Applicability of Neuber’s Rule to the Analysis of Stress and Strain Concentration Under Creep Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 224-229 ◽  
Author(s):  
G. Ha¨rkega˚rd ◽  
S. So̸rbo̸
Keyword(s):  
Stress Relaxation ◽  
Elastic Response ◽  
Strain History ◽  
Stress And Strain ◽  
Stress Strain ◽  
Strain Concentration ◽  
Long Time ◽  
Concentration Factors ◽  
Neuber's Rule ◽  
Good Agreement

A differential form of Neuber’s rule, originally proposed by M. Chaudonneret, has been formulated for a generic viscoplastic notch problem, making extensive use of suitably normalised stress, strain and time. It has been shown that the stress-strain history at the root of a notch in a viscoplastic body can be determined directly from the elastic response, provided far-field viscoplastic strains can be neglected. Neuber’s rule has also been applied to the more general cases of stress and strain concentration at notches under (i) nominal creep conditions (constant nominal stress) and (ii) stress relaxation (constant nominal strain). Predictions are in good agreement with results from finite element analyses. Stress and strain concentration factors have been observed to approach stationary values after long-time loading. The stationary stress concentration factor under stress relaxation falls below that under nominal creep conditions.

scholarly journals A Simplified Method for Elastic-Plastic-Creep Structural Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 231-237 ◽  
Author(s):  
A. Kaufman
Keyword(s):  
Finite Element ◽  
Stress Relaxation ◽  
Kinematic Hardening ◽  
Nonlinear Finite Element ◽  
Strain History ◽  
Stress Strain ◽  
Element Analysis ◽  
Inelastic Analysis ◽  
Simplified Method ◽  
Time Required

A simplified inelastic analysis computer program (ANSYMP) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects can be calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials, and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

Application of the Deformation Theory of Plasticity for Determining Elastoplastic Stress and Strain Concentration Factors

1976 ◽  
Vol 98 (4) ◽  
pp. 1152-1156 ◽  
Author(s):  
J. P. Eimermacher ◽  
I.-Chih Wang ◽  
M. L. Brown
Keyword(s):  
Deformation Theory ◽  
Analytical Data ◽  
Local Stress ◽  
Failure Criteria ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Strain Concentration ◽  
Theory Of Plasticity ◽  
Concentration Factors ◽  
Von Mises

The deformation theory of plasticity is considered as a means for obtaining a solution to the problem of calculating stress and strain concentration factors at geometric discontinuities where the local stress state exceeds the yield strength of the material. Through the use of the Hencky-Nadai constitutive law and the Von Mises failure criteria, the elastoplastic element stiffness matrix is derived for a plane stress triangular plate element. An elastoplastic solution is arrived at by considering direct-iterative and finite element techniques. Verification of the analytical results is obtained by considering a numerical example and comparing the calculated results with published experimental and analytical data.

Correlation of Large Longitudinal Deformations with Different Strain Histories

1967 ◽  
Vol 40 (2) ◽  
pp. 506-516 ◽  
Author(s):  
L. J. Zapas ◽  
T. Craft
Keyword(s):  
Stress Relaxation ◽  
Single Step ◽  
Strain History ◽  
Simple Extension ◽  
Stress Strain ◽  
Fluid Equation ◽  
Elastic Fluid ◽  
Strain Behavior ◽  
Elastomeric Materials ◽  
Single Integral

Abstract In 1963 Bernstein, Kearsley, and Zapas1 presented a theory of an elastic fluid which gave the correct stress-relaxation response for a large variety of elastomeric materials, including vulcanized rubbers. A principle attractiveness of this theory is its relative simplicity; with a single integral in time, it describes the stress-strain behavior for all types of deformation histories. In the case of simple extension, it predicts the behavior in any uniaxial strain history from the results of single step stress-relaxation experiments which cover the same range of extension and time. We designed a series of experiments to check the validity of this theory and found, as is shown in this paper, excellent agreement with experiment in all cases. We are aware that experiments cannot prove a theory. From our results, however, we feel strongly that a single integral expression with a nonlinear integrand such as the BKZ elastic fluid equation is sufficient to describe the stress-strain behavior of elastomeric materials.

A Cyclic Stress-Strain Constitutive Model for Polycrystalline Magnesium Alloy and its Application

2007 ◽  
Vol 546-549 ◽  
pp. 81-88
Author(s):  
Xiang Guo Zeng ◽  
Qing Yuan Wang ◽  
Jing Hong Fan ◽  
Zhan Hua Gao ◽  
Xiang He Peng
Keyword(s):  
Magnesium Alloy ◽  
Constitutive Model ◽  
Cyclic Stress ◽  
Stress And Strain ◽  
Slip Systems ◽  
Stress Strain ◽  
Strain Behavior ◽  
Cast Magnesium ◽  
Magnesium Alloy Am60 ◽  
Good Agreement

The stress-strain behavior of cast magnesium alloy (AM60) was investigated by strain-controlled cyclic testing carried out on MTS. In order to describe the cyclic stress and strain properties of AM60 by means of the energy storing characteristics of microstructure during irreversible deformation, a plastic constitutive model with no yielding surface was developed for single crystal by adopting a spring-dashpot mechanical system. Plastic dashpots reflecting the material transient response were introduced to describe the plasticity of slip systems. By utilizing the KBW self-consistent theory, a polycrystalline plastic constitutive model for Magnesium alloy was formed. The numerical analysis in the corresponding algorithm is greatly simplified as no process of searching for the activation of the slip systems and slip directions is required. The cyclic stress-strain behavior, based on this model, is discussed. The simulation results show good agreement with the experimental data for AM60.

scholarly journals Stress and Strain Concentration Factors in Orthotropic Composites with Hole under Uniaxial Tension

2018 ◽  
Vol 5 (1) ◽  
pp. 213-231
Author(s):  
Samit Ray-Chaudhuri ◽  
Komal Chawla
Keyword(s):  
Uniaxial Tension ◽  
Fiber Orientation ◽  
Composite Plates ◽  
Systematic Investigation ◽  
Stress And Strain ◽  
Governing Parameter ◽  
Strain Concentration ◽  
Wide Range ◽  
Orthotropic Composites ◽  
Concentration Factors

Abstract A systematic investigation is carried out on how different parameters influence stress and strain concentration factors (SCF and SNCF) in a composite plate with a hole under uniaxial tension. Flat and singly curved composite plates have been modelled in ANSYS 15.0. The governing parameter includes: (i) size, shape and eccentricity of hole, (ii) number of plies, (v) fiber orientation and (vi) plate curvature. It is observed that different parameters influence the SCF and SNCF with varying degrees. For example, SCF may be as high as 7.16 for a square shaped hole. Also, SCF and SNCF are found to be approximately same in most of the cases. Finally, simplified design formulas are developed for evaluation of SCF for a wide range of hole size, eccentricity and fiber orientation.

Sign in / Sign up

Export Citation Format

Share Document