Research On Buckling Behavior And Prediction Method Of Large-scale Thin-walled Ellipsoidal Head Under Internal Pressure

Ellipsoidal heads are widely used as end closures of pressure equipments in many applications,such as storage tanks and reactors in chemical and oil industries,and steel nuclear containments.Ellipsoidal heads become larger and thinner as process equipments trends to be large-scale and light.For example,steel nuclear containment has a large-scale,thin-walled ellipsoidal head with a diameter of about 43 m and thickness of only about 43 mm.However,buckling may occur at large-scale and thinwalled ellipsoidal heads under internal pressure.Therefore,buckling is a critical failure mode considered in the design of ellipsoidal heads under internal pressure.However,there is a lack of extensive research on buckling behavior and mechanism for large-scale thin-walled ellipsoidal heads.The current buckling criterion does not consider the effect of head geometric parametres on buckling of ellipsoidal heads.The current prediction formulae for buckling pressure of ellipsoidal heads have disadvantages in application and accuracy.In ASME BPVC Section VIII-1 and Section VIII-2,and EN 13445-3,ellipsoidal heads are designed as torispherical heads using geometric equivalent approaches to prevent buckling failure,that is,there is no design equation only for ellipsoidal heads that fail by buckling.However,the design rules based on the geometric equivalency approaches result in uneconomical design.For Chinese pressure vessel codes GB/T150 and JB4732,there is no design equation against buckling failure of ellipsoidal heads subjected to internal pressure.Therefore,in order to develop a design method for preventing buckling failure of ellipsoidal head,it is essential to investigate prediction on buckling of ellipsoidal head under internal pressure.Research on the buckling behavior and prediction method of large-scale thinwalled ellipsoidal head under internal pressure is conducted,which is supported by the National Science and Technology Major Project of China.The main content and conclusions are shown as follows:(1)We investigated the buckling experiments of large-scale,thin-walled ellipsoidal heads(Φ5000)under internal pressure.A test fixure was designed to permits pressurizing ellipsoidal head during the test until its rupture.The initial shape and deformations of the ellipsoidal head were measured by using 3D laser scanners.A technology is studied to guarantee that large strain gauges are sealed in pressure water.The detailed experimental buckling behavior including shapes,deformations,strains of buckles and buckling pressures were obtained to verify the accuracy of the FE models for buckling analysis and to study buckling behavior of ellipsoidal heads.(2)We created FE models of ellipsoidal heads with perfect shape and shape imperfections.The arc-length method was used to perform on the FE models,taking into account the effects of material and geometrical nonlinearity.The measured initial shapes are imported into FE models.In addition,on the basis of the measured overall shape,shape imperfections were determined,and an equation was proposed to quantitatively characterize bulging of weld in the knuckle.The equation was used to develop FE models with shape imperfections.Initial buckling pressures of ellipsoidal heads were determined by nonlinear finite element analysis.The agreement between the initial experimental results and those predicted by the FE models is good.(3)Based on FE models and test results for buckling of large-scale ellipsoidal heads,we investigate buckling behavior and mechanism of ellipsoidal heads,and the effects of several parameters on buckling behavior.One or more buckles first occur at local positions in the knuckle and more buckles form progressively with increasing pressure.Some buckles gradually grow.Buckles become smaller or even disappear at relatively higher pressure.In summary,the buckling of an internally pressurized ellipsoidal head has three basis characteristics,that is,locality,progressivity and selflimitation.Higher yield strength increases buckling pressure.As the radius-to-height or diameter-to-thickness ratios decrease,buckling pressure increases,and the growth of a buckle changes from sudden to gradual.Bucking pressure increases as yield strength increases.Strain hardening can increase the resistance to buckling for ellipsoidal heads with smaller diameter-thickness ratios,but has no or little effect on buckling pressure of ellipsoidal heads with larger diameter-thickness ratios.Shape imperfection(bulging of weld)promotes the occurrence of a buckle,and buckling pressure reduces as bulging height of weld increases.The reason for the occurance of buckling is that the knuckle is under compressive stresse as the knuckle deforms inward.Compressive stresses in the knuckle become smaller or even change into tensile stresses because ellipsoidal head tends to be hemisphere with increasing pressure.Therefore,this buckling is selflimited.(4)Based on FE models and test results for buckling of ellipsoidal heads,we develop a criterion and a formula for the buckling of ellipsoidal heads in practice.Test data for twenty-one heads covers different diameters(Φ500,Φ1200,Φ1800,Φ4797,Φ5000 et al.),diameter-thickness ratios(250,400,600,872,909 et al.),diameter-height ratios(1.728,2,2.2,2.4,2.5 et al.),material(carbon steel,austenitic stainless steel et al.,)and fabrication(cold stamping,cold spinning and assembly from segments).Compared with other criterion,the criterion proposed in this paper is more accurate and more appropriate.The predictions of the new formula for actual ellipsoidal heads are in reasonably good agreement with experimental results.Compared with other formulae,the new formula has comprehensive advantage in accuracy and applicability.Based on the criterion and the new formula developed in this papar,a new design method will be developed for preventing buckling failure of internal pressurized ellipsoidal heads.