Effectiveness of Non-Linear Crack Mechanics under Plane Strain Conditions

2007 ◽  
Vol 348-349 ◽  
pp. 497-500
Author(s):  
T. Teranishi ◽  
Hironobu Nisitani
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Large Scale ◽  
Stress Condition ◽  
Plane Strain Condition ◽  
Strain Condition ◽  
Plane Stress Condition ◽  
Crack Mechanics ◽  
Non Linear ◽  
Scale Yielding

The non-linear crack mechanics (NLCM) is a concept assuring the occurrence of the same phenomena in two cracked bodies under large scale yielding. It has been recognized that NLCM is effective in the cases of plane stress conditions. In this study, it was made clear that NLCM is effective not only in the case of plane stress condition but also in the case of plane strain condition.

A Numerical Study on CMOD Compliance for Single-Edge Notched Bending Specimens

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Enyang Wang ◽  
Wenxing Zhou ◽  
Guowu Shen ◽  
Daming Duan
Keyword(s):  
Crack Length ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Condition ◽  
Three Dimensional ◽  
Plane Strain Condition ◽  
Strain Condition ◽  
Two Dimensional ◽  
Single Edge ◽  
Plane Stress Condition

Several well-known equations for estimating the crack length in the single-edge notched bending (SE(B)) specimens from the normalized crack mouth opening displacement (CMOD) compliance are evaluated based on two-dimensional (2D) and three-dimensional (3D) finite element analyses (FEAs). Two-dimensional FEAs are first carried out to verify the reported accuracy and applicable ranges for each equation based on the plane strain models with six different crack lengths. Three-dimensional FEAs are then carried out to estimate the errors of prediction of equations that evaluate the crack length from the plane stress- and plane strain-based CMOD compliances. Both plane-sided and side-grooved models are included in 3D FEAs and have seven different thickness-to-width ratios. The error of prediction of a given equation is largely impacted by the thickness-to-width ratio, the crack length, the presence of side grooves, and the use of the plane stress- or plane strain-normalized CMOD compliance. Based on the errors of prediction, the relevance of the actual state of stress in the ligament of the SE(B) specimens to the plane strain condition or the plane stress condition is inferred. Knowledge of the relevance of the plane stress condition or the plane strain condition can be used to select the corresponding CMOD compliance in crack length-CMOD equations, and, therefore, the corresponding predictive accuracy can be improved.

scholarly journals Analytical Solution of Mixed Boundary Value Problems Using the Displacement Potential Approach for the Case of Plane Stress and Plane Strain Conditions

2017 ◽  
Vol 22 (2) ◽  
pp. 269-291
Author(s):  
S.K. Deb Nath
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Mixed Boundary ◽  
Stress Component ◽  
Plane Strain Condition ◽  
Strain Condition ◽  
Plane Stress Condition ◽  
Potential Approach ◽  
Displacement Potential ◽  
Fixed End

AbstractTwo elastic plate problems made of duralumin are solved analytically using the displacement potential approach for the case of plane strain and plane stress conditions. Firstly, a one end fixed plate is considered in which the rest of the edges are stiffened and a uniform load is applied to the opposite end of the fixed end. Secondly, a plate is considered in which all of the edges are stiffened and a uniform tension is applied at its both ends. Solutions to both of the problems are presented for the case of plane stress and plane strain conditions. The effects of plane stress and plane strain conditions on the solutions are explained. In the case of stiffening of the edges of the plate, the shape of the plate does not change abruptly, which is clearly observed in both of the cases. For the plane strain condition, the plates become stiffer in the loading direction as compared to the plane stress condition. For the plane strain condition, there is a significant variation of the normal stress component, σzzat different sections of the plate. The graphical results, clearly identify the critical regions of the plate for the case of the plane stress and plane strain condition.

Drained solution for cylindrical cavity expansion in modified Cam clay soil under constant vertical stress

2020 ◽  
pp. 1-14
Author(s):  
D. Su
Keyword(s):  
Plane Strain ◽  
Cylindrical Cavity ◽  
Stress Condition ◽  
Vertical Stress ◽  
Plane Strain Condition ◽  
Cavity Expansion ◽  
Strain Condition ◽  
Cylindrical Cavity Expansion ◽  
Modified Cam Clay ◽  
Cam Clay

Cavity expansion is a fundamental theoretical problem in geomechanics. For the cylindrical cavity expansion problem, derivations of solutions are usually based on the assumption that the soil is subject to the plane strain condition. However, this is untrue for cavity expansion in pressuremeter tests. This study first derived the equilibrium equation for cylindrical cavity expansion under the constant vertical stress condition. Then, the equilibrium equation was solved for modified Cam clay soils with different overconsolidation ratios (OCRs). The solutions were compared with the responses in the same soils under the plane strain condition. It was found that the ratio of the limiting cavity pressure in the latter to that in the former ranged from 1.31 to 2.76 and increased with an increase in the OCR. Under the constant vertical stress condition, significant heaving occurred in the vicinity of the cavity, and volumetric strain evolved from contraction to dilation as the OCR increased. Significant differences were noted in the stress paths of the two different loading conditions. These results indicate that the assumption of the plane strain condition will lead to overestimation of the limiting cavity pressure and inaccurate prediction of the stress path in the pressuremeter test, especially for heavily overconsolidated soils.

scholarly journals Damaged behavior under plane stress

2011 ◽  
pp. 341-368
Author(s):  
Thomas Paris ◽  
Khémaïs Saanouni
Keyword(s):  
Plane Stress ◽  
Constitutive Equations ◽  
Stress Condition ◽  
Time Integration ◽  
Reference Case ◽  
Plane Stress Condition ◽  
Integration Schemes ◽  
Hyperbolic Sine ◽  
Time Integration Schemes ◽  
Fully Coupled

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.

Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems

1976 ◽  
Vol 98 (4) ◽  
pp. 289-295 ◽  
Author(s):  
C. F. Shih ◽  
J. W. Hutchinson
Keyword(s):  
Plane Stress ◽  
Large Scale ◽  
Crack Opening ◽  
Opening Displacement ◽  
Stress Strain ◽  
Linear Elastic ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Crack Problems ◽  
Scale Yielding

Fully plastic plane stress solutions are given for a center-cracked strip in tension and an edge-cracked strip in pure bending. In the fully plastic formulation the material is characterized by a pure power hardening stress-strain relation which reduces at one limit to linear elasticity and at the other to rigid/perfect plasticity. Simple formulas are given for estimating the J-integral, the load-point displacement and the crack opening displacement in terms of the applied load for strain hardening materials characterized by the Ramberg-Osgood stress-strain relation in tension. The formulas make use of the linear elastic solution and the fully plastic solution to interpolate over the entire range of small and large scale yielding. The accuracy of the formulas is assessed using finite element calculations for some specific configurations.

Sign in / Sign up

Export Citation Format

Share Document