PSI - Issue 18

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Ivica Čamagić et al. / Procedia Structural Integrity 18 (2019) 385 – 390 Author name / Structural Integrity Procedia 00 (2018) 000–000 Author name / Structural Integrity Procedia 00 (2018) 000–000 Author name / Structural Integrity Procedia 00 (2018) 000–000 Author name / Structural Integrity Procedia 00 (2018) 000–000 Author name / Structural Integrity Procedia 00 (2018) 000–000

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Life is determined by integrating eq. 1: Life is determined by integrating eq. 1: Life is determined by integrating eq. 1: Life is determined by integrating eq. 1: Life is determined by integrating eq. 1:

 a  a  a  a  a

0 0 0 0 d 0 d d d d

a a a

d d d

(2) (2) (2) (2) (2)

N           N N N N

     , f K R  f K R  f K R  d f K R  a d f K R  a , , , ,

    

a a a a a

Since the function f (  K , R ) is typically composite, the solution of this integral can be rarely determined in closed form, thus the integration must be carried out numerically. The simplest form of function f (  K , R ) is the Paris model, thus expression 2 now becomes. [10]: Since the function f (  K , R ) is typically composite, the solution of this integral can be rarely determined in closed form, thus the integration must be carried out numerically. The simplest form of function f (  K , R ) is the Paris model, thus expression 2 now becomes. [10]: Since the function f (  K , R ) is typically co posite, the solution of this integral can be rarely determined in closed form, thus the i tegration must be carried out nu erically. The simplest form of function f (  K , R ) is the Paris model, thus expression 2 now becomes. [10]: Since the function f (  K , R ) is typically composite, the solution of this integral can be rarely determined in closed form, thus the i tegration must be carried out numerically. The simplest form of function f (  K , R ) is the Paris model, thus expression 2 now becomes. [10]: Since the function f (  K , R ) is typically co posite, the solution of this integral can be rarely determined in closed form, thus the integration must be carried out numerically. The simplest form of function f (  K , R ) is the Paris model, thus expression 2 now becomes. [10]: d

 a a 0  d a a 0  d a a 0  d a a 0  d a a 0

a a a a a

(3) (3) (3) (3) (3)

C C 1 C 1 C 1 C 1 1

d d

  N   N   N   N   N

         d    d    d

               m m m m m a           a a a a

a a a a a

              

              

Y Y Y Y Y

W W W W W

where Δ N is the number of cycles needed for crack growth, from initial crack length a 0 to critical length a c . The correction factor Y = Y (a /W ) for a crack in a component is typically represented as a long polynomial or in table form, thus assuming that Δ σ = const. and that it does not depend on a, numerical integration imposes itself as the solution. Such integration is best solved using computers, although even without them the procedure is not unacceptably long. It should be pointed out that during the aforementioned linear integration procedures, positive retardation is not taken into account, thus the results obtained are conservative, from the safety standpoint. In the case that the first approximation is adopted so that Y does not depend on crack length a , equation 3 can be written as: where Δ N is the number of cycles needed for crack growth, from initial crack length a 0 to critical length a c . The correction factor Y = Y (a /W ) for a crack in a component is typically represented as a long polynomial or in table form, thus assuming that Δ σ = const. and that it does not depend on a, numerical integration imposes itself as the solution. Such integration is best solved using computers, although even without them the procedure is not unacceptably long. It should be pointed out that during the aforementioned linear integration procedures, positive retardation is not taken into account, thus the results obtained are conservative, from the safety standpoint. In the case that the first approximation is adopted so that Y does not depend on crack length a , equation 3 can be written as: where Δ N is the number of cycles needed for crack growth, f om initial crack length a 0 to critical length a c . The correct on factor Y = Y (a /W ) for a crack in a component is typically repres nted as a long polynomial or in table form, thus assuming that Δ σ = const. and that it does n t depend on a, numerical integration imp ses itself as the solution. S ch integration is bes solved using computers, although even without them the procedure is not unacceptably long. It should be pointed out that during the afore entioned linear integration procedures, positive retardation is not taken into account, thus the results obtained are conservative, from the safety stand oint. In the case that the first approximation is adopted so that Y does not depend on crack length a , equation 3 can be written as: where Δ N is the number of cycles needed for crack growth, f om initi l crack length a 0 to critical length a c . The correct on fac or Y Y (a /W ) for a crack in a component is typically repres nted as a long polynomial or in table form, thus assuming that Δ σ = const. and that it does not depend on a, numerical integration imposes itself as the solution. Such integration is best solved using compu ers, although even without them the rocedure is not unacceptably long. It should be pointed out that during the aforementioned lin ar integration procedures, positive retardation is not taken into account, thus the results obtained are conservative, from the safety standpoint. In the case that the first approximation is adopted so that Y does not depend on crack length a , equation 3 can be written as: where Δ N is the number of cycles needed for cr ck growth, f om initial crack l ngth a 0 to critical length a c . The correction fac or Y Y (a /W ) for a crack in a component is typically represented as a long polynomial or in table form, thus assuming t t Δ σ = const. and that it does t depend on a, num rical integration imposes itself as the solution. Such integration is best solved using co puters, although ven without them the procedu is not u acceptably lo g. It should be point d out that during the aforementioned linear integrati n procedures, p sitive retardati is not taken into account, thus the results obtained are conservative, from the safety standpoint. In the case that the first approximation is adopted so that Y does not depend on crack length a , equation 3 can be written as:

d a a

m m m m m 2 2 2 2 2

1 1 1 1 1

    

a a a a a a a a a a

  m a a 0   d m a a 0   d m a a a 0   d m a a a 0   d m a a a 0

(4) (4) (4) (4) (4)

  N   N   N   N   N

d d d d d

     C Y C Y C Y C Y C Y

    

    

thus, after integration, the solution is obtained in closed form as: thus, after integration, the solution is obtained in closed form as: thus, after integration, the solution is obtained in closed form as: thus, after integration, the solution is obtained in closed form as: thus, after integration, the solution is obtained in closed form as: m m

1     1     1     1     1     0 0 0

           

1     1     1     1     1     d d d

              

2 2 m 2 m 2 m 2 m

2 2 m 2 m 2 m 2 m

0 a a a a 0 a

d a a a a d a

1 1 1 1 1

    

(5) (5) (5) (5) (5)

  N   N   N   N   N

    

     C Y C Y C Y C Y C Y

     a  a  a  a  a 

2 2 m 2 m 2 m 2    m m

m m m m m

    

1 1 1 1 1

    

It should be pointed out that this approximation leads to a non-conservative solution compared to solutions which take into account that Y = Y(a) and which need to be determined using numerical methods [10]. Structural integrity and remaining life assessment of the reactor, for a nearly constant amplitude load, similar to loads in exploitation, i.e. the number of cycles necessary for crack growth from initial to critical length, is calculated using equation 5. Input test parameters are the following:  Location of the potential crack , i.e. whether it occurs in the PM, WM or the HAZ  Initial crack is the crack which can be detected by external non-destructive test methods, and for the reactor in question, it must not exceed 5 mm in length.  Load variation in the reactor , from the least favourable case, wherein the stress σ is close to yield stress R p 0.2 of the tested material (211 MPa), to the real working mode, i.e. the levels of maximum working stress for the reactor in question, measured using tensometry, in exploitation (46 MPa), [5,7].  Critical (allowed) crack length , which was varied from 5 mm to critical crack length a c , obtained by fracture mechanics parameters testing at working temperature of 540°C, for new and exploited PM, WM and HAZ, on both new and exploited PM sides.  Paris equation constants, C and m, determined by fatigue crack growth parameter testing, at temperature of 540°C, for new and exploited PM, WM and HAZ, on new and exploited PM sides [4].  Coefficient Y , a geometric term, which depends on the ratio of crack length and reactor PM thickness, and can be found in literature [2], for the case of a surface cracks and for different a/W ratios. Results of remaining life assessment of the reactor, i.e. the number of cycles Δ N , are shown in tables 5 and 6 for new and exploited PM, table 7 for WM and tables 8 and 9 for HAZ, from new and exploited PM sides, while taking into account that reactors in exploitation are constantly subjected to variable loads. It should be pointed out that this approximation leads to a non-conservative solution compared to solutions which take into account that Y = Y(a) and which need to be determined using numerical methods [10]. Structural integrity and remaining life assessment of the reactor, for a nearly constant amplitude load, similar to loads in exploitation, i.e. the number of cycles necessary for crack growth from initial to critical length, is calculated using equation 5. Input test parameters are the following:  Location of the potential crack , i.e. whether it occurs in the PM, WM or the HAZ  Initial crack is the crack which can be detected by external non-destructive test methods, and for the reactor in question, it must not exceed 5 mm in length.  Load variation in the reactor , from the least favourable case, wherein the stress σ is close to yield stress R p 0.2 of the tested material (211 MPa), to the real working mode, i.e. the levels of maximum working stress for the reactor in question, measured using tensometry, in exploitation (46 MPa), [5,7].  Critical (allowed) crack length , which was varied from 5 mm to critical crack length a c , obtained by fracture mechanics parameters testing at working temperature of 540°C, for new and exploited PM, WM and HAZ, on both new and exploited PM sides.  Paris equation constants, C and m, determined by fatigue crack growth parameter testing, at temperature of 540°C, for new and exploited PM, WM and HAZ, on new and exploited PM sides [4].  Coefficient Y , a geometric term, which depends on the ratio of crack length and reactor PM thickness, and can be found in literature [2], for the case of a surface cracks and for different a/W ratios. Results of remaining life assessment of the reactor, i.e. the number of cycles Δ N , are shown in tables 5 and 6 for new and exploited PM, table 7 for WM and tables 8 and 9 for HAZ, from new and exploited PM sides, while taking into account that reactors in exploitation are constantly subjected to variable loads. It should be pointed out that t is approximation l ads to a no -conservative solution compared to solutions which take into ac o nt that Y = Y(a) and wh ch need to be determined using numerical methods [10]. Structural integri y and remaining life assessment of the reactor, for a nearly constant amplitude load, simi r to loads in exploitation, i.e. the number of cycles necessary for crack growth from initial to critical length, is calculated using equation 5. Input test parameters are the following:  Location of the potential crack , i.e. wh her it occurs in the PM, WM or the HAZ  Initial crack is he crack which can be de ected by external non-destructive test methods, and for the reactor in question, t must ot xc ed 5 mm in length.  Load variation in the reactor , from the least favourable case, wherein the stress σ is close to yield stress R p 0.2 of the tested materi l (211 MPa), to the real working mode, i.e. the levels of maximum working stress for the reactor in question, measured using tensometry, in exploitation (46 MPa), [5,7].  Critical (allowed) crack length , which was varied from 5 mm to critical crack length a c , obtained by fracture mechanics parameters testing at working temperature of 540°C, for new and exploited PM, WM and HAZ, on both new and exploited PM sides.  Paris equation c nstants, C and m, determined by fatigue crack growth parameter testing, at temperature of 540°C, for new a d exploited PM, WM and HAZ, on new and exploited PM sides [4].  Coefficient Y , a geomet ic term, which depends on the ratio of crack length and reactor PM thickness, and can be found in literature [2], for the case of a surface cracks and for different a/W ratios. R su ts of remaining life assessment of the reactor, i.e. the number of cycles Δ N , are shown in tables 5 and 6 for new nd exploited PM, table 7 for WM and tables 8 and 9 for HAZ, from new and exploited PM sides, while taking into account that reactors in exploitation are constantly subjected to variable loads. It should be pointed out that this approximation leads to a non-conservative solution compared to solutions which take into account that Y = Y(a) and which ne d to be d termined using numerical methods [10]. Structural integrity and remaining life assessment of the reactor, for a nearly constant amplitude load, simi r to loads in exploitation, i.e. the number of cycles necessary for crack growth from initial to critical length, is calculated using equation 5. Input test parameters are the following: Location of the potential crack , i.e. whether it occurs in the PM, WM or the HAZ  Initial crack is the crack which can be detected by external non-destructive test methods, and for the reactor in question, it must not exceed 5 mm in length.  Loa variation in the reactor , from the least favourable case, wherein the stress σ is close to yield stress R p 0.2 of the tested materi l (211 MPa), to the real working mode, i.e. the levels of maximum working stress for the reactor in question, measured using tensometry, in exploitation (46 MPa), [5,7].  Critical (allowed) crack length , which was varied from 5 mm to critical crack length a c , obtained by fracture mechanics parameters testing at working temperature of 540°C, for new and exploited PM, WM and HAZ, on both new and exploited PM sides.  Paris equation constants, C and m, determined by fatigue crack growth parameter testing, at temperature of 540°C, for new and exploited PM, WM and HAZ, o new and exploited PM sides [4].  Coefficient Y , a geometric term, which depends on the ratio of crack length and reactor PM thickness, and can be found in literature [2], for the case of a surfac cracks and for different a/W ratios. R su ts of remaining life assessment of the reactor, i.e. the number of cycles Δ N , are shown in tables 5 and 6 for new and exploited PM, table 7 f r WM and tables 8 and 9 for HAZ, from new and exploited PM sides, while taking into account that reactors in exploitation are constantly subjected to variable loads. It should be pointed out that this approximation leads to a non-conservative solution compared to solutions which take into account that Y = Y(a) and which ne d to be d termined using numerical methods [10]. Structural integrity and remaining life assessment of the reactor, for a nearly constant amplitude load, simil r to loads in exploitation, i.e. the number of cycles necessary for crack growth from initial to critical length, is calculated using equation 5. Input test parameters are the following: Location of the potential crack , i.e. whether it occurs i the PM, WM or the HAZ  Initial crack is the crack which can be detected by external non-destructive test methods, and for the reactor in question, it must not exceed 5 mm in length.  Load variation in the reactor , from the least favourable case, wherein the stress σ is close to yield stress R p 0.2 of the tested materi l (211 MPa), to the real working mode, i.e. the levels of maximum working stress for the reactor in question, measured using tensometry, in exploitation (46 MPa), [5,7].  Critical (allowed) crack length , which was varied from 5 mm to critical crack length a c , obtained by fracture mechanics parameters testing at working temperature of 540°C, for new and exploited P , and HAZ, on both new and exploited PM sides.  Paris equation constants, C and m, determined by fatigue crack growth parameter testing, at temperature of 540°C, for new a d exploited PM, WM and HAZ, o new and exploited PM sides [4].  Coefficient Y , a geometric term, which depends on the ratio of crack length and reactor P thickness, and can be found in literature [2], for the case of a surface cracks and for different a/W ratios. Results of remaining life assessment of the reactor, i.e. the number of cycles Δ N , are shown in tables 5 and 6 for new nd exploited PM, table 7 f r WM and tables 8 and 9 for HAZ, from new and exploited PM sides, while taking into account that reactors in exploitation are constantly subjected to variable loads.