Crosslinking, Filler, or Transition Constraint of Polymer Networks. II

1971 ◽  
Vol 44 (5) ◽  
pp. 1227-1248
Author(s):  
A. F. Blanchard
Keyword(s):  
Strain Hardening ◽  
Polymer Networks ◽  
Stress Strain ◽  
New Concepts ◽  
Filler Reinforcement ◽  
Hard Fraction ◽  
Rubber Filler

Abstract The theory of Part I is developed by application to filler reinforcement of NR and SBR. For unswollen but prestretched networks it quantifies entire stress-strain curves and applies new concepts of extensibility and strain hardening. Constraint of swelling is expressed by a constant Ø, termed linkage reinforcement, and by an effective hard fraction Cm per cm2 of compound. For rubber-filler swelling vc the modified Flory functions F(νc) in Part I need 3% correction.

A Theory of Elastic, Plastic, and Creep Deformations of an Initially Isotropic Material Showing Anisotropic Strain-Hardening, Creep Recovery, and Secondary Creep

1958 ◽  
Vol 25 (4) ◽  
pp. 529-536
Author(s):  
J. F. Besseling
Keyword(s):  
Plastic Deformation ◽  
Energy Dissipation ◽  
Strain Hardening ◽  
Isotropic Material ◽  
Creep Recovery ◽  
Secondary Creep ◽  
Stress Strain ◽  
Microscopic Scale ◽  
Anisotropic Strain ◽  
Creep Deformations

Abstract Stress-strain relations are given for an initially isotropic material, which is macroscopically homogeneous, but inhomogeneous on a microscopic scale. An element of volume is considered to be composed of various portions, which can be represented by subelements showing secondary creep and isotropic work-hardening in plastic deformation. If the condition is imposed that all subelements of an element of volume are subjected to the same total strain, it is demonstrated that the inelastic stress-strain relations of the material show anisotropic strain-hardening, creep recovery, and primary and secondary creep due to the nonuniform energy dissipation in deformation of the sub-elements. Only quasi-static deformations under isothermal conditions are considered. The theory is restricted to small total strains.

A Characteristic and a Precisely Constitutive Model for Undrained Clay

2020 ◽  
Vol 975 ◽  
pp. 203-207
Author(s):  
Shih Tsung Hsu ◽  
Wen Chi Hu ◽  
Yu Heng Lin ◽  
Zhuo Ling
Keyword(s):  
Shear Strength ◽  
Plastic Strain ◽  
Constitutive Model ◽  
Strain Hardening ◽  
Undrained Shear Strength ◽  
Triaxial Tests ◽  
Stress Strain ◽  
Proposed Model ◽  
Taipei Basin ◽  
Undrained Shear

Constitutive models for soils are usually adopted in numerical method to analyze the behavior of geotechnical structures. This study performs a series of consolidated-undrained triaxial tests to establish the stress-strain curve of clay. A constitutive model that considers continuous strain hardening-softening is proposed based on the results of triaxial tests. Triaxial test results reveal that undrained shear strength linearly increases with an increase in consolidated pressure , the normalized undrained shear strength is about 0.52 not only for this study but also for the other two cases around Taipei Basin. Due to undrained condition, an associated flow rule between plastic strain increment and stress tensor is adopted. As accumulative plastic strain or/and consolidated pressure change, the mobilized undrained shear strength also changes. All parameters needed for the proposed model can be expressed as a function of undrained shear strength Su, The mobilized undrained shear strength for the proposed model during strain hardening-softening can be in term of accumulative plastic strain. This model can calculate the stress-strain curves of clayed soils accurately.

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

A full-range stress-strain model for metallic materials depicting non-linear strain-hardening behavior

2020 ◽  
pp. 030932472095779
Author(s):  
Digendranath Swain ◽  
S Karthigai Selvan ◽  
Binu P Thomas ◽  
Ahmedul K Asraff ◽  
Jeby Philip
Keyword(s):  
Constitutive Model ◽  
Strain Hardening ◽  
Image Correlation ◽  
Linear Strain ◽  
Stress Strain ◽  
Material Parameters ◽  
Hardening Behavior ◽  
Non Linear ◽  
Strain Hardening Behavior ◽  
Strain Model

Ramberg-Osgood (R-O) type stress-strain models are commonly employed during elasto-plastic analysis of metals. Recently, 2-stage and 3-stage R-O variant models have been proposed to replicate stress-strain behavior under large plastic deformation. The complexity of these models increases with the addition of each stage. Moreover, these models have considered deformation till necking only. In this paper, a simplistic multi-stage constitutive model is proposed to capture the strain-hardening non-linearity shown by metals including its post necking behavior. The constitutive parameters of the proposed stress-strain model can be determined using only elastic modulus and yield strength. 3-D digital image correlation was used as an experimental tool for measuring full-field strains on the specimens, which were subsequently utilized to obtain the material parameters. Our constitutive model is demonstrated with an aerospace-grade stainless steel AISI 321 wherein deformation response averaged over the gauge length (GL) and at a local necking zone are compared. The resulting averaged and local material parameters obtained from the proposed model provide interesting insights into the pre and post necking deformation behavior. Our constitutive model would be useful for characterizing highly ductile metals which may or may not depict non-linear strain hardening behavior including their post necking deformations.

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