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An approach for prediction of fatigue strength of shot peened components
Engineering Fracture Mechanics 71 (2004) 501–512 www.elsevier.com/locate/engfracmech
An approach for prediction of fatigue strength of shot peened components M. Guagliano *, L. Vergani Dipartimento di Meccanica, Politecnico di Milano, Via La Masa, 34-20158 Milano, Italy Received 30 October 2002; accepted 31 October 2002
Abstract In this paper the problem of predicting and optimising the fatigue strength of shot peened specimens is dealt with. A series of notched cylindrical specimens, peened by using different parameters, was fatigue tested, being the aim to determine the improvement of the fatigue limit of the treated specimens. After the tests, the specimens were observed at the SE microscope and non-propagating microcracks were found. On the basis of this experimental evidence it was considered that the fatigue alleviation due to shot peening is mainly due to the ability of stopping crack propagation. A finite element procedure of the cracked notched specimens was established, with the aim of calculating the stress intensity factor including the applied load, the residual stresses and the contact between the crack faces. The results enable the prediction of the improvement of fatigue strength due to shot peening. 2003 Elsevier Ltd. All rights reserved. Keywords: Shot peening; Residual stresses; Fatigue threshold
1. Introduction Shot peening is a common process to improve the fatigue strength of metal components [1,2]. It consists in impacting a surface by a flow of spheroidal shots with a kinetic energy sufficient to cause plastic strain of the sub-surface layer of material and, consequently, to induce a residual stress field, compressive near the surface, useful to prevent fatigue crack initiation or to stop fatigue crack propagation. Notwithstanding the wide diffusion of shot peening and several studies about it, this treatment is today considered more an art than a science. This is due to the fact that the fatigue strength improvement induced by shot peening are not clearly related to the treatment parameters (shot type, dimensions, velocity, angle of impact, . . .). In fact, the peening intensity is measured by means of the Almen intensity, that is the residual arc height of a peened strip of assigned material and dimensions: this type of measure cannot give useful information about the residual stress profile in the material and, consequently, gives only an qualitative indication about the fatigue strength improvement [3–5]. Besides, it is well known that, till nowadays, a
*
Corresponding author. Tel.: +39-2-2399-8206; fax: +39-2-2399-8202. E-mail address: [email protected] (M. Guagliano).
0013-7944/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0013-7944(03)00017-1
502
M. Guagliano, L. Vergani / Engineering Fracture Mechanics 71 (2004) 501–512
quantitative criterion able to take into consideration the residual stress induced by shot peening on fatigue strength has not been developed. However, recent researches agree in evidencing that fatigue alleviation due to shot peening or other plastic deformation treatment is mainly due to the ability of the residual stresses in stopping the microcrack propagation and not in preventing fatigue crack initiation [6–9]. Moreover, a certain importance is attributed to the hardening of the plastically deformed layer of material [2], even if, till nowadays, this effect has not been well quantified. With this fact in mind, it follows that the definition of an approach for predicting the fatigue strength of shot peened elements should be based on fracture mechanics. Consequently, it requires the knowledge of the stress intensity factor range in a load cycle. This latter should be compared with the fatigue threshold value of the material to determine the fatigue improvement induced by shot peening. When the dimension of the crack is comparable with the one of the microstructural barriers the threshold stress intensity factor should the one concerning the effective crack dimension. An approach of this type is not immediate since it requires the introduction of the residual stress field in the calculation and also needs to take into account the contact between the crack faces during the load cycle. This latter is influenced by the residual stress profile and can strongly affect the crack opening and closure cycle, thus modifying the actual stress intensity factor range. This makes the problem non-linear and the superposition principle unsuitable. On the other hand, neglecting the crack face contact can strongly affect the crack closure behaviour and lead to inaccurate results [10,11]. In the present paper an approach for fatigue alleviation prediction of shot peened specimens based on the considerations just underlined is presented. Fatigue test on shot peened notched specimens were executed, being the aim the determination of the fatigue limit. Subsequent observations at a SE microscope allowed researchers to verify the presence of non-propagating microcracks. The residual stresses were measured by means of an X-ray diffractometer. Finite element analyses simulating the notched and cracked specimens were carried out and the stress intensity factor calculated by considering the residual stress state and the crack closure due to the contact of the crack faces. The complexity of the case made necessary to use the ‘‘sub-modelling’’ technique, that requires to define two models; the first one simulating the entire specimen, the second one reproducing the cracked zone. The results show how the residual stresses modify the effective crack opening cycle and the fatigue strength. In particular, after a calibration based on some experimental results, the present approach allows for the determination of the residual stress trend that maximise fatigue alleviation and, consequently, the optimal peening parameters.
2. Material and experimental tests The material tested is a low alloy steel known as 39NiCrMo3 according the Italian code (UTS ¼ 1053 MPa, Yield strength ¼ 940 MPa, E ¼ 206 000 MPa, elongation ¼ 20%). The steel was quenched in oil and tempered. Experimental rotary bending fatigue tests carried out on unnotched specimens allowed to determine the fatigue limit of the material, rFaf ¼ 440 MPa. In Fig. 1 the geometry of the tested specimens is shown: it is possible to note the geometrical discontinuity that causes a numerically evaluated theoretical stress concentration factor Kt equal to 1.45. The application of the ‘‘stair-case’’ method allowed to determine the fatigue limit of the notched specimens under rotary bending fatigue cycles, r0Faf ¼ 295 MPa. Two series of shot peened specimens with the same geometry were tested: the first one was peened by using shots with a diameter equal to 0.6 mm, the second one was peened by using shots with a diameter equal to 0.3 mm. For both the specimen series the Almen intensity was equal to 12 A and the impact angle was 90. The hardness of the shots was 50 HRC. The fatigue tests were performed in air at a speed of 2000
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Fig. 1. Geometry of the notched specimens tested.
rpm up to a duration of 107 cycles. In this case too, the results were analyzed by the ‘‘stair case’’ sequence and they showed that the same Almen intensity lead to different fatigue limit if different peening parameters are used. In fact the fatigue limit was r0Faf ¼ 420 MPa for the specimens peened by using 0.6 mm shots and r0Faf ¼ 370 MPa for the specimens peened by using 0.3 mm shots. Experimental measurements carried out by using the X-ray diffraction technique (Italstructures APD 2000 diffractometer, sin2 W method, Cr radiation, Vn filter, 2h 156) measurements allowed one to obtain the residual stress profiles in the shot peened specimens. The in-depth measurements were performed by removing the surface material with an electropolishing device. In Fig. 2 the trend of the residual stresses experimentally measured is shown. It is possible to note that the residual stress trend changes by using the different peening parameters: in particular it is possible to not that the residual stress value on the surface and the maximum compressive residual stress are larger by using 0.6 mm shots.
(a)
Depth (mm) 0.0
0.1
0.2
0.3
0.4
0.5
Residual Stress (MPa)
0 -200 -400 -600 -800
(b)
Depth (mm)
Residual Stress (MPa)
0.0
0.1
0.2
0.3
0.4
0.5
0 -200 -400 -600 -800
Fig. 2. Axial residual stress trend for the specimens peened by using (a) 0.3 mm shots and (b) 0.6 mm shots.
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Fig. 3. Front view of some non-propagating crack.
In this latter case also the depth at which the maximum compressive residual stress takes place is larger. On the contrary, the depth of the compressed area is not significantly influenced by the peening parameters used. Further measurements performed at the end of the fatigue test on the run-out specimens allowed to determine that the residual stress relaxation during the test is no larger than 20%. Microhardness measurements (applied weight equal to 2 N) on longitudinal sections of the specimens, permitted researchers to assess that hardness is almost uniform in both the specimen series and equal to 350 HV.
Fig. 4. Section view of one non-propagation crack, at different magnification factors (275·, 420·).
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At the end of the fatigue tests, SEM analyses were carried out on the run-out specimens to verify the presence of non-propagating crack and to measure their dimensions. Moreover, sections of the same specimen allowed one to determine the depth of the non-propagating cracks. In Fig. 3 some images of the most stressed zone (at the beginning of the shoulder fillet) taken at the SEM are reported: it is possible to note the typical circumferential extension of a non-propagating crack. Further information was taken from the observation of some section of the run-out specimens; in this way it was possible to evaluate the depth of the non-propagated cracks. In Fig. 4 two images show a nonpropagated crack at different magnification factors. By these investigations it was possible to evaluate that the depth of the arrested cracks varies from about 0.15 to about 0.3 mm.
3. Finite element models The estimation of the fatigue strength of the shot peened specimens needs the knowledge, not only of the stress state due to the applied load but also of the residual stresses. In fact, it is well known that the fatigue life can be strongly influenced by the residual stresses induced by both mechanical processes or surface treatments. If elements with complex geometry are considered, the effective stress state determination requires the use of some numerical technique. Among these latter the finite element methods is particularly suited for this objective, both for its versatility and for the possibility to use very powerful commercial codes. However, the correct utilisation of this technique needs the analysis to be accurately defined and the results to be carefully evaluated. The experimentally observed cracks suggested the definition of a finite element model of the cracked specimen for the prediction of the fatigue strength by considering the applied loads and the residual stresses. Thus, the crack front geometry and the load cycle (rotary bending) make necessary to define a threedimensional model with 20 nodes brick elements: besides, the correct simulation of the linear elastic crack simulation needs the standard brick element requires to distort them according to the ‘‘one-quarter’’ point technique. Finally, the correct simulation of the problem makes necessary to model the contact between the crack faces: this aspect was solved by using some special contact element included in the finite element code (Abaqus) library. The contact algorithm uses a weighted master–slave one, and enforces the constraint that one surface may not penetrate in the other. In this way it was possible to check the crack opening–closure cycle and to simulate sliding between the crack faces. The respect of all these requirements makes difficult the definition of an adequate FE model; to overcome this difficult the ‘‘sub-modelling’’ technique was used. This latter needs two different models, one for the entire model, the other one relative to the particular of the crack, but allows for accurate determination of the stress intensity factors in the three-dimensional cases in which the geometry prevents the construction of an accurate global finite element model including the crack. In fact, it is possible to define a very refined mesh for the crack front zone in the local model while the global model has the only requisite to correctly simulate the behaviour of the specimen far from the zone of interest. The global model schematises the notched specimen (Fig. 5a and b) and was realised by using 20 node brick elements and by using contact elements; the crack was included in the model to avoid the overestimation of the stiffness even if the mesh was not so focussed on the crack front. Due to the geometric and load symmetry, only one half of the cylinder was schematised and the nodes lying on the symmetry plane constrained with symmetric boundary conditions. The second model (called ‘‘local model’’) considers only the zone of the specimen surrounding the crack: also for this model the element used are bricks with 20 nodes and second order shape functions (see Fig. 5c and d).
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Fig. 5. Global (a, b) and local (c, d) models of the cracked specimen.
The ‘‘sub-modelling’’ technique needs to perform two analyses: in the first one the global model is used. The second analysis considers the local model at which the displacements calculated with the global model in correspondence of the boundary surfaces of the local model are applied as boundary conditions. To introduce the residual stresses field both in the global and in the local model a sub-routine was developed: this latter is able to assign a residual stress value at every integration point as a function of the distance from the free surface. In this way it was possible to reproduce the residual stress state experimentally measured and to numerically test the effectiveness of some residual stress profiles. Numerical analysis of the entire rotary bending fatigue cycle of the cracked specimen was executed. The shape and the dimensions of the cracks included in the models were similar to the ones experimentally measured. The shape was assumed semi-elliptical. The surface semi-lengths a considered varies from 0.2 to 0.8 mm while the depth c is one half of the surface semi-length for all the models constructed. The stress intensity factor was then calculated from the value of the J -integral by means of the ‘‘virtual crack extension technique’’ and by applying the nodal displacement substitution method. Once the trend of the stress intensity factor in a rotary bending fatigue cycle is known it is possible to calculate the effective KI range, defined as: DKeff ¼ Kmax Kopening in which Kopening indicates the value of the smallest stress intensity factor values that makes the crack completely opened. The residual stress fields reported in Fig. 2 were included in the FE analyses.
4. Numerical results At first, the displacement field continuity between the global and the local model was verified. In Fig. 6 the total displacement map is shown: it can be noted that along the boundary of the local model the
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Fig. 6. Global and local FE model displacement field superposition: the continuity is verified.
correspondence between the global and the local model displacement is satisfactory (the maximum deviation is 6%). An entire loading cycle was simulated, by varying the direction of the applied loads with respect of the crack orientation. Then the crack opening–closure was analyzed: in Fig. 7 the map of the relative displacement of the crack faces during the load application is shown (the picture refers to the residual stress trend obtained with 0, 6 mm shots and a nominal stress equal to 420 MPa, that is to say the fatigue limit of the peened specimen): Fig. 7a refers to a null bending moment, Fig. 7b refers to one half of the maximum bending moment and Fig. 7c refers to the entire applied bending moment. It is possible to note that the crack opening takes place after a relevant part of load is applied: this is due to the residual stresses applied that strongly affects the actual crack opening cycle. The same considerations can be done by looking at Fig. 8, that shows the contact pressure on the crack faces during the same load cycle. It is clear that the deepest point of the crack front is the first one that opens, while the zone near the crack front remains closed for most part of the cycle. This is good agreement with [12,13]. In Fig. 9 the map of the axial stresses (S33) near the crack front is shown, both when the crack is partially close and when the crack is completely open. In the partially closed configuration it is possible to observe that the crack tip on the free surface is closed while the tip at the deepest point of the crack front is opened: this is caused by the trend of the residual stresses. The same qualitative considerations can be drawn for the analyses of the 0.3 mm shot peened specimen. The analyses showed that the effective opening cycle depends on the residual stress state induced by shot peening. So it is possible to affirm that not only the surface residual stress affects the fatigue strength of the peened components but also the maximum compressive residual stress and its depth with respect to the surface of the specimen. Since this latter quantity is the one mostly influenced by the peening conditions, the choice of the treatment parameters should be oriented to have a compressed depth related to the length of the stopped cracks, that seem to be included in a interval characteristic of the peened material. In other words, the Almen intensity should be chosen on the basis of generating a residual stress field with an inversion point (depth at with the residual stresses change sign) approximately equal to the crack depth and a depth of the maximum compressive stress shorter than the crack depth.
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Fig. 7. Trend of the relative displacements (mm) of the crack faces during the load application (the dark area indicates the crack closure zone).
To confirm the previous consideration, the effective stress intensity factor range (DKeff ¼ Kmax Kopening ), was calculated, considering the residual stresses induced by the two peening conditions tested and an applied nominal stress equal to the fatigue limit of each treatment condition. In Table 1 the results are shown:
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Fig. 8. Trend of the contact pressure (MPa) of the crack faces during the load application (the dark area indicates the crack opening zone).
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Fig. 9. Axial stress (MPa) near the crack front: (a) partially closed crack and (b) totally opened crack.
Table 1 DKeff for different crack depths considering two different peening conditions (the applied stress is equal to the fatigue limit) p p Crack depth (lm) DKeff (MPa m) DKeff (MPa m) (0.6 mm shot, r ¼ 420 MPa) (0.3 mm shot, r ¼ 370 MPa) 150 200 250 300 400
1.20 3.21 5.47 6.45 13.80
1.71 3.33 5.62 7.42 14.32
it is possible to note that for crack depths similar to those experimentally observed (0.15–0.3 mm), DKeff is similar for the two peening conditions. Consequently, since for these depths the cracks have stopped, it is possible to consider the calculated values close to the effective threshold stress intensity factor of the peened specimens. It is interesting to observe that the crack depth at which the cracks have stopped are entirely subjected to the compressive residual stress field induced by shot peening: this can help in choosing the optimal peening parameters. This is also confirmed by the high values of DKeff when the crack is deep enough to include the tensile residual stress field, that makes faster fatigue crack propagation. Furthermore, to verify the above considerations, an analysis was made considering a residual stress trend with the same surface value, the same maximum compressive residual stress but at a distance from the surface equal to one half with respect of the one shown in Fig. 2b. Also the compressed zone depth was one half of the experimental one. The result showed an effective stress intensity factor range 30% greater of the ones shown in Table 1: this means that in this case the effectiveness of shot peening will be minor. Other simulations were executed considering the residual stresses field but not the crack face contact (that is to say by applying the superposition between the residual and the applied stress intensity factor): the results do not allow the interpretation of the experimental data. This evidence permits to underline one more time the importance of considering the contact between the crack faces for the estimation of the fatigue strength of the peened components. At last, calculations were done by considering very short cracks (0.03–0.1 mm), the experimentally measured residual stresses and the crack face contact: the results show that the crack remains close for all the fatigue cycle. This fact can be interpreted bearing in mind that the crack depth is now similar to the material grain size and the fatigue crack is in stage I [2], is influenced by the shear stresses and not by the residual stresses. Since the real cracks did not arrest for these small sizes but propagated till 0.1–0.2 mm, it can be considered an indirect confirmation of the goodness of the numerical model.
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5. Conclusions Fatigue alleviation due to shot peening was investigated by means of experimental tests and observations and by means of numerical analyses. The experimental fatigue tests allowed to determine the presence of non-propagating crack with typical depth (0.15–0.3 mm), that seems to depend mainly on the material used. On the basis of the experimental evidence, it was assumed that the beneficial effect of shot peening is to relate to the residual stress ability to arrest crack propagation. A finite element approach was developed able to simulate the cycling variation of loading on the notched specimens, the presence of the crack, the closure due to the crack faces and the residual stresses induced by shot peening. This approach allowed to analyze the role played by the residual stresses in preventing crack opening and arrest fatigue crack propagation. The calculations permitted to evidence that, for an applied stress equal to the fatigue limit of the treated specimens, the DKeff value does not vary appreciably by varying the peening conditions, and can be assumed as the threshold value of DK. The influence of the peening parameters that characterise the residual stress profile on DKth was studied: the results shows that the depth at which the maximum compressive residual stress occurs with respect of the material grain size is the most important factor in determining the fatigue threshold. The approach can help in optimising the shot peening parameters in relation of the application of interest and, if the results will be confirmed also on material different from the one considered here, can help to correctly choose the shot peening parameters with limited experimental effort.
Acknowledgements The research was supported by a Ministerial grant, whose responsible, Prof. Edoardo Rovida is thanked. We would like to thank Ing. Michele Bandini (Peen Service srl) for shot peening execution.
References [1] Marsh KJ, editor. Shot peening: techiques and applications. London, UK: EMAS; 1993. [2] Miller KJ. Materials science perspective of metal fatigue resistance. Mater Sci Technol 1993;9:453–62. [3] Guagliano M. Relating the Almen intensity to residual stresses induced by shot peening: a numerical approach. J Mater Process Technol 2001;110:277–86. [4] Cao W, Fathallah R, Castex L. Correlation of Almen arc height with residual stresses in shot peening process. Mater Sci Technol 1995;11(9):967–73. [5] Guagliano M, Vergani L, Bandini M, Gili F. An approach to relate the shot peening parameters to the induced residual stresses. In: Nakonieczcy A, editor. Proceedings of the ICSP7, 7th International Conference on Shot Peening. Warsaw: IMP; 1999. p. 274– 82. [6] Kloos KH, M€ uller C, Gregory JK. Fatigue properties of specimens similar to components deep rolled under optimised conditions. Int J Fatigue 1987;9:35–42. [7] Wagner L, M€ uller C, Gregory JK. Effect of surface rolling and shot peening on notched fatigue strength in A1 2024. DGM 1993;9:181–6. [8] Batista AC, Dias AM, Lebrun JL, Le Flour JC, Inglebert G. Contact fatigue of automotive gears: evolution and effects of residual stresses introduced by surface treatments. Fatigue Fract Engng Mater Struct 2000;23:217–28. [9] Song PS, Wen CC. Crack closure and crack growth behaviour in shot peened fatigued specimen. Engng Fract Mech 1999;63:295– 304. [10] Zhu XY, Shaw JD. Correlation of fatigue crack growth behaviour with crack closure in peened specimens. Fatigue Fract Engng Mater Struct 1995;18:811–20.
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[11] Vallellano C, Navarro A, de los Rios ER. Application of microstructural fracture mechanics to shot-peened components. In: Proceedings of the ECF 12––Fracture from Defects, Sheffield. 1998. p. 145–50. [12] Lin XB, Smith RA. Stress intensity factors for semi-elliptical internal surface cracks in autofrettaged thick-walled cylinders. J Strain Anal 1997;32:351–63. [13] Dai DN, Nowell D, Hills DA. Partial closure and friction slip of 3-D cracks. Int J Fract 1993;63:89–99.
An approach for prediction of fatigue strength of shot peened components M. Guagliano *, L. Vergani Dipartimento di Meccanica, Politecnico di Milano, Via La Masa, 34-20158 Milano, Italy Received 30 October 2002; accepted 31 October 2002
Abstract In this paper the problem of predicting and optimising the fatigue strength of shot peened specimens is dealt with. A series of notched cylindrical specimens, peened by using different parameters, was fatigue tested, being the aim to determine the improvement of the fatigue limit of the treated specimens. After the tests, the specimens were observed at the SE microscope and non-propagating microcracks were found. On the basis of this experimental evidence it was considered that the fatigue alleviation due to shot peening is mainly due to the ability of stopping crack propagation. A finite element procedure of the cracked notched specimens was established, with the aim of calculating the stress intensity factor including the applied load, the residual stresses and the contact between the crack faces. The results enable the prediction of the improvement of fatigue strength due to shot peening. 2003 Elsevier Ltd. All rights reserved. Keywords: Shot peening; Residual stresses; Fatigue threshold
1. Introduction Shot peening is a common process to improve the fatigue strength of metal components [1,2]. It consists in impacting a surface by a flow of spheroidal shots with a kinetic energy sufficient to cause plastic strain of the sub-surface layer of material and, consequently, to induce a residual stress field, compressive near the surface, useful to prevent fatigue crack initiation or to stop fatigue crack propagation. Notwithstanding the wide diffusion of shot peening and several studies about it, this treatment is today considered more an art than a science. This is due to the fact that the fatigue strength improvement induced by shot peening are not clearly related to the treatment parameters (shot type, dimensions, velocity, angle of impact, . . .). In fact, the peening intensity is measured by means of the Almen intensity, that is the residual arc height of a peened strip of assigned material and dimensions: this type of measure cannot give useful information about the residual stress profile in the material and, consequently, gives only an qualitative indication about the fatigue strength improvement [3–5]. Besides, it is well known that, till nowadays, a
*
Corresponding author. Tel.: +39-2-2399-8206; fax: +39-2-2399-8202. E-mail address: [email protected] (M. Guagliano).
0013-7944/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0013-7944(03)00017-1
502
M. Guagliano, L. Vergani / Engineering Fracture Mechanics 71 (2004) 501–512
quantitative criterion able to take into consideration the residual stress induced by shot peening on fatigue strength has not been developed. However, recent researches agree in evidencing that fatigue alleviation due to shot peening or other plastic deformation treatment is mainly due to the ability of the residual stresses in stopping the microcrack propagation and not in preventing fatigue crack initiation [6–9]. Moreover, a certain importance is attributed to the hardening of the plastically deformed layer of material [2], even if, till nowadays, this effect has not been well quantified. With this fact in mind, it follows that the definition of an approach for predicting the fatigue strength of shot peened elements should be based on fracture mechanics. Consequently, it requires the knowledge of the stress intensity factor range in a load cycle. This latter should be compared with the fatigue threshold value of the material to determine the fatigue improvement induced by shot peening. When the dimension of the crack is comparable with the one of the microstructural barriers the threshold stress intensity factor should the one concerning the effective crack dimension. An approach of this type is not immediate since it requires the introduction of the residual stress field in the calculation and also needs to take into account the contact between the crack faces during the load cycle. This latter is influenced by the residual stress profile and can strongly affect the crack opening and closure cycle, thus modifying the actual stress intensity factor range. This makes the problem non-linear and the superposition principle unsuitable. On the other hand, neglecting the crack face contact can strongly affect the crack closure behaviour and lead to inaccurate results [10,11]. In the present paper an approach for fatigue alleviation prediction of shot peened specimens based on the considerations just underlined is presented. Fatigue test on shot peened notched specimens were executed, being the aim the determination of the fatigue limit. Subsequent observations at a SE microscope allowed researchers to verify the presence of non-propagating microcracks. The residual stresses were measured by means of an X-ray diffractometer. Finite element analyses simulating the notched and cracked specimens were carried out and the stress intensity factor calculated by considering the residual stress state and the crack closure due to the contact of the crack faces. The complexity of the case made necessary to use the ‘‘sub-modelling’’ technique, that requires to define two models; the first one simulating the entire specimen, the second one reproducing the cracked zone. The results show how the residual stresses modify the effective crack opening cycle and the fatigue strength. In particular, after a calibration based on some experimental results, the present approach allows for the determination of the residual stress trend that maximise fatigue alleviation and, consequently, the optimal peening parameters.
2. Material and experimental tests The material tested is a low alloy steel known as 39NiCrMo3 according the Italian code (UTS ¼ 1053 MPa, Yield strength ¼ 940 MPa, E ¼ 206 000 MPa, elongation ¼ 20%). The steel was quenched in oil and tempered. Experimental rotary bending fatigue tests carried out on unnotched specimens allowed to determine the fatigue limit of the material, rFaf ¼ 440 MPa. In Fig. 1 the geometry of the tested specimens is shown: it is possible to note the geometrical discontinuity that causes a numerically evaluated theoretical stress concentration factor Kt equal to 1.45. The application of the ‘‘stair-case’’ method allowed to determine the fatigue limit of the notched specimens under rotary bending fatigue cycles, r0Faf ¼ 295 MPa. Two series of shot peened specimens with the same geometry were tested: the first one was peened by using shots with a diameter equal to 0.6 mm, the second one was peened by using shots with a diameter equal to 0.3 mm. For both the specimen series the Almen intensity was equal to 12 A and the impact angle was 90. The hardness of the shots was 50 HRC. The fatigue tests were performed in air at a speed of 2000
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Fig. 1. Geometry of the notched specimens tested.
rpm up to a duration of 107 cycles. In this case too, the results were analyzed by the ‘‘stair case’’ sequence and they showed that the same Almen intensity lead to different fatigue limit if different peening parameters are used. In fact the fatigue limit was r0Faf ¼ 420 MPa for the specimens peened by using 0.6 mm shots and r0Faf ¼ 370 MPa for the specimens peened by using 0.3 mm shots. Experimental measurements carried out by using the X-ray diffraction technique (Italstructures APD 2000 diffractometer, sin2 W method, Cr radiation, Vn filter, 2h 156) measurements allowed one to obtain the residual stress profiles in the shot peened specimens. The in-depth measurements were performed by removing the surface material with an electropolishing device. In Fig. 2 the trend of the residual stresses experimentally measured is shown. It is possible to note that the residual stress trend changes by using the different peening parameters: in particular it is possible to not that the residual stress value on the surface and the maximum compressive residual stress are larger by using 0.6 mm shots.
(a)
Depth (mm) 0.0
0.1
0.2
0.3
0.4
0.5
Residual Stress (MPa)
0 -200 -400 -600 -800
(b)
Depth (mm)
Residual Stress (MPa)
0.0
0.1
0.2
0.3
0.4
0.5
0 -200 -400 -600 -800
Fig. 2. Axial residual stress trend for the specimens peened by using (a) 0.3 mm shots and (b) 0.6 mm shots.
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Fig. 3. Front view of some non-propagating crack.
In this latter case also the depth at which the maximum compressive residual stress takes place is larger. On the contrary, the depth of the compressed area is not significantly influenced by the peening parameters used. Further measurements performed at the end of the fatigue test on the run-out specimens allowed to determine that the residual stress relaxation during the test is no larger than 20%. Microhardness measurements (applied weight equal to 2 N) on longitudinal sections of the specimens, permitted researchers to assess that hardness is almost uniform in both the specimen series and equal to 350 HV.
Fig. 4. Section view of one non-propagation crack, at different magnification factors (275·, 420·).
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At the end of the fatigue tests, SEM analyses were carried out on the run-out specimens to verify the presence of non-propagating crack and to measure their dimensions. Moreover, sections of the same specimen allowed one to determine the depth of the non-propagating cracks. In Fig. 3 some images of the most stressed zone (at the beginning of the shoulder fillet) taken at the SEM are reported: it is possible to note the typical circumferential extension of a non-propagating crack. Further information was taken from the observation of some section of the run-out specimens; in this way it was possible to evaluate the depth of the non-propagated cracks. In Fig. 4 two images show a nonpropagated crack at different magnification factors. By these investigations it was possible to evaluate that the depth of the arrested cracks varies from about 0.15 to about 0.3 mm.
3. Finite element models The estimation of the fatigue strength of the shot peened specimens needs the knowledge, not only of the stress state due to the applied load but also of the residual stresses. In fact, it is well known that the fatigue life can be strongly influenced by the residual stresses induced by both mechanical processes or surface treatments. If elements with complex geometry are considered, the effective stress state determination requires the use of some numerical technique. Among these latter the finite element methods is particularly suited for this objective, both for its versatility and for the possibility to use very powerful commercial codes. However, the correct utilisation of this technique needs the analysis to be accurately defined and the results to be carefully evaluated. The experimentally observed cracks suggested the definition of a finite element model of the cracked specimen for the prediction of the fatigue strength by considering the applied loads and the residual stresses. Thus, the crack front geometry and the load cycle (rotary bending) make necessary to define a threedimensional model with 20 nodes brick elements: besides, the correct simulation of the linear elastic crack simulation needs the standard brick element requires to distort them according to the ‘‘one-quarter’’ point technique. Finally, the correct simulation of the problem makes necessary to model the contact between the crack faces: this aspect was solved by using some special contact element included in the finite element code (Abaqus) library. The contact algorithm uses a weighted master–slave one, and enforces the constraint that one surface may not penetrate in the other. In this way it was possible to check the crack opening–closure cycle and to simulate sliding between the crack faces. The respect of all these requirements makes difficult the definition of an adequate FE model; to overcome this difficult the ‘‘sub-modelling’’ technique was used. This latter needs two different models, one for the entire model, the other one relative to the particular of the crack, but allows for accurate determination of the stress intensity factors in the three-dimensional cases in which the geometry prevents the construction of an accurate global finite element model including the crack. In fact, it is possible to define a very refined mesh for the crack front zone in the local model while the global model has the only requisite to correctly simulate the behaviour of the specimen far from the zone of interest. The global model schematises the notched specimen (Fig. 5a and b) and was realised by using 20 node brick elements and by using contact elements; the crack was included in the model to avoid the overestimation of the stiffness even if the mesh was not so focussed on the crack front. Due to the geometric and load symmetry, only one half of the cylinder was schematised and the nodes lying on the symmetry plane constrained with symmetric boundary conditions. The second model (called ‘‘local model’’) considers only the zone of the specimen surrounding the crack: also for this model the element used are bricks with 20 nodes and second order shape functions (see Fig. 5c and d).
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Fig. 5. Global (a, b) and local (c, d) models of the cracked specimen.
The ‘‘sub-modelling’’ technique needs to perform two analyses: in the first one the global model is used. The second analysis considers the local model at which the displacements calculated with the global model in correspondence of the boundary surfaces of the local model are applied as boundary conditions. To introduce the residual stresses field both in the global and in the local model a sub-routine was developed: this latter is able to assign a residual stress value at every integration point as a function of the distance from the free surface. In this way it was possible to reproduce the residual stress state experimentally measured and to numerically test the effectiveness of some residual stress profiles. Numerical analysis of the entire rotary bending fatigue cycle of the cracked specimen was executed. The shape and the dimensions of the cracks included in the models were similar to the ones experimentally measured. The shape was assumed semi-elliptical. The surface semi-lengths a considered varies from 0.2 to 0.8 mm while the depth c is one half of the surface semi-length for all the models constructed. The stress intensity factor was then calculated from the value of the J -integral by means of the ‘‘virtual crack extension technique’’ and by applying the nodal displacement substitution method. Once the trend of the stress intensity factor in a rotary bending fatigue cycle is known it is possible to calculate the effective KI range, defined as: DKeff ¼ Kmax Kopening in which Kopening indicates the value of the smallest stress intensity factor values that makes the crack completely opened. The residual stress fields reported in Fig. 2 were included in the FE analyses.
4. Numerical results At first, the displacement field continuity between the global and the local model was verified. In Fig. 6 the total displacement map is shown: it can be noted that along the boundary of the local model the
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Fig. 6. Global and local FE model displacement field superposition: the continuity is verified.
correspondence between the global and the local model displacement is satisfactory (the maximum deviation is 6%). An entire loading cycle was simulated, by varying the direction of the applied loads with respect of the crack orientation. Then the crack opening–closure was analyzed: in Fig. 7 the map of the relative displacement of the crack faces during the load application is shown (the picture refers to the residual stress trend obtained with 0, 6 mm shots and a nominal stress equal to 420 MPa, that is to say the fatigue limit of the peened specimen): Fig. 7a refers to a null bending moment, Fig. 7b refers to one half of the maximum bending moment and Fig. 7c refers to the entire applied bending moment. It is possible to note that the crack opening takes place after a relevant part of load is applied: this is due to the residual stresses applied that strongly affects the actual crack opening cycle. The same considerations can be done by looking at Fig. 8, that shows the contact pressure on the crack faces during the same load cycle. It is clear that the deepest point of the crack front is the first one that opens, while the zone near the crack front remains closed for most part of the cycle. This is good agreement with [12,13]. In Fig. 9 the map of the axial stresses (S33) near the crack front is shown, both when the crack is partially close and when the crack is completely open. In the partially closed configuration it is possible to observe that the crack tip on the free surface is closed while the tip at the deepest point of the crack front is opened: this is caused by the trend of the residual stresses. The same qualitative considerations can be drawn for the analyses of the 0.3 mm shot peened specimen. The analyses showed that the effective opening cycle depends on the residual stress state induced by shot peening. So it is possible to affirm that not only the surface residual stress affects the fatigue strength of the peened components but also the maximum compressive residual stress and its depth with respect to the surface of the specimen. Since this latter quantity is the one mostly influenced by the peening conditions, the choice of the treatment parameters should be oriented to have a compressed depth related to the length of the stopped cracks, that seem to be included in a interval characteristic of the peened material. In other words, the Almen intensity should be chosen on the basis of generating a residual stress field with an inversion point (depth at with the residual stresses change sign) approximately equal to the crack depth and a depth of the maximum compressive stress shorter than the crack depth.
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Fig. 7. Trend of the relative displacements (mm) of the crack faces during the load application (the dark area indicates the crack closure zone).
To confirm the previous consideration, the effective stress intensity factor range (DKeff ¼ Kmax Kopening ), was calculated, considering the residual stresses induced by the two peening conditions tested and an applied nominal stress equal to the fatigue limit of each treatment condition. In Table 1 the results are shown:
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Fig. 8. Trend of the contact pressure (MPa) of the crack faces during the load application (the dark area indicates the crack opening zone).
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Fig. 9. Axial stress (MPa) near the crack front: (a) partially closed crack and (b) totally opened crack.
Table 1 DKeff for different crack depths considering two different peening conditions (the applied stress is equal to the fatigue limit) p p Crack depth (lm) DKeff (MPa m) DKeff (MPa m) (0.6 mm shot, r ¼ 420 MPa) (0.3 mm shot, r ¼ 370 MPa) 150 200 250 300 400
1.20 3.21 5.47 6.45 13.80
1.71 3.33 5.62 7.42 14.32
it is possible to note that for crack depths similar to those experimentally observed (0.15–0.3 mm), DKeff is similar for the two peening conditions. Consequently, since for these depths the cracks have stopped, it is possible to consider the calculated values close to the effective threshold stress intensity factor of the peened specimens. It is interesting to observe that the crack depth at which the cracks have stopped are entirely subjected to the compressive residual stress field induced by shot peening: this can help in choosing the optimal peening parameters. This is also confirmed by the high values of DKeff when the crack is deep enough to include the tensile residual stress field, that makes faster fatigue crack propagation. Furthermore, to verify the above considerations, an analysis was made considering a residual stress trend with the same surface value, the same maximum compressive residual stress but at a distance from the surface equal to one half with respect of the one shown in Fig. 2b. Also the compressed zone depth was one half of the experimental one. The result showed an effective stress intensity factor range 30% greater of the ones shown in Table 1: this means that in this case the effectiveness of shot peening will be minor. Other simulations were executed considering the residual stresses field but not the crack face contact (that is to say by applying the superposition between the residual and the applied stress intensity factor): the results do not allow the interpretation of the experimental data. This evidence permits to underline one more time the importance of considering the contact between the crack faces for the estimation of the fatigue strength of the peened components. At last, calculations were done by considering very short cracks (0.03–0.1 mm), the experimentally measured residual stresses and the crack face contact: the results show that the crack remains close for all the fatigue cycle. This fact can be interpreted bearing in mind that the crack depth is now similar to the material grain size and the fatigue crack is in stage I [2], is influenced by the shear stresses and not by the residual stresses. Since the real cracks did not arrest for these small sizes but propagated till 0.1–0.2 mm, it can be considered an indirect confirmation of the goodness of the numerical model.
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5. Conclusions Fatigue alleviation due to shot peening was investigated by means of experimental tests and observations and by means of numerical analyses. The experimental fatigue tests allowed to determine the presence of non-propagating crack with typical depth (0.15–0.3 mm), that seems to depend mainly on the material used. On the basis of the experimental evidence, it was assumed that the beneficial effect of shot peening is to relate to the residual stress ability to arrest crack propagation. A finite element approach was developed able to simulate the cycling variation of loading on the notched specimens, the presence of the crack, the closure due to the crack faces and the residual stresses induced by shot peening. This approach allowed to analyze the role played by the residual stresses in preventing crack opening and arrest fatigue crack propagation. The calculations permitted to evidence that, for an applied stress equal to the fatigue limit of the treated specimens, the DKeff value does not vary appreciably by varying the peening conditions, and can be assumed as the threshold value of DK. The influence of the peening parameters that characterise the residual stress profile on DKth was studied: the results shows that the depth at which the maximum compressive residual stress occurs with respect of the material grain size is the most important factor in determining the fatigue threshold. The approach can help in optimising the shot peening parameters in relation of the application of interest and, if the results will be confirmed also on material different from the one considered here, can help to correctly choose the shot peening parameters with limited experimental effort.
Acknowledgements The research was supported by a Ministerial grant, whose responsible, Prof. Edoardo Rovida is thanked. We would like to thank Ing. Michele Bandini (Peen Service srl) for shot peening execution.
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