Relating Almen intensity to residual stresses induced

Journal of Materials Processing Technology 110 (2001) 277±286

Relating Almen intensity to residual stresses induced by shot peening: a numerical approach M. Guagliano* Dipartimento di Meccanica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy Received 27 October 1999; received in revised form 31 July 2000; accepted 24 November 2000

Abstract Shot peening is a surface impact treatment widely used to improve the performance of metal parts and welded details subjected to fatigue loading, contact fatigue, stress corrosion and other damage mechanisms. The better performance of the peened parts is mainly due to the residual stresses resulting from the plastic deformation of the surface layers of the material caused by the impact of the shot. Shot peening intensity is usually quanti®ed by means of the Almen-scale, which measures the residual arc height of a strip made of a speci®c material, and of a pre-de®ned size. The scale does not, in other words, apply solely to the residual stress ®eld of a component of unspeci®ed material and size. In this paper, a ®nite element to predict the residual stresses induced by shot peening in a metal part and to relate these stresses to Almen intensity is proposed; the aim is to provide the designer with a useful tool with which to choose the optimal treatment parameters with respect to the mechanical behaviour of the peened parts. Experimental measurements of residual stresses and a comparison with existing experimental data validate this approach. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Shot peening; Almen intensity; Residual stresses; Finite element

1. Introduction Shot peening is widely used to improve the mechanical behaviour of structural parts, notched machine elements or welded details [1]. Its bene®cial effects are mainly due to the residual stress ®eld caused by the plastic deformation of the surface layer of material resulting from multiple impacts of the shot, although strain hardening and grain distortion caused by the multiple impacts of the shot also play a role in the modi®ed mechanical behaviour of the peened components [2]. It is, therefore, important to know the values of the residual stresses in order to predict the mechanical strength of peened parts, and to know how these stresses vary by changing the shot peening parameters (dimensions and material of the shot, speed and the direction of impact, coverage). The problem is that experimental measurement of residual stresses is expensive and time consuming and requires, at least for in-depth measurements, the use of semidestructive methods. In fact, both hole-drilling and X-ray diffraction, the most common methods, require the removal of material around the measurement area, thus preventing *

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further in-service use of the measured element. For this reason, it can be argued that a method to quantify the peening intensity based on these measurements is dif®cult to de®ne and apply. The method used until now to quantify peening intensity is not related solely to the residual stress pro®le: known as Almen intensity, it was introduced by John Almen [3] and involves peening a strip (Almen strip) of given dimensions and material (typically SAE 1070 spring steel), ®xed to a mounting ®xture (Almen block) by means of four roundhead bolts with nuts. The peening time must be suf®cient to ensure coverage of 200%, in accordance with [4]. Once the bolts are removed, the residual arc height over a ®xed length is measured by means of a modi®ed depth gauge (Almen gauge). This measurement de®nes Almen intensity. Other details can be found in [4,5]. This type of measurement cannot, however, give accurate information about the residual stress ®eld in the components because different stress pro®les may give the same arc height, the height being related to the integral of the residual stress ®eld on the strip thickness. Moreover, the material used for the strip is pre-de®ned, while that of the peened part can be of any metal; for this reason too, knowledge of the Almen intensity alone does not provide useful information about the residual stress ®eld induced by shot peening in

0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 8 9 3 - 1

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M. Guagliano / Journal of Materials Processing Technology 110 (2001) 277±286

structural parts [6]. The Almen method is relatively cheap, though, and it is likely to continue to be used to quantify peening intensity. It is, then, important to relate the residual stress ®eld induced by shot peening in any mechanical part to Almen intensity. The problem is not easy to solve as it requires knowledge of the speed of impact and the relationship between the stresses caused by the impact of shot of a given dimension against an elasto-plastic material. In fact, if the type of the shot remains the same and the material of the Almen strip does not vary, the Almen intensity depends mainly on the shot velocity perpendicular to the impact surface [7,8]. The problem is that measurement of shot velocity is dif®cult and expensive. Only recently, in fact, has some equipment been developed for this purpose [9,10], the results obtained are still limited. Some approximate analytical models have, however, been developed to relate residual stresses to Almen intensity, in particular, the one proposed by Al-Obaid [11] is able to distinguish the contribution of the residual stress ®eld due to the impact from that due to the limited thickness of the strip. However, in order to obtain reliable results, some values (i.e. the depth of the maximum compressive stress) need to be assumed. Hills et al. [12] developed an analytical model to predict the residual stress ®eld due to the impact of shot on a ¯at surface and to predict the Almen intensity once the shot type and speed are known. If one looks at the results, while the approach gives an accurate estimation of the maximum compressive residual stress, it only gives approximate predictions of the residual stress pro®le below the surface; the Almen intensity calculated will be in¯uenced by the latter. Although, an approximate model able to relate Almen intensity to shot velocity [7] was also developed, the relationship with the residual stresses in a mechanical part was not dealt with. Other approaches found in published research deal with the prediction of residual stresses due to shot peening [13,14] but do not relate them with Almen intensity, and are therefore of limited practical interest. In this paper, an approach based on ®nite-element calculations is proposed; it is able to relate the residual stress ®eld induced by shot peening in metal parts with the Almen intensity. The ®nite-element analyses simulate the impact of one or more shot on a plate and make it possible to determine the residual stress pro®le of a metal part on the basis of the shot material and diameter. The residual stress distribution due to the impact on a plate, the same thickness as the Almen strip are subsequently taken to be uniformly distributed along the strip length; it is well known that they are not self-equilibrated. Consequently, the strip will curve and by using the theory of elasticity, it is possible to relate the arc height to the shot velocity and then to the residual stresses induced by shot peening on a metal part.

Experimental veri®cation of the proposed approach was carried out by means of residual stress measurements. The Almen intensity values obtained were also compared with those found in existing research. In both cases, the agreement found was good. 2. Finite-element impact analyses Research into the relationship between Almen intensity and residual stress ®eld within any mechanical part is based on the calculation of the residual stress ®eld induced by one or multiple impacts on an elasto-plastic body. This calculation requires the development of analytical or numerical procedures, increasingly popular because of increased computer power [15±17]. Nowadays, in documented research, it is possible to ®nd different approaches simulating shot peening. They all consider static contact between the shot and the treated body, or apply the contact pressure between elastic bodies calculated by means of the Hertz theory [18,19]. However, the pressure between two bodies in contact may signi®cantly vary from the Hertz results if the yield limit of the material is reached; the residual stresses calculated will be affected by this approximation. A common procedure in all the analyses, numerical and theoretical, is to consider a body with a ¯at surface even though, in practical situations, most of the time, mechanical parts have single or double curvature. This is due to the large difference in the curvatures of the shot and the mechanical parts, which makes the latter similar to ¯at bodies; this assumption is also used in the present study. Shot peening involves dynamic deformations, and the formulas relating to static contact lead to approximate results in terms of residual stresses. A recent experimental study [20] showed that the residual stress ®eld due to static contact between the shot and a metal part is quite different from that obtained by dynamic impact between the same bodies. Bearing in mind this last consideration, one can say that shot peening simulation requires the use of appropriate numerical techniques, able to take into account the double non-linearity of the problem due to the contact of two bodies and the elasto-plastic material of the impacted component. Thus, a ®nite-element procedure was developed with the aim of simulating the dynamic impact of one or more shots against a deformable body. The explicit integration scheme was used in this research together with diagonal or ``lumped'' mass matrix. The major advantage of the explicit solution scheme is its computation ef®ciency because iterative calculation is not used and the tangent stiffness matrix is not formed. Furthermore, if a correct increment time is chosen, there are no convergence problems. In fact, the equations of motion for the shot-plate system are integrated using the explicit central difference integration rule. This operator is stable under certain conditions and the stability


limit is given in terms of the highest eigen value of the system. Consequently, this limit depends on the dimensions of the smallest ®nite element. Due to very small dimensions of the element in the zone of impact, the resulting time increment was 3Eÿ09 s. The main problem with the use of explicit techniques is that the analysis is purely dynamic: if some approximate damping is not included in the analysis, once the shot on rebound separated from the plate and the plastic deformation phenomena have ended, the model will never reach a state of static equilibrium. In other words, the stresses in the plate will oscillate around an average value which, in the present research, is taken to be the stable residual stress. The contact algorithm uses a weighted master±slave algorithm and enforces the constraint that one surface may not penetrate the other. In these analyses, the shot (rigid surface) is always the master surface and the default values of the weighting factors were not changed. Further details about the model and the contact algorithm can be found in [21]. The analyses were made by means of the ABAQUS Explicit Code. As previously stated, the shot was modelled as a rigid body after preliminary tests carried out with deformable elastic shot gave results close to those obtained with rigid spheres. The shot velocity range considered varies from 20 to 110 m/s. The material characteristics considered are cyclic ones; this is due to the fact that multiple impacts cause the material to be subjected to many load cycles. The kinematic work hardening rule was assumed to describe the material's mechanical behaviour. The FE code does not include this work hardening rule; so a FORTRAN user subroutine was developed by the user to simulate the kinematic work hardening rule. The strain rate sensitivity of the material was not taken into account according with [14], in which the author remarks that due to the heating following multiple impacts, this effect results attenuated, and due to the lacking of material data concerning the strain rate range of the present case. However, a re®nement of the approach would require to take the strain rate sensitivity into account [22]. The simulation of multiple impacts made it necessary to build a 3D ®nite-element model. Fig. 1 shows the mesh of the ¯at body and of the spheres; only 1/4th of the plate was modelled, with a considerable saving in calculation time. The nodes located on the symmetry planes were constrained with symmetric boundary conditions; consequently, it is assumed that the impacts, too, are symmetrical with respect to those planes. There are 13,949 solid elements (8 nodes, linear shape functions, reduced integration) and 15,625 nodes. In Fig. 2, the scheme of positions A, B, C and D of the simulated impacts is illustrated; different sequences were tested to evaluate the effect of the chronology of impacts on

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the residual stresses. The effect of contemporary impacts was also considered. The results shown in the following part of the paper refer to the centreline of impact A. The analyses were carried out considering two types of material: the ®rst is 39NiCrMo3 steel (UTS 1053 MPa, yield stress 950 MPa, elongation 40%) according to Italian standards, while the second is the material used for Almen strips (SAE 1070 steel, UTS 1270 MPa, yield stress 1120 MPa, elongation 8:2%). Two different thickness were also considered: the ®rst one (50 mm) with the aim of calculating the residual stresses in a thick part, the second is the thickness of the Almen strip (type A, thickness 1:27 mm), and was chosen to calculate the residual stress ®eld induced by the multiple impacts in such a strip. The shot velocity was set as an initial condition. 2.1. Calculation of Almen intensity For the Almen intensity calculation, the residual stress distribution calculated in the FE analysis in the centreline of the impact zone A (Fig. 2) is assumed to be uniformly distributed over the whole Almen strip, ®xed to the Almen block. The results obtained from the previous analyses are not suf®cient to relate the Almen intensity to the residual stress ®eld induced in a metal part. This is because it is not directly possible to predict the residual arc height of the strip by knowing only the residual stresses due to the impacts. In fact, once the ®xing bolts are removed, the Almen strip, originally straight, becomes curved and modi®es the residual stress ®eld. Thus, the residual stresses due to impact are not equilibrated; consequently, the thin plate will bend and elongate. These effects are prevented by the boundary conditions. In other words, a compressive force F and a bending moment M are applied in order to keep the strip straight (see Fig. 3). If we assume that the impact residual stresses are elastic, we can calculate F and M as: Z Z M sres;imp y y dA (1) F sres;imp y dA A

A

where sres,imp are the residual stresses due to the shot impacts, A the strip section and y the distance from the neutral axis. The removal of the bolts can be interpreted as the application of a moment and a force of equal value but with an opposite sign with respect to M and F. The stresses, strain and de¯ections of M and F are determined, once the residual stresses due to the impacts are known, by using the Theory of Elasticity; with reference to Fig. 3, it is possible to af®rm that the residual stress ®eld in the strip after the bolts are removed is equal to sres y sres;imp y ÿ

F My ÿ A Inÿn

(2)

280


Fig. 1. 3D ®nite-element model used for the determination of residual stresses due to the multiple impact of shot.

where Inÿn is the moment of inertia and A the area of the strip. The residual arc height, or Almen intensity, is h

3Ml2 2Ebh31

(3)

(l reference distance for measuring Almen intensity, b strip width, h1 strip thickness). In this model, the effect of the transverse curvature is not taken into consideration.

3. Experimental measurements The results obtained by means of the ®nite-element simulations were compared with the data obtained from experimental measurements of the residual stresses carried out on some Almen strips and some cylindrical specimens. The measurements were carried out by means of an ItalStructures X-ray diffractometer (sin2c method, linear detector, Chromium radiation, Vanadium ®lter, {2 1 1} peak 2Y 156 ). The area subjected to the X-ray measured 1 mm2; the chemical removal of thin layers of materials


281

Fig. 2. Scheme of the position of the centrelines of the impacts (r radius of the impact dimples; its value depends on the diameter of the shot and on its velocity).

allowed the measurement of the residual stresses under the free surface, thus making it possible to determine the residual stresses below the surface. The strips were peened with the same Almen intensity (0.3 mm A) but with different steel shot (diameters of 0.3 and 0.6 mm). Residual stress measurements carried out on the Almen strips before shot peening made it possible to verify that the residual stress of the strips was negligible and that the values obtained after peening them were only due to shot peening. As regards the characteristics of the cylindrical specimens, they were made of 39NiCrMo3 steel, according to Italian standard, and their diameter was 8 mm. The specimens were peened with an Almen intensity of 0.3 mm A and shot with diameters of 0.3 and 0.6 mm. Other veri®cations of the accuracy of the results were obtained by the comparison between Almen intensity±speed

of shot (of given dimensions and material) and the experimental values found in [7,10]. 4. Results and discussion 4.1. Residual stress prediction In Fig. 4, the deformed shape of the 50 mm thick plate after 1, 2, 3, 4 and 5 (sequence A, B, C, D and A) impacts is shown. The material considered is 39NiCrMo3 steel and the shot have the same density as the steel. Fig. 5 shows the residual stress pro®le in-depth, in the centreline of impact zone A after 1, 2, 3, 4 and 5 impacts (shot diameter, 0.5 mm; shot velocity, 100 m/s), with an impact sequence of A, B, C, D and A. Other sequences did not give signi®cantly different trends. The stress component

Fig. 3. Calculation of the residual stresses in the Almen strip after bolt removal: when the strip is straight due to reaction forces. When the boundary conditions are removed the strip elongates and bends.

282


Fig. 4. Deformed shape of the plate after 1, 2, 3, 4 and 5 impacts (A, B, C, D and A sequence).

plotted in Fig. 5 and in the following ones is in direction 1 of Fig. 1. The stress component 3 was not signi®cantly different from the stress component 1 and the similar values enables the use of both, for following comparison with experimental residual stresses on specimens and Almen strips. The stress component 2 is smaller than the previous ones and it is negligible on the free surface. From the same ®gure, it can be noted that the strongest effect in terms of residual stresses is due to the ®rst impact. This does not mean that, in reality, the residual stress pro®le does not change after the ®rst impact because calculations assumed the cyclic properties of the material.

They assumed, in other words, that many impacts took place before the one considered. However, it does make it possible to say that in the FE analyses, it is suf®cient to consider only the impacts around the zone of interest in order to get the residual stress pro®le. In fact, it is reasonable to assume that impacts in zones more distant than the ones considered in these calculations do not affect the residual stress in zone A. In Fig. 6, it is possible to note the trend obtained for different shot and different velocities. From this ®gure, it is clear that the quantities de®ning the residual stress pro®le that are most in¯uenced by the size and velocity of the shot


283

Fig. 5. Residual stress pro®les in the centreline of impact A due to impacts A, B, C, D and A (shot diameter, 0.5 mm; shot velocity, 100 m/s), stress component in direction 1 (see Fig. 1).

are the depth of the maximum compressive residual stress and the depth at which the residual stresses change sign. The surface residual stress and the maximum compressive stress are not greatly affected by the shot peening conditions but are mainly related to the mechanical characteristics of the treated material. The results were compared with the residual stress values experimentally measured by means of an X-ray diffractometer on a cylindrical specimen with a diameter of 8 mm,

shot peened with an intensity of 0.3 mm A with steel shot with a diameter of 0.6 mm. The large difference between the curvature of the specimen and that of the shot enables the use of the meshes previously described. In Fig. 7, the numerically obtained longitudinal residual stress pro®les are compared with ones that were experimentally measured by means of an X-ray diffractometer, the agreement is satisfactory. The differences fall within the usual variability of this process [23].

Fig. 6. Residual stress pro®les in depth due to shot peening in a thick part (taken on the centreline of zone A, stress component in direction 1 of Fig. 1): (a) shot diameter 0.3 mm, (b) shot diameter 0.5 mm, (c) shot diameter 0.7 mm, (d) shot diameter 1.0 mm.

284


and to relate it to shot type and velocity. It is possible, in other words, to relate residual stresses in a general part (see Section 4.1) to peening intensity. The results show that, once the shot type is de®ned (once, that is, material and dimensions are known), the Almen intensity depends only on the speed of shot, or, more precisely, on the speed component perpendicular to the contact surface. This is in agreement with the existing data [7]. In Fig. 8a, the trend of Almen intensity±steel shot speed for diameters varying from 0.3 to 1 mm and density equal to that of steel (7860 Kg/m3) is shown. Fig. 8b shows that of ceramic shot (3800 kg/m3). The trend is well described by the following best-®tting equations (A Almen intensity (mm), v shot velocity (m/s), R2 regression coef®cient). For the steel shot they are: Av 2E ÿ 07v3 ÿ 6E ÿ 05v2 0:007v

R2 0:98

shot diameter 0:3 mm Av 2E ÿ 07v3 ÿ 5E ÿ 05v2 0:0053v Fig. 7. Numerical and experimental trend of the longitudinal residual stresses obtained on cylindrical specimens: (a) Almen intensity 0.3 mm A, shot diameter 0.3 mm; (b) Almen intensity 0.3 mm A, shot diameter 0.6 mm.

4.2. Almen intensity prediction The same type of analysis was performed considering a plate of the same thickness and material as that of Almen strip A. Thus, by following the procedure previously described, it is possible to calculate the Almen intensity

R2 0:99

shot diameter 0:5 mm Av 5E ÿ 07v3 ÿ 0:0001v2 0:0081v 0:0118 R2 0:99 shot diameter 0:7 mm Av 9E ÿ 07v3 ÿ 0:0002v2 0:0179v R2 0:99 shot diameter 1 mm (4) For the ceramic shot the following equations were obtained: Av 2E ÿ 07v3 ÿ 4E ÿ 05v2 0:0033v

R2 0:98

shot diameter 0:3 mm Av 2E ÿ 07v3 ÿ 4E ÿ 05v2 0:0049v

R2 0:99

shot diameter 0:5 mm

Fig. 8. Almen intensity (strip type A) trends vs. shot velocity for the shot diameter indicated in the key: (a) steel shot, (b) ceramic shot.

Av 2E ÿ 07v3 ÿ 6E ÿ 05v2 0:0065v shot diameter 0:7 mm

R2 0:99

Av 4E ÿ 07v3 8E ÿ 05v2 0:0094v shot diameter 1:0 mm

R2 0:99 (5)

The total residual stresses were veri®ed by means of XRD residual stress measurements on two Almen strips shot peened with the same Almen intensity (0.3 mm A) but with different steel shot (diameter 0.3 and 0.6 mm). In these cases, the Almen intensity should be obtained with different shot speed and presumably, with a different residual stress pro®le. In fact, if we enter these shot diameters in Eq. (1), we obtain the speeds that cause the Almen intensity which was experimentally considered. Now, by looking at the residual stresses obtained after the removal of the boundary conditions in the Almen strip analysis, it is possible to compare them with the experimental stress pro®le obtained by means of measurements carried out on the strips not ®xed to the Almen block. In Fig. 9, the comparison of the numerically


285

Fig. 9. Experimental and numerical longitudinal residual stress trends obtained on the Almen strip: (a) Almen intensity 0.3 mm A, shot diameter 0.3 mm, (b) Almen intensity 0.3 mm A, shot diameter 0.6 mm.

calculated and experimentally measured longitudinal residual stresses is illustrated. The agreement is good for the compressed part of the strip. When the residual stresses change sign and become tensile, the numerical values exceed the experimental ones. This can be justi®ed bearing in mind that, for measurements below the surface, it is necessary to remove much of the thickness of the strip. Moreover, the removed part is the most stressed zone

and this means that the residual stress state in the rest of the strip remains greatly altered and tends to unstress. Another test of the quality of the proposed approach was made by comparing the values of Almen intensity±shot velocity with experimental data found in [7,10]. The experimental velocities compared with the numerical ones are the highest of the shots because the residual stresses are mainly due to the shot with the highest kinetic energy, even though they are less frequent than the slower ones. This comparison is shown in Fig. 10, again the agreement is good. 5. Conclusions A relationship between Almen intensity and the residual stress ®eld induced by shot peening was found. From the analyses performed, the following conclusions can be drawn:

Fig. 10. Comparison of the Almen intensities calculated and experimental data from references [7,10].

A procedure was established to relate the value of the Almen-scale to the residual stresses in metal parts. It is based on the FE simulation of the impact of shot against a flat deformable body and the calculation of the residual

286


curvature of the Almen strip after the residual stresses are imposed on the strip itself. Analytical functions relating Almen intensity to shot velocity were found for the shot considered: the bestfitting equations were found and the regression coefficient is always good. It is thus possible to relate the residual stresses in a mechanical part to Almen intensity. Comparison between the numerical results and the experimental values of residual stresses reveals satisfactory agreement both on the Almen strips and on the cylindrical specimens. The relationship found between Almen intensity and shot speed was compared with the experimental values found in published research and the agreement was good. By using the present approach, it is possible to estimate the residual stress profile induced by shot peening in a general metal part and to relate it to the peening intensity. This can guide the designer towards the optimal choice of treatment parameters in view of optimising the mechanical strength of the peened components, at the same time minimising the experimental measurements necessary to achieve this scope.

Acknowledgements We would like to thank Norblast s.a.s. for ®nancially supporting this research. References [1] K.J. Marsh (Ed.), Shot Peening: Techniques and Applications, Engineering Materials Advisory Services Ltd., London, 1993. [2] K.J. Miller, Materials science perspective of metal fatigue resistance, Mater. Sci. Technol. 9 (6) (1993) 453±462. [3] J. Almen, J.P.H. Black, Residual Stresses and Fatigue in Metals, McGraw-Hill, Toronto, 1963, pp. 64±69. [4] Anon., Shot Peening of Metal Parts, Military Speci®cation Mil-S13165c, 1989. [5] Anon., Shot Peening Applications, 7th Edition, Metal Improvement Company, 1995. [6] R. Herzog, W. Zinn, B. Scholtes, H. Wohlfahrt, The signi®cance of Almen intensity for the generation of shot peening residual stresses,

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