The Effect of Strain Hardening in an Annular Slab

1953 ◽  
Vol 20 (4) ◽  
pp. 530-536
Author(s):  
P. G. Hodge
Keyword(s):  
Strain Hardening ◽  
Biaxial Tension ◽  
Complete Solution ◽  
Maximum Shear Stress ◽  
Strain Curve ◽  
Linear Strain ◽  
Stress Strain Curve ◽  
Line Segments ◽  
Straight Line ◽  
Strain Components

Abstract A procedure is outlined for obtaining the stresses and strains in a circular slab with a cutout, subject to uniform biaxial tension. An arbitrary stress-strain curve in tension is approximated by any number of straight-line segments. For biaxial states of stress the material is assumed to satisfy a flow law based on the maximum shear stress, and to be incompressible throughout. The general equations are given and then simplified by assuming that boundary motions may be neglected if the strains are small, and that elastic strain components may be neglected if the strains are large. For the case of linear strain hardening a complete solution is given in closed form. If the rate of strain hardening is small, these results may be simplified further.

A General Autofrettage Model of a Thick-Walled Cylinder Based on Tensile-Compressive Stress-Strain Curve of a Material

2005 ◽  
Vol 40 (6) ◽  
pp. 599-607 ◽  
Author(s):  
X. P Huang
Keyword(s):  
Strain Hardening ◽  
Compressive Stress ◽  
Bauschinger Effect ◽  
Strain Curve ◽  
Accurate Prediction ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Perfectly Plastic ◽  
Hardening Models ◽  
Elastic Perfectly Plastic

The basic autofrettage theory assumes elastic-perfectly plastic behaviour. Because of the Bauschinger effect and strain-hardening, most materials do not display elastic-perfectly plastic properties and consequently various autofrettage models are based on different simplified material strain-hardening models, which assume linear strain-hardening or power strain-hardening or a combination of these strain-hardening models. This approach gives a more accurate prediction than the elastic-perfectly plastic model and is suitable for different strain-hardening materials. In this paper, a general autofrettage model that incorporates the material strain-hardening relationship and the Bauschinger effect, based upon the actual tensile-compressive stress-strain curve of a material is proposed. The model incorporates the von Mises yield criterion, an incompressible material, and the plane strain condition. Analytic expressions for the residual stress distribution have been derived. Experimental results show that the present model has a stronger curve-fitting ability and gives a more accurate prediction. Several other models are shown to be special cases of the general model presented in this paper. The parameters needed in the model are determined by fitting the actual tensile-compressive curve of the material, and the maximum strain of this curve should closely represent the maximum equivalent strain at the inner surface of the cylinder under maximum autofrettage pressure.

Strain-hardening parameters determined from the stress-strain curve

1977 ◽  
Vol 9 (6) ◽  
pp. 704-707 ◽  
Author(s):  
V. K. Babich ◽  
V. A. Pirogov ◽  
I. A. Vakulenko
Keyword(s):  
Strain Hardening ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain

Bending of Elastoplastic Circular Plates With Large Deflection

1952 ◽  
Vol 19 (3) ◽  
pp. 293-300
Author(s):  
P. M. Naghdi
Keyword(s):  
General Theory ◽  
Numerical Solutions ◽  
Complete Solution ◽  
Strain Curve ◽  
Circular Plates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Symmetrical Loading ◽  
Large Elastic Deformation ◽  
Concentrated Loading

Abstract A general theory for the elastoplastic bending of thin circular plates with polar symmetrical loading is developed, and a numerical integration method is given for the complete solution of problems within the scope of the general theory. In the development of the theory, stress-strain relations of the deformation type (theory of plastic deformation) are employed. As special examples, simply supported circular plates with a central concentrated loading are considered. Using a stress-strain curve for 24S-T aluminum which is determined experimentally, numerical solutions for bending moments, membrane forces, and deflections are obtained for two cases. In one case, the plate experiences large elastic deformation and in the second case, the plate undergoes large elastoplastic deformation. Several plate specimens, made of the same sheet of 24S-T aluminum for which the foregoing stress-strain curve was determined, are tested and a comparison is made between the theoretically determined and the experimentally obtained values of deflection.

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

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.

Modelling of the Strain Hardening Behaviour of Die-Cast Magnesium-Aluminium-Rare Earth Alloy

2020 ◽  
Vol 35 ◽  
pp. 1-8
Author(s):  
Hua Qian Ang
Keyword(s):  
Strain Hardening ◽  
Tensile Deformation ◽  
Deformation Behaviour ◽  
Strain Curve ◽  
Deformation Mode ◽  
Prismatic Slip ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Die Cast ◽  
Cast Magnesium

The tensile deformation behaviour of magnesium alloy AE44 (Mg-4Al-4RE) under strain rates ranging from 10-6 to 10-1 s-1 has been investigated. Present study shows that the deformation mode begins with the activation of elastic (Stage 1), followed by <a> basal slip and twinning (Stage 2), <a> prismatic slip (Stage 3) and finally to <c+a> pyramidal slip (Stage 4). The commencement of these deformation mechanisms results in four distinct stages of strain hardening in the stress-strain curve. In this work, the four stages of deformation behaviour are modelled, and an empirical equation is proposed to predict the entire stress-strain curve. Overall, the model predictions are in good agreement with the experimental data. This study on the decomposition of stress-strain curve into four stages provides insights into the contribution of individual deformation mechanism to the overall deformation behaviour and opens a new way to assess mechanical properties of die-cast magnesium alloys.

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.”

Strain-Hardening Properties of High Grade Line Pipes

2018 ◽  
Vol 913 ◽  
pp. 331-339 ◽  
Author(s):  
Ling Kang Ji ◽  
Hui Feng ◽  
Ji Ming Zhang ◽  
Hong Yuan Chen
Keyword(s):  
Strain Hardening ◽  
Pipeline Steel ◽  
Strain Curve ◽  
Study Phase ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Line Pipe ◽  
Hardening Behavior ◽  
Transverse Tensile ◽  
Strain Hardening Behavior

The strain-hardening performance and characteristics of pipeline steel material have an important influence on the deformation behavior and arrest behavior of the line pipe. In this paper X70, selected, and the longitudinal and transverse tensile stress-strain curve and strain-hardening characteristics were analyzed. The results showed that the strain hardening exponent of the double-phased line pipes derived from the transvers stress-strain curve maintains relatively low level at early stage and increased gradually with variation of strain, which was different from the strain hardening behavior for the rest line pipes in this study. Phase ratio, grain size and dislocation density, precipitation, texture, etc. have an effect to the strain hardening behavior of pipeline steel.

Theories and Experiments on Tube Sinking through Conical Dies

1967 ◽  
Vol 182 (1) ◽  
pp. 19-32 ◽  
Author(s):  
G. G. Moore ◽  
J. F. Wallace
Keyword(s):  
Experimental Data ◽  
Velocity Field ◽  
Strain Hardening ◽  
Lower Bounds ◽  
Coulomb Friction ◽  
Strain Curve ◽  
Upper Bounds ◽  
Stress Strain Curve ◽  
Hardening Material ◽  
Field Techniques

Earlier theories of tube sinking through conical dies have been considered and the factors important in the calculation of stresses and strains have been determined. Using these theories drawing stresses have been calculated for a particular stress-strain curve by assuming an exponential strain hardening characteristic. These drawing stresses are essentially ‘lower bounds’ but comparative ‘upper bounds’ have been obtained using velocity field techniques; Coulomb friction has been included. Thickness strains for a smooth die and a non-strain hardening material have been computed. Experimental data has been obtained using conical dies under normal industrial conditions and comparisons made with theory. In addition, the problems encountered in the inlet and exit of the die are discussed. It is suggested that drawing stresses and thickness strains determined for conical dies can be applied to other die profiles when the die inlet semi-angle does not exceed 15°.

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