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

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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High Strain Rate Test of a Steel Plate under Blast Loading from High Explosive

Materials Science Forum ◽

10.4028/www.scientific.net/msf.767.144 ◽

2013 ◽

Vol 767 ◽

pp. 144-149 ◽

Cited By ~ 1

Author(s):

Tei Saburi ◽

Shiro Kubota ◽

Yuji Wada ◽

Tatsuya Kumaki ◽

Masatake Yoshida

Keyword(s):

Strain Rate ◽

Dynamic Stress ◽

Steel Plate ◽

High Strain ◽

Strain Curve ◽

Stress Strain Curve ◽

Stress Strain ◽

Time Deformation ◽

Rate Test ◽

High Strain Rate Test

In this study, a high strain rate test method of a steel plate under blast loading from high explosive was designed and was conducted by a combined experimental/numerical approach to facilitate the estimation process for the dynamic stress-strain curve under practical strain rate conditions. The steel plate was subjected to a blast load, which was generated by Composition C4 explosive and the dynamic deformation of the plate was observed with a high-speed video camera. Time-deformation relations were acquired by image analysis. A numerical simulation for the dynamic behaviors of the plate identical to the experimental condition was conducted using a coupling analysis of finite element method (FEM) and discrete particle method (DPM). Explosives were modeled by discrete particles and the steel plate and other materials were modeled by finite element. The blast load on the plate was described fluid-structure interaction (FSI) between DPM and FEM. As inverse analysis scheme to estimate dynamic stress-strain curve, an evaluation using a quasistatic data was conducted. In addition, two types of approximations for stress-strain curve were assumed and optimized by least square method. One is a 2-piece approximation, and was optimized by least squares method using a yield stress and a tangent modulus as parameters. The other is a continuous piecewise linear approximation, in which a stress-strain curve was divided into some segments based on experimental time-deformation relation, and was sequentially optimized using youngs modulus or yield stress as parameter. The results showed that the piecewise approximation can gives reasonably agreement with SS curve obtained from the experiment.

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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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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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Evaluation of Anisotropic Pipe Steel Stress-Strain Relationships Influence on Strain Demand

Volume 4: Pipelining in Northern and Offshore Environments; Strain-Based Design; Risk and Reliability; Standards and Regulations ◽

10.1115/ipc2012-90495 ◽

2012 ◽

Author(s):

James D. Hart ◽

Nasir Zulfiqar ◽

Joe Zhou

Keyword(s):

Strain Hardening ◽

Pipe Steel ◽

High Strain ◽

Strain Curve ◽

High Strength ◽

Strain Response ◽

Stress Strain Curve ◽

Stress Strain ◽

Hardening Modulus ◽

Strain Relationship

Buried pipelines can be exposed to displacement-controlled environmental loadings (such as landslides, earthquake fault movements, etc.) which impose deformation demands on the pipeline. When analyzing pipelines for these load scenarios, the deformation demands are typically characterized based on the curvature and/or the longitudinal tension and compression strain response of the pipe. The term “strain demand” is used herein to characterize the calculated longitudinal strain response of a pipeline subject to environmentally-induced deformation demands. The shape of the pipe steel stress-strain relationship can have a significant effect on the pipe strain demands computed using pipeline deformation analyses for displacement-controlled loading conditions. In general, with sufficient levels of imposed deformation demand, a pipe steel stress-strain curve with a relatively abrupt or “sharp” elastic-to-plastic transition will tend to lead to larger strain demands than a stress-strain curve with a relatively rounded elastic-to-plastic transition. Similarly, a stress-strain curve with relatively low strain hardening modulus characteristics will tend to lead to larger strain demands than a stress-strain curve with relatively high strain hardening modulus characteristics. High strength UOE pipe can exhibit significant levels of anisotropy (i.e., the shapes of the stress-strain relationships in the longitudinal tension/compression and hoop tension/compression directions can be significantly different). To the extent that the stress-strain curves in the different directions can have unfavorable shape characteristics, it follows that anisotropy can also play an important role in pipeline strain demand evaluations. This paper summarizes a pipeline industry research project aimed at evaluation of the effects of anisotropy and the shape of pipe steel stress-strain relationships on pipeline strain demand for X80 and X100 UOE pipe. The research included: a review of pipeline industry literature on the subject matter; a discussion of pipe steel plasticity concepts for UOE pipe; characterization of the anisotropy and stress-strain curve shapes for both conventional and high strain pipe steels; development of representative analytical X80 and X100 stress-strain relationships; and evaluation of a large matrix of ground-movement induced pipeline deformation scenarios to evaluate key pipe stress-strain relationship shape and anisotropy parameters. The main conclusion from this work is that pipe steel specifications for high strength UOE pipe for strain-based design applications should be supplemented to consider shape-characterizing parameters such as the plastic complementary energy.

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Correcting the Stress-Strain Curve in Hot Compression Process to High Strain Level

Metallurgical and Materials Transactions A ◽

10.1007/s11661-009-9783-7 ◽

2009 ◽

Vol 40 (4) ◽

pp. 982-990 ◽

Cited By ~ 61

Author(s):

Y. P. Li ◽

E. Onodera ◽

H. Matsumoto ◽

A. Chiba

Keyword(s):

High Strain ◽

Strain Curve ◽

Hot Compression ◽

Strain Level ◽

Stress Strain Curve ◽

Compression Process ◽

Stress Strain

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Determination of the Constants of Zerilli-Armstrong Constitutive Relation Using Genetic Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.264-265.862 ◽

2011 ◽

Vol 264-265 ◽

pp. 862-870

Author(s):

G.H. Majzoobi ◽

S. Faraj Zadeh Khosroshahi ◽

H. Beik Mohammadloo

Keyword(s):

Genetic Algorithm ◽

High Strain ◽

Optimization Technique ◽

Strain Curve ◽

Strain Rates ◽

Stress Strain Curve ◽

Stress Strain ◽

Material Models ◽

The Difference

Identification of the constants of material models is always a concern. In the present work, a combined experimental, numerical and optimization technique is employed to determine the constants of Zerilli-Armstrong model. The experiments are conducted on a compressive Hopkinson bar, the simulations are performed using finite element method and optimization is carried out using genetic algorithm. In the method adopted here, there is no need for experimental stress-strain curve which is always accompanied by restricting phenomenon such as necking in tension and bulging in compression. Instead of stress-strain curve, the difference between the post-deformation profiles of specimens obtained from experiment and the numerical simulations is adopted as the objective function for optimization purposes. The results suggest that the approach introduced in this work can substitute costly instrumentations normally needed for obtaining stress-strain curves at high strain rates and elevated temperature.

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