Derivation of Stress, Strain, Temperature, Strain-Rate Relation for Plastic Deformation

1947 ◽  
Vol 14 (3) ◽  
pp. A229-A230
Author(s):  
J. D. Lubahn
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Flow ◽  
Stress Strain ◽  
Rate Relation ◽  
Temperature Strain

Abstract This paper carries out the derivation and correction of an equation previously presented by J. H. Hollomon and the author, relating to stress for plastic flow (σ), plastic strain (ϵ), strain rate (ϵ.), and temperature (T).

scholarly journals APPLICATION OF CURRENT LINES IN DETERMINING KINEMATIC CHARACTERISTICS IN STATIONARY PROCESSES OF PLASTIC FLOW OF METAL

2021 ◽  
pp. 92-98
Author(s):  
Roman Sivak ◽  
Iryna Нunko ◽  
Roman Zalizniak
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Plastic Flow ◽  
Strain State ◽  
Stationary Processes ◽  
Strain Rate Tensor ◽  
Stress Strain ◽  
Stress Strain State ◽  
Kinematic Characteristics ◽  
Current Lines

Methods of theoretical solution of problems in the processing of metals by pressure are insufficiently developed for practical use in the development and implementation of new technologies and improvement of existing ones. To meet the stringent requirements for the accuracy of determining the stress-strain state, it is necessary to have reliable information about the evolution of the development of the plastic deformation process at each point of the metal from the very beginning of the deformation. This will allow to obtain with high accuracy the important characteristics of the technological heredity of the products that they acquire as a result of their plastic processing. The first and important step in the calculations of the stress-strain state is to obtain the kinematic characteristics of the plastic flow of metal in the form of analytical dependences, which will formulate the patterns of deformation in the technological processes of metal forming. The article considers the possibility of applying the method of current functions to determine the components of the strain rate tensor in established stationary processes of plastic deformation. It is assumed that in the case of axisymmetric plastic deformation of a metal in a channel with curvilinear boundaries, the kinematics of the process is similar to a plane flow. In obtaining the equations, the differential equation of current lines taking into account the incompressibility condition was used to determine the components of the strain rate tensor. To explain the physical meaning of the current functions, two infinitely close current lines were considered in the flow plane, and an expression was obtained for the flow through a finite transverse current tube. In the absence of radial velocity components at the boundaries, constraints are obtained that are imposed on derivatives of current functions at these boundaries. The developed method of calculating the kinematic characteristics of plastic deformation for established axisymmetric stationary processes will simplify the mathematical processing of the obtained results and increase the reliability of the determination of the stress-strain state.

scholarly journals Effective Shear Viscosity and Effective Bulk Viscosity of Firn of a Temperate Glacier (Kesselwandferner, Ötztal Alps, 1967-1978)

1983 ◽  
Vol 4 ◽  
pp. 10-13
Author(s):  
Walter Ambach ◽  
Heinrich Eisner
Keyword(s):  
Strain Rate ◽  
Bulk Viscosity ◽  
Shear Viscosity ◽  
The State ◽  
Stress Strain ◽  
Rate Relation

Strain-rate measurements were carried out over eleven years on a firn pit 20 m deep in a temperate glacier. The stress strain-rate relation was applied in terms of invariants, because of the multiaxial state of stresses. The shear viscosity and the bulk viscosity were calculated as a function of depth and density. The result must be understood in terms of effective viscosities as the dependence of the viscosity from the state of stresses is unknown in this analysis.

scholarly journals How to Realize Volume Conservation During Finite Plastic Deformation

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Heling Wang ◽  
Dong-Jie Jiang ◽  
Li-Yuan Zhang ◽  
Bin Liu
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Strain Rate ◽  
Strain Rate Tensor ◽  
Cauchy Stress ◽  
Volume Conservation ◽  
Tangential Stiffness ◽  
Manufacture Process ◽  
Universal Approach

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

scholarly journals PLASTIC DEFORMATION OF THICK-WALLED SNOW-ICE CYLINDERS UNDER HYDROSTATIC PRESSURE

1962 ◽  
Vol 40 (10) ◽  
pp. 1310-1318 ◽  
Author(s):  
H. H. G. Jellinek
Keyword(s):  
Activation Energy ◽  
Plastic Deformation ◽  
Hydrostatic Pressure ◽  
Strain Rate ◽  
Plastic Flow ◽  
Constant Pressure ◽  
Circumferential Stress ◽  
Sine Function ◽  
Kcal Mole ◽  
Flow Process

The results of experiments on the plastic deformation of hollow snow-ice cylinders, closed at one end, as a function of circumferential stress and temperature are discussed. Data are graphed on deformation as a function of time for a snow-ice cylinder under 7.03 and 14.06 kg/cm2 hydrostatic pressure at −4.5 °C, deformation as a function of hydrostatic pressure from 2.11 to 7.03 kg/cm2, and deformation as a function of temperature at a constant pressure of 10.55 kg/cm2. The natural strain rate of closure at constant circumferential stress and temperature was a constant, which varied with circumferential stress as a sine function and was "exponentially dependent on temperature, with an activation energy of 14.1 kcal/mole at an average circumferential stress of 3.1 kg/cm2. The experiments agree well with an earlier interpretation of the plastic flow process representing flow between grain boundaries.

Discussion: Stress—strain—strain rate relation for the compressibility of sensitive natural clays

Géotechnique ◽  
1986 ◽  
Vol 36 (2) ◽  
pp. 283-290 ◽  
Author(s):  
S. Leroueil ◽  
M. Kabbaj ◽  
F. Tavenas ◽  
R. Bouchard
Keyword(s):  
Strain Rate ◽  
Stress Strain ◽  
Natural Clays ◽  
Rate Relation

Plastic Flow Instabilities of L12 Ni3(Si,Ti) Alloys at Intermediate Temperature

2002 ◽  
Vol 17 (3) ◽  
pp. 705-711 ◽  
Author(s):  
H. Honjo ◽  
Y. Kaneno ◽  
H. Inoue ◽  
T. Takasugi
Keyword(s):  
Strain Rate ◽  
Plastic Flow ◽  
Flow Behavior ◽  
Rate Sensitivity ◽  
Tensile Tests ◽  
Lattice Diffusion ◽  
Intermediate Temperature ◽  
Fine Grained ◽  
Ti Alloys ◽  
Temperature Strain

The serrated plastic flow of L12 Ni3 (Si,Ti) alloys at intermediate temperature was investigated by tensile tests in terms of the effects of temperature, strain rate, composition, and microstructure. Serrated plastic flow was most strongly observed at 473 K and at a strain rate of 1.6 × 10–4 s–1. Correspondingly, the maximum stress amplitude and the lowest (negative) strain-rate sensitivity were observed at 473 K. Serrated plastic flow took place irrespective of boron doping and was more significant in a fine-grained Ni3 (Si,Ti) alloy. The static aging at 473 K resulted in reduced flow stress. The activation energy for serrated plastic flow was estimated to be about 57 kJ mol–1, suggestive of being smaller than that for lattice diffusion of solutes. The serrated plastic flow behavior of Ni3 (Si,Ti) alloys was compared with that of L12 Co3Ti alloys, and is qualitatively explained on the basis of the dynamics of solutes in the core of a dissociated screw dislocation.

A Model to Predict the Effect of Pre-Strain on the Fracture Toughness of Line Pipe Steel

2002 ◽  
Author(s):  
Andrew Cosham ◽  
Naoto Hagiwara ◽  
Naoki Fukuda ◽  
Tomoki Masuda
Keyword(s):  
Fracture Toughness ◽  
Plastic Deformation ◽  
Theoretical Model ◽  
Plastic Strain ◽  
Ductile Fracture ◽  
Experimental Studies ◽  
Uniaxial Tensile ◽  
Stress Strain ◽  
Line Pipe ◽  
Strained Material

New and existing pipelines can be subjected to high plastic strains. Denting a pipeline causes permanent plastic deformation. Onshore pipelines subject to subsidence, frost heave or earthquake loading can experience significant plastic strain during service. Offshore pipelines that are reeled prior to laying, or are laid in deep water, or are operating at high temperatures and high pressures, can experience significant plastic strain both prior to, and during, service. Experimental studies have indicated that pre-strain (permanent plastic deformation) has a detrimental effect on the fracture toughness of steel; it reduces the resistance to crack initiation, reduces the resistance to crack growth, and increases the transition temperature. Consequently, there is a need for a thorough understanding of the effect of pre-strain on the fracture toughness of line pipe. Accordingly, a theoretical model for predicting the effect of tensile pre-strain on the ductile fracture toughness has been developed using the local approach. The effect of pre-strain is expressed in terms of an equation for the ratio of the fracture toughness of the pre-strained material to that of the virgin (not pre-strained) material. The model indicates that the effect of tensile pre-strain on the material’s fracture toughness can be characterised in terms of the effect of pre-strain on the stress-strain characteristics of the material, the critical fracture strain for a stress state corresponding to that during pre-strain, and several parameters that relate to the conditions for ductile fracture (or cleavage fracture). The implications of the model are that it may be possible to estimate the reduction in toughness caused by pre-strain simply from a full stress-strain curve of the virgin material. The model has been validated against the results of crack tip opening displacement (CTOD) tests conducted by Tokyo Gas on two line pipe steels subject to uniaxial tensile pre-strain. It is shown that the predictions and trends of the theoretical model are in broad agreement with the test results.

Stress–strain–strain rate relation for the compressibility of sensitive natural clays

Géotechnique ◽  
1985 ◽  
Vol 35 (2) ◽  
pp. 159-180 ◽  
Author(s):  
S. Leroueil ◽  
M. Kabbaj ◽  
F. Tavenas ◽  
R. Bouchard
Keyword(s):  
Strain Rate ◽  
Stress Strain ◽  
Natural Clays ◽  
Rate Relation
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