Calculation of Stress Intensity Factors and Crack Opening Displacements for Cracks Subjected to Complex Stress Fields

2003 ◽  
Vol 125 (3) ◽  
pp. 260-266 ◽  
Author(s):  
A. Kiciak ◽  
G. Glinka ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Fatigue Cracks ◽  
Crack Opening ◽  
Complex Stress ◽  
Pressure Vessels ◽  
Stress Fields ◽  
Function Technique ◽  
Weight Functions ◽  
Intensity Factors

Fatigue cracks in shot peened and case hardened notched machine components and high-pressure vessels are subjected to the stress fields induced by the external load and the residual stress resulting from the surface treatment or autofrettage. Both stress fields are usually nonuniform and available handbook stress intensity factor solutions are in most cases unavailable for such configurations, especially in the case of two-dimensional surface breaking cracks such as semi-elliptical and quarter-elliptical cracks at notches. The method presented in the paper makes it possible to calculate stress intensity factors for such cracks and complex stress fields by using the generalized weight function technique. It is also shown that the generalized weight functions make it possible to calculate the crack opening displacement field often used in the determination of the critical load or the critical crack size.

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.

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.

Interface Crack in a Three-Phase Composite Constitutive Model

1991 ◽  
Vol 58 (2) ◽  
pp. 428-434 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
Material Model ◽  
Complex Stress ◽  
Intensity Factors ◽  
Reinforced Composite ◽  
Three Phase ◽  
Shaped Crack

An arc-shaped crack in fiber-reinforced composite material is the subject of this paper. A three-phase composite cylinder is taken as the material model to take into account the effect of surrounding fibers. Using Muskhelishvili’s complex variable method, an exact elastic solution is derived based on the conventional crack opening assumption. The complex stress intensity factors for the interface crack, in the sense defined by Hutchinson, Mear, and Rice, are determined. Some numerical examples are given. It is shown that, as the volume concentration of the fiber is increased, the magnitude of the complex stress intensity factors varies considerably.

Mode I and Mode II Stress Intensity Factors Based on Crack Opening and Sliding Displacements

2011 ◽  
Vol 179-180 ◽  
pp. 1417-1422
Author(s):  
You Li Ma
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Stress Ratio ◽  
Fatigue Cracks ◽  
Crack Opening ◽  
Intensity Factors ◽  
Slant Angle ◽  
Measured Stress ◽  
Discontinuous Displacement ◽  
Made In

It is necessary to study crack opening and sliding discontinuous displacement behavior under mixed-mode conditions because parts or structures of a machine with a crack maybe subject to stress from various directions. In this study ,therefore, using the cracks with different slant angle, which are made in circle stress of modeⅠwith stress ratio of R=0, the opening and sliding discontinuous displacements are measured ,so that modeⅠand mode Ⅱ stress intensity factors (KⅠ)mes and (KⅡ)mes at the crack tip are calculated. As a result, the measured stress intensity factors value of (KⅠ)mes from the fatigue crack with the slant angle β=60 deg. is smaller than the theoretical one (KⅠ). But for mode Ⅱ,(KⅡ)mes is about the same with (KⅡ). On the other hand, for the fatigue cracks with smaller slant angle β=45 deg.,(KⅡ)mes declined because of the crack-surface contact while (KⅠ)mes reduced.

Weight functions for curved crack fronts using bem

1993 ◽  
Vol 28 (2) ◽  
pp. 67-78 ◽  
Author(s):  
R Bains ◽  
M H Aliabadi ◽  
D P Rooke
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Three Dimensional ◽  
Function Technique ◽  
Weight Functions ◽  
Intensity Factors ◽  
Penny Shaped Crack ◽  
Curved Crack ◽  
Shaped Crack

This paper presents an efficient numerical weight function technique, based on the boundary element method, for the determination of stress intensity factors of curved crack fronts in three-dimensional finite bodies. The weight functions are based on the notion of fundamental fields, which are defined from point loads acting at the crack front. A regularization procedure that incorporates the fundamental fields of the penny-shaped crack in an infinite elastic body is used to obtain weight functions for a penny-shaped edge crack in a cylindrical bar. Stress intensity factors for elliptical crack fronts can be generated by employing the properties of the fundamental fields at the load points on the crack front. Stress intensity factor variations along the crack-fronts are presented when these finite cracked geometries are subjected to various loads that produce mode I deformation of the crack faces. Wherever possible, solutions are compared with values published in the literature and are found to be in good agreement.

Determination of Stress Intensity Factors for Gradient Stress Fields

1977 ◽  
Vol 99 (3) ◽  
pp. 477-484 ◽  
Author(s):  
J. M. Bloom ◽  
W. A. Van Der Sluys
Keyword(s):  
Stress Intensity ◽  
Crack Length ◽  
Stress Intensity Factors ◽  
Maximum Stress ◽  
Nuclear Industry ◽  
Stress Fields ◽  
Polynomial Method ◽  
Intensity Factors ◽  
Asme Code ◽  
Linear Envelope

This paper evaluates eight different analytical procedures used in determining elastic stress intensity factors for gradient or nonlinear stress fields. From a fracture viewpoint, the main interest in this problem comes from the nuclear industry where the safety of the nuclear system is of concern. A fracture mechanics analysis is then required to demonstrate the vessel integrity under these postulated accident conditions. The geometry chosen for his study is that of a 10-in. thick flawed plate with nonuniform stress distribution through the thickness. Two loading conditions are evaluated, both nonlinear and both defined by polynomials. The assumed cracks are infinitely long surface defects. Eight methods are used to find the stress intensity factor: 1–maximum stress, 2–linear envelope, 3–linearization over the crack length from ASME Code, Section XI, 4–equivalent linear moment from ASME Code, Section III, Appendix G for thermal loadings, 5–integration method from WRC 175, Appendix 4 for thermal loadings, 6–8-node singularity (quarter-point) isoparametric element in conjunction with the displacement method, 7–polynomial method, and 8–semi-infinite edge crack linear distribution over crack. Comparisons are made between all eight procedures with the finding that the methods can be ranked in order of decreasing conservatism and ease of application as follows: 1–maximum stress, 2–linear envelope, 3–linearization over the crack length, 4–polynomial method, and 5–singularity element method. Good agreement is found between the last three of these methods. The remaining three methods produce nonconservative results.

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