Buckling stresses of composite tubes under biaxial compressive loads

An analytical model describing the instability of specially orthotropic composite tubes with geometric imperfections subject to biaxial compressive loads and under clamped-clamped boundary conditions is developed. Furthermore, the range of validity of the present solution is clarified, and comparisons are made to some studies on isotropic cylindrical shells. Six E-glass woven fabric-epoxy composite tubes with the same internal radius and different thicknesses and longitudinal lengths were fabricated and subjected to various combinations of external hydrostatic pressure and axial compressive load simultaneously. The normalized buckling stresses were found to agree in general with the theoretical predictions at various biaxial loadings. The buckling envelopes in normalization form provide useful design data on the strength of specially orthotropic composite tubes under a realistic range of biaxial loading conditions.     

Hysteretic damping of structural materials under biaxial dynamic stresses

Results of damping measurements for mild steel under biaxial dynamic stresses are discussed. Experimental methods are described, and a phenomenological theory of damping is presented to set the context for the discussion. The experiments indicate that dilatational as well as distortional stresses are important in the damping of polycrystalline materials.     

Some considerations on instability of combined loaded thin-walled tubes with a crack

Instability of a thin-walled stainless steel tube with a crack-shaped defect under combined loading is studied in this paper. Furthermore, the effects of the tube length, crack orientation, and crack length on the buckling behavior of tubes are investigated. The behavior of tubes subjected to combined is analyzed by using the finite element method (by Abaqus software). For cracked tubes with a fixed thickness, the buckling load decreases as the tube length and the ratio of the tube length to its diameter increase. Moreover, the buckling load of cracked tubes under combined loading also decreases with increasing crack length.     

A simple testing technique for fracture under biaxial stresses

Evidence is accumulating to suggest that the fracture toughness of and cyclic crack-propagation rates in a material may be affected by stresses acting parallel to the crack plane. This effect contradicts the justifiable assumption, implicit in fracture-mechanics theory, that only loads causing a stress singularity at the tip of a crack can affect its behavior. More extensive investigation of this important problem involves the development of special testing equipment and specimens. This article offers a simple design for such a system, which has proved in practice to be highly reliable and of adequate accuracy. Preliminary tests on polymethylmethacrylate (PMMA) under biaxial fatigue and ramp loading are described, to demonstrate the technique itself and the phenomena under investigation. The results suggest that, for this material at least, the effects of transverse stresses are indeed slight.     

An experimental investigation of plastic flow under biaxial stress

Due to the extreme complexity of the problem, it has been necessary to formulate theories of plasticity which grossly simplify the material behavior. While, in many cases, these theories give satisfactory results, there are other cases in which they fail. Therefore an investigation has been initiated with the purpose of evaluating presently used theories and assessing the possibilities for improvement for the cases in which the classical theories are not satisfactory. The present paper describes a system for testing, which includes a data-acquisition system and a computer program for comparisons between test and theory. A few test results are included which verify the adequacy of the system and illustrate some facets of the problem.     

Experimental studies on thin-walled grooved tubes under axial compression

We study experimentally the axial crushing behavior and crashworthiness characteristics of thin-walled steel tubes containing annular grooves. The grooves determine the positions of the folds and control the buckling mode of deformation. In the present work we aim to improve the uniformity of the load-displacement behavior and to predict the energy absorption capacity of the tubes. Grooves are cut circumferentially and alternately inside and outside the tubes at predetermined intervals. Quasi-static axial crushing tests are performed with different groove distances. Photographs are taken during axial buckling and the specimens after crushing are sectioned axially to carry out the measurements. The deformation modes and load-displacement curves are described and energy absorption and mean post-buckling load are determined. The convolutions are achieved by folding in an axisymmetric concertina mode about the circumferential grooves. The results show that the load-displacement curve and energy absorbed by the axial crushing of tubes can be controlled by the introduction of grooves with different distances.     

Isoclinic parameters for biaxial creep of celluloid under variable stresses

The behavior of isoclinic parameters for biaxial creep under variable stresses was investigated by creep tests with cyclic stress reversal or stepwise changes in stress including unloading for thin-walled tubes of softened celluloid under combinations of axial and torsional stresses. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

Free-surface roughness of thin-walled tubes in reduction

The problem of the stress-strain state of thin-walled tubes in axisymmetric steady-state deformation is solved using the membrane theory of shells and the model of an ideal rigid-plastic material satisfying the Mises yield condition and the associated flow law. The obtained solution is used together with the empirical relation between the strain state at an arbitrary point of the free surface and the surface roughness parameters at the same point to determine the influence of some tube reduction parameters on the surface roughness parameters in the product. The employed empirical relation is derived assuming that the free surface roughness parameters depend on two independent kinematic variables.     

轴向冲击载荷下薄壁折纹管的屈曲模态与吸能

在方管的基础上引入折纹结构, 利用几何关系建立折纹管的折角公式。采用LS-DYNA软件研究了6种折纹管在轴向冲击下的屈曲模态与能量吸收性能, 并与方管进行对比分析。结果表明, 折纹管在冲击载荷作用下屈曲变形过程可分为3个阶段, 初始峰值阶段、稳定渐进屈曲阶段和密实化阶段。折角是影响初始峰值载荷和平均载荷的重要因素之一, 折纹结构的引入有效的降低了初始峰值载荷, 减小了冲击力的波动幅度; 折纹管的比吸能低于方管, 但是在特定折角下, 折纹管的压缩力效率和比总体效率高于方管。     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

A high-strain biaxial-testing rig for thin-walled tubes under axial load and pressure

It is well know that high-strain biaxial testing with axial force and pressure on thin-walled tubes can be interesting from several points of view: capability of testing over the whole range of strain or stress ratios, great versatility of testing. and because of the physical system, the measured strains and stresses are principal. Nevertheless, there are few experimental-biaxial-fatique data due to the complexity of the testing equipment involved. In this paper, an experimental testing rig capable of subjecting thin-walled tubes to combined dynamic loadings in tension-compression with torsion and tension-compression with internal-external pressure is presented. The following components are described: the mechanical and hydraulic system, servohydraulic control, specimen configuration, strain-measuring equipment and data-acquisition system. The computation of stresses and strains, as well as examples of data acquisition, are also shown.     

Imperfection-sensitivity in the plastic range

The effect of small imperfections on the buckling of continuous structures loaded into the plastic range is studied. A simple model study is presented and several additional examples are discussed. The rôle of the load at which elastic unloading first occurs is emphasized, and a general asymptotic analysis is given for the behavior prior to the onset of elastic unloading for a class of elastic-plastic solids subject to loads characterized by a single load parameter. Asymptotic imperfection-sensitivity formulae are obtained whose features are similar to analogous formulae for elastic structures.     

低速冲击下泡沫金属填充薄壁圆管的弯曲行为

采用实验方法研究了低速冲击下泡沫金属填充薄壁圆管的弯曲行为,详细说明了实验方法和原 理。通过与准静态实验结果的比较发现,冲击加载使泡沫金属填充圆管跨中截面的局部压入变形增大,跨中 截面高度变小,结构下缘拉裂破坏延迟。由于结构的惯性效应,锤头总冲击力高于准静态加载时的对应值。     

Residual stresses in roller-expanded thin tubes

The residual-stress distribution of through-the-wall thickness in the roller-expanded region of thin-walled incoloy-800 Fe–Ni–Cr alloy tubing was determined. Such tubes are commonly used in the fabrication of steam generators for nuclear-power stations. For the present study, the test specimens consisted of short lengths of tubing which were roller-expanded into tubesheet simulation blocks. Some of the specimens were then heat treated. The measurement method involved the installation of strain-gage rosette strips on the inner tube wall. Strain measurements were first taken after the removal of the tubesheet simulation block. Residual stresses were then released by progressive chemical etching of the outer tube wall. In some cases the inner tube wall was etched instead and this required the removal of the inner strain-gage strip and its replacement by one attached to the outer wall. A calculation procedure based on the Sachs approach, first proposed for straight unrolled tubes, was used for determining the residual-stress distribution in the vicinity of the roller-expanded zone and through-the-wall thickness. Surface residual stresses of the order of 250 MPa were determined in the as-received specimens. Residual stresses in the stress-relieved heat-treated specimens were generally lower by about 40 percent. Contact stresses were nearly eliminated by the heat-treating process. The residual stresses in the various specimens of the same type compared to within a standard deviation of 35 MPa.     

Combined plastic waves in a thin-walled tube

A theory of plasticity without a yield surface is applied to obtain the simple wave solution of a thin-walled tube subject to the combined step loading. Four wave speeds are obtained in this analysis; all speeds involve the coupling of the longitudinal and the torsional motions as well as the loading and the unloading behaviors. Several numerical examples of our theoretical analysis and their comparisons with the experimental data and with the existing theory are also presented. The constant state region between slow and fast waves is not apparent in the present analysis. This is in good agreement with the experiment. Moreover, the predicted final state of shear strain is higher than the experimental, but less than Lipkin and Clifton's result.     

The initiation of necking in rectangular elastic/plastic specimens under uniaxial and biaxial tension

Necking in a rectangular parallelepiped of incompressible elastic/plastic material under uniaxia tension is studied as a bifurcation problem. Approximate upper-bound bifurcation stresses are found which show that bifurcation can occur immediately after the load on the specimen reaches a maximum if the length of the specimen is sufficiently great compared to the width and thickness. A simple formula applicable to sufficiently thin specimens is obtained for the approximate bifurcation stress. Sufficient conditions for uniqueness are found for elastic/plastic solids subjected to a general homogeneous stress-field. The particular case of the rectangular specimen under equal biaxial tension is investigated further, and the magnitude of the bifurcation stress is found to be very sensitive to the particular boundary conditions imposed.