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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2016, Vol. 10 Issue (3) : 345-362     https://doi.org/10.1007/s11709-016-0333-2
RESEARCH ARTICLE
A toughness based deformation limit for X- and K-joints under brace axial tension
Bo GU,Xudong QIAN(),Aziz AHMED
Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576, Singapore
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Abstract

This study reports a deformation limit for the initiation of ductile fracture failure in fatigue-cracked circular hollow section (CHS) X- and K-joints subjected to brace axial tension. The proposed approach sets the deformation limit as the numerically computed crack driving force in a fatigue crack at the hot-spot location in the tubular joint reaches the material fracture toughness measured from standard fracture specimens. The calibration of the numerical procedure predicates on reported numerical computations on the crack driving force and previously published verification study against large-scale CHS X-joints with fatigue generated surface cracks. The development of the deformation limit includes a normalization procedure, which covers a wide range of the geometric parameters and material toughness levels. The lower-bound deformation limits thus developed follow a linear relationship with respect to the crack-depth ratio for both X- and K-joints. Comparison of the predicated deformation limit against experimental on cracked tubular X- and K-joints demonstrates the conservative nature of the proposed deformation limit. The proposed deformation limit, when extrapolated to a zero crack depth, provides an estimate on the deformation limits for intact X- and K-joints under brace axial loads.

Keywords circular hollow section (CHS)      tubular joint      fracture failure      deformation limit      J-integral     
Corresponding Author(s): Xudong QIAN   
Online First Date: 16 March 2016    Issue Date: 25 October 2016
 Cite this article:   
Bo GU,Xudong QIAN,Aziz AHMED. A toughness based deformation limit for X- and K-joints under brace axial tension[J]. Front. Struct. Civ. Eng., 2016, 10(3): 345-362.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-016-0333-2
http://journal.hep.com.cn/fsce/EN/Y2016/V10/I3/345
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Bo GU
Xudong QIAN
Aziz AHMED
parameter values
a 16
b 0.30, 0.60, 0.90
g 10, 15, 20, 25
t 1.00, 0.75, 0.50
a/c 0.20
a/t0 0.07, 0.30, 0.50
sy (MPa) 350, 460, 690
n 5, 10, 20
JIc (kJ/m2) 100, 150, 200, 250, 300
Tab.1   Geometric and material parameters considered for CHS X-joints
parameter values
a 16
b 0.30, 0.60, 0.90, 1.0
g 15, 20, 25
g’ 2,6,10
a/c 0.25
a/t0 0.20, 0.50, 0.70
JIc (kJ/m2) 100, 150, 200, 250, 300
Tab.2  Geometric and material parameters considered for CHS K-joints
Fig.1  Geometric configuration of: (a) a CHS X-joint with q = 90°; (b) a CHS K-joint with q = 60°; and (c) a semi-elliptical surface crack
Fig.2  Uniaxial true stress versus the true strain relationship for S355 steel materials
Fig.3  A typical finite element (FE) model for CHS X-joint with q = 90° with a surface crack near the weld toe in the chord with mesh-tieing between the local crack front mesh and the global model
Fig.4  A typical finite element (FE) model CHS K-joint with q = 60°; with a surface crack near the tension brace weld toe, (a) global model; (b) mesh-tieing between the local crack front mesh and the global model; (c) crack-tip mesh (d) loading and boundary conditions
Fig.5  Comparison of the elastic-plastic crack driving force computed from this study and that from a previous work [45]
Fig.6   J-DLLD relationships for X-joints with q = 90° (b = 0.6, g = 15 and t = 1.0) for: (a) different crack-depth ratios for sy = 355 MPa; (b) different crack-depth ratios for sy = 690 MPa and n = 20; (c) different yield strength for a/t0 = 0.3 and n = 5; and (d) different n values for a/t0 = 0.3 and sy = 690 MPa
Fig.7   J-DLLD relationships for X-joints with q = 90° for: (a) different b ratios for g = 15, t = 1.0 and a/t0 = 0.3; (b) different g ratios for b = 0.6, t = 1.0 and a/t0 = 0.3; and (c) different t ratios for b = 0.6, g = 15, and a/t0 = 0.3
Fig.8   J-DLLD relationships for K-joints with q = 60° for: (a) different crack-depth ratios for b = 0.3, g = 15, g’ = 6 and t = 1.0; (b) different b ratios for g = 20, g’ = 6, t = 1.0 and a/t0 = 0.3; (c) different g ratios for b = 0.6, g’ = 6, t = 1.0 and a/t0 = 0.2; and (d) different g? ratios for b = 0.6, g = 20 and a/t0 = 0.2
Fig.9  Variations of J-value at constant axial joint deformations in X-joints with respect to: (a) a/t0 ratios for b = 0.6, g = 15 and t = 1.0; (b) b ratios for g = 15 and t = 1.0; and (c) 1/g ratios for b = 0.6 and t = 1.0
Fig.10  Variations of J-value at constant axial joint deformations in K-joints with respect to: a/t0 ratios for b = 0.3, g = 15 and g' = 6; (b) b ratios for g = 15 and g' = 6; (c) 1/g ratios for b = 0.6 and g' = 6; and (d) g' ratio for b = 0.6 and g = 15
Fig.11   Variation of the critical joint deformation dcr against a/t0 ratio for X-joints with: (a) different JIc values for b = 0.6, g = 15, and t = 1.0; (b) different b ratios for JIc = 100 kJ/m2, g = 15 and t = 1.0; and (c) different g ratios for JIc = 100 kJ/m2, b = 0.60 and t = 1.0
Fig.12  Variations of the critical joint deformation dcr at different material fracture toughness levels for K-joints with respect to: (a) a/t0 ratio for b = 0.3, g = 15 and g' = 6; (b) b ratios g = 20 and g' = 6; and (c) 1/g ratios for b = 0.60 and g’ = 6; and (d) g' ratios for b = 0.3, g = 20 and g' = 6
Fig.13  Variation of the normalized critical deformation δ c r against a/t0 ratios for X-joints: (a) at different JIc levels for b = 0.6 and g = 15; (b) at different b ratios for JIc = 100 kJ/m2, g = 15 and t = 1.0; and (c) different g ratios for JIc = 100 kJ/m2, b = 0.6 and t = 1.0
Fig.14  Variation of the normalized critical deformation δ c r at different fracture toughness levels for K-joints with respect to: (a) a/t0 ratios for b = 0.3, g = 15 and g' = 6; (b) b ratios for g = 20 and g’ = 6; (c) 1/g ratios for b = 0.6 and g' = 6; and (d) g' ratios for b = 0.3 and g = 20
Fig.15  Comparison of the proposed lower-bound deformation limits against the numerical data for: (a) X-joints with different b ratios; (b) X-joints with different g ratios; (c) K-joints with different b ratios; and K-joints with different g’ ratios
joint loading d0 (mm) b g t g' crack type JIc (kJ/m2) a/t0 crack area (%)
X1 [48] axial 572 0.48 15.1 0.5 N.A. through thickness 178 1 15
X1 [48] axial 572 0.48 15.1 0.5 N.A. through thickness 178 1 30
X2 [48] axial 572 0.48 15.1 0.5 N.A. surface Crack 178 0.75 15
X3 [48] axial 572 0.95 14.3 1 N.A. through thickness 315 1 15
X3 [48] axial 572 0.95 14.3 1 N.A. through thickness 315 1 30
K [49,50] balanced axial 114 0.53 15.8 0.89 1.9 through thickness N.A. 1 27
K [49,50] balanced axial 114 0.53 15.8 0.89 1.9 through thickness N.A. 1 36
K [49,50] balanced axial 114 0.53 15.8 0.89 1.9 through thickness N.A. 1 36
Tab.3   Selected experimental data for verification of the proposed deformation limit
Fig.16  Comparison of proposed lower-bound deformation limits with the reported experimental data on: (a) X-joints; and (b) K-joints
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