Thermal Shock Loading Research Articles

Two-Dimensional Solution for Coupled Thermoelasticity of Functionally Graded Beams Using Semi-Analytical Finite Element Method

This article presents the two-dimensional solution for a simply supported beam made of functionally graded material (FGM) subjected to arbitrary time-dependent lateral thermal shock loads by the semi-analytical finite element method. The method of finite Fourier series is combined with the Galerkin finite element method to solve the two-dimensional coupled thermoelasticity equations. The series solution is assumed along the length of the beam and finite element procedure is adopted across the thickness of the beam such that the two-dimensional character of the solution is preserved. The FGM beam is assumed to be graded across the thickness direction. The material properties across the thickness direction follow the volume fraction of the constitutive materials in power law form. The equation of motion and the conventional coupled energy equation are simultaneously solved to obtain the displacement components and temperature distribution in the beam. The C 1-continuous shape functions are used in the Galerkin finite element method. The Laplace transform technique is used to transform the governing equations into the space domain, where the Galerkin finite element is employed to obtain the solution in the space domain. The inverse of the Laplace transform is performed numerically to obtain the final solution in the real time domain. Finally, the results are validated with the known data reported in the literature.

Finite element analyses and lifetime predictions for SnAgCu solder interconnections in thermal shock tests

PurposeThe purpose of this paper is to study the reliability of SnAgCu solder interconnections under different thermal shock (TS) loading conditions.Design/methodology/approachThe finite element method was employed to study the thermomechanical responses of solder interconnections in TS tests. The stress‐strain analysis was carried out to study the differences between different loading conditions. Crack growth correlations and lifetime predictions were performed.FindingsNew crack growth data and correlation constants for the lifetime prediction model are given. The predicted lifetimes are consistent with the experimental results. The simulation and experimental results indicate that among all the loading conditions studied the TS test with a 14‐min cycle time leads to the earliest failure of the ball‐grid array (BGA) components.Originality/valueThe paper presents new crack growth correlation data and the constants of the lifetime prediction models for SnAgCu solder interconnections, as well as for the BGA components. The paper adds insight into the thermomechanical reliability evaluation of SnAgCu solder interconnections.

Dynamic responses of a solid wall in contact with a bubbly liquid excited by thermal shock loading

Several MW-class spallation neutron sources are being developed in the world. Specifically, intensive and high energy protons are injected into heavy liquid metals (mercury, lead or lead–bismuth eutectic) to induce the spallation reaction that produces neutrons. At the moment when the proton beams are injected, thermal shock occurs in the liquid metal, causing pressure waves to propagate in the liquid metal, collide against the container and damage it. It is proposed that microbubbles are injected into the liquid metal to mitigate the impulsive pressure waves by means of absorption and attenuation effects. These effects are dependent on the relationship between bubble size and the rate of pressure increase. In the present experiment, a very rapid rise in pressure in the order of MPa/μs, equivalent to the rise in pressure due to proton beam injection, was simulated by the electric discharge method in a water loop test to investigate the impulsive pressure mitigation effect of injected microbubbles. The solid wall response was measured using an accelerometer, and the dynamic responses of microbubbles were observed using an ultra-high-speed camera filming at 5 × 10 5 frame/s. The sound velocity in bubbly water was estimated using a differential image technique. It was confirmed from the experimental results that microbubbles are effective in reducing impulsive pressure waves and to suppressing the impact vibration of the solid wall in contact with the liquid.

Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties

This article attempts to study the stochastic coupled thermo-elasticity of thick hollow cylinders subjected to thermal shock loading considering uncertainty in mechanical properties. The thermo-elastic governing equations based on Green–Naghdi theory (without energy dissipation) are stochastically solved using a hybrid numerical method (combined Galerkin finite element and Newmark finite difference methods). The mechanical properties are considered as random variables with Gaussian distribution, which are generated using Monte Carlo simulation method with various coefficients of variations (COVs). The effects of uncertainty in mechanical properties with various coefficients of variations on thermo-elastic wave propagation are studied in detail. Also, the maximum, mean and variance of temperature, displacement and stresses are illustrated across thickness of cylinder in various times.

CFD Tool for Assessment of the Reactor Pressure Vessel Integrity in Pressure Thermal Shock Conditions: Influence of Turbulence Model and Mesh Refinement on the Vessel Thermal Loading During PTS Transient

Integrity evaluation methods for nuclear reactor pressure vessels (RPVs) under pressurized thermal shock (PTS) loading are applied by French Utility. They are based on the analysis of the behavior of relatively shallow cracks under loading PTS conditions due to the emergency cooling during small break loss of coolant accident (SBLOCA) transients. This paper presents the research and development program started at EDF on the computational fluid dynamics (CFD) determination of the cooling phenomena of a PWR vessel during a pressurized thermal shock. The numerical results are obtained with the thermal-hydraulic tool Code̱Saturne, in combination with the thermal-solid code SYRTHES to take into account the coupled effect of heat transfer between the fluid flow and the vessel. Based on the global and local thermal-hydraulic analysis of a small break loss of coolant accident transient, this paper presents mainly a parametric study that helps to understand the main phenomena that can lead to better estimating the margin factors. The geometry studied represents a third of a PWR pressure vessel, and the configuration investigated is related to the injection of cold water in the vessel during a SBLOCA transient. Conservative initial and boundary conditions for the CFD calculation are derived from the global thermal-hydraulic analysis. Both the fluid behavior and its impact on the solid part formed by cladding and base metal are considered. The main purpose of the numerical thermal-hydraulic studies is to accurately estimate the distribution of fluid temperature in the downcomer and the heat transfer coefficients on the inner RPV surface for a fracture mechanics computation, which will subsequently assess the associated RPV safety margin factors.

Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method

This work is aiming to present an analytical method to study the dynamic behavior of thermoelastic stresses in a finite-length functionally graded (FG) thick hollow cylinder under thermal shock loading. The thermo-mechanical properties are assumed to vary continuously through the radial direction as a nonlinear power function. Using Laplace transform and series solution, the thermoelastic Navier equations in displacement form are solved analytically. The solution of the displacement field in the FG cylinder is obtained in the Laplace domain. Also, the fast Laplace inverse transform method (FLIT) is employed to transfer the results from Laplace domain to time domain. The effects of thermal shock loading on the dynamic characteristics of the FG thick hollow cylinder are studied in various points across the thickness of cylinder for various grading patterns of FGMs. A good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data.

Enhanced fracture assessment under biaxial external loads using small scale cruciform bending specimens

The present study is concerned with an enhanced fracture mechanics characterization of engineering materials using small scale cruciform bending specimens. Based on the regular SE(B) specimen geometry with a shallow crack, two additional loading legs allow the application of an additional stress component acting longitudinally to the crack front. Compared to standard specimen types, the biaxial loading conditions for the cruciform specimens are in general closer to the situation in pressurized vessels and pipes, especially under thermal shock loading conditions. In a combined experimental and numerical approach, detailed assessments of the local stress and strain fields in comparison to the crack front stress and strain states of standard specimens with deep and shallow cracks are provided. The cruciform bending specimen geometry is demonstrated to be suitable even in small scale dimensions. It permits the application of different combined external loading situations and thus a fracture assessment under conditions close to various situations in engineering application. Due to its small size, the specimen geometry can be employed even if only a limited amount of material is available.

Meshless local Petrov–Galerkin method for coupled thermoelasticity analysis of a functionally graded thick hollow cylinder

In this article, coupled thermoelasticity (without energy dissipation) based on Green–Naghdi model is applied to functionally graded (FG) thick hollow cylinder. The meshless local Petrov–Galerkin method is developed to solve the boundary value problem. The Newmark finite difference method is used to treat the time dependence of the variables for transient problems. The FG cylinder is considered to be under axisymmetric and plane strain conditions and bounding surfaces of cylinder to be under thermal shock loading. The mechanical properties of FG cylinder are assumed to vary across thickness of cylinder in terms of volume fraction as nonlinear function. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a Heaviside test function. Nodal points are regularly distributed along the radius of the cylinder and each node is surrounded by a uni-directional subdomain to which a local integral equation is applied. The Green–Naghdi coupled thermoelasticity equations are valid in each isotropic subdomain. The temperature and radial displacement distributions are obtained for some grading patterns of FGM at various time instants. The propagation of thermal and elastic waves is discussed in details. The presented method shows high capability and efficiency for coupled thermoelasticity problems.

Stochastic meshless local Petrov-Galerkin (MLPG) method for thermo-elastic wave propagation analysis in functionally graded thick hollow cylinders

The thermo-elastic wave propagation based on Green-Naghdi (GN) coupled thermo-elasticity (without energy dissipation) is studied in a function- ally graded thick hollow cylinder considering uncertainty in constitutive mechan- ical properties under thermal shock loading. The meshless local Petrov-Galerkin method accompanied with Monte-Carlo simulation is developed to solve the stochas- tic boundary value problem. In the presented method, the mechanical properties of FGM are considered to be as random variables with Gaussian distribution and mean values equal to deterministic values reported in previous works, which are gener- ated using Monte-Carlo simulation with various coefficients of variations (COVs). The time evolution for transient problems is treated by using the Newmark finite difference method. The FG cylinder is assumed to be under axisymmetric and plane strain conditions. The mechanical properties of FGM are nonlinearly graded along the radial direction. A weak formulation for the set of coupled governing equations is transformed into local integral equations on local subdomains by using a Heav- iside test function. All nodal points are regularly distributed along the thickness of the FG cylinder in radial direction and each node is located in a uni-directional subdomain to which a local integral equation is applied. The distributions of the temperature and radial displacements as well as the time history of them are ob- tained for some grading patterns of FGM at several time instants and for some COVs. The propagation of thermal and elastic waves along the radial direction in the FG thick hollow cylinder as well as the statistical characteristics of the variance and maximum values of the temperature and displacement are discussed in details.

Transient Finite-Volume Analysis of a Graded Cylindrical Shell Under Thermal Shock Loading

A major failure mechanism in thermal barrier coatings involves delamination of the ceramic top coat from the substrate, which is accompanied and/or aided by transverse cracks that initiate at the outer surface. Techniques to mitigate these failure modes include grading the transition region between the ceramic top coat and the metallic bond coat by gradually varying the content of the two phases. This concept is explored herein for a graded cylinder subjected to transient thermal cyclic loading, that simulates a thermal shock durability test, using the parametric finite-volume theory for functionally graded materials. Previous investigation into the transient response of a three-layer cylinder under the considered thermal shock loading revealed two potential failure modes, one of which was a direct result of transient effects. Herein, examination of average phase-level stress fields indicates that grading influences the initiation of delamination and potential radial cracking through redistribution of the radial and hoop stress components in the thermal coating's graded region upon rapid heating. The large hoop stress reversal responsible for radial crack initiation at the outer surface, however, is not reduced upon rapid cooling, pointing to the importance of accurately modeling transient effects in thermal shock testing as well as crack-growth management through grading.

Sensitive Analyses of Probabilistic Fracture Mechanics for Reactor Pressure Vessel during Pressurized Thermal Shock and Comparison with the Results of International Round Robin Analyses in Asian Countries

This paper demonstrates sensitive analyses of probabilistic fracture mechanics (PFM) for reactor pressure vessel (RPV) during pressurized thermal shock (PTS) loading, and comparison of our calculation with the results of the international round robin (RR) analyses in Asian countries (Korea, Taiwan and Japan). The international Round Robin activity was performed in PFM sub-committees in the Atomic Energy Research Committee of Japan Welding Engineering Society (JWES) in conjunction with Korea and Taiwan research groups. The purposes of this program are to establish reliable procedures to evaluate fracture probability of reactor pressure vessels during pressurized thermal shock and to maintain the continuous cooperation among Asian institutes in the probabilistic approach to nuclear safety. Some parameters to RPV failure probabilities are chosen to evaluate their significance quantatively. The differences caused by selection of analyzing programs and some input parameters will be discussed.

1107 自由表面に平行な二個の軸対称き裂を有する傾斜機能圧電厚板の電気熱弾性応答(OS11.機能性材料の応力解析と機能発現に関する数値シミュレーション(2),OS・一般セッション講演)

Thermoelectroelastic response of Two parallel axisymmetric cracks in a plate of a functionally graded piezoelectric material (FGPM) is studied under thermal shock loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are supposed to be insulated thermally and electrically. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated.

OS1403 自由表面に平行な二個の軸対称き裂を有する傾斜機能圧電厚板の電気熱弾性応答(OS14-1 圧電材料・セラミックス・傾斜機能材料の弾性数理解析,OS-14 弾性数理解析の発展と新展開1)

Thermoelectroelastic response of Two parallel axisymmetric cracks in a plate of a functionally graded piezoelectric material (FGPM) is studied under thermal shock loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are supposed to be insulated thermally and electrically. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to two systems of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated.

Thermal shock characterization of tungsten deformed in two orthogonal directions

The increasing importance of tungsten and tungsten alloys for future nuclear fusion facilities and reactors requires an increasing understanding of the materials behavior under operational loading conditions. Among others this comprises the thermal shock and thermal fatigue resistance of the material before and after recrystallization.This study in particular aims for the qualification of deformed tungsten forged in two orthogonal directions intending to obtain a dense and nearly isotropic grain structure. The material is investigated in its stress relieved and recrystallized state and acts as a reference material for a better understanding of the cracking process when exposed to transient thermal loads, e.g. Edge Localized Modes (ELMs: f⩾1Hz, t=hundreds of μs). This is addressed by multiple thermal shock loadings in the electron beam facility JUDITH at different base temperatures. Hereby the influence of the DBTT on the onset of crack formation is verified and the latter qualified and quantified by metallographic means.

Machinability Investigation in High Speed Turning of Powder Metallurgy Nickel-Based Superalloy with Sialon Ceramic Inserts

An experimental investigation was carried out to understand the behavior of a powder metallurgy nickel-based superalloy when machined with sialon ceramic insert tools. Turning experiments were carried out at different cutting speeds and feed rates while depth of cut was kept constant. Cutting tool performance was evaluated with respect to temperature and cutting forces generated during turning, and tool wear. The sialon ceramic cutting tool showed high performance when increasing cutting speed, the machining experiments showed that sialon ceramic tools performed better at cutting speed up to 80 m/min. Abrasion and adhesion was the dominant wear mechanisms. Chipping on the tool rake and flank faces, as well as catastrophic failure under thermal shock and mechanical loading, was also observed in experiments. As cutting temperature was very high when turning powder metallurgy nickel-based superalloy, good high-temperature strength and thermal shock resistance were indispensable to the cutting tools for machinging this kind of material.

Computational modeling of titanium structures subjected to thermo-chemo-mechanical environment

This manuscript provides a new coupled thermo-chemo-mechanical computational model for titanium structures subjected to extreme loading and environment. The proposed model accounts for the formation of oxygen enriched (alpha-case) titanium, as well as the coupling effects between the response characteristics of mechanical and oxygen infiltration processes into titanium at high temperature environment. The formation of alpha-case at the surface of the structure is modeled as diffusion of oxygen into the titanium substrate. The mechanical response of the structure is idealized using the Johnson–Cook model, which is generalized to account for the effects of oxygen induced embrittlement and hardening. The interplay between mechanical damage, oxygen infiltration and temperature on the chemo-mechanical response is evaluated using numerical simulations. The fully coupled mechanical and diffusion processes are solved based on a staggered coupling algorithm. The capabilities of the computational model are assessed by the analysis of a panel composed of Ti-6Al-2Sn-4Zr-2Mo titanium alloy subjected to thermal shock loading.

Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings

Abstract Based on the first-order shear deformation theory (FSDT), approximate solution for FG (functionally graded) laminated piezoelectric cylindrical shells under thermal shock and moving mechanical loads is given utilizing Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the functionally graded layer are acted as distributed sensor and actuator to control dynamic characteristics of the FG laminated cylindrical shells. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of FG laminated cylindrical shells. Constant-gain negative velocity feedback approach is used for active vibration control. The active vibration control to a single moving concentrated loading, thermal shock loading and a continuous stream of moving concentrated loadings is, respectively, investigated. Results indicate that the control gain and velocity of moving loadings have significant effects on the dynamic response and resonance of the system.

Thermal fatigue evaluation of cast iron discs for railway vehicles

Thermal fatigue of brake discs for railway vehicles has been a troublesome problem since the advent of disc brake. To develop cast-iron brake discs with high heat resistance to thermal shock loading, three candidate materials with different components were developed. Main components of the cast irons are Fe, C, Si, Mn, Ni, Cr, Mo, Cu and Al. Mechanical and thermal properties were measured. Then thermal fatigue tests were carried out by a thermal fatigue test equipment developed by the authors. The possible temperature range of the equipment is 20∼1500 °C. Cylindrical solid specimens ϕ20×80 mm were heated by an induction coil and cooled in water. At an interval of 20∼30 thermal cycles, the surfaces of the specimens were examined with an optical microscope to check thermal cracks. To quantify the total length of cracks an image analyzing program that can measure the length of cracks from micrographs was developed. It was found the fatigue lifetime of cast iron can be elongated by regulating composition and metallurgical structures.

Thermo-mechanical and thermal shock characterization of potassium doped tungsten

One potential plasma facing material candidate for future nuclear fusion facilities and reactors like ITER and especially DEMO is potassium doped tungsten, better known from lighting industry. Herein, in particular the potassium doped tungsten grade WVMW produced by PLANSEE AG is qualified in its as-received and annealed/recrystallized state (annealing at 1800 °C) and compared with a standard W-rod. One qualification criteria is the crack formation under fusion relevant short transient events which is addressed by single and multiple thermal shock loading in the electron beam facility JUDITH at different power densities and base temperatures. Therein annealed WVMW is showing the best performance with the lowest transition temperature from crack formation to no crack formation between 150 and 200 °C. This might be also taken as a measure for the ductility and the DBTT of the material. For a better understanding of the cracking process as well as for the establishment of a data base for finite element modelling tensile tests are performed up to 2000 °C and at different speed (0.2 and 42 mm/min).

Design against fracture of functionally graded thermal barrier coatings using transformation toughening

This study presents a new theoretical model for design against fracture of zirconia-toughened functionally graded thermal barrier coatings (FG TBCs). A micromechanics-based model, which investigates the effect of the mismatch in material properties of the constituent phases on the transformation toughening mechanism in zirconia-enriched multi-phase composites, has been incorporated with the lamination theory. The developed model enables to engineer ZrO 2-toughened multi-phase FG TBCs with required or pre-determined fracture properties by utilizing the synergetic characteristics of their constituent phases. A simulation for ZrO 2/Ni FG TBC plates subjected to thermal shock loadings has been conducted. The results demonstrated that within the compositional gradation investigated, the substrate metal (Ni)-rich compositional gradation contributed to high fracture-resistant properties based on fracture-mechanics considerations. This tendency was theoretically and experimentally confirmed with results available in the open literature.