Thermo-mechanical Model Research Articles

A coupled thermo-mechanical peridynamic model for fracture behavior of granite subjected to heating and water-cooling processes

Thermal damage and thermal fracture of rocks are two important indicators in geothermal mining projects. This paper investigates the effects of heating and water-cooling on granite specimens at various temperatures. The laboratory uniaxial compression experiments were also conducted. Then, a coupled thermo-mechanical ordinary state-based peridynamic (OSB-PD) model and corresponding numerical scheme were developed to simulate the damage of rocks after the heating and cooling processes, and the change of crack evolution process was predicted. The results demonstrate that elevated heating temperatures exacerbate the thermal damage to the specimens, resulting in a decrease in peak strength and an increase in ductility of granite. The escalating occurrence of thermal-induced cracks significantly affects the crack evolution process during the loading phase. The numerical results accurately reproduce the damage and fracture characteristics of the granite under different final heating temperatures (FHTs), which are consistent with the test results in terms of strength, crack evolution process, and failure mode.

Unified thermomechanical model of Ti-6Al-4V titanium alloy considering microstructure evolution and damage fracture under different stress state

Unified thermomechanical model of Ti-6Al-4V titanium alloy considering microstructure evolution and damage fracture under different stress state

Numerical modeling of induced subduction initiation: Insights from the oceanic plateau accretion

Subduction initiation is a crucial process for plate tectonics. Two scenarios of induced subduction initiation–subduction polarity reversal and subduction transference–are primarily attributed to the accretion of oceanic plateaus. However, the factors governing these two distinct types of subduction initiation remain elusive. Here, we employ 2D thermomechanical numerical models to investigate the dynamics of induced subduction initiation during oceanic plateau accretion. Specifically, we explore the impact of the thickness, density, and rheological strength of the oceanic plateau on subduction initiation. Our results reveal three geodynamic regimes: continuous subduction, subduction transference, and subduction polarity reversal. Thin oceanic plateaus tend to subduct along with slabs into the deep mantle, while thick oceanic plateaus often accrete to the margin, triggering subduction initiation. The rheological strength and density of an oceanic plateau play a significant role in determining whether subduction transference or polarity reversal occurs. Increasing the viscosity and decreasing the density of the oceanic plateau promotes strain concentration in front of the oceanic plateau, resulting in subduction polarity reversal. Our model results provide insights into the dynamics of subduction transference in the Caroline Sea and polarity reversal in Solomon in the western Pacific Ocean.

Predicting residual stresses in SLM additive manufacturing using a phase-field thermomechanical modeling framework

Additive manufacturing (AM) of metallic components has recently become a viable option for series production. In this, the powder of various metallic materials such as steel and aluminum can be processed layer-by-layer to produce dense parts with excellent properties. One of the major challenges in this process is the occurrence of residual stresses, which negatively affect the strength and functionality of the produced components. Understanding the mechanism of distribution of these stresses and the detrimental deformations is one of the main themes covered in this work. In the numerical treatment with the finite element method, a phase-field model (PFM) for phase-change materials is utilized together with a thermo-elastoplastic model to simulate the multi-layer AM process and to evaluate the occurring residual stresses. Using the PFM allows tracking the diffusive melting front and, thus, distinguishing between the melted (soft) and the unmelted (hard) states of the material. One of the novel contributions is the definition of a phase-field history variable, which can capture the irreversible process of metallic powder melting. Additionally, phase-field-dependent material properties are proposed. The coupled governing equations are solved in the open-source FE package FEniCS Project, where three-dimensional initial-boundary-value problems are introduced and the results are compared with reference data from the literature.

Modeling of coupled thermo-mechanical crack propagation in brittle solids using adaptive phase field method with scaled boundary finite element method

Complex crack patterns caused by thermally induced stresses commonly occur during thermal shrinkage in brittle materials, such as ceramic. Modeling the propagation of complex cracks can be tedious, computationally intensive and time consuming when multiple cracks initiate simultaneously. In this paper, the coupled thermo-mechanical Phase Field Model (PFM) is adopted, which facilitates the treatment of crack initiation, growth, bifurcation and coalescence in a unified framework. However, to represent the crack, the PFM requires a very fine mesh which increases the computational burden especially when the crack locations are not known as a priori. Aiming to efficiently reveal the crack morphogenesis and evolution in brittle material subjected to thermal shock, a space adaptive PFM is developed by refining the elements in the vicinity of crack propagating path on the fly, which reduces the number of elements and reduces the computational cost eventually. The Scaled Boundary Finite Element Method is applied with the quadtree mesh in this work to achieve the adaptive approach in the PFM as it is highly complementary. The presented numerical examples are showing good agreement with experiments and other results available in the literature, further, higher computational efficiency is achieved by employing the adaptive approach.

Tyre–Road Heat Transfer Coefficient Equation Proposal

Tyres are one of the most important elements of a vehicle because they are the link to the road and have a huge impact on traffic-related pollution. Knowing their behaviour, thus being able to use them at their best and reducing their wear rate, is one of the means of improving their lifetime, which means decreasing traffic environmental impact. In order to understand how tyres behave and to predict the real-time tyre–road coefficient of friction, which is strongly influenced by the temperature, in the last few years several complex thermo-mechanical models of heat transfer inside the tyre have been developed. However, in the current state of the art of the literature and practice, there is still an important parameter regarding such models that is not deeply studied. This parameter is the heat transfer coefficient between the tyre and the road at the contact patch, which usually is considered as a constant. The current research paper allows understanding that such an approximation is not always valid for all of the speeds and tyre loads of city and race cars; instead, it is developed an equation that, for the first time, calculates the real-time, dynamic tyre–road heat transfer coefficient, taking into account the tyre’s travelling speed and the footprint length. The equation results are in good agreement with the empirical values coming from the literature and permit understanding how much such a parameter can vary, depending on the tyre use range. The formulation is simple enough to be easily implemented in existing thermodynamic tyre models without requiring meaningful computational time.

Numerical Investigation of the Thermal Distortion in Multi-Laser Powder Bed Fusion (ML-PBF) Additive Manufacturing of Inconel 625

Metal additive manufacturing, especially laser powder bed fusion (L-PBF), is increasingly being used to fabricate complex parts with fine features. Emerging L-PBF systems have large build volumes and several lasers that operate simultaneously. Hence, they can produce large and complex parts at reduced costs and short build times. However, the thermal distortion remains a critical challenge. Hence, a thorough understanding of the impact of multiple lasers on part distortion in multi-laser PBF (ML-PBF) is imperative. Although experimental investigation is possible, a more conducive approach is to design and create suitable predictive models to understand the impact of multiple lasers consolidating a part into layers. To fulfill this goal, in this study, a commercially available and widely used thermo-mechanical model, Netfabb, was used to investigate the effects of multiple lasers for complex scan patterns such as raster, spiral, and Hilbert on the temperature distribution and thermal distortion. The results show that the thermal distortion is minimal for the spiral scan pattern. Additionally, multiple lasers were found to decrease the build time (as expected) while maintaining or reducing the thermal distortion compared with their single-laser counterparts for all scan patterns (except Hilbert). Therefore, the newly developed ML-PBF predictive model is capable of providing critical insights into the effects of using multiple lasers, thereby opening new possibilities for the faster production of complex parts. In the future, small-scale computational models will be expanded to include large-scale parts, and probabilistic models will be developed to establish correlations.

A thermo-mechanical simulation for the stability analysis of a horizontal wellbore in underground coal gasification

The stability analysis of horizontal wells is essential for a successful underground coal gasification (UCG) operation. In this paper, a new 3D coupled thermo-mechanical numerical modeling is proposed for analyzing the stability of UCG horizontal wells. In this model, the effect of front abutment stresses, syngas pressure, syngas temperature and thermal stresses is considered to predict the mud weight window and drilling mud pressure during UCG process. The results show that the roof caving in UCG panel has a greatest impact on the stability of horizontal well. Moreover, when the time of coal gasification is increased, the well convergence increases and for more stability it is necessary to increase the drilling mud pressure. This research was carried out on the M2 coal seam in Mazino coal deposit (Iran). The results showed that the mud weight window for horizontal well drilling is between 0 and 33 MPa. The appropriate stress for the maximum stability of the horizontal well, taking all the thermal and mechanical parameters into account, is 28 MPa. The suggested numerical method is a comprehensive and consistent way for analyzing the stability of horizontal wells in UCG sites.

Assessing the potential for ice flow piracy between the Totten and Vanderford glaciers, East Antarctica

Abstract. The largest regional drivers of current surface elevation increases in the Antarctic Ice Sheet are associated with ice flow reconfiguration in previously active ice streams, highlighting the important role of ice dynamics in mass balance calculations. Here, we investigate controls on the evolution of the flow configuration of the Vanderford and Totten glaciers – key outlet glaciers of the Aurora Subglacial Basin (ASB) – the most rapidly thinning region of the East Antarctic Ice Sheet (EAIS). We synthesise factors that influence the ice flow in this region and use an ice sheet model to investigate the sensitivity of the catchment divide location to changes in surface elevation due to thinning at the Vanderford Glacier (VG) associated with ongoing retreat and thickening at the Totten Glacier (TG) associated with an intensification of the east–west snowfall gradient. The present-day catchment divide between the Totten and Vanderford glaciers is not constrained by the geology or topography but is determined by the large-scale ice sheet geometry and its long-term evolution in response to climate forcing. Furthermore, the catchment divide migrates under relatively small changes in surface elevation, leading to ice flow and basal water piracy from the Totten to the Vanderford Glacier. Our findings show that ice flow reconfigurations occur not only in regions of West Antarctica like the Siple Coast but also in the east, motivating further investigations of past, and the potential for future, ice flow reconfigurations around the whole Antarctic coastline. Modelling of ice flow and basal water piracy may require coupled ice sheet thermomechanical and subglacial hydrology models constrained by field observations of subglacial conditions. Our results have implications for ice sheet mass budget studies that integrate over catchments and the validity of the zero flow assumption when selecting sites for ice core records of past climate.

Influence of Interface Morphology on the Thermal Stress Distribution of SOFC under Inhomogeneous Temperature Field

Excessive thermal stress can cause the failure of a solid oxide fuel cell (SOFC), and an inhomogeneous temperature field is one of the reasons for thermal stress in the cell. In the present work, the bi-dimensional thermo-mechanical coupling models of SOFCs with different interface morphologies including planar and corrugated cells are proposed. The temperature distribution of two types of cells under the action of heat conduction is analyzed. Further, the inhomogeneous temperature field caused by gas flow is used as the thermal load to compare the thermal stress distribution of planar and corrugated cells. The influence of interface morphology on the temperature distribution, stress distribution and the contribution of the temperature gradient to stress distribution are investigated. This research provides a reference for reducing thermal stress and improving the stability of SOFC.

A Thermomechanical Model for Time-Varying Deformations of Spigot Interference Connection under Shrink-Fitting Assembly

The interference fit connection structure is widely employed in various industries. Different from the conventional connection structure, the aero-engine rotor connection has a spigot-bolt structure. The quality of the shrink-fitting assembly process directly affects the final assembly performance of the rotor. The complexity of the connection structure and the time-varying thermal deformation bring great challenges in analyzing the formation patterns of connection performance. However, existing methods of interference connection analysis are mainly used in the wide range of interference connection structures, which makes them difficult to apply in low height interference connection for aero-engine rotors. This paper introduces a thermomechanical interference fit pressure model. First, a theoretical model for interference fit pressure considering temperature-variable loads is established to obtain the time-varying pressure during the assembly process. Second, a finite element model is established to explore the influence of interference and temperature loads on the spigot pressure and the mounting edge deformation. Finally, the experiments validate the accuracy of both the theoretical model and the finite element analysis. The results indicate that during the shrink-fitting assembly process, the interference fit pressure exhibits a nonlinear evolution trend, and the warping deformation of the mounting edge is a result of the combined influence of temperature and interference fit pressure. The law found in this paper has an application prospect in the process parameter setting of shrink-fitting assembly for special structures.

Modelling the historical and future evolution of six ice masses in the Tien Shan, Central Asia, using a 3D ice-flow model

Abstract. In the Tien Shan, few modelling studies exist that examine in detail how individual ice bodies are responding to climate change. Nonetheless, earlier research demonstrated that the glacier response to climate change in this mountain range is heterogeneous. Here, we use several measurements and reconstructions of the ice thickness, surface elevation, surface mass balance, and ice temperature to model in depth six different ice bodies in the Kyrgyz Tien Shan: five valley glaciers and one ice cap. The selected ice masses are located in different sub-regions of the Tien Shan with different climatic and topographic settings, and they are all characterized by detailed recent glaciological measurements. A three-dimensional higher-order thermomechanical ice-flow model is calibrated and applied to simulate the evolution of the ice masses since the end of the Little Ice Age (1850) and to make a prognosis of the future evolution up to 2100 under different Coupled Model Intercomparison Project Phase 6 (CMIP6) shared socioeconomic pathway (SSP) climate scenarios. The results reveal a strong retreat of most of the ice masses under all climate scenarios, albeit with notable variations in both timing and magnitude. These can be related to the specific climate regime of each of the ice bodies and their geometry. Under a moderate warming scenario, the ice masses characterized by a limited elevation range undergo complete disappearance, whereas the glaciers with a larger elevation range manage to preserve some ice at the highest altitudes. Additionally, our findings indicate that glaciers that primarily receive precipitation during the late spring and summer months exhibit a more rapid retreat in response to climate change, while the glaciers experiencing higher precipitation levels or more winter precipitation remain for a longer duration. Projections concerning the overall glacier runoff reveal that the maximum water discharge from the ice masses is expected to occur around or prior to the middle of the 21st century and that the magnitude of this peak is contingent upon the climate scenario, with a higher warming scenario resulting in a higher peak.

Influence of swirl and ingress on windage losses in a low-pressure turbine stator-well cavity

As part of the drive towards achieving net-zero flight by 2050, the development of ultra-high bypass ratio engines will place greater importance on the efficiency of the low-pressure turbine. Stator-well cavities can be a significant source of loss within this system, primarily due to the ingestion of annulus air, which can rotate at a speed less than that of the disc. This paper presents the results of a joint experimental/numerical campaign to relate windage torque to the flow physics in a scaled, engine-realistic stator-well geometry with superposed flows. The primary variables were the pressure ratio across the stator row and the swirl ratio at inlet to the cavity. This is the first paper to relate simultaneous torque and swirl measurements in a stator-well cavity. The numerical simulations have also provided insight into the fluid dynamic behaviour. A reduction in cavity windage torque with superposed flow rate was shown, consistent with the increase in swirl measured by experiments and predicted by computations. The pre-swirled superposed flows reduce the ingestion of negatively swirling fluid from the annulus, effectively increasing the swirl ratio of the flow in the cavity towards that of the rotor. This reduces windage losses; at the design condition with superposed flow, the cavity windage torque reduced by 60% of that of the reference case. Sealing effectiveness increased with superposed flow rate. This was demonstrated through gas concentration measurement/simulations, a reduced radial flow velocity into the cavity and a reduced mass flow rate across the interstage seal. The application of a turbulent transport model showed that ingestion could be explained by shear-driven diffusion. Ingestion increased as inlet swirl ratio reduced, while the pressure ratio was found to have a negligible influence on windage moment coefficient, swirl ratio and sealing effectiveness. In addition to providing fluid dynamic insight, the gas concentration results can be used for validating thermomechanical models. The results in this paper will be of practical interest to the engine designer who wishes to scale information to engine-operating conditions.

Numerical thermomechanical modelling of lava dome growth during the 2007–2009 dome-building eruption at Volcán de Colima

SUMMARY Lava domes form during effusive eruptions due to an extrusion of highly viscous magmas from volcanic vents. In this paper we present a numerical study of the lava dome growth at Volcán de Colima, Mexico during 2007–2009. The mathematical model treats the lava dome extrusion dynamics as a thermomechanical problem. The equations of motion, continuity and heat transfer are solved with the relevant boundary and initial conditions in the assumption that magma viscosity depends on the volume fraction of crystals and temperature. We perform several sets of numerical experiments to analyse the internal structure of the lava dome (i.e. the distributions of the temperature, crystal content, viscosity and velocity) depending on various heat sources and thermal boundary conditions. Although the lava dome growth at Volcán de Colima during short (a few months) dome-building episodes can be explained by an isothermal model of lava extrusion with the viscosity depending on the volume fraction of crystals, we show here that cooling plays a significant role during long (up to several years) episodes of dome building. A carapace develops as a response to a convective cooling at the lava dome–air interface. The carapace becomes thicker if the radiative heat loss at the interface is also considered. The thick carapace influences the lava dome dynamics preventing its lateral advancement. The release of the latent heat of crystallization leads to an increase of the temperatures in the lava dome interior and to a relative flattening of the dome. Meanwhile, the heat source due to viscous dissipation inside the lava dome is negligible, and it does not influence the lava dome growth. The developed thermomechanical model of the lava dome dynamics at Volcán de Colima can be used elsewhere to analyse effusive eruptions, dome morphology and carapace evolution including its failure potentially leading to pyroclastic flow hazards.

Crack suppression in wire-arc directed energy deposition of a γ-TiAl alloy

It was a big challenge to effectively eliminate cracks in wire arc directed energy deposition of TiAl alloys. Crack-free γ-TiAl alloy deposition layers were fabricated by a combining technique of preheating and heat preservation. A coupled thermo-mechanical model was developed to calculate the thermal stress evolution in the deposited layer. A first-principle model was employed to calculate the free energy and ductility of the γ and α2 phases. Based on the numerical and microstructural analyses, the crack suppressing mechanism was revealed. The α2 phase had a higher residual stress state at the boundary, and was more stable and brittle than the γ phase. The cracks were suppressed by decreasing the thermal stresses and brittle α2 phase formation.

Towards linking slab window geodynamics with the geophysical and geochemical signature of the upper mantle

Slab windows have clear consequences for surface observations that are the manifestations of asthenospheric upwelling and uppermost mantle temperature anomalies. In this contribution we link geophysical and geochemical observations from modern slab windows to the asthenospheric flow, temperature field and extent of melting using different geometries. We use an analytical solution for the slab window geometry and implement this solution in 3D steady-state thermomechanical models to calculate the temperature and velocity field. Our results show that upwelling (>1 cm/yr) and temperature anomalies (>1400 °C) are controlled by the ratio between the half-spreading rate and velocity of the overriding plate. The extent of melting depends on both the ratio of these velocities and ridge obliquity while flow patterns are controlled only by ridge obliquity. Finally, we construct ternary diagrams to estimate the efficiency of matrix/melt upwelling and maximum mean mantle temperatures based on plate kinematics and ridge obliquity. This novel approach was used to investigate the slab windows in Antarctica, South America and western North America.

Experimental Investigation of Transient Flow Phenomena in Rotating Compressor Cavities

Abstract The clearance of compressor blade tips during aero-engine accelerations is an important design issue for next-generation engine architectures. The transient clearance depends on the radial expansion of the compressor discs, which is directly coupled to conjugate heat transfer in co-rotating discs governed by unsteady and unstable buoyancy-induced flow. This paper discusses an experimental and modeling study using the Bath Compressor Cavity Rig, which simulates a generic axial compressor at fluid-dynamically scaled conditions. The rig was specifically designed to generate heat transfer of practical interest to the engine designer and validate computational codes. This work presents the first study of the fundamental fluid dynamic and heat transfer phenomena under transient conditions. The rotating flow structure was seen to be characterized by coherent pairs of cyclonic/anticyclonic vortex pairs; the strength, rotational frequency, stability, and number of these unsteady structures changed with changing rotational Reynolds and Grashof numbers during the transients. These structures, measured by unsteady pressure transducers in the rotating frame of reference, were only present when the flow in the rotating cavity was dominated by buoyancy. Experimental correlations of both Nusselt number and radial mass flowrate in the rotating core were correlated against Grashof number. Remarkably, the experiments revealed a consistent correlation for both steady-state and transient conditions over a wide range of Gr. The results have a practical application to thermo-mechanical models for engine design.

Enhancement of mechanical and microstructural properties of friction stir welded AA2024 by eccentric square tool pin

Grain size significantly affects joint strength and mechanical properties after friction stir welding (FSW). The tool pin shape/feature is an important factor influencing weld quality and microstructural features. The current work investigates the FSW of AA2024 with eccentric (distance between the axis of tool pin and shoulder) square tool pin and its influence on mechanical and microstructural characteristics. A square tool pin with three different eccentricities (0.0, 0.1, and 0.2 mm) is considered with a tilt angle of zero, one and two degrees. A defective weld is observed for the zero eccentricity, while the defect is reduced for the eccentricity of 0.2 mm with the reduction in grain sizes. Ultimate tensile strength enhanced to 407 MPa, contributing to a weld efficiency of 87 % obtained with a 0.2 mm pin eccentricity and two-degree tool tilt angle. Also, the average grain size and hardness at the stirred zone are 3.4 μm and 164 HV, respectively. Tool eccentricity produced 50, 14.7, and 11.2 % increase in tensile strength for 0o, 1o, and 2o tool tilt angles respectively, while increasing eccentricity from 0.0 to 0.2 mm. It is also found that eccentricity results in a higher dynamic area of 8 and 16 % for 0.1 and 0.2 mm, leading to more plastic deformation and better material mixing, resulting in enhanced mechanical and microstructural features. Also, higher rotational paths due to eccentricity cause interacting material to deform more with enhanced plasticization. Average grain size reduces by 25 %, 18.5 %, and 46 % when tool pin eccentricity is increased from 0 to 0.2 mm for a tilt angle of zero, one and two degrees, respectively. thermomechanical and mechanistic models are developed to explain the grain refinement and defect reduction mechanism due to eccentricity.

Theoretical and experimental investigations in thermo-mechanical properties of fused silica with pulsed CO2 laser ablation.

Laser ablation is widely used as a flexible and non-contact processing technology for the fabrication of fused silica. However, the introduction of thermal stress inevitably leads to crack growth and reduces the lifetime of fused silica. Due to the complicated coupling interaction and properties of fused silica, the unclear thermal stress formation is the bottleneck restricting further development of laser ablation. In this article, a three-dimensional multi-physics thermo-mechanical model was developed to reveal the evolution mechanism, and experiments were performed to validate the simulated results. The surface morphology evolution was elaborated during process cycles, with recoil pressure identified as the key factor in determining surface morphology. Moreover, thermal stress was quantified utilizing optical retardance and stress birefringence, effectively distinguishing between non-thermal and thermal stress induced by laser ablation. The theoretical simulations fit well with experimental measurements. Meanwhile, stress distribution and evolution behaviors were revealed under different processing parameters by this model. This work not only contributes to a profound understanding of the laser ablation process but also establishes a theoretical foundation for achieving high surface quality and non-thermal stress laser ablation.

A semi-analytical model for rapid prediction of residual stress and deformation in laser powder bed fusion

The build-up of residual stress and the resultant deformation in laser powder bed fusion (LPBF) play vital roles in the performance of the as-built parts. Due to the complex physical phenomena across multi-scales during LPBF, the accurate prediction of residual stress and the deformation related to the temperature variation have exposed the requirement for the computationally efficient modeling of thermo-mechanical field evolution. However, an efficient solution scheme for residual stress and deformation histories is still challenging. In this paper, a three-dimensional thermo-mechanical model is developed based on the semi-analytical method. The complex physical phenomena that occur during LPBF and a moving volumetric heat source is considered in the model. The residual stress and deformation evolutions are predicted using the separation of variables and the state space method. The accuracy of the proposed model is verified by the comparison with the previous prediction in the literature. The effect of the process parameters, geometrical parameters, and laser loads on the history and distribution of residual stress and displacement within the LPBF-printed parts is also investigated. The results show that residual stress and displacement increase with higher energy densities and the elevated length-to-thickness ratio of printed parts. In addition, it is shown that the computational cost of the proposed model is highly small, which can be served as an effective path for designing and guiding the manufacturing of parts via LPBF.