Large strain creep analysis of thick-walled cylinders

The finite-strain theory has been used to study the creep behaviour of a thick-walled cylinder under large strains. The analysis is divided into two parts. In part 1 the creep deformation of a thick-walled cylinder of an anisotropic material subjected to internal pressure has been discussed. The effect of the anisotropy has been depicted graphically. It is found that the anisotropy of the material has a significant effect on the axial stress, strain and strain rate. Part 2 of the paper deals with the creep analysis of cylinders of either isotropic or anisotropic materials subjected to combined internal and external pressures. The effect of the anisotropy is found to be similar to that found in part 1. It is seen, however, that the introduction of external pressure results in decreasing the strain rate and thus increasing the life of the cylinder.     

Collapse of thick-walled cylinders under external pressure

Hydrostatic collapse tests performed on thick-walled capped cylinders are described. Finite-element predictions which incluce the effects of end-cap stiffening, cross-section ovalities and material strain hardening are compared to experimental results. The analyses correctly predict the sequence of events leading to collapse, but experimental failure pressures are significantly below predictions. It is concluded that the von Mises yield criterion used in the analysis did not accurately represent the yield behavior of the 1018 steel tubing material of the test-cylinders for the triaxial-stress conditions of interest.     

Strain behavior of pressurized cracked thick-walled cylinders

External circumferential strains were measured on large thick-wall pressure vessels containing internal fatigue cracks, using bonded strain gages. When strains measured over the cracks become compressive they predict impending failure. Normalization by the Lamé strain relates them to the fraction of fatigue life consumed and provides estimates of longevity.     

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

In this paper, a new method for analysis of the pseudoelastic response of shape memory alloy thick-walled cylinders subjected to internal pressure is proposed. Two cases of short and long cylinders are considered by assuming the plane stress and plane strain conditions. In each case, a three-dimensional phenomenological SMA constitutive model is simplified to obtain the corresponding two-dimensional constitutive relations. The cylinder is partitioned into a finite number of narrow annular regions, and appropriate assumptions are made in order to find a closed-form solution for the equilibrium equations in each annular region. The global solution is obtained by enforcing the stress continuity condition at the interface of the annular regions and imposing the boundary conditions. Several numerical examples are presented to demonstrate the efficiency of the proposed method, and the results are compared with three-dimensional finite element simulations.     

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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Photoelastic stress analysis of machines under dynamic load

Stress processes within the elastic limit are investigated by the method of single shots in repeating the impact. Model laws and methods of interpreting results of experiments in different types of processes have been developed. Their application in practical problems and separation of principal stresses are explained.     

Photoelastic stress analysis using an object step-loading method

Sensitive, computer-aided retardation phase measurement methods suffer from the problem of discontinuity, which, in turn, hinders faultless phase unwrapping for stress determination in photoelasticity. An object step-loading method is introduced in this paper to overcome such a problem. One advantage of the technique is that the entire loading-to-stress history is computed. In this paper, the theoretical aspects related to implementation of the object step-loading method in computer-aided photoelasticity are outlined, and experimental verification is performed on a birefringent model subjected to compressive loading by comparing stress values with those computed using the theory of elasticity.     

Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading

Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading was studied by the testing of specimens made of C1045 steel and of annealed copper. Several theories were reviewed. A closed-form solution proposed by Mendelson¹² was used to predict external strains for open-end and closed-end thick-walled cylinders. An incremental theory proposed by Chu¹³ was used to provide incremental solutions for open-end thick-walled cylinders, and for cylinders subjected to nonproportionate loading. Test data for open-end and closed-end thick-walled cylinders made of C1045 steel and of annealed copper were in excellent agreement with the incremental theory. Larger values were predicted by use of the closed-form solution for circumferential strains than actual test data for open-end thick-walled cylinders at large depth of yielding. For cylinders subjected to nonproportionate loading, excellent agreement was indicated between the incremental theory and the experiments for the plot of axial load vs. circumferential strain for specimens made of both metals. Agreement between the incremental theory prediction of axial strains for the specimens made of annealed copper and test data is quite satisfactory. Larger values were predicted by the incremental theory for axial strain than experimental data for specimens made of C1045 steel. The error was conservative.     

Unloading of thick-walled cylinders that have been plastically deformed

Two analytical solutions are used to predict load-strain relations for unloading of thick-walled cylinders. The solutions assume that the material is an isotropic-hardening material that obeys the von Mises yield condition. The loading function for the material for the unloading of the cylinders was obtained from tension-compression specimens that were unloaded and reverse loaded from several points along the tension stress-strain diagram. Good agreement is indicated between the unloading load-strain curves obtained from two thick-walled cylinders made of SAE 1045 steel and the curves predicted by the analytical solutions. The analytical solutions predict that the beneficial circumferential compressive residual stresses at the inside of the cylinders decrease by about 50 percent during the unloading.     

Finite-strain pressure-tension loading of thick-walled cylinders including temperature effects

Experimental data were obtained from thick-walled cylinders made of hot-rolled SAE 1045 steel at room temperature, annealed OFHC copper at room temperature and at 500°F (260°C), and annealed aluminum alloy 1100 at room temperature and at 305° F (152° C). Experimental pressure-strain curves were compared with curves predicted by two different analytical solutions. One solution is a finite-strain, incremental, compressible analytical solution. The second solution is a finite-strain, total-strain, incompressible analytical solution which was corrected to make it applicable for compressible materials. With both solutions, the material is assumed to be an isotropic-hardening material that obeys the von Mises yield condition. The loading function for the material was obtained from tension specimens tested at the some temperature and loading rate as the thick-walled cylinders. Good agreement was found between each solution and experimental data.     

Photoelastic stress freezing analysis of total shoulder replacement systems

Photoelastic stress freezing analyses in the orthopaedic literature have, in the past, been limited to studies where bone-on-bone, bone-on-metal or ultra-high molecular weight polyethylene (UHMWPE)-on-metal constructs are modeled. In these cases photoelastic plastics are used to simulate either bone or UHMWPE as it interacts with a metal implant. In joints such as the shoulder, a UHMWPE component is often cemented directly into the scapula's glenoid concavity using polymethylmethacrylate (PMMA). While a photoelastic material can be used to simulate bone with proper load scaling, UHMWPE and PMMA have very different mechanical properties at elevated stress freezing temperatures as compared within vivo body temperature. In this study, materials were identified such that proper scaling of elastic properties at elevated temperatures was utilized to simulate the metal-UHMWPE-PMMA-bone construct. Stresses on orthogonal planes throughout the glenoid were compared for two different UHMWPE component anchoring geometries (keeled and pegged). High stresses were found at the neck of the glenoid and also at the component-bone interface beneath simulated PMMA inclusions.     

Photoelastic tests on complex intersections of reinforced thin-shell cylinders

This paper presents the three-dimensional photoelastic analyses accompanied by extensive finite-element studies of several thin-shell pressure vessels with various cylindrical intersections. The models consisted of right circular cylindrical shells with diameter-to-thickness ratios of 220, reinforced with circumferential, longitudinal and diagonal T-stiffeners. The cylindrical shells and stiffeners were intersected by various smaller cylinders producing complex intersection joints which included radial and angular fillets. Each of the models was constructed from 80 to 150 parts prepared from flat sheets, “contour-cast” shells, and milled machined parts. The model techniques as well as the machining, assembling and testing methods of the pressure vessels are presented.     

Photoelastic stress analysis of a nuclear reactor pressure vessel

Summary The state of stress from internal pressure in a nuclear reactor pressure vessel was examined using photoelastic models.The results were compared with those obtained from Eringen theoretical analysis.The Poisson ratio effect was investigated with reference to a cylinder-sphere junction.The results were also compared with photoelastic results for similar dimensions and with the values of a numerical analysis with finite element method of other authors.

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Sommario La ricerca ha come oggetto l'analisi fotoelastica dello stato di tensione in campo elastico, dovuto a pressione interna e a serraggio iniziale, nel contenitore e nella testata di un reattore nucleare.I risultati ottenuti sono stati valutati sulla base degli errori di misura e sulla base di un confronto con quelli ottenuti sperimentalmente da altri autori per geometrie non troppo diverse da quella relativa al caso studiato e con metodi numerici per la stessa geometria.Si è cercato di estendere i risultati, confrontandoli con quelli ottenuti con l'applicazione della teoria di Eringen in modo da dare loro una validità più generale.

     

Fatigue crack growth through residual stress fields—theoretical and experimental studies on thick-walled cylinders

Experiments are described which determined the effects of various residual stress distributions on the growth rate of fatigue cracks. For each stress distribution, the contribution (K_RS) to the net stress intensity at the crack tip is determined, and a comparison is then made with the behaviour predicted using a fracture mechanics approach based on a weight function analysis and a simple crack closure model. The example studied is a thickwalled pressure vessel containing a longitudinal crack which grows radially from the inner surface; fatigue cracks were grown under laboratory conditions in ring test specimens. sectioned from vessels which had been cold-expanded by different amounts to increase their pressure limits, and so contained various complex residual stress distributions. The experiments provide direct evidence that the effects of residual stress (and by extension, thermal stress) on the crack tip stress intensity may be modelled conveniently using weight function techniques, and can be incorporated satisfactorily in fatigue crack growth analyses.     

Photoelastic holography—A modern tool for stress analysis

The possibility of recording a photoelastic pattern with holography was first suggested in the literature in 1951. In the ensuing years, the capabilities and limitations of the method were examined, discussed and refined. However, the next logical step, the application of the method to the solution of engineering problems, has not followed any significant degree. One possible reason for this is a lack of appreciation of the positive benefits of the method. This paper is a survey of the role of holography in an operating photoelastic laboratory. Its intent is to emphasize the capabilities and advantages of the method, illustrate the variety of patterns that can be obtained and, finally, introduce a variation of real-time holography which offers considerable versatility.     

Photoelastic analysis of the stress field surrounding a fatigue crack

A photelastic analysis was carried out on plane polyester specimens containing a fatigue crack, in order to study the effect of plastic yielding around the crack tip on the elastic stress distribution in the vicinity of the crack. In general, results were in good agreement with values calculated for the case of a sharp-tipped crack. However, very near the crack tip, principal stresses obtained experimentally were slightly lower than calculated stresses, probably due to the bluntness of the fatigue crack. Also lines of constant stress tended to move behind the crack tip, in contrast with the calculated stresses, which occurred further forward over the field of investigation.     

Photoelastic stress analysis of a V-shaped die for plastic work

The stress state in the V-shaped die for plastic compression was investigated by using a photoelastic stress analysis in which an Araldite in a glassy elastic state and a softened celluloid were used as model materials for the die and work specimen, respectively. It was found that the direction of the frictional shear stress is reversed at a certain point on the die surface. Because the frictional shear stress of the die mainly depends on the flow speed of the work material, the popular assumption that the coefficient of friction is a constant over the die surface such as in the case of Coulomb friction appears unrealistic.