Anisotropic Pipe Research Articles

Application of state vector formalism and Legendre polynomial hybrid method in the longitudinal guided wave propagation analysis of composite multi-layered pipes

In this research, we applied a polynomial hybrid approach for modeling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of Legendre polynomial series, the dispersion curves of longitudinal guided waves for arbitrary multi-layered anisotropic pipes can be obtained efficiently and accurately. As an alternative serial approach, it solves the wave propagation problem of complex anisotropic cylinders, and also avoids the tedious integral operations in the traditional Legendre polynomial method. The reliability of the numerical results of longitudinal guided waves propagating in arbitrary multi-layered anisotropic pipes was investigated based on the state matrix and Legendre polynomial hybrid method. At first, we calculated the multi-layered pipes composed of isotropic materials (steel and aluminum) with different diameter-thickness ratios and circumferential orders, and the results are consistent with the ones from the global matrix method. Then, the numerical analysis for a triple-layered adhesive pipe was implemented. Finally, the composite multi-layered pipes with at most 16 layers, which are the T300/914 in different orientations, were studied. Meanwhile, the effect of the layer number, fiber angle and circumferential order on the propagation characteristics of longitudinal guided waves were analyzed. To demonstrate the generality of this approach, we compared the dispersion curves of flat plate case with the results from the cylindrical case using the same physical properties by making the geometrical diameter to thickness ratio infinity. Furthermore, the displacements and stress distributions were also illustrated at given frequencies.

Anisotropic pipelines in deep-sea mining: an approximate model for stability analysis

FLOW-INDUCED INSTABILITY ANALYSIS of long, fibre-reinforced, pipes used for deep-sea mining applications is performed. The transfer-matrix method is implemented to the motion equation of a multi-layered anisotropic pipe for critical flow-velocity calculation. The mechanical properties of the laminated material as well as the mass of the hanged pump and the flow parameters are taken into account. Numerical results of representative examples are provided and discussed.

An Approximate Method for Stress Analysis in Butt Joints of FRP Pipelines

Butt joint is a standard connection type for FRP pipelines. Shear stresses are taking place on the interfaces between the wrapping layer and the pipeline. An analytical model for calculating above stresses for joints subjected to axial loading is presented. The model is based on the equilibrium equations of an adhesive element and the bonded pipe elements, as well as the material properties of the anisotropic pipe wall, the wrapping element and the adhesive. Numerical results for typical FRP joints are derived and commented.

Limiting deformation in rotary drawing of anisotropic pipe blanks with wall thinning

The limiting deformation in rotary drawing of anisotropic pipe blanks with wall thinning is studied theoretically. The maximum tensile stress at exit from the plastic deformation region is determined.

The application of the acoustoelasticity method for the determination of stresses in anisotropic pipe steels

Elastoacoustic coupling coefficients (EACCs) are links between acoustic parameters and mechanical stresses during their determination by the acoustoelasticity method. The magnitudes of the EACCs of a structural material can be calculated if its elasticity constants of the second and third orders are known or determined experimentally for a known stress state of a material. Unfortunately, the calculation variant is little used practically because not all moduli of nonlinear elasticity of even basic structural materials are known with sufficient accuracy. Here, the results are given of the experimental determination of the magnitudes of EACCs for three grades of low-alloy structural steels with different magnitudes of proper acoustic anisotropy, which is determined by the anisotropy of the elastic properties of a material. During the mechanical tests, samples were subjected to uniaxial tension at stepped load magnitudes. They were cut from longitudinal welded tubes of the K60 strength class, which are applied in the mounting of a linear section of gas-main pipelines. Experiments were carried out using an acoustic bench (based on an I2-26 off-the-shelf device) and an IN-5101A automated device that was developed by the ENCOTES Engineering firm, which use the ultrasonic echo method for nondestructive testing. The results of the acoustomechanical tests showed that during the calculation of biaxial stresses according to the data of precise ultrasonic measurements in pipe steels with a magnitude of greater than 3% for the proper acoustic anisotropy, computational algorithms that take the differences of the magnitudes of EACCs into account for stresses that work along and across the direction of the rolling of pipe steel should be used, i.e., along and across the longitudinal axis of the pipe.

Measurement of the Distribution of Residual Stresses in Layered Thick-Walled GFRP Pipes

The objective of this study is to measure the axial, circumferential, shear and radial residual stress distributions in three thick-walled glass fibre reinforced plastic (GFRP) filament-wound pipes, two of which are layered. The measurement of residual stresses was carried out using a recently published layer removal method which overcomes the limitations of previous techniques and can be applied to layered anisotropic pipes of any wall thickness. Layers of approximately 0.3 mm thickness were incrementally ground from the outer surface of the pipes. The resulting strains were measured on the inner surfaces. A least-squares polynomial was fitted to each measured data set, and used to calculate the corresponding stress distributions. All of the resulting axial, hoop and shear stress distributions adhere to the requirement of self-equilibrium and the radial stress distributions all vanish to zero at the inner and outer surfaces. The radial stresses of the layered pipes showed a tendency to have two peaks, one for each layer, a consequence of the two-stage manufacturing process of these pipes. The measured axial and hoop stresses of all three pipes were similar at the inner surfaces despite significant differences in the stiffnesses in the principal directions arising from different wind angles.

Extension of the layer removal technique for the measurement of residual stresses in layered anisotropic cylinders

An extension of the layer removal technique is presented that allows the residual stresses within multilayered anisotropic pipes of any wall thickness to be determined. The method inherently satisfies the self-equilibrium requirement and limits the effects of measurement errors to the region local to the error. The thickness of each layer that is removed need not be uniform and is entirely independent of the thickness of each ply of material. Four example problems are considered. The first three allow results to be compared between the present method and previous work. The fourth problem demonstrates the method on a thick walled anisotropic pipe built up of +45°/-45° plies for which no solution was previously available.

Long Destruction of Structurally Damaged Composite Pipe

Composite materials represent the important class of anisotropic materials. Unlike the previous works of authors in which estimations of long durability of an anisotropic pipe are given within the bounds of criterion of the destruction being generalization of the first theory of durability on the maximal stretching or compressing strain on the account of the process of damageability, in the given work the estimation of long durability is given within the bounds of the structural criterion of durability offered in work of one of the authors. According to him, destruction of a material is defined by the greatest level of the accumulated volume of damageability on some of proper stress-strain states. A problem in revealing stages of scattered destruction of an anisotropic pipe with the use of the simplified variant of criterion of durability, has been solved in the given work.

Low‐frequency symmetric waves in fluid‐filled boreholes and pipes with radial layering

ABSTRACTMany tasks in geophysics and acoustics require estimation of mode velocities in cylindrically layered media. For example, acoustic logging or monitoring in open and cased boreholes need to account for radial inhomogeneity caused by layers inside the borehole (sand screen, gravel pack, casing) as well as layers outside (cement, altered and unaltered formation layers). For these purposes it is convenient to study a general model of cylindrically layered media with inner fluid layer and free surface on the outside. Unbounded surrounding media can be described as a limiting case of this general model when thickness of the outer layer is infinite. At low frequencies such composite media support two symmetric modes called Stoneley (tube) and plate (extensional) wave. Simple expressions are obtained for these two mode velocities valid at zero frequency. They are written in a general form using elements of a propagator matrix describing axisymmetric waves in the entire layered composite. This allows one to apply the same formalism and compute velocities for n‐layered composites as well as anisotropic pipes. It is demonstrated that the model of periodical cylindrical layers is equivalent to a homogeneous radially transversely isotropic media when the number of periods increases to infinity, whereas their thickness goes to zero. Numerical examples confirm good validity of obtained expressions and suggest that even small number of periods may already be well described by equivalent homogeneous anisotropic media.

Dispersion of circumferential waves in cylindrically anisotropic layered pipes in plane strain

Dispersion spectra of circumferential waves along the periphery of circular pipes made of layered anisotropic materials do not seem to be available in literature. This note attempts to partially fill this gap by providing the dispersion spectra in two and three layered cylindrically anisotropic pipes in plane strain motion. The spectra for pipes executing time harmonic vibrations in plane strain condition are obtained as roots of a numerical characteristic equation derived extending a weighted residual method of solution of the governing equations for a single layer pipe [Towfighi et al., J. Appl. Mech. 69, 283-291 (2002)] to a general N layered pipe. The anisotropic elastic coefficients are considered to be independent of position coordinates and the bond condition at interfaces of the layers is assumed to be perfect. Numerical illustrations are presented for two and three layered pipes with anisotropy directions differing in adjacent layers. Increase in curvature of the pipe and inclination of the fiber orientation in the outermost layers to propagation direction are factors that seem to influence the mode number and pattern within the limited examples worked out.

Rotary extension of anisotropic pipe blank with wall thinning

Rotary extension is being increasingly used in the manufacture of thin-walled axisymmetric parts. Theoretical study of this process with thinning is complicated by local deformation and by the three-dimensional stress and strain states of the material in the plastic region [1‐4]. The pipe blank subjected to rotary extension is characterized by anisotropy of the mechanical properties due to the material and the manufacturing conditions. Anisotropy of the mechanical properties of the material may have both positive and negative effects on the stability of pressure treatment of metals [5]. Consider the rotary extension of a thin-walled pipe blank made of anisotropic material, by a direct method (Fig. 1); conical rollers are employed (conical angle α ro and strain e = 1 ‐ t co / t 0 ). In one turn of the blank, the roller moves by an amount equal to the working supply S . With supply of the roller by S , the actual supply will be S ac = St co / t 0 . Plane deformation along the axis is assumed here. On the basis of geometric considerations, it is simple to determine the maximum contact angle θ b of the roller with the blank [4]

Analytical Calculation of the Transient Thermoelastic Stresses in Thick Walled Composite Pipes

This article aims at assessing the internal stresses in thick laminated pipes, composed of orthotropic plies, subjected to transient thermal fields. The original contribution of the work is to provide novel analytical solutions, based on well-founded assumptions, to compute the internal stresses due to transient thermal fields throughout the pipe thickness, within the framework of thermoelasticity. The structures considered here are thick, laminated and anisotropic pipes of infinite length. They are subjected to heat flux conditions on their inner and outer surfaces due to the environmental conditions. The transient thermal field is determined and the thermoelastic stresses are derived by using the classical equations of solid mechanics and assuming a thermoelastic orthotropic ply behavior. Finally, particular attention is paid to wall thickness effect.

厚肉フィラメントワインディングパイプの構造解析

The stress distribution of anisotropic multilayer filament-wound composite pipes was analyzed. Based on the three-dimensional anisotropic elasticity and the classical laminated-plate theory, exact elastic solutions of stress and deformation were presented for the filament-wound pipes subjected either to internal pressure, axial force or torsion. The shear coupling effect is considered in the analysis. The influence of winding angle and winding sequence on stress distribution in pipes was investigated. The ratio of hoop-to-axial stress is 2:1 in orthotropic pipes; however, the ratio proved to be not 2:1 in anisotropic pipes due to the coupling effect. The stress and deformation of filament-wound pipes strongly depend on the winding angle and the winding sequence.