Thermal Stresses in Severe Environments

I want to thank the organizers of this Congress for asking me to present the opening lecture. I thought it would be appropriate if I were to start with a rapid review of the field of thermal stresses and give some thoughts regarding an assessment (although necessarily a very personal one) of the present state of the field, and finally include guesses as to what the future might bring.

On the macroscopic level, the difference in the thermoelastic behavior between crystalline solids and amorphous polymeric solids such as rubber is striking. While crystalline solids expand with increase in temperature, stretched rubber contracts upon heating. On the atomic level this difference may be traced to the greater degree of disorder in amorphous polymeric solids and consequently to the central role played by entropy in their mechanical behavior.In this paper we present two simple linear chain atomistic models with prescribed nearest-neighbor interactions, one which represents, in highly idealized form, a crystalline solid and the second a long-chain molecule under tension. For these models, it is possible to calculate the thermoelastic relation by the application of the basic principles of classical equilibrium statistical mechanics. The model1 for the long-chain molecule is found to exhibit a transition in behavior, over a narrow range of temperature, from that expected for a harmonic crystal at low temperature levels, to that characteristic of a polymer at higher temperature levels.

At present there are at least two different generalizations of the classical linear thermoelasticity. The first one proposed by Green and Lindsay (1972) (G-L Theory) involves two relaxation times of a thermoelastic process, while the second theory due to Lord and Shulman (1967) (L-S Theory) admits only one relaxation time. Both theories have been developed in an attempt to eliminate the paradox of an infinite velocity of thermoelastic propagation inherent in the classical case. In this paper a number of general results concerning these theories for a homogeneous isotropic solid are presented. They include (G-L Theory): 1. Domain of Influence Theorem, 2. Decomposition Theorem, 3. Uniqueness Theorem, and 4. Variational Principle. Theorem 1 asserts that in the new theory thermoelastic disturbances produced by the data of bounded support propagate with a finite velocity only. Theorem 2 which is quite similar to a Boggio result in linear elastodynamics shows that a thermoelastic disturbance can be split into two fields each of which propagates with a different finite velocity. Theorem 3 covers uniqueness for a stress-temperature boundary value problem with arbitrary initial tensorial data. Finally, the variational principle gives an alternative description of the theory in terms of a thermoelastic process (S,q), where S and q represent the stress tensor and the heat flux vector, respectively. In the L-S theory uniqueness of a stress-flux initial-boundary value problem is discussed. A number of suggestions concerning those areas of the theory that are critically in need of further investigation are also given.

Under certain circumstances and in certain materials, (transient) thermal stresses can give rise to permanent stresses. The mechanisms involved in the genesis of such “frozen-in” thermal stresses are briefly reviewed in the context of the tempering of glass. The main purpose of the paper is to trace the development of theoretical treatments of this process. Some well developed computational schemes are now available, which may well find wider application.

A coupled, isotropic, infinitesimal theory of thermoviscoplasticity was developed in [32,33] and applied to a variety of loadings including thermal monotonic and cyclic straining [32]. In this paper we rederive the coupled equatioris using the first law of thermodynamics. The predictions of the theory in torsion are examined qualitatively and by numerical experiments. They simulate monotonic loading at loading rates differing by four orders of magnitude. Jumps in loading rate are also included. The theory exhibits initial linear elastic response followed by nonlinear, rate-dependent plastic behavior. The adiabatic temperature changes are initially isothermal followed by heating. The theory exhibits rate-dependence, a difference in strain and stress controlled loading and deformation induced temperature changes which are qualitatively in agreement with recent experiments.

It is usual to assume in thermal stress calculations that material properties are independent of temperature. Significant variations do however occur over the working temperature range of the “engineering ceramics”, particularly in the coefficient of thermal conductivity, k. (Godfrey1 has reported decreases of up to 45 per cent in the thermal conductivity of various samples of silicon nitride between 0 and 400 °C.) The question arises: what are the effects of these variations on the stress distributions in ceramic components?

The mechanical response and the failure of composite solid propellants are known to be related to the formation and growth of vacuoles on the microscopic or macroscopic scale. Failures in composite materials such as composite propellants originate at the filler particle or binder molecular level. These microscopic failures, whether adhesive failures between the binder and filler particles or cohesive failures in the binder, result in vacuole formation. The cumulative effect on all vacuole formation and growth is observed on the macroscopic scale as strain dilatation. The strain dilatation in composite propellants varies with binder type, binder formulation, filler particles, and presumably filler particle size distribution. The strain dilatation caused by vacuole growth and formation results in a nonlinear stress-strain behavior for these materials.

The uncoupled thermoelastic brittle fracture problem is discussed in terms of the types of stress fields produced by surface heating or cooling and the generic characteristics of the thermally generated stress intensity factors. Examples of experimental measurements and numerical calculations are given to demonstrate these general characteristics.

A problem of increasing interest and importance is the numerical calculation of stress intensity factors for cracked or otherwise imperfect structures due to thermal as well as mechanical loading. The finite element method has become one of the most popular and effective computational approaches to stress analysis, and a large number of fairly successful schemes have been introduced to treat the stress singularities of interest in fracture mechanics as outlined in [1]. One of the simplest yet most effective methods for treating such problems is the introduction of special “singular elements” to model the fields in the immediate neighborhood of the exceptional point without requiring an overly refined (and expensive) mesh.

The concept of structural safety is reconsidered. In order to get a computable standard value for safety, the term reliability is introduced. A structure can be regarded as “reliable” if the given loading is not greater than its structural resistance. It is evident that the total analysis directly depends on the accuracy with which the load intensity is determined. The loading “fire”, in comparison to conventional loads such as dead and live loads, etc., is considerably more complicated because of its physical complexity. This paper deals with the loading “fire” and demonstrates how fire can be embedded in a thermomechanical analysis.

A plate which is fixed at its edges to a strong edge support structure will develop large compressive stresses when heated from ambient temperature more rapidly than the support structure. Determining the response of the plate to this situation requires stability analysis to ascertain whether the plate might buckle, or whether the constrained thermal expansion will lead to compressive stresses exceeding the yield point because it did not buckle. A special case is considered here, both analytically and experimentally, in which the plate is curved slightly into a cylindrical shape and the convex face of the plate is against a supporting surface. This case is more complex because the buckling mode will be a harmonic rather than the fundamental mode which is usually encountered.

Analytical results are presented for the thermal stresses resulting from “thermal trapping” in semi-absorbing materials subjected to symmetric and assymmetric radiation heating and convective cooling with finite heat transfer coefficient, h. The transient stresses during heat-up in both cases were found to be an inverse function of the heat transfer coefficient, h, and increase monotonically with the optical thickness, μa. In contrast, the steady state stresses were independent of h and exhibited a maximum at μa ≃ 1.3 for symmetric heating and at μa = 2 for assymmetric heating with zero stresses at μa = 0 and ∞. For the symmetrically heated plate, the transition from the transient to the steady-state condition involved a reversal in the sign of thermal stress at any position. For the assymmetrically heated plate the steady state maximum tensile thermal stresses occur at the position of the highest temperature, ie. the front surface.

Review of recent work on instabilities of crack systems and applications to the hot-dry rock geothermal energy scheme is presented. The basic variational formulation of the crack stability problem is outlined and the critical states of a system of parallel equidistant cooling cracks propagating into a halfspace are explained and analyzed. The solution, which shows that at a certain critical crack length-to-spacing ratio every other crack suddenly jumps ahead at constant temperature while the remaining cracks stop growing and subsequently close, determines the crack width and is of importance for heat withdrawal from hot rock by circulation of water in cooling cracks. Some typical numerical results obtained by finite elements are presented and the effect of the temperature drop profile on the critical crack length is discussed. Finally, some other applications, such as parallel cooling cracks or drying shrinkage cracks in reinforced solids, such as concrete, are pointed out.

Radially varying temperature and thermal stress distributions in layered pressure vessels designed for use in coal conversion processes are investigated. A least-squares residual method which incorporates Lagrange multipliers for satisfaction of initial, boundary and interface conditions is employed in the case of transient heat conduction. Assuming orthotropic elastic behavior, a general solution is formulated for the stresses induced by combined temperature, pressures and initial interferences between layers. The effects of heat-transfer resistance at layer contact surfaces are illustrated through several numerical examples. Representation of a layered vessel as a homogeneous cylinder having an effective thermal conductivity, for the purpose of predicting thermoelastic response, is also explored.

During normal operations, the heat exchanger shells of domestic gas furnaces experience alternately rising and falling temperatures. These cyclic temperatures in turn induce cyclic strain patterns in the shell. The fatigue life of the shell is primarily dependent upon the temperature range of the heating cycle, rate of heating and cooling, the cyclic strain amplitudes, the cyclic straining rates, the material of which the shell is made, and the ambient environment.

Thermal stress fracture in brittle materials is treated with a Weibull statistical analysis technique. The probability of failure and size effect is predicted by combining a risk analysis with finite element heat transfer and stress analysis. In a thermal transient the maximum probability of failure can occur at times greater than the time of maximum thermal stress. In many situations the thermal stress in a structure increases with size while, due to the size effect, the strength of the structure decreases. Thermal shock tests of silicon carbide and alumina demonstrate the scatter in the fracture strength. The average fracture strength of alumina is well-predicted, but the strength of silicon carbide disks is apparently affected by a nonhomogeneous flaw population. Applications of the statistical analysis technique to thermal stress situations in gas turbine vanes and combustors are reviewed.

The survivability of a ceramic cylinder liner for an internal combustion engine was investigated. The study is deemed to be important because the use of such liners in fuel-injected engines may increase fuel efficiency by reducing quench zone thickness and heat loss through the cylinder wall and by permitting effective secondary power extraction. Four ceramic liner candidates having potential for surviving this extreme environment were examined, viz. two densities of both silicon nitride and silicon carbide.

The jamb frame is one of the major structural elements of a coke-oven end-closure system. The structural behavior of the jamb interacting with other end-closure elements determines the sealing performance of the system as a whole. One of the main causes of poor sealing is the accumulation of reversible and/or irreversible jamb distortions. In particular, the jamb frame often deforms in its plane so that the posts deflect towards each other--a deformation called hourglassing.

A problem which has received considerable attention in the past few years is the analysis of a cracked reactor beltline region which is subjected to a thermal shock loading condition. This attention has resulted in many techniques for estimating the Stress Intensity Factor (K_I) distributions along the front of part through cracks for this problem. The purpose of the study presented herein is to utilize some of these more recent developments for a linear elastic analysis of hypothetical elliptical surface cracks subjected to a time-varying non-uniform stress distribution which results from a thermal shock loading. The problem is further complicated because the initial crack is assumed to be in a weld region with the possibility of extending into a base material region with different material properties. A technique which is based on linear elastic fracture mechanics is chosen to predict K_I distributions for the geometry and loading employed. In order to gain confidence in the solution, it is compared with other available analytical and numerical solutions from the literature. It is then used to predict crack extension and subsequent arrest with consideration given to the varying material parameters present.

An analysis of mechanical and thermal stresses for LOFT Gamma Densitometer mounting lugs, bolts and pipe to which the lugs are attached is presented in this paper. The analysis does not include the densitometer of the supporting structure. The mechanical loads under consideration include internal pressure, seismic loads and dynamic loads due to blow down. Thermal transients associated with normal and upset operating conditions have been considered. Appropriate finite element models were constructed for obtaining stresses and deflection analyses due to mechanical loads and thermal transients. Existing computer code of SAPIV modified for Large core Memory (LCM) for CDC 7600 and SAASIII were used for the computation of mechanical and thermal stresses. Procedures to analyze the data obtained from computer analyses for ASME code evaluation are outlined. A stress summary is presented.

Correct design of building glass installations against failure by fracture is an engineering problem of particular importance, especially because of the increasing tendency of their all-out use in modern building fronts. Existing guidelines for design ensure satisfactory structural performance in most cases, as empirical findings show, but they often lack a detailed theoretical foundation. This deficiency should be reduced by an intensified analysis of the loading conditions which glass panes are subjected to in the field. Such efforts will also help to avoid uneconomical, conservative solutions.

The results are presented for the effect of spatially varying thermal conductivity on the tensile thermal stress developed in a solid and a hollow circular cylinder subjected to different heating conditions. It is shown that the maximum tensile thermal stress in brittle ceramics can be reduced significantly by redistributing the temperature profile using (a) a spatial variation in thermal conductivity, (b) a spatial variation in pore content which in turn changes the density, thermal conductivity and modulus of elasticity and (c) by considering the effect of temperature on the thermal conductivity and specific heat. Possible methods for creating such variations in the material properties are discussed.

The quantitative description of the thermal shock of refractories is reviewed with emphasis focused on those physical properties pertinent to the calculation of damage resistance parameters. The excellent correspondence between theoretical damage resistance parameters and a variety of laboratory thermal shock tests of refractories is summarized. Microstructural features are discussed both from a crack propagation resistance viewpoint and their effects on other physical properties that affect thermal shock behavior.

The general approach to the selection of materials with high resistance to thermal stress fracture is to follow criteria which would identify materials resistant to crack initiation or having low crack propagation. A third approach is presented here having the basis of retarding propagation wherein the propagating crack is allowed to heal during service, thus arresting premature crack completion and specimen fracture. The discussion presented in this paper suggests that in order to promote crack healing and delay crack fracture completion, the material should be selected on the basis of high surface diffusion coefficient, high surface energy, small grain size and small crack width. Service temperatures where grain growth and bulk diffusion are promoted should be avoided.

This paper discusses the effect of unstabilized zirconia dispersions on the thermal shock resistance of brittle structural ceramics.A general discussion is given of the preferred direction of modification of the pertinent material properties which affect thermal shock resistance. The nature of the crystallographic phase transformation in the zirconia and its effect on these properties is presented. The zirconia dispersed phase can lead to significant improvements in fracture toughness by transformation - or microcrack toughening. The volume change during the zirconia phase transformation also lowers the effective coefficient of thermal expansion. Surface compressive stresses which result from the phase transformation during surface grinding also are beneficial in improving thermal shock resistance. The zirconia phase also can change the unstable (cȧtastrophic) mode of failure to the more preferred stable one with decrease in fracture stress. These effects are illustrated by experimental data for composites, consisting of zirconia dispersions in aluminum oxide, silicon nitride and zircon matrices.

The nature of the dependence of the thermal shock resistance of ceramics on the various thermo-mechanical properties of these materials can be used to design, in a systematic way, ceramics with improved thermal shock resistance. Great versatility in designing for thermal shock resistance and other desired properties can be achieved via ceramic composite approaches where properties of the two (or more) phases can be used to tailor the properties of the composite.

In order to ensure the reliability of microelectronic packages, these packages are subjected to various tests which simulate the environments which the packages may experience in service. The present study concerns a detailed investigation of the Thermal Shock Test (Method 1011.2 in MIL-STD-883B [1]).

Probabilistic models for predicting the service life of missile structures subjected to random thermal loads have been developed. The models are applicable to both elastic and viscoelastic materials and utilize the finite element method. Statistical descriptions of the stresses, strains and damage parameters are generated using Monte Carlo computer simulation techniques and mathematical models of the thermal environments in arctic temperate, and desert geographical locations. The statistical descriptions of the induced stresses, strains, and damage are compared with similar descriptions of allowable parameters using interferrence techniques to compute a probability of failure. Realibility concepts are then used to generate service life estimates.

Several areas in a given grain design often require special consideration other than the usual strength analysis. Linear elastic stress analysis often predicts infinite stresses at material discontinuities and notches associated with bond end terminations, roots of release flaps, and defects such as cracks and localized unbond regions in a rocket motor grain. Many of the limitations of strength analyses may be overcome by the application of the energy balance concept of fracture mechanics. The energy balance concept is based on an exchange of strain energy stored in a propellant grain under a specified loading condition and the energy expended due to the formation of new surface area by fracture and/or crack growth.

Experimental data indicate that stress response predictions based on the normal assumption of thermorheologically simple material behavior can underpredict observed stress response by a factor of two or more when applied to combined thermal and mechanical load histories. In highly filled polymeric systems, such as solid propellants, combined thermal and mechanical synergistic effects induce high local stress gradients in the polymer binder between filler particles that are not accounted for in conventional analysis methods. An experimental and analytical methodology is demonstrated which accounts for these interaction effects and is applied to slow thermal-mechanical loading of a solid propellant rocket motor.

Solid propellant rocket motors stored outdoors without thermal protection are subjected to variable amplitude thermal stresses. It has been shown(1,2) that the storage life of such motors can be calculated from the probability of failure that in turn is determined from a stress-strength interference analysis. Such a techique compares the statistical distribution of induced thermal stresses with the distribution of material strength. For visco-elastic materials both the induced stress and the allowable strength are functions of temperature and rate of loading as well as aging and cumulative damage.

A method is presented which will allow the failure probability of a brittle structure to be evaluated from a thermal stress solution. It is based on a statistical approach, a generalisation of the simple Weibull distribution, and takes into account material variability, component size and anistropic strength. The principal stress values at the nodes of a finite element mesh are assumed to be known for the structure. The stress distribution within each element is then expressed in terms of these nodal values through suitably derived shape functions. Certain stress volume integrals are evaluated and the failure probability of each element, and hence that of the whole structure, is calculated. The accuracy of the method is assessed for various types of finite elements by analysing a simple structure.

M392 projectiles have exhibited a high percentage of erratic exterior ballistic flight trajectories, especially in firing series which had been conditioned for elevated temperature testing. This erratic flight behavior has resulted in unacceptably large dispersion patterns on target. The sources of the erratic rounds tested were stockpile lots after extended storage and lots shipped to and tested in hot, dry climatic areas. The poor performance has been observed to occur with greater frequency in gun tubes with high secondary wear characteristics. Examination of the vulcanized fiber rotating bands indicated a shrinkage of the material from the dimensions specified in the technical data package. Failure of the bands in shear was also reported. Significantly different results have been obtained with rotating bands manufactured from vulcanized fiber produced by different suppliers. Preliminary tests of the M728 projectile indicated that there was a high probability of the same problem existing, particularly after extended storage.

The arc discharge method was applied to determine the effect of neutron irradiation on the thermal shock fracture toughness and thermal shock resistance of reactor graphites. Experimental results show that the fracture toughness and resistance to thermal shock of four varieties of reactor graphite decrease remarkably when the materials are subjected to neutron irradiation of (1.6 ∿ 2.3)×1021 neutrons/cm2 (>0.18 Mev) at 600 ∿ 850°C.

Thermal stress tests are conducted to determine the failure strengths of a material in a thermal stress environment. This can only be done if an accurate thermostructural analysis of the test can be made. An accurate analysis of the test requires a precise definition of both the heat flux and the time of failure. Other thermal stress tests often lack one or both of these requirements. A test technique has been developed, using a flat top laser to provide the heat flux, which offers both a well defined thermal environment and an accurate indication of the time of catastrophic failure. This paper describes the test procedure and the corresponding analytical technique. Additionally the results of some recent tests are presented demonstrating the test applicability.

This paper presented the theoretical and experimental background for understanding of opaque and transparent brittle materials subjected to continuous wave laser irradiation. At irradiations above ~ 1 kw/cm2, the time to failure of opaque materials was proportional to the thickness squared and inversely proportional to the thermal diffusivity. The time to fracture of transparent materials was nearly independent of thickness but was highly dependent on the absorption coefficient. The burnthrough time of both opaque and transparent materials was proportional to the thickness and thermodynamic parameters and inversely proportional to the irradiance.Laser irradiation can be used to rank the thermal stress resistance of opaque brittle materials. This ranking was the same as that obtained from thermal quenching into water, as long as the thickness, wavelength, and heating rates were equivalent. The reason for the similarity was that the analytical expressions describing both behaviors were similar.

The report describes the equipment and test method for the thermal stress resistance of ceramic hollow cylindrical specimens under programmed heating conditions. The experimental data are recorded with the use of a computer. The analysis of the state of thermal stress of the specimens for elastic and nonelastic materials has been conducted, and the dependence of thermal shock resistance of ceramic materials upon their brittleness has been demonstrated. The relationships between the optimum thermal loading condition and specimen size have been established. The expedience of using the described technique in statistical investigations of ceramic materials is demonstrated.

Composite materials are highly anisotropic thermally with the coefficient of thermal expansion in the fiber direction much lower than that in the transverse to the fiber direction. Coefficients of thermal expansion in unidirectional and multidirectional laminates can be calculated by using the properties of the constituents and lamination theory. Residual stresses are introduced in multidirectional laminates during curing as a result of thermal anisotropy. These stresses have been investigated analytically and experimentally It was found that the significant strains recorded during the cooling stage of curing correspond to thermal expansion of the laminate. Residual or restraint strains are computed from measured restrained and unrestrained thermal expansions. Residual stresses are computed using appropriate orthotropic constitutive relations. Results have been obtained from a variety of materials including boron, graphite, Xevlar, S-glass and hybrids with epoxy or polyimide matrices, for a variety of lamination angles. It was found that residual stresses do not relax appreciably with time. Results show that, for graphite and Kevlar laminates, residual stresses at room temperature are high enough to have caused damage in the transverse to the fiber direction.

Brittle materials are subject to microcrack formation at grain boundaries and at second phase particles. These cracks are induced by residual stress that results from incompatibilities in thermal contraction. The development of residual stress and its partial relaxation by diffusion (at elevated temperatures) are described. The evolution of microcracks within the residual stress fields are then examined. Particular attention is devoted to considerations of the critical microstructural dimension at the onset of microcracking.

Six laminate configurations were subjected to five different thermal exposures in the temperature range 78K to 603K (−320°F to 625°F), and then studied using microscopy and x-ray to determine the characteristics of microcracks formed during the thermal loadings. The laminates studied were: [0₃90₃]_s, [0₂/90₂]_s, [(0/90)₃]_s, [45/−45/0/90]_s, [0/45/90/−45]_s, and [0/60/0/−60]_s. The material system investigated was found to be free of cracks after curing, but microcracks did develop in most laminates when cooled from 603K (625°F) by quenching in ice water or liquid nitrogen. Crack density was dependent on laminate configuration and rate of cooling. Microcracks present at free edges extended across the entire width of the specimens. The [45/−45/0/90]_s laminate proved to be very resistant to microcracking for all thermal loadings. The thermal load required to initiate microcracking, determined using laminate analysis with stress and temperature dependent material properties, compared reasonably well with experimental results.

This paper deals with the state of stress in an infinite elastic solid with an external crack which is subjected to a prescribed temperature distribution. The infinite elastic medium consists of two materials which are separated by a cylindrical surface. It is assumed that there is perfect bonding at the common cylindrical surface. By assuming a suitable representation for the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Then, using suitable biharmonic functions as thermoelastic potentials, the thermoelastic problem is also reduced to the solution of a Fredholm integral equation of the second kind. Both the integral equations are solved numerically. The numerical values of the stress intensity factor are displayed graphically.

The merits of composite materials for potential use in structural design are well established. Their high strength to weight ratio make them attractive in aerospace and automotive applications where improved fuel economy by weight reduction is desirable. Unfortunately, a number of factors have inhibited the ready acceptance of such materials. First, costs are high compared to conventional materials. With increased usage, however, costs are likely to become increasingly competitive in the future. Another, perhaps more serious limitation, is the current lack of understanding of the mechanical behavior of polymer based laminates under long term environmental exposure.

Thermal nondestructive testing and evaluation of materials has attracted increased attention in recent years with the appearance of commercially available, real-time infrared scanning devices. Previous work in our laboratory and others has indicated that material damage can be studied in situ, as well as in initiation and growth stages during the application of load. To develop the thermal techniques quantitatively, appropriate physical and mathematical models which will delineate the interdependence of damaged regions and the observed thermal patterns need to be found. This paper investigates some of the current physical models which have been discussed in the literature for such phenomena as internal friction, viscoelasticity, thermoelasticity, etc., in relation to their possible utility in explaining “Stress Related Thermal Emission.” The parametric dependence of stress related thermal emission on variables such as wavelength, size of the damage zone, thermal conductivity, material inhomogeneity, and others are discussed along with factors affecting the possible observed heat patterns.