Exact solution of flow theory problems with isotropic-kinematic hardening. Part 2. Setting of the deformation trajectory in the spaces of total and plastic strains

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

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Localized Necking in Elastomer-Supported Metal Layers: Impact of Kinematic Hardening

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4035183 ◽

2017 ◽

Vol 139 (6) ◽

Cited By ~ 2

Author(s):

Mohamed Ben Bettaieb ◽

Farid Abed-Meraim

Keyword(s):

Parametric Study ◽

Strain Path ◽

Kinematic Hardening ◽

Metal Layer ◽

Initial Imperfection ◽

Flow Theory ◽

Rigid Plastic ◽

Localized Necking ◽

Metal Sheets ◽

Metal Layers

This paper deals with localized necking in stretched metal sheets using the initial imperfection approach. The first objective is to study the effect of kinematic hardening on the formability of a freestanding metal layer. To this end, the behavior of the metal layer is assumed to follow the rigid-plastic rate-independent flow theory. The isotropic (respectively, kinematic) hardening of this metal is modeled by the Hollomon (respectively, Prager) law. A parametric study is carried out in order to investigate the effect of kinematic hardening on the formability limits. It is shown that the effect of kinematic hardening on the ductility limit is noticeably different depending on the strain path considered. The second aim of this paper is to analyze the effect of an elastomer substrate, perfectly bonded to the metal layer, on the formability of the whole bilayer. It is found that the addition of an elastomer layer substantially enhances the formability of the bilayer, in agreement with earlier studies.

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Analysis for Thermal Elasto-Plasticity and Creep of Turbine Disks

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Process Industries; Technology Resources; General ◽

10.1115/85-igt-54 ◽

1985 ◽

Author(s):

Shung Chang-Bing ◽

Peng Zhi-Yong

Keyword(s):

Kinematic Hardening ◽

Hold Time ◽

Three Dimensional ◽

Plastic Strains ◽

Creep Life ◽

Hardening Rule ◽

Elasto Plasticity ◽

Stress Surface ◽

Turbine Disks ◽

Plastic Creep

This paper analyzes the thermal elastic-plastic-creep at the bottom of slots in turbine disks using three-dimensional finite elements. Considering the low cycle of engine parts during takeoff-operating-landing process, the yield stress surface of the material is treated according to the kinematic hardening rule. Since the plastic strains are caused by transient loads when starting the engine, being time-independent, while the creep strains are caused by hold time and large loads under high temperature, being time-dependent, the calculation is performed for these two cases, respectively. This would be more correspondent to the practical states of engine. The computation results show that the creep of turbine disks is under neither constant stresses nor constant strains, but is under the combination of both. This phenomenon brings forward a new concept to predict the fatigue/creep life of turbine disks.

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Load Controlled Cyclic Loading of Transversely Isotropic Cylindrical Vessels Based on the Anisotropic Kinematic Hardening Models

Journal of Pressure Vessel Technology ◽

10.1115/1.4035727 ◽

2017 ◽

Vol 139 (3) ◽

Cited By ~ 1

Author(s):

M. Ejtemajou ◽

H. Mahbadi ◽

M. R. Eslami

Keyword(s):

Yield Criterion ◽

Kinematic Hardening ◽

Transversely Isotropic ◽

Flow Rule ◽

Anisotropy Ratio ◽

Plastic Strains ◽

Isotropic Materials ◽

Theory Of Plasticity ◽

Hardening Theory ◽

The Hill

This study evaluates the plastic responses of thick cylinders made of transversely isotropic materials under mechanical cyclic loads, using the kinematic hardening theory of plasticity. The Hill yield criterion is adapted to the kinematic hardening theory of plasticity. The constitutive equations of plastic strains are obtained using the adapted yield criterion. The flow rule based on the kinematic hardening theory of plasticity associated with the Hill yield criterion is represented to evaluate the cyclic behavior of transversely isotropic cylindrical vessels. A numerical method is proposed to calculate the stresses and plastic strains in this structure due to the cycling of pressure at its inside surface. The numerical solution is validated simplifying the results with those of isotropic materials. Using the proposed method, the effect of anisotropy on ratcheting and shakedown response of the vessel is evaluated. It has been shown that the ratcheting or shakedown response of the vessel and the rate of ratcheting are highly affected by the anisotropy ratio. The numerical results of this paper show that the yield strength ratio, which is affected by initial work hardening of the metal, may control the ratcheting behavior of the cylindrical vessels.

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A new method of complex structure analysis by electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100110283 ◽

1978 ◽

Vol 36 (1) ◽

pp. 628-629

Author(s):

V.V. Rybin ◽

E.V. Voronina

Keyword(s):

Complex Structure ◽

Reciprocal Lattice ◽

Stacking Faults ◽

Plastic Strains ◽

Base Position ◽

Structural Regularity ◽

Orientation Matrix ◽

Computerized Processing ◽

Fully Automatic ◽

Diffraction Patterns

Recently, it has become essential to develop a helpful method of the complete crystallographic identification of fine fragmented crystals. This was maainly due to the investigation into structural regularity of large plastic strains. The method should be practicable for determining crystallographic orientation (CO) of elastically stressed micro areas of the order of several micron fractions in size and filled with λ>1010 cm-2 density dislocations or stacking faults. The method must provide the misorientation vectors of the adjacent fragments when the angle ω changes from 0 to 180° with the accuracy of 0,3°. The problem is that the actual electron diffraction patterns obtained from fine fragmented crystals are the superpositions of reflections from various fragments, though more than one or two reflections from a fragment are hardly possible. Finally, the method should afford fully automatic computerized processing of the experimental results.The proposed method meets all the above requirements. It implies the construction for a certain base position of the crystal the orientation matrix (0M) A, which gives a single intercorrelation between the coordinates of the unity vector in the reference coordinate system (RCS) and those of the same vector in the crystal reciprocal lattice base : .

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