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 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 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.

Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

Limit Loads for Pipelines With Axial Surface Flaws

1996 ◽  
Author(s):  
G. Shen ◽  
W. R. Tyson
Keyword(s):  
Experimental Data ◽  
Plastic Zone ◽  
Failure Stress ◽  
Back Surface ◽  
Collapse Load ◽  
Yield Model ◽  
Limit Loads ◽  
Surface Flaws ◽  
Strip Yield Model ◽  
Axial Surface

The limit loads for pipelines with axial surface flaws have been evaluated by using a strip yield model at levels of ligament yield and ligament collapse. The former was defined as that at which the plastic zone first reaches the back surface, and the later is that at which the plastic zone spreads over the entire ligament. The evaluated collapse load has been used to estimate the failure stress of pipelines containing axial surface flaws. Predictions have been compared with existing experimental data.

Basic solution of two collinear mode-I cracks in the orthotropic medium by use of the non-local theory

2017 ◽  
Vol 13 (1) ◽  
pp. 100-115 ◽  
Author(s):  
Haitao Liu
Keyword(s):  
Stress Singularity ◽  
Local Theory ◽  
Mode I ◽  
Basic Solution ◽  
Orthotropic Medium ◽  
Dual Integral Equations ◽  
Content Type ◽  
Present Solution ◽  
Crack Tips ◽  
Non Local

Purpose The purpose of this paper is to present the basic solution of two collinear mode-I cracks in the orthotropic medium by the use of the non-local theory. Design/methodology/approach Meanwhile, the generalized Almansi’s theorem and the Schmidt method are used. By the Fourier transform, it is converted to a pair of dual integral equations. Findings Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks and the lattice parameter on the stress field near the crack tips in the orthotropic medium. Originality/value The present solution exhibits no stress singularity at the crack tips in the orthotropic medium.

Contact Analysis for Collinear Multiple Cracks in Residual Stress Field

1994 ◽  
Vol 116 (2) ◽  
pp. 169-174 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Infinite Plate ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Residual Stress Field ◽  
Crack Face

A method is proposed for analyzing stress intensity factors and crack profiles for collinear multiple cracks perpendicular to welded joints in an infinite plate. Using the basic solution of a single crack and taking unknown density of fictitious tractions, Fredholm integral equations and algebraic equations are formulated based upon traction-free conditions and crack face displacements, respectively. These equations are solved simultaneously, considering the contact effect of crack surfaces. Using the derived density of fictitious tractions, the stress intensity factors and displacements of multiple cracks are determined. Some numerical examples are analyzed.

The interaction problem of two Zener–Stroh cracks with a nearby inhomogeneity

2017 ◽  
Vol 24 (3) ◽  
pp. 542-558
Author(s):  
M Fan ◽  
ZM Xiao ◽  
YM Zhang
Keyword(s):  
Plastic Zone ◽  
Influence Factors ◽  
Crack Tip ◽  
Singular Integral Equations ◽  
Plastic Zone Size ◽  
Circular Inclusion ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Crack Tips ◽  
Crack Tip Opening

In this paper, the interaction among two Zener–Stroh cracks (with plastic zone correction) and a nearby circular inclusion are investigated. To evaluate the plastic zone sizes at crack tips in the current physical problem is a great challenge. As the first attempt to explore the multiple defects’ interaction effect on the yielding behavior of a crack, we focused on the analysis of one target crack, while the other crack and the circular inhomogeneity are treated as influence factors. With the help of coordinate transformation and superposition procedure, the formulated singular integral equations can be solved numerically. The influence of material properties, crack–crack positions and other parameters, such as crack length and Burgers vector of the Zener–Stroh crack, on the target crack tip stress intensity factor, plastic zone size and crack tip opening displacement are examined. It is found that the effects of the aforesaid parameters on the cracks are all inter-related and dependent on each other. This observation reveals the complexity of fracture analysis and the necessity to have a deep research on interacting defects in composite materials.

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.

Stress Intensity Factors for Multiple Cracks in an Adhesively Bonded Sandwich Sheet

1993 ◽  
Vol 115 (1) ◽  
pp. 134-139 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Mutual Interaction ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Shear Stresses ◽  
Basic Solution ◽  
Intensity Factors ◽  
Adhesively Bonded ◽  
Sandwich Sheet

A new method is proposed for analyzing stress intensity factors of multiple cracks in an adhesively bonded metallic sandwich sheet. Using a basic solution of a single crack and taking unknown density of surface tractions and adhesive shear stresses, Fredholm integral equations and compatibility equations are formulated based upon stress free condition along each crack and displacement continuity between the sheets and adhesive layers, respectively. These equations are solved simultaneously, and the stress intensity factors of multiple cracks are determined from the derived density of tractions. It is shown that the mutual interaction of multiple cracks in a sandwich sheet is smaller than that in a monolithic sheet. Also, mutual interaction of cracks in the same sheet is smaller than that of cracks in the different sheets.

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