Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates

2000 ◽  
Vol 139 (1-4) ◽  
pp. 91-103 ◽  
Author(s):  
A. Meyers ◽  
P. Schie�e ◽  
O. T. Bruhns
Keyword(s):  
Strain Rates ◽  
Eulerian Strain ◽  
Objective Rates

Application of Objective Rates in Mechanical Modeling of Solids

1996 ◽  
Vol 63 (3) ◽  
pp. 692-698 ◽  
Author(s):  
W. D. Reinhardt ◽  
R. N. Dubey
Keyword(s):  
Simple Shear ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Logarithmic Strain ◽  
Mechanical Modeling ◽  
Rigid Plastic ◽  
Eulerian Strain ◽  
Objective Rate ◽  
Simple Shear Deformation ◽  
Objective Rates

A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and thermodynamical restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.

Comparison of Recovery and Recrystallization in Stainless Steel Following Plane-Wave Shock Loading and Explosive Forming

1970 ◽  
Vol 28 ◽  
pp. 428-429 ◽  
Author(s):  
J. A. Korbonski ◽  
L. E. Murr
Keyword(s):  
Stainless Steel ◽  
Shock Loading ◽  
Pressure Pulse ◽  
Shock Pressure ◽  
304 Stainless Steel ◽  
Strain Rates ◽  
Two Dimensional ◽  
Aisi 304 Stainless Steel ◽  
Aisi 304 ◽  
Explosive Forming

Comparison of recovery rates in materials deformed by a unidimensional and two dimensional strains at strain rates in excess of 104 sec.−1 was performed on AISI 304 Stainless Steel. A number of unidirectionally strained foil samples were deformed by shock waves at graduated pressure levels as described by Murr and Grace. The two dimensionally strained foil samples were obtained from radially expanded cylinders by a constant shock pressure pulse and graduated strain as described by Foitz, et al.

Solid Solution Effects and Deformation Micros trueture of Shock-Loaded Iron Manganese Alloys

1970 ◽  
Vol 28 ◽  
pp. 420-421
Author(s):  
A. Christou ◽  
J. V. Foltz ◽  
N. Brown
Keyword(s):  
Solid Solution ◽  
Shock Loading ◽  
High Strain ◽  
Local Stress ◽  
Strain Rates ◽  
Local Stress Concentration ◽  
Bcc Metals ◽  
Manganese Alloys ◽  
Iron Manganese ◽  
Transmission Microscope

In general, all BCC transition metals have been observed to twin under appropriate conditions. At the present time various experimental reports of solid solution effects on BCC metals have been made. Indications are that solid solution effects are important in the formation of twins. The formation of twins in metals and alloys may be explained in terms of dislocation mechanisms. It has been suggested that twins are nucleated by the achievement of local stress-concentration of the order of 15 to 45 times the applied stress. Prietner and Leslie have found that twins in BCC metals are nucleated at intersections of (110) and (112) or (112) and (112) type of planes.In this paper, observations are reported of a transmission microscope study of the iron manganese series under conditions in which twins both were and were not formed. High strain rates produced by shock loading provided the appropriate deformation conditions. The workhardening mechanisms of one alloy (Fe - 7.37 wt% Mn) were studied in detail.

The effects of strain and strain rate on residual microstructures in copper

1986 ◽  
Vol 44 ◽  
pp. 420-421
Author(s):  
M. F. Stevens ◽  
P. S. Follansbee
Keyword(s):  
Strain Rate ◽  
Applied Stress ◽  
Threshold Stress ◽  
Rate Sensitivity ◽  
Viscous Drag ◽  
Strain Rates ◽  
Strain And Strain Rate ◽  
Threshold Strength ◽  
Mechanism Transition ◽  
Intrinsic Strength

The strain rate sensitivity of a variety of materials is known to increase rapidly at strain rates exceeding ∼103 sec-1. This transition has most often in the past been attributed to a transition from thermally activated guide to viscous drag control. An important condition for imposition of dislocation drag effects is that the applied stress, σ, must be on the order of or greater than the threshold stress, which is the flow stress at OK. From Fig. 1, it can be seen for OFE Cu that the ratio of the applied stress to threshold stress remains constant even at strain rates as high as 104 sec-1 suggesting that there is not a mechanism transition but that the intrinsic strength is increasing, since the threshold strength is a mechanical measure of intrinsic strength. These measurements were made at constant strain levels of 0.2, wnich is not a guarantee of constant microstructure. The increase in threshold stress at higher strain rates is a strong indication that the microstructural evolution is a function of strain rate and that the dependence becomes stronger at high strain rates.

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