Stress-Strain Curve of Mild Steel in the Initial Stage of Cyclic Loading

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.

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

Proceedings of the Institution of Mechanical Engineers ◽

10.1243/pime_proc_1937_135_031_02 ◽

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.

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Calibration and Validation of Stress–Strain Curve in High-Strain Region of Mild Steel Sheet

Forming the Future - The Minerals, Metals & Materials Series ◽

10.1007/978-3-030-75381-8_79 ◽

2021 ◽

pp. 949-958

Author(s):

Hideo Tsutamori ◽

Takeshi Nishiwaki ◽

Hiroaki Onishi

Keyword(s):

Mild Steel ◽

Steel Sheet ◽

High Strain ◽

Strain Curve ◽

Stress Strain Curve ◽

Stress Strain ◽

Calibration And Validation

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1942.0018 ◽

1942 ◽

Vol 179 (979) ◽

pp. 450-460 ◽

Cited By ~ 8

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.

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Torsional hysteresis of mild steel

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1917.0021 ◽

1917 ◽

Vol 93 (651) ◽

pp. 313-332 ◽

Cited By ~ 3

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.”

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Subultimate Prestrain and Aging in Mild Steel

Journal of Basic Engineering ◽

10.1115/1.3650547 ◽

1965 ◽

Vol 87 (2) ◽

pp. 319-324 ◽

Cited By ~ 2

Author(s):

D. K. Felbeck ◽

W. G. Gibbons ◽

W. G. Ovens

Keyword(s):

Mild Steel ◽

High Speed ◽

Strain Curve ◽

Local Stress ◽

Tensile Tests ◽

Stress Strain Curve ◽

Stress Strain ◽

Limited Region ◽

Small Increments ◽

Necessary And Sufficient

Room-temperature tensile straining of mild steel followed by aging at 350 F causes return of the upper yield and a raising of the stress-strain curve. Tensile tests on a special rimmed steel of low Mn/C ratio show not only the expected raising of the stress-strain curve, but raising by an additional amount when several small increments of strain are each followed by aging at moderate temperatures. Longitudinal tensile prestrain by rolling gives substantially the same results. Tests of specimens prestrained in a limited region by impact or in slow tension and aged indicate that embrittlement of the whole specimen may result. The combined theories of Griffith and Orowan, plus an extension of the Ludwik triaxiality concept, can provide a consistent description of the local stress and average stress (energy) criteria that are necessary and sufficient for high-speed low-energy fracture to occur.

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Stress-Strain Analysis of Cyclic Plastic Bending and Torsion

Journal of Engineering Materials and Technology ◽

10.1115/1.3443465 ◽

1978 ◽

Vol 100 (2) ◽

pp. 157-163 ◽

Cited By ~ 11

Author(s):

N. E. Dowling

Keyword(s):

Cyclic Loading ◽

Alloy Steel ◽

Strain Analysis ◽

Strain Curve ◽

Cyclic Stress ◽

Curve Analysis ◽

Pure Bending ◽

Stress Strain Curve ◽

Stress Strain ◽

Plastic Bending

Analysis of stresses, strains, and damping energies is considered for cyclic loading of simple geometries. For beams under pure bending and for circular shafts under torsion, it is shown that cyclic loading may be handled by analysis that differs from that applicable to monotonic loading only by the substitution of a cyclic stress-strain curve. Analysis and experiment are successfully compared for rectangular beams of an alloy steel.

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