Tp ratio on fatigue life prediction of SMAW cruciform joints of ASTM 517 ‘F’ Grade steels

International Journal of Pressure Vessels and Piping 75 (1998) 907–918

Effect of L/Tp ratio on fatigue life prediction of SMAW cruciform joints of ASTM 517 ‘F’ Grade steels V. Balasubramanian, B. Guha* Mechanical Testing Lab, Department of Metallurgical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India Received 3 September 1998; accepted 24 September 1998

Abstract New fracture mechanics equations have been developed to predict the fatigue life of shielded metal arc welded (SMAW) cruciform joints of ASTM 517 ‘F’ Grade steels, containing lack of penetration (LOP) defects. These equations have been developed by combining the Paris law with the DKi-endurance equation The initiation life (Ni) and the propagation life (Np) of the joints were accounted for, to obtain the total fatigue life (Nf). The initiation life was obtained experimentally using crack initiation criteria. The propagation life was evaluated using the numerically developed equations. The accuracy of the developed equations were tested by comparing the predicted data with the experimental data and it was found that the correlation is quite good. Further, the effect of L/Tp ratio (weld size) on fatigue life prediction was analysed in detail. 䉷 1998 Elsevier Science Ltd. All rights reserved. Keywords: Fracture mechanics; Fatigue life; SMAW cruciform joints; ASTM 517 ‘F’ Grade steels

1. Introduction ASTM 517 ‘F’ Grade steels are high strength, fine grain structural steels of Q&T type, which are used for welded construction of all kinds such as pressure vessels, penstocks, bridges and structures as well as transport vehicles, hoisting and earthmoving equipment and which are utilised in different climatic conditions [1]. The fillet welded, cruciform joints are most common ones in various structures including offshore and nuclear applications. Although the quality of welding has improved over the past decades, welding discontinuities are still unavoidable. The sizes of internal discontinuities present in the weld has a large effect on the measured fatigue life. The most important variable in determining the fatigue life of a flawed weldment would seem to be the nature of internal flaws contained within the weld and the manner in which these flaws interact within the stress field in and around the weld during its fatigue life [2]. Linking the effects of weld defects and failure analysis of weldments pointing towards that the fatigue alone is considered to account for most of the disruptive failures and often precedes the onset of brittle failure [3]. The fatigue resistance of the weld metal and heat affected zone of various steels are better or equal to the base metal. However, * Corresponding author. Tel.: ⫹ 91-44-2351-365; Fax: ⫹ 91-44-2350509; e-mail: [email protected].

problems arises when there is an abrupt change in section by excess weld reinforcement, undercut, inclusion of slag or lack of penetration or fusion [4]. 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 [5]. There are two types of cracking in a fillet welded joints: (i) root cracking and (ii) toe cracking. Fatigue cracks initiate at fillet weld toe when the fillet weld size is large enough and initiate at weld root when weld size is inadequate [6]. The root failures cannot be prevented unless the weld dimensions are made appropriate to the plate thickness [7]. The lack of penetration (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 [8]. The fatigue crack growth behaviour of welded joints depends on the material, loading and in particular, the geometric configurations of the weld and plate [9]. Previous works [10–13] on cruciform joints showed that the fatigue life of the joint could be influenced by three geometric parameters. They are: (i) the ratio between leg length to plate thickness, (ii) the ratio between initial LOP size to fillet width, and (iii) fillet angle. Most of these works have given more emphasis to the effect of weld profiles on fatigue crack growth behaviours and hence the present investigation, has been carried out to study the influence of L/Tp (weld size) on fatigue life. Fatigue life prediction of welded

0308-0161/98/$ - see front matter 䉷 1998 Elsevier Science Ltd. All rights reserved. PII: S0308-016 1(98)00103-3

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Fig. 1. Dimensions of cruciform specimen.

joints is very complex, costly and time consuming. This is because of its complex joint geometry, number of stress concentration points and heterogeneous weld metal property making the joint. So, to avoid a costly and complex procedure, traditionally the fatigue life assessments of such joint for structural applications have followed the S-N type of approach covered by BS 5400 and IIW [14]. But, for critical structural applications where both initiation and propagation behaviour are equally important for the purpose of safety, the fracture mechanics approach is more appropriate in the place of traditional methods to predict the fatigue life of the component [15]. It is customary to predict the fatigue life of welded joint with defect in terms of crack growth parameters such as da/dN against DK obtained by crack growth experiment. Practically, this type of data merely indicates the fatigue crack growth behaviour of the weldments and does not predict the actual fatigue life. From the literature [9–11], it is evident that most of the investigations on fatigue life prediction of the fillet welded joints are based on toe failure. Very few investigators [12,13] have studied the fatigue behaviour of fillet welded joints failing from root region. Hence, in this study new fracture mechanics equations were developed to predict the fatigue life of shielded metal arc welded (SMAW) cruciform joints of ASTM 517 ‘F’ Grade steels, failing from root (LOP) region.

2. Experimental ASTM 517 ‘F’ Grade steel of weldable quality in the form of rolled plates of 8 mm thickness were used as the base material throughout the investigation. The rolled plates

were cut into the required sizes and profiles by oxy-fuel cutting and grinding. The initial joint configuration was obtained by securing the long plates (200 × 100 mm) and stem plate (200 × 75 mm) in a cruciform position by tack welding. Subsequently the fillets were made between the long plate and stem plate laying weld metal using the SMAW process with matching weld metal consumable (AWS E11018-M). Single pass welding method was used to fabricate small welds (for the weld size of L/Tp ˆ 0.6) and multipass welding procedures were employed to fabricate larger welds (for the weld size of L/Tp ˆ 0.8 and 1.0). All the four fillets forming the joint were made identical leaving an unfused gap between the pair of fillets. This gap, i.e., LOP was controlled by providing proper root faces, obtained by a prior machining process known as bevelling [16]. The various root faces enabled the joints to have different LOP lengths after welding. The fillet leg lengths were varied from 4 to 10 mm and LOP length from 5 to 8 mm. The dimensions of cruciform joints are shown in Fig. 1. All necessary care was taken to avoid joint distortions and the joints were made without applying any clamping devices. The fatigue crack growth experiments were conducted in a mechanical resonance controlled vertical pulsator (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 [15]. The specimen was loaded at a particular stress level (range) and crack initiation and its subsequent propagation from LOP defect was recorded from time to time until complete failure of the specimen. A similar crack growth experiment was conducted on a number of specimens at various stress levels and experimental data were recorded. Tables 1 and 2 show the chemical composition and mechanical properties, respectively, of the base metal and the weld metal.

3. Results and discussion 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), at four different stress levels (Ds ) i.e., 120, 160, 200 and 240 MPa. But for comparison purposes, only three weld sizes i.e., L/Tp ˆ 0.6, 0.8 and 1.0, were considered.

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 0.5

0.95 1.6

0.01 0.01

0.002 0.03

0.8 0.35

0.35 0.27

0.07 1.73

0.03 0.1

0.004 0.01

0.002 0.001

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Table 2 Mechanical properties Material

Yield strength (MPa)

Tensile strength (MPa)

Vicker’s hardness (v30kg)

Impact value (J)

Elongation (%)

Base metal Weld metal

690 740

790 845

210 320

110 175

19 24.5

3.1. Effect of L/Tp on crack propagation life (Np)

and

The fracture mechanics analysis is based on the Paris power law [17] given as follows:

A2 ˆ 0:218 ⫹ 2:7717…L=Tp † ⫺ 10:171…L=Tp †2

da=dN ˆ C…DK†m

⫹ 13:122…L=Tp †3 ⫺ 7:775…L=Tp †4 ⫹ 1:785…L=Tp †5 :

…1†

where da/dN is the crack growth rate, DK the stress intensity factor (SIF) range, and C and m are constants. Eq. (1) can be normalised and adopted for cruciform joints, as in the following form:

By normalising and re-arranging [15], Eq. (4) is simplified as follows:

d…2a=2W† C…DK†m Dsm ˆ · dN Dsm 2W

where

…2†

where Ds is the nominal stress range, 2a the LOP defect size, and 2W the fillet width as shown in Fig. 1. After re-arranging the equation, da* C ˆ ·f*m …a†·Dsm ·W …m=2†⫺1 dN 2

…3†

where f* (a) is the normalised SIF range (ˆ DK=Ds·W 1=2 ) and a* the normalised crack length ( ˆ a/W). The expression for SIF range (DK), at the apex of a root (LOP) defect of load carrying cruciform joint developed by Frank and Fisher [12] is given as: Ds DK ˆ ‰A ⫹ A2 a*Š‰pa·sec…pa*=2†Š1=2 1 ⫹ 2…L=Tp † 1

…4†

where L/Tp is the weld size as defined in Fig. 1. The values of A1 and A2 are functions of weld size (L/Tp) as given in the following: A1 ˆ 0:528 ⫹ 3:287…L=Tp † ⫺ 4:361…L=Tp †2 ⫹ 3:696…L=Tp †3 ⫺ 1:874…L=Tp †4 ⫹ 0:415…L=Tp †5

DK ˆ Dsf*…a†W 1=2

f*…a† ˆ

…5†

‰A1 ⫹ A2 a*Š‰pa*·sec…pa*=2†Š1=2 : 1 ⫹ 2…L=Tp †

Fig. 2 shows the normalised SIF range, f*(a) versus crack length, a* for different values of weld size, L/Tp. The calculated values of SIF range of all the joints, for the growing crack, were plotted as shown in Figs. 3–5. From the figures it is evident that larger welds endure more number of cycles than the smaller welds at a particular SIF range value. The term of DK in Eq. (5) for cruciform joint can be inserted in Eq. (2) to get da* Cf*m …a†·Dsm ·W 1=2 : ˆ 2W dN

…6†

After re-arranging the terms for integration: Z Zaf * da* C ˆ ·Dsm ·W …m=2†⫺1 dN 2 ai * dN

…7†

where ai* is the initial defect size after initiation cycles (NI) and af* the final defect size at failure,or Ip ˆ

C ·Dsm ·W …m=2†⫺1 ·Np 2

…8†

where Ip is the value of integration for propagation of cycles leading to failure Np the number of cycles to crack propagation. Re-arranging the equation, Np ˆ

Fig. 2. Relationship between f*(a) and a*.

2Ip ·Dsm ·W …m=2†⫺1 : C

…9†

The integration was performed on normalised SIF range, f*(a) between initial, ai* and final crack length af* with an increment of 0.01. The integration was done for various crack growth exponent values m and it was also found that the value of integration, Ip is a function of crack length, a* for all values of m as shown in Fig. 6 as a log–log plot.

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Fig. 3. SIF range values for growing crack in welds of L/Tp ˆ 0.6.

Fig. 4. SIF range values for growing crack in welds of L/Tp ˆ 0.8.

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Fig. 5. SIF range values for growing crack in welds of L/Tp ˆ 1.0.

3.2. Evaluation of m and C The crack growth rate, da/dN, for the propagation stage was 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 SIF range (DK) and the corresponding crack growth rate, d(2a)/dN on a log–log scale in terms of best fit line (BFL) is shown in Figs. 7–9, for all the weld sizes. The data points mostly correspond to

Fig. 6. Relationship between Ip and a.

the second stage of sigmoidal relationship of Paris Eq. (1). At a fixed value of K, the smaller welds show higher crack growth rates than the larger welds. The propagation life of the welds can be predicted by using the following equations: d…2a† ˆ 2:5 × 10⫺10 …DK†3:9 dN

for L=Tp ˆ 0:6;

…10†

d…2a† ˆ 7:6 × 10⫺10 …DK†3:5 dN

for L=Tp ˆ 0:8;

…11†

d…2a† ˆ 4:2 × 10⫺9 …DK†2:9 dN

for L=Tp ˆ 1:0:

…12†

From these propagation life equations and from Figs. 7– 9, it is clear that the L/Tp ratio has 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 during the fabrication of the joints. The small welds of size 0.6 were fabricated by single pass technique but the other welds, of sizes 0.8 and 1.0, were fabricated by using multipass technique. In multipass deposits, the weld metal consists partly of a tertiary transformation microstructure. Since, in the multipass technique, each successive bead tempers previous ones, consequently the secondary microstructures, such as pro-eutectoid (grain boundary) ferrite, side plate ferrite and acicular ferrite, will partly be heated into the region. This extra transforma-

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Fig. 7. Crack growth rate curve for L/Tp ˆ 0.6.

tion results in the formation of tertiary microstructure. This structure normally has higher toughness than the non-transformed weld metal (the secondary microstructure) [18–20]. The secondary reason is that the crack has to grow longer distance before failure in the larger welds than the smaller welds. 3.3. Effect of L/Tp on crack initiation life (Ni)

cycles are calculated as follows: 1 mm ˆ Ci …DKi †m ; Ni or Ni ˆ

1 ; Ci …DKi †m

or

The crack initiation life Ni was evaluated experimentally using the crack ‘‘initiation criteria’’. The initiation criterion was based on the assumption that 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 particular stress range. Similar criteria have been adopted by other investigators [21–23]. Paris type equation for early crack growth is given as:

where C1 ˆ 1/Ci. By substituting the experimental values of Ni, the calculated values of DKi, and the evaluated values of m in Eq. (14), the value of C1 was obtained for all the three joints and they are presented in the form of initiation life equations as follows: Ni ˆ 5:0 × 109 …DKi †⫺3:9

for L=Tp ˆ 0:6;

…15†

d…2a† ˆ Ci …DKi †m dN

Ni ˆ 1:5 × 109 …DKi †⫺3:5

for L=Tp ˆ 0:8;

…16†

Ni ˆ 3:8 × 108 …DKi †⫺2:9

for L=Tp ˆ 1:0:

…17†

…13†

where Ci is a constant and DKi the initial SIF range. For the 1 mm crack growth, the required number of

Ni ˆ C1 …DKi †⫺m

…14†

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Fig. 8. Crack growth rate curve for L/Tp ˆ 0.8.

Fig.10 shows the relationship exist between initial SIF range (DKi) and crack initiation life (Ni). From Fig. 10 and from Eqs. (15)–(17), it is clear that the L/Tp ratio has an effect on the crack initiation life to a small extent and that it is mainly because of the fact that the initial SIF range value depends on the L/Tp ratio i.e., if the L/Tp ratio is large then the initial SIF range value will become small and hence the crack initiation will be delayed and vice versa. 3.4. Effect of L/Tp on total fatigue life prediction (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. When a crack growing from a notch or defect, whose growth behaviour is in variance with steady growth regime, is a function of test variables [24] as in the case of cruciform joint with LOP it called for a separate evaluation of the crack initiation life by experimental method as discussed earlier. In contrast, the segment of the crack length, i.e., af* ⫺ ai*, of the crack considered for the integration, for the purpose of fatigue

life prediction was for a steady growing crack whose crack growth rate belongs to the intermediate crack growth regime and obeys Paris power law. Therefore, the total fatigue life (Nf) is evaluated by the following equation [22,23]: Nf ˆ Ni ⫹ Np :

…18†

With the knowledge of crack growth parameters (m and C) and incorporating the crack initiation cycles (Ni) from Eqs. (15)–(17), the total fatigue life (Nf) of all the joints can be predicted using Eq. (18). Instead of predicting the total fatigue life by the aforementioned method, an attempt was made to predict the life from the relationship existing between initial SIF range (DKi) and the fatigue life (Nf) values obtained from the experiments. The fatigue life (Nf) of cruciform joint can be predicted by the following equations for the endurance lines shown in Fig. 11. Nf ˆ 1:1 × 1010 …DKi †⫺3:9

for L=Tp ˆ 0:6;

…19†

Nf ˆ 4:2 × 109 …DKi †⫺3:5

for L=Tp ˆ 0:8;

…20†

Nf ˆ 1:2 × 109 …DKi †⫺2:9

for L=Tp ˆ 1:0:

…21†

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Fig. 9. Crack growth rate curve for L/Tp ˆ 1.0.

The S-N behaviours of the three welds are shown in Fig. 12, for comparison purpose. A graph relating L/Tp and crack growth exponent m is shown in Fig. 13. It is observed from the figure that for all the values of L/Tp, the m values fall on a straight line (linear relationship). Further, a graph was plotted relating m and C2 (Fig. 14). By using these two graphs (Figs. 13 and 14), the value of constants m and C2 can be evaluated and DKi can be calculated from Eq. (5) for a given L/Tp ratio (weld size). Substituting these values in the following equation (Eq. (22)), the total fatigue life of the SMAW cruciform joints of ASTM 517 ‘F’ Grade steels containing LOP defects can be predicted successfully. Nf ˆ C2 …DKi †⫺m

…22†

The accuracy of this equation was tested by comparing the predicted fatigue life data using Eq. (22) with the experimental data. The resultant scatter diagram is shown in Fig. 15. It is understood from the figure that this method can be effectively used to predict the fatigue life of the welded cruciform joints with reasonable accuracy.

4. Conclusions 1. The fatigue life of shielded metal arc welded (SMAW)cruciform joints of ASTM 517 ‘F’ Grade steels, containing LOP defects, can be successfully predicted by using the fracture mechanics equations developed in this paper, with reasonable accuracy. 2. The L/Tp ratio (weld size) has a significant effect on crack initiation life (Ni), crack propagation life (Np) and the total fatigue life (Nf) of the welded cruciform joints. 3. The resistance to fatigue crack growth offered by the welds deposited by the multipass technique, i.e., larger welds, were found to be marginally superior compared to the smaller welds deposited by the single pass technique.

Acknowledgement The authors are indebted to M/s. Bharat Heavy Electricals Limited (BHEL), Ranipet, Tamil Nadu, India for the material supplied to carry out the investigations.

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Fig. 10. Relationship between crack initiation life and initial SIF range.

Fig. 11. Relationship between initial SIF range and fatigue life.

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Fig. 12. Fatigue life of three welds.

Fig. 13. Relationship between L/Tp and m.

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Fig. 14. Relationship between m and C2.

Fig. 15. Scatter diagram.

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