Creep and relaxation in thick-walled shrink-fitted cylinders

Summary We deal with the problem of time dependent stresses and, particularly, of the contact pressure in two thick-walled coaxial shrink-fitted cylinders, when neither of the two elements is rigid.We apply Rabotnov's phenomenological theory of creep in such a way that the integral equation, which gives the time dependent ratio between the contact pressure at a given moment and the starting pressure, is linear. We assume no volume deformation and a plane state of strain.We give the explicit solution in three examples both for an elastic inner cylinder and for a viscoelastic one, solving the integral equations of the problem both by quadratures and by the Laplace transformation inverting the transforms by a numerical method[21].

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Sommario Si affronta il problema della ricerca dell'andamento nel tempo delle tensioni e, in particolar modo, della pressione di contatto in un accoppiamento forzato tra due cilindri cavi coassiali nel caso che nessuno dei due elementi sia rigido.Si applica la teoria fenomenologica per lo scorrimento viscoso del Rabotnov in un modo tale per cui l'equazione integrale, che dà l'andamento nel tempo del rapporto tra la pressione di contatto in un dato istante e la pressione iniziale, è lineare. Si considera nulla la variazione di volume e piano lo stato di deformazione.Si dà la soluzione esplicita in tre esempi per cilindro interno sia elastico sia viscoelastico, risolvendo le equazioni integrali del problema sia per quadrature sia con l'uso della trasformata di Laplace trovando l'antitrasformata con un particolare metodo numerico di inversione[21].

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Experimental determination of stress-concentration factors in thick-walled cylinders with crossholes and sideholes

In a companion paper¹ submitted to ASME, the theoretical determination of stress-concentration factors in thick-walled cylinders was reported. The present paper reports the results of experiments conducted to check the predictions of the theory. The configuration is a thick-walled cylinder with crossholes or sideholes oriented perpendicular to the bore. Stress concentrations occur at the “tee” intersections of the holes with the bore. The loadings considered are internal pressure and external pressure. Both steel and plastic models were tested. Experiments were also conducted to determine the reduction of the stress-concentration factor by intersection radii at the crosshole intersection. Experimental results were found to agree well with theory. The best configuration was found to be one with crosshole (or sidehole) diameter equal to the bore diameter, and with an intersection radius at the tee intersection equal to the bore radius.     

A note on thermal stresses in hollow cylinders

Conclusions The extensions of Trostel's solutions derived in this paper may be employed tor general over wide conditions with a resulting error less than 3%, the stress values being too small in magnitude by this amount. The error decreases as the variation of physical properties of the media decreases or as 1/2. M. M. Stanii, Lectures in Mathematical Elasticity during summer semester 1958, Purdue University.     

Residual stresses in roller-expanded thin tubes

The residual-stress distribution of through-the-wall thickness in the roller-expanded region of thin-walled incoloy-800 Fe–Ni–Cr alloy tubing was determined. Such tubes are commonly used in the fabrication of steam generators for nuclear-power stations. For the present study, the test specimens consisted of short lengths of tubing which were roller-expanded into tubesheet simulation blocks. Some of the specimens were then heat treated. The measurement method involved the installation of strain-gage rosette strips on the inner tube wall. Strain measurements were first taken after the removal of the tubesheet simulation block. Residual stresses were then released by progressive chemical etching of the outer tube wall. In some cases the inner tube wall was etched instead and this required the removal of the inner strain-gage strip and its replacement by one attached to the outer wall. A calculation procedure based on the Sachs approach, first proposed for straight unrolled tubes, was used for determining the residual-stress distribution in the vicinity of the roller-expanded zone and through-the-wall thickness. Surface residual stresses of the order of 250 MPa were determined in the as-received specimens. Residual stresses in the stress-relieved heat-treated specimens were generally lower by about 40 percent. Contact stresses were nearly eliminated by the heat-treating process. The residual stresses in the various specimens of the same type compared to within a standard deviation of 35 MPa.     

Residual stresses in squeeze-cast aluminum rods

The longitudinal slitting technique has been applied to determining and comparing the residual stresses in as-cast and squeeze-cast aluminum rods. Residual stresses in the squeeze-cast aluminum alloy rods are found to increase with applied punch pressures under a constant die-base thermocouple reference temperature. For the variations of residual stresses with varying die-base thermocouple reference temperatures, a peak residual stress is found to occur at a die-base thermocouple reference temperature of 100° C. A semi-empirical formula is derived for the determination of the maximum longitudinal residual stress in the tapered cylindrical as-cast aluminum alloy, from which the maximum longitudinal residual stresses for squeeze cast can be determined, using the residual-stress ratios obtained experimentally     

Residual stresses in gas-assisted injection molding

Residual stresses are a major issue in the mechanical and optical behavior of injection-molded parts. In this study, we analyze their development in the case of gas-assisted injection molding (GAIM) of amorphous polymers. Flow-induced residual stresses are computed within a decoupled approach, in which elastic effects are neglected in the momentum balance, assuming a generalized Newtonian material behavior. In a staggered procedure, the computed viscous flow kinematics are used to calculate normal stresses employing a compressible version of the Rolie-Poly model. For the computation of thermally and pressure-induced residual stresses, a linear thermo-viscoelastic model is used. A 3-D finite element model for GAIM is employed, which is able to capture the kinematics of the flow front and whose capabilities to predict the thickness of the residual material layer have been validated by Haagh and Van de Vosse (Int J Numer Methods Fluids 28:1355–1369, 1998). In order to establish a clear comparison, the development of residual stresses is analyzed using standard injection molding and GAIM for a test geometry.     

Residual stresses in evaporated AI-Si films

Residual stresses in vacuum evaporated thin Al-Si films were evaluated by measuring the deflection of a thin cantilevered substrate during removal of the film. Post-thermal treatment and thermal cyclings at temperatures between ?269° C and 560° C were also introduced to determine their effects on the residual stresses of the films.     

Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties

This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.     

Residual stresses in cyclically loaded two-phase solid

A plane-stress finite element model of a two-phase solid is analyzed for residual stresses that develop under cyclic loading. One phase is assumed to be dilute and to yield at stresses below those of the matrix. Simple triangular constant strain finite elements are used and the soft material is assumed to be a linear work hardening one. The load is applied incrementally and the stiffness matrix is updated at each step to its tangential values. The emphasis is on the residual stresses which develop within the soft element and in the neighborhood. Several distributions of soft material were examined. In the cases we consider, the residual stresses change sign on each load cycle, that is, they are not constant. They are also an appreciable percentage of the yield stress of the soft phase. The residual stresses primarily develop in the first cycle and settle down in just a few cycles. The location of a soft element is somewhat of a factor in how far away its effect is felt by other elements. In addition to the calculation of residual stresses, the temperature changes are also calculated. The plastic work is converted into heat in the soft elements and this in turn is conducted to the cooler elastic matrix. It is found that adiabatic conditions can be assumed for steel specimens for strain rates above .033 sec⁻¹ and at rates above .23 sec⁻¹ for aluminum.     

Residual stresses in turned AISI 4340 steel

The residual-stress distribution in the surface region of workpieces of annealed AISI 4340 steel that is turned under unlubricated conditions is determined using a deflection etching technique. The absolute value of the residual stresses at the machined surface are low and increase with an increase in depth beneath the machined surface to a maximum. They then decrease with a further increase in depth eventually becoming vanishingly small. Peak residual stresses are tensile at cutting speeds of 0.5 and 1.0 ms⁻¹ and are compressive at a cutting speed of 1.5 ms⁻¹ for all feed rates and depths of cut. Peak residual stresses and depth of the stressed region increase with an increase in feed rate and depth of cut, but decrease with an increase in cutting speed. The results of this investigation can be interpreted in terms of the variation of tool forces with cutting conditions.     

Residual stresses in plastically encapsulated microelectronic devices

The residual stresses in a model of a plastically encapsulated microelectronic device are determined photoelastically using birefringent transfer-molding compounds. The measured stresses are compared with a laminated-platetheory analysis and then used to guide a two-dimensional finite-element analysis of the device. Photoelasticity was also used to determine the effects of postcure on the residualstress distribution.     

Residual stresses in silicon-on-sapphire thin film systems

This paper uses the finite element method to analyse the generation and evolution of residual stress in silicon-on-sapphire thin film systems during cooling. The effects of material properties, thin film structures and processing conditions, on the stress distribution were explored in detail. It was found that under certain conditions, significant stress concentration and discontinuity can take place to initiate crack and/or delamination in the systems. However, these can be minimised by controlling the buffer layer thickness.     

Residual stresses in thick electrodeposits of a nickel-cobalt alloy

Some electroplated metals contain residual stresses which can cause warpage or premature failure of parts plated or electrofomed with these materials. Noticeably absent from the literature are residual-stress data for finished parts. Typically for plated or electroformed parts, residual stresses are determined independently on thin strips and then piece parts are plated. This research describes a technique which can be used to measure stress on finished parts. The method involves drilling a hole in the part and measuring the resulting change of strain in the vicinity of the hole. Viability of this technique was demonstrated by measuring the stress in a nickel-cobalt deposit plated on an aluminum cylinder. Two separate runs, one 50 deg removed from the other, provided almost identical results; stress was 160 MN/m² (23,200 psi). Two other runs in a region where plating was somewhat thinner provided slightly lower results probably because all boundary-condition requirements were not met. The computed residual-stress values compared quite favorably with independent rigid-strip measurements of 131 MN/m² (19,000 psi) obtained for the solution before and after plating of the cylinder.