Procedia Materials Science 3 ( 2014 ) 8 – 14

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2211-8128 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineeringdoi: 10.1016/j.mspro.2014.06.003

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20th European Conference on Fracture (ECF20)

Scaling Up – From Material Fracture Resistance to Fracture Representation in Welded Structures

Xudong Qian*, Yang Zhang and Ya Li Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576

Abstract

This paper presents a procedure to integrate the material fracture resistance, quantified by the experimentally measured J-R curve, in the fracture representation of welded tubular joints. This method incorporates a validated η-approach to estimate the elastic-plastic crack driving forces for fatigue cracks initiated at hot-spot locations of the welded tubular joints. The proposed scaling approach predicates on the fundamental assumption that the fracture resistance measured from the J-R curve, with a small and limited amount of crack extension, characterizes the material fracture resistance independent of the specimen geometry. The maximum crack extension allowed in the material testing standard marks the transferability limit of the material J-R curve to the welded joints. The extension of the fatigue crack in the welded joint leads to an increasing fracture resistance and a decreasing load resistance due to the increased crack area. The validation of this approach utilizes load-deformation responses from two scales of experimental specimens: 1) the large-scale welded tubular connection with a fatigue pre-crack; and 2) the large-scale frame test with predominantly fracture failure at the welded tubular joint. The load-deformation relationship based on the proposed scheme presents a close agreement with the experimentally recorded load-deformation behavior of the welded tubular joints. The proposed approach, when integrated into the push-over analyses of the large-scale tubular frames, presents an accurate estimation on the deformation level at which unstable fracture failure occurs and a conservative prediction of the corresponding failure load. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering.

* Corresponding author. Tel.: +65-65166827; fax: +65-67791635.

E-mail address: qianxudong@nus.edu.sg

© 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering

9 Xudong Qian et al. / Procedia Materials Science 3 ( 2014 ) 8 – 14

Keywords: fracture resistance; η-approach; J-R curve; welded connection.

1. Introduction

Unstable fracture failure in the welded connections creates critical threats to the safety of large-scale steel structures operating under either an onshore or an offshore environment. The quantitative measurement of the fracture resistance, by the material fracture toughness (KIc or JIc values) or the material J-R curve measured from standard fracture specimens under a plane-strain, small-scale yielding condition, provides a convenient and distinctive requirement at the material level. These fracture measurements, however, do not, lead directly to a transferable representation on the load-deformation relationships of the structural members or connections in global structural analyses. The scalability of the material J-R curve to the structural application faces a few bottlenecks, e.g., the severe local unloading at finite crack extensions, as well as the geometry and plasticity induced constraint loss in various structural connections.

Nomenclature

Alig effective ligament area ARF area reduction factor E’ equivalent Young’s modulus J energy release rate KI mode I stress-intensity factor Lw weld length along the brace-to-chord intersection P load Upl plastic strain energy a crack depth di diameter of the chord or brace (i = 0 for chord, i = 1 for brace) g gap in the K-joint li length of the chord or brace (i = 0 for chord, i = 1 for brace) ti thickness of the chord or brace (i = 0 for chord, i = 1 for brace) δ deformation ηpl plastic non-dimensional factor

Over the past few decades, researchers have attempted to address the fracture failure through a wide range of

approaches, including the continuous damage mechanics model (Chi et al. 2006, Kossakowski 2012, Qian et al. 2005), the semi-empirical approach (Ge et al. 2013, Wang et al. 2010), the empirical strain limits (Dexter and Lee 1999), etc. These approaches focus on determining the occurrence of the fracture failure at the structural component level. The continuous damage mechanics model involves numerous material parameters, which require extensive calibrations using detailed finite element models. The semi-empirical approaches often provide geometry-dependent methods in evaluating the ductile fracture failure in the structural components. The strain limit approach remains similar to the strain-based approach widely used in the assessment of pipelines. However, numerical implementation of the strain limit faces critical barriers such as the element size dependence and the selection of a proper fracture strain level.

This study presents an approach, which integrates the material J-R curve in the load-deformation responses of tubular joints. The proposed approach overcomes the transferability issue of the J-R curve by limiting the validity of the J-R curve data within a small amount of crack extensions determined using the 1.5 mm offset approach outlined in ASTM E-1820 (2011). The validation of the proposed approach makes use of both the experimental results on the structural connection (Qian et al. 2013) and those on the large-scale steel frames (Bolt 1994).

10 Xudong Qian et al. / Procedia Materials Science 3 ( 2014 ) 8 – 14

2. Proposed Approach

Figure 1 illustrates schematically the procedure to integrate the material J-R curve in the load-deformation representation of a welded tubular connection. The key challenge here remains the existence of an explicit relationship between the load-deformation (P-δ) curve and the crack driving force. Detailed numerical analyses with domain-integral calculations provide a fundamental and comprehensive approach to link the P-δ curve and the J-integral values. A previously proposed η-approach (Zhang and Qian 2013) allows simple and direction calculations of the crack driving force, J, from the area under the load-deformation curves,

2

'pl plI

lig

UKJE A

(1)

where KI refers to the linear-elastic stress-intensity factor, E’ stands for the equivalent elastic modulus, ηpl denotes the non-dimensional parameter and equals 1.0 for welded tubular joints (Zhang and Qian 2013), Upl is the area under the load versus the plastic deformation area, and Alig represents the effective area in the remaining ligament along the brace-to-chord intersection in resisting the plastic deformations.

Fig. 1. Integration of the material J-R curve in the P-δ representation of a welded tubular joint.

Initiation

Crack extension

IP

δ

Unstable fracture at Jmax

300

600

0

900

0 0.005 0.0150.010 0.020

a/t0 = 0.2 a/t0 = 0.5

2(kJ/m )J

0/ d

(a)

δ

20sin / yP t

0 0.02 0.030.01

Intacta/t0 = 0.2 a/t0 = 0.5 a/t0 = 0.7

20

15

10

5

0

S355 Steel

0/ d

(b)

11 Xudong Qian et al. / Procedia Materials Science 3 ( 2014 ) 8 – 14

Fig. 2. (a) P-δ curves for tubular K-joints with different crack depths; and (b) the domain-integral values versus the applied displacements for shallow to median cracks in tubular K-joints.

Figure 2a compares the P-δ relationships for a welded tubular K-joint fabricated using the S355 steels. The K-joint has a weld-toe surface crack at the crown point of the tension brace, as indicated in Fig. 2b. The presence of a surface crack does not introduce significant changes in the P-δ relationship for the K-joints. The domain-integrals calculated at the deepest crack-front locations in shallow to median surface cracks show similar evolutions with respect to the remotely applied displacement loading.

The schematic scheme proposed in Fig. 1 requires a pre-assumed surface at the hot-spot location of a welded tubular joint. The comparison in Fig. 2 implies that the crack driving force calculated (both from the domain-integral and from the area under load-deformation curves) shows negligible dependence on the assumed crack size. The initiation of the ductile tearing, corresponding to the JIc values shown in Fig. 1, for different surface crack sizes therefore translates to a similar load level in the P-δ curve. As the crack extension process initiates, the load resistance of the cracked joint, Pu,crack, deteriorates as the crack size increases, and follows,

,u crack u RFP P A (2)

where Pu denotes the ultimate strength of the intact joint while ARF refers to the area reduction factor, or,

0

1 crackRF

w

AA

L t (3)

The weld length derives from the closed-form solution by Qian (2013). The proposed formulation in Fig. 1 utilizes the maximum J value measured in the standard fracture specimens to

mark the final unstable fracture failure. The maximum J value corresponds to the intersection between a 1.5 mm offset line and the J-R curve, as illustrated in Fig. 1. The material testing standards (ASTM E-1820, 2011) has used this 1.5 mm exclusion line to denote the validity of the measured J versus Δa values. This Jmax value restricts the amount of crack extension in a realistic welded tubular joint to be within a very small amount and therefore retains the validity of J-value as a crack-driving parameter without severe local unloading.

3. Validation on Welded Tubular Joints

This study verifies the proposed approach using an experimental work on a high-strength steel tubular X-joint. Figure 3a shows the configuration of a large-scale X-joint fabricated from high-strength S690 steels. The yield strength measured from standard tension tests of the chord material equals 827 MPa, while the ultimate strength is 899 MPa. Table 1 lists the key dimensions of the joint specimen. The fabrication procedure of the specimen introduces a machined notch near the weld toe at the crown location of the chord member, as indicated in Fig. 3a. The machined notch has an initial depth of 10 mm and an initial length of 120 mm. The experimental procedure also measures the J-R curve from standard compact tension, C(T) specimens (Qian et al. 2013). The experimental procedure includes a constant-amplitude cyclic loading to generate a sharp front along the machined notch, prior to the monotonic loading test on the fatigue pre-cracked joint. The X-joint shown in Fig. 3a experiences the in-plane bending generated by an applied displacement loading on the top end of the chord member.

Figure 3b compares the experimentally measured load-deformation response with a final unstable fracture failure, the large-deformation finite element analysis based on the classical continuum mechanics, and the proposed formulation. The proposed approach predicts closely the load magnitude and deformation level corresponding to the unstable fracture failure in this high-strength steel connection.

Table 1. Dimension of the X-joint specimen.

d0 (mm) d1 (mm) t0 (mm) t1 (mm) l0 (mm) l1 (mm)

12 Xudong Qian et al. / Procedia Materials Science 3 ( 2014 ) 8 – 14

356 245 27.8 24 1500 951

Fig. 3. (a) Geometry of the X-joint specimen; and (b) comparison between the experimental results, finite element analysis and the proposed formulation.

4. Validation on Tubular Frames

Bolt (1994) has reported a series of large-scale tubular frames as a part of a joint industry program. This paper selects two of the tested K-frames as the benchmark cases to verify the proposed approach. Figure 4 shows the configuration of the two single-by K-frames, Frame VII and Frame VIII. Frame VII has a K-joint with the same chord and brace diameter, while Frame VIII has a K-joint with a larger chord diameter compared to the brace diameter.

Fig. 4. Configuration of the single-bay K-braced frames (a) Frame VII; and (b) Frame VIII.

Figure 5 compares the experimental results with the frame response predicted using the proposed approach implemented in a nonlinear structural analysis code, USFOS (Ultimate Strength for Framed Offshore Structures)

Crown

Chord

Brace

0t

1t

1d

0d

1l

0l

P (kN)P2000

1500

1000

500

00 10 403020 50 60

TestFEProposed

Initiation

Brittle failure

(mm)

(a) (b)

5944

168OD 7.1WT35

6OD

x12.

7WT

All members168OD 4.5WT

219OD 4.9WT

1524

5123

1524

0

4.5gt0

3.7gt

5944

1524

5123

1524

168OD 7.1WT

356O

Dx1

2.7W

T

All members168OD 4.5WT

(a) (b)

13 Xudong Qian et al. / Procedia Materials Science 3 ( 2014 ) 8 – 14

(2010). The comparison in Fig. 5 includes four different types of numerical analyses. A rigid joint assumption predicts a buckling failure of the compression member instead of the fracture failure in the joint, as observed in the frame test. The rigid joint assumption also fails to predict the deterioration in the frame stiffness caused by the initiation and extension of the cracks. The MSL joint formulation (USFOS 2010) derives from empirical results obtained from a joint industry project. The MSL crack formulation assumes a joint fracture failure at a very early deformation level and leads to severe under-estimations of the frame capacity for both frames. The proposed method predicts closely the frame response for both Frames VII and VIII measured during the experiments.

Fig. 4. Comparison of the numerical analysis and experimental frame response for: (a) Frame VII; and (b) Frame VIII.

5. Conclusions

This study presents an approach to integrate the J-R curve in the load-deformation formulation for welded tubular connections. This approach translates the material J-R curve measured from a standard fracture specimen under high-constraint small-scale yielding conditions to describe the fracture resistance in welded tubular joints and thence tubular frames. The close agreement between the experimental results (for both the welded tubular joints and tubular frames) and the numerical estimation based on the proposed approach confirms the validity of the proposed method.

References

American Society of Testing and Materials (ASTM) International (2011), ASTM E-1820-11 Standard test method for measurement of fracture toughness.

Bolt, H. (1994). Results from large scale ultimate strength tests of K-braced jacket frame structures. Offshore Technology Conference, Texas, Houston, USA.

Chi, W. M., Kanvinde, A. M. and Deierlein, C. G. (2006). Prediction of ductile fracture in steel connections using SMCS criterion. Journal of Structural Engineering – ASCE, 132, 171-181.

Dexter, E. M. and Lee, M. M. K. (1999). Static strength of axially loaded tubular K-joints. I: behavior. Journal of Structural Engineering – ASCE, 125, 194-201.

Ge, H., Kang, L. and Hayami, K. (2013). Recent research developments in ductile fracture of steel bridge structures. Journal of Earthque and Tsunami, 7, 1350021.

Kossakowski, P. G. (2012). Prediction of ductile fracture for S235JR steel using the stress modified critical strain and Gurson-Tvergaard-Needleman models. Journal of Materials in Civil Engineering, 24, 1492-1500.

Qian, X. (2013). Failure assessment diagrams for circular hollow section X- and K-joints. International Journal of Pressure Vessels and Piping, 104, 43-56.

Qian, X., Choo, Y. S., Liew, J. Y. R. and Wardenier, J. (2005). Simulation of ductile fracture of circular hollow section joints using the Gurson model. Journal of Structural Engineering – ASCE, 131, 768-780.

Qian, X., Li, Y. and Ou, Z. (2013). Ductile tearing assessment of high-strength steel X-joints under in-plane bending. Engineering Failure Analysis, 28, 176-191.

0 0.3 1.20.90.6 1.5

Global load (kN)

Global displacement m

600

500

400

300

0

200

100

TestRigidProposedMSLMSL (crack)

Frame VII

(a) (b)

0 0.2 0.80.60.4 1.0

Global load (kN)

Global displacement m

Frame VIII600

500

400

300

0

200

100

TestRigidProposedMSLMSL (crack)

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USFOS (2010). USFOS course manual, Marintek SINTEF group. Wang, Y. Q., Zhou, H., Shi, Y. J. and Chen H. (2010). Fracture behavior analyses of welded beam-to-column connections based on elastic and

inelastic fracture mechanics. International Journal of Steel Structures, 10, 253-265. Zhang, Y. and Qian, X. (2013). An eta-approach to evaluate the elastic-plastic energy release rate for weld-toe cracks in tubular K-joints.

Engineering Structures, 51, 88-98.