Studies of the Line-Spring Model for Nonlinear Crack Problems

1985 ◽  
Vol 107 (4) ◽  
pp. 412-420 ◽  
Author(s):  
V. Kumar ◽  
M. D. German
Keyword(s):  
Finite Element ◽  
Deformation Theory ◽  
Crack Tip ◽  
Surface Cracks ◽  
Spring Model ◽  
Crack Problems ◽  
Line Spring Model ◽  
Nonlinear Crack ◽  
Shell Finite Element ◽  
The Continuum

This paper presents an investigation of the line-spring model (LSM) of Rice and Levy as applied to nonlinear crack problems. A J2 deformation theory of plasticity formulation of a LSM for obtaining the fully plastic crack solutions is first described in the framework of a shell finite element method. Results are obtained for 2-D axial and circumferential cracks in cylinders and are compared against those developed by detailed finite element crack tip analyses. Discrepancies are found in the case of axially cracked cylinders under internal pressure. To overcome this problem a modified approach, termed the continuum-LSM, is presented, and its finite element implementation is described in some detail. It is shown that in contrast to the shell-LSM, the results obtained by the continuum-LSM for internally pressurized axially cracked cylinders are in close agreement with detailed finite element crack-tip calculations. Lastly, a discussion on the fully plastic analysis of surface cracks by the LSM is also given.

Analysis of Elastic Surface Cracks in Cylinders Using the Line-Spring Model and Shell Finite Element Method

1985 ◽  
Vol 107 (4) ◽  
pp. 403-411 ◽  
Author(s):  
V. Kumar ◽  
M. D. German ◽  
B. I. Schumacher
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Spring Model ◽  
Aspect Ratios ◽  
Surface Flaws ◽  
Line Spring Model ◽  
Shell Finite Element ◽  
Flaw Location ◽  
Element Method

This paper presents elastic analysis of axial and circumferential semielliptical surface flaws in cylinders using the line-spring model of Rice and Levy [1-3] and a shell finite element method. Results for the stress intensity factor are obtained at various points along the crack front, and are compared in some cases against published literature solutions. A broad range of values for the cylinder radius-to-wall thickness ratio, flaw depth and aspect ratio are considered including surface flaws with very large aspect ratios. The critical values of aspect ratio at which the surface flaws can be treated as 2-dimensional cracks are determined. Effect flaw location (internal or external) and flaw shape (semielliptical, circular or rectangular) are also investigated. Finally, the significance of these results in the elastic-plastic fracture analysis procedures is discussed.

Constraint of Semi-Elliptical Surface Cracks in T and L-Joints

2006 ◽  
Vol 326-328 ◽  
pp. 939-944
Author(s):  
Hyung Yil Lee ◽  
Yun Jae Kim
Keyword(s):  
Finite Element ◽  
Structural Characteristics ◽  
Pressure Vessels ◽  
Surface Cracks ◽  
Spring Model ◽  
Constraint Effect ◽  
T Stress ◽  
Line Spring Model ◽  
Parameter Approach ◽  
Two Parameter

Critical defects in pressure vessels and pipes are generally found in the form of a semielliptical surface crack, and the analysis of which is consequently an important issue in engineering fracture mechanics. Furthermore, in addition to the traditional single parameter K or J-integral, the second parameter like T-stress should be measured to quantify the constraint effect. In this work, the validity of the line-spring model is investigated by comparing line-spring J-T solutions to the reference 3D finite element J-T solutions. A full 3D-mesh generating program for semi-elliptical surface cracks is employed to provide such reference 3D solutions. Then some structural characteristics of the surface-cracked T and L-joints are studied by mixed mode line-spring finite element. Negative T-stresses observed in T and L-joints indicate the necessity of J-T two parameter approach for analyses of surface-cracked T and L-joints.

J-Integral Analysis of Surface Cracks in Round Bars under Bending Moments

2011 ◽  
Vol 52-54 ◽  
pp. 43-48 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Limit Load ◽  
Fe Model ◽  
Surface Cracks ◽  
Element Analysis ◽  
Reference Stress ◽  
Proposed Model

This paper presents a non-linear numerical investigation of surface cracks in round bars under bending moment by using ANSYS finite element analysis (FEA). Due to the symmetrical analysis, only quarter finite element (FE) model was constructed and special attention was given at the crack tip of the cracks. The surface cracks were characterized by the dimensionless crack aspect ratio, a/b = 0.6, 0.8, 1.0 and 1.2, while the dimensionless relative crack depth, a/D = 0.1, 0.2 and 0.3. The square-root singularity of stresses and strains was modeled by shifting the mid-point nodes to the quarter-point locations close to the crack tip. The proposed model was validated with the existing model before any further analysis. The elastic-plastic analysis under remotely applied bending moment was assumed to follow the Ramberg-Osgood relation with n = 5 and 10. J values were determined for all positions along the crack front and then, the limit load was predicted using the J values obtained from FEA through the reference stress method.

scholarly journals Stiffness Derivative Finite Element Technique to Determine Nodal Weight Functions With Singularity Elements

1983 ◽  
Author(s):  
George T. Sha
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Weight Functions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Crack Face ◽  
Crack Geometry ◽  
Crack Problems

The use of the stiffness derivative technique coupled with “quarter-point” singular crack-tip elements permits very efficient finite element determination of both stress intensity factors and nodal weight functions. Two-dimensional results are presented in this paper to demonstrate that accurate stress intensity factors and nodal weight functions can be obtained from relatively coarse mesh models by coupling the stiffness derivative technique with singular elements. The principle of linear superposition implies that the calculation of stress intensity factors and nodal weight functions with crack-face loading, σ(rs), is equivalent to loading the cracked body with remote loads, which produces σ(rs) on the prospective crack face in the absence of crack. The verification of this equivalency is made numerically, using the virtual crack extension technique. Load independent nodal weight functions for two-dimensional crack geometry is demonstrated on various remote and crack-face loading conditions. The efficient calculation of stress intensity factors with the use of the “uncracked” stress field and the crack-face nodal weight functions is also illustrated. In order to facilitate the utilization of the discretized crack-face nodal weight functions, an approach was developed for two-dimensional crack problems. Approximations of the crack-face nodal weight functions as a function of distance, (rs), from crack-tip has been successfully demonstrated by the following equation: h a , r s = A a √ r s + B a + C a √ r s + D a r s Coefficients A(a), B(a), C(a) and D(a), which are functions of crack length (a), can be obtained by least-squares fitting procedures. The crack-face nodal weight functions for a new crack geometry can be approximated using cubic spline interpolation of the coefficients A, B, C and D of varying crack lengths. This approach, demonstrated on the calculation of stress intensity factors for single edge crack geometry, resulted in a total loss of accuracy of less than 1%.

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