Strip Yield Analysis on Coalescence of Plastic Zones for Multiple Cracks in a Riveted Stiffened Sheet

1999 ◽  
Vol 121 (3) ◽  
pp. 352-359 ◽  
Author(s):  
Toshihiko Nishimura
Keyword(s):  
Stress Singularity ◽  
Multiple Cracks ◽  
Algebraic Equations ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tips ◽  
Fictitious Crack ◽  
Plastic Zones ◽  
Crack Tip Opening ◽  
Remote Stress

The coalescence conditions of plastic zones are calculated for multiple cracks in a riveted stiffened sheet using a strip yield model. The multiple cracks and their plastic zones are treated as a fictitious crack, and algebraic equations are formulated on compatibility of displacements, no stress singularity at the fictitious crack tips, and zero displacement at the coalesced points of plastic zones. These equations are iteratively solved, and critical values of remote stress, fastener forces, plastic zone sizes, and crack tip opening displacements are calculated. Some numerical results are presented for two cracks in a sheet with and without stiffeners.

Strip Yield Analysis for Multiple Cracked Sheet With Riveted Stiffeners

1993 ◽  
Vol 115 (4) ◽  
pp. 398-403 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Plastic Zone ◽  
Stress Singularity ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tips ◽  
Fictitious Crack ◽  
Crack Tip Opening

An elasto-plastic analysis is conducted based upon a strip yield model for analyzing multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown fictitious surface tractions and fastener forces, Fredholm integral equations are formulated from the equilibrium condition along multiple cracks in the sheet. In addition compatibility equations of displacements are formulated among the sheet, fasteners and stiffeners. Based upon no stress singularity at the fictitious crack tips, these equations are iteratively solved as a single system of equations. Then the unknown fictitious surface tractions, fastener forces, and plastic zone sizes ahead of the crack tips are determined. The crack tip opening displacements for a multiple cracked sheet with riveted stiffeners are determined from the derived fictitious surface tractions and plastic zone sizes. Four example calculations and predictions are presented.

Strip Yield Analysis of Plastic Zone Coalescence for Collinear Edge Crack and Internal Crack in a Semi-Infinite Sheet

1999 ◽  
Vol 122 (1) ◽  
pp. 86-89 ◽  
Author(s):  
Toshihiko Nishimura
Keyword(s):  
Plastic Zone ◽  
Integral Equations ◽  
Edge Crack ◽  
Stress Singularity ◽  
Crack Tip ◽  
Internal Crack ◽  
Crack Face ◽  
Plastic Zones ◽  
Crack Tip Opening ◽  
Remote Stress

The coalescence conditions of plastic zones are calculated for an edge crack and an internal crack in a semi-infinite sheet. The cracks and their plastic zones are treated as a fictitious crack, and integral equations are formulated on equilibrium of surface traction, no stress singularity at the crack tip, and zero crack face displacement at the coalesced point of plastic zones. The integral equations are iteratively solved, and critical values of remote stress, plastic zone sizes, and crack tip opening displacements are determined. Numerical results for an edge crack and an internal crack due to remote stress are presented. [S0094-9930(00)00301-2]

Plastic Zone Coalescence and Edge Break Conditions of Internal Cracks in a Semi-infinite Sheet

2006 ◽  
Vol 129 (1) ◽  
pp. 142-147 ◽  
Author(s):  
Toshihiko Nishimura
Keyword(s):  
Plastic Zone ◽  
Integral Equations ◽  
Numerical Results ◽  
Critical Conditions ◽  
Surface Traction ◽  
Crack Face ◽  
Fictitious Crack ◽  
Plastic Zones ◽  
Crack Tip Opening ◽  
Remote Stress

The problem of two cracks in a semi-infinite sheet is analyzed. The critical conditions when adjacent plastic zones just coalesced are obtained. Also, the conditions when a plastic zone just reached the sheet edge are obtained. Assuming the crack and plastic zones as a fictitious crack, the integral equations are formulated in terms of surface traction, nonsingular stress, and zero crack face displacement at the coalescent point or at the sheet edge. By solving the equations, critical remote stress, plastic zone sizes, and crack tip opening displacements are obtained. Numerical results are presented.

Strip yield model for multiple straight cracks with coalesced yield zones: A theoretical study

2021 ◽  
pp. 1-15
Author(s):  
S. Hasan ◽  
N. Akhtar ◽  
S. Shekhar
Keyword(s):  
Numerical Study ◽  
Multiple Cracks ◽  
Principle Of Superposition ◽  
Yield Model ◽  
Zone Length ◽  
Yield Zone ◽  
Strip Yield Model ◽  
Opening And Closing ◽  
The Impact ◽  
Analytical Expressions

The paper presents a complicated case of coalescence of yield zones between two internal cracks out of four collinear straight cracks weakened an infinite isotropic plate. Two solutions are presented for the case of opening and closing of multiple cracks under general yielding conditions. Using these two solutions and the principle of superposition, we found the analytical expressions for load-bearing capacity of the plate using complex variable method. A numerical study has been carried out to investigate the behavior of yield zone length concerning remotely applied stresses at the boundary of the plate and the impact of two outer cracks on the propagation of inner cracks due to coalesced yield zones. Results obtained are reported graphically.

Comparison of Strip Yield and Net Section Plasticity Models for a Bar in Bending With a Single Edge Crack

2017 ◽  
Author(s):  
Wolf Reinhardt ◽  
Don Metzger
Keyword(s):  
Edge Crack ◽  
Large Scale ◽  
Stress Singularity ◽  
Crack Tip ◽  
Small Scale ◽  
Single Edge ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tip Plasticity ◽  
Stress And Deformation

The strip yield model is widely used to describe crack tip plasticity in front of a crack. In the strip yield model the stress in the plastic zone is considered as known, and stress and deformation fields can be obtained from elastic solutions using the condition that the crack tip stress singularity vanishes. The strip yield model is generally regarded to be valid to describe small scale plasticity at a crack tip. The present paper examines the behavior of the strip yield model at the transition to large-scale plasticity and its relationship to net section plasticity descriptions. A bar in bending with a single edge crack is used as an illustrative example to derive solutions and compare with one-sided and two-sided plasticity solutions.

scholarly journals Strip Yield Model for a Crack in a Plate of Arbitrary Thickness

2005 ◽  
Vol 293-294 ◽  
pp. 253-260
Author(s):  
Andrei G. Kotousov
Keyword(s):  
Plate Thickness ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Fe Model ◽  
Crack Tip Opening Displacement ◽  
Yield Model ◽  
Opening Displacement ◽  
Strip Yield Model ◽  
Arbitrary Thickness ◽  
Crack Tip Opening

This paper presents new analytical results on the crack tip opening displacement (CTOD) for a through-the-thickness crack in an infinite plate of arbitrary thickness. These results are based on a new fundamental solution for an edge dislocation obtained earlier and published elsewhere. The analytical predictions of CTOD for various ratios of the crack length to the plate thickness are compared with an independent three-dimensional elasto-plastic finite element (FE) study. It is shown that both analytical and numerical results are in a good agreement when the numerical calculations are not affected by the size of the FE mesh and finite boundaries of the FE model.

Application of the Strip Yield Model to Crack Growth Predictions for Structural Steel

2010 ◽  
Vol 57 (1) ◽  
pp. 1-20
Author(s):  
Małgorzata Skorupa ◽  
Tomasz Machniewicz
Keyword(s):  
Structural Steel ◽  
Crack Growth ◽  
Model Calibration ◽  
Load History ◽  
Yield Model ◽  
Variable Amplitude Loading ◽  
Variable Amplitude ◽  
Constraint Factors ◽  
Strip Yield Model ◽  
Closure Mechanism

Application of the Strip Yield Model to Crack Growth Predictions for Structural SteelA strip yield model implementation by the present authors is applied to predict fatigue crack growth observed in structural steel specimens under various constant and variable amplitude loading conditions. Attention is paid to the model calibration using the constraint factors in view of the dependence of both the crack closure mechanism and the material stress-strain response on the load history. Prediction capabilities of the model are considered in the context of the incompatibility between the crack growth resistance for constant and variable amplitude loading.

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