Steel Cylindrical Shells Research Articles

Effect of pre-shock on the expanding fracture behavior of 1045 steel cylindrical shell under internal explosive loading

Explosively driven expansion fractures in metallic shells will be preceded by a compression shock wave, which inevitably changes the mechanical and microstructural state of the shell materials and thus affects their subsequent dynamic deformation and expansion fracture processes. To understand the influence of pre-shock pressure on the dynamic expansion fracture behavior of metallic shells, the incident shock waves with varying peak pressure were generated in a 1045 steel cylindrical shell by sweeping detonation wave loading. The pre-shock and subsequent expansion fracture processes were continuously diagnosed by combining a high-speed framing camera and the arrayed Photon Doppler Velocimetry (PDV) measurements to obtain the fracture strains at different axial positions (corresponding to different pre-shock pressures). The results clearly show that the pre-shock pressure during detonation loading has a significant effect on the expansion fracture properties of the 1045 steel cylinder; the fracture strain remarkably decreases with the increase of pre-shock pressure from ∼19 GPa to ∼20 GPa and then changes gently in the range of ∼20 GPa to ∼22 GPa. Metallurgical analyses reveal increased densities of microstructural defects, including dislocations and deformation twins, when a shock wave passes through, resulting in a reduced capacity for further defect storage in the shocked metals, ultimately leading to a decrease in the fracture strain during the subsequent expansion deformation process.

Optimization of Vibro-Acoustic Characteristics of Cold Rolled Sandwich Steel Cylindrical Shell with Internal Voids Using Response Surface Methodology

Optimization of Vibro-Acoustic Characteristics of Cold Rolled Sandwich Steel Cylindrical Shell with Internal Voids Using Response Surface Methodology

Theoretical calculation methods of stable bearing capacity for thin-walled shells with corrosion and variable temperature

AbstractThin-wall shells (steel plates, steel cylindrical shells, steel spherical shells, etc.) are widely used in many engineering fields such as construction, machinery, chemical industry, navigation, and aviation because of their light weight and high strength. Their failure modes under static pressure or impact dynamic load are mostly buckling instability, and the failure is very sudden, often causing structural failure or even catastrophic accidents without obvious symptoms. In this framework, the significance of this paper is that it considers the influence of external environment corrosion on steel shells' bearing capacity using plate and shell classical stability theory, and investigates the stable bearing capacity of thin-wall steel shells in view of corrosion impact. By this approach, a theoretical calculating method for the time-varying stable bearing capacity of plate and shell thin-walled steel members under the simultaneous action of corrosion and temperature changes is obtained, providing a useful theory for complex engineering practices such as corrosion and temperature changes, including fire actions. Noted that for this method with no analytical solution found, its numerical solutions are given in the appendixes.

Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed. This study investigated the fragmentation performance of a new high-carbon silicon-manganese (HCSiMn) steel cylindrical shell through fragment recovery experiments. Compared with the conventional 45Cr steel shell, the number of small mass fragments produced by the HCSiMn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model. The fragmentation process of the HCSiMn shell exhibited more brittle tensile fracture characteristics, with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation. On the one hand, the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite, so that microscopic intergranular fracture reduces the characteristic mass of the fragments; on the other hand, the distribution of alloy carbides can exert a "pinning" effect on the substrate grains, causing more initial cracks to form and propagate along the brittle carbides, further improving the shell fragmentation. Although the killing power radius for light armored vehicles was slightly reduced by about 6%, the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26% based on theoretical assessment. These results provided an experimental basis for high fragmentation warhead design, and to some extent, revealed the correlation mechanism between metallographic structure and shell fragmentation.

Behaviour of circumferential and helical guided waves in two-layered composite cylindrical shell

A model of the acoustic scattering of a plane wave incident obliquely upon an infinite elastic bi-layered cylindrical shell is developed based on normal mode expansion technique. The far field backscattering form function for the composite copper/stainless steel cylindrical shell is calculated for reduced frequency range of k⊥a1=0–70 and for different values of incident angles α (k⊥=k1cos⁡α, k1 is the wave number in the fluid surrounding the shell and a1 is the outer radius of the shell). Numerical calculations show the behaviour of the resonances of circumferential and helical guided waves as the angle of incidence increases. The obtained results are compared with those of copper and stainless steel one-layered cylindrical shells. The use of frequency-angle representation depicts the helical propagation of surface waves along the axis of the shell. This representation, along with the identification plan, enables to describe the evolution of acoustic scattering as a function of incidence angle and vibration mode n. Furthermore, a comparative analysis of the resonance trajectory evolution between mono-layered and composite cylindrical shells is performed. The evolution of the helical guided waves, the bifurcation of the A0 wave into the A0− and A0+ waves, and a region with high backscattering are investigated. The presented results show that the extension of the region with high backscattering depends on the thickness and physical properties of the bi-layered cylindrical shell.

Experiment‐based statistical distribution of buckling loads of cylindrical shells

AbstractA silo structure is usually constructed in the form of a cylindrical steel shell. It has the advantages of being lightweight, having a short construction period, and possessing a large storage space. It has been widely used in many fields of industry. Thin‐walled cylindrical shells often exhibit buckling failure and the experimental buckling load is usually lower than calculation results from classical theory and simulation without geometrical imperfection. Besides, test results with carefully conducted similar specimens still have substantial scatter due to imperfection sensitivity. The nonlinear analysis with FEM can obtain a high‐precision result comparing the experiment if the geometric parameters of the shell are fully known. However, this is almost impossible in practical engineering. The initial geometric imperfections and shell thickness of cylindrical shells are complex and random properties. Theoretically, these geometric imperfections can be described using a random field. This paper presents the experimental investigation of buckling analysis of cylindrical shells under axial compression considering the randomness of geometric imperfections and thickness. A total of 12 cylindrical shell specimens were fabricated and tested. Based on the test results, the optimal statistical distribution is obtained by the maximum entropy fitting method and the obtained results were compared with geometric imperfections based on laser scan measurements.

Localized Perturbation Load Approach for Buckling Design of Thin-Walled Steel Cylindrical Shells under Partial Axial Compression

A thin-walled steel cylindrical shell is a common engineering structure that has an efficient load-carrying capacity. This structure is more easily subjected to partial axial compression loads in application, and buckling is the main failure mode. However, there are few available design methods for partial axially compressed steel cylindrical shells. Motivated by this, a design method called the localized perturbation load approach (LPLA) is proposed in this paper. The finite element framework for the application of LPLA is established. The location and number of perturbation loads are determined by considering the imperfection sensitivity and the buckling failure mode of partial axial compressed cylinders. A series of buckling experiments are carried out to validate the LPLA method. In addition, the reliability of LPLA for the design of cylindrical shells with different imperfection locations and dimensions is also verified. The results show that LPLA can give conservative and reliable lower-bound buckling loads. Therefore, LPLA can be used as a design method for thin-walled steel cylindrical shell structures under partial axial compression in actual engineering.

Backscattering enhancements by partially exposed cylindrical shells due to reflected flexural waves at air–water interfaces

For smooth curved objects in contact with a flat interface, the propagation paths of supported surface elastic waves can be altered by the interface, thereby enhancing the characteristics of the backscattered echo returns. In this study, backscattering experiments are conducted on an empty stainless steel cylindrical shell that breaks through an air–water interface and is insonified from below at grazing incidence. The shell has a thickness-to-radius ratio of 5%. The frequencies of interest fall within the vicinity of and below the coincidence frequency, which corresponds to a ka range of 13.8–20.1. The experimental results demonstrate that, for the partially exposed cylindrical shell, the flexural waves can traverse the interface and circumnavigate the shell multiple times. The flexural waves experience mode transitions upon passing through the interface, existing as a0− waves below the interface and a0 waves above the interface. Simultaneously, the flexural waves undergo partial reflection each time they pass through the interface, guiding them to follow a reverse path and generating a periodic series of echo returns, which leads to the enhancement of backscattering. The shift in resonance frequency in relation to the changing exposure is analyzed and predicted using the phase matching theory.

Nonlinear stability analysis of high-strength steel cylindrical shells under global bending

Most of the current research in high-strength steel focuses on high-strength steel axial compression members, and the cross-section forms are mainly welded H-shaped sections and box sections. However, few studies focus on the mechanical behaviour of high-strength steel cylindrical shells in bending, especially the different failure characteristics with changing slenderness ratios have not been comprehensively studied. Many thin cylindrical shells with dominant loading conditions of global bending are normally in medium aspect ratios, and their thickness lies in an uncomfortable range with buckling behaviour affected by both imperfections and plasticity. The key common applications of these shells are turbine towers, transmission towers, tall silos and tubular piles.It is not easy to define the strength of these shells due to the difficulty to harmonise the different failure modes as the slenderness ratio of the member changes. This paper explores the load-bearing capacity of high-strength steel cylindrical shells with a yield strength of 690 MPa under global bending. The effects of residual stress, pre-buckling deformation and material plasticity on load-bearing capacity were investigated. Different failure characteristics were defined as the slenderness ratio is changed. The bearing capacity curves were obtained based on the method in the European Code for Design of Steel Structures EN1993-1-6(2007). The expressions of the parameters to describe the bearing capacity curves were proposed. It is hoped that the results will provide a scientific and useful reference for the design of high-strength steel cylindrical shells in medium length under global bending.

Geometric properties and imperfections influence on buckling behavior of Variable-Thickness steel cylindrical shells subjected to combined Loading: Experimental and numerical study

In this study, a total of five cylindrical shells with different stepwise wall thicknesses and varying geometric ratios (including Length-to-radius ratio (L/R) and radius-to-thickness ratio (R/t)) were subjected to the same axial pre-compression, followed by a uniform external pressure load, with the axial pre-compression value being constant. The primary objective of this study was to evaluate the buckling capacity, crustal cross-section deformation in the middle of each strake, and failure mechanism in the specimens. The results indicated that the shell with the lowest L/R and R/t ratios demonstrated the highest buckling capacity and exhibited more stability during failure.Furthermore, the experiments were conducted to verify the accuracy of nonlinear finite element analyses by employing ABAQUS FEA. Then, the simulated method was utilized to numerically investigate the effect of the geometric properties, pattern distribution thickness in the height of shells, the number of strakes, and geometric imperfection of the full-scale cylindrical shells. The findings revealed that the distribution of buckling waves and buckling capacity for cylindrical shells with variable thickness strongly depended on the thickened region and the coefficient of distribution thickness pattern in the height of shells. Additionally, in cylindrical shells with varying stepwise wall thickness, the sensitivity to imperfection increased with increasing axial pre-compression.

Formation of a corrugated inner surface of a steel cylindrical shell by local deformation

Formation of a corrugated inner surface of a steel cylindrical shell by local deformation

Uncovering the fracture behavior of metallic cylindrical shells under internal explosive loadings via careful design of densely-arranged multi-point photon Doppler velocimetry measurements

While the expanding process of cylindrical shells under internal explosive loadings is fundamental and ubiquitous in engineering applications, the comprehensive understanding of the underlying mechanism is still a challenge due to the limitation of the spatial resolution on the current diagnostic techniques. To address this issue, an improved densely-arranged multi-point photon Doppler velocimetry (DMPDV) technique with enough spatial resolution to capture the local dynamical evolution was carefully designed. The DMPDV technique was then applied to investigate the expanding behavior of an explosively driven 304 L stainless steel cylindrical shell. As a step beyond the coarse understanding of the overall dynamical response, the expanding process can then be demonstrated comprehensively with more exact concentrations on one fragment. By the combination of DMPDV and high-speed photography, we uncovered the evolution of the expanding process which can be divided into three stages: (1) In the beginning, due to the symmetries of the specimen and the loading, the cylinder expands uniformly and all the velocity-time curves at different hoop positions are coincide with each other. (2) after the emergence of cracks at the outer surface of the cylinder, the velocity-time curves start to separate from each other and are regularly arranged according to their test positions. (3) following the penetration of the crack through the thickness of the cylinder, there is a reverse in the velocity-time curves and the fragments begin to rotate, the rotation angle can be estimated using the velocity difference. The hidden mechanism is then revealed with the help of unloading wave theory and rigid body dynamics. Here the second stage is dominated by unloading wave while the last stage is controlled by the denotation products. These experimental results provide deep insight into the detailed fracture behavior of expanding cylindrical shell and are further validated by the Mott wave models as well as numerical simulations, respectively.

Buckling response of externally pressurised sealed and retrofitted steel cylindrical shells

Buckling response of steel cylindrical shells with no reinforcement or seal, cylindrical shells reinforced with CFRP, and cylindrical shells sealed against leakage was experimentally compared. Twelve cylindrical shells were tested; four had no reinforcement/seal, four were reinforced with CFRP, and four were sealed. The cylindrical shells had the same radius-to-thickness ratio of 445 but had various height-to-radius ratios of 2, 4, and 6. Results indicated that the buckling capacity of the shells decreased with increasing the shell height. Whilst a post-buckling response was established for the sealed shells, CFRP-reinforced shells had no post-buckling response. CFRP reinforcement significantly increased the shells' initial and overall buckling load, but the sealing was only effective in the initial buckling load.

A numerical perspective for CFRP‐wrapped thin‐walled steel cylinders

AbstractThe failure of steel cylindrical shells with carbon fiber‐reinforced polymers (CFRP) under hydrostatic pressure is studied in this article by experimental tests and the finite element method. Simulations were performed for 12 cylindrical shells with different dent numbers, dent depths, and two perfect models with and without CFRP. The finite element models are built to simulate the buckling behavior. The nonlinear stabilization method is preferred to simulate the buckling behavior. The finite element results agree well with the corresponding experimental tests and theories. A parametric study is conducted, and the number, depth, width of dents, and the effects of CFRPs on the critical buckling pressure are discussed. The dents are placed symmetrically around the cylinder with a thickness of tc (thickness of cylinder) and 2tc mm. The initial and overall buckling load decreased with increasing amplitude for dent numbers with different dent depths on all models. The results show that the number and depth of dents generally have a negative effect on the buckling strength, while CFRPs increase the critical buckling strength and are effective in repair as a retrofitting concept.

Structural Response of Double-Layer Steel Cylinders under Inside-Explosion Loading

The research on the structural response of explosive vessel is an important basis for the design of explosive vessels. Double-layer cylinder structures are widely used in the design of various explosive vessels. This paper studied the deformation of a steel cylindrical shell under internal explosion and proposes a new method for measuring shell deformation by PDV (photonic Doppler velocimetry). We carried out many spherical explosive experiments and obtained useful results that show displacement of the double-layer cylinders and the explosion time. The above process is a simulated LS-DYNA with a finite element numerical simulation. The vibration period of the outer cylindrical shell and the time for reflection of the stress wave in the outer cylindrical shell were obtained by numerical simulation and PDV measurement, respectively. The results of both can be verified against each other. Through the above research, the structural response of the multilayer cylinders can be obtained, which can provide further help with research of the structural design of multilayer cylinders.

Fatigue of a cylindrical shell lying on a rigid bed

In the extractive industries of the oil and gas industry, multi-span pipelines with lodgement-type supports are widely used. In the contact area of the pipeline with the support, contact stresses arise, created by the internal pressure of the pipeline, weight and wind load, and which can change during operation depending on the load. The assessment of the service life of such pipeline structures is an urgent technical and economic problems, which allows not only to prevent man-made and environmental disasters, but also to save material. This paper presents a method for calculating the fatigue of a steel cylindrical shell that is in contact with a rigid or elastic support of the lodgement type. Shell fatigue analysis is performed for contact stresses, which are determined by solving the corresponding contact problem. When calculating the fatigue of the shell, the linear damage summation hypothesis and the modified model of cyclic degradation of the material were used.

Creation of a universal housing for a liquid purification filter made of corrosion-resistant steels

Scientists from different countries are engaged in the development of new or improvement of existing water purification technologies. At the same time, not enough attention is paid to the development of equipment for water purification and technologies for their manufacture. The article presents a model of a universal filter housing for cleaning liquids from solid particles. Mechanical filters of cartridge or bag type can be used as filter elements. The main supporting element of the filter housing is a thin-walled cylindrical flask. The use of rotary rolling in the process of manufacturing a cylindrical flask makes it possible to reduce the negative effect of welded seams and increase the strength of the cylindrical shell. The results of experimental studies on assessing the effect of the relative deformation value along the wall thickness during rotary rolling of steel cylindrical shells on their strength and stability are presented.

Formulation and Numerical Solution of the Stability Loss Problem of Elastic-Plastic Shells of Revolution with an Elastic Filler under Combined Axisymmetric and Torsional Loadings

A dynamic statement and a method for numerically solving the buckling problems of elastoplastic shells of revolution with filler in axisymmetric and non-axisymmetric shapes under quasi-static and dynamic loading are presented within the framework of two approaches. In the first approach, the problem of elastic-plastic deformation and buckling of shells of revolution with an elastic filler under combined axisymmetric loading with torsion is formulated in a two-dimensional (generalized axisymmetric) formulation based on the hypotheses of the shells theory of the Timoshenko type and the Winkler foundation. The constitutive relations are written in the cylindrical system of Euler coordinates. For each shell element, a local Lagrangian coordinate system is introduced. Kinematic relations are recorded in the current state metric. The distribution of the displacement velocity components over the shell thickness and strain rate tensors in the local basis is written as the sum of the momentless and moment components, which, in turn, are written as the sum of the symmetric and asymmetric parts in the local and in the general basis. The elastoplastic properties of the shell material are taken into account within the framework of the theory of flow with nonlinear isotropic hardening. To take into account non-axisymmetric forms of buckling, the desired functions (both displacements and forces, moments, contact pressure) are expanded into a Fourier series in the circumferential direction. The variational equations of shell motion are derived from the general equation of dynamics. The contact between the shell and the deformable filler is modeled based on the conditions of non-penetration along the normal and free slip along the tangent. The variational equations of shell dynamics for axisymmetric and nonaxisymmetric processes are interconnected through the physical relations of the theory of plasticity. They take into account large axisymmetric shape changes and the instantaneous stress-strain state of the shell. At the initial stage of the nonaxisymmetric buckling process, the deflections are small; therefore, the equations of nonaxisymmetric buckling are obtained as linearized with respect to nonaxisymmetric forms. To initiate nonaxisymmetric buckling modes, initial nonaxisymmetric deflections are introduced. To solve the defining system of equations, a finite-difference method and an explicit time integration scheme of the “cross” type are used. The second approach is based on continuum mechanics hypotheses and implemented in a three-dimensional setting. Both approaches make it possible to simulate the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the ultimate (critical) loads in a wide range of loading rates, taking into account geometric shape imperfections, to study the processes of buckling in axisymmetric and non-axisymmetric shapes under dynamic and quasi-static complex loading by tension, compression, torsion, internal and external pressure. The results of numerical simulation are compared with experimental data on the torsion of steel cylindrical elastoplastic shells ( R / h = 1.45) with an elastic filler.

Analytical vibration of middle rotor of coaxial magnetic gear with complicated structure due to holes and screws

Coaxial magnetic gear is a cutting-edge technology introduced a few years ago. Its middle rotor is a rotating steel cylindrical shell with a variable array of holes that are filled by brass screws, hence it is such a complicated structure due to these holes. At first glance, it seems impossible to apply shear deformation theories to this unusual geometry, but for the first time, this article has introduced a novel mathematical methodology that creatively makes this possible. Consequently, an analytical formulation is presented for free vibration of this complicated structure, with no need to finite element software. The final aim is to extract natural frequencies and critical speeds in terms of different parameters. The formulation begins with the first-order shear deformation theory as the displacement field and continues with the Hamilton approach to gain governing equations of motion. Additionally, the effect of an external radial magnetic field is modeled by Maxwell’s relation. In the end, the Galerkin scheme is followed for discretization of the governing equations. This scheme is compared to an older article to guarantee its accuracy. Subsequently, the natural frequencies are estimated in terms of physical parameters of the rotor such as angle and number of holes, hole-thickness to total-thickness ratio, magnetic field and some other parameters. The mode shapes are also depicted for better interoperation of rotor’s behavior. The findings show that unlike geometric parameters (e.g., angle and number of holes), the radial magnetic field does not significantly affect the natural frequency.

Microstructure, Mechanical Properties and Cross‐sectional Behaviour of Additively Manufactured Stainless Steel Cylindrical Shells

AbstractPowder bed fusion (PBF) is an additive manufacturing method that enables complex metallic components to be manufactured with high precision. The microstructure, mechanical properties and cross‐sectional behaviour of PBF additively manufactured stainless steel circular hollow sections are investigated through experiments in this paper, with a view to applications in construction. The experimental programme included tensile coupon tests, microstructural characterisation, initial geometric imperfection measurements and compression tests on PBF 316L stainless steel cylindrical shells with large diameter‐to‐thickness (D/t) ratios. Advanced measurement methods – 3D laser scanning and digital image correlation, were employed to measure the specimen geometries prior to testing and deformation fields during testing, respectively. The possible anisotropy in mechanical properties was examined through tensile coupon tests and correlated with the underlying microstructural and textural features. Compression tests were performed to investigate the resistance against local buckling of thin‐walled cylindrical shells produced by PBF. All cylindrical shells buckled below their yield loads with a chequerboard failure mode and revealed the anticipated trend of reducing capacity relative to the yield load with increasing local slenderness, reflecting the increasing susceptibility to local buckling.