Stress intensity factors of the rib-to-deck welded joint at the crossbeam conjunction in OSDs

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Delft University of Technology

Stress intensity factors of the rib-to-deck welded joint at the crossbeam conjunction in

OSDs

Wu, Weijian; Kolstein, Henk; Veljkovic, Milan DOI

10.1016/j.prostr.2018.12.214 Publication date

2018

Document Version Final published version Published in

Procedia Structural Integrity

Citation (APA)

Wu, W., Kolstein, H., & Veljkovic, M. (2018). Stress intensity factors of the rib-to-deck welded joint at the crossbeam conjunction in OSDs. Procedia Structural Integrity, 13, 2017-2023.

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ScienceDirect

Available online at Available online at www.sciencedirect.comwww.sciencedirect.com

ScienceDirect

Structural Integrity Procedia 00 (2016) 000–000

www.elsevier.com/locate/procedia

Peer-review under responsibility of the Scientific Committee of PCF 2016.

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal

Thermo-mechanical modeling of a high pressure turbine blade of an

airplane gas turbine engine

P. Brandão

a

_{, V. Infante}

b

_{, A.M. Deus}

c

_*

a_{Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,}

Portugal

b_{IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,}

Portugal

c_{CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,}

Portugal

Abstract

During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +351 218419991.

E-mail address: amd@tecnico.ulisboa.pt

Procedia Structural Integrity 13 (2018) 2017–2023

2452-3216  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.214

10.1016/j.prostr.2018.12.214 2452-3216

ECF22 - Loading and Environmental effects on Structural Integrity

Stress intensity factors of the rib-to-deck welded joint at the

crossbeam conjunction in OSDs

Weijian Wu

a,∗

_{, Henk Kolstein}

a

_{, Milan Veljkovic}

a

a_{Faculty of Geoscience and Engineering, Delft University of Technology, Delft 2628 CN, Netherlands}

Abstract

The orthotropic steel decks (OSDs) are one of the most widely used bridge components, especially in moveable and long span bridges. Numerous cracks have been detected in this type of deck in existing bridges, mainly in the welded joints. The fatigue performance of the bridge deck dominates its design. Among them, the crack at the rib-to-deck joint is one of the most representative types. At the crossbeam conjunction, high stress concentration makes the joint more sensitive to fatigue loading. In this paper, finite element models are built using software program Abaqus integrated with FRANC3D. The calculated stress at uncracked stage is validated with measured data obtained from laboratory tests. Afterwards, cracks are inserted at the weld root and the stress intensity factor ranges in mode I (∆KI) are calculated. Parametric analysis with various cracks is carried out. General correction factors are

calculated from the finite element calcualtion with the power fit values. c

2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers.

Keywords: OSDs, rib-to-deck joint, weld root crack, stress intensity factors;

1. Introduction

Orthotropic steel deck is a common type of deck plates used in the steel bridges. The component uses welding technique to connect steel plates and provides high load capacity in longitudinal direction with low self-weight (7) and (5). During the 70 years of application, the deck plates have been sucessfully used in the long span bridges and movable bridges. However, the all welded component is prone to fatigue loading. Under the heavy truck loading, cracks appear at various positions of the decks, mainly in the welded joints. Among them, the rib-to-deck crack at the crossbeam conjucntion is one the most representative types, see Fig. 1. Cracks 1 and 2 (C1 and 2) initiates from the weld root of the stiffeners and grow in the deck plate. Compared with the C2, the stress concentration at C1 is higher due to the existance of crossbeam. Because of the high inspection and repair cost for this kind of crack, it is important to avoid or control the crack within its service life.

In recent years, the newly designed OSDs trend to use thicker deck plates and improved welding techniques which affect its fatigue performance. A research programme is therefore started in the Netherlands to study the fatigue

∗_{Corresponding author. Tel.: +31-152784752.} E-mail address: W.Wu-1@tudelft.nl

2210-7843 c 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers.

ECF22 - Loading and Environmental effects on Structural Integrity

Stress intensity factors of the rib-to-deck welded joint at the

crossbeam conjunction in OSDs

Weijian Wu

a,∗

_{, Henk Kolstein}

a

_{, Milan Veljkovic}

a

a_{Faculty of Geoscience and Engineering, Delft University of Technology, Delft 2628 CN, Netherlands}

Abstract

The orthotropic steel decks (OSDs) are one of the most widely used bridge components, especially in moveable and long span bridges. Numerous cracks have been detected in this type of deck in existing bridges, mainly in the welded joints. The fatigue performance of the bridge deck dominates its design. Among them, the crack at the rib-to-deck joint is one of the most representative types. At the crossbeam conjunction, high stress concentration makes the joint more sensitive to fatigue loading. In this paper, finite element models are built using software program Abaqus integrated with FRANC3D. The calculated stress at uncracked stage is validated with measured data obtained from laboratory tests. Afterwards, cracks are inserted at the weld root and the stress intensity factor ranges in mode I (∆KI) are calculated. Parametric analysis with various cracks is carried out. General correction factors are

calculated from the finite element calcualtion with the power fit values. c

2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers.

Keywords: OSDs, rib-to-deck joint, weld root crack, stress intensity factors;

1. Introduction

Orthotropic steel deck is a common type of deck plates used in the steel bridges. The component uses welding technique to connect steel plates and provides high load capacity in longitudinal direction with low self-weight (7) and (5). During the 70 years of application, the deck plates have been sucessfully used in the long span bridges and movable bridges. However, the all welded component is prone to fatigue loading. Under the heavy truck loading, cracks appear at various positions of the decks, mainly in the welded joints. Among them, the rib-to-deck crack at the crossbeam conjucntion is one the most representative types, see Fig. 1. Cracks 1 and 2 (C1 and 2) initiates from the weld root of the stiffeners and grow in the deck plate. Compared with the C2, the stress concentration at C1 is higher due to the existance of crossbeam. Because of the high inspection and repair cost for this kind of crack, it is important to avoid or control the crack within its service life.

In recent years, the newly designed OSDs trend to use thicker deck plates and improved welding techniques which affect its fatigue performance. A research programme is therefore started in the Netherlands to study the fatigue

∗_{Corresponding author. Tel.: +31-152784752.} E-mail address: W.Wu-1@tudelft.nl

2210-7843 c 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers.

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2018 Weijian Wu et al. / Procedia Structural Integrity 13 (2018) 2017–2023 2 W.Wu etc. / Structural Integrity Procedia 00 (2018) 000–000

behaviour of the new OSDs. Full-scale fatigue tesing and numerical modelling is included in the programme. The testing part of the rib-to-deck joint at crossbeam conjunction is reported in the reference (11). The relationship of total fatigue life and coresponding stress ranges is provided from the testing. It is known that the marcocrack propagation period dominates the fatigue behaviour of welded joints. By using fracture mechanics approach, the whole process in the crack propagation period can be studided. In recent years, the method has been sucessfully used for the fatigue life assessment of steel structures (1) and (8).

In this paper, an advanced finite element model is built containing the cracks using software Abaqus 6.14-1 (10) integrated with FRANC3D 7.1 (4). The stress intensity factors are calcualted within the frame of linear elastic fracture mechanics based on M-integrity (4). Through parametric analysis, the best fit curves of general correction factors are found. The data can be used for the hand calcualtion following the weight function procedure (2).

Crossbeam

Closed stiffeners

Top deck

Bottom flange

C1

C2

C1: at crossbeam

C2: between crossbeams

Crossbeam

Fig. 1. Sketch of rib-to-deck joint at crossbeam conjunciton (3), (7)

2. Finite element models

2.1. Loading and boundary condition

An advanced finite element model is built following the testing specimen and loading set-ups in reference (11). In Fig. 2, the load range of 144 kN with ratio of 0.1 is applied from the top of the steel plate to simulate the loading situation of Stiffener 7 in reference (11). It is found that the stress situation of the rib-to-deck joint is mostly affected by the closest 2 stiffeners (5). In the model, the bottom flange is fixed on the ground. Sysmetric conditions are applied at the sides.

2.2. Geometric information and interaction properties

In Fig. 2, the 3 trapezoid stiffeners support the 20 mm thick top deck (represented by t in the following sections). The crossbeam is 968 mm high with “Haibach” cutout at the bottom of stiffeners. Sub models A and B are created

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Steel plate

Rubber plate

Specimen

20

6 Sub model A

Sub model B

16

Fig. 2. Sketch of the FE model (unit:mm)

with “tie” constraints at the intersect faces. In this way, the area of interest can be refine meshed while keeping the remaining area coarse meshed. At the center of top deck, the contact behaviour of the 180 mm×320 mm rubber plate and steel plate is considered with “hard” contact in normal direction and “penatly” function in tangential direction with friction coefficient 0.3 (10). Above it, the “tie” constraint is applied at the intersection of steel and rubber plates.

2.3. Crack insert

In the model different sizes and shapes of the crack is inserted in the weld root of the joint, see Figs. 3 and 4. As observed from the previous testing, it is found that the angle between the crack and the vertical line is around 30◦ which is used when inserting the cracks in the model. In general, the cracks are described as semi-ellipse shape with half depth a (with d in the deck thickness direction) and half length c. ∆KI at 3 positions are considered (P1 at the edge, P2 at the deepest point, and P3 at the middle point of edge and deepest point) with various sizes and shapes of the crack.

Fig. 3. Crack and meshing of the FE model

2.4. Meshing and material properties

In the model, solid element C3D8H is used for the global area and sub model A (10). In sub model B, 3 cirlce element is created around the crack tip with the inner circle with element C3D15H and the outer ones C3D20H (4).

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30O

2c

d

P1

P2

P3

Fig. 4. Shape of the crack in FEM

The remaining element in sub model B is C3D10H. Young’s modulus of steel, Es, is 210 GPa with νs0.3. For the

hyperealasitc rubber material, the C10and C20are 0.4613 MPa and 0.0175 MPa, repectively. D1and D2are 2.5 × 10−5 MPa−1_{and 2.0 × 10}−5_MPa−1_(12).

3. Validation of the uncracked model

As mentioned before, the model is built following the testing specimen in the reference (11). One of the tested joint, the north side of Stiffener 7, is selected for the analysis in this paper. A comparison of the measured stress ranges (mutiply the measured strain range with Es) and FE calculation is shown in Fig. 5. The measured stress ranges

are compared with the calculated ones which shows good agreement in both the top and bottom of the deck plate.

0 50 100 150 200 250 300 0 4 8 12 16 20 Stress range [MPa] Distance [mm] measured values FE calculation 0 50 100 150 200 250 300 0 10 20 30 40 50 Stress range [MPa] Distance [mm] measured values FE calculation 0 20 40 60 80 100 -100 -50 0 50 100 Stress range [MPa] Distance [mm] measured values FE calculation

(a) top of the deck, longitudinal direction

0 50 100 150 200 250 300 0 4 8 12 16 20 Stress range [MPa] Distance [mm] measured values FE calculation 0 50 100 150 200 250 300 0 10 20 30 40 50 Stress range [MPa] Distance [mm] measured values FE calculation 0 20 40 60 80 100 -100 -50 0 50 100 Stress range [MPa] Distance [mm] measured values FE calculation

(b) top of the deck, transverse direction 0 50 100 150 200 250 300 0 4 8 12 16 20 Stress range [MPa] Distance [mm] measured values FE calculation 0 50 100 150 200 250 300 0 10 20 30 40 50 Stress range [MPa] Distance [mm] measured values FE calculation 0 20 40 60 80 100 -100 -50 0 50 100 Stress range [MPa] Distance [mm] measured values FE calculation

(c) bottom of the deck, transvers direction

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4. Results

4.1. SIFs at the crack tips

In Fig. 6, 4 different sizes of the crack with shape c/a = 3 is shown. When the crack is small (a = 1 mm) the largest ∆KI locates at relative distance range 0.1-0.9 with value around 750 N/mm3/2. With the growth of crack, the values are dropping which ends with 480 N/mm3/2_{at a = 15 mm. In general, ∆K}_I _{distributes evenly in the middle} area (relative distance 0.3-0.7) along the crack length and decrease with the crack growth. Detailed change of ∆KIat P2 can be found in Fig. 7. This finding is in a line with the ∆KIin Fig.6.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 relative distance 400 500 600 700 800 900 1000 1100 K I [N/mm 3/2 ] a10c30 a15c45 a1c3 a5c15

Fig. 6. ∆KIalong crack tip in the case c/a=3

4.2. Effect of crack shapes

Three different cases, c/a= 1, 3, and 5, are considered for the effect of the crack shapes on the ∆KIat P2. In Fig. 7, ∆K_I decreases almost linearly with the d/t in case c/a = 1. When the crack is more shallow, with c/a= 3 and 5, the change of the ∆KIis much more gentle and almost stable when d/t < 0.4. Afterwards a linear change is observered. This indicates the constant propagation speed at the early stage of shallow cracks. In the later stage, the speed drops due to the change of structural integrity at the cracked area which is in a line of the observed strain range redistribution reported in reference (11).

4.3. General correction factors

In the crack propagation analysis using weight function approach, ∆KIis calculated by equation (1). The accurate general correction function Y(d

t) is important for the propagation analysis. For this joint, limited information is

pro-vided to caculate the weight founction and there is no formula for the newly designed deck with 20 mm thick deck plate. In Fig. 8, Y(d

t) at P2 of different sizes (d/t) and shapes (a/c) of the crack is shown with the best fit equations.

Hot spot stress ranges ∆σHS S is 226 MPa, calculated by the surface extrapolation using data in Fig. 5c. The crack

depth at its component in the deck thicness direction d is used in calculation Y(d

t). The power function relationship

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quite close which indicate that the propagation speeds are close at the deepest position for these cases. It should be noticed that the sigularity exists with d/t is close to 0. More calculation needs to be carried out when the crack is small. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 d/t 0 200 400 600 800 1000 1200 1400 1600 K I [N/mm 3/2 ] c/a=1 c/a=3 c/a=5

Fig. 7. ∆KIat P2 with c/a=1, 3, and 5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 d/t 0 0.5 1 1.5 2 2.5 Y( d/t ) c/a=1 Y=0.8748 (d/t)-0.3147-0.9064, R2=0.999 c/a=3 Y=1.206 (d/t)-0.2914-1.031, R2=0.997 c/a=5 Y=1.332 (d/t)-0.2776-1.072, R2=0.997

Fig. 8. General correction function at P2 with c/a=1, 3, and 5

∆K = Y(d

t) · ∆σHS S ·

√

(8)

5. Conclusions

Cracks initiates at the weld root of the rib-to-deck joint at crossbeam conjunction in OSDs is numerically studied in this paper. Advanced finite element models with different shapes of cracks are built to calculate the ∆KI and Y(dt)

at different stages. The following conclusions can be drawn:

• In case c/a = 3, ∆KIdistributes evenly in the middle area (relative distance 0.3-0.7) along the crack length and decrease with the crack growth.

• In case c/a = 1, a linear decrease trend of ∆KIis found at the deepest point with crack growth. For more shallow cracks, c/a = 3 and 5, ∆KIis stable when d/t < 0.4.

• The general correction function Y(d

t) for the deepest points shows a power relationship with the relative crack

depth d/t. Close value is found in the cases c/a = 3 and 5. Acknowledgements

The first author would like to thank the financial support from China Scholarship Council (CSC) for the PhD study. References

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[4] Fracture Analysis Consultants.,2017. FRANC3D V7.1 ABAQUS Tutorial. Fracture Analysis Consultants.

[5] de Jong,F.B.P.,2007. Renovation techniques for fatigue cracked orthotropic steel bridge decks. PhD thesis, TU Delft, Delft University of Technol-ogy.

[6] Hobbacher,A.,2016. Recommendations for fatigue design of welded joints and components. Springer International Publishing.

[7] Kolstein,M.H.,2007 Fatigue classification of welded joints in orthotropic steel bridge decks. PhD thesis, TU Delft, Delft University of Technology. [8] Nagy,W.,2017. Fatigue assessment of orthotropic steel decks based on fracture mechanics. PhD thesis, Ghent University.

[9] Pachoud,AJ.,Manso.PA, and Schleiss,AJ. Stress intensity factors for axial semi-elliptical surface cracks and embedded elliptical cracks at longi-tudinal butt welded joints of steel-lined pressure tunnels and shafts considering weld shape. Engineering Fracture Mechanics, 179:93–119, 2017.

[10] Simulia.,2014. ABAQUS analysis user’s Manual, Version 6.14. Simulia.

[11] Wu,W., Kolstein,M.H., Veljkovi,M., Pijpers,R., and Vorstenbosch-Krabbe,J.,2017. 09.04: Fatigue behaviour of the closed rib to deck and crossbeam joint in a newly designed orthotropic bridge deck. Eurosteel2017, 1(2-3):2378–2387.

[12] Xu,X.,Liu,Y.,He,J.,2014. Study on mechanical behavior of rubber-sleeved studs for steel and concrete composite structures. Construction and Building Materials, 53:533 – 546.