Thermo-mechanical Model Research Articles

A coupled thermomechanical peridynamic correspondence model for damage prediction in a freezing rock

This study presents a coupled thermomechanical (TM) bond-associated non-ordinary state-based peridynamic (BA-NOSB PD) (correspondence) model for simulating the thermal behavior and crack propagation in a saturated rock due to freeze. Considering the change in thermal property and the latent water–ice phase transition at low-temperature conditions, the PD form of the nonlinear thermal conduction equation is derived by using the PD differential operator (PDDO). The deformation response is obtained in the framework of BA-NOSB PD model considering the pore ice pressure and thermal expansion. The accuracy of the TM BA-NOSB PD model is verified by simulating the thermal behavior of tuff and sandstone and crack propagation in specimens with pre-existing cracks at low-temperature conditions. The PD predictions of temperature and frost heaving strain are in close agreement with the experimental and previous numerical results. The present model also accurately predicts crack propagation and coalescence in saturated rocks due to the freezing frost.

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.

Product, process, property, and performance (PPPP) relationship of 3D-Printed polymers and polymer composites: Numerical and experimental analysis

Understanding the external and internal factors during an additive manufacturing (AM) process is crucial, as they can significantly affect the final product's performance. Efforts have been made to unwind the product, process, property, and performance (PPPP) relationships. The conventional experimental approaches can lead to boundless runs, resulting in exorbitant costs for research and development. Hence, developing, adapting, and validating numerical models is essential to achieving the desired performance of 3D-printed products with lesser resource utilization. In this study, numerical and experimental techniques were used to perform the PPPP relationship assessment on material extrusion 3D-printed parts. Three infill designs (rectangular, triangular, and hexagonal), with layer heights (0.1 mm, 0.125 mm, and 0.2 mm), and three different materials (carbon fiber-reinforced polyamide-6 (PA6-CF), polyamide-6 (PA6), and acrylonitrile butadiene styrene (ABS)), were selected for the investigation. Taguchi's design of experiments (DOE) method was used to limit the number of numerical simulations and experimental runs. A thermomechanical numerical model was utilized to perform the material extrusion process simulations and mechanical performance prediction of the specimens. Subsequently, the samples were 3D-printed and tested mechanically to validate the numerical simulation results. The dimensional, distortion, and mechanical analysis performed on numerical simulation results agreed well with the experimental observations.

A thermo-mechanical model for hot cracking susceptibility in electron beam powder bed fusion of Ni-base superalloys

Hot cracking is a major challenge in the additive manufacturing of Ni-base superalloys. Most cracking indicators only consider the alloy composition and its effects on solidification behavior, strength, and ductility. We propose a new model that extends these classical cracking indicators by additionally incorporating the transient thermo-mechanical state during melting and solidification. The model is derived from insights into the cracking of thin layers and is mainly based on the elastic strain energy available to drive crack opening in a critical temperature interval. The underlying thermo-mechanical process simulations are implemented in a custom computational framework designed to efficiently model powder bed fusion. The model predictions are validated against experimentally measured crack densities in CMSX-4 processed by electron beam powder bed fusion. The proposed model allows for rationalizing the dependence of cracking susceptibility on the thermal history, which is controlled by scan speed and beam power. Finally, the model is applied to develop a crack mitigation strategy by reducing the built-up strain energy density. This is achieved by heating the melting area to a high temperature before melting, thereby reducing the temperature gradient.

Microstructural and neutron residual stress characterization of 316L laser-powder bed fusion simplified end-use part: A modelling benchmark

In this work, a double hollow cylinder with a joint region, representative of nozzles, pipe systems, valves, or pressure regulators, was chosen to measure and simulate its 3D residual stress (RS) distribution. The part was printed by Laser-Powder Bed Fusion (L-PBF) using commercial 316L steel powders, and a mapping of residual stress along the joint cross-section was measured at three geometrical sample directions. The distribution of RS in the printed part was not homogeneous, showing important gradients of about ±1200 με from the inner to the outer surface of the wall, as well as along the building direction, translated into an equivalent Von Mises stress gradient up to 400 MPa towards the inner surface. After heat treatment only axial strains are significantly affected and relieved 200 με in average, but not necessarily in a homogeneous manner. The comparison of the Von Mises equivalent stress against available simulation tools based on mechanical and thermomechanical models concluded that although these models succeeded in the benchmarking of total macroscopic distortion of components, they do not capture the asymmetric distribution of RS within the bulk in end-use complex geometries and/or joints and those should be implemented from the microstructural level.

Investigating the Impact of an Exsolved H2O‐CO2 Phase on Magma Chamber Growth and Longevity: A Thermomechanical Model

AbstractMagmatic volatiles drive pressure, temperature, and compositional changes in upper crustal magma chambers and alter the physical properties of stored magmas. Previous studies suggest that magmatic H2O content influences the growth and longevity of silicic chambers through regulating the size and frequency of eruptions and impacting the crystallinity‐temperature curve. However, there has been comparatively little exploration of how CO2 impacts the evolution of magma chambers despite the strong influence of CO2 on H2O solubility and the high concentrations of CO2 often present in mafic systems. In this study, we integrate the thermodynamic effects of dissolved and exsolved H2O and CO2 with the mechanics of open‐system magma chambers that interact thermally and mechanically with the crust. We applied this model to investigate how intrinsic variations in magmatic H2O‐CO2 content influence the growth and longevity of silicic and mafic magma chambers. Our findings indicate that even with a tenfold increase in CO2 content (up to 10,000 ppm), CO2 plays a minimal role in long‐term chamber growth and longevity. While CO2 content affects the magma compressibility, the resulting changes in eruption mass are balanced out by a commensurate change in eruption frequency so that the time‐averaged eruptive flux and long‐term chamber behavior remain similar. In contrast, H2O content strongly influences chamber growth and longevity. In silicic systems, high H2O contents hinder magma chamber growth by increasing the total eruptive flux and steepening the slope of the crystallinity‐temperature curve. In mafic systems, high H2O contents promote magma chamber growth by flattening the slope of the crystallinity‐temperature curve.

Rapid qualification of fused filament fabrication thermoplastics for cryogenic applications

Thermoplastic additive manufacturing (AM) is an attractive process for fabricating cryogenic componentry, due to the potential for rapid, on-site parts replacement. However, using a process intended for low-feature prototypes in such a demanding application creates survivability concerns. AM further introduces significant material variability that complicates materials qualification. Herein, a highly-repeatable test procedure is developed to qualify as-manufactured samples. Fused Filament Fabrication (FFF) is used to produce both test samples and custom immersion equipment for cryogenic tensile testing, and data quality is improved by modifying the ASTM Type IV geometry. Tensile strength is measured directly, while elastic modulus is calculated using temperature measurements and thermomechanical model fitting. Via this methodology, cryogenic performance is characterized for Polylactic Acid (PLA), Acrylonitrile Butadiene Styrene (ABS), and Glycol-Modified Polyethylene Terephthalate (PETG). PLA notably demonstrates acceptable strain to failure of 2.6 % and a favorable increase in strength from 47 to 120 MPa when cooled. Testing of carbon fiber filled PLA (CF-PLA) finds a remarkable 250 % increase in strength, from 37 to 130 MPa. Both materials withstand 10 high-stress thermal cycles with mild strength gain, causing a loss of room temperature ductility in neat PLA but not CF-PLA. Dynamic Mechanical Analysis (DMA) indicates a β-transition at −20 to −40 °C, which correlates with the observed changes. These findings show AM thermoplastics are promising for use in cryogenic laboratory environments, and could be modified for use in production applications.

Monolithic FE2 approach for the thermomechanical modeling of beam structures

AbstractIn the present contribution, the FE2 scheme for beam elements is extended to thermomechanically coupled problems. Beam elements have the advantage of drastically reducing the number of degrees of freedom compared to solid elements. However, the major challenge in modeling structures with beam elements lies in developing sophisticated non‐linear beam material models. This drawback resides in the fact that these elements require effective cross‐sectional properties involving material and geometric properties. The FE2 method, combined with a homogenization scheme based on the Hill‐Mandel condition, solves this problem. Within this scheme, homogenization of a representative volume element (RVE) on the mesoscopic scale provides effective cross‐sectional properties for the macroscopic scale. This homogenization procedure allows the consideration of non‐linear material formulations and cross‐sectional deformation within the analysis of a beam structure. The applicability of such a FE2 scheme for purely mechanical problems was already shown. In the present contribution, an extension to thermomechanically coupled problems is provided. In the proposed setting, the macroscopic scale is represented by beam elements with displacement, rotation, and temperature degrees of freedom. Solid elements with displacements and temperature degrees of freedom describe the behavior of the RVE. Hence, the proposed extension solves both scales in a monolithic approach. The assumption of a steady state problem at both scales allows a focus on a consistent scale transition and a discussion about the choice of suitable boundary conditions under the assumption of beam kinematics.

Nonlinear thermo-mechanical stress-driven modeling of nano arches augmented by higher order double-scaled kernel

Modeling the nonlocal behavior of small-scale structures is almost controversial. The recently developed approach, known as the stress-driven nonlocal model, in which the stress is the input of nonlocal integral, has been proved to pose as a remedy for the ill-posing behavior of strain-driven solutions. Though it is still in its early stages, stress-driven modeling of the nonlinear behavior of nano-scaled problems needs further thought. The coupled displacement field, in particular, makes nano-arches more challenging. The stress-driven formulation, enhanced by constitutive boundary conditions, reveals the thermo-mechanical buckling and post-buckling features of shallow nano-arches for the first time in this research. Furthermore, the single-scaled Helmholtz kernel is replaced with the more appropriate double-scaled kernel known as the bi-Helmholtz averaging nonlocal kernel. Higher-order continuity of the bi-Helmholtz kernel and, hence, constitutive boundary conditions and higher-order differential equations corresponding to the stress-driven scheme hold the key to efficiency. The arch is subjected to uniform temperature and radial pressure at the same time. To demonstrate the response of the nano-arch during buckling and post-buckling, the nonlinear equilibrium path, whether for mechanical or thermal loading, is given for the first time by prevailing on the challenges of the higher-order problems. Moreover, it would be beneficial if one could have the chance to recognize how and when the arch buckles. These valuable data are available in this study to give the limiting parameters at the moment of buckling, including limiting temperature, nonlocal parameter, and geometry.

Heterogeneous slab thermal dehydration driving warm subduction zone earthquakes

Changing thermal regime is one of the key mechanisms driving seismogenic behaviors at cold megathrusts, but it is difficult to interpret warm subduction zones such as Vanuatu for the temperatures are higher than that accommodates shallow brittle failures. We construct a 3-D thermomechanical model to clarify the thermal structure that controls tectonic seismicity in Vanuatu and predict a warm circumstance associated with abundant seismicity. Results reveal a heterogeneous slab ranging from 300 °C to over 900 °C from the Moho to subvolcanic depth. The subduction seismicity corresponds well to the plate interface where dynamic thermal dehydration is focused. The transformation from hydrated basalts to eclogites along the slab facilitates the occurrence of intense earthquakes and slips. Multistage mineralogical metamorphism affects the dynamic stability of megathrusts and favors the generation of active interplate large events. Therefore, slab thermal dehydration plays a greater role than slab temperature condition in influencing the subduction earthquake distribution in warm subduction systems.

Thermo-mechanical stability analysis of thermosyphons for pipeline soil and their optimal layout in permafrost regions

In permafrost regions, warm-oil buried pipelines release vast amounts of heat energy to surrounding soils and lead to rapid permafrost degradation. Settlement disasters induced by permafrost degradation significantly increase the probability of pipeline failure. The two-phase closed thermosyphon (TPCT) can cool soil, inhibiting permafrost degradation, but its deployment is still at the experimental stages along the China–Russia Crude Oil Pipeline (CRCOP). Therefore, it is important to determine an optimal layout for TPCTs that can achieve both effective cooling and cost control. In this study, a strategy for a nonlinear thermo-mechanical coupled model is proposed through Python–Abaqus secondary development. Based on it, the thermal and mechanical effects of TPCTs under different spacings, as well as their optimal layout, are numerically investigated. Closer TPCT spacing leads to a lower degradation rate of frozen soil and a lower peak TPCT heat flux. In addition, the peak pipeline von Mises stress in the transition zone increases for greater TPCT axial distances over time. When the TPCT axial distance is ≤8 m, the minimum pipeline principal strains remain below the critical compression strain over 50 years. Finally, a backpropagation neural network is constructed to predict the maximum pipeline compressive strain, and most prediction results fall within the 95% confidence interval.

Coupled Thermo-Mechanical Phase-Field Modeling to Simulate the Crack Evolution of Defective Ceramic Materials under Flame Thermal Shock

Coupled Thermo-Mechanical Phase-Field Modeling to Simulate the Crack Evolution of Defective Ceramic Materials under Flame Thermal Shock

Themomechanical Response of an Additively Manufactured Hybrid Alloy by Means of Powder Bed Fusion

The laser powder bed fusion (L-PBF) technique was utilized to manufacture a hybrid M789-N709 alloy by depositing M789 steel on wrought N709 steel. The tensile strength of the M789-N709 interface generated during the process has been established to be higher than that of the base materials. In the previous work of the current authors, extensive characterization of the M789-N709 interface (before and after heat treatment) was performed by means of electron backscatter diffraction, electron probe microanalysis, transmission electron microscopy with energy dispersive spectroscopy, and atom probe tomography analyses, to understand the mechanisms associated with its superior strength. In the present work, since the application of the hybrid alloy is targeted towards an elevated temperature environment, the individual high-temperature mechanical properties of M789 and N709 steels were acquired at various temperatures and strain rates using a Gleeble 563 thermomechanical system. Then, based on the flow curves, phenomenological-, and physical-based constitutive material models were established. These constitutive models can be utilized to accurately assess the high-temperature response of the hybrid alloy system using finite element analysis programs. This work demonstrates the application of thermomechanical processing and constitutive modeling in the field of metal additive manufacturing.

The Effect of Powder Temperature on Semi-Solid Powder Rolling AA2024 Based on Experiments and Numerical Simulation

Semi-solid powder rolling (SSPR) is widely used to produce alloy strips with fine grains and excellent performances in the automotive, aerospace and shipbuilding industries. During SSPR, powder temperature, as a very important parameter, greatly affects strips’ microstructures and mechanical properties, which have been investigated by many researchers, but its effect on the forming process and mechanism has rarely been studied. Therefore, based on online experimental detection and transient simulation, the microstructures, strip temperatures, relative densities and rolling forces at different conditions were, respectively, measured, calculated, compared and analyzed in order to study the deformation process and mechanism during SSPR. The result shows that with the increase in powder temperature, the strip temperature and relative density increase, while the rolling force decreases. The grains of the strips are refined after SSPR, and fine and dense microstructures are obtained at 600 °C, which is the optimum powder temperature. In the main deformation sections (II and III), when the contact normal force exists and reaches a maximum, the relative density and rolling force increase rapidly. At these sections, the strips rolled at 600 °C are mainly in a porous solid state, and powder crushing dominates the strip deformation. Therefore, SSPR at 600 °C and below can be considered porous or powder hot rolling, integrating powder crushing, solidification, deformation, densification and grain coarsening. Moreover, as the simulated values are basically consistent with experimental values, the thermomechanical coupling model based on the Fourier equation and its parameters are confirmed to be reasonable.

A thermomechanical model for argillaceous hard soils–weak rocks: application to THM simulation of deep excavations in claystone

The paper presents the enhancement of an existing constitutive model for argillaceous hard soils–weak rocks to incorporate non-isothermal conditions, to be used in coupled thermo-hydro-mechanical (THM) simulations of underground excavations subjected to temperature variations within the context of deep geological nuclear waste disposal. The proposed thermo-elastoplastic extension accounts for the effect of temperature on the yield and plastic potential functions and on the elastic stiffness. The resulting model is validated through the simulation of relevant non-isothermal laboratory tests reported in the literature. The model is then applied to the coupled THM simulation of an in situ heating test conducted at the Meuse/Haute-Marne underground research laboratory in Bure, France, excavated in the Callovo-Oxfordian claystone. Results show that the incorporation of thermal effects into the constitutive description of the host rock plays a significant role in the behaviour of the excavation when subjected to thermal loading, particularly in the evolution of the excavation fractured zone.

Numerical development of a thermo-mechanical prediction model at high temperature: case of rubber concretes

The constitutive models have an important role in understanding the thermo-mechanical behavior of concrete and predicting its durability under fire loading. In this paper, the authors have developed a new constitutive temperature-dependent model for rubber concrete based on several models, such as European and American models, to predict the mechanical behavior of rubber concrete subjected to fire loading. The thermal parameters such as thermal conductivity, heat capacity, and density are variables as a function of temperature. First, the temperature is computed using the finite difference method (FDM) using the implicit scheme. The mechanical parameters in the literature are computed and plotted, such as compressive strength, tensile strength, peak strain, and stress-strain relationship, and then the mean value is estimated to develop a new probabilistic model at elevated temperatures. To validate the developed model, we compare the behavior of rubber concrete with experimental measurements.

Thermodynamics of continental deformation

Continental deformation is known to be controlled by the interplay between tectonic and gravitational forces modulated by thermal relaxation-controlled lithospheric strength leading to oscillations around an equilibrium state, or to runaway extension. Using data-driven thermomechanical modelling of the Alpine Himalayan Collision Zone, we demonstrate how deviations from an equilibrium between mantle dynamics, plate-boundary forces, and the thermochemical configuration of the lithosphere control continental deformation. We quantify such balance between the internal energy of the plate and tectonic forces in terms of a critical crustal thickness, that match the global average of present-day continental crust. It follows that thicker intraplate domains than the critical crust (orogens) must undergo weakening due to their increased internal energy, and, in doing so, they dissipate the acquired energy within a diffused zone of deformation, unlike the localized deformation seen along plate boundaries. This evolution is controlled by a dissipative thermodynamic feedback loop between thermal and mechanical relaxation of the driving energy in the orogenic lithosphere. Exponentially growing energy states, leading to runaway extension are efficiently dampened by enhanced dissipation from radioactive heat sources. This ultimately drives orogens with their thickened radiogenic crust towards a final equilibrium state. Our results suggest a genetic link between the thermochemical state of the crust and the tectonic evolution of silicate Earth-like planets.

A coupled 3D thermo-mechanical peridynamic model for cracking analysis of homogeneous and heterogeneous materials

This paper proposes a variable timestep-strategy that can speed up the peridynamic modeling of thermomechanical cracking in both homogeneous and heterogeneous materials. A piecewise continuous time-step variation function is incorporated into the peridynamic framework that dynamically adjusts the time-step size, which ranges from a small value to a maximum value that remains below the critical stable time-step. The advantages of this variable timestep strategy are threefold: (1) The exceptional computational efficiency of this approach is mainly manifested in enabling peridynamic simulation that is 20 times faster compared to that employing a constant time step; (2) Taking advantage of the proposed method, both two- and three-dimensional peridynamic modeling of thermomechanical deformation and crack propagation has been demonstrated to be of great accuracy and robustness; (3) Facilitated with this variable timestep strategy, we achieve a remarkable advancement in peridynamics to capture intricate 3D crack patterns with complex topological structures in homogeneous specimens subjected to water quenching. Furthermore, the effects of the temperature difference, specimen geometrical configurations and the initial water entry velocity on the crack patterns of the specimens under water quenching are systematically explored.

Residual stresses and distortion in additively-manufactured SS316L-IN718 multi-material by laser-directed energy deposition: A validated numerical-statistical approach

In the present work, a numerical-statistical approach was used to study the distortion and residual stress in the additive manufacturing (AM) of SS316L-IN718 multi-material structure. Also, the structure was fabricated by laser-directed energy deposition (L-DED), and experimental measurements via thermocouple and micro X-ray diffraction were performed to validate the numerical results. In a good agreement with the experiments, the thermomechanical modeling of the process showed that through-thickness residual stresses (build direction) are distributed as a large accumulation of compressive residual stress in the mid-length of the structure-substrate interface and the maximum tensile residual stress at its two free ends. The critical development of longitudinal residual stresses (scanning direction) at the interface of the structure due to the sudden change in properties has caused the formation of the maximum tensile residual stress (up to 475 MPa) in this area and immediately changed its nature to compressive that can easily lead to localized cracking. Besides, Von Mises stress distribution indicated the concentration of stress at the interfaces of structure-substrate and base alloys, in such a way that it causes yielding in the SS316L section. On the contrary, less (plastic) strain occurred in the IN718 section due to higher yield strength. The results of the statistical modeling using multiple response analysis in the response surface method (RSM) also determined the desirable minimum level of longitudinal strain and stress of the structure (about 0.013 and 320 MPa, respectively) in the laser power range of 300–380 W and the powder per unit length of 5–25 g/m. In addition to minimization, it was demonstrated that sharp changes in longitudinal strain and stress at the interface of multi-material structure can be effectively reformed to mild changes by designing compositional gradients through thermodynamic calculations, owing to the approximation of the properties of adjacent layers.

The gravitational signature of the dynamics of oceanization in the Gulf of Aden

We perform a new gravity analysis in the Gulf of Aden with the aim of finding new constraints on the geodynamic evolution of the area. Our analysis is developed within the frame of the recent GO_CONS_GCF_2_TIM_R6 global gravity model solution (Brockmann et al., 2021) that reflects the Earth's static gravity field as observed by GOCE (Gravity field and steady-state Ocean Circulation Explorer). We analyzed the solution at different harmonic degrees, to account for different depths and dimensions of the sources. Terrain correction has been performed by means of a spherical tesseroidal methodology (Marotta and Barzaghi, 2017) and the obtained corrected Geodetic Residual Gravitation has been compared to the Model Residual Gravitation predicted by means of a 2D visco-plastic finite element thermo-mechanic model that simulates the dynamics of the Gulf of Aden, from rifting to oceanization. In order to perform the comparison between observed and predicted gravitational features, data have been extracted along five profiles crossing the Gulf of Aden at different sectors, from the south-east to the north west. Via the Model Residual Gravitation we reproduce its geodetic counterpart, obtaining a characteristic hat-shaped pattern, with a central plateau portraying the highest values, flanked by two regions where the residual gravitation diminishes, finally reaching the lowest values at the far continental domains. The maximum variations of the residual gravitation values, from ridge to continental domain, range between 280 and 420 mGal and the steepest decrease occurs over distances of 200 km for the thick crust model and of 100–150 km for the thin crust model. Finally, the comparison between Geodetic and Model Residual Gravitation allows to further constrain the dynamics of the Gulf of Aden oceanization occurring by a slow passive rift of a hot 150 km thick lithosphere characterized by an initial 40 km thick crust.