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.

Online First Date: 16 March 2016Issue 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.

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/t_{0}

0.20, 0.50, 0.70

J_{Ic} (kJ/m^{2})

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-D_{LLD} relationships for X-joints with q = 90° (b = 0.6, g = 15 and t = 1.0) for: (a) different crack-depth ratios for s_{y} = 355 MPa; (b) different crack-depth ratios for s_{y} = 690 MPa and n = 20; (c) different yield strength for a/t_{0} = 0.3 and n = 5; and (d) different n values for a/t_{0} = 0.3 and s_{y} = 690 MPa

Fig.7 J-D_{LLD} relationships for X-joints with q = 90° for: (a) different b ratios for g = 15, t = 1.0 and a/t_{0} = 0.3; (b) different g ratios for b = 0.6, t = 1.0 and a/t_{0} = 0.3; and (c) different t ratios for b = 0.6, g = 15, and a/t_{0} = 0.3

Fig.8 J-D_{LLD} 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/t_{0} = 0.3; (c) different g ratios for b = 0.6, g’ = 6, t = 1.0 and a/t_{0} = 0.2; and (d) different g? ratios for b = 0.6, g = 20 and a/t_{0} = 0.2

Fig.9 Variations of J-value at constant axial joint deformations in X-joints with respect to: (a) a/t_{0} 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/t_{0} 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 d_{cr} against a/t_{0} ratio for X-joints with: (a) different J_{Ic} values for b = 0.6, g = 15, and t = 1.0; (b) different b ratios for J_{Ic} = 100 kJ/m^{2}, g = 15 and t = 1.0; and (c) different g ratios for J_{Ic} = 100 kJ/m^{2}, b = 0.60 and t = 1.0

Fig.12 Variations of the critical joint deformation d_{cr} at different material fracture toughness levels for K-joints with respect to: (a) a/t_{0} 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‾cr against a/t_{0} ratios for X-joints: (a) at different J_{Ic} levels for b = 0.6 and g = 15; (b) at different b ratios for J_{Ic} = 100 kJ/m^{2}, g = 15 and t = 1.0; and (c) different g ratios for J_{Ic} = 100 kJ/m^{2}, b = 0.6 and t = 1.0

Fig.14 Variation of the normalized critical deformation δ‾cr at different fracture toughness levels for K-joints with respect to: (a) a/t_{0} 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

d_{0} (mm)

b

g

t

g'

crack type

J_{Ic} (kJ/m^{2})

a/t_{0}

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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