Thermomechanical Response Research Articles

Modeling the thermo-mechanical response and phase changes in metallic additive manufacturing (MAM) processes using a dissipative phase-field model

Additive manufacturing (AM) has emerged as a highly promising manufacturing technique, offering unprecedented possibilities for creating complex geometries and functional structures. However, harnessing the full potential of AM requires the development of a robust computational framework capable of capturing the intricate multi-scale and multi-physics nature of the process. The constitutive and structural responses encountered in AM are particularly challenging to reproduce due to the complex behavior of the material involved. This research aims to address these challenges by presenting a comprehensive computational approach that incorporates a material model capable of accurately representing the behavior of different phases occurring during AM. To achieve this, the finite element method, using the Lagrangian framework in the implicit time scheme, is employed through the widely adopted ABAQUS software. Computational implementation is facilitated using the FORTRAN programming language. By employing weakly coupled thermal and mechanical constitutive equations, the framework enables the analysis of thermal stresses, strains, and displacements during realistic solidification processes, which inherently involve highly nonlinear constitutive relations. Through a series of numerical examples, the capabilities of the proposed model are demonstrated across various computational scales, particularly during the rapid melting and solidification phases. These simulations reveal the formation of residual stresses, which can lead to part distortion and have detrimental effects on the mechanical properties of the manufactured components. This research contributes to the advancement of additive manufacturing by providing a reliable computational tool that integrates the complex interplay between thermal and mechanical phenomena. The developed framework enhances our understanding of the AM process, offering valuable insights into the factors influencing the structural integrity and performance of additively manufactured parts.

Ispitivanje vršeno savijanjem napredne generacije kompozitnih struktura sa specifičnim svojstvima izloženih različitim opterećenjima

Introduction/purpose: This article presents the bending examination of advanced-generation composite structures with specific properties exposed to different loads. Methods: This paper thus proposes and introduces a new generalized five-variable shear strain theory for calculating the static response of functionally graded rectangular plates made of ceramic and metal. Notably, our theory eliminates the need for a shear correction factor and ensures zero-shear stress conditions on both the upper and lower surfaces. Numerical investigations are introduced to interpret the influences of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the bending behavior of FGPs. These analyzes are then compared to the results available in the literature. Results: Preliminary results include a comparative analysis with standard higher-order shear deformation theories (PSDPT, ESDPT, SSDPT), as well as Mindlin and Kirchhoff theories (FSDPT and CPT). Conclusion: Our theory contributes alongside established theories in the field, providing valuable insights into the static thermomechanical response of functionally graded rectangular plates. This encompasses the influence of volume fraction exponent values on non-dimensional displacements and stresses, the impact of aspect ratios on deflection, and the effects of the thermal field on deflection and stresses. Numerical examples of the bending examination of advanced-generation composite structures with specific properties exposed to different loads demonstrate the accuracy of the present theory.

A deep material network approach for predicting the thermomechanical response of composites

Recent progress combining micromechanics and machine learning holds promise for accurately and rapidly predicting the mechanical behavior of complex composite materials. This study extends the Deep Material Network (DMN), a binary-tree network trained on linear direct-numerical-simulation data, to predict the thermo-elasto-viscoplastic behavior of composites. This extension incorporates the thermal expansion properties homogenization into the network’s building blocks and expands the online formulation to consider thermal boundary conditions. By comparing various implementations of these building blocks, we demonstrate the network’s extrapolation to thermomechanical problems. We then show how this extended DMN can be applied to uncertainty quantification and inverse design problems.

Legendre wavelet collocation method for investigating thermo-mechanical responses on biological tissue during laser irradiation

Objective of the present work is to propose a numerical approach based on the Legendre wavelet to address a problem of biological tissue in the presence of superficial cancer and analyze the thermo-mechanical behavior during laser irradiation. The model of thermoelasticity with variable thermal conductivity is considered to investigate transient thermoelastic coupling response in the framework of Moore–Gibson–Thompson (MGT) bioheat transfer. The Kirchhoff mapping is first performed to linearize the nonlinear governing equations due to variable thermal properties, then finite difference discretization is applied for the time domain and subsequently space domain is approximated using Legendre wavelets. The collocation points are taken to transform the system of partial differential equations into a set of algebraic equations, from which the solution can be determined. A thorough parametric analysis is carried out to examine the effects of some material and geometrical parameters on the behavior of various fields such as the displacement, temperature, stress and the tumor-normal tissue interface. The outcomes of the present work are graphically shown and compared to the predictions of other existing models. The advantages of the current numerical procedure include its simplicity, effectiveness and low computational cost even with the few collocation points.

Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Coalescence of Al2O3/Al, MgO/Mg, and MgO/Al two nanoparticles during combustion

Metal and metal oxide aggregates are easily sintered by migration–diffusion in combustion, and the aggregates hold a complex morphological and structural variability that increases with temperature. The underlying thermomechanical response remains a challenging mystery for active nanoparticles. Here, a computational strategy based on ReaxFF molecular dynamics were performed to shed much light on the coalescence behavior of Al2O3/Al, MgO/Mg, and MgO/Al nanoparticles – a doublet of two spheres. The complex sintering phenomenon was further quantitatively described in terms of coordination number, charge distribution, density distribution, atomic displacement, radius ratio, shrinkage, and sintering time, etc. Results showed that the Al2O3/Al and MgO/Mg two nanoparticles undergo collision and coalescence, and the two were connected through the neck. MgO/Al aggregates are unstable at higher temperatures (T > 1200 K) and segregate at junctions, followed by re-coalescence in the simulation box. A stable neck structure can be formed when enough O atoms are dissolved in MgO nanoparticles or at a lower temperature. The diffusion of Mg, Al, and O atoms in aggregates is driven by concentration gradients and self-generated electromotive forces. The Al2O3 passivation layer forms and hinders the diffusion of O atoms, and the oxygen-rich regions are distributed in the neck (Al2O3/Al) or the contact surface on the side of the Al nanoparticles (MgO1.5/Al) during sintering. In MgO/Al aggregates, Mg atoms tend to wrap Al nanoparticles by surface diffusion.

Evaluation of the Thermomechanical Response of Geopolymeric Mortars Manufactured from Peruvian Mining Residues and its Comparison with Portland Cement Mortars

Geopolymeric mortars made from a mixture of waste from the Peruvian informal mining industry, sodium hydroxide activating solution, and fine sand were studied, comparing them physically and mechanically with conventional Portland cement mortars. Both conventional and geopolymeric mortars were prepared in parallel and then subjected to uniaxial compression tests at various temperatures (ambient, 200 °C and 500 °C). The mechanical results found revealed maximum average resistance values of 63, 84 and 79 MPa for conventional mortars, and 12, 32 and 36 MPa for geopolymeric mortars, when they were tested at room temperature, 200 °C and 500 °C, respectively. The best mechanical results in geopolymeric mortars were found when considering a binder: fine sand ratio of 1:2, molarity of the hardening solution of 12 M and a hardening solution: binder ratio of 0.6. It was possible to demonstrate a good agreement between the distribution of particle sizes observed microstructurally and those found by granulometry studies by laser light diffraction.

Thermomechanical modeling of dissimilar-material interfaces in composite structures

Due to the heterogeneities in material properties of strongly-bonded multi-material composite structures, there exist singularities of the stress fields at the material interface as well as the interface corners on the bounding surfaces. The finite-element method is probably the only plausible option to analyze the stress around such interfaces between dissimilar materials subjected to combined thermo-mechanical loading. In this article, we propose a novel mathematical model for the computational analysis of coupled thermo-elastic fields with perfectly bonded interfaces of dissimilar isotropic/orthotropic composite-material structures. A scalar function of the spatial variables, namely, the displacement function, is used to integrate the temperature field and the associated displacement-function field to obtain two nonhomogeneous partial-differential equations of equilibrium that govern two thermo-mechanical sub-problems defined in terms of the appropriate conditions of orthogonal temperature gradients. For a specific temperature field, obtained as a steady-state solution of the given thermal problem, the two thermo-mechanical sub-problems are solved independently to obtain the full-field solution of the thermo-elastic problem using the method of superposition. As an alternative to the conventional computational approach, we employed a single variable semi-analytical method of solution to determine the thermo-mechanical response of the multi-material composite structures. The continuity of the temperature and the heat flux in the thermal field problem and the continuity of the displacement and the traction vectors are utilized in the elastic field problem to determine the appropriate algebraic equations suitable for nodal application at the interfaces as well as interface corners on the boundaries of the respective problems. The quantitative comparison of the present displacement-function solutions to several mixed-boundary-value problems with those obtained by the conventional finite-element method verifies the high accuracy and effectiveness of the present method. This computational model has potential applications in identifying near-interface high-stress locations as well as possible critical regions of the physical boundary of composite structures subjected to mixed modes of thermal and mechanical loadings.

The effects of the foam and FGM distributions on thermomechanical buckling response of sandwich plates

The effects of the foam and FGM distributions on thermomechanical buckling response of sandwich plates

Dynamic thermo-mechanical responses of road-soft ground system under vehicle load and daily temperature variation

A complete road-soft ground model is established in this paper to study the dynamic responses caused by vehicle loads and/or daily temperature variation. A dynamic thermo-elastic model is applied to capturing the behavior of the rigid pavement, the base course, and the subgrade, while the soft ground is characterized using a dynamic thermo-poroelastic model. Solutions to the road-soft ground system are derived in the Laplace-Hankel transform domain. The time domain solutions are obtained using an integration approach. The temperature, thermal stress, pore water pressure, and displacement responses caused by the vehicle load and the daily temperature variation are presented. Results show that obvious temperature change mainly exists within 0.3 m of the road when subjected to the daily temperature variation, whereas the stress responses can still be found in deeper places because of the thermal swelling/shrinkage deformation within the upper road structures. Moreover, it is important to consider the coupling effects of the vehicle load and the daily temperature variation when calculating the dynamic responses inside the road-soft ground system.

Semi-analytical solution for dynamic thermo-mechanical responses of multi-layered thermo-poroelastic media

Dynamic thermo-mechanical responses of multi-layered thermo-poroelastic media induced by internal thermal and mechanical loads are investigated utilizing a semi-analytical approach. To investigate the transient behavior of the thermo-poroelastic media, the governing equations that consider both the fluid inertia and the soil skeleton inertia are established. The Laplace–Hankel transform is then applied to derive solutions for a single thermo-poroelastic layer and a half-space in the transformed domain. The multi-layered thermo-poroelastic model is assembled using the layer and half-space elements with the continuity assumptions. Solutions for the multi-layered thermo-poroelastic model are obtained in the transformed domain using boundary conditions, while the final solutions are calculated using a numerical procedure. Comparisons with published results validate the accuracy of the multi-layered model. Finally, effects of the coupled internal dynamic thermo-mechanical load, as well as the influences of material stratification and permeability, on the dynamic responses, including vertical displacement, temperature, vertical stress, and pore water pressure, are graphically presented.

Thermally and mechanically induced strain gradient fields in architected 2D materials and beam structures

The current contribution investigates the strain-gradient thermomechanical performance of architected materials and structures with uniform and graded inner designs. To that scope, an integral representation of strain-gradients in thermoelasticity, along with its Galerkin Boundary Element Method (GBEM) implementation are elaborated. The formulation accounts for both mechanical and thermal strain-gradients for the first time. Thereupon, the complete strain-gradient response upon uniaxial tensile (UT) and thermal loading (Th) is analyzed, performing direct comparisons among the strain-gradient fields induced in each case and providing summarizing statistics that associate higher-order thermal and mechanical effects. The numerical framework is used as a basis for the quantification of the impact of the underlying structural patterns on the equivalent internal length parameters of architected beam-type structures under thermomechanical loads in the context of simple gradient theory. It is found that thermal loads relate to comparable, yet lower, internal length parameters with respect to the ones obtained for uniaxially tensioned structures with uniform inner cellular designs. Both internal length and temperature variation contributions determine the strain-gradient thermomechanical response of beam-type architected structures, for which, exact, higher-order equivalent 1D displacement field solutions are first derived. Thermally-induced, higher-gradient displacements are found to be comparable with the ones obtained in UT-loaded structures with uniform inner cellular topologies. Moreover, inner material gradings are found to be able to considerably mitigate higher-order effects, a sensitivity that is not reproduced in the UT loading case. The results provided, along with the numerical and analytical methodologies elaborated, set the basis for the thermomechanical strain-gradient analysis of advanced architected media well-beyond the designs here investigated.

Ultrafast dynamics and ablation mechanism in femtosecond laser irradiated Au/Ti bilayer systems

Abstract The significance of ultrafast laser-induced energy and mass transfer at interfaces has been growing in the field of nanoscience and technology. Nevertheless, the complexity arising from non-linear and non-equilibrium optical-thermal-mechanical interactions results in intricate transitional behaviors. This complexity presents challenges when attempting to analyze these phenomena exclusively through modeling or experimentation. In this study, we conduct time-resolved reflective pump-probe imaging and molecular-dynamics coupled two-temperature model (MD-TTM) simulations to investigate the ultrafast dynamics and ablation mechanism of Au/Ti bilayer systems. The calculated energy absorption curves indicate that Au film reduces the energy deposition in the underlying Ti layer, resulting in reduced melting and evaporation rate of Ti. The phase transition process induces different mechanical responses. The potential energy patterns indicate that the expansion of vapor Ti extrudes the surface Au layer outward. In simulated stress distribution images, the Au layer can hamper the expansion of the vapor-phase Ti and brings dynamic compressive stress to the residual Ti layer. When the compressive stress transforms into tensile stress, the material is removed through mechanical damage. Therefore, both Au and Ti in the 20 nm Au-covered Ti are completely removed. Our approach elucidates the ablation mechanism within the Au/Ti bilayer system and offers fresh insights into managing thermo-mechanical responses within analogous systems.

Phenomenon-Based Model for Virtual Hot Strip Rolling

Every year digitalization is taking a bigger role in the steel industry. Models for predicting metallurgical phenomena, roll forces and microstructure have been commonly used in development of novel steel grades. These individual models may predict certain phenomena thoroughly, but input values are usually based on an assumption or on a “good guess”. To produce reliable boundary conditions for these models of individual phenomena, a virtual rolling model is developed. This model computes the whole process of the hot strip mill from roughing to accelerated water cooling on a run-out table. Strip location and temperature evolution is calculated continuously. Thermal and thermo-mechanical (rolling stands) boundary conditions are according to process layout. Input data for the model is automatically read from raw process data. Rolling parameters are calculated using a coupled ARCPRESS model, which is developed by authors, and calculates normal and frictional shear stress distributions in the roll gap to predict roll forces and displacements of the work roll surface. Recrystallization is considered when calculating the flow stress of the rolled strip. Phase fractions during water cooling are calculated as well. The virtual rolling model minimizes the need for parameter speculation as all parameters are calculated throughout the process. All the input values are read from actual process data and the metallurgical and mechanical state of the strip are computed throughout the whole process. As required by the state-of-art virtual rolling model, this model is based on generally accepted theories and experimentally studied metallurgical and physical phenomena along with the thermo-mechanical response of the actual rolling process.

Thermomechanical behavior and microstructural characteristics of 7055 aluminum alloy during friction stirring welding

This study employed a viscoplastic finite element model and re-meshing technique to investigate the thermomechanical response of 7055 aluminum alloy during friction stir welding (FSW). The stirring pin rotates at 800–1200 rpm and moves at 80–120 mm/min (i.e., welding speed) during the FSW process. The temperature field and viscoplastic flow were mathematically modeled based on a computational solid mechanics method and predicted by a three-dimensional coupled thermomechanical numerical simulation. To validate the simulation results, real-time temperature measurements at the welded joint were acquired via thermocouples embedded in the plate prior to the welding process. Additionally, optical microscopy and electron backscatter diffraction techniques were used to examine the metallographic structure and grain orientation of the welds, respectively. The results revealed a temperature difference of 5–10 ℃ between the advancing and retreating sides of the plate. The material on the advancing side was extruded upward in a circular motion and eventually reached the surface. Meanwhile, the material on the retreating side moved half a revolution around the pin and remained at the original depth of the plate. Complete dynamic recrystallization occurred in the weld nugget, resulting in the formation of fine equiaxed grains with random orientation. In the thermomechanically affected zone, the proximity to the weld nugget was associated with an increased proportion of high-angle grain boundaries and recrystallized structures. Simultaneously, the intensity of the deformation texture decreased, while the recrystallized texture showed an initial strengthening followed by a subsequent weakening. This comprehensive investigation contributes to a deeper understanding of the thermomechanical behavior and metallographic characterization of 7055 aluminum alloy during the FSW process.

Multiscale modeling of shape memory polymers foams nanocomposites

Shape memory polymer foams (SMPFs) are defined as lightweight cellular materials with the ability to recover their undeformed shape by applying an external stimulus like light, temperature, magnetic field, etc. Reinforcement of the material with nano-clay filler leads to a significant improvement in its physical properties. As a result, a wide range of applications is occupied by SMPFs, especially in industry and biomedical applications. Because of the heterogeneous nature of the SMPFs at different scale levels, modeling the material with one scale numerical model which able to capture all the effects of the lower scale material structure is really a complex task. Within this work, a full multiscale modeling approach is employed to investigate the thermomechanical response of the SMPFs. Furthermore, a combination of the 3D Representative Volume Element (RVE) and finite element method is used to explore the effects of the nano-filler weight fractions and the material's cellular structure at different length scales on the material dynamics. The multiscale modeling process gives great and promising results with good agreement with the experimental results. Moreover, the model shows relatively high sensitivity parameters that are initiated from the lower scale level.

The effect of the foam structure on the thermomechanical vibration response of smart sandwich nanoplates

This study aimed to model the thermomechanical vibration behavior of sandwich nanoplates consisting of a foam or solid core layer and smart surface layers. The sandwich plate’s mechanical behavior is analyzed using the nano-size effect, nonlocal strain gradient theory, and sinusoidal higher-order plate theory. Hamilton’s principle is employed to derive the equations of motion, which are subsequently solved using the Navier method. The impacts of temperature, foam structure, foam void ratio, smart materials, and the external electric and magnetic potentials applied to the surface layers on the thermomechanical behavior of a sandwich plate have been analyzed.

Deep learning-based modeling of the strain rate-dependent thermomechanical processing response for a novel HIPed P/M nickel-based superalloy

Understanding and modeling the thermomechanical processing (TMP) response of a novel HIPed powder metallurgy (P/M) superalloy is crucial for its industrial application. This research characterizes the TMP-responding behavior of a novel HIPed FGH4113A P/M superalloy at 1000–1150 ℃ with strain rates of 0.01–5 s−1. The results depict that the adiabatic temperature rise during high-strain-rate TMP will accelerate the stress softening. A two-stage deep learning (DL)-based constitutive model framework, coupled with the deformation-induced temperature rise and its influence on flow stress, was first proposed and compared with the traditional Arrhenius-type model. Two types of DL approaches including the backpropagation (BP) and long short-term memory (LSTM) neural networks were trained and compared separately. It is noted that the LSTM neural network, considering previous deformation history in its unique gate structure, depicts the best prediction accuracy and generalization ability under large strains than other models. Then the strain rate-dependent hot workability and flow softening mechanisms were modeled and discussed. High-strain-rate deformation (5 s−1) in certain temperatures (1110–1150 ℃) can avoid unstable defects and transform the generated deformation heat into the driving force for the activation of multiple dynamic recrystallization mechanisms. Therefore, the near fully recrystallized microstructure can be achieved similarly to that at 0.01 s−1, indicating the feasibility and superiority of the high-strain-rate TMP of P/M superalloys in a certain temperature range.

Effect of cavity radiation on aluminium hollow tubes and facade system subjected to fire

PurposeThis paper numerically investigates the effect of cavity radiation on the thermal response of hollow aluminium tubes and facade systems subjected to fire.Design/methodology/approachFinite element simulations were performed using ABAQUS 6.14. The accuracy of the numerical model was established through experimental and numerical results available in the literature. The proposed numerical model was utilised to study the effect of cavity radiation on the thermal response of aluminium hollow tubes and facade system. Different scenarios were considered to assess the applicability of the commonly used lumped capacitance heat transfer model.FindingsThe effects of cavity radiation were found to be significant for non-uniform fire exposure conditions. The maximum temperature of a hollow aluminium tube with 1-sided fire exposure was found to be 86% greater when cavity radiation was considered. Further, the time to attain critical temperature under non-uniform fire exposure, as calculated from the conventional lumped heat capacity heat transfer model, was non-conservative when compared to that predicted by the proposed simulation approach considering cavity radiation. A metal temperature of 550 °C was attained about 18 min earlier than what was calculated by the lumped heat capacitance model.Research limitations/implicationsThe present study will serve as a basis for the study of the effects of cavity radiation on the thermo-mechanical response of aluminium hollow tubes and facade systems. Such thermo-mechanical analyses will enable the study of the effects of cavity radiation on the failure mechanisms of facade systems.Practical implicationsCavity radiation was found to significantly affect the thermal response of hollow aluminium tubes and façade systems. In design processes, it is essential to consider the potential consequences of non-uniform heating situations, as they can have a significant impact on the temperature of structures. It was also shown that the use of lumped heat capacity heat transfer model in cases of non-uniform fire exposure is unsuitable for the thermal analysis of such systems.Originality/valueThis is the first detailed investigation of the effects of cavity radiation on the thermal response of aluminium tubes and façade systems for different fire exposure conditions.

Impact of titanium content on the thermo-mechanical and oxidation response of TiAlTa

This study aimed to analyze how the addition of titanium (Ti) to TiAlTa alloys affects their mechanical properties (Young’s modulus and hardness) and oxidation behavior. Alloys with three different Ti additions and equi-atomic Al and Ta were fabricated with nominal compositions of 33Ti-33Al-33Ta at%, 50Ti-25Al-25Ta at%, and 70Ti-15Al-15Ta at%. Phase identification of as-processed and compositionally homogenized alloys was conducted by coupling various electron microscopy, diffraction, and chemical analysis techniques. Composition and structures were modeled using CALPHAD-based phase predictions and compared with experimental results. Each of the alloys exhibited a unique set of microstructures with distinctly different ordered precipitates, dependent on cooling rate and chemical composition. Subsequently, nanoindentation tests were performed at temperatures of 25 °C, 250 °C, 500 °C, and 750 °C. Oxidation studies were conducted under static air at 750°C for up to 200 h. 33Ti-33Al-33Ta at% and 70Ti-15Al-15Ta at% alloys showed higher hardness and modulus than 50Ti-25Al-25Ta at% at room temperature. The 50Ti-25Al-25Ta at% alloy exhibited higher hardness and modulus values but lower oxidation resistance at 750°C when compared with the other specimens. The X-ray photoelectron spectroscopy experiments were conducted to further analyze the oxides present in the samples. Despite each sample displaying combinations of mixed oxide layers, TiO2 was the preferred oxide forming in the 50Ti-25Al-25Ta composition, while the other samples preferred to form Al2O3. The findings from this systematic exploration of phase evolution in the TiAlTa alloy space provide insights for optimized material chemistries, processing, and properties.