scholarly journals Wide-Range Weight Functions for the Strip with a Single Edge Crack

2008 ◽  
pp. 95-95-11 ◽  
Author(s):  
TW Orange
Keyword(s):  
Edge Crack ◽  
Weight Functions ◽  
Single Edge ◽  
Wide Range

Weight Functions for T-Stress for Edge Cracks in Thick-Walled Cylinders

2004 ◽  
Author(s):  
J. Li ◽  
C. L. Tan ◽  
X. Wang
Keyword(s):  
Boundary Element ◽  
Edge Crack ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Internal Edge ◽  
Crack Face ◽  
Nonlinear Stress ◽  
Wide Range ◽  
T Stress

This paper presents T-stress solutions for an internal edge crack in thick-walled cylinders under complex stress distributions. First, the background of the weight function method for the calculation of T-stress is discussed. Then the T-stress results for edge-cracked cylinders obtained from extensive boundary element analyses are summarized. The crack geometries analyzed cover a wide range of radius ratios and relative crack lengths. The loading cases considered in the BEM analysis for the cracked cylinder are: i) crack face pressures with polynomial stress distributions acting on the crack face and ii) internal pressure or steady state thermal loading in the cylinder. Then, the T-stress results for uniform and linearly varying crack face pressure cases are used as the reference solutions to derive weight functions for T-stress. Boundary element results of T-stress for other nonlinear stress distributions are used to validate the derived T-stress weight functions. Excellent accuracy has been achieved. The weight functions derived are suitable for obtaining T-stress solutions for thick-walled cylinders with an internal edge crack under any complex stress fields.

Weight Functions for T-Stress for Edge Cracks in Thick-Walled Cylinders

2005 ◽  
Vol 127 (4) ◽  
pp. 457-463 ◽  
Author(s):  
Jian Li ◽  
Choon-Lai Tan ◽  
Xin Wang
Keyword(s):  
Boundary Element ◽  
Edge Crack ◽  
Thermal Loading ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Internal Edge ◽  
Crack Face ◽  
Wide Range ◽  
T Stress

This paper presents T-stress solutions for an internal edge crack in thick-walled cylinders. Elastic fracture mechanics analysis using the boundary element method (BEM) is performed to determine the T-stress solutions for a wide range of radius ratios and relative crack lengths. The loading cases considered in the BEM analysis for the cracked cylinder are crack-face pressures with polynomial stress distributions acting on the crack face. T-stress results for the uniform and linearly varying crack-face pressure cases are subsequently used as the reference solutions to derive weight functions for T-stress. Boundary element results of T-stress for other stress distributions, namely, other nonlinear crack face loading, internal pressure, and steady-state thermal loading, are used to validate the derived T-stress weight functions. Excellent agreement between the results from the weight function predictions and those directly computed is shown to be obtained. The weight functions derived are suitable for obtaining T-stress solutions for thick-walled cylinders with an internal edge crack under any complex stress fields.

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.

Wide Range Compliance Solutions for Various Fracture Test Specimens Using Crack Mouth Opening Displacement

2017 ◽  
Author(s):  
Claudio Ruggieri ◽  
Rodolfo F. de Souza
Keyword(s):  
Mouth Opening ◽  
Crack Mouth Opening Displacement ◽  
Width Ratio ◽  
Fracture Test ◽  
Single Edge ◽  
Opening Displacement ◽  
Element Analysis ◽  
Single Edge Notch ◽  
Wide Range ◽  
Edge Notch

This work addresses the development of wide range compliance solutions for tensile-loaded and bend specimens based on CMOD. The study covers selected standard and non-standard fracture test specimens, including the compact tension C(T) configuration, the single edge notch tension SE(T) specimen with fixed-grip loading (clamped ends) and the single edge notch bend SE(B) geometry with varying specimen spam over width ratio and loaded under 3-point and 4-point flexural configuration. Very detailed elastic finite element analysis in 2-D setting are conducted on fracture models with varying crack sizes to generate the evolution of load with displacement for those configurations from which the dependence of specimen compliance on crack length, specimen geometry and loading mode is determined. The extensive numerical analyses conducted here provide a larger set of solutions upon which more accurate experimental evaluations of crack size changes in fracture toughness and fatigue crack growth testing can be made.

Lateral Vibration of a Consistent Continuous Beam With a Crack

1997 ◽  
Author(s):  
Thomas G. Chondros ◽  
Andrew D. Dimarogonas ◽  
Jonathan Yao
Keyword(s):  
Displacement Field ◽  
Edge Crack ◽  
Fatigue Cracks ◽  
Lateral Vibration ◽  
Single Edge ◽  
Cracked Beam ◽  
Beam Vibration ◽  
Vibration Theory ◽  
Lateral Vibrations ◽  
Double Edge

Abstract A continuous cracked beam vibration theory is developed for the lateral vibration of cracked Euler-Bernoulli beams with single-edge or double-edge cracks. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked beam as an one-dimensional continuum. The displacement field about the crack was used to modify the stress and displacement field throughout the bar. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations for beams with a single-edge crack are presented: the continuous cracked beam vibration theory developed here, the lumped crack beam vibration analysis, and an asymptotic solution. Experimental results from aluminum beams with fatigue cracks are very close to the values predicted. A steel beam with a double-edge crack was also investigated with the above mentioned methods, and results compared well with experimental data.

Numerical solutions and analysis of diffusion for new generalized fractional Burgers equation

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Yufeng Xu ◽  
Om Agrawal
Keyword(s):  
Finite Difference ◽  
Diffusion Process ◽  
Weight Function ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Weight Functions ◽  
Linear Recurrence ◽  
Scale Function ◽  
Special Cases ◽  
Wide Range

AbstractIn this paper, numerical solutions of Burgers equation defined by using a new Generalized Time-Fractional Derivative (GTFD) are discussed. The numerical scheme uses a finite difference method. The new GTFD is defined using a scale function and a weight function. Many existing fractional derivatives are the special cases of it. A linear recurrence relationship for the numerical solutions of the resulting system of linear equations is found via finite difference approach. Burgers equations with different fractional orders and coefficients are computed which show that this numerical method is simple and effective, and is capable of solving the Burgers equation accurately for a wide range of viscosity values. Furthermore, we study the influence of the scale and the weight functions on the diffusion process of Burgers equation. Numerical simulations illustrate that a scale function can stretch or contract the diffusion on the time domain, while a weight function can change the decay velocity of the diffusion process.

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