A Simple Procedure for Remaining Life Assessment

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Structures, Fracture Mechanics, Assessment Procedure. ... fatigue and creep-fatigue analysis which make this almost impossible for practical engineers to get ...
A SIMPLE PROCEDURE FOR REMAINING LIFE ASSESSMENT OF CRACKED COMPONENTS BASED ON PD 6493/BS 7910 AND REMAINING LIFE CURVES

Ninh T. Nguyen Abstract Most of the steel welded structures around the world today are ageing and in need of repair. Pressure vessels in power and process plants are a typical example. Normally a tiny crack would first initiate at a location of high stress concentration and then propagates under the typical thermal cyclic operating regimes of these vessels. Once cracks have been detected during routine inspection they need to be assessed before any decision about equipment integrity can be made. During this process, the two most common questions are: (i) Is it safe to keep the cracked vessel to continue its operation until the next scheduled outage?, and (ii) What is the remaining life of the cracked pressure vessel ? This paper shows the potential answers to these question via new simple assessment procedure for remaining life of cracked components (either non-welded or welded) based on BSI PD 6493/BS 7910 and the remaining life curves which have been developed for the effective crack lengths subjected to various quality categories. Following this new assessment procedure the owners/operators could obtain an almost immediate answer to the remaining life of the cracked component under cyclic loading conditions. Keywords Fatigue Assessment, Remaining Life Curves, Remaining Life Assessment, Welded Joints & Structures, Fracture Mechanics, Assessment Procedure. Author Details Dr Ninh T. Nguyen is Senior Integrity Assessment Engineer with Materials Consulting Group, HRL/ETRS Pty Ltd, 677 Springvale Road, Mulgrave VIC 3170, Australia.

1

1.

INTRODUCTION

Most of the steel welded structures around the world today are ageing and in need of repair. Pressure vessels in power and process plants are a typical example. Normally a tiny crack would first initiate at a location of high stress concentration and then propagates under the typical thermal cyclic operating regimes of these vessels. Once cracks have been detected during routine inspection they need to be assessed before any decision about equipment integrity can be made. During this process, the two most common questions are: (i) Is it safe to keep the cracked vessel to continue its operation until the next scheduled outage?, and (ii) What is the remaining life of the cracked pressure vessel ? There has been a considerable development of “fitness-for-purpose” assessment procedures over the last few decades. This has resulted in several national standard assessment procedures such as fracturemechanics-based approaches in AS-4100 [1], WES-2850 [2] and BSI PD 6493 [3], BS 7910 [4] or hotspot-stress approaches [5]. Based on any one of these “fitness-for-purpose” assessment procedures, the owners or operators can normally obtain the answer for the first question raised above by following relatively simple calculation procedures. However, this is not the case when one needs to obtain the answer for the second question. This task would involve rather complicated numerical integration of crack growth rate laws (eg. Paris’ law) which requires the solutions for stress intensity ranges subjected to complicated crack geometries and loading conditions. Furthermore, this task would require a range of expert knowledge of broad areas such as stress analysis, fracture mechanics, creep, fatigue and creep-fatigue analysis which make this almost impossible for practical engineers to get the answer for this problem. This paper describes a new simple assessment procedure for remaining life of cracked components (either non-welded or welded) based on BSI PD 6493/BS 7910 and the remaining life curves developed for the effective crack lengths subjected to various quality categories. Following this new assessment procedure the owners/operators could obtain an almost immediate answer to the remaining life of the cracked component under cyclic loading conditions. 2.

BACKGROUND

Presently, the design of welded components involves one calculation to find static strength of a component and another calculation to find its endurance. This design is carried out separately and any dependence of static strength on endurance is neglected. It is implicitly assumed that the strength of a component does not change during the fatigue life and remains equal to the static strength [7]. The main aim of this work is to develop a simple assessment procedure for remaining life of cracked welded-components whilst the crack continues to propagate until component’s failure. 2.1

Remaining Life Curves

Let us consider a simple model of central through thickness crack with length 2a in a flat plate of infinite width under uniform remote tension loading const. Stress intensity range K at the crack tip can be calculated by basic fracture mechanics as

K   a

(1)

Under cyclic loading, the crack propagates according to well-known Paris’ law as

da m  C K   C (  a ) m dN

(2) 2

Where C and m are material properties and N is loading cycles. There are three common classes of steels namely martensitic, ferrite-perlite and austenite. It has been found that for typical martensite high strength steel with yield strength larger than 552 MPa the crack propagation properties are C = 2.E-10 and m = 2.25. For ferrite-perlite steel of yield strength between 200 and 552 MPa the material constants are C=2.3E-13 and m=3 where crack growth rate is in mm/cycle. Most of the structural steels used in practice fall in this category. For austenite type of steel of yield strength from 200 to 350 MPa the values of C and m are 1.5E-11 and 3.25 respectively [8]. If the initial and final crack lengths are known, the total numbers of cycles NT to failure can be calculated by integrating the Eq. (2) as af

NT 

da

 C (

ai

a )

m



a

1m / 2 1m / 2 f i m m/2

a

C   



1  m / 2

(3)

Similarly, the number of remaining cycles to failure from an arbitrary crack length ax can be obtained for an arbitrary cyclic constant load range x as

Nx 

a

C 

1m / 2 1m / 2 f x m m/2 x

a





(4)

1  m / 2

The remaining life curves can be constructed based on Eq. (4) by plotting Nx against ax for various constant stress ranges x if the crack propagation properties and final crack length are known. In practice, crack propagation properties are determined by standard crack propagation test and final crack length is determined by fracture mechanics based failure criteria. There are 10 quality categories defined in British standard document BSI PD 6493 [3] or BS 7910 [4] as 10 parallel S-N curves labelled Q1 to Q10 which have the slope of –1/3 in the log and logN plot. Thus, each curve representing a certain quality category is defined by NT( )3 = const.= AQi (for i =1 to 10), values of which are also given in the document for each quality category. Quality category Q1 to Q6 are identical, for steels, to the design S-N curves, corresponding to 97.7 % survival limits for class D to W in BS 5400 [9]. Substituting m = 3 and (x)m = AQi /NT into Eq. (4) and rearranging gives 0.5 0.5 N x 2a x  a f   NT CAQi 

(5)

where C = 3E-13 for steel [3]. Equation (5) gives the fraction of remaining life over the total design life of any selected quality category Qi (i = 1 to 10) for any detected crack length ax. An illustration of the series of remaining life curves subjected to quality categories as given by Eq. (5) for a propagating central though thickness crack (ax) in a flat plate of a finite width 2W = 50 mm is shown in Fig. 1.

3

Remaining life fraction, Nx / NT

1 0.8 0.6 0.4

Q3

Q4

Q5

Q7

Q6

Q8 Q9

Q10

Q2 0.2

Q1

0 0

0.2

0.4

0.6

0.8

1

Normalized crack length, a/W

Fig. 1 Remaining fraction life vs. normalized crack length It can be seen from Fig. 1 that for a particular crack length, the remaining fraction life increases with as the index of quality category increases. This means that for a particular detected crack length, the poorer quality category would allow for larger residual fraction life. The remaining fraction life of higher quality category won’t be affected until the crack length has reached a certain “fitness-forpurpose” acceptable level inherent in the standard. m=3, m=3, m=3, m=3, m=3,

1.00E+08

N (cycles)

1.00E+07

S= S= S= S= S=

60 MPa 100 MPa 140 MPa 180 MPa 220 MPa

1.00E+06 1.00E+05 1.00E+04 1.00E+03 1.00E+02 0

0.2

0.4 0.6 0.8 Normalized crack length, a/W

1

Fig. 2 Remaining life curve of flat A36 steel plate with infinite width Figure 2 shows an example of the remaining life curves which have been calculated for standard mild steel ASTM A36 with fu = 420 MPa, fracture toughness KIC = 1400 MPamm and material constants for crack growth C = 3E-13 and m = 3. The final critical crack lengths have been calculated by comparing the critical crack lengths at both plastic collapse and unstable crack propagation. It can be seen from this figure the remaining life of the specimen with known crack length depends heavily on the stress ranges. The higher the stress range the lower is the remaining life. The mode of failure has 4

gradually changed from plastic collapse at lower stress range to unstable crack growth at higher stress range as shown in Fig. 3.

Fig. 3 Critical crack length and failure modes subjected to applied stress range It is worth noting here that this remaining life curve can be used to assess the block cyclic loads combined of various individual constant stress ranges by means of equivalent stress range eqv which would cause equivalent damage to the component. Let us again consider the central through thickness crack in infinite width flat plate with two blocks of constant stress ranges 1 and 2 for n1 and n2 cycles, respectively. Also let us assume that the initial crack length ai has grown to a1 after n1 cycles and a2 after n2 cycles. The equivalent stress range eqv that causes crack grown from ai to a2 is sought. Applying Eq. (4) for each cyclic loading block and the equivalent block of n1+ n2 cycles at eqv gives

n1 

n2 

a

C 

1m / 2 1 m / 2 1 i m m/2 1

a

C 

n1  n2 



a

a

C 

(6a)

1  m / 2

1m / 2 1 m / 2 2 1 m m/2 2





a



(6b)

1  m / 2

1m / 2 1 m / 2 2 i m m/2 eqv

a



  1  m / 2

(6c)

Substituting Eqs. (6a) & (6b) to (6c) and solve for eqv gives

 n  m  n2  2m      1 1 n1  n2  

1/ m

 eqv

(7)

Equation (7) determines the equivalent stress range to two individual block loads and can be used for assessment of remaining life of the component using remaining life curve shown in Fig. 1. It is noted that the equivalent stress range does not depend on the sequence of loading here. This can be explained 5

by the fact that for a flat plate with infinite width, the correction factor for stress intensity factor is equal to 1 (Y = 1). 2.2 Remaining Life Curves for a Finite Cracked Plate 2.2.1 General equation If the general case of a cracked welded plate is considered, Eq. (3) should be rewritten in more general form incorporating the crack geometry and loading correction factor Y as af

Nx 

da

 C (Y (a )

ax

a ) m

(8)

where Y(a) = f(a, Loads) is a function of crack geometry and loading conditions Nx is the remaining life of a welded plate with a crack length ax Based on Eq. (8) the fraction of remaining life over total fatigue life NT can be calculated as af

Nx  NT

da

 C ( Y (a )

ax af

a ) m

da a C ( Y (a ) a ) m i

(9)

If Y(a) is known, the remaining life curves Nx can be obtained for any initial detected crack length ax. Function Y(a) depends on weld joint and crack geometry, residual stresses and loading configurations (tension or bending or both) can be obtained using the procedures developed by the author’s earlier work [10]. Therefore, in order to develop reliable remaining life curves for cracked welded components and structures, the effects of weld joint geometry, crack geometry, residual stresses and loading configurations needs to be considered. The effect of the residual stresses can be incorporated in terms of effective stress ranges. 2.2.2 Construction of remaining life curves Initial work has been carried out to construct the remaining life curves for constant amplitude tensileloaded edge-crack in the finite plate of various thickness B from 5 to 100 mm for 10 quality category Q1 to Q10 as defined in PD 6493 [3] on the basis of Eq. (9). The correction function Y(a) is calculated by using Bueckner’s weight function for edge crack which has been described in details elsewhere [10]. The crack propagation properties was C = 3.E-13 and m = 3 as has been recommended for structural steels [3] and the value of initial crack lengths were taken from graphs Fig. 8(b) [3] subjected to plate thickness and quality categories. A Fortran program has been written for this calculation purpose using Runge-Kutta method for crack growth as described in WES-2805:1997 [2]. Figure 4(a) and 4(b) shows the remaining life curves of A36 steel flat plate with an edge-crack (ai = 0.1 mm) calculated for 10 mm thickness plate subject to various levels of cyclic tensile loading. Figure 4(a) shows similar trend of remaining life subject to loading levels as obtained for the plate with infinite width (as in Fig. 2). However, if the remaining life curves vs. crack lengths is plotted in dimensionless form (Nx/NT) as in Fig. 4(b), the effect of loading levels would be ignoble. Therefore, 6

the remaining life curves can be constructed in terms of (Nx/NT) vs. (a/B) independent of loading levels.

Number of remaining cycles, N x

10000000

B= B= B= B=

1000000

10 mm, S = 10 mm, S = 10 mm, S = 10 mm, S =

80 MPa 100 MPa 150 MPa 180 MPa

100000

10000

1000 0

0.1

0.2

0.3

0.4

0.5

Normalized crack length, a / B

a) Effect of loading levels on remaining cycles Nx

Normalized remaining life, Nx / NT

1

B = 10 mm, S = 80 MPa B = 10 mm, S = 100 MPa B = 10 mm, S = 150 MPa 0.1

B = 10 mm, S = 180 MPa

0.01

0.001 0

0.1

0.2

0.3

0.4

0.5

Normalized crack length, a / B

b) Effect of loading levels on normalised remaining cycles Nx /NT Fig. 4 Effect of loading levels on the remaining life of finite plate containing edge crack Figure 5 shows the effect of plate thickness on the normalised remaining cycles (Nx /NT). It can be seen from this figure that as the plate thickness increases the remaining life portion over the total life cycles becomes smaller for the same portion of the normalised crack length (a/B). This behavior can be explained by the fact that the critical crack length for a component to fails under unstable crack growth 7

failure is independent of plate thickness and it is unchanged for a certain material and loading range as given by Eq. (8). Therefore, for a given value of (a/B) the absolute value of crack length (a) increases as plate thickness increases. As a result, the remaining life portion of thicker plate decreases. It can be concluded from Figs. 4 and 5 that the remaining life of a cracked component depends mainly on two parameters: plate thickness (B) and initial crack length (ai) which can be classified by various quality category as described in BSI PD 6493 [3].

Normalized remaining life, Nx / NT

1

B = 5 mm B = 10 mm B = 20 mm B = 50 mm B = 100 mm

0.1

0.01

0.001

0.0001 0

0.1

0.2

0.3

0.4

0.5

Normalized crack length, a / B

Fig. 5 Effect of plate thickness on the normalised remaining cycles (Nx /NT) A series of remaining life curves constructed for plate thickness from 5 to 100 mm subjected to quality categories Q1 to Q10 are shown in Figs. A1 to A5 in the Appendix. 3. REMAINING LIFE ASSESSMENT FOR CRACKED COMPONENTS There are established fitness-for-purpose assessment procedures for known surface cracks based on quality category [3-4]. However, no information regarding the remaining life of the cracked components is given in these procedures. Based on remaining life curves, developed in previous section for the edge cracks (as shown in Figs. 6 to 10), the remaining life of any cracked component can be evaluated in conjunction with already established assessment procedure given in PD 6493 [3] (or BS 7910 [4]) as follow: 1. Select quality category required Qreq based on service load (refer to clause 18.3 [3] or 8.5.3[4]) (Both constant and variable amplitude loading is considered). 2. Determine equivalent flaw parameter aeqv from actual planar flaw dimensions (refer to clause 19.2 [3] or 8.6 [4]) 3. Determine tolerable value of flaw parameter amax or crack growth limit (refer to step 6, Table 9 and also clause 19.2[3] or Table 2 step 5[4]) 8

4. If aeqv  amax, then go on to the next step, else stop because practically no remaining life exists. 5. Determine the remaining life of the component (Nx/NT) subjected to the required category Qreq, plate thickness B and equivalent flaw parameter (a = aeqv) by using suitable remaining life curves given in Figs. A1 to A5. Assessment Example 1: Remaining life of a finite plate with a surface crack Let us consider a plate of 10 mm thick containing a surface crack of semi-ellipse shape where dimensions of semi-minor & major axes are a = 1 mm and c = 5 mm, respectively. The plate is subjected to cyclic tensile loading of stress range S = 100 MPa and have been designed for service life of 1 million cycles (NT = 1.E6). The question asked is to assess the remaining life of the plate. Solution: Following are step by step remaining life assessment according to the above procedure. 1. Based on S = 100 MPa and NT = 1.E6 the required quality category is determined from Fig. 17 in PD6493 [3] (or Fig. 16 in BS 7910 [4]) as Q1. 2. Since a = 1 mm, c = 5 mm and B = 10 mm then a/2c = 0.1 and a/B = 0.1, subsequently, equivalent edge flaw aeqv = ai = 0.3 mm has been determined from Fig. 18(a) in PD6493 [3] (or Fig 17(a) [4]). 3. Tolerable value of crack amax = (1/2)(1400/100)2 = 31.2 mm 4. Since aeqv < am then go to step 5 5. Entering Fig. A2 for remaining life curve of 10 mm thick plate of equivalent edge flaw aeqv= 0.3 mm i.e. a/B = 0.03 then interpolate for required quality category Q1 gives remaining life ratio Nx / NT = 0.6. This means the remaining life is Nx = 600,000 cycles. Noting that if S = 80 MPa and NT = 1.E6, then the requited category becomes Q2. Subsequently, the remaining life for the same crack would be 0.85NT = 850,000 cycles. This means that lower applied stress range corresponding to lower quality category would results in better remaining life. Assessment Example 2: Remaining life of a finite plate with an embedded surface crack Let us consider a plate of 10 mm thick again but containing an embedded crack of elliptical shape where dimensions of semi-minor & major axes are a = 1 mm and c = 5 mm, respectively. The plate is subjected to cyclic tensile loading of stress range S = 100 MPa and have been designed for service life of 1 million cycles (NT = 1.E6). The same question asked is to assess the remaining life of the plate. Solution: Following are step by step remaining life assessment according to the above procedure. 1. Based on S = 100 MPa and NT = 1.E6 the required quality category is determined from Fig. 17 in PD6493 [3] (or Fig. 16 [4]) as Q1. 2. Since a = 1 mm, c = 5 mm and B = 10 mm then a/2c = 0.1 and 2a/B = 0.2, subsequently, equivalent edge flaw 2aeqv=2ai = 0.8 mm has been determined from Fig. 20(a) [3] (or Fig. 19(a) [4]). 3. Tolerable value of crack amax = (1/2)(1400/100)2 = 31.2 mm 4. Since aeqv < am then go to step 5

9

5. Entering Fig. A2 for remaining life curve of 10 mm thick plate of equivalent edge flaw aeqv= 0.4 mm i.e. a/B = 0.04 then interpolate for required quality category Q1 gives remaining life ratio Nx / NT = 0.4. This means the remaining life is Nx = 400,000 cycles. It is worth noting here that under the same cyclic loading, the 10 mm thick plate containing an embedded elliptical crack would reduce its remaining life 33 % further than that if it contains a semielliptical surface crack (with the same ellipse axes) instead. Assessment Example 3: Remaining life of a finite welded plate with surface crack Let us consider a welded plate of 10 mm thick again but containing a surface crack of semi-elliptical shape where dimensions of semi-minor & major axes are a = 1 mm and c = 5 mm, respectively. The plate is subjected to cyclic tensile loading of stress range S = 100 MPa and have been designed for service life of 1 million cycles (NT = 1.E6). The same question asked is to assess the remaining life of the plate. Solution. Following are step by step remaining life assessment according to the above procedure. 1. Based on S = 100 MPa and NT = 1.E6 the required quality category is determined from Fig. 17 in PD6493 [3] (or Fig. 16 [4]) as Q1. 2. Since a = 1 mm, c = 5 mm and B = 10 mm, then a/2c = 0.1 and a/B = 0.1, subsequently, equivalent edge flaw aeqv = 0.5 mm has been determined from Fig. 21(a) [3] (or Fig. 20(a) [4]). 3. Tolerable value of crack amax = (1/2)(1400/100)2 = 31.2 mm 4. Since aeqv < am then go to step 5 5. Entering Fig. A2 for remaining life curve of 10 mm plate of equivalent edge flaw aeqv = 0.5 mm i.e. a/B = 0.05 then interpolate for required quality category Q1 gives remaining life ratio Nx / NT = 0.35. This means the remaining life is Nx = 350,000 cycles. It is noted here that the remaining life of cracked welded plate is reduced by 42 % compared with that of the flat plate with similar crack size & shape under same loading condition. This is evidently due to stress concentration induced by weld geometry. 4. CONCLUSIONS A new simple procedure for assessing the remaining life of cracked component including cracked welded joint has been established based on the developed remaining life curves. The procedure is simple and practical whenever a crack is detected and evaluated in conjunction with already established assessment procedure given in PD 6493/BS7910. Subsequently, the remaining life of the cracked component/joint can be determined using the series of remaining life curves subjected to quality category and plate thickness as given in Figs. A1 to A5. Theoretical concept has been soundly established for this assessment procedure and examples of assessment have been given. However, additional experimental data are needed for its firm validation. ACKNOWLEDGEMENT This work has been carried out under University of Sydney U2000 Research Fellowship program and author would like to express his gratitude for the sponsorship. 10

REFERENCES [1] [2] [3] [4] [5] [6] [7]

[8]

[9] [10]

AS 4100: 1990. Fatigue, Section 11, Standards Association of Australia. WES 2850-1997: 1997. Method of Assessment for Flaws in Fusion Welded Joints with Respect to Brittle Fracture and Fatigue Crack Growth. Japanese Welding Engineering Society Standard. BSI PD 6493: 1991. Guidance on methods for assessing the acceptability of flaws in fusion welded structures. British Standard Institution, London. BS 7910: 1999. Guidance on methods for assessing the acceptability of flaws in metallic structures. British Standard Institution, London. IIW-XV-E - Doc. SC-XV-582-85: 1985. Recommended Fatigue Design Procedure For Hollow Section, Joints. International Institute of Welding, Strasbourg, France. Oehlers D. J., Gosh A. and Wahab M.A. 1995. Residual Strength Approach to Fatigue Design and Analysis. Journal of Structural Engineering, ASCE, Vol. 121, No. 9, pp. 1271-79 Nguyen, N. T. 2001. Residual-Strength-Based Assessment for Remaining Life of Cracked Welded Steel Structures. Research Report, U2000 project code: H1515 U2061. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney. Gosh A. 1996. A Residual Strength Approach for the Fatigue Analysis of Welded Components. Ph.D. Thesis, Department of Civil and Environmental Engineering, The University of Adelaide, Australia. BS 5400: 1980. Steel, concrete and composite bridges. Part 10: Code of practice for fatigue. British Standard Institution, London, UK. Nguyen, N. T. 1996. Advanced Modelling of the Fatigue of Butt -Welded Structures. Ph.D. Thesis, Department of Mechanical Engineering, The University of Adelaide, Australia.

APPENDIX Remaining Life Curves of a Cracked Component Subjected to Tensile Loading

Normalized remaining life, N x / NT

1

B = 5 mm 0.1

Q10 (62 MPa) Q9 (73 MPa) Q8 (85 MPa) Q7(100 MPa) Q6 (W), 115 MPa

0.01

Q5 (G), 135 MPa Q4 (F2), 163 MPa Q3 (F), 185 MPa Q2 (E), 218 MPa Q1 (D), 248 MPa

0.001 0

0.1

0.2

0.3

0.4

0.5

Normalized crack length, a / B

11

Fig. A1 Remaining life curves for 5 mm thick plate subjected to quality categories

Normalized remaining life, N x / NT

1

B = 10 mm Q10 (62 MPa)

0.1

Q9 (73 MPa) Q8 (85 MPa) Q7(100 MPa) Q6 (W), 115 MPa

0.01

Q5 (G), 135 MPa Q4 (F2), 163 MPa Q3 (F), 185 MPa Q2 (E), 218 MPa Q1 (D), 248 MPa

0.001 0

0.1

0.2

0.3

0.4

Normalized crack length, a / B

Fig. A2 Remaining life curves for 10 mm thick plate subjected to quality categories

Normalized remaining life, N x / NT

1

B = 20 mm Q10 (62 MPa)

0.1

Q9 (73 MPa) Q8 (85 MPa) Q7(100 MPa) Q6 (W), 115 MPa

0.01

Q5 (G), 135 MPa Q4 (F2), 163 MPa Q3 (F), 185 MPa Q2 (E), 218 MPa Q1 (D), 248 MPa

0.001 0

0.1

0.2

0.3

0.4

0.5

Normalized crack length, a / B

Fig. A3 Remaining life curves for 20 mm thick plate subjected to quality categories

12

Normalized remaining life, Nx /NT

1

B = 50 mm Q10 (62 MPa) 0.1

Q9 (73 MPa) Q8 (85 MPa) Q7(100 MPa) Q6 (W), 115 MPa

0.01

Q5 (G), 135 MPa Q4 (F2), 163 MPa Q3 (F), 185 MPa Q2 (E), 218 MPa Q1 (D), 248 MPa

0.001 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Normalized crack length, a / B

Fig. A4 Remaining life curves for 50 mm thick plate subjected to quality categories

Normalized remaining life, Nx / NT

1

B = 100 mm 0.1 Q10 (62 MPa) Q9 (73 MPa) Q8 (85 MPa)

0.01

Q7(100 MPa) Q6 (W), 115 MPa Q5 (G), 135 MPa Q4 (F2), 163 MPa

0.001

Q3 (F), 185 MPa Q2 (E), 218 MPa Q1 (D), 248 MPa

0.0001 0

0.1

0.2

0.3

0.4

Normalized crack length, a / B

Fig. A5 Remaining life curves for 100 mm thick plate subjected to quality categories

13