Analysing the influences of weld size on fatigue life prediction of FCAW cruciform joints by strain energy concept

International Journal of Pressure Vessels and Piping 76 (1999) 759–768 www.elsevier.com/locate/ijpvp

Analysing the influences of weld size on fatigue life prediction of FCAW cruciform joints by strain energy concept V. Balasubramanian*, B. Guha Mechanical Testing Laboratory, Department of Metallurgical Engineering, Indian Institute of Technology, Madras, Chennai 600 036, India Received 8 April 1999; accepted 20 April 1999

Abstract The effect of weld size on fatigue life of flux cored arc welded (FCAW) cruciform joints containing lack of penetration (LOP) defect has been analysed by using the strain energy density factor (SEDF) concept. Moreover, new fracture mechanics equations have been developed to predict the fatigue life of the cruciform joints. Load carrying cruciform joints were fabricated from ASTM 517 ‘F’ grade steel. Fatigue crack growth experiments were carried out in a vertical pulsar (SCHENCK 200 kN capacity) with a frequency of 30 Hz under a constant amplitude loading …R ˆ 0†: It was found that the crack growth rates were relatively lower in the larger welds fabricated by the multipass welding technique than the smaller welds fabricated by the single pass welding technique. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: Flux cored arc welding; Cruciform joint; Lack of penetration; Strain energy density factor; Fatigue life

1. Introduction Fillet welded cruciform joints are widely used in many structures including offshore and nuclear installations. In such joints, the frequently encountering defect is the lack of penetration (LOP), which occurs due to inaccessibility of the root region during welding [1]. Many of the fatigue failures that occur in welded joints involve fatigue cracking from severe imperfections, which are actually an inherent part of the joint. There are two types of cracking in a fillet welded joint: (i) root cracking and (ii) toe cracking. The root failures cannot be prevented unless the weld dimensions are appropriate to the plate thickness [2]. The LOP defect will affect the fatigue behaviour of fillet welds when it exceeds a critical value of half of the plate thickness to be welded [3]. Fatigue cracks initiate at the fillet weld toe when the fillet weld size is large enough and initiate at weld root when weld size is inadequate [4]. The fatigue crack growth behaviour of welded joints depends on the material, loading and in particular, the geometric configurations of the weld and plate [5]. Previous works [6–8] on cruciform joints showed that the fatigue life of the joint could be affected by the three geometric parameters. They are: (i) the ratio between leg length (L) to plate thickness (Tp); (ii) the ratio between initial LOP size (2a) to fillet width (2W); and (iii) the

weld profile or fillet angle. However, most of the works have given much emphasis to the weld profile effect on fatigue life, and that too on toe cracking behaviour of fillet welds. Moreover, all the above works were mainly based on the following fatigue crack growth equation [9] da=dN ˆ C…DK†m :

…1†

The above expression may not be adequate to analyse the crack growth behaviour of cruciform joints failing from (LOP) root region for the two reasons [10]. (i) The above equation involves Ds only but any crack growth expression, da=dN, should contain in principle, at least two loading parameters, say the stress amplitude, Ds and the mean stress level, s ; so that the fatigue loading is properly defined. (ii) The above equation is restricted to the cracks running ahead but the crack from root region of the cruciform joint does not propagate in the direction normal to the applied load because of a complex joint geometry. Hence, in this paper, an attempt has been made to apply the strain energy density factor concept to analyse the influences of weld size on the fatigue life prediction of flux cored arc welded (FCAW) cruciform joints of ASTM 517 ‘F’ grade steels, failing from the LOP region. 2. Experimental work

* Corresponding author. Tel.: 1 91-44-2351365/3820; fax: 1 91-442352545. E-mail address: [email protected] (V. Balasubramanian)

ASTM 517 ‘F’ grade steel (high strength, quenched and tempered, fine grain structural steels) of weldable quality in

0308-0161/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0308-016 1(99)00038-1

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Table 1 Chemical composition (wt%) Material

C

Si

Mn

P

S

Cr

Mo

Ni

Cu

Co

V

Base metal Weld metal

0.19 0.08

0.72 0.4

0.95 1.5

0.01 0.02

0.002 0.01

0.8 0.56

0.35 0.44

0.07 2.25

0.03 0.2

0.004 0.02

0.002 0.002

Table 2 Mechanical properties Material

Yield strength (MPa)

Tensile strength (MPa)

Vicker’s hardness (v30 kg)

Impact value (J)

Percentage of elongation (%)

Base metal Weld metal

690 720

790 830

210 280

110 150

19 26

the form of rolled plates of 8 mm thickness was used as the base material throughout the investigation. These steels are used for the welded construction of all kinds such as pressure vessels, pen stocks, bridges and structures as well as transport vehicles, hoisting and earth moving equipments which are utilised in different climatic conditions. FCAW process with matching weld metal consumable (AWS E100 T5K4) was used to fabricate the cruciform joints. Tables 1 and 2 show the chemical composition and mechanical properties of the base metal and weld metal. Single pass welding method was used to fabricate small welds (for L=Tp ˆ 0:6) and multi-pass pass welding procedures were employed to fabricate larger welds (two weld passes for L=Tp ˆ 0:8 and three weld passes for L=Tp ˆ 1:0). Further details about the fabrication and specimen sectioning were given elsewhere [8]. The dimensions and profile of a cruciform test specimen are shown in Fig. 1. The fatigue crack growth experiments were conducted in a mechanical resonance controlled vertical pulsar (200 kN capacity) with a frequency of 30 Hz under constant amplitude loading …R ˆ 0†: Before loading, the specimen surface near the LOP was polished to enable the crack growth measurement. A travelling microscope was used to monitor the crack length with an accuracy of 0.01 mm. The specimen was loaded at a particular stress level (range) and crack initiation and its subsequent propagation from the LOP defect was recorded from time to time until complete failure of the specimen.

where da=dN is the crack growth rate; DS the strain energy density factor (SEDF) range and A and n are constants.The SEDF S takes the following form [12], S ˆ a11 K12 1 2a12 K1 K2 1 a22 K22 1 a33 K32

in which K1, K2 and K3 are stress intensity factor (SIF) to tensile, inplane shear and out of plane shear loads, whereas in our case K2 ˆ K3 ˆ 0: [S ˆ a11 K12 :

16ma11 ˆ …3 2 4n 2 cos u†…1 1 cos u†

…5†

where n is the Poisson’s ratio …ˆ 0:30†, m the shear modulus

The fatigue crack growth experiments were conducted on a large number of specimens having different dimensions (a=W ˆ 0:25–0:45, L=Tp ˆ 0:4–1:2). But for the comparison purposes, only three weld sizes i.e. L=Tp ˆ 0:6, 0.8 and 1.0, have been considered in this paper. 3.1. Influence of weld size on crack propagation life (Np) The fracture mechanics analysis is based on the following equation [11] …2†

…4†

The coefficient a11 can be determined from the following expression [12]:

3. Results and discussion

da=dN ˆ A…DS†n

…3†

Fig. 1. Dimensions of the cruciform specimen.

V. Balasubramanian, B. Guha / International Journal of Pressure Vessels and Piping 76 (1999) 759–768

761

Fig. 2. SEDF range values for growing crack in welds of L=Tp ˆ 0:6.

…ˆ 77 GPa† ˆ E=2…1 1 n†, E the Young’s modulus …ˆ 200 GPa†: The direction of crack growth is first found by taking 2S=2u ˆ 0 which gives u ˆ 0: [a11 ˆ …1 2 2n†=4m:

…6†

The SEDF is reduced to the following form: S ˆ ‰…1 2 2n†=4mŠ·K12

…7†

and therefore, the SEDF range can be calculated from the following expression: DS ˆ ‰…1 2

2n†=4mŠ·DK12

ˆ …1 2

2 2n†=4m·‰K1max

2

2 K1min Š:

…8† The SIF range (DK1), at the apex of a root (LOP) defect of load carrying cruciform joint can be calculated using the expression given below [7], DK ˆ

Ds ‰A 1 A2 ap Š‰pa·sec…pap =2†Š1=2 1 1 2…L=Tp † 1

…9†

where a is the half crack length at the root of fillet in the cruciform joint, a p the normalised crack length, a=W and

L=Tp the weld size as defined in Fig. 1. The values of A1 and A2 are functions of weld size (L=Tp ) as given below: A1 ˆ 0:528 1 3:287…L=Tp † 2 4:361…L=Tp †2 1 3:696…L=Tp †3 2 1:874…L=Tp †4 1 0:415…L=Tp †5 and A2 ˆ 0:218 1 2:7717…L=Tp † 2 10:171…L=Tp †2 1 13:122…L=Tp †3 2 7:775…L=Tp †4 1 1:785…L=Tp †5 By normalising and rearranging, the above equation was simplified [13] and given below as: DK ˆ Dsf p …a†W 1=2

…10†

where f p a† ˆ

‰A1 1 A2 ap Š‰pap sec…pap =2†Š1=2 1 1 2…L=Tp †

By using the above equations, the SEDF range values are calculated at each 1 mm crack length increment and the corresponding endurance cycles are also recorded (experimentally) and they are related as shown in Figs. 2–4. From the figures, it is evident that the larger welds gave longer endurances than the smaller welds, at a particular stress range. The crack growth rate, da=dN for a propagation stage, was

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Fig. 3. SEDF range values for growing crack in welds of L=Tp ˆ 0:8.

calculated considering the slope at the steady state growth regime at different intervals of crack length increment against the associated number of cycles to propagation. For all calculations, the ASTM E-647 guidelines were followed. The relationship between the SEDF range (DS) and the corresponding crack growth rate, d…2a†=dN on a log–log scale in terms of the best fit line is shown in Fig. 5, for all the weld sizes. From the graphs, the exponent n which is the slope of the line on the log–log plot and the value of the constant A which is the intercept of the line on the log–log plot have been evaluated. At a fixed value of DS, the smaller welds have shown higher crack growth rates than the larger welds. The propagation life of the welds can be predicted by using the following equations: d…2a†=dN ˆ 3:65 × 10

211

…DS†

d…2a†=dN ˆ 1:35 × 10

210

…DS†

29

2:35

d…2a†=dN ˆ 1:03 × 10 …DS†

2:12

1:71

for L=Tp ˆ 0:6

…11†

for L=Tp ˆ 0:8

…12†

for L=Tp ˆ 1:0:

…13†

From the above propagation life equations and from Fig. 5, it is clear that the weld size …L=Tp † has a significant effect on the propagation life of the welded cruciform joints. The

little variations in the crack growth behaviour and propagation life is mainly attributed to the difference in the number of weld passes involved in fabrication of the joints [8,14]. The term DS in Eq. (8) for the cruciform joint can be inserted in Eq. (2) to get dap A‰1 2 2n†=4mŠn …Ds†2n ·f p2n …a†W n21 ˆ : dN 2

…14†

After re-arranging the terms for integration Zaf p aip

dap =f p2n …a† ˆ A=2‰…1 2 2n†=4mŠn …Ds†2n ·W n21

Z dN …15†

where api is the initial defect size after initiation cycles (Ni) and apf the final defect size at failure, or Ipse ˆ A=2‰…1 2 2n†=4mŠn …Ds†2n ·W n21 ·Np

…16†

where Ipse is the values of integration for propagation of cycles leading to failure and Np the number of cycles to crack propagation.Re-arranging the equation, Np ˆ 2Ipse =A·‰…1 2 2n†=4mŠn …Ds†2n ·W n21 :

…17†

The integration was done for various crack growth exponent

V. Balasubramanian, B. Guha / International Journal of Pressure Vessels and Piping 76 (1999) 759–768

763

Fig. 4. SEDF range values for growing crack in welds of L=Tp ˆ 1:0.

values n and it was also found that the value of integration, Ipse is a function of crack length, a p for all values of n as shown in Fig. 6 in a double log plot.

the evaluated values of n, the value of A1 is obtained for all the three joints and they are presented below in the form of initiation life equations.

3.2. Influence of weld size (L=Tp ) on crack initiation life (Ni)

Ni ˆ 7:8 × 1010 …DSi †22:35

for L=Tp ˆ 0:6

…20†

Ni ˆ 1:2 × 1010 …DSi †22:12

for L=Tp ˆ 0:8

…21†

Ni ˆ 1:8 × 109 …DSi †21:71

for L=Tp ˆ 1:0:

…22†

The crack initiation life Ni was evaluated experimentally using the crack “Initiation Criteria”. The initiation criterion was based on the assumption for the number of cycles required to grow 1 mm length of crack in excess of its original length (LOP) at the earlier crack growth stage under a particular stress range [13]. Paris-type equation for early crack growth is given below; d…2a†=dN ˆ Ai …DSi †n

…18†

where Ai is a constant and (DSi) is the initial SEDF range. For the 1 mm crack growth, the required number of cycles are calculated as shown below: 1 mm=Ni ˆ Ai …DSi †n or

or

Ni ˆ A1 …DSi †2n

Ni ˆ 1=Ai …DSi †n

…19†

where A1 ˆ 1=Ai : In the above equation, by substituting the experimental values of Ni, the calculated values of DSi and

From the above equations, it is clear that the L=Tp ratio has an effect on the crack initiation life which is mainly due to the fact that the initial SEDF range value depends on the L=Tp ratio i.e. if the L=Tp ratio is large then the initial SEDF range value will become small and hence the crack initiation will be delayed and vice versa. 3.3. Influence of weld size (L=Tp ) on total fatigue life (Nf) To predict the total fatigue life of the cruciform joints, it is necessary to account for the crack initiation life (Ni) and crack propagation life (Np) separately. Therefore, the total fatigue life (Nf) is evaluated by the following equation: Nf ˆ Ni 1 Np :

…23†

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Fig. 5. Crack growth rate curves.

With the knowledge of crack growth parameters (n and A) and incorporating the crack initiation cycles (Ni) from Eqs. (20)–(22), the total fatigue life (Nf) of all the joints can be predicted using Eq. (23). Instead of predicting the total

fatigue life by the above method, an attempt has been made to predict the life from the relationship that exist between initial SEDF range (DSi) and the fatigue life (Nf) values obtained from the experiments and it is graphically

Fig. 6. Relationship between Ipse and a p.

V. Balasubramanian, B. Guha / International Journal of Pressure Vessels and Piping 76 (1999) 759–768

Fig. 7. Relationship between initial SEDF range and fatigue life.

Fig. 8. Fatigue life of three welds.

765

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Fig. 9. Relationship between L=Tp and n.

shown in Fig. 7. The fatigue life (Nf) of the cruciform joint can be predicted by the following equation: Nf ˆ A2 …DSi †2n :

…24†

In the above equation, by substituting the experimental values of Nf, the calculated values of DSi and the evaluated

values of n (in Section 3.1), the value of A2 is obtained for all the three joints and they are presented below in the form of endurance equations. Nf ˆ 1:2 × 1011 …DSi †22:35

for L=Tp ˆ 0:6;

…25†

Nf ˆ 2:4 × 1010 …DSi †22:12

for L=Tp ˆ 0:8

…26†

Fig. 10. Relationship between n and A2.

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767

Fig. 11. Scatter diagram.

and Nf ˆ 4:4 × 109 …DSi †21:71

for L=Tp ˆ 1:0:

…27†

The S–N behaviour of the three welds is shown in Fig. 8, for a comparison purpose. A graph has been plotted relating L=Tp and crack growth exponent n as shown in Fig. 9. It is observed from the figure that for all the values of the L=Tp , the n value is falling on a straight line (linear relationship). Further, a graph has been plotted relating n and A2 as shown in Fig. 10. By using these two graphs (Figs. 9 and 10), the value of constants n and A2 can be evaluated and the DSi can be calculated from Eq. (8) for a given L=Tp ratio (weld size) and substituting these values in Eq. (24), the total fatigue life of the FCAW cruciform joints of ASTM 517 ‘F’ grade steels containing the LOP defects can be predicted successfully. The accuracy of the above developed equation is tested by comparing the predicted fatigue life data by using Eq. (24) with the experimental data and the scatter diagram is shown in Fig. 11 and it is understood from the figure that the above method can be effectively used to predict the fatigue life of the welded cruciform joints within the reasonable accuracy. 4. Conclusion 1. The fatigue life of FCAW cruciform joints of ASTM 517

‘F’ grade steels, containing LOP defects, can be successfully predicted, using the new fracture mechanics equations developed by strain energy concept, within a reasonable accuracy. 2. The weld size (L=Tp ) is having significant effect on the crack initiation life (Ni), crack propagation life (Np) and total fatigue life (Nf) of the welded cruciform joints.

Acknowledgements The authors are grateful to Professor G.C. Sih, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, USA for his valuable suggestions and guidance. The authors are indebted to M/s Bharat Heavy Electrical Limited (BHEL), Ranipet, Tamil Nadu, India for the material supplied to carry out the investigation.

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