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Mode II fatigue failures at rail butt-welds
Engineering Failure Analysis 12 (2005) 157–165 www.elsevier.com/locate/engfailanal
Mode II fatigue failures at rail butt-welds S. Beretta *, M. Boniardi, M. Carboni, H. Desimone Dipartimento di Meccanica, Politecnico di Milano, Via La Masa 34, Milano 20158, Italy Received 9 February 2004; accepted 10 February 2004 Available online 24 June 2004
Abstract Some typical fatigue failures of butt-welded rails consist of fractures of the web. In the early stage, the crack propagates parallel to the rail surface but, after a while, it tends to propagate with a slant surface. The aim of the present work is to analyse the mechanisms involved in crack propagation in rail webs and the crack path, which are the two essential elements for a future determination of the rail inspection intervals. At first, a fractographic analysis of a typical failure revealed the typical features of mode II and showed that mode I is involved only after the final crack kinking. Then, FEM analyses of an observed fracture were carried out in order to determinate the KI and KII history at different positions of the crack tip during the passage of the typical loads induced by trains. The results have shown that the initial flaw tends to follow a path where DKII is close to maximum values and a small superimposed KI traction is present and after the kinking, the flaw tends to maximise mode I crack propagation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Railway engineering; Rail failures; Fatigue crack growth; Finite elements analysis; Fractography
1. Introduction and failure description Fig. 1 shows two typical crack failures found in rail webs and whose origin are the butt-welded joints. As it can be observed in Fig. 1(a) and (b), the crack path is characterised by a first part where the flaw grows in longitudinal direction, almost parallel to the surface and a second part where it presents two kinking angles: at the leading tip (in the rolling direction sense) the crack grows towards the rail tread while at the trailing tip the crack grows towards the rail base. Fig. 1(c) shows the scheme of another typical fracture pattern, where the crack initially grows in longitudinal direction and then it exhibits a bifurcation, both at the leading and trailing tips. The two described types of change in crack path suggested that, in these failures, firstly cracks grow under mode II and then, at the kinking or branching point, they switch to mode I growth. Several cracks produced by rolling contact fatigue, due to wheel/rail contact, have been reported in literature [1–5]. In *
Corresponding author. Tel.: +39-02-2399-8246; fax: +39-02-2399-8202. E-mail address: [email protected] (S. Beretta).
1350-6307/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2004.02.004
158
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
Fig. 1. (a) and (b) Crack with double kinking. (c) Schematic of another typical crack presenting branching.
these cases, mode II propagation has been detected and it has been proven [6] that this crack propagation mode is enhanced by the high compression stresses due to contact. However, the failures here considered are located near to the rail neutral axis, where compression stresses are not so important because of the distance from the contact affected zone. As in the cases of surface cracks started by rolling contact fatigue, a downward crack branching or kinking may lead to fracture of the whole rail and to danger of derailment [7], so it is important to analyse the criteria governing crack branching. Indeed, if a mode II propagation in the first part of the crack is confirmed, it would be an important basis for future defect assessment design criteria of welding joints and the location of them along the rail line.
2. Fractographic observations In order to understand the fracture mechanism, SEM observations were carried out. In all the considered samples, the fracture surfaces were damaged by frictional rubbing and wear of the opposing surfaces themselves, as reported by Wong et al. [7]. Thus, in practice, it was neither possible to identify the crack nucleation point nor the fatigue striations. For this reason, the rail fracture surface was cut along its symmetry plane, as it can be seen in Fig. 2(a). Then, after polishing the inner face, the specimens were observed by SEM, in order to see the main properties of the crack path. Fig. 2(b) shows the crack path before and after the kinking. It can be noted that before the kinking (Fig. 2(c)), the fracture surface shows a high damaged pattern while, after the kinking (Fig. 2(d)), the damage strongly decreases. It has been reported in literature [8,9], that mode II is associated with a higher level of plasticity damage and short branching. This observation seems to support the starting hypothesis: the change in damage pattern can be associated with the change of crack propagation mode, from a starting mode II to a final mode I.
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
159
Fig. 2. SEM analyses of the leading kinking region: (a) general view of cracked rail; (b) the kinking (rotated 180°); (c) surface fracture before the kinking; (d) surface fracture after the kinking.
Fig. 3 shows the SEM photographs for the central part of the crack (nucleation region). It can be seen, once again, a high level of damage associated with the propagation. Furthermore, Fig. 3(d) shows a secondary fracture surface presenting a stepwise pattern: this is a typical kind of damage associated with mode II propagation [10,11].
3. FEM analysis 3.1. General description In order to confirm the hypothesis of a first mode II propagation followed by branching or kinking transition to mode I, 3D FEM analysis were carried out using the commercial finite element package ABAQUS Version 6.2 [12]. Twenty-node solid elements have been used and crack surfaces contact was introduced by master–slave surface method. Fig. 4 shows the finite element mesh for the first step. KI and KII values at the crack tip were obtained from relative crack opening displacement DUz and sliding displacement DUx of crack nodes, by means of well known formulations [13]: KI ¼
2pGDUz pffiffiffiffiffiffiffiffi ð3 4mÞ 2pL
as L ! 0
ð1Þ
KII ¼
pGDUx pffiffiffiffiffiffiffiffi 2ð1 mÞ 2pL
as L ! 0
ð2Þ
160
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
Fig. 3. SEM analyses at the welded joint: (a)–(c) mode II damage on the fracture surface; (d) a secondary crack showing a stepwise pattern.
where G is the shear modulus, m is the Poisson’s ratio and L is the distance from the crack tip. The variation of KI and KII for leading crack tip with various positions of the wheel is shown in Fig. 5. The local KI and KII for a prospective a kinking angle are obtained by [14]: K I ðaÞ ¼ C11 KI þ C12 KII ;
ð3Þ
K II ðaÞ ¼ C21 KI þ C22 KII ;
ð4Þ
where K I ðaÞ and K II ðaÞ are the local stress intensity factors at the tip of the kink and KI and KII are the stress intensity factors for the main crack, obtained by FEM analysis and Eqs. (1) and (2). Indeed, the coefficients Cij are given by: C11 ¼
a 1 3 3a cos þ cos ; 4 2 4 2
a 3 3a sin þ sin ; C12 ¼ 4 2 2
ð5aÞ
ð5bÞ
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
161
Fig. 4. Finite element mesh.
Fig. 5. Variation of stress intensity factors with different position of the wheel load.
a 1 3a sin C21 ¼ þ sin ; 4 2 2
ð5cÞ
a 3 1 3a þ cos : C22 ¼ cos 4 2 4 2
ð5dÞ
For each angle and for each simulated step (in Fig. 5 is only represented the case of a ¼ 0, that means no kinking), two main values are obtained: DKII and DKI . For the last one, crack closure is neglected. 3.2. Crack growth direction Several FEM simulations were carried out for different steps of crack propagation. Fig. 6 shows, for the rail failure represented on Fig. 1(a), the three simulated crack tip positions. Figs. 7–9 show the results for
162
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
Fig. 6. (a) Analysed points for the leading tip. (b) The convention for co-ordinate axes and for kinking angle ‘‘a’’. (c) The mesh for the step #3.
the leading tip. In all cases, a represents the angle between possible kinking and the present direction of the crack: a ¼ 0 means non deviation (Fig. 6). At the first and second step, it could be appreciate (Figs. 7 and 8)
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
163
80
real
KI
70
∆K [Mpa.mm^0.5]
KII 60 50 40 30 20 10 0 -90
-60
-30
0
30
60
90
α [degree] Fig. 7. Leading tip at step 1: variation of KI and KII with the kink angle.
140 real
KI
∆K [Mpa.mm^0.5]
120
KII
100 80 60 40 20 0 -90
-60
-30
0
30
60
90
α [degree] Fig. 8. Leading tip at step 2: variation of KI and KII with the kink angle.
that propagation is associated with a maximum level of DKII together with a small KI . In particular, the actual direction of propagation corresponds to a DKII value near to the maximum one which is ‘‘helped’’ by a small KI . Fig. 9, in turn, shows the results for the stress intensity factors when the crack is just before kinking. As it can be observed, the real angle of propagation corresponds to maximum mode I, so it is clear that kinking is produced in order to change mode II propagation in mode I propagation. Similar results were obtained for the trailing tip.
4. Concluding remarks and future work The propagation of fatigue crack paths in welded rails has been analysed. It was confirmed, by both SEM observations and Finite Element analysis, that this kind of crack, starting from a welded joint,
164
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
160
∆K [Mpa.mm^0.5]
140
final kinking
KI KII
120 100 80 60 40 20 0 -90
-60
-30
0
30
60
90
α [degree] Fig. 9. Leading tip at step 3: variation of KI and KII with the kink angle. It can be see that the final kinking angle maximises KI .
propagates firstly in mode II and then, by a crack path deviation realised in a kinking or branching, switches to mode I propagation. As the starting mode of propagation is mode II, it would be important to analyse the influence of the position of the welded joint in the rail on the variation of DKII . In all the cases considered here, the weld were always at the middle between two sleepers. Furthermore, it would be important to analyse crack grow rate, in order to define the inspection intervals for welded rails.
Acknowledgements We wish to thank Mr. S. Bavila and Mr. D. Polidori for their contribution (FEM Analysis) to the present work.
References [1] Ishida M, Abe N. Experimental study on rolling contact fatigue from the aspect of residual stress. Wear 1996;191:65–71. [2] Kondo K, Yoroizaka K, Sato Y. Cause, increase, diagnosis, countermeasures and elimination of Shinkansen shelling. Wear 1996;191:199–203. [3] Bold PE, Brown MW, Alien RJ. Shear mode crack growth and rolling contact fatigue. Wear 1991;144:307–317. [4] Bogdanski S, Brown MW. Modelling the three-dimensional behaviour of shallow rolling contact fatigue cracks in rails. Wear 2002;253:17–25. [5] Kim JK, Kim CS. Fatigue crack growth behaviour of rail steel under mode I and mixed mode loadings. Mater Sci Eng 2002;A338:191–201. [6] Melin S. When does a crack grow under mode II conditions? Int J Fract 1986;30:103–114. [7] Wong SE, Bold PE, Brown MW, Alien RJ. A branch criterion for shallow angled rolling contact fatigue cracks in rails. Wear 1996;191:45–53. [8] Murakami Y, Takahashi K. Torsional fatigue of a medium carbon steel containing an initial small surface crack introduced by tension-compression fatigue: crack branching, non propagation and fatigue limit. Fatigue Fract Eng Mater Struct 1998;21(12):1473–1484. [9] Murakami Y, Sakae C, Hamada S. Mechanism of rolling contact fatigue and measurement of DKII;th for steels. In: Beynon JH, Brown MW, Lindley TC, Smith RA, Tomkins B, editors. Engineering against fatigue. Balkema: Rotterdam; 1999. p. 473–485. [10] ASM Handbook. Fractography, vol. 12. Ohio: ASM International; 1997.
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165 [11] [12] [13] [14]
165
ASM Handbook. Fatigue and Fracture, vol. 19. Ohio: ASM International; 1996. ABAQUS User’s Manual. Hibbit: Karlsson & Sorensen Inc; 2000. Anderson TL. Fracture mechanics. Boca Raton: CRC Press; 1995. Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. J Basic Eng 1963;85:519–527.
Mode II fatigue failures at rail butt-welds S. Beretta *, M. Boniardi, M. Carboni, H. Desimone Dipartimento di Meccanica, Politecnico di Milano, Via La Masa 34, Milano 20158, Italy Received 9 February 2004; accepted 10 February 2004 Available online 24 June 2004
Abstract Some typical fatigue failures of butt-welded rails consist of fractures of the web. In the early stage, the crack propagates parallel to the rail surface but, after a while, it tends to propagate with a slant surface. The aim of the present work is to analyse the mechanisms involved in crack propagation in rail webs and the crack path, which are the two essential elements for a future determination of the rail inspection intervals. At first, a fractographic analysis of a typical failure revealed the typical features of mode II and showed that mode I is involved only after the final crack kinking. Then, FEM analyses of an observed fracture were carried out in order to determinate the KI and KII history at different positions of the crack tip during the passage of the typical loads induced by trains. The results have shown that the initial flaw tends to follow a path where DKII is close to maximum values and a small superimposed KI traction is present and after the kinking, the flaw tends to maximise mode I crack propagation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Railway engineering; Rail failures; Fatigue crack growth; Finite elements analysis; Fractography
1. Introduction and failure description Fig. 1 shows two typical crack failures found in rail webs and whose origin are the butt-welded joints. As it can be observed in Fig. 1(a) and (b), the crack path is characterised by a first part where the flaw grows in longitudinal direction, almost parallel to the surface and a second part where it presents two kinking angles: at the leading tip (in the rolling direction sense) the crack grows towards the rail tread while at the trailing tip the crack grows towards the rail base. Fig. 1(c) shows the scheme of another typical fracture pattern, where the crack initially grows in longitudinal direction and then it exhibits a bifurcation, both at the leading and trailing tips. The two described types of change in crack path suggested that, in these failures, firstly cracks grow under mode II and then, at the kinking or branching point, they switch to mode I growth. Several cracks produced by rolling contact fatigue, due to wheel/rail contact, have been reported in literature [1–5]. In *
Corresponding author. Tel.: +39-02-2399-8246; fax: +39-02-2399-8202. E-mail address: [email protected] (S. Beretta).
1350-6307/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2004.02.004
158
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
Fig. 1. (a) and (b) Crack with double kinking. (c) Schematic of another typical crack presenting branching.
these cases, mode II propagation has been detected and it has been proven [6] that this crack propagation mode is enhanced by the high compression stresses due to contact. However, the failures here considered are located near to the rail neutral axis, where compression stresses are not so important because of the distance from the contact affected zone. As in the cases of surface cracks started by rolling contact fatigue, a downward crack branching or kinking may lead to fracture of the whole rail and to danger of derailment [7], so it is important to analyse the criteria governing crack branching. Indeed, if a mode II propagation in the first part of the crack is confirmed, it would be an important basis for future defect assessment design criteria of welding joints and the location of them along the rail line.
2. Fractographic observations In order to understand the fracture mechanism, SEM observations were carried out. In all the considered samples, the fracture surfaces were damaged by frictional rubbing and wear of the opposing surfaces themselves, as reported by Wong et al. [7]. Thus, in practice, it was neither possible to identify the crack nucleation point nor the fatigue striations. For this reason, the rail fracture surface was cut along its symmetry plane, as it can be seen in Fig. 2(a). Then, after polishing the inner face, the specimens were observed by SEM, in order to see the main properties of the crack path. Fig. 2(b) shows the crack path before and after the kinking. It can be noted that before the kinking (Fig. 2(c)), the fracture surface shows a high damaged pattern while, after the kinking (Fig. 2(d)), the damage strongly decreases. It has been reported in literature [8,9], that mode II is associated with a higher level of plasticity damage and short branching. This observation seems to support the starting hypothesis: the change in damage pattern can be associated with the change of crack propagation mode, from a starting mode II to a final mode I.
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
159
Fig. 2. SEM analyses of the leading kinking region: (a) general view of cracked rail; (b) the kinking (rotated 180°); (c) surface fracture before the kinking; (d) surface fracture after the kinking.
Fig. 3 shows the SEM photographs for the central part of the crack (nucleation region). It can be seen, once again, a high level of damage associated with the propagation. Furthermore, Fig. 3(d) shows a secondary fracture surface presenting a stepwise pattern: this is a typical kind of damage associated with mode II propagation [10,11].
3. FEM analysis 3.1. General description In order to confirm the hypothesis of a first mode II propagation followed by branching or kinking transition to mode I, 3D FEM analysis were carried out using the commercial finite element package ABAQUS Version 6.2 [12]. Twenty-node solid elements have been used and crack surfaces contact was introduced by master–slave surface method. Fig. 4 shows the finite element mesh for the first step. KI and KII values at the crack tip were obtained from relative crack opening displacement DUz and sliding displacement DUx of crack nodes, by means of well known formulations [13]: KI ¼
2pGDUz pffiffiffiffiffiffiffiffi ð3 4mÞ 2pL
as L ! 0
ð1Þ
KII ¼
pGDUx pffiffiffiffiffiffiffiffi 2ð1 mÞ 2pL
as L ! 0
ð2Þ
160
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
Fig. 3. SEM analyses at the welded joint: (a)–(c) mode II damage on the fracture surface; (d) a secondary crack showing a stepwise pattern.
where G is the shear modulus, m is the Poisson’s ratio and L is the distance from the crack tip. The variation of KI and KII for leading crack tip with various positions of the wheel is shown in Fig. 5. The local KI and KII for a prospective a kinking angle are obtained by [14]: K I ðaÞ ¼ C11 KI þ C12 KII ;
ð3Þ
K II ðaÞ ¼ C21 KI þ C22 KII ;
ð4Þ
where K I ðaÞ and K II ðaÞ are the local stress intensity factors at the tip of the kink and KI and KII are the stress intensity factors for the main crack, obtained by FEM analysis and Eqs. (1) and (2). Indeed, the coefficients Cij are given by: C11 ¼
a 1 3 3a cos þ cos ; 4 2 4 2
a 3 3a sin þ sin ; C12 ¼ 4 2 2
ð5aÞ
ð5bÞ
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
161
Fig. 4. Finite element mesh.
Fig. 5. Variation of stress intensity factors with different position of the wheel load.
a 1 3a sin C21 ¼ þ sin ; 4 2 2
ð5cÞ
a 3 1 3a þ cos : C22 ¼ cos 4 2 4 2
ð5dÞ
For each angle and for each simulated step (in Fig. 5 is only represented the case of a ¼ 0, that means no kinking), two main values are obtained: DKII and DKI . For the last one, crack closure is neglected. 3.2. Crack growth direction Several FEM simulations were carried out for different steps of crack propagation. Fig. 6 shows, for the rail failure represented on Fig. 1(a), the three simulated crack tip positions. Figs. 7–9 show the results for
162
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
Fig. 6. (a) Analysed points for the leading tip. (b) The convention for co-ordinate axes and for kinking angle ‘‘a’’. (c) The mesh for the step #3.
the leading tip. In all cases, a represents the angle between possible kinking and the present direction of the crack: a ¼ 0 means non deviation (Fig. 6). At the first and second step, it could be appreciate (Figs. 7 and 8)
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
163
80
real
KI
70
∆K [Mpa.mm^0.5]
KII 60 50 40 30 20 10 0 -90
-60
-30
0
30
60
90
α [degree] Fig. 7. Leading tip at step 1: variation of KI and KII with the kink angle.
140 real
KI
∆K [Mpa.mm^0.5]
120
KII
100 80 60 40 20 0 -90
-60
-30
0
30
60
90
α [degree] Fig. 8. Leading tip at step 2: variation of KI and KII with the kink angle.
that propagation is associated with a maximum level of DKII together with a small KI . In particular, the actual direction of propagation corresponds to a DKII value near to the maximum one which is ‘‘helped’’ by a small KI . Fig. 9, in turn, shows the results for the stress intensity factors when the crack is just before kinking. As it can be observed, the real angle of propagation corresponds to maximum mode I, so it is clear that kinking is produced in order to change mode II propagation in mode I propagation. Similar results were obtained for the trailing tip.
4. Concluding remarks and future work The propagation of fatigue crack paths in welded rails has been analysed. It was confirmed, by both SEM observations and Finite Element analysis, that this kind of crack, starting from a welded joint,
164
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165
160
∆K [Mpa.mm^0.5]
140
final kinking
KI KII
120 100 80 60 40 20 0 -90
-60
-30
0
30
60
90
α [degree] Fig. 9. Leading tip at step 3: variation of KI and KII with the kink angle. It can be see that the final kinking angle maximises KI .
propagates firstly in mode II and then, by a crack path deviation realised in a kinking or branching, switches to mode I propagation. As the starting mode of propagation is mode II, it would be important to analyse the influence of the position of the welded joint in the rail on the variation of DKII . In all the cases considered here, the weld were always at the middle between two sleepers. Furthermore, it would be important to analyse crack grow rate, in order to define the inspection intervals for welded rails.
Acknowledgements We wish to thank Mr. S. Bavila and Mr. D. Polidori for their contribution (FEM Analysis) to the present work.
References [1] Ishida M, Abe N. Experimental study on rolling contact fatigue from the aspect of residual stress. Wear 1996;191:65–71. [2] Kondo K, Yoroizaka K, Sato Y. Cause, increase, diagnosis, countermeasures and elimination of Shinkansen shelling. Wear 1996;191:199–203. [3] Bold PE, Brown MW, Alien RJ. Shear mode crack growth and rolling contact fatigue. Wear 1991;144:307–317. [4] Bogdanski S, Brown MW. Modelling the three-dimensional behaviour of shallow rolling contact fatigue cracks in rails. Wear 2002;253:17–25. [5] Kim JK, Kim CS. Fatigue crack growth behaviour of rail steel under mode I and mixed mode loadings. Mater Sci Eng 2002;A338:191–201. [6] Melin S. When does a crack grow under mode II conditions? Int J Fract 1986;30:103–114. [7] Wong SE, Bold PE, Brown MW, Alien RJ. A branch criterion for shallow angled rolling contact fatigue cracks in rails. Wear 1996;191:45–53. [8] Murakami Y, Takahashi K. Torsional fatigue of a medium carbon steel containing an initial small surface crack introduced by tension-compression fatigue: crack branching, non propagation and fatigue limit. Fatigue Fract Eng Mater Struct 1998;21(12):1473–1484. [9] Murakami Y, Sakae C, Hamada S. Mechanism of rolling contact fatigue and measurement of DKII;th for steels. In: Beynon JH, Brown MW, Lindley TC, Smith RA, Tomkins B, editors. Engineering against fatigue. Balkema: Rotterdam; 1999. p. 473–485. [10] ASM Handbook. Fractography, vol. 12. Ohio: ASM International; 1997.
S. Beretta et al. / Engineering Failure Analysis 12 (2005) 157–165 [11] [12] [13] [14]
165
ASM Handbook. Fatigue and Fracture, vol. 19. Ohio: ASM International; 1996. ABAQUS User’s Manual. Hibbit: Karlsson & Sorensen Inc; 2000. Anderson TL. Fracture mechanics. Boca Raton: CRC Press; 1995. Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. J Basic Eng 1963;85:519–527.