Surface layer modifications of micro-shot-peened Al-7075-T651: Experiments and stochastic numerical simulations

Surface & Coatings Technology 321 (2017) 265–278

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Surface layer modifications of micro-shot-peened Al-7075-T651: Experiments and stochastic numerical simulations M. Marini a,⁎, V. Fontanari a, M. Bandini b, M. Benedetti a a b

Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123 Trento, Italy Peen Service S.r.l., Via Augusto Pollastri 7, 40138 Bologna, Italy

a r t i c l e

i n f o

Article history: Received 10 March 2017 Revised 21 April 2017 Accepted in revised form 23 April 2017 Available online 27 April 2017 Keywords: Shot peening Finite element method (FEM) Explicit dynamic simulation Surface roughness Residual stress

a b s t r a c t Shot peening is widely used to improve the fatigue resistance of metallic components, but the optimal tuning of the treatment parameters is not an easy task. Finite element (FE) dynamic simulations proved to be a reliable tool to estimate the effect of the main treatment parameters on surface roughness and residual stresses. This paper presents one of the first attempts to numerically simulate a micro-shot peening treatment; indeed, this is a tremendous numerical challenge given the large number of impacts to be simulated and the fine mesh needed to discretize the small impact dimples. The target material is the aeronautical aluminium grade Al-7075-T651. To best represent the hardening rule of the target material, the Lemaitre-Chaboche model is tuned on the basis of fully reverse axial strain tests. The statistical nature of the peening treatment is taken into account by randomly generating sets of bead individuals characterized by stochastic variability in dimension, velocity and impact location. Surface roughness and residual stresses resulting from the numerical analyses are compared with experimental measurements. A specific novel procedure is proposed to take into account the effect of surface roughness and radiation penetration on the in-depth residual stress profile measured by XRD. In addition, a static finite element model is devised to estimate the concentration effect exerted by the surface roughness on the external stress field. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Shot peening is a surface treatment widely applied to improve the fatigue resistance of mechanical components; it is particularly effective in reducing the detrimental stress concentration effect exerted by geometrical details commonly encountered in machine parts, such as connecting rods, gears and turbine blades [1–3]. Recently, this treatment has become popular in the biomedical context too, where it is employed to enhance the fatigue strength and biocompatibility [4] as well as the adhesion of coatings [5] to the surface of prosthetic implants. It consists in blasting small beads of hard (metallic or ceramic) material onto the surface of a metallic target, so that a thin surface layer is subject to plastic deformation. In this way, compressive residual stresses and work hardening are introduced into the surface layers, conferring a beneficial effect on both fatigue and fretting-fatigue strength, even though at the cost of an increased surface roughness due to impingement dimples. A large number of variables are involved in the shot peening process, such as the material, dimension and velocity of the peening medium, the morphology and material of the treated component, the tribologic ⁎ Contacting author. E-mail address: [email protected] (M. Marini).

http://dx.doi.org/10.1016/j.surfcoat.2017.04.054 0257-8972/© 2017 Elsevier B.V. All rights reserved.

phenomena, and others. The control of all these variables is mandatory for the success of the shot peening process. Indeed, an excessive treatment may be detrimental because of both the high deformation of the surface layer and the potential stress concentration caused by the impact dimples. On the other hand, surface compressive residual stresses may not be as intense as desired, since their magnitude is not directly correlated to the treatment coverage [6,7]. The intensity of the process is conventionally characterized by the Almen test. It consists in peening a thin steel strip on one side to measure the curvature caused by the treatment. Coverage is another measure of the treatment intensity and is defined as the percentage of the treated surface over the total surface area. Until now, neither the effect of each variable nor their mutual interaction have been completely understood yet. Since the experimental investigation of all the involved phenomena would be extremely expensive and time-consuming, a more suitable way to the process comprehension is the numerical simulation. This might permit to identify the proper combination of process parameters to obtain the desired residual stress state and surface condition tailored to the specific application. In the past, numerical simulations have been mainly focused on the estimation of the residual stress field. Recently, the attention of researchers has moved towards the prediction of the strain field of the

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treated surface and the resulting surface morphology. Until recently, the major concern of the researchers was to adapt the numerical simulations to the restricted computational resources available at that time. For this purpose, the symmetry cell approach was devised. According to this heavy simplification, the impinging beads are designed to impact in deterministic regularly distributed locations, thus simulating the process considering only a small volume of material and few impacts. This approach, first proposed in the pioneering studies of Meguid [8–10], has then been followed by many authors, such as Majzoobi [11,12] and Hassani-Gangaraj [13]. However, these authors were already aware of the poor capability of this method to reproduce the actual treatment coverage. To improve this critical aspect, Hassani-Gangaraj proposed a symmetry cell of variable size, with the intent of mitigating the limits of this approach, yet in a not conclusive way. Much more drastic is the conclusion reached by Bagherifard [14], who affirmed the need for a stochastic FE model, not based on symmetry considerations. Even though a fully realistic representation of the process would require the simulation of shot-shot and shot-target interactions, as in the discrete element models developed by Hong [15] and Mylonas [16], simpler stochastic models, wherein the impacts are randomly distributed on the target surface, proved to give satisfactory results. Bagherifard [17] made a remarkable effort in identifying the best material constitutive law to reproduce the cyclic stress-strain behavior of the material and to correctly estimate the coverage level; this latter task is done by comparing the plastic equivalent strain (PEEQ) of every point on the target surface with a threshold value. In the following studies, Bagherifard [14] tried to reduce the computational cost of the FE simulations by introducing a Python procedure to optimize the distribution of the impact points and include stochastic phenomena in the FEM simulation, even though this slightly alters the statistical distribution of the impingements. Later studies [18] focused on surface roughness and the relation between dimple dimension and shot velocity and size. HassaniGangaraj et al. [19] adopted a very similar approach, where several steel shots with same diameter and velocity impinge on a steel disk at random locations. The coverage level is calculated as in [17], taking into account the occurrence of partial overalapping between adjacent dimples. Miao [20] addressed the problem of correctly simulating the treatment coverage. For this purpose, the Almen test was simulated numerically, considering different numbers of impacts arranged in random positions and assuming shots of same speed and size. The coverage was evaluated as in [17], and many peening process parameters were deduced from the Almen intensity and the surface roughness development. Similarly, Gariepy et al. [21] simulated the shot peening of an aluminium alloy, taking into account statistical variability in shot size and velocity, and deriving some simulation parameters from the Almen intensity. More recently, Peñuelas [22] devised a realistic model of the hardening behavior of the target material and developed a MatLab procedure generating random impacts of shots of given size and speed. The numerical investigations undertaken so far have mainly addressed surface treatments using steel shots with a diameter larger than 0.5 mm. On the other hand, several experimental investigations have pointed out that the fatigue resistance of light alloys benefits more from gentle peening treatments employing small ceramic beads with a diameter lower than 0.15 mm, often referred to as micro- or fine-particle shot peening [23–27]. Indeed, such treatments introduce a compressive residual stress peak located close to the surface where the cracks are likely to nucleate and induce a less detrimental surface roughening. Clearly, the numerical analysis of treatments employing small beads represents a tremendous computational challenge given the large number of impacts to be simulated to achieve complete coverage and the very fine mesh required for the FE model to appreciate low surface roughness and thin surface layers affected by the compressive residual stress. The outcomes of FE models are usually validated by comparison with in-depth residual stress measurements undertaken with diffractometric techniques, but often the effect of radiation penetration into the sample is overlooked. This is acceptable when target materials

to be investigated have low penetration depth, such as steels and superalloys [28–30]. This, however, can lead to significant errors if the numerically estimated residual stresses are directly compared with measures taken on light alloys characterized by X-ray penetration depth (on the order of tens of microns) comparable with the thickness of the surface layer where the compressive residual stress develops. On the other hand, the simulation of micro-shot peening treatments would be of great industrial interest, as the effects of fundamental process parameters could be estimated without requiring expensive experimental techniques. In addition, the numerical reproduction of the surface morphology would allow a direct estimation of the stress concentration effect at surface dimples in place of semi-analytical simplified models based on large-scale roughness parameters, whose applicability to micro-shot peening treatments has yet to be validated. The present paper describes one of the first FEM procedures aimed at simulating a micro-shot peening process. Specifically, a treatment employing small ceramic beads is applied to the aeronautical grade Al-7075-T651 aluminium alloy. This treatment has proved to be very effective in improving the fatigue resistance of Al-alloys with respect to conventional steel shots, as it confers a shallow and intense compressive residual stress peak without excessive surface roughening [6,7,23,31– 33]. The numerical simulation of the shot peening process is carried out using the explicit dynamic FE code Ansys/LS-Dyna. The LemaitreChaboche hardening rule is enforced to represent the cyclic stress-strain behavior of the target material. The parameters of this material model are calibrated on the base of the results of fully reversed strain axial testing. A MatLab procedure is developed in order to randomly generate sets of beads characterized by stochastic variability in dimension, velocity and impact location. Each set is composed by the minimum number of beads required to achieve the desired coverage level, estimated through a predictive model. The results of the numerical simulations are validated by comparison with 2D and 3D surface roughness and in-depth XRD residual stress measurements. To consistently compare experimental and numerical estimations of the residual stress field, the effect of radiation penetration and surface roughness is taken into account according to an approach specifically devised in this paper. Finally, the nodal locations estimated at the end of the dynamic analyses are imported into a static FE model to evaluate the effect of surface roughness on the external stress field. In this way, it is possible to estimate the stress concentration factor and notch fatigue factor induced by the surface treatment. 2. Experimental material and procedures 2.1. Target material Shot peening is applied to Al-7075-T651 hourglass prismatic specimens having gage cross-section 6 mm × 4 mm. Monotonic tensile and mass properties are listed in Table 1. To evaluate the cyclic stress-strain of the target material, fully reversed strain axial tests are performed on uniform-gage specimens (gage length 12 mm, cross-section 4 mm × 4 mm) in the L-orientation using an automated, closed-loop servohydraulic testing system equipped with hydraulic grips, a load cell of 100 kN (nonlinearity ± 0.1% of R.O.) and an axial extensometer (10 mm gauge length, nonlinearity ± 0.15% of R.O.). The tests are carried out according to ASTM E606-04 by single step (one sample per strain amplitude) at a constant strain rate of 1 × 10− 2 s− 1 and at strain amplitudes ranging from 0.006 to 0.014 in steps of 0.002. The tests are carried out until stabilization of the stress-strain cycles, which occurred after about 50 cycles. 2.2. Shot peening treatment Shot peening is carried out using fused ceramic micro-beads B120. Material composition, mechanical and mass properties are listed in

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Table 1 Mechanical properties of the Al-7075-T651 alloy. Young modulus E (GPa)

Poisson ratio ν

Yield strength σY0.2 (MPa)

Ultimate tensile strength σUTS (MPa)

True fracture stress σF (MPa)

Total elongation T.E. (%)

Reduction in area R.A. (%)

Density ρ (g/cm3)

73 (±1)

0.33

515 (±5)

565 (±5)

760 (±10)

18 (±2)

24 (±2)

2.810

Table 2. The size distribution of the beads is estimated through a granulometric analysis using a Rotap sieve shaker. Measures are carried out according to the standard ASTM-C-136 using 6 sieves with decreasing size comprised between 150 and 53 μm. After 10 min shaking time, the beads retained by the sieve are measured. The weight percent of passing beads vs. the sieve size is shown in Fig. 1(A). It can be noted that the average beam diameter is about 105 μm and that the diameter of a significant portion of the beads is smaller than 90 μm. The beads are propelled with a mass flow rate of 5 kg/min onto the target surface by an air-blast machine equipped with a Tetra nozzle with 12 mm diameter and operating at 100 mm working distance. The main shot peening parameters are listed in Table 3. Shot velocity is measured by means of a DSLR camera based equipment. The DSLR camera equipped with a magnifying lens is pointed towards the bead stream, passing in front of a reference screen. Some photo-shoots are taken using a synchronized flash, to estimate the bead velocity from the known shutter speed. 2.3. Characterization of the target surface layers Surface roughness of the peened surface is characterized through 2D and 3D measurements. Surface profiles are acquired using a contact profilometer over an assessment length of 5 mm, both along the transversal and longitudinal direction of the sample. In addition, a confocal optical profilometer Sensofar Plu Neox (plane surface spatial sampling resolution of 0.83 μm, z-axial measurement resolution of 0.02 μm) is employed to evaluate surface topography and roughness on an assessment area 636 μm × 477 μm. The in-depth residual stress profile induced by the shot peening treatment is measured with an AST X-Stress 3000 diffractometer employing the Sin2ψ X-ray diffraction (XRD) experimental technique. The zone analysed by a Cr Kα radiation beam is limited using a collimator of 1 mm2 in area. In-depth measurements are done using an incremental layer removal electro-polishing technique, which is arrested when layers subject to tensile residual stresses, i.e. about 50 μm below the surface, are exposed. Since this depth is much lower than the sample thickness, no residual stress correction for layer removal is deemed to be necessary, as indicated in [34]. On the other hand, the thickness of this layer is comparable with the penetration depth of the Cr radiation into Al, viz. about 12 μm. To make possible a direct comparison with the residual stresses estimated by the numerical analyses, the deconvolution techniques proposed in [23] is adopted to estimate the true in-depth residual stress profile. For this purpose, the true profile σ-xx RS (z) is expressed as series of exponential functions, whose coefficients are deduced from the experimental data σ RS xx ðzÞ taken at different depths z, as the latter can be expressed by the following integral weighted average of form:

σ RS xx ðzÞ ¼

0
0 0  −z ∞ ξ dz ∫ 0 σ RS xx z þ z e

∞

∫0 e

0

−zξ

ð1Þ

0

dz

Table 2 Physical properties of the shots. Young modulus E (GPa)

Poisson ratio ν

Vickers hardness HV1

Composition

Density ρ (g/cm3)

300

0.30

700

ZrO2 67% SiO2 31%

2.3

where ξ is the information depth [35], which has been estimated in [23] equal to 5 μm for Cr radiation. 3. The finite element model 3.1. Geometry and mesh The dynamic FE simulations are carried out with the explicit Ansys/ LS-Dyna® 17 commercial software. The FE model consists in a target body, representing a part of the peened component, and in a certain number of beads impinging on it, as shown in Fig. 2(A). Symmetry considerations would suggest adopting the cylindrical shape for the target, also in view of the spherical shape of the beads. Unfortunately, Ansys/ LS-Dyna does not permit to define a cylindrical coordinate system, so the target is modelled as a square-based prism, with 300 μm side and 240 μm height; this solution ensures perfectly homogeneous and regularly distributed elements. The thickness of the target body is chosen according to the indications provided in [10] with the intent of not perturbing the development of residual stresses; similarly, the target size is chosen according to [19]. The impacts are confined in a circular area of 110 μm diameter in the center of the target upper face, hereinafter denoted as impact area. The beads are modelled as hemispheres with the aim of discretizing them with sufficiently small elements without penalizing the computational efficiency of the simulation. The shot density is doubled in order to preserve their kinetic energy. All the bodies are meshed with 4 nodes brick elements SOLID164 with reduced integration and hourglassing control; the prismatic volume encompassing the impact area, with 156 μm side and 120 μm height, is finely meshed with 1.3 μm size elements, while the surrounding volume of the target body, subject to low-gradients of elastic strains, is discretized with elongated elements to reduce the node number (Fig. 2(B)). The fine-mesh element size is about 1/20 of the average impact dimple diameter as suggested in [17]; this allows an adequate resolution of the residual stress state, without an excessive computational cost. Moreover, a convergence analysis is performed starting from 5 μm sized elements, to verify the accuracy of the solution. The boundary of the target volume is constrained to prevent normal nodal displacements in order to take into account the constraint exerted by the surrounding material, and silent boundaries are applied on all the constrained surfaces to prevent the reflection of the shock waves. A surface-to-surface automatic contact couple is established between the target surface and each bead surface, where the beads represent the master surface, which rules the penalty stiffness necessary to minimize the contact interference. 3.2. Material models As the beads are made of ceramic material, a linear elastic model should be the most obvious choice, but some experience suggests that solver stability increases if an artificial elastic-plastic behavior of the shots is implemented. For this purpose, a bilinear elastoplastic model is assumed, wherein very high yield strength (3 GPa) and tangent modulus (30 GPa) are taken to make the plastic deformation negligible. Particular care is taken in modelling the elastic-plastic behavior of the target material. This is not an easy task, also in view of strain-hardening, anisotropy and strain-rate effects usually displayed by structural metallic materials. Since experiments did not reveal pronounced anisotropy [31] and strain rate sensitivity [36] of the Al-7075 alloy, these last two effects have been neglected, while the attention has rather been

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Fig. 1. (A) Distribution of the bead dimension from a sieve analysis. (B) Comparison between the results of the sieve analysis on the dimension of the beads and the fitting Weibull distribution used in the simulation.

focused on the material strain hardening. To this regard, it can be noted that many authors, with the aim of accounting for material strain-ratesensitivity, which plays an important role in steels and superalloys, adopted the Johnson-Cook [12,17,19,37] or the Cowper-Symonds model [9,11,16]. However, both models rely on a purely isotropic hardening law, which can be an oversimplification of the material behavior. In fact, peened parts are subject to repeated elastic-plastic impacts necessary to achieve full coverage [22,38], experiencing complex nonmonotonic load histories. Under these conditions, the strain-hardening of most metallic materials displays a significant kinematic component, responsible for the Bauschinger effect, which is completely neglected by the aforementioned material models. Looking at Fig. 3, where the experimental stress-strain curves are compared with the ones obtained from the FE model applying the Johnson-Cook model, the excessive material hardening is evident, resulting in a large discrepancy between the

curves, increasing with rising accumulated strain. The same consideration applies to the Cowper-Symonds model. While the first branch of the stress strain curve is well reproduced, viz. the one based on the monotonic axial strain test, the cyclic strain behavior of the material is not equally well simulated. The isotropic hardening model does not reproduce the stabilization of the hysteresis loop, and the accumulated strain makes the hardening model lose all its nonlinear components. This leads to a wrong representation of the true material behavior. In view of these observations, we decided to adopt the Lemaitre-Chaboche mixed hardening model [39–41] in order to incorporate both kinematic and isotropic hardening components. The Lemaitre-Chaboche model appears in the form: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðs−βÞ  ðs−βÞ−σ Y ¼ 0 3

ð2Þ

Table 3 Parameters of the peening process. Almen intensity

Nozzle

Working distance (mm)

4.5 N

Tetra ø12 mm 100

Flowing rate (kg/min)

Angle of impingement

Coverage Average shot velocity (m/s)

Shot diameter range (μm)

5

90°

100%

63–125

57 (±5)

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269

Fig. 2. (A) The FEM model with the stack of beads standing above the target body. (B) Mesh of the target body, section. a: full coverage area; b: impact point area; c: impinged area.

where s is the deviatoric stress tensor and β is the backstress tensor, determined as: β_ ¼ C ε_ pl −γβλ

ð3Þ

where C is the hardening parameter, γ is the rate of decrease of hardening modulus that rules the non-linearity of the model, ϵpl is the plastic strain and λ is the accumulated plastic deformation, while σY is: σ Y ¼ σ Y0 þ Hεpl

low strain rate sensitivity of Al7075-T651 [36,42] and the bead impact velocities, which are far lower than the ballistic velocities used to characterize the strain rate sensitivity [43]. The Lemaitre-Chaboche material parameters are obtained through a nonlinear optimization procedure aimed at minimizing the deviation of the outcomes a FE static model simulating the strain-controlled axial tests from the experimental stress-strain cycles. The best-fit parameters are listed in Table 4. The very good agreement of the numerical model with the experimental data is shown in Fig. 4A, B, and C.

ð4Þ 3.3. Coverage and impact positions

where H represents the isotropic strain hardening modulus, not used in this study. This material model does not account for strain rate sensitivity, but this aspect is of minor importance in the present study, given the

A MatLab routine is developed to create, prior to the FEM simulation, a set of shots capable to achieve the 100% nominal coverage on the

Fig. 3. Comparison between the experimental mechanical behavior under cyclic strain and the numerical simulation of the Johnson-Cook model.

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Table 4 Parameters for the Lemaitre-Chaboche material model. σY (MPa)

C (GPa)

γ

370

75

460

circular area of 100 μm of radius, in the center of the upper surface of the target body, denoted as the control area. In practice, each set is a bunch of data, containing the impact point coordinates, as well as the dimension and velocity of the shots. As shown in Fig. 5, the script at first randomly assigns the dimension value to the first bead on the base of the stochastic size distribution shown in Fig. 1(A). The sieve analysis results are converted in terms of number of bead by simply assuming an average radius for each size interval. A Weibull cumulative distribution function is fitted to the shot size distribution as shown in Fig. 1(B): shot dimensions in the model are chosen between 53 and 125 μm, in order to avoid the generation of unrealistically large or ineffective small beads. The shot velocity is assumed to be normally distributed, with mean 57 m/s and standard deviation σ = 2.5 m/s, as suggested by the experimental measurements. In order to avoid unrealistic values of the shot speed generated by the theoretical distribution, the velocity values are chopped below 52 m/s and above 62 m/s, in conformity with experimental observations. Some authors, e.g. [15,16], developed discrete element models (DEM) to be integrated with the FEM simulation in order to estimate the impact velocity and position of each impinging shot. However, these simulations encounter some problems, viz. a significant increment in computation cost and a 2D DEM layout that makes the model not completely realistic. For these reasons, we preferred to estimate the shot speed from available experimental data rather than from complicated DEM simulations.

A specific simulation campaign is carried out to estimate the dimple dimension on the base of the shot dynamics. Using three levels for both shot size and velocity, 9 single impact 2D axisymmetric simulations are carried out. The resultant impact dimple dimensions fill a factorial plane having the beads velocity and radius as variables, and through a linear regression it is possible to compute the coefficients of the bilinear relation having the form: DDimple ¼ c00 þ c01 DShot þ c10 Sshot

ð5Þ

where DDimple is the dimple diameter, Sshot is the bead diameter and VShot is the impact velocity; the best fit parameters are reported in Table 5. Eq. (5) is used by the MatLab routine to compute the dimension of the dimple caused by the impact of shots randomly located inside the control area. The shots are stacked up over the target, equally spaced out along the height direction. From the speed and the distance from the surface, it is possible to evaluate quite precisely the impact time of each shot. Previous studies [9–11] showed that it is not indispensable to consider the interaction among shots, as long as the shots do not interfere in the impact stage [17]. Therefore, the shots interpenetrate when stacked, and no interaction is considered among them; however, a check is performed in order to prevent two or more shots from imping at the same time in the same place. The number of shots generated in each simulation is the minimum number to achieve full coverage (when at least 98% of the target surface is affected by dimples). It is worth noting that the applied method does not consider at all the effect of material strain hardening, even if it is not rare to observe overlapping dimples (both in the simulation and in the experimental practice). However, only the not-overlapping part of every dimple really affects the coverage evaluation, being the overlapping part already considered in the previous impingement. As regards the overlapping part of the

Fig. 4. Comparison between the experimental mechanical behavior under cyclic strain and the numerical simulation of the Lemaitre-Chaboche model.

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271

Fig. 5. Schematic representation of the MatLab algorithm that generates the FEM model.

indentations, the strain hardening of the alloy is not very marked, and is supposed not to change significantly the dimension of the dimples. Therefore, it is reasonable not to consider the strain hardening in the coverage computation. This method is valid as long as the coverage is less than 100%; for higher coverage level, not only the impact dimples must be considered but also the mass flow rate and the treatment time. When the MatLab routine reaches the desired coverage level, the Ansys commands file is created, and the FEM simulation is started. 3.4. Damping Only α damping is used, acting on the mass matrix of the target body, as it seems to be simpler and more effective to use. Two approaches are found in the literature [9,19] to compute the α coefficient, both based on the formula:

A second method, used in [19] for a disk-shaped target, computes α as: 2π α ¼ ω0 ¼ h

sffiffiffiffiffiffi 2E ρ

ð8Þ

resulting in α ≈ 180 106 s−1. The latter method widely overestimates the damping factor, setting the system in overdamping, so the former approach is chosen. A small set of simulations, developed to check the local vibration of the impact point after the shot impingement, is used to adjust the damping parameter and to reduce it slightly, in order to obtain an effective damping ratio having a subcritical oscillation regime. The final value is set to α = 24 106 s− 1. 3.5. Shot-target friction

α ¼ 2ςω0

ð6Þ

where ω0 is the fundamental frequency of the target body and a suitable value for the modal damping coefficient is ζ = 0.5. The first one, used in [9], suggests computing α as:

1 α ¼ ω0 ¼ h

sffiffiffiffiffiffi 2E ρ

ð7Þ

that gives α ≈ 30 106 s−1, being h the thickness of the target body, E his Young's modulus and ρ his density. Table 5 Best fitting parameters for Eq. (5). c00

c01

c10

−7341

0.1657

0.1347

Very little information is available about the tribological conditions occurring at the contact between ceramic materials and aluminium, even less in the specific case of alumina or zirconia and Al-7075. Moreover, the few data available in the scientific literature refer to tests in vacuum, where higher friction coefficients are measured than under ambient conditions [44,45]. For this reason, the way chosen to adjust the friction coefficient follows a top-down approach: a small set of 4 simulations having different number of impacting shots is generated. It is verified in the simulation that even a big change in the friction coefficient does not modify considerably the impact dimple dimension. Hence, the simulations set can be carried out with different friction coefficients without altering the coverage level. This simulation set, therefore, is developed with 6 different values of the friction coefficient, namely [0,0.05,0.1,0.2,0.3,0.4]. The average value of surface roughness and a residual stress profile is computed for every friction coefficient value (Fig. 6). The frictionless simulation gave the best results in terms of surface roughness but showed an irregular trend of the residual stress profile; on the other hand, higher fiction coefficients showed a marked tendency to

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Fig. 6. Residual stress profile for different friction coefficient (fd). Notice the saturation trend in the stress profile.

saturation, so that the three highest value gave approximately the same results. In the real process, the metal components are subject to a degreasing treatment, but no other surface treatment is done; during the shot peening no lubrication is provided. For these reasons, neither a zero nor a high friction coefficient seems to be realistic. The simulations and the previous considerations indicate a friction coefficient value of 0.05 as the best choice; this value of the friction coefficient is applied to all the simulations. 3.6. Number of simulations Given all the statistical aspects involved in the process and the importance of their correct representation, it is clear that many

simulations are needed to obtain reliable results. The parameters chosen to monitor the correct distribution are both the overall kinetic energy of the entire bead stack and the number of impacts in each simulation. Quite unexpectedly, the two parameters showed to be roughly equivalent. 30 simulations are randomly generated by the MatLab routine, and they are processed without any selection in order not to alter the stochastic representativeness of the sample. The cumulative probability distribution is computed for the entire population, both in terms of kinetic energy (Fig. 7) and number of shots, through a MatLab code that generates over three thousand shot arrangements. The results in term of surface roughness and residual stress seem to be very close to the convergence value at the end of the simulation campaign. Moreover, the kinetic energy and number of shots reproduced by the set of simulations are in satisfactory conformity with the expected

Fig. 7. Comparison between the distribution of the kinetic energy of the bead stream in the simulations and in the entire population.

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cumulative probability distribution, thus the experimental campaign is considered to be statistically representative. 4. Data processing, discussion and results 4.1. Control volume The nodal solutions are extracted in terms of nodal displacements and stresses after a short relaxing/springback period (0.5 μs) when the damping coefficient is raised to α = 60 106; in this way, the nodal velocities and acceleration are very low and the dynamical effects are negligible. Transverse displacements of the nodes lying in the control area (Section 3.3) are extracted to compute the surface roughness. The residual stress field is computed from nodal stresses contained in the cylindrical volume having base equal to the control area and height of 120 μm in depth; in this way, all the nodes on the control volume are well inside the projection of the 100% coverage area, and the nodal results are not affected by undesired border effects. 4.2. Surface roughness The surface roughness is calculated from simulations reproducing the measurements done by the 2D contact and 3D scan profilometers. 2D and 3D roughness parameters are evaluated considering out-ofplane displacements of nodes lying on two orthogonal diameters and on the whole control area, respectively. Specifically, Ra and Rq line-integral as well as Sa and Sq area-integral roughness parameters are numerically evaluated using the same domain discretization scheme of the FE model. The only controversial issue in this phase concerns the choice of the reference plane to be used to compute the surface roughness. According to the common definition of roughness, the average out-of-plane displacement of the nodes should be used. However, as shot impacts have been concentrated only in the central portion of the target surface, the drop in the average height of the impacted area is accompanied by a rise of the surrounding areas because of the material incompressibility. In this way, the overall surface average height does not change significantly. In the realistic case, however, the whole target surface would be peened, and no great change in the average surface height is expected; for this reason, the reference plane chosen for the roughness computing is the original plane where the nodes lie in the undeformed model. The results are shown in Table 6. It can be seen that the numerical simulation slightly underestimates the actual surface roughness, both in the 2D and (even if to a lower extent) in the 3D measurement. Specifically, the underestimation is 17.7% considering the Sa parameter and 27.4% considering the Ra parameter. It is also worth highlighting that the experimental values are well estimated by the maximum recorded surface roughness obtained in the simulations, and they also lie inside the 96% confidence interval around the average numerical value. The systematic underestimation of the surface roughness can be, at least partly, imputed to the FEM discretization of the target surface. Even if the impact area is finely meshed, the size of the elements may not be Table 6 Surface roughness resulting from the simulations. Roughness FEM parameter average value (μm)

FEM standard deviation (μm)

FEM max value (μm)

Experimental Experimental Error % value (μm) standard deviation (μm)

Ra Rq Sa Sq Rt

0.22 0.25 0.11 0.13 0.70

1.48s 1.67 1.29 1.54 14.0

1.35 1.67 1.24 1.54 7.12

0.98 1.16 1.02 1.23 6.12

0.14 0.15 0.05 0.07 0.61

−27.4 −30.5 −17.7 −20.1 −14.0

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able to entirely capture the sharp peaks of the impinged surface. In other words, the FE mesh might low-pass filter the surface topology, thus eliminating the contribution of displacement with high spatial frequency on the surface roughness. In addition, Fig. 8 indicates an increasing trend in surface roughness Sa with rising kinetic energy of the bead stream (in the figure normalized with respect to a reference kinetic energy value). Assuming constant, with a certain approximation, the portion of kinetic energy transferred to the target body in the form of strain energy, the kinetic energy of the stream scales with the treatment intensity. This confirms the intuitive feeling that more intense peening treatments tend to produce higher roughness values. 4.3. Residual stress state The thickness of the surface layer where plasticization occurs is a significant estimator of the treatment intensity. EBSD analyses undertaken in [46] on the same peened material attested that this thickness is about 25 μm; this experimental value is in good agreement with the numerical simulations, which indicate an average thickness of the plasticized surface layer of about 20 μm. This layer is subjected to intense compressive residual stresses. The comparison between numerically estimated and experimentally measured residual stresses is not straightforward and requires a data processing method specifically developed in the present paper. In many papers, the in-depth residual stress profile is evaluated from nodal stresses and nodal coordinates expressed in the undeformed reference system (e.g. [10,22]). In a few papers (e.g. [38]), it is made clear that the nodal coordinates of the deformed model are considered with the aim of achieving a more realistic estimation of the spatial distribution of the residual stress values. This issue is marginal in conventional shot peening, as the depth of the surface layer, where significant nodal displacement take place, is small with respect to that interested by compressive residual stresses. Conversely, in micro shot peening treatments, the depth of such layers is comparable; therefore, a realistic estimation of the residual stress profile requires the nodal displacements to be taken into account. In addition, the effect of X-ray penetration on the residual stress measurements must be considered for a consistent comparison of experimental and numerical data. In the present paper, three main strategies are applied to address these issues. The first one consists in ideally slicing the control volume in 2 μm thick layers starting from the highest peak on the surface and proceeding towards the specimen depth. An average of the nodal stress value for all the nodes in every slice is computed, and a residual stress profile is obtained as a function of the depth below the surface. This profile is compared with the profile obtained in Section 2.3 (see [23] for further detail) removing the radiation penetration effects from the XRD measures. Fig. 9(A) shows experimental data corrected for penetration and the numerical estimates corrected for layer deformation. It can be noted that the 95% confidence interval of the numerical profile is almost completely comprised in that of the experimental measure. The depth of surface layers interested by compressive residual stresses (about 50 μm) and the intensity of compressive residual stress peak (about −400 MPa) are well reproduced by the numerical simulations, while these latter tend to underestimate the peak location below the surface (12 μm vs 20 μm) and to overestimate the compressive residual stresses in the outer 10 μm thick layer. It is also interesting to observe that the numerical simulations indicate, below the surface layer interested by compressive residual stresses, a fairly low tensile residual stress peak (about 50 MPa) followed by a gradual extinction of them. This is in good agreement with neutron diffraction measurements done in [47] and contradicts the concerns that shot peening could induce an intense localized tensile residual stress peak thus jeopardizing the beneficial effect exerted by the surface compressive residual stresses. The second strategy is based on a completely different approach. Considering the known X-ray penetration depth, the nodal stresses

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Fig. 8. Surface roughness Sa vs. the normalized overall kinetic energy of the bead stream.

are treated in order to obtain a residual stress profile comparable with the experimental residual stress profile directly obtained from the XRD measure. At each depth below the surface, the residual stress value is computed by numerical integration of Eq. (1), whereby the integral is replaced by the following weighted average of discrete residual stress estimations: ∑i¼1 σ i e−

z−z ξ

N

σ xx ðzÞ ¼

0 z−z ξ

∑i¼1 e− N

0

ð9Þ

where N is the number of nodes laying deeper than the chosen y value, yi and σi are respectively the depth and the residual stress value for each of the selected nodes and ξ is the information depth discussed in Section 2.3. Fig. 9(B) compares raw experimental residual stress data with the numerical estimations done according to this second strategy, namely corrected for layer deformation and X-ray penetration. Also in this case the agreement is very good, especially in terms of overlapping between the confidence intervals, apart from a very superficial layer (8 μm thickness), where the simulations overestimate the compressive residual stresses. This could be related to the fact that the structure of this

Fig. 9. (A) Comparison between true RS profile from the FEM and the RS profile as computed in [22]. (B) Comparison between RS profile from the FEM, considering the penetration effect of the x-ray, and the RS profile detected with the XRD analysis. (C) Comparison between RS profile from the FEM, considering the penetration effect of the X-ray and the pseudo density of the peened surface, and the RS profile detected with the XRD analysis.

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layer is greatly affected by the surface roughness, as its thickness is comparable with the maximum peak-to-valley distance. The last approach attempts to take into account the effect of both surface roughness and radiation penetration on the XRD measurement of the residual stress profile. Specifically, the outer surface layers are not continuous owing to the irregular surface morphology composed of peaks and valleys. Surface layers can then be referred to as a continuum of pseudo-density lower than that of the bulk. For this reason, they are expected to contribute less to the residual stress information collected by the XRD technique. Therefore, in a first approximate attempt to estimate the true residual stress profile, the contribution of each material layer to the XRD measure is scaled proportionally to its pseudo-density. To evaluate this parameter, the control volume is divided into thin “slices” (1 μm thickness) and the material continuity is estimated as the ratio of the number of nodes in every slice to the number of nodes on the undeformed surface. The stress value of each material layers is scaled as follows: 1) the penetration coefficient ξ is supposed to be related to the actual material density, being the material a filter to the radiation penetration, so for each material layer a different ξl coefficient is computed:

ξl ¼

Nsurf Nl

ð10Þ

where ξl is the penetration coefficient for the l-th layer, Nl is the number of nodes in the l-th layer and Nsurf is the number of nodes on the undeformed material surface; 2) The residual stress is thus computed from the following expression:

N

σ xx ðzÞ ¼

−z−z

0

Npv ∑i¼1 σ i e ξl 0 Nu −z−z N ∑i¼1 e ξl

ð11Þ

where Npv is the number of node having height lower than the highest peak and higher than the deepest valley, and Nu is the number of nodes enclosed in the same volume in the undeformed configuration. As a first attempt to take into account this effect, the third strategy based on a pseudo-density of the surface layers is adopted in the comparison shown in Fig. 9(C). In this case, the stress profile appears somehow artificial, indicating the need of a more sophisticated algorithm in the pseudo-density computation. Anyway, it is clear that the stress profile correction moves in the right direction, reducing the surface stress value; a better algorithm could make the stress curve smoother and presumably closer to the experimental curve. In conclusions, these comparisons demonstrate how difficult it is to interpret the experimental surface residual stress values, as they are greatly affected by the actual penetration depth of the radiation into the roughness asperities. The irregular surface morphology makes also complicate establishing the origin of the depth coordinate used to map the residual stress profile. 4.4. Stress concentration factor The stress concentration exerted by the surface roughness is a key parameter to evaluate the capability of the surface treatment to improve the fatigue behavior of the peened part. In order to compute the stress concentration factor, an implicit procedure is performed after the explicit dynamic simulation. The finely meshed central volume of the target body, where all the shots are already impinged, is exported into the static implicit simulation environment (Fig. 10). The new model has roughly the shape of a square based parallelepiped with side 156 μm and height 120 μm, and preserves the deformed shape of the previous

275

model but not the residual stress state. The model undergoes two static simulations, consisting in the application of a uniform tensile stress of 1 MPa on two opposite side faces, first in the x then in the z direction. The results are analysed in terms of Von Mises equivalent stress to estimate the stress concentration factor. The simplest method for the estimation of the Kt factor consists in computing the ratio between the nominal stress applied to the model and the maximum stress in the model. This method leads to a large overestimation of the stress concentration factor, since it considers the stress state that develops in very small volumes (virtually, in a single node) without taking into account the stress state in the surrounding material. Indeed, in the shallowest points of the impingement dimples an intense stress state develops during the simulation of the tensile test, and the stress peak is higher if the dimple is deeper; anyway, its value decreases rapidly moving away from the bottom of the dimple. The concept of material notch sensitivity was introduced to account for this effect; more recently, the theory of critical distance has been developed and formalized to predict the fatigue resistance of parts carrying stress raisers [48]. To predict the fatigue strength of notched shot-peened parts, we proposed in [49] a critical distance theory in which the stress averaging domain is a circular area lying on the plane normal to the direction of load application and centred in the crack initiation site. The size of this circular area depends on the material and the number of cycles to failure and was estimated equal to 54 μm for predicting the highcycle fatigue strength of Al-7075-T651. In the present paper, we adopt the same approach to estimate the notch fatigue factor, whereby the equivalent von Mises stress is averaged over a half-circular area centred in the bottom of the crater characterized by the highest stress value and therefore in the most likely crack initiation site (Fig. 11(A)). The plot representing Kt parameter versus the radius of the hemi-circular area is shown in Fig. 11(B). The results obtained from the FE simulation show good accordance with the experimental/empirical results, also considering a critical distance of 54 μm, which gives a Kt value of 1.05. The semi-analytical approach devised in [50] and used in [46] predicts a value of 1.11 when the roughness parameters listed in Table 6 are used, while the 2D FEM model developed in [49] using the experimental surface profiles estimates a Kt value of 1.09. Also in this case the slight discrepancy of FE predictions from experimental measures can be ascribed to the numerical underestimation of the surface roughness, which is supposed to play the most important role on the stress concentration effect. 4.5. Some observations on the stress concentration factor The population of shot peening experiments created in the present work has been analysed to search for possible relationships between the peening process parameters and the effects on the target material in terms of roughness and residual stresses. No evident relationship has been found between the stress concentration factor and the average shots energy in the simulation (Fig. 12(A)), the maximum energy of a single shot in the simulation, the standard deviation of the kinetic energy in the shots stream. Moreover, no correlation has been found between maximum compressive residual stress and the overall kinetic energy (Fig. 12(B)). Even if the link between the surface roughness and the stress concentration is a matter of fact, the Kt value (computed using a 54 μm radius) does not show a clear correlation to the overall kinetic energy of the shots stream (Fig. 12(C)) while the resulting value of the surface roughness does (Fig. 8). We must remind, however, that the surface roughness is a distributed phenomenon, which depends on the dynamics of a high number of beads impinging on a surface, while Kt is a local phenomenon, depending on the morphology of a limited portion of the surface. In conclusion, it is very complicated to identify the critical conditions leading to the development of a high surface roughness and to intense stress concentration. So far, it seems that harder shot peening

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Fig. 10. Representation of the procedure developed for the explicit-to-implicit simulation used to compute the Kt factor.

Fig. 11. (A) Schematic section representation of the model used to compute Kt. The striped area highlight the area used to compute the average stress value. (B) Stress intensity factor vs. radius of the hemi circular area used for its computation. a: maximum stress concentration near a single node; b: Kt computed using a 54 μm critical distance, c: Kt computed using the semi-analytical formula in [46], d: Kt computed with a 2D FEM model in [49].

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277

Fig. 12. (A) Kt factor vs. normalized average kinetic energy of the beads in the simulation; (B) Maximum compressive RS in the target vs. normalized overall kinetic energy of the bead stream.; (C) Kt factor vs. normalized overall kinetic energy of the bead stream.

treatments promote this detrimental effect without giving a concomitant improvement of the residual stress state able to counterbalance the former one. However, it is worth noting that the surface condition at the end of the treatment does not only depend on the process intensity, but is also influenced by the impacts interaction that may determine material rearrangement under specific (and until now unknown) treatment conditions. 5. Conclusions The present paper describes one of the first attempts to simulate a micro-shot peening treatment. Special care is taken in reproducing the statistical variability that affects the process parameters: coverage, shot size distribution, shot velocity distribution, random impacts point. The Lemaitre-Chaboche material model is used to take into account the correct material behavior under repeated strain. A number of 30 explicit dynamic simulations in Ansys/LS-Dyna are carried out to produce a population of numerical results that is statistically significant. The simulations are validated through surface roughness and residual stress measurements. For this purpose, several procedures have been specifically developed in the present paper to permit a consistent comparison between experimentally measured and numerically estimated residual stresses. The following conclusions can be drawn: 1. The numerical simulations are in good agreement with both 2D and 3D roughness measurements. Nevertheless, the discretization of the target surface produce a systematic underestimation of the surface roughening effect. 2. If the numerically estimated residual stresses are corrected for layer deformation and experimentally measured values are corrected for X-ray penetration, a good agreement is obtained both in terms of stress magnitude and depth of the residual stress peak, even if the deep deformation of the surface layers in the target generates some uncertainties in the estimation of the stress profile.

3. If the numerically estimated residual stresses are corrected for both effects (radiation penetration and layers deformation), again a good agreement is obtained with the experimental data, especially in the stress peak region. 4. The discrepancy between numerically simulated and experimentally predicted residual stress in the outer layer can be reduced by considering the effect of surface roughness on the pseudo-density of the material. 5. The numerical simulations permit to estimate the stress concentration effect exerted by the surface roughness, in good agreement with analytical and numerical values taken from the literature. 6. It is very hard to identify clear correlations between the parameters governing the dynamics of the bead stream and the treatment effects. Only the surface roughness seems to be correlated with the overall kinetic energy of the bead stream. References [1] G. Fett, Understanding shot peening - a case-history, Mod. Cast. 73 (1983) 29–31. [2] N. Burrell, Controlled Shot Peening of Automotive Components, SAE Technical Paper, 1985. [3] G. Nachman, Shot peening - past present and future, The 7th International Conference on Shot Peening, Warsaw, 1999. [4] M. Benedetti, E. Torresani, M. Leoni, V. Fontanari, M. Bandini, C. Pederzolli, C. Potrich, The effect of post-sintering treatments on the fatigue and biological behavior of Ti6Al-4V ELI parts made by selective laser melting, J. Mech. Behav. Biomed. Mater. 71 (2017) 295–306. [5] A. Ahmed, M. Mhaede, M. Basha, M. Wollmann, L. Wagner, The effect of shot peening parameters and hydroxyapatite coating on surface properties and corrosion behavior of medical grade AISI 316L stainless steel, Surf. Coat. Technol. 280 (2015) 347–358. [6] M. Benedetti, V. Fontanari, C. Santus, M. Bandini, Notch fatigue behaviour of shot peened high-strength aluminium alloys: experiments and predictions using a critical distance method, Int. J. Fatigue 132 (2010) 1600–1611. [7] M. Benedetti, V. Fontanari, M. Bandini, E. Savio, High- and very high-cycle plain fatigue resistance of shot peened high-strength aluminum alloys: the role of surface morphology, Int. J. Fatigue 70 (2015) 451–462. [8] S.A. Meguid, G. Shagal, J.C. Stranart, J. Daly, Three-dimensional dynamic finite element analysis of shot-peening induced residual stress, Finite Elem. Anal. Des. 31 (1999) 179–191.

278

M. Marini et al. / Surface & Coatings Technology 321 (2017) 265–278

[9] S.A. Meguid, G. Shagal, J.C. Stranart, 3D FE analysis of peening of strain-rate sensitive materials using multiple impingement model, Int. J. Impact Eng. 27 (2002) 119–134. [10] S.A. Meguid, G. Shagal, J.C. Stranart, Development and validation of novel FE models for 3D analysis of peening of strain-rate sensitive materials, J. Eng. Mater. Technol. ASME 129 (2007) 271–283. [11] G.H. Majzoobi, R. Azizi, A. Alavi Nia, A three-dimensional simulation of shot peening process using multiple shot impacts, J. Mater. Process. Technol. 164–165 (2005) 1226–1234. [12] G.H. Majzoobi, K. Azadikhah, J. Nemati, The effects of deep rolling and shot peening on fretting fatigue resistance of aluminum 7075-T6, Mater. Sci. Eng. A 516 (2009) 235–247. [13] S.M. Hassani-Gangaraj, M. Guagliano, G.H. Farrahi, Finite element simulation of shot peening coverage with the special attention on surface nanocrystallization, Proc. Eng. 10 (2011) 2464–2471. [14] S. Bagherifard, R. Ghelichi, M. Guagliano, On the shot peening surface coverage and its assessment by means of finite element simulation: a critical review and some original developments, Appl. Surf. Sci. 259 (2012) 186–194. [15] T. Hong, J.Y. Ooi, B. Shaw, A numerical simulation to relate the shot peening parameters to the induced residual stresses, Eng. Fail. Anal. 15 (2008) 1097–1110. [16] G.I. Mylonas, G. Labeas, Numerical modelling of shot peening process and corresponding products: residual stress, surface roughness and cold work prediction, Surf. Coat. Technol. 205 (2011) 4480–4494. [17] S. Bagherifard, R. Ghelichi, M. Guagliano, A numerical model of severe shot peening (SSP) to predict the generation of a nanostructured surface layer of material, Surf. Coat. Technol. 204 (2010) 4081–4090. [18] S. Bagherifard, R. Ghelichi, M. Guagliano, Numerical and experimental analysis of surface roughness generated by shot peening, Appl. Surf. Sci. 258 (2012) 6831–6840. [19] S.M. Hassani-Gangaraj, M. Guagliano, G.H. Farrahi, An approach to relate shot peening finite element simulation to the actual coverage, Surf. Coat. Technol. 243 (2014) 39–45. [20] H.Y. Miao, S. Larose, C. Perron, M. Levesque, On the potential applications of a 3D random finite element model for the simulation of shot peening, Adv. Eng. Softw. 40 (2009) 1023–1038. [21] A. Gariepy, S. Larose, C. Perron, M. Levesque, Shot peening and peen forming finite element modelling - towards a quantitative method, Int. J. Solids Struct. 48 (2011) 2859–2877. [22] I. Penuelas, P. Sanjurjo, C. Rodrıguez, T.E. Garcıa, F.J. Belzunce, Influence of the target material constitutive model on the numerical simulation of a shot peening process, Surf. Coat. Technol. 258 (2014) 822–831. [23] M. Benedetti, V. Fontanari, B. Winiarski, M. Allahkarami, J.C. Hanan, Residual stresses reconstruction in shot peened specimens containing sharp and blunt notches by experimental measurements and finite element analysis, Int. J. Fatigue 87 (2016) 102–111. [24] M. Benedetti, T. Bortolamedi, V. Fontanari, F. Frendo, Bending fatigue behaviour of differently shot peened Al 6082 T5 alloy, Int. J. Fatigue 26 (2004) 889–897. [25] G.S. Was, R.M. Pelloux, The effect of shot peening on the fatigue behavior of alloy 7075-T6, Metall. Mater. Trans. A 10 (1979) 656–658. [26] Y. Mutoh, G.H. Fair, B. Noble, R.B. Waterhouse, The effect of residual stresses induced by shot peening on fatigue crack propagation in two high strength aluminium alloys, Fatigue Fract. Eng. Mater. Struct. 10 (1987) 261–272. [27] K. Oguri, Fatigue life enhancement of aluminum alloy for aircraft by fine particle shot peening (FPSP), J. Mater. Process. Technol. 211 (2011) 1395–1399. [28] T. Kim, J.H. Lee, H. Lee, S. Cheong, An area-average approach to peening residual stress under multi-impacts using a three-dimensional symmetry-cell finite element model with plastic shots, Mater. Des. 31 (2010) 50–59. [29] H.Y. Miao, D. Demers, S. Larose, C. Perron, M. Levesque, Experimental study of shot peening and stress peen forming, J. Mater. Process. Technol. 210 (2010) 2089–2102.

[30] T. Chaise, J. Li, D. Nelias, R. Kubler, S. Taheri, G. Douchet, V. Robin, P. Gilles, Modelling of multiple impacts for the prediction of distortions and residual stresses induced by ultrasonic shot peening (USP), J. Mater. Process. Technol. 212 (2012) 2080–2090. [31] M. Benedetti, V. Fontanari, B.D. Monelli, Numerical simulation of residual stress relaxation in shot peened high-strength aluminum alloys under reverse bending fatigue, J. Eng. Mater. Technol. 132 (2010) 11012-1–11012-9. [32] M. Benedetti, V. Fontanari, P. Scardi, C.L.A. Ricardo, M. Bandini, Reverse bending fatigue of shot peened 7075-T651 aluminium alloy: the role of residual stress relaxation, Int. J. Fatigue 31 (2009) 1225–1236. [33] M. Benedetti, V. Fontanari, M. Bandini, D. Taylor, Multiaxial fatigue resistance of shot peened high-strength aluminum alloys, Int. J. Fatigue 61 (2014) 271–282. [34] M.G. Moore, W.P. Evans, Mathematical correction for stress in removed layers in Xray diffraction residual stress analysis, SAE Trans. 66 (1958) 340–345. [35] I.C. Noyan, J.B. Cohen, Residual Stress: Measurement by Diffraction and Interpretation, Springer-Verlag, New York, 1987. [36] N.S. Brar, V.S. Joshi, B.W. Harris, Constitutive model constants for Al7075-T651 and Al7075-T6, AIP Conference, Ann Arbor, 2009. [37] L. Schwer, Optional strain-rate forms for the Johnson Cook constitutive model and the role of the parameter epsilon 01, 6th European LS-DYNA Users' Conference, Gothenburg, 2007. [38] K. Dai, J. Villegas, Z. Stone, L. Shaw, Finite element modeling of the surface roughness of 5052 Al alloy subjected to a surface severe plastic deformation process, Acta Mater. 52 (2004) 5771–5782. [39] J. Lemaitre, J.L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, Cambridge, 1990. [40] J. Lemaitre, A Course on Damage Mechanics, Springer-Verlag Berlin Heidelberg GmbH, Berlin, 1998. [41] E. Dill, The Finite Element Method for Mechanics of Solids with Ansys Application, CRC Press, Boca Raton, 2012. [42] J.R. Pothnis, Y. Perla, H. Arya, N.K. Naik, High strain rate tensile behavior of Aluminum alloy 7075 T651 and IS 2062 mild steel, J. Eng. Mater. Technol. 133 (2011) pp. 021026-021026-9. [43] K.C. Jørgensen, V. Swan, Modeling of armour-piercing projectile perforation of thick aluminium plates, 13th International LS-DYNA Users Conference, Detroit, 2014. [44] P. Blau, Friction Science and Technology from Concepts to Applications, CRC Press, Boca Raton, 2008. [45] J.P. Davim, E. Santos, C. Pereira, J. Ferreira, Comparative study of friction behaviour of alumina and zirconia ceramics against steel under water lubricated conditions, Indust. Lubr. Tribol. 60 (2008) 178–182. [46] B. Winiarski, M. Benedetti, V. Fontanari, M. Allahkarami, J.C. Hanan, P.J. Withers, High spatial resolution evaluation of residual stresses in shot peened specimens containing sharp and blunt notches by micro-hole drilling, micro-slot cutting and micro-X-ray diffraction methods, Exp. Mech. 56 (2016) 1449. [47] R. Menig, L. Pintschovius, V. Schulze, O. Vohringer, Depth profiles of macro residual stresses in thin shot peened steel plates determined by X-ray and neutron diffraction, Scr. Mater. 45 (8) (2001) 977–983. [48] L. Susmel, D. Taylor, The theory of critical distances to estimate finite lifetime of notched components subjected to constant and variable amplitude torsional loading, Eng. Fract. Mech. 98 (2013) 64–79. [49] M. Benedetti, V. Fontanari, M. Allahkarami, J.C. Hanan, M. Bandini, On the combination of the critical distance theory with a multiaxial fatigue criterion for predicting the fatigue strength of notched and plain shot-peened parts, Int. J. Fatigue 93 (2016) 133–147. [50] J.K. Li, Yao Mei, Wang Duo, Wang Renzhi, An analysis of stress concentration caused by shot peening and its application in predicting fatigue strength, Fatigue Fract. Eng. Mater. Struct. 15 (1992) 1271–1279.