Through-thickness Temperature Distribution Research Articles

Development of a real-time ultrasonic monitoring tool for high-cycle thermal fatigue

Pipe networks within nuclear power plants (NPPs) are susceptible to high-cycle thermal fatigue (HCTF) failures especially in so-called mixing zones where fluids with different thermal and hydraulic properties interact. The 1998 incident at Civaux 1 NPP is a good example of such a failure and its potential consequences. Given the critical impact on safety of these NPP components, a non-invasive method for HCTF progression monitoring in real time is expected to be of great use. Previous ultrasonic monitoring work showed that it is possible to predict the through-thickness temperature distribution and its temporal evolution of a mild steel block to within ±2 °C, relative to a resistance temperature device. These predictions were achieved using time of flight measurements from an ultrasonic transducer placed on the accessible surface with the so-called inverse thermal model (ITM) to invert the data. However, experiments to date have been limited to slow (10 minute) thermal transients at low temperatures (T < 100 °C). Given that HCTF is driven by thermal gradients, the ITM method seems promising to monitor its progression. In this work the performance of the ITM method was investigated under more realistic conditions: faster (1 minute) thermal transients at higher temperatures (≈ 250-300 °C). A special high temperature electromagnetic acoustic transducer (EMAT) and a fast acquisition and inversion methodology were created to collect the data. The measurement setup and the collected data will be presented in this paper.

On the optimum process parameters of infrared curing of carbon fiber-reinforced plastics

Autoclave-cured carbon fiber-reinforced plastics (CFRPs) are widely used in aerospace and aviation industries. However, they have a limited field in automotive or marine industries in which both the unit costs of the products and applicability to mass production are of primary concern. Therefore, out-of-autoclave (OoA) processed products having similar mechanical properties with autoclave cured ones have been extensively studied. In this study, infrared (IR) curing, an OoA curing method, was investigated. The aim of the study is to propose a reliable temperature control method for an IR CFRP curing oven. A methodology that provides the surface and through-thickness temperature distribution of IR cured epoxy matrix CFRP was introduced. Optimum ply number and the distance between the heat source and the material were determined. Material surface was separated into nine virtual regions and region-based thermal evaluations were made by means of the thermal camera images and thermocouple data. Temperature distribution through thickness was determined. When designing a robust IR thermoset CFRP curing process, one should consider the temperature distribution on the surface and through the thickness of the material.

Temperature analysis for the laser-assisted tape winding process of multi-layered composite pipes

Tubular structures of fiber-reinforced polymer composites are utilized in various applications such as risers in the oil and gas industry and hydrogen pressure vessels in the automotive sector. The laser-assisted tape winding process presents an automated and efficient solution for the manufacturing of these structures out of thermoplastic composites. However, in order to guarantee reliable and high-quality process results, the temperature distribution within the laminate governing the consolidation between successively wound layers has to be understood and taken into account for process design. In an experimental setup, thermocouples were embedded between the layers in multiple spots along the perimeter during the manufacturing of pipe samples with five layers wound on a pure thermoplastic liner. This enabled capturing the through-thickness temperature distribution at different transversal locations. In addition to the temperature data recorded by the thermocouples, a stationary infrared thermographic camera focused on the laser-heated area was mounted on the tape winding head. The temperature data points of both sources were contrasted to evaluate how the through-thickness temperature distribution reflects the temperature input on the surface. Furthermore, the experimentally determined temperature distribution was compared with the results of a numerical process model, drawing conclusions with regard to the modelling and control of the multi-variable process.

Nonlinear thermal buckling analyses of functionally graded circular plates using higher-order shear deformation theory with a new transverse shear function and an enhanced mesh-free method

This study presents nonlinear buckling analyses of functionally graded (FG) circular plates in thermal environments using a mesh-free method. The thermal buckling response is formulated based on higher-order shear deformation plate theory in which a new transverse shear function is incorporated to better represent the displacement fields. An enhanced mesh-free radial point interpolation method (RPIM) in which the shape functions are constructed without any fitting parameters by virtue of the radial basis function in a compactly supported form is developed and utilized to explore the thermal buckling behavior. A radial basis function in a compactly supported form is proposed and included in the RPIM. Two types of FG circular plates with different FGM orientation, i.e., metal–ceramic FG circular plates and ceramic–metal FG circular plates, are considered in the analyses. The effectiveness and accuracy of the enhanced RPIM based on the higher-order shear deformation theory is first confirmed by simulating a numerical example found in the literature and comparing the results with the analytical solutions. Detailed parametric studies are then performed to investigate the effects of the volume fraction, plate thickness-to-radius ratio and metallic surface temperature on the critical buckling temperatures of FG circular plates subjected to various through-thickness temperature distributions. Results demonstrate that the enhanced mesh-free RPIM based on the higher-order shear deformation plate theory with the proposed transverse shear function can effectively predict the thermal buckling responses of FG circular plates, and that the volume fraction, plate thickness-to-radius ratio, bottom surface temperature and FGM orientation have considerable effects on the critical buckling temperatures.

Experimental and numerical investigation into temperature histories and residual stress distributions of high strength steel S690 welded H-sections

In order to exploit full structural benefits offered by high strength steel materials in construction, it is important to examine and quantify effects of welding on these steel materials for development of effective structural design. A systematic experimental and numerical investigation into thermal and mechanical responses in four S690 welded steel H-sections with different cross-sectional dimensions during and after welding was conducted.During welding, surface temperatures of the welded sections at specific locations in close vicinity of welding lines were measured continuously using thermocouples. After welding, surface residual stresses in these welded sections were measured using an established hole-drilling method. Based on codified data and measured temperatures, three-dimensional finite element models with thermomechanical coupled analyses were established to simulate heat transfer from a welding arc onto the welded sections. After a careful calibration of predicted surface temperature histories of these sections against measured data, both through-thickness temperature and residual stress distributions of these sections were obtained. Predicted and measured surface residual stresses at specific locations of these sections were found to be in a good agreement. Hence, accuracy of the proposed models in predicting temperature histories and residual stress distributions of these welded sections are established. Averaged through-thickness residual stresses are provided as representative residual stress patterns for these sections. It should be noted that the maximum residual stresses in these welded sections are proportionally smaller than those in S355 welded sections.Consequently, the proposed finite element models are demonstrated to be able to predict accurate temperature histories and residual stress distributions of S690 welded H-sections through thermomechanical coupled analyses. The proposed models will be readily employed to investigate welding-induced residual stresses in welded H-sections and I-sections of various steel grades and plate thicknesses with different welding parameters. Predicted residual stress patterns will then be employed for numerical investigation into (i) axial buckling behavior of slender columns made of S690 welded H-sections, and (ii) lateral torsional buckling of unrestrained beams made of S690 welded I-sections. These numerical investigations will be reported separately.

Control of the through-thickness temperature distribution in carbon composite aerospace parts during induction welding

The increasing content of thermoplastic composites in the aerospace industry requires the application of new joining technologies. Their main assembly advantage is rivetless joining, which needs to be examined in greater detail in order to compensate the higher costs of these materials. Induction welding is already used in aerospace industry and shows a high potential for the application in helicopter manufacturing. In order to implement this technology in serial production, the main requirement is to determine and control the process temperature distribution. A wide range of literature describing various approaches that characterize the aforementioned temperature distribution exists. Although all approaches validate their findings by temperature measurement on the surfaces of their parts, their results seem inconsistent due to different results. In this article, a new approach is presented and validated by interlaminar temperature measurement. Based on this new approach, for induction welding, effects that are not yet described are discussed. Hereby, cooling of the surface by air jets is investigated as a mean to influence the thermal effects of the induction welding process.

Transient thermal analysis of laser-assisted thermoplastic tape placement at high process speeds by use of analytical solutions

This article presents a transient thermal analysis of laser-assisted thermoplastic tape placement at high process speeds. The article revises modeling simplifications made in the literature and introduces novel ones. Analytical solutions to the thermal problem are proposed, for the heating and the cooling period. The process analysis of high speeds assumes a high-power laser in combination with a well-functioning temperature control. Due to this assumption, the final (surface) temperature is kept equal in all analyzed cases. The process analysis will show that the through-thickness temperature distribution changes significantly at higher speeds and becomes the determining factor for the bond interface temperature. General conclusions about process design and limits of tape placement are drawn. Finally, novel control methods are presented, which promote a dual control of surface temperature and temperature distribution. It will be shown how this is achieved by appropriate setting of the laser power and heating length.

Static behavior of thermally loaded multilayered Magneto-Electro-Elastic beam

The present article examines the static response of multilayered magneto-electro-elastic (MEE) beam in thermal environment through finite element (FE) methods. On the basis of the minimum total potential energy principle and the coupled constitutive equations of MEE material, the FE equilibrium equations of cantilever MEE beam is derived. Maxwell\'s equations are considered to establish the relation between electric field and electric potential; magnetic field and magnetic potential. A simple condensation approach is employed to solve the global FE equilibrium equations. Further, numerical evaluations are made to examine the influence of different in-plane and through-thickness temperature distributions on the multiphysics response of MEE beam. A parametric study is performed to evaluate the effect of stacking sequence and different temperature profiles on the direct and derived quantities of MEE beam. It is believed that the results presented in this article serve as a benchmark for accurate design and analysis of the MEE smart structures in thermal applications.

A computational analysis of coupled thermal and electrical behavior of PV panels

In this work, the objective is to develop a simple approach for the prediction of temperature and electrical efficiency of a PV panel. This modeling work constitutes a basic task towards better understanding of the behavior and capabilities of a PV panel when it is subjected to changing meteorological conditions. Different approaches may be used to determine the thermal response of a PV panel depending on the level of details needed for the temperature distribution. For a through-thickness temperature distribution, a one dimensional analysis is necessary. Therefore, only a one-dimensional finite difference model is proposed. Three different formulations of boundary conditions were used and compared in the numerical simulations. To build a full approach for thermal and efficiency analysis, the proposed thermal model is coupled with a solar radiation model and an electrical model. The parameters of the electrical model were estimated by the particle swarm optimization algorithm. Numerical simulations were performed with the meteorological inputs from Ajaccio (France) and for a commercial PV panel BP 350U. The predictions were compared to existing models and to experimental results.

Mechanical characterisation of carbon fibre–PEEK manufactured by laser-assisted automated-tape-placement and autoclave

Obtaining autoclave-level mechanical properties using in-situ consolidation of thermoplastic composites by Automated Tape Placement (ATP) is challenging. However, relatively recent availability of high quality ATP grade pre-preg material and tape heads equipped with more efficient heat sources (e.g. lasers) offers an opportunity to achieve improved mechanical properties and deposition rates. In the present study, carbon fibre–PEEK laminates, manufactured by laser-assisted ATP (LATP) and autoclave, are compared. Analysis of the through-thickness temperature distribution during LATP processing using thermocouples indicates that LATP cooling rates are extremely rapid and suggests full through-thickness melting of the pre-preg tape may not occur. Inadequate crystallinity, in conjunction with voids, compromised mechanical properties compared to autoclaved laminates but was beneficial in terms of the toughness of LATP laminates. Optimisation of pre-preg properties and processing parameters is required to realise the full potential of the LATP process in terms of mechanical properties, energy requirements, cost and deposition rates.

Analysis and optimization of temperature distribution in carbon fiber reinforced composite materials during microwave curing process

Vacuum assisted microwave curing technologies and modified optical sensing systems have been employed to investigate the influence of ply orientation and thickness on through-thickness temperature distribution of carbon fiber reinforced composite laminates. Two different types of epoxy systems have been studied. The results demonstrated that the ply orientation did not affect the temperature distribution of composite materials. However, the thickness was an important influencing factor. Nearly 10°C temperature difference was found in 22.5mm thick laminates. Through analyzing the physical mechanisms during microwave curing, the temperature difference decreased when the heat-loss in surface laminates was reduced and the absorption of microwave energy in the center laminates was improved. The maximum temperature difference of the samples formed using the modified microwave curing technologies in this research could be reduced by 79% to 2.1°C. Compared with the 5.29°C temperature difference of laminates using thermal heating process, the maximum temperature difference in laminates using modified microwave curing technologies was reduced by 60%, and the curing time was cut down by 25%.

An analytical investigation on thermomechanical stress analysis of adhesively bonded joints undergoing heat conduction

Thermomechanical loading, in the same way that mechanical loading can cause significant stress violations, may give rise to significant stress variations and concentrations and in some circumstances can result in structural destruction or even failure. This clearly shows the importance of accurate stress analysis of thermal-loaded structures. This paper presents three-dimensional thermomechanical stress analysis of heterogeneous adhesively bonded joints undergoing steady-state one-dimensional heat conduction using the full layerwise theory. In this approach, the fully coupled three-dimensional governing equilibrium equations are derived generally for an orthotropic joint based on the use of variational calculus and the principle of minimum total potential energy. The through-thickness temperature distribution is determined using the equivalent thermal-resistant model and is rewritten in the layerwise form. The governing equations of equilibrium then are analytically solved using the state space approach. The accurate results presented in this study are compared and verified via analytical as well as numerical investigations, and the study shows rapid converging solutions.

Aerothermal-aeroelastic two-way coupling method for hypersonic curved panel flutter

A method to compute aerothermal-aeroelastic two-way coupling for hypersonic curved panel flutter is proposed. The aero-thermo-elastic governing equations of a simply-supported two dimensional curved panel are developed based on the von Karman geometrically non-linear theory. The Galerkin approach is used to simplify the equations into discrete forms, which are solved by the fourth-order Ronger-Kutta method. The third-order piston theory is applied to the aerodynamics. The Eckert’s reference temperature method and the panel heat flux formula are used to compute the aerodynamic heat flux. Several important effects are included, namely 1) two-way coupling considering the effect of elastic deformation on aerodynamic heating and aerodynamic heating on stiffness of structure, 2) accumulation of the aerodynamic heating in real cruise, 3) arbitrary, non-uniform, in-plane and through-thickness temperature distributions, and 4) the effect of initial deformation of curved panel on the flight time to the onset of flutter. Compared with the results of aerothermal-aeroelastic one-way coupling, it is revealed that the two-way coupling which induces decrease of the flight time to the onset of flutter is more dangerous. In addition, importance should be attached to this method in actual analysis.

Studies on Fluid-Thermal-Structural Coupling for Aerothermoelasticity in Hypersonic Flow

The field of aerothermoelasticity plays an important role in the analysis and optimization of airbreathing hypersonic vehicles, impacting the design of the aerodynamic, structural, control, and propulsion systems at both the component and multi-disciplinary levels. This study aims to expand the fundamental understanding of hypersonic aerothermoelasticity by performing systematic investigations into fluid-thermal-structural coupling, and also to develop frameworks, using innovative modeling strategies, for reducing the computational effort associated with aerothermoelastic analysis. Due to the fundamental nature of this work, the analysis is limited to cylindrical bending of a simply-supported, von K arm an panel. Multiple important effects are included in the analysis, namely: 1) arbitrary, nonuniform, in-plane and through-thickness temperature distributions, 2) material property degradation at elevated temperature, and 3) the effect of elastic deformation on aerodynamic heating. It is found that including elastic deformations in the aerodynamic heating computations results in non-uniform heat flux, which produces non-uniform temperature distributions and non-uniform material property degradations. This results in reduced flight time to the onset of flutter and localized regions in which the material temperature limits may be exceeded. Additionally, the trade-off between computational cost and accuracy is evaluated for aerothermoelastic analysis based on either quasi-static or time-averaged dynamic fluid-thermal-structural coupling, as well as computational fluid dynamics based reduced-order modeling of the aerodynamic heat flux. It is determined that these approaches offer the potential for significant improvements in aerothermoelastic modeling in terms of efficiency and/or accuracy.

Postbuckling and Vibration Analysis of Antisymmetric Angle-Ply Composite Plates

ABSTRACT Postbuckling and postbuckled vibration analysis of antisymmetric angle-ply composite plates subjected to a thermo-mechanical loading is investigated in this article. The nonlinear partial differential equations of equilibrium are derived based on higher-order shear deformation theory, incorporating von Kármán nonlinear strain displacement relations and initial geometric imperfections. The solutions to the governing nonlinear partial differential equations are sought using the multi-term Galerkin technique. The nonlinear equilibrium paths are traced using the Newton-Raphson method in conjunction with the Riks approach. The free vibration frequencies of postbuckled plate about the static equilibrium state are reported by solving the associated linear eigenvalue problem. Results are presented for a simply supported antisymmetric angle-ply laminated plate, clearly bringing out the effects of uniform through-thickness temperature distribution and mechanical edge load on postbuckling and vibration behavior of the plate.

Criteria for Heated Band Width Based on Through-thickness Temperature Distribution. Numerical Study on Local PWHT of Butt Welded Pipe. Report 1.

The heated band width is the most important processing parameter for local postweld heat treatment of tubes and pipes.A correct heated band width must be chosen so that the allowable maximum temperature difference in the soak band is maintained and a sufficient degree of stress relaxation is achieved.In this paper, the effects of the geometrical and the thermal parameters in the postweld heat treatment are investigated using axisymmetric FEM.The most severe condition in which the heat input and insulation are only applied to the outside surface of the pipe has been studied in detail. The effect of the geometrical and the thermal parameters on the through thickness temperature gradients is investigated.Through this study, it is found that the required heated band width is mainly influenced by the wall thickness and the heat transfer coefficient on the internal surface.The computed results show that the Hi number is inadequate for practical use under general conditions.A more general Hi number is proposed as a linear function of the thickness. Further, based on the computed results, the authors propose criteria for the heated band width which includes the effect of the geometrical and the thermal parameters.

Modeling the microstructural changes during hot tandem rolling of AA5XXX aluminum alloys: Part III. Overall model development and validation

Part III of this article presents the overall mathematical development for the microstructural and textural evolution during industrial hot tandem rolling of AA5182 and AA5052 alloys and validation of the mathematical model, by comparison to both industrial data and information from the literature. The model consists of a plasticity module to simulate the temperature and deformation in the roll bite and an interstand module to characterize the changing microstructure, texture, and temperature in the strip between the rolling stands. The plasticity module was developed using a commercial finite-element package, DEFORM, a two-dimensional transient Lagrangian model which couples the thermal and deformation phenomena and is able to predict the temperature, strain rate, and strain distribution in the strip at any position in the roll bite. The interstand module incorporates semiempirical equations, developed in this study, which quantify the microstructural (percent recrystallization and recrystallized grain size) and textural changes in the strip between the rolling stands. The interstand model also includes a temperature module to predict the through-thickness temperature distribution in the strip based on one-dimensional heat conduction. Validation of the model against industrial data indicated that it gave reasonable predictions for the temperature, grain size, and volume fraction of some of the deformation texture components after recrystallization was completed. However, the model overestimated the mill loads in the last stands for both the AA5182 and AA5052 alloys and underestimated the amount of cube ({100}〈uvw〉) and S ({123}〈634〉) texture in the recrystallized strip.

On the Feasibility of Using Thermal Gradients for Active Control of Interlaminar Stresses in Laminated Composites

In this paper, a method is proposed to actively control interlaminar stresses near the free edges of laminated composites by through-thickness thermal gradients. Theoretical solutions are given for optimal steady-state through-thickness temperature distributions under uniaxial loading that are required to elmininate or reduce the interlaminar stresses below a prescribed level. The optimal solutions are obtained by minimizing appropriate performance indices that are functions of the far-field properties, with respect to the through-thickness temperature differences. In the second part, an experimental investigation is conducted on a glass/epoxy cross-ply laminate with embedded piezoelectric sensors and a thermal heater. Through the experiment, the feasiblity of the thermal control of interlaminar stresses is demonstrated.

On the feasibility of using thermal gradients for active control of interlaminar stresses in laminated composites

In this paper, a method is proposed to actively control interlaminar stresses near the free edges of laminated composites by though-thickness thermal gradients. Theoretical solutions are given for optimal steady-state through-thickness temperature distributions under uniaxial loading that are required to eliminate or reduce the interlaminar stresses below a prescribed level. The optimal solutions are obtained by minimizing appropriate performance indices that are functions of the far-field properties, with respect to the through-thickness temperature differences. In the second part, an experimental investigation is conducted on a glass/epoxy cross-ply laminate with embedded piezoelectric sensors and a thermal heater. Through the experiment, the feasibility of the thermal control of interlaminar stresses is demonstrated.

Modelling hot flat-rolling of components having curved profiles—part II. Characterization of heat transfer and flow stress

To obtain the mean temperature of the workpiece, a temperature sub-model is formulated based on one-dimensional transient flow in the roll-bite and two-dimensional transient flow outside the roll-bite. The model is capable of predicting (i) the through-thickness temperature distribution in the roll-bite, (ii) the mean temperature of the deforming body, and (iii) the approximate mean temperature distribution along the workpiece. The influence of rolling speed and reduction ratio is also investigated. To characterize the high temperature behaviour of steels, the well-known unified creep relationship is chosen as the flow stress sub-model. It is shown that reasonably accurate prediction of the flow stress is achieveable, by using experimental data reported in the literature.