General relations of strain-gradient stress analysis

Some particular fields of stress gradients in plates are investigated analytically and experimentally. Carriers of empirical information are light beam deflections caused by stress or strain gradients in homogeneous beams subjected to a particular case of flexure with shear. This study is based on theories and techniques of the strain-gradient method that was recently introduced by the authors. This is a generalization of prior analytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where information of interest is collected along a line of symmetry of the stress field and where both the information carrying light beams are deflected in the plane of symmetry only. The developed relations were tested experimentally, by using an S-beam as representative example of general plane stress field. The main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state and to test the ranges of applicability of the accepted mathematical models and of the subsequently derived relations. In this respect, the most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and longitudinal axes of the beam are in pure shear. The obtained results are compared, at each step, with the predictions of the developed analytical models and with the predictions of Filon's stress function. The results of comparison are satisfactory. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively. The developed method can yield valuable information on the actual features of stress states in fracture mechanics. Part of the problems and first results of this investigation will be presented in the authors' paper “Strain-gradient stress analysis in Saint-Venant bending”.     

Formation of shock waves in gas-liquid foams

The purpose of the present investigation is to analyze the phenomenon of shock wave formation in gas-liquid foams and to explain the qualitative differences which are found when comparing results from shock tube experiments performed with foams and bubbly liquids. It is well known that oscillatory pressure waves in bubbly liquids may reach an amplitude twice as large as that of the original pressure impulse. However, experiments showed that pressure disturbances in foams always attenuate without significant change in the wave pressure profile. In the present study this behavior is explained by analyzing shock wave formation using the Burgers equation which is derived from the conservation laws for a bubbly liquid. It is shown that the parameter of non linearity in the Burgers equation describing wave propagation in bubbly liquids is about 40 times higher than in foams. At the same time coefficient of bulk viscosity of a foam is about 10³ times greater than that of a bubbly liquid. This explains why in shock tube experiments with foams shock waves are not detected while they are easily observed when bubbly liquids are used under similar conditions.     

Comparison of low-cycle fatigue results with axial and diametral extensometers

Low-cycle fatigue tests at room temperature have been carried out on a stainless steel and an aluminum alloy utilizing an axial extensometer with cylindrical specimens and a diametral extensometer with hour-glass specimens. In all cases, the axial strain was the controlled parameter. The results obtained with both extensometers are compared. For the materials studied, it is found that the data obtained with a diametral extensometer correspond to a somewhat longer life (by a factor of the order of 1.6 for the parameters used). Furthermore, two tests have been carried out on cylindrical specimens with both extensometers where the axial-strain computed through the diametral strain was controlled throughout the material life and the measured axial strain was simultaneously recorded. Results indicate that geometry of specimen is the predominant factor influencing fatigue life.     

Determination of thermal-expansion characteristics of metals using strain gages

A method has been developed to measure thermal-expansion characteristics of metals using bonded resistance strain gages. The method allows rapid and accurate determination of expansion properties at similar or lower cost (depending on the particular application) than conventional dilatometric techniques. Other advantages include elimination of a need for perfectly flat sample material, elimination of specimen machining, and applicability to structures and components. To utilize this technique, the ‘apparent strain’ of the gage is determined by attaching it to a ‘standard’ material for which the thermal-expansion characteristics are accurately known and subtracting the known thermal response of the material from the total gage output. ‘Apparent strain’ is therefore the temperature-induced output of the gage when bonded to a material having a thermal-expansion coefficient of zero. When the gage is then attached to a test material and cycled through the same temperature range, this ‘apparent strain’ is subtracted from the total gage output to obtain the actual unit-length change of the test material. Using this technique, mean-expansion coefficients of experimental alloys were determined over the temperature range ?320°F (?196°C) to room temperature.     

The biaxial loading response of powder aluminum at elevated temperature

Nuclear fuel can be fabricated using powder-metallurgy processes by compacting uranium-oxide powder with aluminum powder to form a cermet and then extruding the cermet to form fuel tubes. This method of production allows greater control of uranium-oxide particle size and distribution in the tube, making the production of fuel with greater concentrations of uranium oxide possible, and thus decreasing the volume of radioactive waste remaining after the fuel is spent. As the concentration of uranium oxide increases, however, there is an increase in failures during extrusion. To address this problem, an experimental procedure was developed to examine the response of powder aluminum, a material with a structure similar to that of the cermet fuel, to biaxial loadings such as those experienced during extrusion. Biaxial loadings can be varied from pure shear to simple tension or compression, or to combinations of these loadings in a numerically controlled ‘tension-torsion’ testing machine. Data obtained using this system were used to develop a model for the post-yield behavior in extruded powder aluminum which includes information derived both from the macroscopic stress-strain behavior of 1100 aluminum and extruded powder aluminum and from the observed microscopic structure of the extruded powder aluminum. This paper describes the development of the experimental system and shows the different biaxial mechanical behavior of the two materials. Test fixtures were developed and software was written to control constant strain-rate tension, compression, torsion, combined tension-torsion, and combined compression-torsion tests performed using a computer-controlled MTS biaxial testing machine. Extruded powder aluminum and 1100 aluminum specimens were tested at 427°C, the powder-aluminum extrusion temperature, under those loading conditions. Each specimen was subjected to only one loading cycle. Data were recorded during loading only. Tested specimens were also sectioned and examined microscopically.     

Explorative study of costs, effects and savings of screening for female fragile X premutation and full mutation carriers in the general population

OBJECTIVE: Evaluation of the costs, effects and savings of three strategies for female fragile X premutation and full mutation carrier screening in the general population. METHODS: We calculated the costs, effects and savings by using a general model for prenatal, preconceptional, and school carrier screening. Assumptions were based on literature data, expert opinions, prices and tariffs. RESULTS: Prenatal screening will detect most carriers and will lead to the highest number of avoided fragile X syndrome patients. The costs per detected carrier are quite similar for all screening programmes (around USD 45,000). All screening strategies have a favourable cost-savings balance (USD 14 million for prenatal screening, USD 9 million for preconceptional screening and USD 2 million for school screening). CONCLUSIONS: From an economic point of view, there is no obstacle to fragile X screening. The decision to screen or not can (and should) therefore concentrate on discussion of medical, social, psychological and ethical considerations.     

Thermal stresses in a viscoelastic three-phase composite cylinder

A thermoviscoelastic analysis of a three-phase composite cylinder is presented in this work. The solutions of the heat conduction and thermoelastic problem for three dissimilar media are derived based on the method of analytic continuation associated with the alternation technique. A rapidly convergent series solution for both the temperature and stress field, which is expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin–Maxwell model is applied to simulate the thermoviscoelastic properties while a thermorheologically simple material is considered. According to the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real time solution can then be solved numerically by taking inverse Laplace transform. Finally, some typical examples of interfacial stresses are discussed.     

Momentum and energy balances for dispersed two-phase flow

Summary The equations of motion and the mechanical energy balances for two-phase flow systems are derived by integration over a volume containing a large number of elements of the dispersed phase.List of symbols A, A boundary of volumes V, V - dA, dA surface element of A, A - A _s boundary of particles in V - dA _s surface element of A _s - F force per unit volume of the system - g –gz=gravity vector - g acceleration by gravity - I unit tensor - p pressure - Q dissipation in the continuous phase - Q _s dissipation in the dispersed phase - R compression work in the continuous phase - R _s compression work in the dispersed phase - t time - u velocity of continuous phase - u _s velocity of dispersed phase - u magnitude of u - u _s magnitude of u _s - V volume in the two-phase system - V part of V occupied by the continuous phase - W work done by F - z vertical coordinate - local volume fraction of the dispersed phase - pI–=stress tensor of the continuous phase - _s turbulent particle stress tensor - density of the continuous phase - _s density of the dispersed phase - shearing-stress tensor of the continuous phase - _s turbulent particle shearing-stress tensor - nabla operator - u, u _s velocity gradient tensor - substantial derivative (Shell Internationale Research Maatschappij N.V.)(Bataafse Internationale Petroleum Maatschappij N.V.)     

Procedure for describing the deformation of materials to fracture under conditions of near-superplasticity

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 149–157, January–February, 1995.     

Stability of a nonorthogonal stagnation flow to three-dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant-density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have applications to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, we examine the stability of this nonorthogonal flow to self-similar, three-dimensional disturbances. Stability characteristics of the flow are given as a function of the parameters of this study: ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wave number and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case. By use of this scaling, it can be shown that decreasing the angle of attack decreases the wave number and the magnitude of the temporal decay rate, thus making nonlinear effects important. For small wave numbers, it is shown that cooling the plate decreases the temporal decay of the least-stable mode, while heating the plate has the opposite effect. For moderate to large wave numbers, density variations have little effect except that there exists a range of cool plate temperatures for which these disturbances are extremely stable.This work was supported by the National Aeronautics and Space Administration under NASA Contract NAS1-18605 while the authors were in residence at the Institute for Compute Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, U.S.A.