Wavy-edged fractures in axially split aluminium tubes

This paper is motivated by the somewhat unusual need to gain insight into the phenomenology of the mechanism by which a wavy edge is formed on the wreckage of some aircraft fuselage skins associated with aircraft destroyed in flight by on-board explosion.In order to explore the role of the plastic zone adjacent to the crack tip whilst avoiding the practical complications of generating the fractures explosively, simple quasi-static experiments have been carried out on aluminium tubes. Oversized rigid dies were pushed inside the tubes along their axes to generate fractures in Mode I and Mode III. It is conjectured that wavy edges are associated with fractures resulting from internal expansion of the tube by a travelling, internal, radial ring pressure region. The pressurised region behind the crack tip would be produced by explosively generated internal pressure being vented at the crack and, for the purpose of this study, is considered to be equivalent to that generated by the die. The production of such cracks is clearly demonstrated experimentally and contrasted with the plain-edge fractures produces during Mode III tearing fracture.A damage-model-based finite element analysis has been conducted to simulate the propagation of the crack and provide further insight into the strain and stress fields along the fractured edges. Both the experimental and numerical results show that this particular type of ring loading has to be applied to the tube to produce the wavy edge. Such a load expands the fractured flaps in the radial direction, stretching the material in the circumferential direction and, crucially, in the axial direction. The latter generates a relatively wide plastic wake close to and parallel to the fracture edge as the tube fails within which axial plastic strain predominates. Constrained by the remaining part of the tube that has not undergone plastic deformation, sufficient axial residual compressive stress can be produced in the plastic wake to produce a wavy edge which results from local buckling in the plastic wake. This mechanism suggests that ripples observed on the edges of fuselage skin wreckage are possible signatures of an internal explosion. The work described herein is also relevant to the deformation in a failed high-pressure gas pipe following the propagation of a ductile crack as noted previously in the literature.     

Elastic-plastic behaviour with work-hardening: An appropriate model for structural software

Summary A method is proposed for the stress analysis of structures subject to elastic and plastic deformations. The method can be adapted to exploit existing computing programs for elastic stress analysis and is sufficiently subtle to describe a variety of types of work-hardening, on the basis of a limited number of essential material parameters which can be read off usually available test graphs.

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Sommario Si propone un metodo per l'analisi di strutture soggette a deformazioni elasto-plastiche. Il metodo può essere adattato in modo da sfruttare programmi di calcolo, di cui già si disponga, per l'analisi elastica di strutture ed è sufficientemente duttile da consentire la rappresentazione di tipi diversi di incrudimento, con l'uso di un numero limitato di parametri materiali che possono dedursi da grafici sforzo-deformazione generalmente disponibili.

     

Creep of metal torsion-tension members subjected to nonproportionate load changes

The creep behavior of torsion-tension members subjected to nonproportionate loading was studied by testing members made of SAE 1035 steel at 975° F and of copper alloy 360 at 700° F. Creep curves for these members were predicted by an incremental theory using both the strain-hardening rule and the time-hardening rule and a total-strain theory using the incremental-hardening rule. Both incremental theories were based on a creep law which assumed that the total strain in specimens subjected to constant stress was made up of an elastic component and a creep component given by a power function of stress and of time. The total-strain theory was based on isochronous stress-strain curves which were approximated by an arc hyperbolic sine relation. The creep tests were limited to a total duration of 60 min. The nonproportionate loading was obtained by stepped increases of either the axial load, the torque, or both at 30 min. Except for the incremental theory based on the time-hardening rule, good agreement was found between theory and experiment.     

开孔泡沫铝填充圆管的准静态压缩行为

采用开孔结构泡沫铝填充到薄壁圆形铝管中,制备出开孔泡沫铝夹芯铝管,并进行压缩实验,研究了这种结构材料的压缩力学行为和变形特征以及材料的结构特征参数对压缩力学性能和能量吸收特性的影响。在压缩过程中,泡沫铝夹芯铝管的载荷-位移曲线呈现出弹性段、波动的屈服平台段和压实段3个阶段特征;铝管的径厚比及泡沫铝本身的参数和强度对填充管的屈服强度、平均压溃力和吸能特性均有着非常显著的影响。填充泡沫铝后铝管的压缩变形方式发生改变,管壁只发生向外翻折变形,产生的环状褶皱减少。     

Initiation and propagation of fatigue crack in pure aluminium single crystals

The fatigue crack initiation and propagation in the pure aluminum single crystals with different orientations are investigated. Acoustic Emission (AE) technique is used to monitor the fatigue crack initiation and propagation data. The results show that the acoustic emission technique could be used for detecting fatigue crack initiation and propagation. The total counts of AE are plotted as a function of the number of fatigue cycles, and change in slope of the curve corresponded to the initiation of the fatigue crack. The fatigue crack initiation and propagation are related to the specimen crystalline orientation. Specifically, they depend on the ratio K of the Schmid factor of the secondary slip system, to that of the primary one. The greater the ratio K, the easier the fatigue crack initiates and the faster the fatigue crack propagates. When the ratio K is equal or close to one, the fatigue crack grows either along a cleavage plane which intersects both the primary plane and the secondary one or along the primary slip plane and the secondary one. Growth along alternating planes can also occur giving rise to a zigzag path. When the ratio K is much less than one, the fatigue crack grows along the primary slip plane only. The results are explained with a model for the faceted mode of fatigue crack growth.     

A study of directionality of latent hardening behavior in aluminium single crystals

By defining the yield stress in a latent hardening test as the first deviation from the elastic straight line, the yielding and hardening behavior on a latent system in the positive and negative slip direction was studied in aluminium single crystals. It is shown that the yield stresses on both the positive and negative latent systems are about equal to or a little lower than the maximum resolved shear stress in the primary test, but much higher than that of the active system. The influence of relative orientation and prestrain on latent hardening and initial work-hardening in the secondary test was also investigated, and it was found that there is a considerable effect on initial work-hardening, but none on latent hardening. With reasonable approximation, a hardening rule for single crystal could be proposed from the experimental results, that is, except for the yield stress on the system negative to the active system that is very low, hardening on the other systems is nearly the same as self-hardening.     

Acceleration waves in rate type plastic material with general work-hardening

The acceleration waves propagating in the rate type plastic material are investigated, where the material has isotropic and kinematic work-hardening. The waves are classified into unloading and loading waves, and have, in general, different propagation velocities. The propagation velocities of the principal waves are obtained for the Prandtl-Reuss material and the T material.     

Arc Hyperbolic sine creep theory applied to torsion-tension member of circular cross section

A multiaxial creep theory is presented in this paper which will predict the total deformations of a load-carrying member at any specified time after load. Load-deformation relations are derived based on the assumption that the isochronous stress-strain diagram of the material can be represented by an arc hyperbolic sine function [see, eq (2)]. A closed solution was obtained for the torsion-tension member considered in this investigation. Experimental data were obtainsed for nylon and high-density polyethylene members in a controlled-environment room and for 17-7PH stainless-steel members at 972° F. Good agreement was found between theory and experiment.Formerly with Department of Theoretical and Applied Mechaaics, University of Illinois, Urbana, Ill.Paper was presented at 1963 SESA Spring Meeting held in Seatle, Wash., on May 8–10.     

A constitutive model accounting for strain ageing effects on work-hardening. Application to a C–Mn steel

One of the most successful models for describing the Portevin–Le Chatelier effect in engineering applications is the Kubin–Estrin–McCormick model (KEMC). In the present work, the influence of dynamic strain ageing on dynamic recovery due to dislocation annihilation is introduced in order to improve the KEMC model. This modification accounts for additional strain hardening rate due to limited dislocation annihilation by the diffusion of solute atoms and dislocation pinning at low strain rate and/or high temperature. The parameters associated with this novel formulation are identified based on tensile tests for a C–Mn steel at seven temperatures ranging from 20 °C to 350 °C. The validity of the model and the improvement compared to existing models are tested using 2D and 3D finite element simulations of the Portevin–Le Chatelier effect in tension.     

Theoretical latent hardening in crystals—I. General equations for tension and compression with application to F.C.C. crystals in tension

Equations for latent strengths in single slip, based upon the simple theory of finite distortional crystal hardening introduced by K.S. Havner and A.H. Shalaby (1977), are derived for both tensile and compression tests without restriction as to crystal class. Detailed comparisons between theoretical results and the experiments of P.J. Jackson and Z.S. Basinski (1967) on copper crystals in tension are presented. There is good qualitative agreement between theory and experiment regarding the diversity of anisotropic hardening among slip systems. Moreover, there is satisfactory quantitative agreement between the theory and the extrapolated experimental data in the stage III, large-strain range. It is suggested that further experimental investigation of latent hardening at large prestrains would be desirable.The simple theory predicts anisotropic hardening and the perpetuation of single slip in axial loading of cubic crystals initially oriented for single slip, but predicts symmetric, isotropic hardening of specimens initially oriented in positions of 4, 6 or 8-fold multiple-slip. These predictions are in general accord with experimental observations from tests of f.c.c. and b.c.c. crystals.     

Dynamical behaviors of a trimolecular response model with impulsive input

In the paper, we consider a trimolecular response model with impulsive input. Sufficient conditions for globally stable positive equilibrium point of the trimolecular response model with constant input are obtained. By impulsive differential theory, we obtain conditions for permanence of the trimolecular response model with impulsive input. By numerical analysis, we demonstrate complex phenomena such as limit cycles, periodic solutions, and chaos.     

Damage accumulation for growth of anti-plane crack in work-hardening material

Elastic–plastic solutions of an anti-plane crack in an infinite body are used in conjunction with a continuum damage model to describe the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to time dependent events. A power law relates the stress to the strain of the material. The damage, which invokes nucleation, growth and coalescence of microvoids due to elevated strain, is confined to the plastic zone surrounding the crack tip. For applied loading below the yield stress, the small-scale and large-scale yielding solutions are used to determine the influence of strain hardening on crack instability and failure. Crack growth due to cyclic loading and time-dependent deformations are studied using the small-scale yielding solution of the deformation theory of plasticity.     

Problem of gas motion in tubes of variable cross section and its application to solar wind perturbations

A qualitative study of self-similar flows with consideration of possible initial gas motion is performed for the problem of motion of a variable density gas in shock tubes with varying cross section. Asymptotic formulas are obtained near the contact discontinuity, and a numerical solution is obtained for the case of finite density on the contact surface. The equations are applied to the problem of gas motion in solar flares, and the parameters of the disturbed magnetic field are calculated. The results of the computation are compared with data from shock-wave observation in outer space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–89, May–June, 1976.The author thanks V. P. Korobeinikov for his valuable advice and interest in the study.     

Micromechanical model of stage I to stage II crack growth transition for aluminium alloys

Stage I to Stage II crack growth transition is a kinetic process that is particularly studied in this work. Crack growth transition is modelled to occur when small fatigue crack growth is deterred by an effective barrier that reduces the crack growth rate to a minimum. Effective blockage of small crack growth due to barriers is characterised by pile-up of dislocations. Crack tip pile-up sliding displacement is formulated by adopting a continuous configuration of dislocation pile-up. Transition condition is quantitatively determined when a crack tip sliding displacement of Stage I cracks just meets a crack tip opening displacement of Stage II cracks. As a result, a dislocation-based micromechanical model is systematically developed that enables kinetic predictions of crack growth transition and growth rates of small fatigue cracks. Moreover, the concept of microstructurally-affected-zone is further interpreted in terms of local microstructure and load levels, leading to good explanations for scatters of small crack growth. All model-based growth rate predictions show a good coincidence with experimental results.     

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.     

Change in thickness in curved fold model for axial crushing of tubes

A partly inside and partly outside curved fold model with variable straight length and stepped variation in the thickness of tube during folding has been developed in the present paper. The variation of circumferential strain during the formation of fold has been taken into consideration. All model parameters viz. size of fold, optimal value of folding parameter, maximum hinge angle and the final radius of curvature of fold have been evaluated analytically. An expression has been derived for determining the variation of crushing load during the formation of a fold. The total outside and total inside fold models can be easily derived from the present model. The results have been compared with experiments and reasonably good agreement has been observed. The incorporation of change in thickness of tube during folding has been found to reduce the folding parameter thus bringing it closer to the experiments. Some parametric studies by varying the length of straight portion of the fold have also been conducted. The results are of help in understanding the phenomenon of actual fold formation.     

A numerical model for thermal systems with helically-coiled tubes and its experimental verification

 A conjugate numerical model proposed by Nakayama et al. for the steady problem of cooling a fluid flowing through a coiled tube, has been successfully extended to investigate two distinctive thermal problems, namely, the transient cooling processes associated with a beer dispenser, and the transient processes of heat storage and recovery associated with a packed bed saturated with a molten salt. An axisymmetric numerical procedure is adopted for determining the velocity and temperature fields within the chilled water bath of the beer dispenser. A simplified one-dimensional heat transfer model is introduced for coupling the tube flow with the recirculating flow in the bath. A similar axisymmetric finite difference procedure is applied for the heat transfer analysis of the packed bed saturated with a molten salt. For the heat recovery process, a one-dimensional heat balance equation for the two-phase flow with a helically-coiled tube is introduced to update the wall surface temperatures, which are needed to calculate the temperature field in the saturated packed bed. The numerical results for both thermal systems associated with coiled tubes agree very well with the corresponding velocity and temperature data obtained from the experiments. Received on 28 August 2000 / Published online: 29 November 2001     

HILL屈服准则与晶体塑性模型对FCC单晶材料塑性各向异性描述能力的比较

采用宏观HILL模型和晶体塑性模型对面心立方单晶(FCC)材料的非均匀交形进行了数值模拟，意在比较两种不同尺度的模型对塑性各向异性的描述能力的差异。为了使两种模型具有可比性，对于FCC单晶材科，本文提出一种用晶体塑性模型来确定HILL模型中各向异性参数的标定方法。数值分析表明，两类模型对单晶体塑性各向异性的描述能力存在着差异。对FCC单晶材料，HILL模型对各向异性的预测能力没有晶体塑性模型细致，晶体塑性模型更能追踪塑性各向异性的变化。但两种模型对应力应变响应预测的趋势是一致的。对两种模型描述的差异，做了详细的分析。