Necking of elasto-plastic rods under tension

This work is concerned with the modeling of the necking phenomenon in metallic tension members using a non-linear theory of elasto-plastic rods with deformable cross section. The study of the coupling between the axial deformation and the cross section deformation in tensile specimens is a basic step to understand the strain-softening and localization behaviors in more complex metallic structures. The main features of the model are illustrated through the simulation of the necking of an ASTM 6351 aluminium bar under tension.     

Cold drawing of elastic-thermoviscoplastic polymeric films and fibres

Finite element analyses of the process of polymer drawing for elastic-thermoviscoplastic material behaviour are performed. The deformation-induced heat generation and its softening effect are accounted for. Non-adiabatic thermal effects are examined from the beginning of the loading process, to the attainment of the nearly steady-state neck propagation stages. Solutions for both polymeric films as well as fibres are presented.     

Strain distributions in the cold drawing of cylindrical polymeric bars using photoplasticity

Full-field strain distributions in the cold drawing of polycarbonate cylindrical bars are obtained using photoplasticity at three stages of neck propagation. The results indicate that the radial and circumferential strains are almost identical. The strain distributions in the seemingly straight (drawn) portion are nonuiform. The locations of maximum and minimum strains shift when elongations increase. Various sensitivity studies are also reported.     

Analytical derivation of earing in circular cup drawing based on simple tension properties

In the circular cylindrical cup drawing process of sheet materials, an earing profile develops, incurred by the planar anisotropic properties of sheets. Therefore, proper analysis of earing in cup drawing is important to evaluate anisotropic properties and also to control the development of earing. Even though anisotropic properties are commonly measured in the simple tension test, deformation in circular cylindrical cup drawing is in a near plane strain mode (at the flange) so that numerical simulations utilizing yield functions are common practices to analyze earing. In this work, simplified analytical derivation of earing development in circular cylindrical cup drawing is proposed, based on two simple tension anisotropic properties: the yield stress and the r-value. Good performance of the analytical derivation was verified for AA2090-T3, which has strong anisotropy and six ears in cup drawing. Since the current approach directly utilizes measured simple tension data without involving any yield functions, computational cost is significantly lower. Besides, the current derivation can handle any set of detailed anisotropic measurements in the simple tension test, unlike numerical approaches involving yield functions, which need the development of sophisticated yield functions in the first place.     

Inelastic deformation and localization in polycarbonate under tension

It is demonstrated that uniaxial tension deformation in polycarbonate and other polymers that exhibit large inelastic deformation is unstable beyond a certain stretch. The instability first appears as a shear banding phenomenon at a characteristic angle and is then followed by a stabilized neck generation and propagation. The intrinsic material law for polycarbonate is used in a numerical implementation to reproduce completely the deformation behavior observed in uniaxial tension. In particular, it is demonstrated through numerical simulations, that intrinsic material softening is not necessary for the formation of a shear band and continued growth of a stable neck and further that the interpretation of the tensile response in terms of the constitutive behavior of the material poses significant problems.     

Photoviscoplastic investigations of slip-line fields and principal-stress trajectories in viscoelastoplastic strip for drawing with back tension

Photoviscoplasticity is applied to the drawing with back tension through rollers and wedge-shaped dies in model tests of plane-strain state. The effects of the back tension on the slip-line fields and on the principal-stress trajectories for the strips are discussed in the light of experimental results obtained from the model tests. Actual strips are considered as viscoelastoplastic media in the actual drawing processes. The model specimens used are softened celluloid as the viscoelastoplastic medium for the strip and Araldite as the glassy elastic medium for the dies. At a suitable experimental temperature, the viscoelastoplastic strip is drawn viscoplastically through the gap between the dies mentioned above. The slip-line fields, the principal-stress trajectories in the strip and the normal pressure on the contact surface are greatly influenced by the effect of the back tension.     

Fragmentations of solids under impact tension

固体材料在冲击拉伸载荷作用下常常会断裂成多个碎片(碎片化),固体材料碎片化的物理机制是多点损伤同时在固体中成核和发展,导致固体多处破坏.自Mott对固体的动态碎裂问题进行了开创性研究后,几十年来,对固体动态碎裂机制的研究一直是应用物理学、力学、航天和兵器工程等领域共同关心的重要课题.本文介绍了在冲击拉伸载荷作用下固体的动态碎裂研究的发展历史,给出相关的理论分析、实验研究和数值模拟的研究进展,特别针对现有的各种关于碎片尺度、碎片分布、以及碎片化物理机制的理论模型进行了较详尽的阐述和讨论,最后指出现有实验和理论研究中仍然存在的关键科学问题及进一步的研究展望.     

固体的冲击拉伸碎裂

固体材料在冲击拉伸载荷作用下常常会断裂成多个碎片(碎片化),固体材料碎片化的物理机制是多点损伤同时在固体中成核和发展,导致固体多处破坏。自 Mott 对固体的动态碎裂问题进行了开创性研究后,几十年来,对固体动态碎裂机制的研究一直是应用物理学、力学、航天和兵器工程等领域共同关心的重要课题。本文介绍了在冲击拉伸载荷作用下固体的动态碎裂研究的发展历史,给出相关的理论分析、实验研究和数值模拟的研究进展,特别针对现有的各种关于碎片尺度、碎片分布、以及碎片化物理机制的理论模型进行了较详尽的阐述和讨论,最后指出现有实验和理论研究中仍然存在的关键科学问题及进一步的研究展望。     

Fluid-pressure eigenstates and bifurcation in tension specimens under lateral pressure

An analysis is presented of an eigenstate that may be significant in deformation processes where part of the surface of a body is subjected to loading by uniform fluid pressure. The ‘fluid-pressure eigenstate’ is a configuration in which quasi-static incremental deformation is possible under surface traction-rates that are related to the instantaneous velocity field in a certain way, the fluid pressure being momentarily stationary. Deformation processes exist such that, given certain rate boundary-conditions, uniqueness of the incremental deformation is guaranteed at every instant up to a fluid-pressure eigenstate. For a cylindrical specimen, of arbitrary cross-section, of elastic/plastic or incompressible, finite elastic material it is shown that the first fluid-pressure eigenstate to be reached on a path of uniform stretching corresponds to the instant at which the ‘effective load’ reaches a maximum. No fluid-pressure eigenstates are reached in isotropic Cauchy-elastic solids under all-round fluid pressure loading provided the physically reasonable conditions that the instantaneous bulk and shear moduli remain positive are satisfied.     

Fractal characteristics of rocks fractured under tension

Fractal geometry can be useful for explaining the fracture behavior and rock properties. The fractal properties of rock fracture surface developed under tension were examined. Seven different rock samples were selected for the tests. An automated surface scanning device was used to map the fractured surfaces. Variogram analysis (VA) (for 1D self-affine sets) and power spectral density (PSD) measurement (for 2D self-affine sets) were applied to calculate the fractal dimension. On a comparative basis, there exists a trend between the fractal dimension and loading rate. The profiles in the loading direction yield higher fractal dimensions indicating the anisotropic feature of fractal. The fractal dimensions obtained by PSD and VA display a relationship for grain size and porosity. Higher porosity samples give different fractal dimensions for upper and lower fractures surfaces.     

Bifurcation in compressible elastic/plastic cylinders under uniaxial tension

The bifurcation problem of a circular cylinder of elastic/plastic material under uniaxial tension is investigated, with particular reference to the usual engineering criterion that necking is initiated when the load on the specimen reaches a maximum. The material considered is compressible, with a smooth yield surface and associated flow rule. A lower bound analysis shows that for the particular constitutive equation chosen bifurcation cannot occur under a range of loading conditions while the stress is less than a certain value which is itself slightly less than the stress at the maximum load point. Diffuse axisymmetric necking modes under the commonly assumed loading conditions of prescribed axial components of velocity and shear-free traction-rates on the ends are, however, found to be initiated always after maximum load, the delay depending on the same factors shown for an incompressible material in reference [1]. The effect of the elastic compressibility assumption is to reduce the delay for a wide range of geometries, but to increase it for very slender specimens, as compared with the incompressible case. Surface modes are also found, but at stresses of an unrealistically high order of magnitude.     

Influence of the gas flow rate on the drawing of optical fibers from fluoride glasses

Angarsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 84–87, September–October, 1994.