Thick-walled Cylinder Research Articles

Stress Field near Crack Tips in Pressurized Thick-Walled Cylinders with Single and Multiple Cracks in Linear Elastic Fracture Mechanics: Analytical and Numerical Analysis of Stress Field and Crack Behavior

<div>Arrays of radial cracks often appear at the bore of pressurized cylinders, posing potential safety risks and leading to possible structural failures. This article presents an analytical approach to evaluate the stress field arising from single or multiple uniform radial cracks in thick-walled pressurized cylinders within the context of linear elastic fracture mechanics (LEFM) under mode-I loading. This formulation is based on the fundamental equations of elasticity and approximations of stress intensity factors (SIF) reported in the literature. Hence, the SIF were revisited and their range of validity was highlighted. The study considers two types of internal pressure loading: one applied only to the cylinder’s inner surface with no pressure on the crack faces and another applied to both the inner surface and the crack faces. The influence of the number and length of cracks relative to cylinder thickness on the stress field is analyzed. A finite element model of the pressurized vessel is constructed to verify the proposed analytical solution, showing good agreement with numerical results for a limited number of cracks.</div>

Simulation-based analysis of welding process parameters for TC4ELI titanium alloy thick-walled cylinders

Abstract In this paper, ABAQUS is used to numerically simulate the residual stresses during welding of titanium alloy thick-walled cylinders. A detailed simulation analysis of the stress field during the welding process is performed by establishing an accurate finite element model, defining the thermal physical properties, boundary conditions, and heat source model, and using the indirect heat-force coupling method. The results of the study show that the distribution of the weld stress field has an important influence on weld quality, material properties, and structural strength. The movement of the welding heat source results in a dynamic change in the stress field, which gives rise to a significant stress concentration at and in the vicinity of the welding heat source.

Coupled torsion and inflation of functionally graded and residually stressed Mooney–Rivlin hollow cylinders

Functionally graded structures have material properties continuously varying in one or more directions. Examples include human teeth, sea shells, bamboo stems, and mammal organs in which the varying volume fraction and orientation of fibers optimize their functionalities. Here we analytically study large deformations due to combined torsion and inflation of residually stressed and radially graded Mooney–Rivlin hollow circular cylinders to provide insights into how grading their material moduli according to a power law function of the radius can be advantageously used. We simulate residual stresses in a thin wall hollow cylinder by inverting it inside out and in a thick wall cylinder by assuming that a longitudinal wedge opening parallel to the cylinder axis is closed by deforming it axisymmetrically. It is found that positive integer values of the power law exponent are generally advantageous but its negative values can have deleterious effects on stress distributions. Furthermore, a hollow cylinder with residual stresses generated by one of the foregoing methods in the reference configuration should be modeled as orthotropic rather than transversely isotropic for subsequent deformations. The analytical solutions provided here should help numerical analysts verify their algorithms for large deformations of rubber-like materials that are modeled by the Mooney–Rivlin relation, and design engineers for exploiting the radial gradation of the two material moduli to reduce structure’s mass without sacrificing its performance.

Numerical analysis of small-strain elasto-plastic deformation using local Radial Basis Function approximation with Picard iteration

In this paper, we discuss a von Mises plasticity model with nonlinear isotropic hardening assuming small strains in a plane strain example of internally pressurised thick-walled cylinder subjected to different loading conditions. The elastic deformation is modelled using the Navier-Cauchy equation. In regions where the von Mises stress exceeds the yield stress, corrections are made locally through a return mapping algorithm. We present a novel method that uses a Radial Basis Function-Finite Difference (RBF-FD) approach with Picard iteration to solve the system of nonlinear equations arising from plastic deformation. This technique eliminates the need to stabilise the divergence operator and avoids special positioning of the boundary nodes, while preserving the elegance of the meshless discretisation and avoiding the introduction of new parameters that would require tuning. The results of the proposed method are compared with analytical and Finite Element Method (FEM) solutions. The results show that the proposed method achieves comparable accuracy to FEM while offering significant advantages in the treatment of complex geometries without the need for conventional meshing or special treatment of boundary nodes or differential operators.

In-silico heart model phantom to validate cardiac strain imaging

The quantification of cardiac strains as structural indices of cardiac function has a growing prevalence in clinical diagnosis. However, the highly heterogeneous four-dimensional (4D) cardiac motion challenges accurate “regional” strain quantification and leads to sizable differences in the estimated strains depending on the imaging modality and post-processing algorithm, limiting the translational potential of strains as incremental biomarkers of cardiac dysfunction. There remains a crucial need for a feasible benchmark that successfully replicates complex 4D cardiac kinematics to determine the reliability of strain calculation algorithms. In this study, we propose an in-silico heart phantom derived from finite element (FE) simulations to validate the quantification of 4D regional strains. First, as a proof-of-concept exercise, we created synthetic magnetic resonance (MR) images for a hollow thick-walled cylinder under pure torsion with an exact solution and demonstrated that “ground-truth” values can be recovered for the twist angle, which is also a key kinematic index in the heart. Next, we used mouse-specific FE simulations of cardiac kinematics to synthesize dynamic MR images by sampling various sectional planes of the left ventricle (LV). Strains were calculated using our recently developed non-rigid image registration (NRIR) framework in both problems. Moreover, we studied the effects of image quality on distorting regional strain calculations by conducting in-silico experiments for various LV configurations. Our studies offer a rigorous and feasible tool to standardize regional strain calculations to improve their clinical impact as incremental biomarkers.

Development of an efficient design optimization strategy for thick-walled cylinders treated with combinations of autofrettage, shrink-fit and wire-winding processes

Shrink-fit, wire-winding, and autofrettage processes are commonly utilized to enhance fatigue strength and durability of thick-walled cylinders across various mechanical applications. In this study, a novel practical design optimization methodology has been developed to determine the optimal configuration of a thick-walled cylinder, incorporating different combinations of shrink-fit, wire-winding, and autofrettage techniques. The objective is to identify the optimal layer thickness, shrink-fit interference, conventional autofrettage pressure, and reverse autofrettage pressure, if applicable, to maximize the compressive residual stress and minimize the tensile residual stress, thereby extending fatigue lifetime of the cylinder. First, different configurations of thick-walled cylinders, subjected to various combinations of reinforcement processes, are identified. A dataset of residual hoop stress profiles through the cylinder thickness is subsequently generated for these configurations based on the same manufacturing process. Neural network regression is effectively utilized to construct a single fitting function for the residual hoop stress profiles. A parametric study is performed to determine the optimal training functions, activation functions, and hyperparameters, achieving a remarkable agreement with the dataset, indicated by a coefficient of determination of over 0.97. A combination of Genetic Algorithm and Sequential Quadratic Programming algorithms is utilized to determine the accurate optimal values. Fatigue life analysis is subsequently conducted to estimate the fatigue lifetime of the optimal configuration. Results suggest that the optimal configuration, involving conventional autofrettage of the inner layer followed by shrink-fitting with a virgin layer and wire-winding the entire assembly, achieves a maximum fatigue life of 88 × 10⁶ cycles under cyclic pressure load of 300 MPa.

In-silico heart model phantom to validate cardiac strain imaging.

The quantification of cardiac strains as structural indices of cardiac function has a growing prevalence in clinical diagnosis. However, the highly heterogeneous four-dimensional (4D) cardiac motion challenges accurate "regional" strain quantification and leads to sizable differences in the estimated strains depending on the imaging modality and post-processing algorithm, limiting the translational potential of strains as incremental biomarkers of cardiac dysfunction. There remains a crucial need for a feasible benchmark that successfully replicates complex 4D cardiac kinematics to determine the reliability of strain calculation algorithms. In this study, we propose an in-silico heart phantom derived from finite element (FE) simulations to validate the quantification of 4D regional strains. First, as a proof-of-concept exercise, we created synthetic magnetic resonance (MR) images for a hollow thick-walled cylinder under pure torsion with an exact solution and demonstrated that "ground-truth" values can be recovered for the twist angle, which is also a key kinematic index in the heart. Next, we used mouse-specific FE simulations of cardiac kinematics to synthesize dynamic MR images by sampling various sectional planes of the left ventricle (LV). Strains were calculated using our recently developed non-rigid image registration (NRIR) framework in both problems. Moreover, we studied the effects of image quality on distorting regional strain calculations by conducting in-silico experiments for various LV configurations. Our studies offer a rigorous and feasible tool to standardize regional strain calculations to improve their clinical impact as incremental biomarkers.

Comparative Study of Electron Beam Welding and Shielded Metal Arc Welding of 30CrMnSiNi2A Thick Wall Cylinder

Comparative Study of Electron Beam Welding and Shielded Metal Arc Welding of 30CrMnSiNi2A Thick Wall Cylinder

Evaluation Model for Bearing Capacity of Grouting Sleeves Based on Conventional Material Parameters

The existing bearing capacity model for grouting sleeves is synthesized in this study. Utilizing the principles of thick-walled cylinders in elastic mechanics, a comprehensive ultimate bearing capacity model for grouting sleeves is developed using conventional material parameters. To validate the efficacy of the model, 18 steel bar grouting sleeves of varying anchor lengths, steel bar diameters, and designs were tested. The outcomes indicate minimal errors in the computational results and demonstrate superior applicability when juxtaposed with established grouting sleeve bearing capacity formulas.

Analytical model for concrete crack width of steel lined reinforced concrete penstock

Cracking in steel lined reinforced concrete penstock (SLRCP) poses substantial challenges to both serviceability and safety, particularly when crack width exceeds specified limits. Despite its critical implications, accurately calculating crack width remains a persistent challenge. To address this issue, a multi-layer steel-concrete ring analytical model is derived through the concept of orthotropic and thick-walled cylinder theories. In this model, the cracked concrete is assumed to be an orthotropic material incorporating both elastic modulus reduction and tensile softening behavior based on its cracking characteristic of radial penetrating cracks uniformly distributed on the circumference. The steel liner and reinforcing steel bar are modeled as continuous steel rings using equivalent stress theory, while thick-walled cylinder theory is applied due to geometric features and bearing characteristics. Crack width is determined through equilibrium of force and compatibility of deformations at steel-concrete interfaces, utilizing these assumptions and the developed calculation model. To validate the proposed model, data from prototype observations and large-scale model tests of SLRCPs were systematically collected. The crack width results obtained from the proposed model exhibit strong agreement with the collected data, confirming its accuracy and reliability. In conclusion, the proposed analytical model provides an effective solution for calculating the crack width of SLRCP and offers valuable insights for durability evaluation.

ACTION OF A SOLID BODY ON THE INNER SURFACE OF A THICK-WALLED BIMETAL CYLINDER

Purpose. The goal of the work is to obtain an exact solution to the problem of the stress-strain state of a long thick-walled bimetallic cylinder within the framework of the classical theory of elastic materials. Then, using the results obtained with this formulation, it is necessary to propose simpler engineering approaches and explore the possibilities of using asymptotic formulas for express analyzes at the design stage of such structural elements. Research methods. For the main body of the cylinder, the classical equations of the theory of elasticity in displacements are used. For the outer coating (sputtering), the shell theory equations are written based on the Kirchhoff-Love hypotheses. The complex integral Fourier transform and the Failon method are used to approximately find the original stresses and displacements. Asymptotic representations of cylindrical Bessel functions for large values of the argument and representations of improper integrals in the form of combinations of elementary and special tabulated functions are also used. Results. A mathematical model has been constructed to analyze the stress-strain state of a bimetallic cylinder with a thin outer layer of a material different from that of the inner layer. Various boundary conditions are recorded on the inner surface of the cylinder, describing the transmission from a rigid body of either specified forces or specified displacements. For all considered options, using the method of integral transformations, the results were obtained in the form of improper integrals, for the calculation of which a special method was used, aimed at calculating integrals with highly oscillating functions. Examples of specific graphs of changes in the components of the stress-strain state in the cylinder material are given. Depending on the conditions on the inner surface of the cylinder, simpler models are proposed to describe the main body, which are based, depending on the nature of the description of the interaction of the rigid body and the cylinder, on one equation of the theory of elasticity. With this approach, in some important cases it was possible to obtain improper inversion integrals using the asymptotic approach in closed form as a combination of elementary and special tabulated functions. Comparison with the exact approach allowed us to prove the possibility of using approximate models. Scientific novelty. A model of the behavior of a bimetallic cylinder as a body is constructed, the main layer of which is described by the equations of the theory of elasticity, and the theory of shells is used for the outer coating. Various methods of describing the transfer of forces and displacements from a rigid body to the inner surface of the cylinder are considered. The possibility of using the asymptotic approach to obtain relatively simple formulas for carrying out preliminary calculations at the design stage of such structural elements is shown.

Theoretical study on 3D elastic response and first layer failure strength of composite cylinders subjected to axisymmetric loadings

The traditional Lekhnitskii 3D elastic theory can obtain the exact stress and strain response of the composite cylinder under the axially symmetric loadings. However, when the cylinder contains 0° winding layers or isotropic layers, some calculation parameters corresponding to the two kinds of special layers will become singular. By analyzing the continuity of singular parameters and calculating their limits, the problem of singular parameters can be effectively solved and the Lekhnitskii theory can be extended to composite thick-walled cylinders with arbitrary winding angles. Furthermore, based on the Chang-Chang strength criterion of composite layers and the ideal elastic-plastic assumption of isotropic metal layers, the theoretical calculation method of first layer failure strength and the corresponding failure modes of the composite cylinders subjected to axisymmetric loadings was proposed. Then, the composite cylinder with metal liner was fabricated by fiber winding process. The experimental blasting pressure of the cylinder was 52.8 MPa with a major failure mode of fiber tensile fracture. Based on the proposed theoretical method, the cylinder's first layer failure strength of internal pressure was 44.1 MPa, and the initial failure mode was also fiber tensile fracture. The predicted result of the first layer failure strength was lower than the experimental results. The result proved the safety and economy of the proposed theoretical method for the initial design of the composite cylinder.

Residual Stress Analysis of Re-autofrettage of a Swage-Autofrettaged Tube by Computer Modeling Incorporating Accurate Material Representation

Autofrettage processes allow engineers to reduce the thickness of thick-walled cylinders or components in high-pressure applications without sacrificing strength, life, or safety. However, during the autofrettage process, residual stresses will be generated due to plastic deformation. The complex tube material behavior is dominated by the Bauschinger effect. A better understanding and accurate prediction of the residual stress field is critical, which will enable better piping design strategies to minimize deformation and stresses under operating conditions. This study aims to predict and analyze residual stresses resulting from hydraulic re-autofrettage of a swage-autofrettaged thick-walled cylinder by computer modeling. A case study was performed on a thick-walled cylinder of A723 alloy with a radial interference of 2.5%. In order to investigate the effect of the chosen material constitutive representation, results based on the true material constitutive model were compared with the simplified prevalent material model of bi-linear kinematic strain hardening. Computer implementation for the true material was via a user-developed subroutine that incorporates the complex Bauschinger effect. The results indicate that an accurate material constitutive representation is crucial for better and more accurate prediction and understanding of residual stresses induced by autofrettage processes. Computer modeling based on the true material constitutive representation will likely prove to be a powerful tool for the design of autofrettage processes in general and thick-walled cylinders in particular.

Ultrasonic wave simulation in shrink-fit assembly for the estimation of stress at the contact interference

The investigation of stress distribution in an interference fit contact region is essential information required in fatigue and wear calculations to determine design life, regrinding requirements, and maintenance schedules. The aim of this work was to use ultrasound to non-destructively determine stress in the shrink-fit assembly, with the acoustoelastic theory. This one is based on the dependence of the propagation velocity of the ultrasonic wave with the stress state in the material. When a material is subjected to stress, there is a variation of the propagation velocity of the ultrasonic wave. Three methods have been initiated to ensure that the results will be more real, the first is the analytical calculation using thick-walled cylinder theory and Lamé formulation, then a numerical modeling of the contact between the assembled parts using finite element analysis and the third one is using elastic wave simulation and acoustoelastic theory in order to determine the value of the stress distribution at the interference region.

A simple method for mechanical analysis of pressurized functionally graded material thick-walled cylinder

The complex function method is employed to establish a mechanical model for pressurized thick-wall cylinders made of functionally graded materials (FGM). This model is applicable to all radial varying modes of material properties, including both continuous and discontinuous variations in Young’s modulus and Poisson’s ratio. The main concept behind this mechanical model involves dividing the thick-walled cylinder into concentric thin cylinders, each equipped with a pair of analytical functions representing stress functions. By imposing continuity conditions between adjacent thin cylinders and considering the stress boundary conditions of the entire structure, all unknown forms of analytical functions can be determined. Subsequently, by establishing the correspondence relationship between these analytical functions and stress or displacement, it becomes possible to solve for the stress or displacement at any radial position within the thick-walled cylinder. Through comparison and verification against the numerical simulation results, it can demonstrate that as long as the differential scale is sufficiently small, high accuracy can be achieved in the final result. In other words, solutions obtained for multi-layered hollow cylinder converge toward those obtained for continuously graded thick-walled cylinder. Notably, by starting from the level of stress function and avoiding complex differential and integral equations, a linear equation system can provide information on stress and displacement distributions along the radial direction. Therefore, compared to other solving methods available, this proposed approach offers simplicity and applicability.

Bond behavior and modeling of steel-FRP composite bars in engineered cementitious composites

The combination of the steel-FRP composite bar (SFCB) and engineered cementitious composite (ECC) holds favorable applications in terms of durable resilient structures. However, a clear understanding of the interfacial bond performance of this novel combination is currently lacking. Therefore, the bond behavior and mechanism of the SFCB-ECC interface were investigated through direct pullout tests. A total of 48 cube specimens were fabricated, with the test variables including bar type, bar diameter, embedment length, and matrix type. The experimental results indicated that the bond failure mode of SFCBs and FRP bars differed from that of deformed steel bars, attributed to the damage of resin-rich ribs in relatively high-strength ECC. The bond-slip curves revealed both the fundamental differences and similarities among steel bars, SFCBs, and FRP bars. The Poisson effect and shear lag effect increased with a decrease in bar stiffness and an increase in diameter. The combined impact of the interaction between the bar stiffness and diameter resulted in varying bond strengths for steel bars, SFCBs, and GFRP bars, despite their similar surface geometries. A theoretical model for the bond strength at the SFCB-ECC interface was derived using the thick-walled cylinder principle and subsequently validated with test data. Finally, a unified empirical model framework for predicting the bond strength of various bar-matrix combinations was proposed based on the theoretical model. The accuracy of this method was evaluated using a collected database.

Bond strength between ductile carbon/glass hybrid fibers-reinforced polymer bar and concrete through plate-type bond samples

The ductile carbon/glass hybrid fibers-reinforced polymer (C/G-HFRP) bar with excellent corrosion resistance is considered as an outstanding alternative to steel bar in structural concrete. The bond strength of C/G-HFRP bar to concrete plays a dominant contribution to fully realize the prominent properties of C/G-HFRP bar-reinforced concrete structures. In this work, the bond strength between ductile C/G-HFRP bar and concrete was investigated through a plate-type bond sample under direct pullout load. The effects of C/G-HFRP bar diameter, rib pitch, carbon/glass ratio, embedment length, concrete strength, cover thickness, bar type and sample type on the bond strength of C/G-HFRP bar to concrete were considered. The experiment outcomes revealed that the bond strength between C/G-HFRP bar and concrete by plate-type bond samples was 32.4 % lower than that by cube-type ones, resulting from that the influence of reaction frame on the crack propagation of concrete was eliminated during the loading procedure of plate-type bond samples. Also, the bond strength of C/G-HFRP bars to concrete increased with the tensile modulus, while the bond strength between C/G-HFRP bar and concrete was 48.5 % lower than that between steel bar and concrete. The failure mode of bond samples was controlled by the cover thickness of concrete when the compressive strength of concrete was not more than 55 MPa. Furthermore, the bond strength of sample was associated with the failure modes of test samples. The bond strength was decided by the mechanical properties of concrete when the bond sample happened splitting failure, while it was decided by the shear-resistant strength of flange ribs for C/G-HFRP bar when the failure mode of bond sample belonged to pull-out failure. Finally, the bond strength of C/G-HFRP bar to concrete was calculated by the thick-walled cylinder model.

Creep analysis of a cylinder subjected to 2D thermoelasticity loads and boundary conditions with inner heat generation source

This paper presents an in-depth investigation of the creep behavior of a thick-walled cylinder subjected to thermomechanical loads with internal heat generation under various boundary conditions. The cylinder is subjected to internal pressure with the incoming heat flux in the inner layer and the outgoing heat flux from the outer layer accompanied by heat generation. The displacement field follows the kinematics of the first-order shear deformation theory (FSDT). Simultaneously, the temperature field is treated as two-dimensional, exhibiting variations both along the thickness and the length of the cylinder, with a linear temperature gradient across the cylinder's thickness. Using the energy method, the equilibrium equations and general boundary conditions are derived for the cylinder. Norton's model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. The redistribution, displacements, strains and stresses over time have been obtained by the semi-analytical iteration method. Moreover, the effectiveness of the proposed method in addressing axisymmetric cylindrical shells under various boundary conditions and thermo-mechanical loading is demonstrated. A parametric study on the creep behavior has also been carried out which reveals critical insights. Notably, the study demonstrates that effective stress and radial displacement during creep can be effectively managed by optimizing the external cooling profile or the internal heating profile. Furthermore, the investigation reveals that the presence of a heat source markedly influences the effective stress and displacement within structure, highlighting the interplay between thermal and mechanical factors in determining the structural integrity. To validate the findings of this study, the finite element method was employed, with the results indicating good agreement between the two approaches.

Nonlinear Deformation of Cylinders from Materials with Different Behavior in Tension and Compression

A new numerical-analytical method for solving physically nonlinear deformation problems of axisymmetrically loaded cylinders made of materials with different behavior in tension and compression has been developed. To linearize the problem, the uninterrupted parameter continuation method was used. For the variational formulation of the linearized problem, a functional in the Lagrange form, defined on the kinematically possible displacement rates, is constructed. To find the main unknowns of the problem of physically nonlinear cylinder deformation, the Cauchy problem for the system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta-Merson method with automatic step selection. The initial conditions were established by solving the problem of linear elastic deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta-Merson’s scheme are found from the solution of the variational problem for the functional in the Lagrange form. Variational problems are solved using the Ritz method. The test problem for the nonlinear elastic deformation of a thin cylindrical shell is solved. Coincidence of the spatial solution with the shell solution was obtained. Physically nonlinear deformation of a thick-walled cylinder was studied. It is shown that failure to take into account the different behavior of the material under tension and compression leads to significant errors in the calculations of stress-strain state parameters.

Shear bands occurrence in collapsing thick-walled cylinders: Role of user-defined perturbations

Self-organization of multiple adiabatic shear bands (ASB) is often investigated through collapsing thick-walled cylinders (TWC). In the present work, the material behavior is described by a thermoviscoplastic constitutive law with a strain energy based failure model. Inhomogeneities in the specimen are somehow represented using Voronoi cells. In addition, a user-defined perturbation is imposed in the numerical perturbation to each Voronoi cell. Therefore, a mesh independent perturbation is obtained. Several draws of initial perturbation are considered to investigate variability in shear band patterns. The numerous realizations are analyzed through an algorithm to track and count shears bands providing statistically significant results. The influence of the failure model and perturbation parameters on shear bands number and length is studied. While short bands are affected by the size of the cells, it is shown that the self-organized pattern of developed bands is relatively independent of the imposed Voronoïcell structure. The amplitude of the perturbation affects neither the pattern nor the length of bands (within the considered range of amplitude of the user-defined perturbation).