On the Mechanical Behavior of Viscoelastic/Plastic Solids

1963 ◽  
Vol 30 (3) ◽  
pp. 321-328 ◽  
Author(s):  
P. M. Naghdi ◽  
S. A. Murch
Keyword(s):  
Plastic Strain ◽  
Time History ◽  
Present Theory ◽  
Plastic Strain Rate ◽  
Plastic State ◽  
Strain Rates ◽  
Stress Space ◽  
Loading Surface ◽  
Rate Vector ◽  
History Of

This paper is concerned with a theory of viscoelastic/plastic solids which reduces to that of the classical (linear) viscoelasticity as one limiting case and to the (inviscid) theory of elastic/plastic solids in another. Whereas the viscoelastic strain rates are assumed to be derivable from the appropriate creep integral laws of classical viscoelasticity, the plastic strain rates in stress space are dependent not only on the path history but also the time history of stress. After postulating the existence of a regular loading surface in the viscoelastic-plastic state and deducing the appropriate criterion for loading, a major portion of the paper is devoted to establishing (a) the convexity of the loading surface, (b) the direction of the plastic strain-rate vector in stress space, and (c) the structure of the constitutive equations for the plastic strain rates. The loading surface of the present theory (in contrast to that of the inviscid theory of plasticity), being dependent on certain measures representing time history of stress, is allowed to change its shape continually; this has implications in the interpretation of experimental results dealing with the determination of the initial and subsequent yield surfaces where corners are observed.

An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity

1985 ◽  
Vol 107 (4) ◽  
pp. 307-315 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Yield Surface ◽  
Hysteresis Loops ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Plastic Strain Rate ◽  
Hardening Modulus ◽  
Rate Vector ◽  
Strain Rate Vector

Three type 304 stainless steel specimens of the same geometry were subjected to complex, cyclic axial-torsional histories characterized by varying degrees of non-proportionality of straining. All tests were at room-temperature. The data from cyclically stable hysteresis loops were reduced and the direction of the plastic strain rate vector, variation of plastic hardening modulus, and direction of translation of a rate and time-independent yield surface were studied. It is shown that the independent variables in a Mroz-type formulation map the experimental results with a higher degree of uniqueness than other popular formulations studied for both the hardening modulus and direction of yield surface translation. Also, the plastic strain rate is not, in general, in the direction of the deviatoric stress or stress rate.

Biaxial Tensile Test of High Strength Steel Sheet for Large Plastic Strain Range

2012 ◽  
Vol 504-506 ◽  
pp. 59-64 ◽  
Author(s):  
Tomoyuki Hakoyama ◽  
Toshihiko Kuwabara
Keyword(s):  
Plastic Strain ◽  
High Strength Steel ◽  
Deformation Behavior ◽  
Equivalent Plastic Strain ◽  
Strain Range ◽  
High Strength ◽  
Test Material ◽  
Strain Rates ◽  
Stress Space ◽  
Plastic Strain Range

Deformation behavior of high strength steel with a tensile strength of 590 MPa under biaxial tension was investigated for a work equivalent plastic strain range of 0.002 0.16. The test material was bent and laser welded to fabricate a tubular specimen with an inner diameter of 44.6mm and wall thickness of 1.2 mm. Using a servo-controlled tension-internal pressure testing machine, many linear stress paths in the first quadrant of stress space were applied to the tubular specimens. Moreover, biaxial tensile tests using a cruciform specimen were performed to precisely measure the deformation behavior of the test material for a small strain range following initial yielding. True stress-true plastic strain curves, contours of plastic work in stress space and the directions of plastic strain rates were measured and compared with those calculated using selected yield functions. The plastic deformation behavior up to an equivalent plastic strain of 0.16 was successfully measured. The Yld2000-2d yield function most closely predicts the general work contour trends and the directions of plastic strain rates of the test material.

Experimentally Evaluating the Equilibrium Stress in Shear of Glassy Polycarbonate

2006 ◽  
Vol 128 (4) ◽  
pp. 537-542 ◽  
Author(s):  
Mehrdad Negahban ◽  
Ashwani Goel ◽  
Pierre Delabarre ◽  
Ruqiang Feng ◽  
Amy Dimick
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Mechanical Response ◽  
Deformation Gradient ◽  
Back Stress ◽  
Glassy Polymers ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Strain Rates ◽  
Equilibrium Stress

One group of models proposed for characterizing the mechanical response of glassy polymers is based on a structure that resembles finite plasticity. In most cases, a constitutive equation for stress is proposed, which depends on the elastic deformation gradient, supplemented by a flow rule for the plastic deformation, which depends on the “over stress.” The over stress is a properly invariant difference between the stress and the back stress (equilibrium stress). The back stress represents conditions under which relaxation events should stop and the material should be able to carry an applied load indefinitely without a need to change the strain. Questions that arise in using these models are whether such equilibrium stresses exist, how can they be evaluated, and what experiments can be used to characterize the flow rule. One challenge in accurately evaluating the locus of equilibrium conditions is the fact that the relaxation process substantially slow down around these points, and, therefore, a method that does not directly require being at the equilibrium is desirable. Focusing on shear, a thermodynamic theory for characterizing the response of glassy polymers, similar to models currently used for this purpose, is developed, and using this model it is shown that one can set up a method to calculate the plastic strain rate. This method is based on evaluating the slope of stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since the equilibrium stress occurs when the plastic strain rate goes to zero, the evaluated plastic strain rates allow evaluation of the needed information for developing the flow rule and obtaining the back stress. This method is used to evaluate the plastic strain rate and back stress at room temperature for polycarbonate. The evaluated results match well with results obtained by direct probing of the equilibrium stress, in which one searches for points at which the stress remains constant at a constant strain over long durations. The method proposed looks promising in evaluating the back stress of glassy polymers. The added advantage of this method is that it also provides a map of plastic strain rate and tangent modulus over a large range of loading conditions.

An Experimental Investigation Into the Plastic Flow and Strain Hardening of Mild Steel Under Proportional and Abruptly Changing Deformation Paths at a Controlled Rate

1983 ◽  
Vol 105 (3) ◽  
pp. 147-154 ◽  
Author(s):  
S. A. Meguid ◽  
L. E. Malvern
Keyword(s):  
Plastic Strain ◽  
Equivalent Stress ◽  
Equivalent Plastic Strain ◽  
Plastic Strain Rate ◽  
Isotropic Hardening ◽  
Rate Vector ◽  
Vector Direction ◽  
Von Mises Equivalent Stress ◽  
Strain Rate Vector ◽  
Von Mises

Tension-torsion tests are reported on thin-walled tubes up to strains of the order of five percent. Attention was given to the question of whether, as has been suggested, in the continued loading after a sudden direction change in the deformation path, the behavior of the material quickly approaches that predicted by a von Mises plastic potential and isotropic hardening. The results show a slower approach of the deviatoric stress vector direction to the plastic strain-rate vector direction than had been expected, as well as considerable variations in the von Mises equivalent stress versus equivalent plastic strain curves.

PROGRAM OF PREDICTION AND MANAGEMENT OF COINTEGED DYNAMIC ECONOMIC PROCESSES BASED ON THE CYBERNETIC APPROACH

2019 ◽  
Author(s):  
Olena Bundak ◽  
Nataliia Zubovetska
Keyword(s):  
Computer Program ◽  
Pair Correlation ◽  
Time History ◽  
Critical Area ◽  
Concrete Object ◽  
Graphic Arts ◽  
Ex Post ◽  
History Of ◽  
Successive Change ◽  
Rms Errors

A method and computer program ConRow, which prognostication of development of the dynamically CPLD economic transients is executed by, is described in the article. Such prognostication of economic processes is very important in the cases when their development can result in undesirable consequences, that to go out in the so-called critical area. Extrapolation in a critical area with the use of information about the conduct of the system at an area, near to it, allows to estimate to the lead through of experiment in the critical area of his consequence. For the imitation of conduct of object the function of review is set on entrance influence. For a concrete object this function can express, for example, dependence of change of level sale from time-history of charges on advertising and set as a numeral row. Statistics as a result of analysis of row are represented in a table, where the level of meaningfulness is set statistician, and also parameters of the handed over criteria. The graphic reflection of information is intended for visualization of analysis. Here represented on the points of graphic arts, the crooked smoothing which are calculated as полиномиальные regressions is added. The best approaching is controlled by sight on the proper graph, and also by minimization of their rms errors. Models of prognostication by sight and as formulas represented on graphic arts, the middle is here determined tailings and their chance is checked up on statistics of signs. After the got models determined also and prognosis values of influences and reviews. Establishing an order models of Сr(p) of co integrate regression is carried out separate custom controls. The coefficient of clay correlation of ruФ shows by itself pair correlation between lines with a successive change in relation to each other on a size to лагу of l = 1, 2, 3 . The program was tested on the example of ex-post prognosis at establishing an integration connection and possibility of prognostication of growth of nominal average monthly settlings on the basis of these statistical indexes of consumer inflation in Ukraine.

scholarly journals Comparison of Novel Seismic Protection Devices to Attenuate the Earthquake Induced Energy

Actuators ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 73
Author(s):  
Osman Hansu ◽  
Esra Mete Güneyisi
Keyword(s):  
Lateral Displacement ◽  
Time History ◽  
Seismic Protection ◽  
Base Shear ◽  
Seismic Demands ◽  
Nonlinear Time History Analyses ◽  
History Of ◽  
Protection Devices ◽  
Nonlinear Time History ◽  
Better Than

This study addresses an alternative use of viscous dampers (VDs) associated with buckling restrained braces (BRBs) as innovative seismic protection devices. For this purpose, 4-, 8- and 12-story steel bare frames were designed with 6.5 m equal span length and 4 m story height. Thereafter, they were seismically improved by mounting the VDs and BRBs in three patterns, namely outer bays, inner bays, and all bays over the frame heights. The structures were modeled using SAP 2000 software and evaluated by the nonlinear time history analyses subjected to the six natural ground motions. The seismic responses of the structures were investigated for the lateral displacement, interstory drift, absolute acceleration, maximum base shear, and time history of roof displacement. The results clearly indicated that the VDs and BRBs reduced seismic demands significantly compared to the bare frame. Moreover, the all-bay pattern performed better than the others.

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