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.

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

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.

Experimental Setup for the Determination of Mechanical Solder Materials Properties at Elevated Temperatures

2010 ◽  
Vol 638-642 ◽  
pp. 3793-3798
Author(s):  
Wolfgang H. Müller ◽  
Holger Worrack ◽  
Jens Sterthaus
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Elevated Temperatures ◽  
Young's Modulus ◽  
Linear Optimization ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Non Linear

The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young’s modulus, yield stress, and hardness are of great interest. Moreover, a complete stress-strain curve is desirable for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). However, since the amount of matter is so small and it is the intention to describe its behavior as realistic as possible, miniature tests are used for measuring the mechanical properties. In this paper two miniature tests are presented for this purpose, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial load is prescribed and the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and by fitting the corresponding parameters to the experimental data (obtained for various microelectronic solders) by means of a non-linear optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Oliver and Pharr this data can be used to obtain hardness and Young’s modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equations for stress and strain are obtained by means of the inverse method. The stress-strain curves from nanoindentation and tensile tests are compared for two mate-rials (aluminum and steel). Differences are explained in terms of the locality of the measurement. Finally, material properties at elevated temperature are of particular interest in order to characterize the materials even more completely. We describe the setup for hot stage nanoindentation tests in context with first results for selected materials.

Sign in / Sign up

Export Citation Format

Share Document