The Evaluation of the Threshold Stress Intensity Factor and the Fatigue Limit of Surface-Cracked Specimen Considering the Surface Condition

Home , Stress intensity factor

International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com The Evaluation of the Threshold Stress Intensity Factor and the Fatigue Limit of Surface-Cracked Specimen Considering the Surface Condition

Ki-Woo Nam1, Won-Gu Lee2 and Seok-Hwan Ahn3,* 1,2 Department of Materials Science and Engineering, Pukyong National University, Busan 48513, Republic of Korea. 3 Department of Aero Mechanical Engineering, Jungwon University, Chungbuk 28024, Republic of Korea.

Abstract cracks[1]. It was reported that the non-propagation of surface cracks is related to the constant threshold stress intensity In this study, the threshold stress intensity factor and fatigue factor for surface crack lengths larger than 0.5 mm [2]. For limit of surface-cracking materials were evaluated according cracks smaller than 0.5 mm, it was not the threshold stress to the variation of stress ratio and aspect ratio with reference intensity factor but rather the stress identical to the fatigue to the fatigue limit of a gentle-grind specimen, severe-grind limit that was the limit condition for very small defect specimen, and shot-peened severe-grind specimen. Surface propagation. For microcrack problems, the assumption of a cracks in the gentle-grind, severe-grind, and shot-peened small nonlinear domain does not hold. Haddad [3] introduced severe-grind specimens could be used to evaluate the a valid formula for the dependency of the threshold stress threshold stress intensity factor and fatigue limit according to intensity factor on the crack length by adding the microcrack the stress ratio and aspect ratio using the equivalent crack length to the crack length. Moreover, Tange et al. [4] provided length. As the surface crack length increased, the fatigue limit a more convenient formula for evaluating the threshold stress decreased rapidly at a small stress ratio and large aspect ratio. intensity factor by removing the microcrack length from the However, the depth of the surface cracks decreased rapidly at Haddad formula, and they conducted research on minimizing a small stress ratio and aspect ratio. As the surface crack the damage to shot-peened welds caused by surface cracks length increased, the threshold stress intensity factor rapidly using this formula and the Newman–Raju formula [5, 6-9]. increased at a small stress ratio and large aspect ratio. Moreover, Ando et al. [10] presented a formula for evaluating However, the surface crack depth rapidly increased at a small the threshold stress intensity factor considering the size of the stress ratio and aspect ratio. The reduction ratio of the fatigue plastic zone, so that the fatigue limits and threshold stress limit at the surface crack length of the same stress ratio was intensity factors of all surface-cracking materials could be larger than 0.4 at an aspect ratio 0.1. However, the surface evaluated. crack depth was larger than 0.1 at an aspect ratio of 0.4. For a surface crack length of the same stress ratio, the rate of In this study, the threshold stress intensity factors and fatigue increase in the threshold stress intensity factor was smaller limits of surface-cracking materials were evaluated according than 1.0 at an aspect ratio of 0.4; however, the surface crack to the stress ratio and surface crack aspect ratio with reference depth was larger than 1.0 at an aspect ratio of 0.4. This is to the fatigue limits of the gentle-grind specimen, severe-grind because when the aspect ratio became large, cracks specimen, and shot-peened severe-grind specimen [11], propagated in the depth direction rather than the surface considering the machining process. direction and at the same time when became similar to the surface crack length. Keywords: threshold stress intensity factor, fatigue limit, 2. FRACTURE MECHANICS OF A SEMIELLIPTICAL stress ratio, aspect ratio, surface crack length, surface crack SURFACE CRACK IN A FINITE PLATE depth The fatigue limit and threshold stress intensity factor of a semielliptical surface crack in a finite plate can be evaluated as follows. 1. INTRODUCTION When a through-wall crack with a crack length of 2푐 in an Most of the experiments to determine the fatigue crack growth infinite plate is subjected to the bending stress of 휎퐵, 퐾 can rate and the threshold stress intensity factor were performed be calculated using Equation (1). for large cracks and large through-wall cracks. As can be seen from actual fatigue failures, however, a failure occurs from 퐾 = 휎퐵√휋푐 (1) very small cracks and is initiated by their growth. The Meanwhile, the semielliptical surface crack 퐾 in a finite importance of small cracks was recognized from scientific and plate can be evaluated using the Newman–Raju formula [5]. practical perspectives, and it was found that small cracks do As shown in Fig. 1, when a semielliptical surface crack with a not follow the crack growth laws obtained from large surface crack length of 2푐 and a surface crack depth of 푎 in

* Corresponding author

802 International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com a finite plate is subjected to the uniform bending stress of 휎퐵, When a through-wall crack with a crack length of 2푐 exists 퐾 can be obtained using Equation (2) [10]. in an infinite plate, however, the threshold stress intensity factor can be evaluated using Equation (7).

푅 푅 ∆퐾푡ℎ(푐) = ∆휎휔푐 √휋푐 (7) 푅 In this case, ∆퐾푡ℎ(푙) according to the stress ratio (R) is obtained using the ASME standard formula in Equation (8).

푅 표 ∆퐾푡ℎ(푙) = ∆퐾푡ℎ(푙)√(1 − 푅) (8) The threshold stress intensity factor of a semielliptical surface crack can be obtained by substituting Equation (4) into Equation (7). When Equation (7) is applied to a semielliptical crack, it is the maximum value of 퐾 that determines ∆퐾푡ℎ. As 퐾 becomes largest when 훽 is largest in Equation (2), the maximum value of 훽 is substituted into Equation (5). Fig. 1. Schematic illustration of a finite plate containing a semi-circular crack 3. EVALUATION METHOD AND SPECIMENS

푎 푎 푐 푎 푎 푐 퐻( , , , ∅)퐹( , , , ∅) The production process is known to have significant effects on 퐾 = 푡 푐 푏 푡 푐 푏 휎 √휋푎 = 훽휎 √휋푎 (2) 푎 퐵 퐵 the fatigue characteristics of parts. Such effects are √푄( ) 푐 detrimental or beneficial, as shown in Table 1. where, 퐹 and 푄 are geometrical correction functions, 퐻 is Table 1. Factors affecting the fatigue characteristics of parts the correction function for the bending stress, 푡 is the thickness of the finite plate, 푏 is the half of the width of the Detrimental Beneficial finite plate, and ∅ is the angle of the tip of the semielliptical Hardening Carburizing surface crack. 훽 is the geometrical correction factor that integrated the geometrical correction functions. When the Grinding Honing length of a through-wall crack in an infinite plate that Machining Polishing represents the same 퐾 under the same stress is assumed to be Plating Burnishing the equivalent crack length 푐푒, Equations (1) and (2) become Equation (3). Welding Rolling EDM and ECM Shot peening 퐾 = 휎퐵√휋푐푒 = 훽휎퐵√휋푎 (3)

Summarizing Equation (3), the relationship between 푐푒 and 푎 can be expressed as shown in Equation (4). From a detrimental aspect, grinding, machining, and welding may cause metal fatigue cracks on the tensile surface. Curing, √푐푒 = 훽√푎 (4) plating, and electrical discharge machining may a leave hard, 푅 brittle surface. Electrochemical machining may damage or Therefore, the dependency of ∆퐾푡ℎ for the semielliptical weaken surface grain boundaries. From a beneficial aspect, all surface crack in a finite plate on the crack length can be the listed processes induce compressive residual stress, evaluated using Equation (5) derived by replacing 푐 of thereby improving the fatigue life. Shot peening is most Equation (1) with 푐푒 of Equation (4). commonly used, because it provides the maximum 2 −1 compressive residual stress to various materials and parts. ∆퐾푅 푅 푅 푎 −1 휋 푡ℎ(푙) ∆퐾푡ℎ = 2훽∆휎휔√ 푐표푠 { 2 ( 푅 ) + 1} (5) 휋 8훽 푎 ∆휎휔 Fig. 2 shows the S–N curves for various types of processing. The reference curve is for the case of the gentle-grind where 훽 is the function of ∅. The evaluation value of 퐾 specimen, which showed a fatigue limit of 414 MPa. The varies depending on the angle of the crack tip that evaluates severe-grind specimen showed a faster cutting speed and a 푅 푅 퐾. 휎휔 is the fatigue limit of the plate, and ∆퐾푡ℎ(푙) is the larger cut. In this case, large surface tensile residual stress that threshold stress intensity factor when a very long through-wall lowers fatigue strength occurs because of fatigue. As the crack 2푐0 exists in an infinite plate. The fatigue limit of a figure shows, the fatigue limit of the severe-grind specimen 푅 surface-cracking material (휎휔푐) can be obtained using was 338 MPa, which was approximately 18% lower than that Equation (6), which was derived by substituting Equation (4) of the gentle-grind specimen. The final curve represents the on the equivalent crack length into Equation (5) [10]. fatigue limit of the shot-peened severe-grind specimen. The 2 figure shows that this specimen exhibited a fatigue limit of 푅 ∆퐾푅 휋∆휎휔푐 휋 푡ℎ(푙) 614 MPa, which was approximately 48% higher than that of 푐푒 {푠푒푐 ( 푅 ) − 1} = ( 푅 ) (6) 2∆휎휔 8 ∆휎휔 the gentle-grind specimen. This increase in the fatigue limit occurred because the tensile residual stress caused by severe

803 International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com grinding was changed to compressive residual stress by shot the stress ratio was constant. Table 2 shows the conditions peening [7, 12-14]. used in the evaluation. Fig. 3 shows the relationship between the yield strength Table 2. Conditions used in the evaluation (휎 ) and threshold stress intensity factor (∆퐾0 ) of DNV 푦 푡ℎ(푙) ∆KR 0 F690 steel for offshore structures [15]. This is the relationship Stress th(푙) Aspect σω 0 ratio (R) (MPa√m) ratio (As) (MPa) between 휎푦 and ∆퐾푡ℎ(푙) obtained from various metal materials. As 휎푦 of DNV F690 steel is 850.32 MPa, 0 5.75 · Gentle grind: 414 0 1.0 · Severe grind: 338 ∆퐾푡ℎ(푙) is found to be approximately 5.75 MPa√m in the 0.4 4.45 figure. 4.0 · Severe grind+ Shot 0.8 2.57 peening : 614 828 4. RESULTS AND DISCUSSION

690 4.1 Relationship between the fatigue limit (훔퐑 ) and the Shot peened severe grind 훚퐜 614 MPa crack dimensions for the surface-cracking materials 푅 552 Figs. 4, 5, and 6 show the fatigue limit (휎휔(푐,푎)) values of the surface-cracking materials obtained from the gentle-grind, Gentle grind severe-grind, and shot-peened severe-grind specimens. In Stress (MPa) Stress 414 MPa 414 each figure, (a) represents the fatigue limit of the cracking Severe grind 338 MPa material according to the surface crack length “c”, and (b) represents the fatigue limit according to the surface crack 276 depth “a”. These were obtained using Equation (6). 7 7 7 7 8 2.0x10 4.0x10 6.0x10 8.0x10 1.0x10 푅 The fatigue limit (휎휔0) values of the gentle-grind specimen Cycles to failure were 414, 248, and 83 MPa at stress ratios of 0, 0.4, and 0.8, 푅 Fig. 2. S-N curves for various types of processing respectively. The fatigue limit (휎휔0) values of the severe- grind specimen were 338, 203, and 68 MPa at stress ratios of 푅 0, 0.4, and 0.8, respectively. The fatigue limit (휎휔0) values of 10 the shot-peened severe-grind specimen were 614, 368, and P P R=0 123 MPa at stress ratios of 0, 0.4, and 0.8, respectively. In this P P : ferrite pearlite 푅 P instance, the threshold stress intensity factors (∆퐾푡ℎ(푙)) when 8 P B : banite M : martensite a very long through-wall crack exists in an infinite plate were ) P 0.5 5.75, 4.45, and 2.57 MPa, respectively.

m 6 B B  B M B Fig. 4(a) shows the relationship between the fatigue limit M M 푅

MPa SB42 (휎 ) and the crack length c for the gentle-grind specimen,

( 휔푐

) 4 S35C B M M

( while Figs. 5(a) and 6(a) show such relationships for the S55C M th SK5 M severe-grind specimen and the shot-peened severe-grind

K  2 SCM4 specimen, respectively. For each specimen, the same results SB42 were obtained as follows. For R = 0, the fatigue limit of each Welten60 surface-cracking material decreased as the crack length 0 0 400 800 1200 1600 increased, regardless of the aspect ratio (As), but it decreased more rapidly when As was 1.0 than when it was 0.4. For R = y (MPa) 0.4, a tendency similar to that of R = 0 was observed. For R = Fig. 3. Relationship between yield strength and threshold 0.8, however, the fatigue limit of each surface-cracking stress intensity factor material decreased more slowly compared with the cases of R = 0 and R = 0.4. The specimens had a 50 mm width and a 10 mm thickness. Surface cracks were considered for the crack shapes, and the Fig. 4(b) shows the relationship between the fatigue limit 푅 aspect ratio (As) was set to 1.0 and 0.4. The stress ratio (R) of (휎휔푎) and the crack depth a for the gentle-grind specimen, the fatigue load was set to 0, 0.4, and 0.8, and a bending load while Figs. 5(b) and 6(b) show such relationships for the 0 was applied. The fatigue limit 휎휔 used was 414 MPa for the severe-grind specimen and the shot-peened severe-grind gentle-grind specimen, 338 MPa for the severe-grind specimen, respectively. For each specimen, the same results specimen, and 614 MPa for the shot-peened severe-grind were observed as follows. For R = 0, the fatigue limit of each specimen, as determined above. surface-cracking material decreased as the crack depth increased, as with the crack length, but it decreased more 푅 The fatigue limit (휎휔(푐,푎)) of each surface-cracking rapidly when the aspect ratio (As) was 0.4 than when it was material was obtained using Equation (6), and the result was 1.0. A similar tendency was observed for R = 0.4. For R = 0.8, 푅 substituted into Equation (7) to obtain ∆퐾푡ℎ(푐,푎) . In this however, the fatigue limit of each surface-cracking material instance, it was assumed that the maximum stress according to

804 International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com decreased more slowly compared with the cases of R = 0 and R = 0.4.

1000 1000

0 1/2 0 0 1/2 0  = 414 MPa, K = 5.75 MPam  = 414 MPa, K = 5.75 MPam w th(l) w th(l)

0.4 0.4 1/2  = 248 MPa, K = 4.45 MPam 0.4 0.4 1/2 , MPa,  = 248 MPa, K = 4.45 MPam , MPa, w th(l)

) w th(l)

)





 0.8 0.8 1/2 0.8 0.8 1/2 100  = 83 MPa, K = 2.57 MPam 100  = 83 MPa, K = 2.57 MPam w th(l) w th(l)

As=1.0 As=0.4 As=1.0 As=0.4 Gentle grind Gentle grind R=0

R=0 Fatigue limit

Fatigue limit 2W=50mm R=0.4 2W=50mm R=0.4 t=10mm R=0.8 t=10mm R=0.8 10 10 1E-3 0.01 0.1 1 1E-3 0.01 0.1 1 Crack length (c), mm Crack depth (a), mm (a) (b) Fig. 4. Fatigue limit according crack length (a) and crack depth (b) on gentle grind specimen

1000 1000

0 0 1/2 0 0 1/2  = 338 MPa, K = 5.75 MPam  = 338 MPa, K = 5.75 MPam w th(l) w th(l)

, MPa, 0.4 0.4 1/2 0.4 0.4 1/2 )  = 203 MPa, K = 4.45 MPam    , MPa, = 203 MPa, K = 4.45 MPa m

R w th(l) w th(l)

)







 100 0.8 0.8 1/2 100 0.8 0.8 1/2

 = 68 MPa, K = 2.57 MPam  = 68 MPa, K = 2.57 MPam w th(l) w th(l)

As=1.0 As=0.4 As=1.0 As=0.4 Severe grind R=0 Severe grind R=0 Fatigue limit 2W=50mm 2W=50mm R=0.4 Fatigue limit R=0.4 t=10mm R=0.8 t=10mm R=0.8 10 10 1E-3 0.01 0.1 1 1E-3 0.01 0.1 1 Crack length (c), mm Crack depth (a), mm (a) (b) Fig. 5. Fatigue limit according crack length (a) and crack depth (b) on severe grind specimen

1000 0 0 1/2 0 0 1/2  = 614 MPa, K = 5.75 MPam  = 614 MPa, K = 5.75 MPam w th(l) w th(l) 0.4 1/2 0.4 0.4 1/2 0.4  = 368 MPa, K = 4.45 MPam  = 368 MPa, K = 4.45 MPam w th(l) w th(l)

, MPa,

)

R R 0.8 0.8 1/2 0.8 0.8 1/2  = 123 MPa, K = 2.57 MPam  = 123 MPa, K = 2.57 MPam

wa wc w th(l) w th(l)



  100

As=1.0 As=0.4 As=1.0 As=0.4 Shot peened severe grind R=0 Shot peened severe grind R=0 2W=50mm

Fatigue limit Fatigue limit R=0.4 2W=50mm R=0.4 t=10mm R=0.8 t=10mm R=0.8 10 10 1E-3 0.01 0.1 1 1E-3 0.01 0.1 1 Crack length (c), mm Crack depth (a), mm (a) (b) Fig. 6. Fatigue limit according crack length (a) and crack depth (b) on shot peened severe grind specimen

805 International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com

4.2 Relationship between the threshold stress intensity exhibited the same results as follows. For R = 0, the threshold 푅 factor (∆퐾푡ℎ(푐,푎)) and the crack dimensions for the stress intensity factor increased as the crack length increased surface-cracking materials regardless of the aspect ratio (As), and it increased more rapidly when As was 1.0 than when it was 0.4. A similar Figs. 7, 8, and 9 show the threshold stress intensity factors tendency was observed for R = 0.4. For R = 0.8, however, the 푅 (∆퐾푡ℎ(푐,푎)) of the gentle-grind specimen, severe-grind threshold stress intensity factor increased more slowly specimen, and shot-peened severe-grind specimen according compared with the cases of R = 0 and R = 0.4. to the crack length and crack depth. In each figure, (a) Fig. 7(b) shows the relationship between the threshold stress represents the threshold stress intensity factor of each surface- 푅 cracking material according to the surface crack length “c”, intensity factor (∆퐾푡ℎ(푎)) and the crack depth a for the and (b) represents the threshold stress intensity factor gentle-grind specimen, while Figs. 8(b) and 9(b) show such according to the surface crack depth “a”. These were obtained relationships for the severe-grind specimen and the shot- using Equation (7). The threshold stress intensity factors peened severe-grind specimen, respectively. For each (∆퐾푅 ) of the three specimens were 5.75, 4.45, and 2.57 specimen, the same results were observed as follows. For R = 푡ℎ(푙) 0, the threshold stress intensity factor increased as the crack MPa at stress ratios of 0, 0.4, and 0.8, respectively. depth increased as with the crack length, but it increased more Fig. 7(a) shows the relationship between the threshold stress rapidly when the aspect ratio (As) was 0.4 than when it was 푅 intensity factor (∆퐾푡ℎ(푐)) and the crack length c for the 1.0. A similar tendency was observed for R = 0.4. For R = 0.8, gentle-grind specimen, while Figs. 8(a) and 9(a) show such however, the threshold stress intensity factor increased more relationships for the severe-grind specimen and the shot- slowly compared with the cases of R = 0 and R = 0.4. peened severe-grind specimen, respectively. Each specimen

6 6 0 0 1/2  = 414 MPa, K = 5.75 MPam w th(l) 0 0 1/2  = 414 MPa, K = 5.75 MPam 5 5 w th(l)

0.4 0.4 1/2  = 248 MPa, K = 4.45 MPam w th(l) 4 4 0.4 1/2 1/2 0.4 1/2  = 248 MPa, K = 4.45 MPam

m w th(l)



 3 3

MPa 0.8 0.8 1/2

MPa

0.8 0.8 1/2 ,  = 83 MPa, K = 2.57 MPam , w th(l)  = 83 MPa, K = 2.57 MPam R R w th(l)

th(a)

th(c) 2 2

As=1.0 As=0.4 

 As=1.0 As=0.4 R=0 Gentle grind 1 Gentle grind 1 R=0 2W=50mm R=0.4 2W=50mm R=0.4 t=10mm R=0.8 t=10mm R=0.8 0 0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Crack length (c), mm Crack depth (a), mm (a) (b) Fig. 7. Threshold stress intensity factor according crack length (a) and crack depth (b) on gentle grind specimen

6 6 0 0 1/2  = 338 MPa, K = 5.75 MPam w th(l)

0 0 1/2 5 5  = 338 MPa, K = 5.75 MPam w th(l)

0.4 0.4 1/2  = 203 MPa, K = 4.45 MPam 4 w th(l) 4

1/2

1/2 0.4 0.4 1/2

m   = 203 MPa, K = 4.45 MPam  w th(l) 3 3

MPa MPa 0.8 0.8 1/2

, 0.8 0.8 1/2 ,  R  = 68 MPa, K = 2.57 MPa m  = 68 MPa, K = 2.57 MPam R w th(l) w th(l)

th(c)

2 th(a) 2

K K  As=1.0 As=0.4 As=1.0 As=0.4  Severe grind R=0 1 Severe grind R=0 1 2W=50mm R=0.4 2W=50mm R=0.4 t=10mm R=0.8 t=10mm R=0.8 0 0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Crack length (c), mm Crack depth (a), mm (a) (b) Fig. 8. Threshold stress intensity factor according crack length (a) and crack depth (b) on severe grind specimen

806 International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com

6 6

0 0 1/2 0 0 1/2  = 614 MPa, K = 5.75 MPam  = 614 MPa, K = 5.75 MPam w th(l) 5 w th(l) 5

1/2 0.4 0.4 1/2

 4 4  = 368 MPa, K = 4.45 MPam 0.4 0.4 1/2 1/2  = 368 MPa, K = 4.45 MPam w th(l)

w th(l) m



MPa

, 3 3 0.8 0.8 1/2

R 0.8 0.8 1/2 MPa  = 123 MPa, K = 2.57 MPam  = 123 MPa, K = 2.57 MPam w th(l) w th(l) ,

th(c)

 2 th(a) 2

As=1.0 As=0.4 K As=1.0 As=0.4  Shot peened severe grind Shot peened severe grind R=0 R=0 1 1 2W=50mm 2W=50mm R=0.4 R=0.4 t=10mm t=10mm R=0.8 R=0.8 0 0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Crack length (c), mm Crack depth (a), mm (a) (b) Fig. 9. Threshold stress intensity factor according crack length (a) and crack depth (b) on shot peened severe grind specimen

5. CONCLUSION first in the depth direction rather than in the surface direction when the aspect ratio is high, and it propagates at the same Microdefects inside the materials or in the exterior of a time when it becomes similar to the crack length. structure develop into cracks over time. Such cracks affect the stability and reliability of the structure, thereby significantly reducing its service life. In this study, the threshold stress REFERENCES intensity factor and the fatigue limit were evaluated according to the stress ratio and the crack aspect ratio, considering the [1] Frost, N. E., 1957, “Non-propagating cracks in vee- surface cracks generated during the material machining notched specimens subject to fatigue loading”, The process. The results are as follows. Aeronautical Quarterly, Vol. 8, Issue 1 , pp. 1-20. (1) For the surface cracks of the gentle-grind, severe-grind, [2] Kitagawa, H. and Takahashi, S., 1976, “Applicability and shot-peened severe-grind specimens, the threshold stress of fracture mechanics to very small cracks or cracks in intensity factor and the fatigue limit could be evaluated the early stage. In: Proceedings of the second according to the stress ratio and the crack aspect ratio using international conference on mech. Behavior of matls., the equivalent crack length. ASM; pp. 627-631. (2) As the crack length increased, the fatigue limit decreased, [3] El Haddad, M. H., Topper, T. H. and Smith, K. N., and it decreased more rapidly when the stress ratio (R) was 1979, “Prediction of non propagating cracks”, lower and the aspect ratio (As) was higher. As the crack depth Engineering Fracture Mechanics, Vol. 11, Issue 3, pp. increased, however, the fatigue limit decreased more rapidly 573-584. when the stress ratio (R) was lower and the aspect ratio (As) was lower. [4] Tange, A., Akutu, T. and Takamura, N., 1991, “Relation between shot-peening residual stress (3) As the crack length increased, the threshold stress distribution and fatigue crack propagation life in spring intensity factor increased, and it increased more rapidly when steel,” Transactions of Japan Society of Spring the stress ratio was lower and the aspect ratio was higher. As Engineers, Vol. 36, pp. 47-53. the crack depth increased, however, the threshold stress intensity factor increased more rapidly when both the stress [5] Newman Jr, J. C. and Raju, I. S., 1981, “An empirical ratio and the aspect ratio were lower. stress-intensity factor equation for the surface crack”, Engineering Fracture Mechanics, Vol. 15, No. 1-2, pp. (4) Under the same stress ratio, as the crack length 185-192. increased, the fatigue limit decreased less rapidly when the aspect ratio was 0.4 than when it was 1.0. As the crack depth [6] Takahashi, K., Hayashi, T., Ando, K. and Takahashi F., increased, however, the fatigue limit decreased more rapidly 2010, “Evaluation of acceptable defect size by shot when the aspect ratio was 0.4 than when it was 1.0. The peening based on fracture mechanics,”Transactions of threshold stress intensity factor, however, increased less Japan Society of Spring Engineers, Vol. 55, pp. 25-30. rapidly when the aspect ratio was 0.4 than when it was 1.0 as the crack length increased under the same stress ratio. As the [7] Nakagawa, M., Takahashi, K., Osada, T., Okada, H. crack depth increased, however, the threshold stress intensity and Koike, H., 2014, “Improvement in fatigue limit by factor increased more rapidly when the aspect ratio was 0.4 shot peening for high-strength steel containing crack- than when it was 1.0. This is because the crack propagates like surface defect (Influence of surface crack aspect

807 International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 6 (2019), pp. 802-808 © International Research Publication House. http://www.irphouse.com

ratio),” Transactions of Japan Society of Spring Engineers, Vol. 59, pp. 13-18. [8] Fueki, R., Abe, H., Takahashi, K., Ando, K., Houjou, K. and Handa, M., 2015 “Harmless by peening for stainless steel containing a crack at the weld toe zone,”High Pressure Institute of Japan, Vol. 53, pp. 30-38. [9] Yamada, Y., Eto, H., Konya, J. and Takahashi, K., 2018, “Influence of crack-like surface defects on the fatigue limit of nitrocarburized carbon steel,” 2018 International Conference on Material Strength and Applied Mechanics, Vol. 372. pp. 1-6. doi:10.1088/1757-899X/372/1/012005 [10] Ando, K., Fueki, R., Nam, K. W., Matsui, K. and Takahashi, T., 2019, “A study on the unification of the threshold stress intensity factor for micro crack growth,” Transactions of Japan Society of Spring Engineers, Vol. 64, pp. 39-44. [11] http://texas-shotpeening.metalimprovement.com/reason _to_shot_peen_metal_fatigue.php [12] Kobayashi, M., Matsui, T. and Murakami, Y., 1998, “Mechanism of creation of compressive residual stress by shot peening,” International Journal of Fatigue, Vol. 20, pp. 351-357. [13] Torres, M. A. S. and Voorwald, H. J. C., 2002, “An evaluation of shot peening, residual stress and stress relaxation on the fatigue life of AISI 4340 steel,” International Journal of Fatigue, Vol. 24, pp. 877-886. [14] Takahashia, K., Osedoa, H., Suzukia, T. and Fukuda, S., 2018, “Fatigue strength improvement of an aluminum alloy with a cracklike surface defect using shot peening and cavitation peening,” Engineering Fracture Mechanics, Vol. 193, pp. 151-161. [15] Kitsunai, y., 1980, “Effect of microstructure on fatigue crack growth behavior of carbon steels”, The Society of Materials Science of Japan, Vol. 29, pp. 1018-1023.

808