Buckling of polymer pipes under internal pressure

In this work, the buckling phenomenon of slender pressurized pipes under concentrically applied indirect axial force is experimentally and theoretically investigated. The axial force is applied via a frictionless piston. The deformation trend of a polyvinylchloride pipe sample under this compressive axial force is monitored by means of a number of strain gauges. The strain readings are processed by a computer equipped with strain processing software. The buckling modes as well as the buckling load of the system are thus experimentally determined. To describe the stability behaviour of the pipe analytically, several theoretical models are employed and the buckling phenomenon in such a pressurized pipe is analytically ascertained. Numerical values for the critical buckling loads are also obtained. The experimental and theoretical buckling studies are correlated. Through these correlations, the buckling of pressurized pipes under indirect axial pressure is substantiated and an appropriate theoretical model to describe the phenomenon is established.     

Influence of winding angle on the strength and deformation of filament-wound composite tubes subjected to uniaxial and biaxial loads

Experimental data are presented to show the effects of winding angle on the strength of 100 mm diameter, 1 mm thick, filament wound E-glass fibre reinforced epoxy resin tubes tested under various combinations of internal pressure and axial tension or compression. Leakage and fracture strength envelopes are presented for ±45°, ±55° and ±75° winding angle tubes subjected to a wide range of different biaxial membrane stress states. Strengths range from 30 to 1250 MPa. Axial compression test results for tubes with wall thicknesses ranging from 1 to 3·6 mm establish the influence of shell buckling. Stress/strain curves up to fracture under three different types of loading show the effects of the winding angle on elastic constants and on nonlinear stress strain behaviour.     

Scaling of impact damage in fiber composites from laboratory specimens to structures

Impact damage in fiber composite structures remains of much concern, and is often the limiting factor in establishing allowable strain levels. The complexity of impact damage formation usually dictates that experiments are required, but scaling of results from small laboratory scale specimens to large structures is not well understood. The following paper presents the results of an analytical and experimental investigation intended to develop procedures for prediction of damage formation and subsequent strength loss, with particular emphasis on scaling of results with respect to structure size. The experimental investigation involved both drop-weight and airgun impact on carbon/epoxy plates and cylinders. Five sizes of plates ranging from 50 × 50 × 1·072 mm to 250 × 250 × 5·36 mm, and two sizes of cylinders with diameters of 96·5 and 319 mm, were employed in the experimental program. Delamination was observed to increase with specimen size more than would be expected if stresses controlled the delamination extent, as would be predicted by fracture mechanics. Regions of broken fibers were observed in the impacted specimens, that were best correlated with the applied specimen stress or strains, independent of specimen size. It is seen that knowledge of the failure mechanisms involved is required to predict scaling of damage with confidence.     

Analysis of the elastic buckling of a plywood column

Buckling tests were conducted on specimens of 5-ply lauan plywood for a range of slenderness ratios to measure its buckling stress. Three-dimensional finite element calculations of buckling stress were performed and their validity examined by comparison with experimental results. Both experimental and calculated results revealed that buckling stress is influenced by Young’s modulus values (a measure of stiffness) obtained not only under flexural loading but also under axial loading. When the axial Young’s modulus is larger than the flexural Young’s modulus, the buckling stress is measured as larger than that obtained using the flexural Young’s modulus alone. Inversely, when the axial Young’s modulus is smaller than the flexural Young’s modulus, the buckling stress is measured as smaller than that obtained using the flexural Young’s modulus alone. Therefore, both the Young’s modulus values should be taken into account for determining the buckling stress of a plywood column.     

轴向受压CFRP管混凝土柱的膨胀模型及应力-应变关系

在实验基础上, 建立了CFRP 管混凝土柱的轴向压缩膨胀模型。利用膨胀模型计算的紧箍力变化规律和主动侧限混凝土柱的轴向压缩本构模型, 结合多轴应力下的混凝土破坏准则, 推导出被动侧限混凝土柱轴向压缩应力-应变关系理论表达式。根据各组份材料性能、含量、轴向压缩荷载作用下各组份的应力状态及变形协调条件, 建立了CFRP 管混凝土柱轴向压缩本构关系。实验结果证明, 理论预测结果与实验值吻合良好。      

Influence of hydrostatic pressure on the mechanical behavior and properties of unidirectional, laminated, graphite-fiber/epoxy-matrix thick composites

This paper reviews and gives new insight into earlier work by the author and his co-workers on the experimental investigation of the influence of superimposed hydrostatic pressure on the mechanical behavior and properties of the epoxy used for the matrix and unidirectionally laminated, graphite-fiber/ epoxy-matrix thick composites. The direction of the fibers was, respectively, 0°, 45° and 90° for the compressive test samples and 0°, 45° -45° and 90° for the shear samples.

Hydrostatic pressure induces very significant, often dramatic changes in the compressive and shear stress/ strain behavior of composites, and consequently in the elastic, yielding, deformation and fracture properties. The range of pressures covered for the compressive experiments was 1 bar to 4 kbar, and for the shear tests 1 bar to 6 kbar. The shear modulus (G) of the epoxy increased bilinearly with pressure, with the break, or the discontinuity point, occurring at 2 kbar. The compressive elastic modulus (E) and the shear modulus (G) of the composites increase in the same manner as for the epoxy. The break, which is located at 2 kbar, represents a pressure at which physical changes in the molecular motion of the matrix epoxy occur. That is, segmental motion of molecules between the cross-links is frozen in by 2 kbar pressure. This pressure is known as the secondary glass transition pressure of the epoxy at room temperature. Alternatively, the sub-zero secondary glass transition temperature of the epoxy is shifted to ambient temperature by 2 kbar pressure. The increase in the moduli may also be given a mechanical interpretation. The elastic or shear modulus of an isotropic, elastic material due to small compressive or shear deformations, respectively, superimposed on a finite volume deformation, which is caused by hydrostatic pressure, increases with pressure. Such an increase in E or G has been predicted using finite deformation theory of elasticity.

The normally brittle epoxy develops yielding when the superimposed hydrostatic pressure exceeds 2 kbar. The shear yield stress (1% off-set) of the epoxy increases linearly with pressure above 2 kbar. This kind of yielding behavior can be predicted by a pressure-dependent yield criterion. The compressive yield strength of the 45° and 90° composites increases bilinearly with pressure, and the shear yield strength of the 0°, 45° and 90° composites also increases bilinearly with pressure. This bilinear behavior is also due to the secondary glass transition pressure of the matrix epoxy, being located at 2 kbar. The fracture strength of the composites also increases with pressure linearly and the greatest increase occurs in the 45° composite in compression and in the −45° composite in shear. The fracture modes of the composites undergo changes with increasing hydrostatic pressure. For instance, the 0° composite undergoes a brittle-ductile transition under shear stress, while no such transition appears to set in under compressive stress. The fracture mode of the 45° composite changes from matrix failure at lower pressures to fiber failure at high pressures under shear stress.     

Three-dimensional finite element analysis of the stress concentration at a single fibre break

A linear elastic analysis is performed of a single broken fibre surrounded by six equally spaced fibres. These fibres and the surrounding epoxy matrix are modelled separately whilst the rest of the composite is treated as a homogeneous, orthotropic material. The distance of the adjacent fibres is fixed based on an assumed fibre volume fraction of 0·60. The analysis shows that the stress concentration in the adjacent fibres is 1·058, much lower than the value of 1·104 predicted by Hedgepeth and van Dyke (J. Comp. Mater., 1 (1967) 294–309). The positively affected length where there is an increase in stress is only about half the ineffective length of the broken fibre. Further away from the break the axial stress in the adjacent fibres actually drops below the nominal axial stress. This results in a very small enhanced probability of failure in the adjacent fibres. Very close local fibre spacing around the broken fibre increases the maximum stress in the adjacent fibres by less than 3%.     

Use of woven CFRP for externally pressurized domes

Sensitivity of bifurcation buckling, first-ply failure (FPF) and last-ply failure (LPF) to the different modelling methods of woven cloth is examined numerically for a range of torispherical shells. Axisymmetric and two two-dimensional models are used for externally pressurized multi-ply domes. In the first two-dimensional model, angles between warp and weft directions on torispheres are obtained through an optical projection of an initially orthogonal woven net. In the second type of modelling, a planar/orthogonal mapping is preserved on the torispherical geometry. Bifurcation buckling seems to be insensitive to the method of modelling. Results for FPF show that differences between axisymmetric and planar models can be as high as 50%, whilst the differences for optical and planar models can reach 30%. The magnitude of LPF pressures is also sensitive to the two-dimensional modelling method adopted. Ultimate collapse loads, associated with LPFs and based on optical modelling, are up to 30% higher than those obtained for planar modelling for carbon cloth.     

Behaviour of ±45° glass/epoxy filament wound composite tubes under quasi-static equal biaxial tension–compression loading: experimental results

The primary aim of this paper is to present results describing in detail the behaviour of ±45° E-glass/MY750 (GRP) tubes, of various wall thicknesses, subjected to equal biaxial tension–compression loading, generated under combined internal pressure and axial compression. The role played by the non-linear lamina shear has also been assessed by comparing various shear stress–strain curves for embedded laminae (extracted from tests on ±45° tubes subjected to circumferential: axial stress ratios SR=1:0, 1:−1 and 2.3:−1) with that of an ‘isolated’ lamina (measured from torsion of 90° tubes). Extracted shear failure strains, for embedded laminae, were more than four fold larger than those measured at ultimate failure for an ‘isolated’ lamina. Soft characteristics were observed in the embedded lamina and these were believed to be due to interaction between early matrix damage initiation (and propagation) and shear. Factors affecting the behaviour of the tubes, such as bulging, scissoring, thermal stresses and stress variation through the thickness are discussed.     

Experimental, numerical, and analytical results for buckling and post-buckling of orthotropic rectangular sandwich panels

Rectangular orthotropic sandwich fiber reinforced plastic (FRP) panels were tested for buckling in uniaxial compression. The panels, with either balsa or linear PVC foam cores, were tested in two sizes: 183 cm×92 cm (72 in.×36 in.) and 122 cm×92 cm (48 in.×36 in.) for aspect ratios of 2.0 and 1.3, respectively. The sandwich panels were fabricated using the vacuum-assisted resin transfer molding (VARTM) technique. The two short edges of the sandwich panels were clamped, while the two long edges were simply supported. The experimental elastic buckling loads of panels with an aspect ratio of 1.3 were 400 kN (90 klb) for balsa core panels and 267 kN (60 klb) for foam core panels. For balsa and foam core panels with an aspect ratio 2.0, the experimental buckling loads were 334 kN (75 klb) and 240 kN (54 klb), respectively. Experimental buckling results for balsa core panels of both sizes differed by 5–8% from numerical and analytical results. Differences in experimental and predicted buckling loads for foam core panels ranged between 15% and 23%. Post-buckling collapse of balsa and foam core panels with an aspect ratio of 1.3 were 694 kN (156 klb) and 347 kN (78 klb), respectively. For balsa and foam core panels with an aspect ratio of 2.0, post-buckling collapse occurred at 592 kN (133 klb) and 334 kN (75 klb), respectively. A numerical post-buckling analysis qualitatively followed that of the experimental results.     

The rate-dependent behaviour of ± 55 ° filament-wound glass-fibre/epoxy tubes under biaxial loading

This paper presents the results of an experimental investigation into the behaviour of glass-fibre-reinforced epoxy tubes subjected to monotonic biaxial loading. Commercially available tubes with a filament winding pattern of ± 55 ° were tested in a biaxial testing machine with various ratios of axial stress to hoop stress. In addition, the tubes were tested at three rates of monotonic loading. The resulting stress/strain curves were analyzed and biaxial failure envelopes in terms of stress and strain were constructed demonstrating the complexity of the behaviour of the tubes. It is shown that the rate and ratio of biaxial loading affect the monotonic failure strength, damage accumulation and the mode of failure. In addition, these results are discussed based on macro and micro observations of damage and failure modes.     

Twin-characteristic-parameters analysis for elastic dynamic buckling of thin cylindrical shells under axial step loading

The relations of the critical stress and transverse inertia effect to the loading duration are investigated for the dynamic buckling of thin cylindrical shells under axial step loading. The critical stress and the inertial exponent are treated as the two characteristic parameters. The criterion of energy conservation is used to derive the supplementary restraint condition for buckling deformations at compression wave front. By use of the Galerkin method, an algebraic eigenvalue problem for the two characteristic parameters is derived from the governing equations and boundary conditions. The solution of the eigenvalue problem, which satisfies the supplementary restraint condition, gives the values of the critical stress and the inertial exponent for the dynamic buckling. The relation of critical stress to loading duration, predicted by the theoretical analysis, is in reasonable agreement with the experimental results.     

新型负泊松比多孔吸能盒平台区力学性能

提出了一种具有负泊松比效应的汽车前纵梁吸能盒(NPRC)结构,通过对元胞平台区的失效模式和平台应力的分析,研究了此结构在失效时的力学性能,即等效弹性模量和平台应力在面内加载过程中均能得到一定程度的增强,表现出较好的能量吸收能力。根据NPRC元胞在平台区的力学模型,分别建立了发生弹性屈曲和塑性塌陷时的临界应力公式,得出塑性塌陷是该结构的主要失效模式。通过Matlab程序建立了NPRC元胞的参数化有限元模型,研究了元胞几何参数与平台应力的关系,即元胞的平台应力与长度系数和元胞夹角呈反比,与厚度系数呈正比。通过NPRC结构3×3样件的面内轴向准静态压缩实验验证了有限元分析结果,实验结果表明:NPRC样件等效负泊松比为-11.97,产生密实化现象,平台应力的峰值随着应变的增加逐渐增大,这对提高能量吸收性能具有重要的研究意义。     

Buckling and postbuckling of composite structures

The postbuckling behaviour of a flat, stiffened, carbon fibre composite compression panel has been studied, theoretically and experimentally. The panel had a collapse load in excess of three times the buckling load. An initial failure mechanism leading to eventual explosive collapse of the panel is identified and the damaging stress resultant is measured in the panel and predicted from a finite element analysis.     

Fatigue behaviour of alumina-fibre-reinforced epoxy resin composite pipes under tensile and compressive loading conditions

Fatigue tests have been conducted on composites consisting of epoxy resin reinforced with alumina fibres (AFRP) under cyclic tensile and compressive loading conditions with the variation of fibre orientation. The behaviour of the stress/strain curve for a ±45° sample is different from those for the ±15 and ±25° composite specimens, whereas, the monotonic strength decreases with increase in fibre angle for all specimens, which satisfies the maximum stress failure criterion. Fatigue results show that the applied stress decreases with an increase in the number of cycles to failure under both loading conditions for all composite pipes, but for the ±45° sample the decrease was slow. The results of fatigue tests on a macroscopic level indicate that the matrix crack density slowly increased with increase in the normalized number of cycles to failure in all the specimens. The normalized apparent stiffness therefore falls with an increase of the normalized number of cycles to failure. However, the maximum stress decreased with the increase in the number of cycles to failure in the case of the ±45° pipe. Finally, it is observed that matrix cracking and delaminations are occurring in the ±45° sample whereas delamination and fibre buckling are appearing in the ±15 and ±25° samples.     

基于多尺度方法的蜂窝夹层复合材料结构轴向压缩稳定性

为有效预测蜂窝夹层复合材料结构压缩失稳载荷和破坏模式,本文基于层压板宏细观多尺度数值分析模型,研究蜂窝夹层复合材料结构在轴向压缩载荷下的屈曲稳定性。基于改进的通用单胞理论模型,并结合ABAQUS用户自定义子程序接口,建立蜂窝夹层复合材料结构宏细观数值模型,预报蜂窝夹层复合材料结构失效载荷和破坏模式,并与试验结果对照,验证了模型的有效性。结果表明:通过本文建立的数值模型可以有效预测蜂窝夹层复合材料结构在压缩载荷下的失稳载荷和破坏模式,其一阶失稳载荷为128.12 kN,与试验结果误差为4.58%,蜂窝夹层复合材料结构破坏模式为先发生屈曲失稳,然后迅速破坏。      

Buckling of filament-wound composite cylinders subjected to hydrostatic pressure for underwater vehicle applications

The buckling and failure characteristics of moderately thick-walled filament-wound carbon–epoxy composite cylinders under external hydrostatic pressure were investigated through finite element analysis and testing for underwater vehicle applications. The winding angles were [±30/90]_FW, [±45/90]_FW and [±60/90]_FW. ACOS, an in-house finite element program, successfully predicted the buckling pressure of filament-wound composite cylinders with 2 ∼ 23% deviation from the test results. The analysis and test results showed that the cylinders do not recover the initial buckling pressure after buckling and that this leads directly to the collapse. Major failure modes in the test were dominated by the helical winding angles.     

Compressive strength of unidirectional fiber composites with matrix non-linearity

A study has been made of the effect of fiber misalignment and non-linear behavior of the matrix on fiber microbuckling and the compressive strength of a unidirectional fiber composite. The initial fiber misalignment constituted the combined axial and shear stress state in the matrix, and the state of stress just prior to the buckling was considered to be the initial state of stress in bifurcation analysis. The expression for the critical microbuckling stress was found to be the same as that for the elastic shear-mode microbuckling stress except that the matrix elastic shear modulus was replaced by the matrix elastic-plastic shear modulus. Incremental theory of plasticity and deformation theory of plasticity were used to model the matrix non-linearity. The analysis results showed reasonable correlation with available experimental data for AS4/3501-6 and AS4/PEEK graphite composites with 2° to 4° range of initial fiber misalignment.     

Effects of winding angle on the behaviour of glass/epoxy pipes under multiaxial cyclic loading

The effects of winding angle on the behaviour of glass/epoxy composite tubes under multiaxial cyclic loading were investigated. The performance of such composite tubes was studied using an indigenous automated test procedure that is compatible with the internal qualification requirements of the composite pipe manufacturers. Glass fibre reinforced epoxy (GRE) composite pipes with three winding angles, namely, [± 45°]₄, [± 55°]₄, and [± 63°]₄, were tested. A novel automated test rig was fabricated to accommodate five stress ratios, ranging from pure axial to pure hoop loadings. The cyclic pressure test was conducted until droplets of water were seen on the outer surface of the pipe. Failure envelopes were then constructed based on the first ply failure (FPF) points determined from the axial stress to hoop strain response at five stress ratios. Three functional failure modes, namely, tensile axial, weepage, and local leakage failures, were observed during the tests. The results indicate that each winding angle dominates a different optimum pressure loading condition, namely, [± 55°]₄ for pure hydrostatic loading, [± 45°]₄ for hoop to axial loading, and [± 63°]₄ for quad hoop to axial loading. The envelopes show a strong dependence on the stress ratio and winding angle.     

Compressive failure and kinking in uniaxially aligned glass-resin composite under superposed hydrostatic pressure

The failure process in uniaxially-aligned 60% fibre volume fraction glass fibre-epoxide compressive specimens strained parallel to the fibre axis was investigated at atmospheric and superposed hydrostatic pressures up to 300 MN m^–2. The atmospheric strength was about 1.15 GN m^–2 (about 20% less than the tensile) and strongly pressure dependent, rising to over 2.2 GN m^–2 at 300 MM m^–2 pressure, i.e. by about 30% per 100 MN m^–2 of superposed pressure. The corresponding figure is 22% if the maximum shear stress and not the maximum principal compressive stress is considered. This is incompatible with atmospheric compressive failure mechanisms controlled by weakly dependent or pressure independent processes, e.g. shear of the fibres. The results also could not be satisfactorily interpreted in terms of microbuckling of individual fibres. Kinking, involving buckling of fibre bundles was proposed as the mechanism of failure propagation, but the critical stage (for this glass reinforced plastic) is suggested as being yielding of the matrix, which initially restrains surface bundles from buckling. A strong pressure dependent failure criterion, about 25% increase per 100 MN m^–2, was derived by modifying the Swift-Piggott analysis of deformation of initially curved fibres. It is postulated that it is the axial compression that causes bundle curvature. Other systems, particularly carbon fibre-reinforced plastic, in which there appears to be a transition in the critical stage of failure from bundle buckling to matrix yielding with increasing superposed pressure, are also considered.