A Simplified Method to Account for Plastic Rate Sensitivity With Large Deformations

1979 ◽  
Vol 46 (4) ◽  
pp. 811-816 ◽  
Author(s):  
N. Perrone ◽  
P. Bhadra
Keyword(s):  
Strain Rate ◽  
Large Deformations ◽  
Three Dimensional ◽  
Rate Sensitivity ◽  
Approximate Solutions ◽  
Dimensional Structure ◽  
Initial Kinetic Energy ◽  
Maximum Strain ◽  
Membrane Action ◽  
Deformation State

A string supported impulsively loaded mass is used to study large deformation rate sensitivity effects where membrane action is dominant. It is found that an overall correction factor can be devised using physical properties associated with the average strain rate. Maximum strain rate occurs with a velocity field corresponding to the deformation state wherein half the initial kinetic energy has been dissipated. (If V0 is initial velocity, V0/2 is associated with maximum strain rate.) Exact and approximate solutions for a broad range of parameters serve to illustrate and verify the procedure. A discussion is presented to show how the same methodology could also be applied via a modal approach to an arbitrary three-dimensional structure undergoing large deformations, if the primary mechanism for energy absorption is from membrane action.

Superplastic Behavior of B- and Gd-Containing β-Solidifying TiAl Based Alloy

2018 ◽  
Vol 385 ◽  
pp. 131-136
Author(s):  
Vitaliy Sokolovsky ◽  
Nikita Stepanov ◽  
Sergey Zherebtsov ◽  
Nadezhda Nochovnaya ◽  
Pavel Panin ◽  
...  
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Strain Rate Sensitivity ◽  
Phase Field ◽  
Rate Sensitivity ◽  
Maximum Strain ◽  
Superplastic Behavior ◽  
Β Phase ◽  
Refined Microstructure ◽  
Phase Fields

Mechanical behavior and microstructure evolution of the cast Ti-43.2Al-1.9V-1.1Nb-1.0Zr-0.2Gd-0.2B alloy were studied at temperatures from 1100 to 1250°С and strain rates in the range 0.001-1 s-1. Following phase fields (α2+γ), (α+γ), (α) and (α+β) during heating of alloy were revealed. Microstructure analysis after deformation and mechanical behavior allowed defining main processes of structure formation. Two temperature-strain rate conditions with pronounced superplastic behaviour were found: the first one corresponded to the (α2+γ)-phase field (1100°C), where the microstructure had mainly a lamellar morphology, and the second was associated with the (α+β)-phase field (1250°C), in which the α-phase dominated. At T=1100°C and έ=0.05 s-1the maximum strain rate sensitivitymwas of 0.40. At T=1250°C and έ=0.5 s-1the maximum strain rate sensitivitymwas of 0.59. In the (α2+γ)-phase field, superplastic behavior was associated with the transformation of the lamellar structure into globular one. In the (α+β)-phase field, it was due to the formation of a homogeneous refined microstructure during dynamic recrystallization. The relationship between coefficient m value and microstructure formed was discussed.

Constitutive Modeling of a Thermoplastic Olefin Over a Broad Range of Strain Rates

2006 ◽  
Vol 128 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Yan Wang ◽  
Ellen M. Arruda
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Elastic Response ◽  
Strain Rates ◽  
Strain Behavior ◽  
Rate Dependent ◽  
State Dependent ◽  
Deformation State ◽  
Ann Arbor

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

Constitutive Relations for the Nonelastic Deformation of Metals

1976 ◽  
Vol 98 (3) ◽  
pp. 193-202 ◽  
Author(s):  
E. W. Hart
Keyword(s):  
Strain Rate ◽  
Real Time ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
State Variables ◽  
Simple Manner ◽  
Loading Direction ◽  
Deformation State ◽  
Experimental Background

Constitutive relations for metal nonelastic deformation are proposed. The descriptiion is entirely in terms of real time strain rate. The equations are fully three-dimensional, and the description is incremental. Changes of loading direction are treated in a simple manner. The current deformation state of the metal is characterized by a set of state variables that themselves evolve by well defined laws. The experimental background for the theory is also described.

Shear band development in polycrystals

1993 ◽  
Vol 443 (1919) ◽  
pp. 547-562 ◽  
Keyword(s):  
Shear Band ◽  
Strain Rate ◽  
Plane Strain ◽  
Simple Shear ◽  
Biaxial Tension ◽  
Short Interval ◽  
Rate Sensitivity ◽  
Band Model ◽  
Plane Strain Tension ◽  
Deformation State

Shear band localizations are studied using a band model involving two polycrystalline aggregates; one representing the material inside the potential band and the other the material outside. Each of these aggregates is assumed to be homogeneously deformed and conditions of compatibility and equilibrium are enforced across the band interfaces. The aggregate constitutive response is obtained from a generalized Taylor polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation, so that no ambiguity arises concerning the choice of active slip systems. Because of the material rate sensitivity a shear band bifurcation is ruled out at achievable strain levels, but localization occurs from the growth of an initial inhomogeneity. Results are presented for imposed loading histories of plane strain tension, biaxial tension and simple shear, both for an initially isotropic aggregate and for an aggregate that has undergone a pre-strain in plane strain compression. Depending on the material properties, the initial conditions and the imposed deformation state, either (i) localization, in the sense of a very high strain rate concentration in the band, takes place; or (ii) the band strain rate increases rapidly for a short interval and then saturates; or (iii) the initial inhomogeneity does not induce a large strain rate concentration in the band. The initial pre-strain promotes earlier localization in plane strain tension and in simple shear. In biaxial tension, localization occurs earlier for the pre-strained material if the initial imperfection is large, but tends to saturate for smaller imperfections. The effects of variations in imperfection amplitude and material strain rate sensitivity are illustrated.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

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