A Simplified Theory of the Constitutive Equations of Metal Plasticity at Finite Deformation

1973 ◽  
Vol 40 (4) ◽  
pp. 941-947 ◽  
Author(s):  
Y.-S. Wang
Keyword(s):  
Constitutive Equations ◽  
Energy Equation ◽  
Finite Deformations ◽  
Plastic Strain Rate ◽  
Internal Variables ◽  
Deformation Model ◽  
Normality Condition ◽  
Rate Vector ◽  
Strain Rate Vector ◽  
Viscoplastic Solids

Derivation of the constitutive equations of elastic-plastic and elastic-viscoplastic solids at finite deformations is discussed. The deformation is uncoupled by using the Lee-Freund three-configuration deformation model. By assuming elastic properties to be independent of plastic deformation, the elastic and plastic (or viscoplastic) constitutive equations are essentially uncoupled. The normality condition of the plastic strain-rate vector to the yield surface in stress space is obtained by incorporating the concept of internal variables in the energy equation.

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.

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.

Shock Thickness in Viscoplastic Solids

1970 ◽  
Vol 37 (1) ◽  
pp. 163-170 ◽  
Author(s):  
J. M. Kelly ◽  
P. P. Gillis
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Finite Deformation ◽  
Constitutive Equations ◽  
Wave Speed ◽  
Constitutive Relations ◽  
Plastic Strain Rate ◽  
Plastic Materials ◽  
Elastic Plastic Materials ◽  
Viscoplastic Solids

In this paper a system of constitutive relations for plane-strain finite deformation in strain-rate sensitive elastic-plastic materials is developed. A method is presented for computing the main features of steady-state one-dimensional plastic-strain waves by elementary numerical techniques in materials of this type. This method is applicable to a wide variety of material constitutive relations and provides an alternative to computing complete wave profiles for investigators interested primarily in the effects of certain numerical parameters on the principal features of waves. The method is illustrated by use of particular constitutive relations but is applicable to a much wider class of relations. Maximum normal stress, pressure, and shear stress are computed, using this method, as a function of wave speed. For two different plastic strain-rate relations the maximum plastic strain rate and total strain are computed as a function of wave speed. Making use of these results, estimates are provided for the wave-front thickness in terms of wave speed and the parameters of the particular viscoplastic constitutive equations used. These results suggest ways in which plastic wave experiments can be used to motivate the construction of constitutive equations for finite deformation in strain-rate sensitive plastic solids.

A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

Improved Constitutive Equations for Modeling Strain Softening—Part II: Predictions for Aluminum

1984 ◽  
Vol 106 (4) ◽  
pp. 343-348 ◽  
Author(s):  
T. C. Lowe ◽  
A. K. Miller
Keyword(s):  
High Purity ◽  
Constitutive Equations ◽  
Strain Softening ◽  
Substantial Improvement ◽  
Deformation Model ◽  
Independent Data ◽  
Model Predictions ◽  
Deformation Behaviors ◽  
High Purity Aluminum

The capabilities of a new deformation model, MATMOD-4V, are demonstrated by comparison of computer predictions against independent data for high purity aluminum. In particular, model predictions of strain softening are presented and discussed. The predictive abilities of MATMOD-4V represent a substantial improvement over earlier versions of the MATMOD constitutive equations. The strength of the approach is illustrated by MATMOD-4V’s ability to predict deformation behaviors not explicitly built into the model.

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.

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