On the effects of through-thickness thermal conduction on stress measurement by thermoelastic techniques

Stress measurement by means of the thermoelastic technique has been growing in popularity since the mid-1980s. This paper looks in detail at the effects of thermal conduction on such measurements. It is shown that for accurate quantitative stress determination, on all but the simplest of geometries, thermal-conduction effects may have to be considered. Such effects can be experimentally observed and modifications which can be made to an experiment affected by thermal conduction are suggested.     

Path dependency in thermoelastic stress analysis

In this paper we review the basis of the technique for thermoelastic stress analysis and, in particular, we examine the relationship between the theory and the technique in common practice. The theory of thermoelastic stress analysis is based on the thermomechanical behavior of bodies, which takes strain and temperature as state variables that are path-independent, whereas the conventional instrumentation used in thermoelastic stress analysis involves an integration of photon flux derived from a body's surface temperature, and hence is time- and path-dependent. This inconsistency might be negligible for some, or perhaps most, applications. However, in those cases where the waveform of the loading is irregular, experiments have shown that the difference can be significant. The nature of most apparatus for thermoelastic stress analysis implies that this results is important when conducting experiments in which the forcing signal is unknown or not sinusoidal. J.R. Estrada Estrada was a Research Student and E.A. Patterson (SEM Member) was a Professor, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield, S 3JD, UK.     

Retardation of a crack with connections between the faces using an induced thermoelastic stress field

This paper considers local temperature variations near the tip of a crack in the presence of regions in which the crack faces interact. It is assumed that these regions are adjacent to the crack tip and are comparable in size to the crack size. The problem of local temperature variations consists of delay or retardation of crack growth. For a crack with connections between the crack faces subjected to external tensile loads, an induced thermoelastic stress field, and the stresses at the connections preventing crack opening, the boundary-value problem of the equilibrium of the crack reduces to a system of nonlinear singular integrodifferential equations with a Cauchy kernel. The normal and tangential stresses at the connections are found by solving this system of equations. The stress intensity factors are calculated. The energy characteristics of cracks with tip regions are considered. The limiting equilibrium condition for cracks with tip regions is formulated using the criterion of limiting stretching of the connections.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 133–143, January–February, 2005     

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

The present paper presents a general treatment of the transient thermoelastic stresses in a rotating nonhomogeneous anisotropic solid under compressive initial stress. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for the temperature, displacement components and stress components. The results indicate that the effects of inhomogeneity and initial stress are very pronounced.     

Determination of all stress components from measurements of the stress invariant by the thermoelastic stress method

A method for the resolution of all stress components from the first invariant J₁ measured by thermoelastic stress analyzer is described. This method may be used to determine, not only surface stress, but also internal stress and stress on the underside.The method is based on the following procedure:

1. (1) Pick an arbitrary domain Ω, within the structure, for which the stresses are required.

2. (2) Measure J₁ on the surface of Ω.

3. (3) Determine the optimum traction along the boundary Γ, which is a part of Ω, by the least squares method such that the difference between the measured J₁ and the calculated J₁ is at a minimum. Either FEM or BEM may be used for this calculation.

Examples of stress resolution for a two-dimensional stress concentration problem and a three-dimensional stress concentration problem are shown. The accuracy of the stress resolution is discussed.     

Calculating the thermoelastic stress state of medium-thickness shells of revolution

Analytic and numerical analyses are carried out to ascertain whether the theories of thin and medium-thickness shells can be used to calculate the thermoelastic state of shells of revolution. It is shown that the theory of thin shells should be used in the case of thermal loading and the theory of medium-thickness shells in the case of mechanical loading __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 58–67, May 2008.     

Numerical simulation of stress intensity factors via the thermoelastic technique

The purpose of this study is to investigate the accuracy of the least squares method for finding the in-plane stress intensity factorsK _I andK _II using thermoelastic data from isotropic materials. To fully understand the idealized condition ofK _I andK _II calculated from thermoelastic experiments, the total stress field calculated from finite element analysis is used to take the place of data obtained from real thermoelastic experiments. In the finite element analysis, theJ-integral is also calculated to compare with (K _I ² +K _II ² )/E evaluated by the least squares method. The stress fields near the crack tip are dominated by the two stress intensity factors; however, the edge effect will cause inaccuracy of the thermoelastic data near the crack tip. Furthermore, the scan area of thermoelastic experiments cannot be too small. Therefore, we suggest that three or four terms of stress function be included in the least squares method for evaluating stress intensity factors via the thermoelastic technique. In the idealized condition, the error can be smaller than 3 percent from our numerical simulations. If only ther ^–1/2 term (K _I andK _II ) is included in the least squares method, even in the idealized case the error can be up to 20 percent.     

Effect of heating rate in thermoelastic stress production

Using pulses of monochromatic MeV electrons from a linear accelerator to heat copper and tantalum samples, measurements of thermoelastic stresses were made as a function of heating rate. The results were compared with the predictions of thermoelastic wave theory, and good agreement was found.     

Local effective thermoelastic properties of graded random structure matrix composites

Summary  We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient, as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated. Received 11 November 1999; accepted for publication 4 May 2000     

Formulation of thermoelastic dissipative material behavior using GENERIC

We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids (generalized standard materials), the state of a material point is described by dissipative internal variables in addition to the elastic deformation and the temperature. The framework GENERIC allows for an efficient derivation of thermodynamically consistent coupled field equations, while revealing additional underlying physical structures, like the role of the free energy as the driving potential for reversible effects and the role of the free entropy (Massieu potential) as the driving potential for dissipative effects. Applications to large and small-strain thermoplasticity are given. Moreover, for the quasistatic case, where the deformation can be statically eliminated, we derive a generalized gradient structure for the internal variable and the temperature with a reduced entropy as driving functional.     

On the effect of the heat generated during a stress-induced thermoelastic phase transformation

In this paper we examine the stress-elongation response of a bar undergoing a thermoelastic phase transition. Attention is focussed on how this response is affected by the heat generated during the transformation. The analysis is based on a continuum model consisting of a two-well Helmholtz free-energy function, a kinetic relation and a nucleation criterion. The governing mathematical problem is related to one that describes a moving heat source, except that here, the strength and speed of the source are not knowna priori and the energy field equation involves coupling between thermal and mechanical effects. A finite difference solution of this moving boundary-value problem is carried out. The heat generated by the transformation is found to have a significant effect on the mechanical response whenever the prescribed elongation-rate is moderately large.     

Wall shear stress measurement in a turbulent pipe flow using ultrasound Doppler velocimetry

A turbulent boundary layer of a water flow is investigated by means of pulsed ultrasound Doppler velocimetry. The advantage of this method is the acquisition of complete velocity profiles along the sound propagation line within very short time intervals. The shear stress velocity, used for normalizing the velocity profiles, was determined by fitting the profiles to the universal profiles in a turbulent boundary layer obtained from Prandtl's mixing length theory. A coordinate transformation in the near-wall region is proposed to allocate the velocity data to "true" wall distances. From the experimental values of the wall shear stress velocity, the friction factors for a turbulent pipe flow are calculated and compared to the Blasius law. The overall error in measurement was estimated to NJ.4%.     

Magnetothermodynamic stress and perturbation of magnetic field vector in a non-homogeneous thermoelastic cylinder

This paper presents a theoretical method for analyzing magnetothermoelastic responses and perturbation of the magnetic field vector in a conducting non-homogeneous thermoelastic cylinder subjected to thermal shock. By making use of finite Hankle integral transforms the analytical expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in the non-homogeneous cylinder are obtained. From sample numerical calculations both magnetothermostress and perturbation of the axial magnetic field vector in a non-homogeneous cylinder is revealed and discussed.     

The measurement of the yield stress of liquids

An analysis has been made of different methods of measuring the yield stress of liquids. In the experimental program, a comparison is made of measurements of the yield stress using an Instron 3250 Rheometer in several geometries (cone-plate, parallel plate and eccentric disk) in shear flow and stress relaxation, a laboratory vane and a cone penetrometer. Good agreement has been obtained between the shear flow data and the laboratory vane, while stress relaxation appears to underestimate the yield stress.     

On the measurement of stress in solid propellant

The problems related to the direct measurement of stresses in solid propellant are identified and reviewed. The piezoresistance phenomenon is discussed and it is shown how this phenomenon can be utilized to measure stresses in elastomers and solid propellant. One version of a piezoresistive stress transducer is used to measure radial stresses in an uncontained thick-walled elastic cylinder which is internally pressurized. A smaller similar version of the piezoresistive stress transducer is employed in a rosette configuration to measure the stress state at five critical locations in a quarter-scale Surveyor solid-propellant motor three times during a four-year storage period. The instrumentation and calibration of these piezoresistive stress transducers are briefly described.