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.

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 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.

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 Torsional hysteresis of mild steel

1917 ◽  
Vol 93 (651) ◽  
pp. 313-332 ◽  
Keyword(s):  
Mild Steel ◽  
Yield Point ◽  
Elastic Limit ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Straight Line ◽  
Straight Portion ◽  
Strain Axis ◽  
Inferior Limit

The stress-strain curve from no load to fracture for mild steel as usually obtained consists of three parts: (1) A straight line, followed by a part deviating only slightly from this straight portion; (2) a sharp bend, followed by a part approximately parallel to the strain axis; and (3) a curved rising part, leading ultimately to the breaking point. It is generally assumed that Hooke’s Law holds throughout the part (1), and is immediately followed by the sharply defined bend which constitutes the yield point. For mild steel first stressed in tension and then in compression, or subjected to positive and then negative torsional stresses, the stress-strain curve within a considerable range of stress is also supposed to be a straight line. It is further well known that if mild steel is stressed in tension beyond the yield point the elastic limit is raised, but only at the expense of lowering it in compression; or, if it is twisted beyond the yield point in one direction, its elastic limit is raised for stresses in that direction, but lowered for those in the opposite direction. Attempts have been made to relate the range of stress through which the stress-strain curve is a straight line with that through which a material, such as mild steel, can be stressed an infinite number of times without fracture. This is expressed by the well known Bauschinger’s Law, which, as stated by Mr. Leonard Bairstow, is as follows:—“The superior limit of elasticity can be raised or lowered by cyclical variations of stress, and at the inferior limit of elasticity will be raised or lowered by a definite, but not necessarily the same, amount. The range of stress between the two elastic limits has therefore a value which depends only on the material and the stress at the inferior limit of elasticity. This elastic range of stress is the same in magnitude as the maximum range of stress, which can be repeatedly applied to a bar without causing fracture, no matter how great the number of repetitions.”

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.

A model of the continuous elastoplastic transition in metals

1971 ◽  
Vol 6 (3) ◽  
pp. 185-192 ◽  
Author(s):  
W J D Jones ◽  
A K Agarwal
Keyword(s):  
Yield Point ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Yield Strain ◽  
Stress Strain ◽  
Strain Behaviour ◽  
Aluminium Copper ◽  
Stress Cycling ◽  
Elastoplastic Transition ◽  
Plastic Parts

Part 1: The heterogeneous character of a real metal is represented by a model in which the metal is considered to consist of a large number of elements with a variation of individual stress-strain responses. The variation of Poisson's ratio which occurs as a function of strain is used to measure the progress of yielding through the material and hence to calculate the variation in elemental yield strains. By use of data obtained from the completely elastic and fully plastic parts of the stress-strain curve and the yield strain distribution, the elastoplastic transition behaviour can be calculated. Comparisons are presented between computed and experimental stress-strain curves for aluminium, copper, magnesium, nickel, and titanium alloy to demonstrate the validity of the proposed model. Part 2: Sufficient cyclic stressing can change the subsequent stress-strain curve of a steel which normally has a yield point into one with a continuous elastoplastic transition. A model of the elastoplastic transition in metals, developed by the authors in Part 1 to represent the stress-strain behaviour of metals with a continuous elastoplastic transition, is then proposed for representing the stress-strain behaviour of steels in which the yield point has been removed, by stress cycling. Results are presented to show good agreement between the model and the observed stress-strain behaviour of four steels, one of which had no yield point and the other three had their yield points removed by cyclic stressing.

scholarly journals Stress-Strain Curve of Mild Steel in the Initial Stage

1972 ◽  
Vol 38 (316) ◽  
pp. 3029-3037
Author(s):  
Yoshio OHASHI ◽  
Koichiro KAWASHIMA ◽  
Sadao MlZUNO
Keyword(s):  
Mild Steel ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Initial Stage
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