scholarly journals A stress-strain curve for the atomic lattice of iron

1941 ◽  
Vol 178 (972) ◽  
pp. 93-106 ◽  
Keyword(s):  
Yield Point ◽  
Applied Stress ◽  
Lattice Spacing ◽  
Strain Curve ◽  
Effect Of Temperature ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Lattice Contraction ◽  
Atomic Lattice ◽  
Regular Manner

Measurements have been made on the stress-strain relationship for the atomic lattice of iron (purity 99·95%). The changes in dimensions of the atomic lattice of tensile specimens have been determined in the direction perpendicular to the applied stress and compared with the contraction in external dimensions which occurs in the same direction. It has been shown that the lattice stress-strain curve, obtained by plotting the lateral change in lattice spacing against the tensile stress, exhibits three main characteristics. Up to the external yield point, the lattice contraction is directly proportional to the applied stress. Beyond the yield point, the lattice contraction slows down as the stress increases. Finally, at still higher stresses, the lattice tends to expand. A further set of experiments, in which cycles of stress are employed, show that when a stress greater than the yield stress is applied and then removed from a specimen, the lattice is left with a permanent expansion which depends in a regular manner upon the value of the stress applied. It is concluded that beyond the external yield point, the iron lattice undergoes two distinct modifications. First, the lattice spacing tends to contract elastically, in conformity with the external elastic contraction exhibited by the specimen in the same direction (perpendicular to the applied stress). Second, the lattice tends to deform in a manner which leads to a superposed expansion of lattice spacing. The actual change of spacing at a particular stress is then the resultant of the two effects; a process which explains the unexpected shape of the lattice stress-strain curve, and affords systematic information on the problem of internal strains in metals. Further experiments indicate that the permanent expansion of the lattice after loading occurs not only in the direction perpendicular to the applied stress, but also in the direction of the stress; the permanent lattice deformation thus represents a decrease in density of the test specimen. Finally, the results of some experiments are recorded on the effect of temperature on the lattice expansion effect, and it is shown that recovery of the lattice can be produced by mild heat treatment at a temperature much lower than that required to renew the properties of the metal by recrystallization.

scholarly journals A stress-strain curve for the atomic lattice of mild steel in compression

1942 ◽  
Vol 181 (984) ◽  
pp. 72-83 ◽  
Keyword(s):  
Mild Steel ◽  
Yield Point ◽  
Applied Stress ◽  
Pure Iron ◽  
Lattice Strain ◽  
Strain Curve ◽  
Partial Recovery ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Atomic Lattice

A stress-strain curve has been obtained for the atomic lattice of mild steel subjected to compression. A set of atomic planes is selected of which the spacing is practically perpendicular to the direction of the stress, and the change in spacing is measured as the magnitude of the applied stress is systematically varied. The behaviour of the lattice is compared with the corresponding stress-strain relation for the external dimensions in the compression test, and also with the lattice stress-strain curve previously obtained for the same material when subjected to tensile stress. Other experiments are described on the behaviour of the lattice of pure iron in compression. It had been previously shown that at the external yield in tension, the atomic spacing exhibited an abrupt change which remained indefinitely on removal of the stress; the effect was interpreted as a lattice yield point. The present work establishes that the lattice possesses a yield point also in compression, again marking the onset of a permanent lattice strain. The direction of this strain, however, is opposite to that found in tension, and the magnitude increases systematically with the applied stress. The experiments on the pure iron show that under extreme deformation the permanent lattice strain tends to a limit and that with continued deformation partial recovery from the strain may occur. The results suggest that the mechanics of the metallic lattice involve the principle that, after the lattice yield point, in a given direction the lattice systematically assumes a permanent strain in such a sense as to oppose the elastic strain induced by the applied stress.

scholarly journals A stress-strain curve for the atomic lattice of mild steel, and the physical significance of the yield point of a metal

1942 ◽  
Vol 179 (979) ◽  
pp. 450-460 ◽  
Keyword(s):  
Mild Steel ◽  
Yield Point ◽  
Lattice Spacing ◽  
Strain Curve ◽  
Sudden Expansion ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Atomic Lattice ◽  
Tensile Test Specimen ◽  
Technical Interest

A stress-strain curve is obtained for the atomic lattice of mild steel subjected to tensile stress. A set of atomic planes is selected of which the spacing is practically perpendicular to the direction of the stress applied to the tensile test specimen, and which should contract with the cross-section as the specimen extends along its length. It is shown that up to the external yield point the lattice spacing contracts in proportion to the applied stress in conformity with Hooke’s Law; but at the external yield point, instead of a continued contraction, the spacing undergoes an abrupt expansion. As the stress is still further increased, the lattice dimension remains approximately constant in the expanded condition. It is further shown that the sudden expansion which sets in at the yield point while the specimen is under load is fully retained as the load is removed. Also that with the application of increasing stress, the permanent expansion imposed on the lattice spacing systematically increases up to the ultimate stress preceding fracture. It is found in addition that the sharp changes in the lattice spacing at the yield are accompanied by a striking drop in the intensity of the X-ray diffraction ring on which the spacing measurements are based. The experiments have established that the atomic lattice of a metal itself possesses a yield point which marks the onset of permanent lattice strains of an unexpected character and of direct technical interest in connexion with the mechanical properties of metals.

Definition of the yield point in plasticity and its effect on the shape of the yield locus

1966 ◽  
Vol 1 (4) ◽  
pp. 331-338 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Yield Point ◽  
Experimental Work ◽  
Strain Curve ◽  
Yield Locus ◽  
Experimental Results ◽  
Stress Strain Curve ◽  
Proportional Limit ◽  
Stress Strain ◽  
Small Section ◽  
Definition Of

Three different definitions of the yield point have been used in experimental work on the yield locus: proportional limit, proof strain and the ‘yield point’ by backward extrapolation. The theoretical implications of the ‘yield point’ by backward extrapolation are examined in an analysis of the loading and re-loading stress paths. It is shown, in connection with experimental results by Miastkowski and Szczepinski, that the proportional limit found by inspection is in fact a point located by backward extrapolation based on a small section of the stress-strain curve, near the elastic portion of the curve. The effect of different definitions of the yield point on the shape of the yield locus and some considerations for the choice between them are discussed.

scholarly journals The influence of rate of deformation on the tensile test with special reference to the yield point in iron and steel.

1938 ◽  
Vol 165 (923) ◽  
pp. 568-592 ◽  
Author(s):  
C. F. Elam ◽  
Henry Cort Harold Carpenter
Keyword(s):  
Tensile Test ◽  
Special Reference ◽  
Yield Point ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Iron And Steel ◽  
Plastic Distortion

The following experiments were carried out with two principal objects in view: (1) to investigate the deformation of those metals, particularly iron and steel, in which the stress-strain curve does not immediately rise at the onset of plastic distortion; (2) to determine the effect of rate of deformation on the yield and subsequent stress-strain curve. It is impossible to give an adequate summary of the literature which deals with this subject, but a bibliography is included in an appendix and some of the most important results are referred to briefly below.

The Development of a Machine for High-Speed Testing of Materials

1937 ◽  
Vol 135 (1) ◽  
pp. 467-483
Author(s):  
R. J. Lean ◽  
H. Quinney
Keyword(s):  
Mild Steel ◽  
Yield Point ◽  
High Speed ◽  
Testing Machine ◽  
Strain Curve ◽  
Maximum Point ◽  
Variable Speed ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
High Speed Machine

The paper contains an account of a research into the effect on metals of different speeds of fracture, using a specially designed high-speed testing machine which is described in detail. The experiments were conducted both in this machine and in a 5-ton variable-speed autographic tensile machine, on five steels, the rate of loading being varied for each. With the high-speed machine toughness, ductility, time to produce fracture, and the stress-strain curve were obtained. The results of these combined tests, given in tables and graphs, show that there is a marked increase in stress due to higher speed of testing; and also that the work required to cause fracture increases with the speed. For mild steel the stress at the initial yield point was found to be in excess of that at the maximum point, when the speed of testing was increased the ductility did not appear to suffer.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

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