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

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.

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.

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.

A Load-Based Depth-Sensing Indentation Technique for Elastic-Plastic Material Mechanical Property Evaluation

2010 ◽  
Author(s):  
K. Lee ◽  
J. M. Tannenbaum ◽  
B. S.-J. Kang ◽  
M. A. Alvin
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Strain Hardening ◽  
Strain Curve ◽  
Strain Hardening Exponent ◽  
Depth Sensing ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Indentation Technique ◽  
Micro Indentation

A load-based depth-sensing micro-indentation technique has been developed for material mechanical properties evaluation including elastic modulus, yield stress, strain hardening exponent and stress-strain curve. Based on a Hertzian contact mechanics approach, this load-based depth-sensing micro-indentation technique does not require system compliance calibration or the use of high precision depth sensors. Furthermore a unique, material independent, indentation based load-depth algorithm has been developed accounting for both elastic and elastic-plastic deformation of the material beneath the indenter. This algorithm, found to be a function of material yield stress, strain hardening exponent and elastic modulus, is shown to be the basis for obtaining a stress-strain curve. Finite element analyses of multiple materials with various mechanical properties were employed to examine and develop the fundamental indention based relationships between these variables and the load/depth curve needed to extract the stress-strain diagram. In addition, experimental results obtained with this load-based micro-indentation technique were found to yield accurate material mechanical properties (elastic modulus, strain hardening, yield strength) at room and elevated temperatures (up to 1200°C).

Empirical Equations for Describing the Strain-Hardening Characteristics of Metals Subjected to Moderate Strains

1974 ◽  
Vol 96 (2) ◽  
pp. 123-126 ◽  
Author(s):  
C. Adams ◽  
J. G. Beese
Keyword(s):  
Strain Hardening ◽  
Elastic Recovery ◽  
Strain Curve ◽  
Stress And Strain ◽  
Accurate Assessment ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Initial Portion ◽  
Design Problems ◽  
Work Hardening Exponent

The strain-hardening characteristics of a metal have often been described by a power function which employs a work-hardening exponent, “n.” Usually the material is assumed to be rigid to the yield point and therefore the possibility of any elastic recovery is denied. The authors show that, particularly for the initial portion of a stress-strain curve, n is not a constant and therefore the curve cannot be described by one power law alone. A method is proposed for fitting equations to experimental stress-strain curves up to strain values of 0.05. The equations take into account possible elastic recovery. The equations should facilitate more accurate assessment of underload stress and strain distributions in various design problems.

ECAs and Lateral Buckling

2019 ◽  
Author(s):  
Andrew Cosham ◽  
Kenneth A. Macdonald ◽  
Ian MacRae ◽  
Malcolm Carr
Keyword(s):  
Fracture Mechanics ◽  
Yield Strength ◽  
Strain Hardening ◽  
Pipe Wall ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Lateral Buckling ◽  
Stress Strain ◽  
Apparent Inconsistency ◽  
Girth Welds

Abstract An engineering critical assessment (ECA) is commonly conducted during the design of an offshore pipeline in order to determine the tolerable size of flaws in the girth welds. API 579-1/ASME FFS-1 2016 and BS 7910:2013+A1:2015 Incorporating Corrigenda Nos. 1 and 2 give guidance on conducting fitness-for-service assessments of cracks and crack-like flaws. DNVGL-RP-F108, 2017 Assessment of flaws in pipeline and riser girth welds describes a methodology to satisfy the fracture and fatigue limit states in DNVGL-ST-F101, 2017 based on Option 2 with ductile tearing in BS 7910:2013. It requires that the stress-strain curve used in a strain-based fracture mechanics analysis should represent a high yield strength combined with low strain-hardening properties (a characteristic high stress-strain curve with low strain hardening), and that used in a stress-based fracture mechanics assessment should represent a low yield strength. A pipeline operating at high temperatures and/or high pressures is subject to high compressive axial forces. The pipeline might then relieve these forces by buckling. A design that incorporates controlled lateral buckling is an efficient solution to the problem of high compressive axial stresses. Lateral buckling does, however, give rise to relatively high tensile axial strains (possibly exceeding 0.4 percent) in the pipe wall, and, relatively high fatigue loading associated with movement of the buckle under start-up and shut-down cycles. The calculated tensile axial strain in the pipe wall in a lateral buckle depends on the assumed stress-strain curve. It tends to be higher if a low yield strength combined with low strain-hardening properties is assumed. There is then an apparent inconsistency between the two sets of assumptions. A deterministic assessment of a circumferentially-orientated, internal surface crack-like flaw in a girth weld in a lateral buckle is used to investigate the significance of this apparent inconsistency.

A Reassessment of Deformation Theories of Plasticity

1959 ◽  
Vol 26 (2) ◽  
pp. 259-264
Author(s):  
Bernard Budiansky
Keyword(s):  
Strain Hardening ◽  
Deformation Theory ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Plasticity Theory ◽  
Stress Strain Curve ◽  
Proportional Loading ◽  
Stress Strain ◽  
Simple Deformation ◽  
Strain Hardening Rate

Abstract It is shown that deformation theories of plasticity may be used for a range of loading paths other than proportional loading without violation of general requirements for the physical soundness of a plasticity theory. The extent to which deviations from proportional loading are admissible on this basis is calculated quantitatively for the simple deformation theory of Nadai. It is shown that the lower the strain-hardening rate of the uniaxial stress-strain curve, the greater are the permissible deviations from proportional loading.

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