The Elastic-Plastic Response of Thin-Walled Tubes Under Combined Axial and Torsional Loads: Part I—Monotonic Loading

1993 ◽  
Vol 115 (3) ◽  
pp. 283-290 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Kinematic Hardening ◽  
Plastic Response ◽  
Proportional Loading ◽  
Closed Form Solutions ◽  
Elastic Plastic ◽  
Hardening Behavior ◽  
Torsional Loads ◽  
Thin Walled ◽  
Path Dependent ◽  
Linear Loading

This paper investigates the elastic-plastic response of thin-walled tubes subjected to combined axial and torsional loads. The kinematic hardening model is used and exact closed-form solutions are obtained for linear loading paths. The characteristics of the stress-strain relationships are discussed and the corresponding movements of the yield center are illustrated. The response of the material under nonproportional loading is proved to be path-dependent, and the hardening behavior is shown to be different from that under proportional loading. The investigation then shows that such a difference will finally disappear when the stresses tend to infinity.

The Elastic-Plastic Response of Thin-Walled Tubes Under Combined Axial and Torsional Loads: Part II—Variable Loading

1993 ◽  
Vol 115 (3) ◽  
pp. 291-296 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Kinematic Hardening ◽  
Material Behavior ◽  
Plastic Response ◽  
Variable Loading ◽  
Proportional Loading ◽  
Elastic Plastic ◽  
Torsional Loads ◽  
Thin Walled ◽  
The Difference ◽  
Elastic Shakedown

This paper continues the investigation of the elastic-plastic response of thin-walled tubes subjected to combined axial and torsional loads. The stress-strain loop under arbitrary variable loading is first discussed. It is then shown that due to the kinematic hardening, a steady state, either one of the reversed plasticity or one of the elastic shakedown, can always be reached under cyclic loadings, with a hysteresis loop in the form of a parallelogram or a straight line. As a result, the difference in response between nonproportional and proportional loading will finally disappear. The investigation indicates that the simple kinematic hardening rule is able to describe, at least qualitatively, certain basic characteristics of the material behavior observed in nonproportional tests.

An Expression of Elastic-Plastic Constitutive Law Incorporating Vertex Formation and Kinematic Hardening

1991 ◽  
Vol 58 (3) ◽  
pp. 617-622 ◽  
Author(s):  
Moriaki Goya ◽  
Koichi Ito
Keyword(s):  
Kinematic Hardening ◽  
Sufficient Conditions ◽  
Constitutive Law ◽  
Elastic Plastic ◽  
Hardening Rule ◽  
Direction Angle ◽  
Plastic Materials ◽  
Path Direction ◽  
Elastic Plastic Materials ◽  
Linear Loading

A phenomenological corner theory was proposed for elastic-plastic materials by the authors in the previous paper (Goya and Ito, 1980). The theory was developed by introducing two transition parameters, μ (α) and β (α), which, respectively, denote the normalized magnitude and direction angle of plastic strain increments, and both monotonously vary with the direction angle of stress increments. The purpose of this report is to incorporate the Bauschinger effect into the above theory. This is achieved by the introduction of Ziegler’s kinematic hardening rule. To demonstrate the validity and applicability of a newly developed theory, we analyze the bilinear strain-path problem using the developed equation, in which, after some linear loading, the path is abruptly changed to various directions. In the calculation, specific functions, such as μ (α) = Cos (.5πα/αmax) and β (α) = (αmax- .5π) α/αmax, are chosen for the transition parameters. As has been demonstrated by numerous experimental research on this problem, the results in this report also show a distinctive decrease of the effective stress just after the change of path direction. Discussions are also made on the uniqueness of the inversion of the constitutive equation, and sufficient conditions for such uniqueness are revealed in terms of μ(α), β(α) and some work-hardening coefficients.

scholarly journals Large elastic-plastic deformation of square membranes subjected to localised pulse pressure loads

2019 ◽  
pp. 126-133
Author(s):  
N. Mehreganian ◽  
A. S. Fallah ◽  
L. A. Louca
Keyword(s):  
Pulse Pressure ◽  
Constitutive Relations ◽  
Energy Functional ◽  
Steel Plates ◽  
Elastic Response ◽  
Plastic Response ◽  
Closed Form Solutions ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Ductile isotropic materials are widely used in protective systems against transient pulse pressure loads, such as those of localised blasts. This is due to the combined elastic-plastic response which contributes to dissipation of total impulse from extensive loading as the energy stored elastically limits deformation while the energy expended plastically limits the level of transferred forces in the structure. In the case of thin, modern armour graded steel plates, the tailored metallurgy helps the structure store energy within the bounds of elastic region, which may be dissipated at a later stage as damping kills it off in subsequent cycles. On the other hand, the plastic work is almost entirely converted to heat and dissipates. The present work focuses on the elastic and plastic energies in the membrane and aims at deducing, from the minimization of Föppl-Von-Kármán (FVK) energy functional combined with enforcing the constitutive relations of limit analysis, the dynamic elastic-plastic response of localised blast loaded square membranes undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various temporal shapes (e.g. rectangular, linear, exponential). Considering the elastic response, a single-degree-of-freedom model was developed from the prescribed displacement field and associated stress tensor having clamped and simply supported boundary conditions. The explicit closed form solutions were sought by using the Ritz-Galerkin’s variational method as well as the Poincaré-Lindstedt perturbation method. The theoretical solutions of rigid-perfectly plastic square membranes subjected to the same blast scenarios were then discussed. From the combined effects we deduce the load displacement curves representing the trajectory of the nonlinear elastic-perfectly plastic structure.

Constitutive Equations of Elastoplastic Materials With Elastic-Plastic Transition

1980 ◽  
Vol 47 (2) ◽  
pp. 266-272 ◽  
Author(s):  
K. Hashiguchi
Keyword(s):  
Yield Surface ◽  
Constitutive Equations ◽  
Granular Media ◽  
Kinematic Hardening ◽  
Careful Consideration ◽  
Elastic Plastic ◽  
Transitional State ◽  
Hardening Behavior ◽  
Softening Behavior ◽  
Elastoplastic Materials

Constitutive equations of elastoplastic materials with an elastic-plastic transition observed in the loading state after a first yield are presented by introducing a new parameter denoting the ratio of the size of a loading surface in the transitional state to that of a yield surface in the classical idealization which ignores the transitional state. These equations involve a reasonably simplified rule for the kinematic hardening. They would describe reasonably not only the hardening behavior but especially the softening behavior which requires our careful consideration about the elastic-plastic transition. From these equations, moreover, we derive plastic constitutive equations specifically of metals and granular media which exhibit very different plastic behaviors. Besides, brief discussions are provided concerning the existing constitutive equations describing the elastic-plastic transition.

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

Elastic-plastic response of a sandwich cylinder subjected to internal pressure

1971 ◽  
Vol 6 (4) ◽  
pp. 273-278 ◽  
Author(s):  
H F Muensterer ◽  
F P J Rimrott
Keyword(s):  
Mild Steel ◽  
Internal Pressure ◽  
Plastic Flow ◽  
Plastic Response ◽  
Concentric Cylinders ◽  
Initial Stage ◽  
Sandwich Type ◽  
Plastic Zones ◽  
Thin Walled ◽  
Von Mises

The propagation of plastic zones in a thin-walled sandwich-type cylinder has been analysed theoretically. Boundary conditions are clamped-clamped at both ends, i.e. no rotation is permitted. The material was assumed to behave isotropically and to obey the yieid criterion of Huber-Hencky-von Mises. Deformation was computed on the assumption that the vector of rate of strain was normal to the plastic-interaction curve. The predicted result was verified experimentally. Four specimens were built by lamination of a hexcell core between two concentric cylinders. In the two mild-steel specimens, the initial stage of plastic flow conformed well with the prediction. This proved that plastic flow is not initiated at the mid-position between the end constraints. In two aluminium specimens, this phenomenon of incipient plastic flow could not be observed owing to the absence of a pronounced yield point. The overall agreement was, however, satisfactory.

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