode I interface crack) and the shear stress s12 parallel to the interface (resulting in mode II interface crack); (3) texture variables—diameter, depth, and spacing. The results revealed that after thermal cycling, the texture in the ceramic top coat (TC) bore tensile stress of around 350 MPa. Both sides of the pit in the metallic bond coat (BC) bore tensile stress, while the bottom bore compressive stress. Among them, the positive tensile stress of the texture with a sinusoidal section was the greatest, whereas the shear stress was the least. The maximum stress in texture increased as the diameter and depth increased, while the minimum principal stress was obtained by adjusting the spacing among the adjacent textures. The stress level in the coating was reduced by selecting the appropriate texture morphology, and the crack propagation was more complex, that is, it took a longer time before reaching failure, which is expected to improve the life.

Coupled CFD-FEM Simulation of Steel Box Bridge Exposed to Fire

Increasing fire-induced bridge failures are demanding more precise behavior prediction for the bridges subjected to fires. However, current numerical methods are limited to temperature curves prescribed for building structures, which can misestimate the fire impact significantly. This paper developed a framework coupling the computational dynamics (CFD) method and finite element method (FEM) to predict the performance of fire-exposed bridges. The fire combustion was simulated in CFD software, Fire Dynamic Simulator, to calculate the thermal boundary required by the thermomechanical simulation. Then, the adiabatic surface temperatures and heat transfer coefficient were applied to the FEM model of the entire bridge girder. A sequential coupled thermomechanical FEM simulation was then carried out to evaluate the performance of the fire-exposed bridge, thermally and structurally. The methodology was then validated through a real fire experiment on a steel beam. The fire performance of a simply supported steel box bridge was simulated using the proposed coupled CFD-FEM methodology. Numerical results show that the presented method was able to replicate the inhomogeneous thermomechanical response of box bridges exposed to real fires. The girder failed due to the buckling of a central diaphragm after the ignition of the investigated tanker fire in no more than 10 min. The framework presented in this study is programmatic and friendly to researchers and can be applied for the estimation of bridges in different fire conditions.

The central deformation calculation and analysis of the heavy steel plate for the gradient temperature rolling

The traditional symmetrical rolling process may result in the insufficient central deformation of the heavy steel plate. The gradient temperature rolling (GTR) based on the ultra-fast cooling was adopted in order to improve the central deformation and keep the deformation along the thickness to be well distributed. The temperature and strain field of the gradient temperature rolling were obtained by the thermo-mechanical coupling finite element method combined with different surface heat transfer coefficient, plate thickness, work roll diameters and so on. The calculated results showed that the deformation was more likely to penetrate into the core compared with uniform temperature rolling (UTR). The central equivalent strain with GTR was increased by 44.3% maximum compared with UTR in the same case. The deformation along the thickness was well distributed compared to the UTR. The central deformation gradually increases with the increase of reduction rate, surface heat transfer coefficient, work roll diameters and speed ratio, while the central deformation almost unchanged with linear velocity. Furthermore, industrial application showed the deformation can penetrate into the core compared with the UTR and it can help to eliminate the band structure. In this study, the influencing law of equivalent strain along the thickness with different parameters was summarized. The fitting model to calculate the central equivalent strain after GTR was established according to the numerical results. It can provide reliable theory and technology support for the setting of various parameters for GTR.

Coupled CFD–FEM Simulation Methodology for Fire-Exposed Bridges

Evaluating the fire performance of bridges is necessary for damage mitigation as more fire-related accidents occurred on bridge structures. Current solutions adopting temperature curves can result in significant inaccuracy by neglecting the inhomogeneous characteristic of the fire-induced thermal environment. This paper proposed a numerical methodology for analyzing the coupled thermomechanical response of various bridges exposed to fires. The computational fluid dynamics (CFD) approach was implemented to reproduce the fire condition more realistically by modeling the combustion process and fire-driven flow. Then, an interface was adopted to extract the thermal boundary from the fire model. At last, the thermomechanical finite-element method (FEM) was coupled with the CFD model for determining the fire-induced response of the global bridge, thermally and structurally. By incorporating the multiscale FEM, this methodology can be extended to various large-scale bridges subjected to localized fires. The proposed approach was validated through a real fire experimental study on a steel column. To demonstrate the application of this strategy, a complex case study was carried out. A long-span cable-stayed bridge was investigated considering its girder segment was exposed to an under-deck tanker fire. Numerical results showed that the proposed method was able to capture the surrounding temperature field with strong thermal gradients and can predict not only the localized thermomechanical response of exposed segments but also the global structural performance evolution for large-scale complex bridges. The under-deck fire can introduce a significant impact on the entire cable-stayed bridge. Thereby, the multiscale FEM modeling strategy is required for the long-span bridges exposed to localized fires.

Thermomechanical Solid Breeder Multiple-Effects Experiment (TESOMEX) with Volumetric Heating and FEM Benchmark Analysis

Available experimental efforts on ceramic pebble beds and their associated constitutive equations are necessarily derived from single-effect tests where one parameter is varied and its effects are isolated and studied separately (e.g., using constant temperatures and externally applied loads). These experiments are incapable of reproducing the true multiple/synergistic effects of the physics that occur in real blankets, and the phenomena arising from the interactions of single effects are yet to be discovered. It is unclear whether the combined effect of plasticity and creep under reactor-relevant loading conditions will either enable the altered pebble bed packing configuration to reach an acceptable self-regulating temperature state or significantly deteriorate its heat transfer efficiency and subsequent tritium release. Therefore, studying the isolated thermal and mechanical effects is not sufficient to predict pebble bed behavior. It is the coupling and interdependence between the dynamic thermal and mechanical fields, as well as the synergistic effects between the various modes of deformation, that are key to fully understanding and predicting pebble bed behavior in a realistic fusion environment. However, previous mock-up experimental campaigns thus far have suffered from critical shortfalls that have severely hamstrung their scientific impact. The lack of experimental data that incorporate multiple-effects interactions in addition to the complexity of building a full-scale breeder unit mock-up triggered the need for this experimental effort. The body of work presented in this paper serves to (1) establish and validate the practicality of various volumetric heating simulation techniques for representative thermomechanical study, (2) recreate a prototypical breeder unit’s thermal-hydraulic behavior using a scaled-down reduced-activation ferritic steel box with optimized manifold design, (3) evaluate the thermomechanical properties of the pebble bed using a novel nonintrusive in situ tactile-pressure-sensing technology capable of generating real-time contact pressure maps that reveal spatial and temporal stress evolution, and (4) develop and benchmark a thermomechanical finite element method code that is able to predict the pebble bed’s thermomechanical evolution under the effects of creep and thermal cycling. The results of this study not only present novel experimental techniques and data that enhance our understanding of synergistic thermomechanical interactions and effects, but they also provide valuable data to serve as a basis for validation of the most recent pebble bed numerical models. Finally, it is worth mentioning that this work is part of a compendium around the Thermomechanical Solid Breeder Multiple Effects Experiment experimental campaign, known as TESOMEX. While this paper primarily focuses on novel heating and instrumentation techniques along with their opportunities and limitations, the other two papers shed more light on the prototypical thermomechanical evolution, pebble sintering, and possible modes of failure.

Mechanical Characteristics Generated by Solidification Crack During High Strength Steel Welding

A multiscale method was developed to elaborate weld solidification crack mechanical field. A sequential thermo-mechanical finite element method (FEM) of butt-joint was performed to provide both of geometry and loading condition of submoel. Then mechanical behaviours generated by impurity was achieved by submodelling with embedded solidification cracks in terms of elasto-plastic FEM. The solidification initial cracks were geometrical discontinuity in nature and modelled as mechanical property discontinuity. Results show that additive stress and back stress are built-up at impurity-weld matrix interface. The developed modelling method was validated by solidification crack tests, X-ray tests together with fractography. The underlying mechanisms in suppression solidification cracking by adjustment of alloy contents in flux cored wire aiming to diminish the impurity size and improve the ductility of weld metal were revealed by developed method. Results show that, given a 9 percent increase of the weld metal ductility, a 29.6 percent decrease of the additive stress is achieved; and the longitudinal oriented impurity readily propagates crossing section rather than along impurity longitudinal tip. The susceptibility to cracking is distance-dependent, heavily on fields near to impurity and little on far field.

Rapid prediction of cured shape types of composite laminates using a FEM-ANN method

The specified cured shapes can be utilized in polymer-matrix composites design, though they might have assembling difficulties or residual stresses. This study develops an integrated methodology to rapidly predict the cured shapes of carbon/epoxy composite laminates under different ply-stacking sequences based on the thermo mechanical finite element method (FEM) and artificial neural networks (ANNs). About 64 million networks were trained and validated to determine the best ANN models, which could approximate the complex nonlinear relationships between lay-up sequences and cured shape types. Six T800/epoxy specimens with different lay-up sequences were manufactured by an autoclave process to verify the FEM and the ANN. The correctness of the FEM model was verified by experiments. Experimental results also demonstrated that four ANN models (network structures: (250, 250, 100), (500, 250, 250, 100), (500, 250, 250, 100, 100), and (500, 100, 250, 250, 100, 100)) performed well with high generalization performance for the cured shape types’ prediction.

Solidification Crack Evolution in High-Strength Steel Welding Using the Extended Finite Element Method.

High-strength steel suffers from an increasing susceptibility to solidification cracking in welding due to increasing carbon equivalents. However, the cracking mechanism is not fully clear for a confidently completely crack-free welding process. To present a full, direct knowledge of fracture behavior in high-strength steel welding, a three-dimensional (3-D) modeling method is developed using the extended finite element method (XFEM). The XFEM model and fracture loads are linked with the full model and the output of the thermo-mechanical finite element method (TM-FEM), respectively. Solidification cracks in welds are predicted to initiate at the upper tip at the current cross-section, propagate upward to and then through the upper weld surface, thereby propagating the lower crack tip down to the bottom until the final failure. This behavior indicates that solidification cracking is preferred on the upper weld surface, which has higher weld stress introduced by thermal contraction and solidification shrinkage. The modeling results show good agreement with the solidification crack fractography and in situ observations. Further XFEM results show that the initial defects that exhibit higher susceptibility to solidification cracking are those that are vertical to the weld plate plane, open to the current cross-section and concentratedly distributed compared to tilted, closed and dispersedly distributed ones, respectively.

Micromechanical investigation of the role of percolation on ductility enhancement in metallic glass composites

In contrast to the catastrophic failure arising from the unconstrained shear band propagation in monolithic bulk metallic glasses (BMGs), the introduction of second phases in BMG composites (BMGCs) provides an extrinsic way of reducing the magnitude of strain localization, and thus may significantly improve the ductility. For this mechanism to be effective, a multitude of experiments have found that the volume fraction should reach a rather high threshold of about 30–40%, corresponding to the percolation limit with variations depending on the second phase morphology. However, we demonstrate here that an enhanced ductility can be realized in a BMGC made from crystalline Ni foam (completely percolated even with a volume fraction of about 11%), suggesting the resistance in the second phase to the impinging shear-force dipole from neighboring shear bands be the dominant factor for such a ductility improvement. The shortcomings of percolation approach, as well as the synergistic effects of microstructure and mismatches in mechanical properties, are investigated here in a thermo-mechanical finite element method based on the free volume model and plasticity-induced heating. The effectiveness of ductility improvement will be demonstrated by calculating the probability distributions of the shear-band effective strain.

FEM strategies for Large Scale Thermo-Mechanical Simulations with Material Non-linearity

Numerical techniques based on the Finite Element Method (FEM) are mature to provide computational tools that permit multi-physical problems to be dealt with. A relevant case concerns thermo-mechanical simulations of industrial components and processes. Nevertheless, a thermo-mechanical FEM model generally requires a transient non-linear analysis where the variation of material properties with temperature, as well as plasticity and creep, have to be considered. It follows that large scale models are often obtained and unfeasible computational time is thus required. The aim of this work is to put in evidence the possible scale reduction that can be achieved introducing model simplifications based on a practical engineering approach.

Analytical and Computational Methods for Solidification Problems of Liquid That Expands During Freezing

Both analytical and computational methods for solidification problems are introduced. First, the inward solidification process in a spherical vessel is studied. Expressions of the stress, displacement in the solid phase, and the liquid pressure are deduced based on the solidification interface position. A phase-change expansion orientation factor is introduced to characterize the nonisotropic expansion behavior at the freezing interface. Then, an efficient coupled thermomechanical finite-element method is proposed to evaluate the thermal stress, strain, displacement, and pressure in solidification problems with highly nonlinear constitutive relations. Two particular methods for treating the liquid phase with fixed-grid approaches are introduced. The thermal stress is computed at each integration point by integrating the elastoviscoplastic constitutive equations. Then, the boundary value problem described by the global finite-element equations is solved using the full Newton–Raphson method. This procedure is implemented into the finite-element package abaqus via a FORTRAN subroutine UMAT. Detailed implementation steps and the solution procedures are presented. The numerical model is validated first by the analytical solutions and then by a series of benchmark tests. Finally, an example of solidification in an open reservoir with a free liquid surface is introduced. Potential industrial applications of the numerical model are presented.

Using 3D-printed tungsten to optimize liquid metal divertor targets for flow and thermal stresses

Liquid metal divertors aim to provide a more robust alternative to conventional tungsten divertors. However, they still require a solid substrate to confine the liquid metal. This work proposes a novel design philosophy for liquid metal divertor targets, which allows for a two orders of magnitude reduction of thermal stresses compared to the state-of-the-art monoblock designs. The main principle is based on a 3D-printed tungsten structure, which has low connectedness in the direction perpendicular to the thermal gradient, and as a result also short length scales. This allows for thermal expansion. Voids in the structure are filled with liquid lithium which can conduct heat and reduce the surface temperature via vapor shielding, further suppressing thermal stresses. To demonstrate the effectiveness of this design strategy, an existing liquid metal concept is re-designed, fabricated, and tested on the linear plasma device Magnum-PSI. The thermo-mechanical finite element method analysis of the improved design matches the temperature response during the experiments, and indicates that thermal stresses are two orders of magnitude lower than in the conventional monoblock designs. The relaxation of the strength requirement allows for much larger failure margins and consequently for many new design possibilities.

Fatigue Life Prediction of Welded Joint by Microstructure-based Simulation

This paper proposes a numerical framework to predict fatigue life on welded joints by integrating several computational techniques. The framework consists of five steps: i) materials properties estimation; ii) welding simulation using thermo-mechanical finite element method; iii) macroscopic stress field analysis under cyclic loading; iv) mesoscopic stress field analysis using crystal plasticity finite element method (CPFEM); v) analysis of fatigue crack growth. The total number of cycles to failure is eventually obtained by the sum of initiation life calculated by CPFEM and propagation life calculated by X-FEM. A fatigue life of butt joint is evaluated by the proposed method. The results demonstrated the possibility of evaluating the fatigue life and its scattering by the proposed framework.

Development of Bead Modelling for Distortion Analysis Induced by Wire Arc Additive Manufacturing using FEM and Experiment

In this research, Wire Arc Additive Manufacturing is modelled and simulated to determine the most suitable bead modelling strategy. This analysis is aimed to predict distortion by means of thermomechanical Finite Element Method (FEM). The product model with wire as feedstock on plate as substrate and process simulation are designed in form of multi-layered beads and single string using MSC Marc/Mentat. This research begins with finding suitable WAAM parameters which takes into account the bead quality. This is done by using robotic welding system with 01.2mm filler wire (AWS A5.28 : ER80SNi1), shielding gas (80% Ar/ 20% CO2) and 6mm-thick low carbon steel as base plate. Further, modelling as well as simulation are to be conducted with regards to bead spreading of each layers. Two different geometrical modelling regarding the weld bead are modelled which are arc and rectangular shape. Equivalent material properties from database and previous researches are implemented into simulation to ensure a realistic resemblance. It is shown that bead modelling with rectangular shape exhibits faster computational time with less error percentage on distortion result compared to arc shape. Moreover, by using the rectangular shape, the element and meshing are much easier to be designed rather than arc shape bead.

Thermo-mechanical modelling of ball screw preload force variation in different working conditions

Ball screws are robust and economical linear positioning systems widely employed in high-speed and high-precision machines. Due to precision and stability requirements, the preload force is considered one of the main parameters defining the axial stiffness and the maximum axial load of the ball screw feed drives. In high-speed motions, thermal effects are also considerably relevant regarding positioning precision and dynamic stability of the machine. The temperature increase and the thermal gradient between the screw, the balls and the nuts result in geometrical variations and, consequently, variations in the preload force. This paper presents a numerical modelling strategy to predict the preload variation due to temperature increase using a thermo-mechanical 3D finite element method (FEM)-based model for double nut-ball screw drives. Two different thermo-mechanical coupling strategies are compared, and the obtained results are validated with experimental measurements for different initial preload and linear speeds. In the mechanical analysis, the nut-screw ball contact interface, the offset-based preloading and the restrictions of the ball bearings are included in the model, while the thermal analysis considers heat generation and heat diffusion. The causes of the thermal preload variation are discussed considering the ball load distribution and the axial and radial thermal displacements of the contacting points.

A quantitative thermal and thermomechanical analysis for design optimization and robustness assessment of microassembled high power Yb:CaF2 thin-disk Laser

While considerable effort in the field of high power laser research has been dedicated to evolving thin-disk Lasers into the kilowatt range, thermal and residual stress management remain a critical issue and need to be addressed. In this paper, a quantitative thermal and thermomechanical analysis is presented for design optimization and robustness of high power diode pumped thin-disk ytterbium Lasers based on thermal and thermomechanical Finite Element Method (FEM) simulations. In particular, Yb:CaF2 Lasers are examined with respect to the design and selection of the bonding interface material. Results propose the use of a metallic Au80Sn20 hard solder of greater than 20 µm thickness as a superior solution to adhesive bonding for the prevention of Laser crystal failure under high optical pumping power while maintaining sufficient resistance to mechanical strain. Thermal IR characterizations under “safe” CW pumping power validate our predicted FEM Multiphysics models. Finally, an essentially void-free Au80Sn20 soldering process has been demonstrated for the mounting of Yb:CaF2 crystals onto a CuW heat sink.

Three-dimensional finite element analysis of residual stresses in circumferential welds of 2205/X65 bimetallic pipe

Corrosion has a great negative influence on the pipe service life, and high welding residual stress will accelerate corrosion and reduce the strength of the pipe. Traditional carbon pipe is highly susceptible to corrosion, especially in the oil transport industry, and the stainless steel pipe is expensive. So bimetallic steel is a good choice for high-pressure and corrosion-resistant pipe. Multi-pass butt-welded 2205/X65 bimetallic pipe in this article is simulated numerically in non-linear thermo-mechanical finite element method (FEM), a three-dimensional (3D) finite element model is developed, the temperature history and the residual stress distribution are plotted, and the results are compared with the available measured data to evaluate the accuracy of the finite element model. In addition, the stresses changing with weld pass and the effect of the welding speed on stress distribution are also studied. The results show that the tensile stresses after cooling are larger than the tensile stresses after pass four on the inside surface, and the compressive stresses after cooling are larger than the compressive stresses after pass four on the outside surface, and the position of the maximum stress is farther away from the weld center when the welding speed decreases.

Development of integrated framework for fatigue life prediction in welded structures

A new fatigue prediction method for wide range of welded structures has been developed by integrating several advanced computational techniques such as thermo-mechanical finite element method, crystal plasticity model and extended finite element method. The method consists of the following procedures: (i) computation of materials properties; (ii) analysis of temperature field, microstructure and residual stress generated during a welding process; (iii) stress distribution analysis under cyclic loading; (iv) fatigue crack initiation analysis by the Tanaka-Mura model; (v) fatigue crack propagation analysis. Using the proposed methodology, the fatigue life of butt joint was evaluated and compared with the experimental data.

Hot Deformation Behavior of High Strength Low Alloy Steel by Thermo Mechanical Simulator and Finite Element Method

The hot deformation behavior of HSLA steel was investigated by using a MMS-200 thermal mechanical machine at different conditions and with deformation temperature of 800-1100 °C and strain rate of 0.1-10 S-1. FEM was analyzed the deformation characteristics of hot compression through Deform-3D software. It was discovered that the flow stress increases with increasing strain rate and decreasing temperature. The activation energy and stress exponent during hot deformation were calculated using hyperbolic sine constitutive equations. The result from the experiment represents the activation energy and stress exponent during hot compression of 222.256 kJ/mol. and 10.84. The prediction of distribution stress values from the constitutive equation in Deform-3D can be matched with the experimental results.