Transverse shear effect in a bimodulus plate

This paper concerns the bending analysis of a bimodulus elastic plate whose stress-strain relation is expressed by two straight lines with a slope discontinuity at the origin. An energy formulation of the problem is made, taking into account a transverse shear deformation. A method of numerical solution is presented for cylindrical bending of a plate.     

Thermal stresses in heterogeneous thick isotropic shells

The application of a thick shell theory in the design of nuclear pressure vessels is given. A derivation for thick shells of revolution with the inclusion effects of transverse shear stress and normal stress, in which the Young's modulus is considered dependent on temperature, is presented. The set of equations so obtained are solved by a numerical integration method. The example of a spherical shell is solved and the results compared with the case in which the Young's modulus is assumed to be constant. It is shown that under large temperature gradients through the thickness, the change in deflections and stresses can be significant, if the present derivation is used.     

Thermal bending of thick rectangular plates

An analysis with a shear deformation capability for the thermal bending of thick rectangular plates is presented. Formulation of the problem, with appropriate thermal terms incorporated and applicable to the bending of moderately thick plates, has been carried out by using Reissner's plate bending theory. Representative plate bending problems have been considered for illustrating the procedure. Numerical results obtained indicate that thick plate solutions to thermal problems deviate from those of the classical theory in practically the same manner as with mechanical loading cases.     

Elasto-plastic behaviour of a thin cylinder under thermal stress cycling

A simple biaxial model is chosen to represent the stress state of a thin cylinder and the elasto-plastic behaviour under thermal stress cycling is studied to determine:

1. 1. shakedown limits,

2. 2. plastic cycling limits,

3. 3. magnitude of cyclic strains and ratchet strains,

4. 4. strain ratios in various regimes.

The studies have been carried out for two material models: elastic-perfectly plastic and Prager-hardening. Results are given in the form of graphs and compared with the results of uniaxial models.     

Thermal stress concentration problem in a plate with a slit

Elliptical coordinates are used for the solution of thermal stress concentration problems at slit-tips by means of the degeneration of an elliptical hole in a square plate. The stress function approach in combination with the point-matching method have been used for the computation of stress concentration factors for various configurations of slits in form of elliptical holes under uniform heat generation.     

Thermal stress problems in tokamak surfaces

The density of power deposited on some surfaces of a tokamak can easily reach the level where the surface may be destroyed by thermal stress. This report is an examination of the thermal stress problem under tokamak conditions. The magnitude of the maximum power density is given for some existing and future devices. As examples which furnish a guide to power absorption limits for surfaces in high-power plasma devices, we have made estimates of thermal stress in a thick wall subjected to transient heating On one side. Also, detailed results are given for a flat plate heated on one face and cooled on the other. Comparative power density limits are tabulated for various materials of interest for plasma device construction.     

Thermal stresses around an elliptic hole in an infinite thick plate subjected to a uniform heat flow

A theoretical three-dimensional analysis is presented for determining the state of thermal stresses around an insulated elliptic hole in an infinitely long thick plate subjected to a uniform heat flow. The maximum stress is found to depend on the ratio of thickness to length of the semi-major axis of the hole and also on Poisson's ratio. In the limiting cases, the solution reduces to the corresponding circular hole solution obtained by Lee, and also to the two-dimensional solution of the elliptic hole problem as given by Florence and Goodier.     

Thermal stress singularities at tips of a Griffith crack in a finite rectangular plate

This paper is concerned with a method for calculating the thermal stresses in a finite rectangular plate with a Griffith crack under a steady state temperature field. In the analysis, based on the complex variable method for determining the stationary two-dimensional thermal stresses, the analytic continuation and the modified mapping-collocation methods are effectively employed. Numerical calculations for the strength of thermal stress singularity of the symmetric and the skew-symmetric types are carried out, and the results are shown in graphs.     

Thermal frequency response studies of a hollow cylinder subject to loads of different amplitude and shape

Thermal fatigue is an important degradation mechanism, which must be considered in life management of nuclear plant piping systems. The analysis is very complex due to a number of complicating factors, with the determination of the load as the primary one. There is clearly a need for simplified engineering approaches, such as simulating the spectrum load by a constant frequency thermal load with the nominal temperature difference between mixing fluids. The fatigue life is determined by the frequency that gives the shortest life using fatigue curves for initiation and Paris law for crack propagation. This paper analyses three aspects that affect the conservatism of such an approach: the thermal load shape (sinusoidal or square shaped), the structural boundary conditions at the edges of the modelled pipe (traction free or clamped) and the defect shape (circumferential or elliptic). Furthermore it is shown how the methodology can be used to determine screening criteria, i.e. a lower limit of the temperature difference below which there will be no component failure due to thermal fatigue.     

Thermal stress analysis for fatigue damage evaluation at a mixing tee

Fatigue cracks have been found at mixing tees where fluids of different temperature flow in. In this study, the thermal stress at a mixing tee was calculated by the finite element method using temperature transients obtained by a fluid dynamics simulation. The simulation target was an experiment for a mixing tee, in which cold water flowed into the main pipe from a branch pipe. The cold water flowed along the main pipe wall and caused a cold spot, at which the membrane stress was relatively large. Based on the evaluated thermal stress, the magnitude of the fatigue damage was assessed according to the linear damage accumulation rule and the rain-flow procedure. Precise distributions of the thermal stress and fatigue damage could be identified. Relatively large axial stress occurred downstream from the branch pipe due to the cold spot. The variation ranges of thermal stress and fatigue damage became large near the position 20° from the symmetry line in the circumferential direction. The position of the cold spot changed slowly in the circumferential direction, and this was the main cause of the fatigue damage. The fatigue damage was investigated for various differences in the temperature between the main and branch pipes. Since the magnitude of accumulated damage increased abruptly when the temperature difference exceeded the value corresponding to the fatigue limit, it was suggested that the stress amplitude should be suppressed less than the fatigue limit. In the thermal stress analysis for fatigue damage assessment, it was found that the detailed three-dimensional structural analysis was not required. Namely, for the current case, a one-dimensional simplified analysis could be used for evaluating the fatigue damage without adopting the stress enhancement factor K_t quoted in the JSME guideline. The results also suggested that, for a precise assessment of the fatigue damage at a mixing tee, the effect of multi-axial stress on the fatigue life together with the mean stress effect should be taken into account.     

Thermal ratcheting under biaxial stress states

Thermal ratcheting, the phenomenon of net strain accumulation due to plastic straining of pressure vessels under cyclic thermal loading, is an important factor in the design of nuclear reactor pressure vessels. In this paper a cyclic thermal gradient loading idealized by means of a step distribution through the pressure vessel wall and biaxial thermoelastic-plastic stress-strain relations are used to calculate the strain accumulation under biaxial mechanical loads. It it shown that the uniaxial stress-strain models presently used in design calculations are adequate for spherical and cylindrical shells under internal pressure; however, for uniaxial loading and for torsional loading, the use of these models may underestimate the accumulated ratchet strain.     

Dissipative heating in a coated viscoelastic cylinder

The thermomechanical responses of a long coated hollow cylinder made of viscoelastic material subjected to cyclic presure fluctuations at high frequency are studied. The accumulation of the continuous energy dissipation induces a significant temperature increase in the material which affects the material behavior and hence the structural response. The paper adopts a numerical approach with the intention of studying the effect of coating. It is found that the coating has little effect on the dissipative heating due to internal pressure fluctuation. However, the heating effect can be greatly reduced when the cyclic pressure is applied on the outside surface.     

Thermal stress resistance of ion implanted sapphire crystals

Monocrystals of sapphire have been subjected to ion implantation with 86 keV Si⁻ and 80 keV Cr⁻ ions to doses in the range of 5 × 10¹⁴–5 × 10¹⁶ cm⁻² prior to thermal stress testing in a pulsed plasma. Above a certain critical dose ion implantation is shown to modify the near-surface structure of samples by introducing damage, which makes crack nucleation easier under the applied stress. The effect of ion dose on the stress resistance is investigated and the critical doses which produce a noticeable change in the stress resistance are determined. The critical dose for Si ions is shown to be much lower than that for Cr⁻ ions. However, for doses exceeding 2 × 10¹⁶ cm⁻² the stress resistance parameter decreases to approximately the same value for both implants. The size of the implantation-induced crack nucleating centers and the density of the implantation-induced defects are considered to be the major factors determining the stress resistance of sapphire crystals irradiated with Si⁻ and Cr⁻ ions.     

Eigenvalues basic to radial diffusion in a hollow cylinder

The eigenvalues of the eigenvalue problem basic to radial diffusion in a hollow cylinder with azimuthal symmetry are determined for nine different combinations of the boundary conditions of the first, second and third kind. The first ten eigen values are systematically tabulated for different values of the radius ratio and Biot number for the inner- and outer-boundary surfaces.     

Thick-walled micropolar cylinder in a state of plane strain

This paper deals with the important boundary value problem of a thick-walled micropolar cylinder loaded with an internal pressure. Use is made of a finite element model to study the influence of the micropolar characteristics on the stresses and displacements in the cylinder.     

Thermal stress initiated fracture as a fragmentation mechanism in the UO2-sodium fuel-coolant interaction

An analytic study was carried out to determine the applicability of the concept of thermal stress fragmentation to the UO₂-Na fuel-coolant interaction. Major emphasis was put on the fracture mechanics approach to assess whether or not the solidifying UO₂ would fracture under the thermally-induced stresses. It was found that the stress levels were sufficient to generate K_I values substantially in excess of the UO₂ fracture toughness K_IC. Thus, rapid instantaneous propagation of inherent flaws is anticipated.     

Thermal stress analysis of containment building in case of a Main Steam Line Break (MSLB)

In Indian PHWR, containment building is one of the primary barriers for mitigating the consequences of a Loss of Coolant Accident (LOCA), and Main Steam Line Break (MSLB) accident. It is desired to know the temperature transients as well as the resulting thermal stresses in the containment structures of 220MW(e) PHWR, Kaiga Nuclear Power plant under postulated MSLB event. The high enthalpy steam discharged into the containment space comes in contact with the Structural Wall (SW) of containment, Inner Containment Wall (ICW) and Raft. The containment wall temperature rises due to heat transfer from steam-air mixture. To calculate the transient temperature distribution across the containment walls, it is necessary to determine containment ambient temperature and heat transfer coefficient for the condensing steam on the internal structures. Hence, at the outset, a thermal hydraulic code was developed to predict the pressure-temperature transients and condensation heat transfer coefficient transients (using various condensation models) based on the mass and energy of high enthalpy steam released into containment. The effect of various condensation models on containment pressure-temperature was evaluated. The thermal boundary conditions such as containment temperature and heat transfer coefficient, evaluated from the thermal hydraulic code using Uchida condensation model, were subsequently applied as boundary conditions to a two-dimensional axi-symmetric containment model developed using a FEM code for estimating two-dimensional temperature profiles and the resulting thermal stresses.     

Thermal stress waves with applications to laser fusion reactors

A closed-form solution is developed for stress waves in a solid resulting from volumetric energy deposition. The material is linear elastic and the geometry a plate or slab-like component. One dimensional waves perpendicular to the surface are considered. Such a model can be used to describe the response for plates or thin shells. The problem is relevant to the design of liners and first wall structure of laser fusion reactors. For demonstration purposes, examples are presented based upon the University of Wisconsin SOLASE conceptual power plant. It is shown that X-rays and reflected long wavelength laser light produce relatively small amplitude waves but short wavelength reflected laser light can produce stresses of significant amplitude.     

Stress intensity factor evaluation of a circumferential crack in a finite length thin-walled cylinder for arbitrarily distributed stress on crack surface by weight function method

A weight function to evaluate the stress intensity factor (SIF) of a circumferential crack, subjected to arbitrarily distributed stress on the crack surfaces, in a finite length thin-walled cylinder was derived based on the closed form SIF equation previously developed by the authors. It is easy to evaluate the effects of structural parameters and stress distribution on the SIF with this weight function. Numerical examples confirmed the validity of the weight function. These examples showed that the effect of cylinder length on the SIF is quite large.