The Activation Energy for Plastic Flow in Stress Relaxation

1966 ◽  
Vol 17 (2) ◽  
pp. K175-K178 ◽  
Author(s):  
R. B. Clough
1999 ◽  
Vol 601 ◽  
Author(s):  
T. Rouxel ◽  
J. Rabier ◽  
S. Testu ◽  
X. Milhet

AbstractThe different scales of plastic flow in silicon nitride were investigated either by indentation experiments and compression under hydrostatic pressure in the 20-850°C temperature range, and by stress relaxation and creep above 1350°C. [0001], 1/3<11-20> and 1/3<11-23> dislocations were evidenced by Transmission Electron Microscopy (TEM) in the low temperature range. Cross-slip events in {10-10} prismatic planes were observed at temperature as low as 20°C by Atomic Force Microscopy (AFM) on micro-hardness indents. By increasing the temperature, the deviation plane becomes {11-20} prismatic planes. The easiest slip system is by far the [0001]{10-10} system. Above 1350°C, the creep strain could be fitted by the sum of a transient component, εt=ε∞[1-exp-(t/τc)bc], where τc reflects the duration of the transient creep stage, and bc is between 0 and 1, and a stationary component, εs=εst =Aσnt, where σ is the stress and n is the stress exponent. The increase of ε∞ with temperature is interpreted on the basis of the formation of liquid intergranulary phases above 1400°C by progressive melting of some of the grains. A creep exponent of 1.8 was determined. A single value could hardly be given to the activation energy since an S-shape curve was observed in the In εs versus l/T plot, as for most glasses over large temperature ranges. The stress relaxation kinetics was found to follow the Kohlrausch-Williams-Watt expression: σ/σo=exp [-(t/τr)br], where br ranges between 0 (solid state) and I (liquid state) and τr is a characteristic relaxation time constant. As in the case of glasses, τr decreases rapidly whereas br increases from about 0.2 to 0.7 as the temperature increases from 1400 to 1650°C. But again, it is very difficult to get a single value for the activation energy from the In τr versus 1/T plot.


Metals ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 1215 ◽  
Author(s):  
Yixian Cai ◽  
Lihua Zhan ◽  
Yongqian Xu ◽  
Chunhui Liu ◽  
Jianguang Wang ◽  
...  

Age forming is an advanced manufacture technology for forming large aluminum panels. Temperature, initial stress level and pre-strains have a great effect on the formability and performance. The stress relaxation aging behavior of AA7150-T7751 under different temperatures, initial stress levels and pre-strains was studied through stress relaxation tests, tensile tests and TEM observations. The results show that the formability can be improved with the increase of temperature, initial stress levels and pre-strains. Deformation mechanisms during stress relaxation of the material were analyzed on the basis of creep stress exponent and apparent activation energy. The aging precipitates of the studied alloy were not sensitive to the age forming conditions, but drastically coarsened at over aging temperature, which decreased the mechanical properties. In addition, the relationship between stress relaxation behavior and aging strengthening is discussed. Based on the dislocation theory and the modified Arrhenius equation, a stress relaxation constitutive equation considering the initial mobile dislocation density and temperature dependent activation energy was established. This model can predict very well the stress relaxation behavior under various temperature, stress level and pre-strain conditions, with an average error of 2%.


1962 ◽  
Vol 40 (10) ◽  
pp. 1310-1318 ◽  
Author(s):  
H. H. G. Jellinek

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.


1972 ◽  
Vol 45 (1) ◽  
pp. 82-93 ◽  
Author(s):  
G. M. Bartenev ◽  
N. M. Lyalina

Abstract 1. In vulcanized rubbers containing blacks a multi-stage mechanism for stress relaxation was observed. It was discovered that the stress relaxation process consists of five fundamental processes: the first three relaxation processes, related to the slow stages of physical relaxation within the bulk of the rubber, have no connection with the fillers (“soft” domains); the fourth process has to do with the relaxation in the black-rubber domain; the fifth process involves the chemical relaxation of vulcanizates. 2. The fundamental mechanisms of the first 3 relaxation processes in the soft domains have the same activation energy values and the same segmental mechanism as the rearranged domains found in supermolecular weight structures, which are also present in unfilled vulcanizates. 3. In the investigated stress range of up to 200% elongation, the activation energy for the first 3 relaxation processes in the soft domains of filled vulcanizates is not a function of the deformation strain, whereas the activation energy of the fourth relaxation process in the black-rubber domains of filled rubbers is a function of the deformation and of the filler content. For these reasons, rubber loaded with carbon blacks, in contrast to unfilled rubbers, possess the typical nonlinearity of viscoelastic materials. 4. The activation energies of the relaxation processes in the black-rubber domains decrease in a linear fashion with the value for the initial tensile stress in filled vulcanizates, and decrease in like manner for vulcanizates containing different proportions of fillers. The kinetic units, determined from the activation energies of these processes, appeared to be segments of chains with activation energies of up to 40% more than the activation energies of the physical relaxation processes in the soft domains. The other kinetic units of the processes proved to be black particles, the dimensions of which were calculated from the values for the coefficients in the formula for relaxation time.


2001 ◽  
Vol 16 (4) ◽  
pp. 938-944 ◽  
Author(s):  
V. L. Tellkamp ◽  
S. Dallek ◽  
D. Cheng ◽  
E. J. Lavernia

A nanostructured 5083 Al–Mg alloy powder was subjected to various thermal heat treatments in an attempt to understand the fundamental mechanisms of recovery, recrystallization and grain growth as they apply to nanostructured materials. A low-temperature stress relaxation process associated with reordering of the grain boundaries was found to occur at 158 °C. A bimodal restructuring of the grains occurred at 307 °C for the unconstrained grains and 381 °C for the constrained grains. An approximate activation energy of 5.6 kJ/mol was found for the metastable nanostructured grains, while an approximate activation energy of 142 kJ/mol was found above the restructuring temperature.


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