Numerical Simulation and Experimental Research on Microstructural Evolution During Compact Hot Extrusion of Heavy Caliber Thick-Wall Pipe

Compact hot extrusion(CHE) process of heavy caliber thick-wall pipe is a new material-saving production process. In order to reveal the optimum hot extrusion parameters in CHE process, the e ects of the extrusion parameters on the microstructural evolution are investigated systematically. The metadynamic recrystallization(MDRX) kinetic models and grain size models of as-cast P91 steel are established for the first time according to the hot compression tests performed on the Gleeble-3500 thermal-simulation machine. Then a thermal-mechanical and micro-macro coupled hot extrusion finite element(FE) model is established and further developed in DEFORM software. The results indicated that the grain size of the extruded pipe increases with the increasing of initial temperature and extrusion speed, decreases when extrusion ratio increases. Moreover, the grain size is more sensitive to the initial temperature and the extrusion ratio. The optimum hot extrusion parameters are including that, the initial extrusion temperature of 1250 °C, the extrusion ratio of 9 and the extrusion speed of 50 mm/s. Furthermore, in order to verify the simulation precisions, hot extrusion experiment verification on the heavy caliber thick-wall pipe is carried out on the 500 MN vertical hot extrusion equipment. The load–displacement curve of the extrusion process and the grain sizes of the middle part extruded pipe are in good accuracy with the simulation results, which confirms that the hot extrusion FE models of as-cast P91 steel could estimate the hot extrusion behaviors. The proposed hot extrusion FE model can be used to guide the industrial production research of CHE process.

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.

Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory

Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets

In this paper,the stresses and buckling behaviors of a thick-walled mi-cro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC)face sheets are considered based on the high-order shear deformation theory(HSDT)and the modified couple stress theory(MCST).The governing equations of equi-librium are obtained based on the total potential energy principle.The effects of various parameters such as the aspect ratio,elastic foundation,temperature changes,and volume fraction of the canbon nanotubes(CNTs)on the critical buckling loads,normal stress,shear stress,and deflection of the thick-walled micro cylindrical sandwich panel consider-ing different distributions of CNTs are examined.The results are compared and validated with other studies,and showing an excellent compatibility.CNTs have become very use-ful and common candidates in sandwich structures,and they have been extensively used in many applications including nanotechnology,aerospace,and micro-structures.This paper also extends further applications of reinforced sandwich panels by providing the modified equations and formulae.

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material(FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

A borehole stability study by newly designed laboratory tests on thick-walled hollow cylinders

At several mineral exploration drilling sites in Australia, weakly consolidated formations mainly consistof sand particles that are poorly bonded by cementing agents such as clay, iron oxide cement or calcite.These formations are being encountered when drilling boreholes to the depth of up to 2 0 0 m. To studythe behaviour of these materials, thick-walled hollow cylinder （TWHC） and solid cylindrical syntheticspecimens were designed and prepared by adding Portland cement and water to sand grains. The effectsof different parameters such as water and cement contents, grain size distribution and mixture curingtime on the characteristics of the samples were studied to identify the mixture closely resembling theformation at the drilling site. The Hoek triaxia! cell was modified to allow the visual monitoring of graindebonding and borehole breakout processes during the laboratory tests. The results showed the significanceof real-time visual monitoring in determining the initiation of the borehole breakout. The sizescaleeffect study on TWHC specimens revealed that with the increasing borehole size, the ductility ofthe specimen decreases, however, the axial and lateral stiffnesses of the TWHC specimen remain unchanged.Under different confining pressures the lateral strain at the initiation point of boreholebreakout is considerably lower in a larger size borehole （2 0 mm） compared to that in a smaller one（10 mm）. Also, it was observed that the level of peak strength increment in TWHC specimens decreaseswith the increasing confining pressure.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

Reduction of the residual stresses in cold expanded thick-walled cylinders by plastic compression

We suppose that in order to maintain high accuracy of holes and to lower residual stresses after cold expansion of thick-walled cylinders, which undergo cross-section plastic deformation, it is necessary to perform axial plastic compression and subsequent cold expansion with small interferences. To test this hypothesis, we studied hoop, radial and axial residual stresses in cylinders made of carbon steel AISI 1050 with hole diameter of 5 mm, outer diameter of 15 mm and length of 30 mm by Sachs method as well as accuracy of expanded holes. It is found that double cold expansion with total interference equal to 5.1% generates hoop residual stresses with largest absolute value equal to 284 MPa and ensures high holes accuracy(IT7). After plastic compression with strain equal to 0.5 and 1% the mentioned stresses reduced to 120 and 75 MPa respectively,and accuracy of the holes reduced as well. Subsequent cold expansion with small interference equal to 0.9% helps to restore holes accuracy(IT7)gained by double cold expansion and ensure that absolute value of hoop residual stresses(177 MPa) is lower compared to double cold expansion.

THEORY OF THICK-WALLED SHELLS AND ITS APPLICATION IN CYLINDRICAL SHELL

In this paper, a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle, with displacement and stress assumptions. The displacements are expanded into power series of the thickness coordinate. Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively. The normal extruding and transverse shear stresses are assumed to be cubic polynomials and to satisfy the boundary stress conditions on the outer and inner surfaces of the shell. The governing equations and boundary conditions are derived by means of variational principle. As an example, a thick-walled cylindrical shell is disscussed with the theory proposed. Furthermore, a photoelastic experiment has been carried out, and the results are in fair agreement with the computations.

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

Ringlike failure experiment of thick-walled limestone cylinder specimens in triaxial unloading tests

In order to study the failure of surrounding rock under high in situ stress in deep underground engineering projects, disturbed by excavation unloading, we carried out triaxial unloading experiments using thickwalled cylinder specimens on a TATW-2000 rock servo-controlled triaxial testing machine in a laboratory. The specimens were made of limestone material, taken from Tongshan county, Xuzhou city, Jiangsu province, China. In our experiments, rock deformation and failure behavior was studied through loading and unloading of inner hole pressure of thick-walled cylinder specimens. At first, the axial stress, confining pressure and inner pressure were increased simultaneously to a specified designed state of stress. Then, keeping the axial stress and confining pressure stable, the pressure on the inner hole was decreased until the specimen was fractured. When the inner pressure was released completely but the specimen did not fracture, the confining pressure was decreased subsequently until complete failure occurred. Our experimental results suggest that traces of major circular ringlike fractures with a number of radial cracks often appear in thick cylinder walls. This type of ringlike failure phenomenon, similar to intermittent zonal fracturing characteristics of deep exploitation, has, so far, not been published. Our experimental results show that rock deformation and failure behavior of thick-walled limestone cylinders vary under different stress paths between loading and unloading. Tensile failure and orderly failure surfaces occur under unloading conditions while irregular damaged rock blocks are produced during loading failure. This type of triaxial unloading experiment provides for new research methodology and approach for thorough investigations on intermittent zonal fracturing in deep underground excavations.

An approach for optimization of the wall thickness (weight) of a thick-walled cylinder under axially non-uniform internal service pressure distribution

Today, improving the weight/load carrying capacity ratio of a part is the matter of studies in most of the scientific and industrial areas.Autofrettage dimensions, the amount of material removed from outer and inner radius while manufacturing and the service pressure applied affect the residual stress distribution throughout the wall thickness and hence the load-bearing capacity of a thick-walled cylinder. Calculation of residual stresses after autofrettage process and optimization of autofrettage outline dimensions by using the amount of service pressures applied are common issues in literature.In this study, mandrel-cylinder tube interference dimensions were renovated by using traditional methods for swage autofrettage process of a gun barrel. Also, the residual stresses in the cylinder after autofrettage process, inside and outside material removal process and the variable service pressure throughout the cylinder applied were taken into consideration and incorporated into the design. By using the constrained optimization method, wall thickness(thus the weight) was optimized(minimized)to achieve the specified safety factor along the length of the cylinder. For the same cylinder, the results of the suggested analytical/with residual stress calculation approach were compared to analytical/without residual stress calculation results and numerical topology optimization method calculation results. Since the experimental measurement results are not yet available, it was not possible to compare them with the calculation results.The suggested approach enabled 22.9% extra weight reduction in proportion to numerical topology optimization and enabled 4.2% extra weight reduction in proportion to analytical/without residual stress optimization.Using this approach, the gain from residual stresses after autofrettage operation, the loss of residual stresses after material removal, and the effects of service pressures can be taken into account for each stage of design.

Numerical evaluation of an autofrettaged thick-walled cylinder under dynamically applied axially non-uniform internal service pressure distribution

A dynamical moving pressure structural numerical calculation model using the internal ballistics calculation pressure-time results was constituted and the vicinity of the internal ballistics and quasiinternal ballistics structural model was checked. The Von Mises stresses obtained by the dynamical structural numerical model calculations and the Von Mises stresses calculated from the shot test strain measurements were compared. The difference for the worse case was 20% and for the best case was 0.1%.Furthermore, the model gave better agreement for the higher charge masses. The numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design.

Effect of sodium modification on microstructure and mechanical properties of thick-walled AlSi6Cu2.5 rheocast component

The microstructure and tensile properties were investigated in a thick-walled section (approximately 45 mm×43 mm) of a rheocast component produced by the RheoMetalTM process.Due to the long solidification period of such components, it is expected that the Al-Si eutectic formed will be coarse.Therefore, sodium (Na) was used as a modifying agent to reduce the coarseness of the eutectic.Tensile test bars were machined from three different sets of materials:1) non-modified melt, 2) modified melt cast directly after Na addition, and 3) modified melt cast 30 min after Na addition.The alloy used was a secondary AlSi6Cu2.5 alloy (STENAL Rheo1), specially developed for rheocasting.The material was studied in the as-cast condition as well as after a T6 heat treatment.The results show that the Al-Si eutectic is significantly refined by the Na addition, even after a fading time of 30 min.However, it is observed that the Na modification generally has a detrimental effect on the mechanical properties, despite the structure refinement.This is especially true in the T6 heat treated condition, where the yield strength is reduced by more than 30%.Some possible mechanisms for the degradation of mechanical performance are discussed.

ELASTOPLASTIC ANALYSIS OF THICK-WALLCYLINDER CONSIDERING THE MATERIAL'S DILATANCY CHARACTER

Impermeable bentonite or its mixtures have been proposed as candidate materials to be used in the geotechnical disposal of radioactive nuclear waste. These materials are filled in the space between a canister containing radioactive nuclear waste and an underground chamber to absorb the radionuclide emitting from the canister and simultaneously retard its migration accompanying the perrneation of underground water to prevent the surrounding environment from po1lution. On the basis of the established elastoplastic strain-hardening mechanical model considering the material’s dilatancy character,the authors carry out the stress-strain analysis of a thick-wa1l cylinder in a plane strain state subJected to a pressure difference between internal and external pressures. The analysis may be expected to be a theoretical basis for developing a coupled shear and permeability test apparatus for conducting a permeability test along a sheared plane in a specimen. The apparatus will be used to study the effects of shear strain on the variation of geotechnical materials’ permeability coefficient in order to evaluate the influence of shear strain caused by nonuniform deformation and/or earthquake on the long-term safety of the disposal system of radioactive nuclear waste. The theoretlcal analysls methods in this paper can be directly spread to the analysis of the deformation and stability of tunnels or roadways driven in soft soils or high moisture-bearing soft rocks.

Analytical solution for spatially axisymmetric problem of thick-walled cylinder subjected to different linearly varying pressures along the axis and uniform pressures at two ends

To our best knowledge,in the open literature,there is no analytical solution of thick-walled cylinder subjected to uniform pressures at two ends and different inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis.We now present such a solution.After repeated trials,we have finally succeeded in finding a necessary new displacement function.Based on A.E.H.Love method,the stress,displacement and volume strain formulas are derived by using the new displacement function.The present results include the Lamé’s formulas as special cases.Furthermore,the results obtained here can be applied to not only the thick-walled cylinders subjected to uniform pressures on the inner and outer surface of the thick-walled cylinder,respectively,but also the cylinders subjected to uniform pressures at two ends and dif- ferent inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis,respectively.Finally we give a numerical example to compare our exact method with the approximate method.

Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders:Exact 3D Linear Elastodynamic Response

The forced-vibration response of a simply-supported isotropic thick-walled hollow elastic circular cylinder subjected to two-dimensional harmonic standing-wave excitations on its curved surfaces is studied within the framework of linear elastodynamics.Exact semi-analytical solutions for the steady-state displacement field of the cylinder are constructed using recently-published parametric solutions to the Navier-Lam´e equation.Formal application of the standing-wave boundary conditions generates three parameter-dependent 66 linear systems,each of which can be numerically solved in order to determine the parametric response of the cylinder’s displacement field under various conditions.The method of solution is direct and demonstrates a general approach that can be applied to solve many other elastodynamic forcedresponse problems involving isotropic elastic cylinders.As an application,and considering several examples,the obtained solution is used to compute the steady-state frequency response in a few specific low-order excitation cases.In each case,the solution generates a series of resonances that are in exact correspondence with a unique subset of the natural frequencies of the simply-supported cylinder.The considered problem is of general theoretical interest in structural mechanics and acoustics and more practically serves as a benchmark forced-vibration problem involving a thickwalled hollow elastic cylinder.

Numerical Simulation of Transient 3-D Turbulent Heated Jet into Crossflow in a Thick-Wall T-Junction Pipe

The present work is to investigate the transient three-dimensional heated turbulent jet into crossflow in a thickwall T-junction pipe using CFD package. Two cases with the jet-to-crossflow velocity ratio of 0.05 and 0.5 are computed, with a finite-volume method utilizing κ-ε model. Comparison of the steady-state computations with measured data shows good qualitative agreement. Transient process of injection is simulated to examine the thermal shock on the T-junction component. Temporal temperature of the component is acquired by thermal coupling with the fluid. Via analysis of the flow and thermal characteristics, factors causing the thermal shock are studied. Optimal flow rates are discussed to reduce the thermal shock.

管道超声相控阵全聚焦成像仿真及算法优化

针对厚壁管道内部缺陷识别困难、可视化差等问题,提出基于超声相控阵理论和全聚焦算法对厚壁管道内部缺陷进行图像重构。并针对全聚焦成像效率低的缺点,采用有限元法对外径为550 mm,壁厚为65 mm的厚壁管道超声相控阵全聚焦成像进行仿真,模拟缺陷检测过程和成像结果,并使用稀疏矩阵对算法进行优化。结果表明:在基本满足成像质量要求的情况下,采用激发中心频率为5 MHz,阵元宽度为0.5 mm,阵元间距为1 mm,阵元数量为32时,稀疏激发矩阵比全矩阵全聚焦成像效率提高了74.81%,有效提高了成像速度,满足全聚焦快速成像的需求。

Theoretical and numerical research on the dynamic launch response of carbon fiber composite cartridges

Understanding the dynamic response of composite material cartridges during the firing process is of great significance for improving their reliability and safety.A theoretical model describing the dynamic response of composite material cartridges is established based on the thick-walled cylinder theory and rate-dependent constitutive model of composite materials.The correctness of the theoretical model is validated through finite element simulations of cartridge deformation.The influence of chamber pressure and cartridge wall thickness on the cartridge's deformation process and stress distribution is analyzed.The results indicate that the primary deformation of composite material cartridges inside the chamber is elastic deformation.Compared to metal cartridges,composite material cartridges require higher pressure for touching-chamber and are more prone to developing gaps after unloading to ensure smooth extraction.During the deformation process,the touching-chamber behavior of the cartridge can improve the stress distribution.Under the same chamber pressure,the touching-chamber behavior can reduce the circumferential stress by approximately 30%.The inner wall surface of the cartridge is a critical area that requires attention.The touching-chamber behavior can be facilitated by appropriately reducing the cartridge wall thickness while ensuring overall strength.This study can provide guidance for the optimization design of composite material cartridges.