Bending Modified J-Q Theory and Its Application to Fracture Constraint Analysis

2007 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Brian N. Leis
Keyword(s):  
Pipeline Steel ◽  
Crack Tip ◽  
Bending Stress ◽  
Single Edge ◽  
X80 Pipeline Steel ◽  
Q Theory ◽  
Constraint Analysis ◽  
Scale Yielding ◽  
Crack Tip Constraint ◽  
Fracture Constraint

The J-Q theory [1,2] can characterize the crack-tip fields and quantify fracture constraints for various geometric and loading configurations in elastic-plastic materials, but it fails to do so for bending-dominant geometries at large-scale yielding (LSY). This issue significantly restricts its applications to fracture constraint analysis. A modification of the J-Q theory is thus proposed in this paper as a three-term solution with an additional term to address the global bending stress to offset this restriction. The nonlinear global bending stress is linearly approximated in the region of interest at LSY. To verify the bending-modified J-Q solution, detailed elastic-plastic finite element analysis (FEA) is carried out under plane strain conditions for three conventional bending specimens, i.e., single edge notched bend (SENB), single edge notched tension (SENT) and compact tension (CT) specimens for X80 pipeline steel. Deformation considered varies from small-scale yielding (SSY) to LSY. The results show that the bending modified J-Q solution can well match FEA results of crack-tip stress fields for the bending specimens at all deformation levels from SSY to LSY, and the modified parameter Q is a load- and distance-independent constraint parameter at LSY. Thus, the modified parameter Q can be effectively used to quantify the crack-tip constraint for bending geometries. Its application to fracture constraint analysis is demonstrated by ranking crack-tip constraint levels for fracture specimens and by determining constraint corrected J-R curves for the X80 pipeline steel.

Constraint Quantification of Single Edge Notched Bend Specimens Under Large-Scale Yielding

2003 ◽  
Author(s):  
Yuh J. Chao ◽  
Xian-Kui Zhu ◽  
Yil Kim ◽  
M. J. Pechersky ◽  
M. J. Morgan ◽  
...  
Keyword(s):  
Large Scale ◽  
Crack Tip ◽  
Bending Moment ◽  
Additional Term ◽  
Small Scale ◽  
Bending Stress ◽  
Single Edge ◽  
Crack Tip Fields ◽  
Scale Yielding ◽  
Crack Tip Constraint

Because crack-tip fields of single edge notched bend (SENB) specimens are significantly affected by the global bending moment under the conditions of large-scale yielding (LSY), the classical crack tip asymptotic solutions fail to describe the crack-tip fields within the crack tip region prone to ductile fracture. As a result, existing theories do not quantify correctly the crack-tip constraint in such specimens under LSY conditions. To solve this problem, the J-A2 three-term solution is modified in this paper by introducing an additional term derived from the global bending moment in the SENB specimens. The J-integral represents the intensity of applied loading, A2 describes the crack-tip constraint level, and the additional term characterizes the effect of the global bending moment on the crack-tip fields of the SENB specimens. The global bending stress is derived from the strength theory of materials, and proportional to the applied bending moment and the inverse of the ligament size. Results show that the global bending stress near the crack tip of SENB specimens is very small compared to the J-A2 three-term solution under small-scale yielding (SSY), but becomes significant under the conditions of LSY or fully plastic deformation. The modified J-A2 solutions match well with the finite element results for the SENB specimens at all deformation levels ranging from SSY to LSY, and therefore can effectively model the effect of the global bending stress on the crack-tip fields. Consequently, the crack-tip constraint of such bending specimens can now be quantified correctly.

Experimental Determination of Constraint Dependent J-R Curves for X80 Pipeline Steel Using Normalization Method

2006 ◽  
Author(s):  
Xi. K. Zhu ◽  
B. N. Leis ◽  
G. Shen ◽  
W. R. Tyson
Keyword(s):  
Pipeline Steel ◽  
Crack Tip ◽  
Normalization Method ◽  
Resistance Curve ◽  
X80 Pipeline Steel ◽  
Basic Procedure ◽  
Unloading Compliance ◽  
Crack Tip Constraint ◽  
Cracked Specimens ◽  
Elastic Unloading

The normalization method is adopted for standard specimens and extended for nonstandard specimens in this paper to develop J-R curves for X80 pipeline steel directly from load versus load-line displacement records without the need of crack length measurement. Standard deep cracked specimens usually contain high crack-tip constraint, while nonstandard shallow cracked specimens involve low crack-tip constraint. To examine constraint effect on fracture toughness, six single-edge notched bend (SENB) specimens with different crack lengths for an X80 pipeline steel are tested according to ASTM standard E1820-05. The normalization method is then used to determine the constraint dependent J-R curves for these SENB specimens. To validate the experimental results obtained from the normalization method, the conventional elastic unloading compliance method is also used to measure crack extension, and determine the J-R curves for the X80 steel. The results show that the J-R curves determined using the normalization method agree well with those based on the elastic unloading compliance method for all SENB specimens, except for those experiencing severe splitting. Therefore, the normalization method can be used to determine J-R curves for the X80 pipeline steel for standard as well as nonstandard specimens. In determining the J-integral values, the resistance curve procedure, the basic procedure and the modified basic procedure specified in ASTM E1820-05 are evaluated. Comparisons of the resulting J-R curves indicate that the modified basic procedure can be equivalent to the resistance curve procedure.

Application of Constraint Corrected J-R Curves to Fracture Analysis of Pipelines

2005 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Brian N. Leis
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Pipeline Steel ◽  
Crack Depth ◽  
Crack Tip ◽  
Mathematical Expression ◽  
Width Ratio ◽  
Single Edge ◽  
X80 Pipeline Steel ◽  
Element Analysis

Fracture properties of API X80 pipeline steel have been developed using a set of single edge notched bend (SENB) and single edge notched tension (SENT) specimens with shallow and deep cracks to generate different crack-tip constraint levels. The test data show that the J-R curves for X80 pipeline steel are strongly constraint dependent. To facilitate transfer of the experimental J-R curves to those for actual cracked components, like flawed pipeline, constraint corrected J-R curves are developed. The two-parameter J-A2 formulation is adopted to quantify constraint effect on the crack-tip fields and the J-R curves. The constraint parameter A2 is extracted by matching the J-A2 solution with finite element results for a specific crack configuration. A constraint corrected J-R curve is then formulated as a function of the constraint parameter A2 and crack extension Δa. A general method and procedure to transfer the experimental J-R curves from laboratory to actual cracked components are proposed. Using the test data of J-R curves for the SENB specimens, a mathematical expression representing a family of the J-R curves is constructed for X80. It is shown that the predicted J-R curves developed in this paper match well with experimental data for both SENB and SENT specimens. To demonstrate its application in assessing flaw instability, a pipeline with an axial surface crack is considered. For a crack depth of 50% of the wall thickness, the predicted J-R curve is found to be higher than that for the SENB specimen with the same crack length to width ratio. From this predicted J-R curve and crack driving force obtained by finite element analysis, the failure pressures of the pipeline at the crack initiation and instability are determined and discussed.

Application of Constraint Corrected J-R Curves to Fracture Analysis of Pipelines

2005 ◽  
Vol 128 (4) ◽  
pp. 581-589 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Brian N. Leis
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Pipeline Steel ◽  
Crack Depth ◽  
Crack Tip ◽  
Mathematical Expression ◽  
Width Ratio ◽  
Single Edge ◽  
X80 Pipeline Steel ◽  
Element Analysis

Fracture properties of an API X80 pipeline steel have been developed using a set of single edge notched bend (SENB) and single edge notched tension (SENT) specimens with shallow and deep cracks to generate different crack-tip constraint levels. The test data show that the J-R curves for the X80 pipeline steel are strongly constraint dependent. To facilitate transfer of the experimental J-R curves to those for actual cracked components, like flawed pipeline, constraint corrected J-R curves are developed. The two-parameter J-A2 formulation is adopted to quantify constraint effect on the crack-tip fields and the J-R curves. The constraint parameter A2 is extracted by matching the J-A2 solution with finite element results for a specific crack configuration. A constraint corrected J-R curve is then formulated as a function of the constraint parameter A2 and crack extension Δa. A general method and procedure to transfer the experimentalJ-R curves from laboratory to actual cracked components are proposed. Using the test data of J-R curves for the SENB specimens, a mathematical expression representing a family of the J-R curves is constructed for the X80. It is shown that the predicted J-R curves developed in this paper agree well with experimental data for both SENB and SENT specimens. To demonstrate its application in assessing flaw instability, a pipeline with an axial surface crack is considered. For a crack depth of 50% of the wall thickness, the predicted J-R curve is found to be higher than that for the SENB specimen with the same crack length to width ratio. From this predicted J-R curve and crack driving force obtained by finite element analysis, the failure pressures of the pipeline at the crack initiation and instability are determined and discussed.

Crack-tip constraint analysis of SENB specimen under creep condition

2015 ◽  
Vol 29 (2) ◽  
pp. 501-506 ◽  
Author(s):  
G. C. Jiao ◽  
W. Z. Wang ◽  
S. J. Tan ◽  
C. Yu ◽  
Y. Z. Liu
Keyword(s):  
Creep Condition ◽  
Crack Tip ◽  
Constraint Analysis ◽  
Crack Tip Constraint ◽  
Senb Specimen

Crack-Tip Stress Field of Fully Circumferential Cracked Pipe Under Combined Tension and Thermal Loads

2014 ◽  
Author(s):  
Jin-Ho Je ◽  
Dong-Jun Kim ◽  
Keun-Hyung Bae ◽  
Yun-Jae Kim
Keyword(s):  
Stress Field ◽  
Degrees Of Freedom ◽  
Crack Tip ◽  
Constraint Effect ◽  
Combined Load ◽  
Crack Geometry ◽  
Combined Loads ◽  
Q Theory ◽  
Crack Tip Constraint ◽  
Crack Tip Stress

In the presence of excessive plasticity, the fracture toughness depends on the size and geometry. For material under fully yielded conditions, the stresses near the crack tip are not unique, but depend on geometry. So Single-parameter; J-approach is limited to high-constraint crack geometry. J-Q theory has been proposed in order to decide crack geometry constraint. This approach assumes that the crack-tip fields have two degrees of freedom. In this paper, based on J-Q theory, crack-tip stress field of fully circumferential cracked pipe under combined load is investigated using FE analysis. Combined loads are tensile axial force and thermal gradient of radial direction. Q-stresses of a crack geometry and it’s loading state are used to determine constraint effect, and give a characteristic order for crack-tip constraint.

Numerical Analyses of Ductile Fracture Behavior in 2D Plane Strain and Axisymmetric Models Using the Complete Gurson Model

2009 ◽  
Author(s):  
Jie Xu ◽  
Zhiliang Zhang ◽  
Erling O̸stby ◽  
Ba˚rd Nyhus ◽  
Dongbai Sun
Keyword(s):  
Crack Growth ◽  
Fracture Behavior ◽  
Large Scale ◽  
Crack Tip ◽  
Ductile Crack ◽  
Geometry Dependence ◽  
Ductile Crack Growth ◽  
Scale Yielding ◽  
Resistance Curves ◽  
Crack Tip Constraint

Ductile crack growth plays an important role in the analyses of fracture behavior of structures. A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding conditions. This geometry dependence is associated with different levels of crack tip constraint. However, an independent relationship between the fracture resistance and crack tip constraint has also been observed in experimental studies for selected specimen geometries. To verify these results, crack growth resistance curves for plane strain, mode I crack growth under large scale yielding have been computed using the complete Gurson model. Single edge notched bending (SENB) and tension (SENT) specimens with three different crack geometries have been selected for the numerical analyses. Specimen size effect on ductile crack growth behavior has also been studied. In addition, the SENT specimen appears as an alternative to conventional fracture specimens to characterize fracture toughness of circumferentially cracked pipes due to its similar geometry constraint ahead of the crack tip with that of cracks in pipes. 2D axisymmetric models have been carried out to investigate the effect of biaxial loading (axial tension combined with internal pressure) on the resistance curves for pipes with long internal circumferential cracks under large scale yielding conditions.

An Experimental Study on J(CTOD)-R Curves of Single Edge Tension Specimens for X80 Steel

2012 ◽  
Author(s):  
Enyang Wang ◽  
Wenxing Zhou ◽  
Guowu Shen ◽  
Daming Duan
Keyword(s):  
Crack Length ◽  
Crack Tip ◽  
Initial Crack ◽  
Single Edge ◽  
X80 Steel ◽  
Toughness Testing ◽  
Unloading Compliance ◽  
Crack Tip Constraint ◽  
The Impact ◽  
Edge Tension

Fracture toughness testing of SE(T) and SE(B) specimens is carried out to experimentally develop J(CTOD)-R curves for the X80 steel based on the unloading compliance method. Six clamped (two shallow-cracked side-grooved, two deep-cracked side-grooved, and two deep-cracked plain-sided) SE(T) and two shallow-cracked side-grooved SE(B) specimens are tested. The impact of crack length on the J(CTOD)-R curves of the SE(T) specimens is investigated. The J(CTOD)-R curves of the shallow-cracked SE(T) specimens are significantly higher than those of the deep-cracked SE(T) specimens once the crack extension exceeds 0.5 mm. A comparison of the J(CTOD)-R curves associated with the SE(B) and SE(T) specimens suggests that the crack tip constraint for the SE(T) specimens is lower than that of the SE(B) specimens with the same nominal initial crack length, and that shallow-cracked SE(T) specimens have less constraint at the crack tip than deep-cracked SE(T) specimens.

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