Experimental and numerical study of hypervelocity impact damage on composite overwrapped pressure vessels

Ground-based tests are important for studying hypervelocity impact(HVI)damage to spacecraft pressure vessels in the orbital debris environment.We analyzed the damage to composite overwrapped pressure vessels(COPVs)in the HVI tests and classified the damage into non-catastrophic damage and catastrophic damage.We proposed a numerical simulation method to further study non-catastrophic damage and revealed the characteristics and mechanisms of non-catastrophic damage affected by impact conditions and internal pressures.The fragments of the catastrophically damaged COPVs were collected after the tests.The crack distribution and propagation process of the catastrophic ruptures of the COPVs were analyzed.Our findings contribute to understanding the damage characteristics and mechanisms of COPVs by HVIs.

Exploration on the Optimization Strategy for the Layup of Composite Material Pressure Vessels Based on Advanced Algorithms

This study aims to explore the influence of the laying angle on the pressure shell structure made of composite materials under the condition of a fixed shape. By using a composite material composed of a mixture of T800 carbon fiber and AG80 epoxy resin to design pressure vessels, this material combination can significantly improve the interlaminar shear strength and heat resistance. The article elaborates on the basic concepts and failure criteria of composite materials, such as the maximum stress criterion, the maximum strain criterion, the Tsai-Hill criterion, etc. With the help of the APDL parametric modeling language, the arc-shaped, parabolic, elliptical, and fitting curve-shaped pressure vessel models are accurately constructed, and the material property settings and mesh division are completed. Subsequently, APDL is used for static analysis, and the genetic algorithm toolbox built into Matlab is combined to carry out optimization calculations to determine the optimal laying angle. The research results show that the equivalent stress corresponding to the optimal laying angle of the arc-shaped pressure vessel is 5.3685e+08 Pa, the elliptical one is 5.1969e+08 Pa, the parabolic one is 5.8692e+08 Pa, and the fitting curve-shaped one is 5.36862e+08 Pa. Among them, the stress distribution of the fitting curve-shaped pressure vessel is relatively more uniform, with a deformation of 0.568E−03 m, a minimum equivalent stress value of 0.261E+09 Pa, a maximum equivalent stress value of 0.537E+09 Pa, and a ratio of 0.48, which conforms to the equivalent stress criterion. In addition, the fitting curve of this model can adapt to various models and has higher practical value. However, the stress distribution of the elliptical and parabolic pressure vessels is uneven, and their applicability is poor. In the future, further exploration can be conducted on the application of the fitting curve model in composite materials to optimize the design of pressure vessels. This study provides important theoretical support and practical guidance for the design of composite material pressure vessels.

Load Bearing Capacity and Safety Analysis for Strain-hardening Austenitic Stainless Steel Pressure Vessels

By increasing the yield strengths of austenitic stainless steels for pressure vessels with strain hardening techniques,the elastic load bearing capacity of austenitic stainless steel pressure vessels can be significantly improved.Two kinds of strain hardening methods are often used for austenitic stainless steel pressure vessels：Avesta model for ambient temperature applications and Ardeform model for cryogenic temperature applications.Both methods are obtained from conventional design rules based on the linear elastic theory,and only consider the hardening effect from materials.Consequently this limits the applications of strain hardening techniques for austenitic stainless steel pressure vessels because of safety concerns.This paper investigates the effect of strain hardening on the load bearing capacity of austenitic stainless steel pressure vessels under large deformation,based on the elastic-plastic theory.Firstly,to understand the effect of strain hardening on material behavior,the plastic instability loads of a round tensile bar specimen are derived under two different loading paths and validated by experiments.Secondly,to investigate the effect of strain hardening on pressure vessels strength, the plastic instability pressure under strain hardening is derived and further validated by finite element simulations.Further,the safety margin of pressure vessels after strain hardening is analyzed by comparing the safety factor values calculated from bursting tests,finite element analyses,and standards.The researching results show that the load bearing capacity of pressure vessels at ambient temperature is independent of the loading history when the effects of both material strain hardening and structural deformation are considered.Finite element simulations and bursting tests results show that the minimum safety factor of austenitic stainless steel pressure vessels with 5% strain hardening is close to the recommended value for common pressure vessels specified in the European pressure vessel standard.The proposed study also shows that in the strain hardening design of austenitic stainless steel pressure vessels,the calculation for plastic instability pressure could use theoretical formula or finite element analyses based on geometrical dimensions and material property parameters before strain hardening,but a 5%strain should be employed as a design limit.The proposed research can be used for the strain hardening design of austenitic stainless steel pressure vessels safely.

Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials

This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement, strains, and stresses are determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.

Recent development in standards of steels used for pressure vessels in China

In this paper,five items of standards of steels used for pressure vessels which are issued recently or about to be issued and put into effect have been introduced.The differences of standards mentioned above and the former standards and the primary qualifications have been formulated.These qualifications indicate that,some qualifications of national standards of steels used for pressure vessels are on the international advanced level.

Microstructure and properties of S30403+Q345R roll-bonded clad steel plate for pressure vessels

To meet the demand of the domestic pressure vessel industry for roll-bonded clad steel plates, Baosteel has developed an S30403 ＋ Q345R roll-bonded clad steel plate. Comprehensive inspections of the composition, microstructure, and properties are made to systematically evaluate the steel plate in the normalized and normalized ＋ stress relieved states. The results show the cladding interface of the S30403 ＋ Q345R roll-bonded clad steel plate has high shear strength, the base metal has good properties, and the mechanical properties of the steel plate head and tail are uniform. The performance is fully consistent with the technical requirements of the roll-bonded clad steel plate for pressure vessels.

Development of S11306+SA516Gr70 roll-bonded clad steel plate for pressure vessels

To meet the demand of the pressure vessel industry, Baosteel has developed an S11306 ＋ SA516Gr70 roll-bonded clad steel plate. Comprehensive inspections of the composition, microstructure, and properties are performed to systematically evaluate the steel plate in normalized state and normalized ＋ stress relieved state. The results show the cladding interface of the Sl1306 ＋ SA516Gr70 roll-bonded clad steel plate has high shear strength, and the base metal has good mechanical properties. The performance is fully consistent with the technical requirements of the roll-bonded clad steel plate for pressure vessels.

Stress Analysis of Thin-Walled Pressure Vessels

This paper discusses the stresses developed in a thin-walled pressure vessels. Pressure vessels (cylindrical or spherical) are designed to hold gases or liquids at a pressure substantially higher than the ambient pressure. Equations of static equilibrium along with the free body diagrams will be used to determine the normal stresses in the circumferential or hoop direction and in the longitudinal or axial direction. A case study of internal pressure developed in a soda can was determined by measuring the elastic strains of the surface of the soda can through strain gages attached to the can and connected to Strain indicator Vishay model 3800.

RADIAL VIBRATIONS OF AXISYMMETRICALLY LOADED STEPPED PRESSURE VESSELS

Differential equations of free/forced radial vibrations of axisymmetrically loaded stepped pressure vessels are established by using singular functions. Furthermore, their general solutions are solved, the expression of vibration mode function and frequency equations on usual supports are derived with W operator and the forced response of such vessels are calculated.

NUMERICAL INVESTIGATION OF THE LIMIT LOADS FOR PRESSURE VESSELS WITH PART-THROUGH SLOTS

A numerical investigation of the limit loads is carried out for pressure vessels with part-through slots using a general computational method for the limit analysis of 3-D structures. The limit pressures are given for a comprehensive range of geometric parameters. Some of the calculated results are compared with the results of 3-D elastic-plastic finite element analysis and existing numerical solutions. The effects of various shapes and sizes of part-through slots on the load carrying capacity of cylindrical shells are investigated and evaluated. Two kinds of typical failure modes corresponding to different dimensions of slots are studied. Based on the numerical results, a geometric parameter G which combines the slot dimensions and the cylinder geometry is presented. It reasonably reflects the overall effect of slots on the limit loads of cylinders. An empirical formula for estimating the limit pressures of cylindrical shells with part-through slots is obtained.

Expert system for evaluating the safety of pressure vessels

With more application of welding technology in important structures more attention was paid to the evaluation of the safety of welded structures, the life prediction and decision to repair the welded structures. Based on material fracture mechanism and Chinese standard of safety evaluations of pressure vessels, an expert system was developed to evaluate the safety of welded pressure vessels. The system can analyze the weld defects in a pressure vessel, convert different kinds of defects into equivalent cracks and obtain their equivalent sizes. Furthermore, the system can calculate the stress and strain in the positions of weld defects and make decision on whether the defects are tolerable or not according to the code. When it is tolerable, the system will calculate the safety margin. The fatigue life can be predicted if the defects undergo fatigue load too. Moreover, data bases are built for storing mechanical properties of material and evaluated results.

Free Vibration Analysis of FG-CNTRC Cylindrical Pressure Vessels Resting on Pasternak Foundation with Various Boundary Conditions

This study focuses on vibration analysis of cylindrical pressure vessels constructed by functionally graded carbon nanotube reinforced composites(FG-CNTRC).The vessel is under internal pressure and surrounded by a Pasternak foundation.This investigation was founded based on two-dimensional elastic analysis and used Hamilton’s principle to drive the governing equations.The deformations and effective-mechanical properties of the reinforced structure were elicited from the first-order shear theory(FSDT)and rule of mixture,respectively.The main goal of this study is to show the effects of various design parameters such as boundary conditions,reinforcement distribution,foundation parameters,and aspect ratio on the free vibration characteristics of the structure.

Finite Element Modeling of Variable Membrane Thickness for Field Fabricated Spherical (LNG) Pressure Vessels

This study investigated thickness requirements for field fabricated (large) spherical liquefied natural gas (LNG) pressure vessels using the finite element method. In the FEM modeling, 3-dimenisonal analysis was used to determine thickness requirements at different sections of a 5-m radius spherical vessels based on the allowable stress of the material as given in ASME Section II Part D. Shallow triangular element based on shallow shell formation was employed using area coordinate system which had been proved better than the global coordinate system in an earlier work of the authors applied to shop built vessels. This element has five degrees of freedom at each corner node-five of which are the essential external degrees of freedom excluding nodal degree of freedom associated with in plane shell rotation. Set of equations resulting from Finite Element Analysis were solved with computer programme code written in FORTRAN 90 while the thickness requirements of each section of spherical pressure vessels subjected to different loading conditions were determined. The results showed membrane thickness decreasing from the base upwards for LNG vessels but constant thickness for compressed gas vessels. The obtained results were validated using values obtained from ASME Section VIII Part UG. The results showed no significant difference (P > 0.05) with values obtained through ASME Section VIII Part UG.

Non-destructive Evaluation of Composite Pressure Vessel by Using FBG Sensors

In recent years, advanced composite structures are used extensively in many industries such as aerospace, aircraft, automobile, pipeline and civil engineering. Reliability and safety are crucial requirements posed by them to the advanced composite structures be- cause of their harsh working conditions. Therefore, as a very important measure, structural health monitoring （SHM） in-service is deft- nitely demanded for ensuring their safe working in-situ. In this paper, fiber Bragg grating （FBG） sensors are surface-mounted on the hoop and in the axial directions of a FRP pressure vessel to monitor the strain status during its pressurization. The experimental results show that the FBG sensors could be used to monitor the strain development and determine the ultimate failure strain of the composite pressure vessel.

Calculations of plastic collapse load of pressure vessel using FEA

This paper proposes a theoretical method using finite element analysis(FEA) to calculate the plastic collapse loads of pressure vessels under internal pressure,and compares the analytical methods according to three criteria stated in the ASME Boiler Pressure Vessel Code. First,a finite element technique using the arc-length algorithm and the restart analysis is developed to conduct the plastic collapse analysis of vessels,which includes the material and geometry non-linear properties of vessels. Second,as the mechanical properties of vessels are assumed to be elastic-perfectly plastic,the limit load analysis is performed by em-ploying the Newton-Raphson algorithm,while the limit pressure of vessels is obtained by the twice-elastic-slope method and the tangent intersection method respectively to avoid excessive deformation. Finally,the elastic stress analysis under working pressure is conducted and the stress strength of vessels is checked by sorting the stress results. The results are compared with those obtained by experiments and other existing models. This work provides a reference for the selection of the failure criteria and the calculation of the plastic collapse load.

Optimal design of pressure vessel using an improved genetic algorithm

As the idea of simulated annealing (SA) is introduced into the fitness function, an improved genetic algorithm (GA) is proposed to perform the optimal design of a pressure vessel which aims to attain the minimum weight under burst pressure con- straint. The actual burst pressure is calculated using the arc-length and restart analysis in finite element analysis (FEA). A penalty function in the fitness function is proposed to deal with the constrained problem. The effects of the population size and the number of generations in the GA on the weight and burst pressure of the vessel are explored. The optimization results using the proposed GA are also compared with those using the simple GA and the conventional Monte Carlo method.

Research on reasonable winding angle of ribbons of Flat Steel Ribbon Wound Pressure Vessel

Flat Steel Ribbon Wound Pressure Vessels (FSRWPVs) are used in many important industry areas. There is no such kind of pressure vessel exploding on operation for its reasonable structure design. Many explosion experiments on Flat Steel Ribbon Wound Pressure Vessel showed that their limited load pressure is related to the winding angle of the steel ribbons. FSRWPVs with reasonable winding angle have better security and lower cost. Reasonable angels given at the end of this paper facilitate engineering design.

Integrated Design of D.D.I., Filament Winding and Curing Processes for Manufacturing the High Pressure Vessel(Type Ⅱ)

As energy crisis and environment pollution all around the world threaten the widespread use of fossil fuels,compressed natural gas(CNG)vehicles are explored as an alternative to the conventional gasoline powered vehicles.Because of the limited space available for the car,the composite pressure vessel(TypeⅡ)has been applied to the CNG vehicles to reach large capacity and weight lightening vehicles.High pressure vessel(TypeⅡ)is composed of a composite layer and a metal liner.The metal liner is formed by the deep drawing and ironing(D.D.I.)process,which is a complex process of deep drawing and ironing.The cylinder part is reinforced by composite layer wrapped through the filament winding process and is bonded to the liner by the curing process.In this study,an integrated design method was presented by establishing the techniques for FE analysis of entire processes(D.D.I.,filament winding and curing processes)to manufacture the CNG composite pressure vessel(TypeⅡ).Dimensions of the dies and the punches of the 1 st(cup drawing),2 nd(redrawing-ironing 1-ironing 2)and 3 rd(redrawing-ironing)stages were calculated theoretically,and shape of tractrix die to be satisfied with the minimum forming load was suggested for life improvement and manufacturing costs in the D.D.I.process.Thickness of the composite material was determined in the filament winding process,finally,conditions of the curing process(number of heating stage,curing temperature,heating rate and time)were proposed to reinforce adhesive strength between the composite layers.

ESTIMATE OF BURSTING PRESSURE OF MILD STEEL PRESSURE VESSEL AND PRESENTATION OF BURSTING FORMULA

In order to get more precise bursting pressure formula of mild steel, hundreds of bursting experiments of mild steel pressure vessels such as Q235（Gr.D） and 20R（1020） are done. Based on statistical data of bursting pressure and modification of Faupel formula, a more precise modified formula is given out according to the experimental data. It is proved to be more accurate after examining other bursting pressure value presented in many references. This bursting formula is very accurate in these experiments using pressure vessels with different diameter and shell thickness. Obviously, this modified bursting formula can be used in mild steel pressure vessels with different diameter and thickness of shell.

PROBLEM OF HYDRODYNAMIC PRESSURE ON SUDDENLY STARTING VESSEL

In this paper, Lagrangian method is applied to discuss the problem of the hydrodynamic pressure on a suddenly starting vessel. The free surface profile and the coefficients of the hydrodynamic pressure im the vessel wall are obtained. And it is verified that the singularity of the pressure near the free surface is only logarithmic.