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 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.

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.

Plastic Strain Distribution at the Tips of Propagating Fatigue Cracks

1976 ◽  
Vol 98 (1) ◽  
pp. 24-29 ◽  
Author(s):  
D. L. Davidson ◽  
J. Lankford
Keyword(s):  
Aluminum Alloy ◽  
Fatigue Crack ◽  
Plastic Strain ◽  
Plastic Zone ◽  
Strain Distribution ◽  
Dimensionless Parameter ◽  
Fatigue Cracks ◽  
Crack Tip ◽  
Cyclic Plastic Zone ◽  
Plastic Zones

The techniques of selected area electron channeling and positive replica examination have been used to study the plastic zones attending fatigue crack propagation in 304 SS, 6061-T6 aluminum alloy, and Fe-3Si steel. These observations allowed the strain distribution at the crack tip to be determined. The results indicate that the concepts of a monotonic and a cyclic plastic zone are essentially correct, with the strains at demarcation between these two zones being 3 to 6 percent. Strain distribution varies as r−1/2 in the cyclic zone and as ln r in the monotonic plastic zone. The strain distributions for all materials studied may be made approximately coincident by using a dimensionless parameter related to distance from the crack tip.

Hybrid Measurement of CT and Strain Distribution of Internal Crack Using Synchrotron High-Energy Monochromatic X-Rays

2010 ◽  
Vol 652 ◽  
pp. 202-209
Author(s):  
Keisuke Tanaka ◽  
Takahisa Shobu ◽  
Hiroshi Kimachi
Keyword(s):  
Strain Distribution ◽  
Crack Opening ◽  
Three Dimensional ◽  
Crack Tip ◽  
High Energy ◽  
Internal Crack ◽  
X Rays ◽  
Crack Face ◽  
Dimensional Shape ◽  
Three Dimensional Shape

Using high-energy monochromatic X-rays of energy 66.4keV from the synchrotron radiation source, SPring-8, we have developed a system to perform a hybrid measurement of imaging of cracks and strain distribution around cracks. This system was applied to a fatigue crack made in a round bar made of carbon steel with a diameter of 4 mm. Computed tomography of the specimen gave the three-dimensional shape of a thumb-nail crack. High tensile strain ahead of the crack was measured at the applied maximum stress, while the strain on the crack face was low because of stress relief due to crack opening. The full width at half maximum (FWHM) increased near the crack tip under loading, and then decreased after unloading. The recoverable part of FWHM by unloading was caused by the steep distribution of the applied stress in the vicinity of the crack tip. The FWHM increased by plastic deformation does not change when unloaded. The measured distributions of the lattice strain and FWHM agreed well with those of the elastic and plastic strains calculated by the finite element method, respectively.

Modeling of the Crack Tip Plastic Zone by Two Slip Lines and the Order of Stress Singularity

2004 ◽  
Vol 127 (1) ◽  
pp. L105-L109 ◽  
Author(s):  
Anatoly A. Kaminsky ◽  
Leonid A. Kipnis ◽  
Michael V. Dudik
Keyword(s):  
Plastic Zone ◽  
Stress Singularity ◽  
Crack Tip ◽  
Slip Lines

Elastic-Plastic Analytical Solution for SEMI’s Horizontal Brace with a Circumferential Through Crack under Tension and Bending

2021 ◽  
pp. 1-8
Author(s):  
Fei Wang
Keyword(s):  
Analytical Solution ◽  
Plastic Zone ◽  
Plastic Behavior ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Elastic Plastic ◽  
Bending Load ◽  
Closed Form Analytical Solution ◽  
Plastic Zones ◽  
Crack Tip Opening

The elastic-plastic behavior of semi-submersible’s horizontal brace with a circumferential through crack which lies at its boundary was studied. Both tension and bending were considered to investigate the closed-form analytical solution. The results indicate that the tensile plastic zone and crack tip opening displacement (CTOD) on the cracked section increase sharply after a smoothly increment when loads became larger. The cracked horizontal brace with a greater initial circumferential through crack has a larger tensile plastic zone and earlier compressive plastic zone appearance on the cracked section. Compared with the load of tension, the bending load has larger effect on the plastic zones of the cracked section and CTOD of the crack.

Stress Distribution Near Internal Crack Tips for Longitudinal Shear Problems

1965 ◽  
Vol 32 (1) ◽  
pp. 51-58 ◽  
Author(s):  
G. C. Sih
Keyword(s):  
Stress Distribution ◽  
Stress Singularity ◽  
Crack Tip ◽  
Longitudinal Shear ◽  
Complex Stress ◽  
Internal Crack ◽  
Vertex Angle ◽  
Crack Tips ◽  
Bending Problems ◽  
Half Power

A method is developed for finding the stress distribution in a cracked body under longitudinal shear and applied to solve a number of problems. Stress solutions are obtained in closed form and discussed in connection with the Griffith-Irwin theory of fracture. The results indicate that current fracture-mechanics theories may be applied directly to longitudinal shear problems. More specifically, the character of the stress distribution near the vertex of a sector cylinder in shear is examined. The inverse half-power law of the stress singularity at a crack tip may be verified by taking a vertex angle of 2π. In addition, crack-tip, stress-intensity factors are defined and evaluated from a complex stress function in a manner similar to those previously given for extension and plate-bending problems. Results of such studies clarified the behavior of branched cracks and other crack systems of interest.

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