Failure of granite cylinders under impact loading

The temporal variation of axial and radial particle velocity components on the surface of granite cylinders was measured when the latter were struck on end by like cylinders of equal diameter. The experimental results were compared with two-dimensional axisymmetric finite difference calculations in which several different constitutive models were evaluated. Fairly good agreement with experiment was obtained with a simple intuitive representation of the brittle fracture process in which locally linear elastic behavior prevailed until such time as any principal stress component exceeded in tension some small prescribed value. The subsequent failure mechanism admits the opening of cracks, multiple cracking to the point of pulverization and possible reclosure under polyaxial compression. The fracture zone development is strongly influenced by a feedback effect from the interaction of the elastic field in the virgin material with signals propagating forward from the existing fracture zone.     

Analysis of multi-layered composite cylinders under hygrothermal loading

In this study, a general stress analysis is developed for thick or thin multi-layered composite cylinders under hygrothermal loadings. The layers are oriented symmetrically and antisymmetrically for [0°/90°]₂, [30°/−30°]₂, [45°/−45°]₂ and [60°/−60°]₂ orientations. The solution is carried out on composite cylinders for plane-strain, open end and closed end conditions. Uniform and parabolic temperature distributions are chosen for the thermal loads. All the integration constants are found from the radial stress and displacement in the normal direction of layers. The hygrothermal and other mechanical properties are measured on a glass-epoxy composite layer. Some analytical solutions are compared with the finite element solutions, in which commercial software ANSYS 7.0 is utilized, and close results are obtained between them.     

Post-buckling finite element analysis of circular cylinders under end load

A simple flat facet triangular finite element, previously developed for the solution of plate and shell problems in the linear and geometrically non-linear range, is here applied to the initial and post-buckling behaviour of complete cylinders and curved panels respectively. The post-buckling calculations reproduce, at least with engineering accuracy, the typical experimentally observed formation of successive diamond shaped dimples. Such results are, of course, inaccessible to a Koiter type analysis of immediate post-buckling behaviour. The initial symmetrical buckling stress of a complete cylinder using equilateral triangular elements may be obtained in closed form and this allows a verification of convergence to the exact solution as the net is refined. Prof. Dr. Drs. h. c.J. H. Argyris is director of the Institut für Statik und Dynamik der Luft- und Raumfahrtkonstruktionen (ISD), University of Stuttgart; Prof.P. C. Dunne is in the same Institute. Paper presented at EUROMECH 69, Balatonszemes/Hungary, 13–15 April 1977.     

Stability of pressurized long inelastic cylinders under radial transverse loads

In the present paper, the structural capacity of relatively thick inelastic steel cylindrical tubes under external or internal pressure and concentrated radial loads is investigated, through a rigorous finite element analysis, as well as using a simplified analytical model. For zero pressure, the tubes exhibit inelastic cross-sectional deformation and are capable of dissipating a significant amount of plastic energy. The energy absorption capacity, as well as the ultimate transverse load, are reduced in the presence of external pressure. The effects of internal pressure are also examined. Results are reported in the form of load-deflection curves for different pressure levels. In addition, collapse envelops showing the interaction of pressure versus radial transverse loads are presented. The conclusions of this study are important for the structural integrity of cylindrical steel tubulars for pipeline and other offshore applications.     

Demagnetizing factors for cylinders

Fluxmetric (ballistic) and magnetometric demagnetizing factors N_f and N_m for cylinders as functions of susceptibility χ and the ratio γ of length to diameter have been evaluated. Using a one-dimensional model when γ⩾10, N_f was calculated for -1⩽χ<∞ and N_m was calculated for χ→∞. Using a two-dimensional model when 0.01⩽γ⩽50, an important range for magnetometer measurements, N_m and N_f were calculated for -1⩽χ<∞. Demagnetizing factors for χ<0 are applicable to superconductors. For χ=0, suitable for weakly magnetic or saturated ferromagnetic materials, N_f and N_m were computed exactly using inductance formulas     

Fatigue crack growth in thick-walled cylinders under pulsating internal pressure

The stress intensity factor is derived for both single and multiple longitudinal, elliptical cracks in the wall of a pressurized thick cylinder of given geometry. For this purpose, it is found necessary to combine known solutions to the stress intensity factor for a straight longitudinal crack with the effects of a curved crack front and multiple cracking. The analysis is appraised from a number of fatigue tests reported for % Ni-Cr-Mo cylinders with diameter ratios of between 2 and 3 under repeated and fluctuating pressure cycles. When cylinders with poorly finished bores are assumed to be initially flawed, it is found that their fatigue lives under high ranges of pressure may be predicted reliably for the single crack propagation failures observed. This analysis employs published WOL or SEN fatigue crack growth data for the alloy. The enhancement in fatigue life that results from an improved surface finish has enabled that proportion of life expended during the initiation phase to be determined. It is further shown that the observed effect of mean stress and surface finish on the fatigue limit may be quantified with a change to the threshold of stress intensity for crack growth. A number of tests were conducted with two-step changes to the amplitude of the pressure cycle. In this instance, nonlinear, stress dependent, cumulative damage rules are shown to offer no advantage over Miner's rule in the prediction of fatigue life.     

Failure of composite cylinders under combined external pressure and axial loading

An experimental and theoretical investigation was carried out into the collapse behaviour of filament wound glass fibre/epoxy cylinders under combinations of external pressure and axial loading in the third quadrant of the stress plane. Samples were tested with length-to-diameter ratios from 2·5 to 20 and diameter-to-thickness ratios in the approximate range of 20 to 40. Four ratios of hoop to axial stress were employed: ∞, 2, 1 and 0·5. The theoretical study employed a special purpose finite element program to calculate first ply failure (FPF) and buckling loads for shells of revolution made from multi-layered orthotropic materials. In all cases the experimental collapse pressure was strongly influenced by the predicted buckling failure mode. For those samples predicted to fail by buckling, agreement between the model and the experimental results was excellent. With the samples predicted to undergo FPF prior to buckling it was found that the residual strength was often sufficient to permit the buckling load to be approached.     

Fatigue and fracture characteristics of aluminum alloy cylinders under internal pressure

This paper presents the results of tensile, plane-strain fracture-toughness, and fatigue evaluations of die forged and premium cast hydraulic cylinders of six high strength aluminum alloys. Comparisons are made of fatigue strengths at stress levels related to design values, and of relations between values of K_Ic and the conditions under which unstable crack growth was observed in the fatigue tests.     

Damage evaluation and strain monitoring for composite cylinders using tin-coated FBG sensors under low-velocity impacts

Background/purposeThe impact-induced damage of composite structures induced by low-velocity impacts were evaluated to verify the damage evaluation concept using the “memory effects” of tin-coated FBG sensors.MethodsLow-velocity impact tests for the composite cylinder with tin-coated FBG sensors were performed at three impact energies. Hoop ring tests for the composite cylinder including impact-induced damage were additionally undertaken in order to measure the burst pressure and to study the parameter correlations. The test results were compared with the numerical results obtained by a finite element analysis (FEA) based on a continuum damage mechanics (CDM) considering damage model. The parameter correlations among the impact parameters and the residual strains induced by tin-coated FBG sensors were investigated based on the tests results.ResultsImpact behaviors obtained by the tests and the numerical simulation were agreed well. It was found that tin-coated FBG sensors can monitor the strain of the composite cylinder under low-velocity impacts and their strain monitoring capability is comparable to that of normally used FBG sensors. The residual strains of tin-coated FBG sensors were correlated with the impact parameters such as the impact energy, the sensing position of the sensors, and the burst pressure of the composite cylinder.ConclusionThe correlations among the residual strains and the parameters proved the damage evaluation concept for composite cylinders using the “memory effects” of tin-coated FBG sensors under low-velocity impact conditions; that is, the impact-induced damage, impact location, and burst pressure can be inversely evaluated by referring to the correlations.     

Flow of non-Newtonian fluid between two coaxial cylinders under complex shear conditions

The flow of a non-Newtonian fluid with an exponential rheological equation is investigated in the barrel of an extruder screw with consideration of the presence of circulating motion of the fluid in it.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 6, pp. 1069–1076, June, 1970.     

The torsional vibrations of marine Diesel engines under fault operation of its cylinders

The torsional vibrations calculation of Diesel engines is usually performed for different speeds of revolutions but for uniform operation and behaviour of each cylinder. This condition is true only for new of very well maintained engines but generally the different cylinders operate with considerable deviations from its design conditions. This situation may influence strongly the torsional vibrations of the system, since the spectrum of the exciting forces is different. In some cases this non uniform operation of the different cylinders may induce severe torsional stresses leading to serious vibrations or even to damage. This contribution presents same theoretical and experimental results obtained on this subject taking into account usual engines conditions showing wrong injection timing, not proper operation of the turbocharging device, incorrect valve timing, excessive wear of piston rings and/or piston liners etc. All these faults result in an exciting force spectrum that is different in frequency and/or phase from the corresponding of uniform normal operation of each cylinder. This deviating spectrum can be predicted and practical measured by the thermodynamic behaviour and the indicators diagrams of the engine and the corresponding stresses can be calculated accordingly. The torsional stresses on the intermediated shaft can measured using strain gauges method and the bridge voltage output converting to numerical file stored on a miniature computer which running with the shaft. The method reported here has been verified for two identical ship engines MIRRLEES JVSS12 having different faults. The corresponding results after both engines has been tuned properly are reported too to show the influence of the improper maintenance. The help of professorD.A. Kouremenos in the present work is greatly appreciated.     

Analyses of the multiple cracking behaviour of brittle hollow cylinders under internal pressure

In order to elucidate the multiple cracking behaviour of brittle hollow cylinders under static internal pressure, two-dimensional dynamic finite element analyses have been performed firstly for graphite hollow cylinders with inner and outer diameter of 16 and 22 mm, respectively, under internal gas pressure. In the analyses, propagation speed of the primary crack was set to be extremely high by instantaneously releasing the nodes that defined the path of the primary crack, and internal pressure was preserved after the primary cracking. The analyses showed that the stress was enhanced due to stress waves generated by the primary cracking. The initial stress enhancement was observed at the side position of the cylinder, which was located at approximately ±90° with respect to the primary cracking site. This implied that secondary cracking could occur at the side positions. Fracture modes of the cylinders might depend on the following parameters: (1) propagation speed of the primary crack, (2) pressure drop rate after the primary cracking, (3) medium to generate internal pressure, (4) geometry of a cylinder, (5) mechanical properties of brittle materials, and (6) presence of a notch. Thus, the effect of the above parameters on the behaviour of the multiple cracking was also analysed. It was found that secondary cracking would still occur at the side positions if (i) the crack propagation speed was between 70% and 100% of the theoretical crack propagation speed, (ii) the pressure drop rate was below 10⁷ Pa/s, (iii) wall thickness of the cylinder was changed, and (iv) other brittle materials were employed. Also, it was found that multiple cracking would not be observed if liquid pressure was employed instead of gas pressure, because of fluid-structure interaction. In addition, the position of the secondary cracking would be shifted by introducing a notch on the outer surface of the cylinder. These results were in good accordance with experiments formerly reported.     

On the buckling and collapse of moderately thick composite cylinders under hydrostatic pressure

This paper presents a summary of the work carried out at Washington University in recent years on the buckling and associated non-linear response and collapse of moderately thick composite cylindrical shells. Ring elements in conjunction with a three-dimensional elasticity formulation are employed in the analysis. The buckling and postbuckling imperfection sensitivity in individual modes is studied first. The problem of interaction between local and overall instabilities is then investigated in detail. Imperfection sensitivity of typical ring-stiffened shells is established by using a simple and effective approach that combines the asymptotic procedure and the amplitude modulation technique. The influence of dynamic application of the hydrostatic pressure is investigated with the simplified model. The results obtained are compared with those produced by a two-dimensional program package which includes full-fledged non-linear analysis with ring elements, and commercial programs wherever possible. The study has thrown light on several issues regarding the modeling and behavioral aspects of thick composite shells which are summarized at the conclusion of the paper.     

Use of material grading for enhanced buckling design of thin-walled composite rings/long cylinders under external pressure

This paper presents a mathematical model for enhancing the buckling stability of composite, thin-walled rings/long cylinders under external pressure using radial material grading concept. The main structure to be analyzed is built of multi-angle fibrous laminated lay-ups having different volume fractions of the constituent materials within the individual plies. This leads to a piecewise grading of the material in the radial direction. The objective is to maximize the critical buckling pressure while preserving the total structural mass at a constant value equal to that of a baseline design. The fiber volume fractions are included among the standard design variables such as fiber orientation angles and ply thicknesses, which are used by many investigators in the field. The model employs the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately is given. The critical buckling pressure contours subject to the mass equality constraint are given for several types of anisotropic rings/long cylinders showing the functional dependence of the constrained objective function on the selected design variables. It is shown that material grading can have significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits.