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.

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.

T-Stress Solutions for Multiple Edge Cracks in Thick-Walled Cylinders

2005 ◽  
Author(s):  
J. Li ◽  
X. Wang ◽  
C. L. Tan
Keyword(s):  
Weight Function ◽  
Boundary Element ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Internal Edge ◽  
Crack Face ◽  
Nonlinear Stress ◽  
T Stress ◽  
Edge Cracks

In this paper, the boundary element method (BEM) is employed to obtain T-stress solutions for multiple internal edge-cracks in thick-walled cylinders under complex stress distributions. Thick-walled cylinders with two, four and eight internal edge cracks, respectively, are analyzed for a wide range of radius ratios and relative crack lengths. The load cases considered for the cracked cylinder are: i) crack face pressure with uniform, linear, quadratic and cubic stress distributions and ii) internal pressure in the cylinder. The T-stress results for the uniform and the linear distribution crack face pressure cases are used as the reference solutions to derive weight function solutions for the T-stress for the corresponding geometries. The direct boundary element results of the T-stress for the other nonlinear stress distributions are used to validate the derived T-stress weight functions. Excellent agreements between the BEM results and weight function predictions are obtained. The weight functions derived are suitable for obtaining T-stress solutions for the corresponding cracked thick-walled cylinder under any complex stress fields.

Weight Functions for an External Longitudinal Semi-Elliptical Surface Crack in a Thick-Walled Cylinder

1997 ◽  
Vol 119 (1) ◽  
pp. 74-82 ◽  
Author(s):  
A. Kiciak ◽  
G. Glinka ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Reference Stress ◽  
Pressurized Cylinder ◽  
Walled Cylinder

Mode I weight functions were derived for the deepest and surface points of an external radial-longitudinal semi-elliptical surface crack in a thick-walled cylinder with the ratio of the internal radius to wall thickness, Ri/t = 1.0. Coefficients of a general weight function were found using the method of two reference stress intensity factors for two independent stress distributions, and from properties of weight functions. Stress intensity factors calculated using the weight functions were compared to the finite element data for several different stress distributions and to the boundary element method results for the Lame´ hoop stress in an internally pressurized cylinder. A comparison to the ASME Pressure Vessel Code method for deriving stress intensity factors was also made. The derived weight functions enable simple calculations of stress intensity factors for complex stress distributions.

T-Stresses for Edge Cracks and Vanishing Ligaments

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
John P. Dempsey
Keyword(s):  
Half Plane ◽  
Edge Crack ◽  
Flexural Rigidity ◽  
Quantitative Relationship ◽  
Crack Mouth ◽  
Crack Face ◽  
T Stress ◽  
Concentrated Loading ◽  
Edge Cracks ◽  
Uncracked Ligament

An edge-cracked half-plane 0 < x < A and a half-plane x > 0 with a semi-infinite crack x > a perpendicular to the edge are examined in this paper. Uniform crack-face loading is thoroughly examined, with a thorough exposition of the Koiter Wiener–Hopf approach (Koiter, 1956, “On the Flexural Rigidity of a Beam Weakened by Transverse Saw Cuts,” Proc. Royal Neth. Acad. of Sciences, B59, pp. 354–374); an analytical expression for the corresponding T-stress is obtained. For the additional cases of (i) nonuniform edge-crack crack-face loading σ(x/A)k (ℜ(k)>-1), (ii) concentrated loading at the edge-crack crack mouth, the Wiener–Hopf solutions and analytical T-stress expressions are provided, and tables of T-stress results for σ(x/A)k and σ(1-x/A)k are presented. A Green's function for the edge-crack T-stress is developed. The differing developments made by Koiter (1956, “On the Flexural Rigidity of a Beam Weakened by Transverse Saw Cuts,” Proc. Royal Neth. Acad. of Sciences, B59, pp. 354–374, Wigglesworth (1957, “Stress Distribution in a Notched Plate,” Mathematika, 4, pp. 76–96), and Stallybrass (1970, “A Crack Perpendicular to an Elastic Half-Plane,” Int. J. Eng. Sci., 8, pp. 351–362) for the case of an edge-cracked half-plane are enhanced by deducing a quantitative relationship between the three different Wiener–Hopf type factorizations. An analytical universal T-stress expression for edge-cracks is derived. Finally, the case of a vanishing uncracked ligament in a half-plane is examined, and the associated Wiener–Hopf solution and analytical T-stress expression are again provided. Several limiting cases are examined.

Weight Functions and Stress Intensity Factors for Longitudinal Semi-Elliptical Cracks in Thick-Wall Cylinders

1995 ◽  
Vol 117 (4) ◽  
pp. 383-389 ◽  
Author(s):  
X. J. Zheng ◽  
G. Glinka
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Stress ◽  
Stress Fields ◽  
Thick Wall ◽  
Weight Functions ◽  
Intensity Factors ◽  
Crack Face ◽  
Reference Stress ◽  
Elliptical Cracks

Weight functions for the surface and the deepest point of an internal longitudinal semi-elliptical crack in a thick-wall cylinder (Ri/t = 1) were derived from a general weight function and two reference stress intensity factors. For several linear and nonlinear crack face stress, fields, the weight functions were validated against finite element data. Stress intensity factors were also calculated for the Lame´ through the thickness stress distribution induced by internal pressure. The weight functions appear to be particularly suitable for fatigue and fracture analysis of surface semi-elliptical cracks in complex stress fields. All stress intensity factor expressions given in the paper are valid for cylinders with the inner-radius-to-wall-thickness ratio, Ri/t = 1.

scholarly journals Photogrammetric Process to Monitor Stress Fields Inside Structural Systems

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4023
Author(s):  
Leonardo M. Honório ◽  
Milena F. Pinto ◽  
Maicon J. Hillesheim ◽  
Francisco C. de Araújo ◽  
Alexandre B. Santos ◽  
...  
Keyword(s):  
Boundary Element ◽  
Real Time ◽  
Stress Fields ◽  
Structural Systems ◽  
Unknown Boundary ◽  
Stress Distributions ◽  
Displacement Fields ◽  
Time Stress ◽  
Beam Surface ◽  
Measured Displacement

This research employs displacement fields photogrammetrically captured on the surface of a solid or structure to estimate real-time stress distributions it undergoes during a given loading period. The displacement fields are determined based on a series of images taken from the solid surface while it experiences deformation. Image displacements are used to estimate the deformations in the plane of the beam surface, and Poisson’s Method is subsequently applied to reconstruct these surfaces, at a given time, by extracting triangular meshes from the corresponding points clouds. With the aid of the measured displacement fields, the Boundary Element Method (BEM) is considered to evaluate stress values throughout the solid. Herein, the unknown boundary forces must be additionally calculated. As the photogrammetrically reconstructed deformed surfaces may be defined by several million points, the boundary displacement values of boundary-element models having a convenient number of nodes are determined based on an optimized displacement surface that best fits the real measured data. The results showed the effectiveness and potential application of the proposed methodology in several tasks to determine real-time stress distributions in structures.

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