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1 Materials Science and Engineering A 532 (2012) Contents lists available at SciVerse ScienceDirect Materials Science and Engineering A journa l h o me pa ge: Laser shock peening of Ti-17 titanium alloy: Influence of process parameters C. Cellard a,d. Retraint a,m. Franç ois a, E. Rouhaud a,, D. Le Saunier b a University of Technology of Troyes (UTT), Charles Delaunay Institute, LASMIS, UMR CNRS 6279, 12 Rue Marie Curie, BP2060, Troyes Cedex, France b SNECMA Evry Corbeil, Route Henry Auguste Desbruères, Evry, France a r t i c l e i n f o Article history: Received 8 June 2011 Received in revised form 28 October 2011 Accepted 29 October 2011 Available online 6 November 2011 Keywords: Hardness Incremental hole drilling Residual stress Work-hardening X-ray diffraction Design of experiments (DoE) a b s t r a c t The influence of the process parameters of laser shock peening was investigated on specimens made of an aeronautic titanium alloy: Ti 5Al 2Sn 2Zr 4Cr 4Mo (Ti-17). In order to quantify the effect of relevant process parameters, an experimental design was carried out. It is based on a full factorial design with four factors (laser fluence, pulse duration, number of impacts and thickness of the sample) and two levels for each factor. The process is characterised with the following variables: the depth of the impacts, the roughness of the treated surface, the hardening of the material (itself evaluated with the hardness and X-ray diffraction peak width), the residual stresses left in the sample and the global curvature of the sample. It is found that all the parameters have an influence on the residual stresses and that laser shock peening has no influence on roughness and low influence on work-hardening. The variables are then analysed in order to evaluate correlations. The increase in hardness is found to be essentially due to compressive residual stresses, cold work-hardening having only a small effect. In thin specimens, the stress redistribution due to self-equilibrium leads to tensile residual stresses at the treated surface and to large deformations of the specimens Elsevier B.V. All rights reserved. 1. Introduction While flying, a turbojet can swallow foreign objects such as birds, fragments, etc. Impacts induced by these objects are known as Foreign Object Damage (FOD), and can lead to the cracking of fan blades. In order to reduce maintenance costs, engine manufacturers try to find ways to increase the fatigue life of blades after FOD by introducing compressive residual stresses. Various processes have been tested. One of them, shot peening, is well established and routinely used in aeronautics. However, it exhibits a number of limitations: the depth of compressive residual stresses is relatively small (about 0.2 mm), the cumulated plastic strains are important and thus the material is strongly work-hardened. This may lead to damage in the material microstructure and may accelerate the relaxation of residual stresses [1]. The application of laser shock peening (LSP) could overcome these drawbacks [2]. Developed in the beginning of the 60 70s [3 5], this treatment is known to introduce, when compared to shot peening, high compressive residual stresses deeper into the part with less hardening, leading to an appreciable increase in fatigue life [6,7]. The principle of laser shock peening process is presented in Fig. 1. It is based on the use of a laser pulse to generate plasma by vaporizing a thin opaque coating layer. The expansion of the plasma generates compressive elastoplastic waves that propagate into the material. Close to the surface, the energy of the waves is high enough to induce plasticity, which, in turn, creates compressive residual stresses. Past a certain depth, the waves become purely elastic. To increase the efficiency of impulse transmission into the material, a confining medium, transparent to laser light, is spread on the surface of the coating. The objective of the present study is to analyse the effect of laser shock peening on the aeronautic titanium alloy Ti 5Al 2Sn 2Zr 4Cr 4Mo (Ti-17) in order to potentially apply this process on fan blades. A design of experiment (DoE) is proposed to quantify the influence of treatment parameters on the material and on the structure. A literature review [8 12] was carried out to determine the effects of the parameters on the process and on the material characteristics. It was noticed that no studies have been carried out on the laser shock peening of Ti-17 titanium alloy and that very little information can be found on certain parameters, such as the nature of the laser pulse [6]. 2. Design of experiments (DoE) 2.1. Choice of the relevant parameters Corresponding author. Tel.: ; fax: address: rouhaud@utt.fr (E. Rouhaud). LSP is controlled by a number of factors such as wavelength of the laser, nature of the pulse, laser fluence, pulse duration, spot /$ see front matter 2011 Elsevier B.V. All rights reserved. doi: /j.msea

2 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Fig. 1. Principle of laser shock peening [2]. A laser pulse with a duration of the order of a few nanoseconds and a fluence range from 1 to 10 GW/cm 2 generates a plasma. The expansion of the plasma generates shock waves into the material leading to plastic deformation and residual stresses. geometry, number of impacts at a given location, coverage method (tiling) and overlapping rate, nature and thickness of the coating layer, nature of the confining medium, angle of incidence. Factors that were not relevant, as reported in the literature [13], or that were imposed by the equipment (and thus could not be varied), were dismissed. The process parameters imposed by the equipment were: the nature of the laser (Nd:Yag), the squared shape of the spot, the size of the spot (5.44 mm with a laser fluence of 3 GW/cm 2, 3.85 mm with 6 GW/cm 2 and 3.14 mm with 9 GW/cm 2 ), the covering rate between two spots ( %), the nature of the confining medium (water) and the nature of the coating (aluminium). Furthermore, although it is not a process parameter stricto sensu, the thickness of the specimen has been studied in order to evaluate its influence on the global deformation of the treated component and on the residual stress profile left after the treatment. Indeed, this thickness affects the balance of stresses, depending on the depth of the plastified layer and consequently the final shape of the component. In addition, the propagation of the elasto-plastic waves may be influenced by the surface opposite to the shock, especially when the typical distance for the decay of the plastic wave is longer than the thickness of the specimen. Specimen thickness varied between 1 and 9 mm, the first being of the same magnitude as fan blades and the second considered as thick enough to be weakly bent by LSP. Thus, four factors were kept in the present study: specimen thickness, laser fluence, pulse duration and number of impacts. For each of these factors, two levels were chosen corresponding to a low level (level 1) and a high level (level +1) such that: - Thickness: 1 mm (low level) and 9 mm (high level). - Laser fluence: 3 GW/cm 2 (low level) and 9 GW/cm 2 (high level). - Pulse duration: 9 ns (low level) and 27 ns (high level). - Number of impacts: 1 impact (low level) and 3 impacts (high level). Laser fluence is of the order of several GW/cm 2. From preliminary tests, the low level was chosen at 3 GW/cm 2 the minimum value to modify the residual stress level in the specimen. According to literature results [8,9], such a fluence gives a plasma pressure of 2.4 GPa. This value is lower than the Hugoniot limit P H which is the threshold above which the plasma pressure is able to plastify the material [6]: P H = y, (1) Fig. 2. Parameters chosen as responses to characterise the residual stress profile. A typical residual stress profile is presented as a function of depth. The surface residual stress ( surf ), the maximum residual stress ( max), the depth at which the residual stress is maximal (e max) and the depth at which residual stress is equal to zero (e = 0) are defined. where y is the dynamic elasticity limit of the material and is Poisson s ratio. The former was estimated from literature data [14,15] to 1700 MPa and the latter was measured by tensile testing to With these values, P H is equal to 2.8 GPa and thus a little above 2.4 GPa. However, the two values are rather close and the fluence of 3 GW/cm 2 was seen as a soft treatment. Pulse duration, in the order of a few ns, was chosen according to values commonly found in the literature [10,1]. The ratio between high and low levels was set to three for the fluence (I), duration () and number of impacts (N). This choice was made in order to get different configurations with either the same total energy (I) transmitted to the material during one impulse or the same total energy (IN) during the treatment. The present study is thus based on a two-level full design [16], which means that all the combinations of high and low levels of the four factors are studied. This leads to 2 4 = 16 treatment conditions Measured responses The creation of compressive residual stresses is the main objective of LSP. Specific attention will thus be given to this information, which is known to have a strong influence on fatigue life. However, the treatment may also affect other aspects of the component, such as work-hardening and surface topography at various scales. The residual stress profile is characterised with four parameters: the surface residual stress ( surf ), the maximum residual stress ( max ), the depth at which the residual stress is maximum (e max ) and the depth at which residual stress is equal to zero (e = 0), as can be seen in Fig. 2. The first parameter was evaluated by X-ray diffraction (XRD), while the others were obtained with the incremental hole drilling method (IHD). The work-hardening state is a complex quantity that cannot be characterised directly. Two methods were chosen to get a semi-quantitative estimate of its variation. Vickers micro-hardness measurements enable the study of yield stress variations; X-ray diffraction peak widths reflect, among other effects such as domain size or inter-granular stresses, the density of crystalline defects like dislocations or stacking faults [17]. As fan blades are slender components, the curvature of the specimens was studied through a Coordinate Measuring Machine in order to quantify possible geometrical distortions induced by LSP. Parameters that could affect the air flow on the surface of the blade

3 364 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Table 1 Summary responses, effects of the factors and second-order interactions on the residual stress profiles of 9 mm specimens. The shadowed cells represent an effect that is not significant with respect to the uncertainty. Surface stress (σ surf ) Maximum stress (σ max ) Depth of σ max (e max ) Depth where σ = 0 (e σ=0 ) Responses Minimum Maximum Thickness -105 Effects Laser fluence Pulse duration Number of impacts Thickness / Fluence -85 Thickness / Duration -80 Interactions Thickness / Impacts -29 Fluence / Duration Fluence / Impacts Duration / Impacts Measurement uncertainty 46 MPa 45 MPa 5 μm 80 μm such as micro-scale geometry (roughness) and meso-scale geometry (depth of impacts) were also analysed. In the present paper, roughness is characterised by two variables: the arithmetic average roughness (Ra) and the total roughness (Rt). Thus, the chosen responses, studied through DoE, are the surface stress ( surf ), the maximum stress ( max ), the depth for which the stress is maximum (e max ) and the depth for which = 0 (e = 0), the width of diffraction peaks, the Vickers micro-hardness, the roughness (Ra and Rt), the depth of the impacts and the curvatures Exploitation of the DoE and uncertainties regarding the responses The aim of a DoE is to quantify the magnitude of the influence of a given factor on the measured response. This is called the effect. It also gives the joint influence of two or more factors on the response and this is called interaction of second, third or higher order. Effects and interactions are computed through matrix calculations involving the 2 4 = 16 measurements according to ISO/TR 29001:2007 Standard. In the sequel, they are presented in a table in which a white box indicates that the effect/interaction is higher than the measurement uncertainty and thus considered influential. On the other hand, a grey box expresses that the effect is smaller than the measurement uncertainty. The values of factor effects reported in the tables must be interpreted as a change with respect to the average value responses measured after LSP treatment. For instance, in Table 1, the laser fluence effect on max is equal to 177 MPa. This means that, when the laser fluence is equal to its high level (9 GW/cm 2 ), max is shifted by 177 MPa with respect to its average value and when the laser fluence is equal to its low level (3 GW/cm 2 ), it is shifted by +177 MPa. As this value of 177 MPa is significantly larger than the measurement uncertainty (46 MPa), the effect of laser fluence on the maximum residual stress is considered significant. The interpretation of interactions is similar. For instance, in Table 1, when both the thickness and the laser fluence are set to their higher level, the value of the surface stress is shifted by 85 MPa with respect to the global average response. To assess the influence of process factors on a given response, it is thus necessary to know the uncertainty associated with the measurement of this response. The uncertainties can be estimated using several methods: - A thorough investigation of uncertainty sources associated with the measurement method according to the Guide for Uncertainty in Measurement (GUM, ISO Standard). - A repetition of measurements and computation of the standard deviation. - An analysis of the higher order interactions given by exploiting the DoE. To conduct a consistent analysis, the last method was used. It is justified by the fact that interactions of order higher than two are usually equal to zero. As a consequence, the effects of 3rd and 4th order interaction obtained through DoE exploitation can be considered as an estimate of the measurement of the standard deviation of the noise. These standard deviations were averaged using their corresponding variances and were multiplied by 2 to get a confidence level of approximately 95 per cent following ISO Standard. It can be noted that the uncertainty levels obtained by this method were consistent with values obtained by repeating the measurements (roughness, hardness) or given by data treatment software (XRD, IHD). The uncertainties corresponding to each response are given in Tables 1, 2, 4 and Studied material and specimens geometry The material studied in the present paper is Ti-17. It is a ˇ metastable titanium alloy constituted of 70% phase (hexagonal close packed) and 30% phase (body-centred cubic). The nominal chemical composition of Ti-17 is the following: Ti 5Al 2Sn 2Zr 4Cr 4Mo (wt%). The mechanical and physical properties of the considered Ti-17 are: - Density: 4650 kg/m 3 - Poisson s ratio: Elastic modulus: 110,000 MPa - Yield stress: 1125 MPa - Hardness: 385 HV 5 The specimens were machined from a disk to the specified thickness and were annealed at 550 C for 2 h and air cooled, to reduce the residual stresses to a minimum level. The specimens are squares of 50 mm 50 mm size and are laser shocked on one side only (Fig. 3a). On the edges, a band of 5 mm width was left untreated. Fig. 3b shows the location where the various measurements were performed. The longitudinal direction was specified on each sample parallel to machining grooves. LSP was performed with successive lines of impacts. The longitudinal direction (L) refers to the direction parallel to the lines and the transversal direction; T corresponds to two successive treated lines.

4 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Table 2 Summary responses, effects of the factors and second-order interactions on work-hardening. Diffraction peak width ( ) Vickers hardness (HV 5) Responses Effects Interactions Reference (untreated material) Minimum Maximum Thickness Laser fluence Pulse duration Number of impacts Thickness/fluence Thickness/duration Thickness/impacts Fluence/duration Fluence/impacts Duration/impacts Measurement uncertainty Fig. 3. (a) Specimen shape showing the treated zone and (b) localisation of the points where the measurements have been performed. T is the transversal direction and L the longitudinal direction. 3. Residual stresses 3.1. Experimental details Surface stresses were measured by X-ray diffraction [18 20] at the centre of the specimen and the depth profiles were obtained using the incremental hole drilling method [21 23] in a corner to allow repeating measurements (Fig. 3b). The two components of the stress along the L and T directions were systematically measured to evaluate the equi-biaxility of the residual stress state. XRD measurements were carried out on a 4-circle diffractometer SEIFERT XRD 3000 PTS. The following parameters were used: - Copper anode tube ( K 1 = nm) with upstream,k 2 Kˇ nickel filter. Table 3 Comparison of the model of Carlsson and Larsson Eq. (4) [36] and the model proposed in this work Eq. (5) for hardness variation. Eq. 4 Eq. 5 Reference values σ y (MPa) H 0 (MPa) β 7765 Least-square residual 8 HV 6 HV - Gas flux Positive Sensitive Detector. - Crystallographic plane family {2 1 3} tilt angle values ranging from 60 to +60 with acquisition mode. Table 4 Summary of the responses, effects of the factors and second-order interactions for the surface topography. Ra (μm) Rt (μm) Depth of impacts (μm) Longitudinal reference (untreated surface) Longitudinal minimum Longitudinal maximum Responses Transversal reference (untreated surface) Transversal minimum Transversal maximum Thickness Effects Laser fluence Pulse duration Number of impacts Thickness / Fluence Thickness / Duration Interactions Thickness / Impacts Fluence / Duration Fluence / Impacts Duration / Impacts Measurement uncertainty 0.05 μm 0.61 μm 0.2 μm

5 366 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Fig. 4. Example of a residual stress profile determined by X-ray diffraction and hole drilling method; specimen 9 mm 9 GW/cm 2 9 ns 3 impacts. The penetration depth (depth at which the stress is measured) is about 4 m with these conditions. Experimental data were processed with a home-made software developed with Mathematica. The program performs: - Lorentz and polarisation corrections. - The removal of the background noise (assumed to be linear). - The least square fitting of diffraction patterns with a Pseudo-Voigt function taking into account the K 1 K 2 doublet with Rachinger assumptions to determine peak positions. - The least square fitting of peak positions with elliptical sin 2 method using X-ray elasticity constant (1/2)S 2 equal to MPa 1 [19]. The hole drilling method was carried out with a home made device. The following parameters were used: - Drilling increments: [20,40, 80, 120, 160, 200, 300, 400, 500, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000 m]. - Two types of milling tool were used: AMAYA M30A with 3 teeth for 2 mm diameter holes and UDSOM UD2331 with 3 teeth for 4 mm diameter holes. - Two types of Vishay strain gages rosettes were used: CEA-XX- 062UM-120 for 2 mm diameter holes and EA-XX-125RE-120 for 4 mm diameter holes. Data from strain gages were processed with CETIM Metro software, using polynomial regression and the incremental method to calculate the residual stress profiles. Fig. 4 shows a typical stress depth profile obtained on a thick specimen. It can be noticed that X-ray and hole drilling give consistent results, as was also the case for the other specimens Results It has been observed that the values of the stresses in the L and T directions are similar and the difference between two comparable stress values never exceeds 20% (e.g. Fig. 4). The residual stress tensor induced by the treatment can thus be considered equi-biaxial. This is consistent with the specimen and treatment symmetry. Thus, the stress tensor can be expressed by only one scalar value, its component along either the transversal or longitudinal direction. LSP is able to introduce compressive stress in 9 mm thick specimens. The thickness of the compressive layer varies between 50 m and 1.8 mm according to the treatment conditions. With the most severe impact conditions, the maximum compressive stress value reaches 714 MPa at a depth of 200 m while the surface stress reaches 690 MPa. Table 1 summarises the variation range for the four parameters characterising the residual stress profiles on thick specimens. Tensile surface residual stresses are noticed on two 9 mm thick samples and on almost all the 1 mm thick samples. The tensile residual stress measured on the surface varies from 13 to 150 MPa. Table 1 also summarises the effects of the different factors and second order interactions. It can be seen that all the factors have an influence on residual stress levels. The influence of the number of impacts is moderate, which may indicate that one impact is enough to bring the material to saturation. Quite logically, an increase of laser fluence and pulse duration increases both the surface stress and the maximum subsurface stress. They also affect significantly the depth of the compressive layer. However, they only have a small influence (about 30 m or 40 m) on the depth at which the stress is maximum. As the hole-drilling method could not be applied on 1 mm thick specimens, the effect of the thickness of the specimens was only studied on the surface residual stress. It can be seen that decreasing the specimen thickness also decreases (in magnitude) the surface stress. As will be seen below, it is mainly due to the redistribution of the stresses to maintain mechanical equilibrium on the crosssection of the specimen. The second order interactions are rather low. The most significant interactions are thickness/fluence and thickness/duration. This can be explained by the fact that high levels of fluence and duration cause an important plastification of the material and thus a stronger redistribution of residual stresses along the depth. It can be noticed that increasing both fluence and duration leads to a slight decrease of the depth of the compressive layer. This may mean that the residual stresses created in the most severe impact conditions (high fluence and duration) are high enough to bend the specimen and redistribute the stress profile: the compressive layer is shifted towards tensile values Discussion To explain the effect of specimen thickness on residual stress results, a more detailed analysis is necessary. On one hand, tensile surface residual stresses were detected on almost all thin specimens, despite the compressive nature of the pressure waves applied by the plasma expansion. On the other hand, negative values were determined on thick specimens treated in the same conditions as the previous ones. Due to large pressures involved in LSP, two-sided peening is recommended for thin specimens. The large pressures on the opposite surfaces of the target balance one another and avoid excessive deformation of the target. However, it

6 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Fig. 5. Determination of the plastic strain profile from the experimental residual stresses; specimen 9 mm 9 GW/cm 2 9 ns 3 impacts. requires access to both surfaces, which can be a problem in complex geometries, and the interaction of the shock waves through the thickness result in a more complex residual stress field [24]. Only a few studies explored two-sided peening on thin plates. Clauer and Lahrman [25] investigated two-sided peening on 1 mm thickness Ti 6Al 4V. Contrary to this study, in fact, circular laser spots were used with a laser fluence of 5.5 GW/cm 2 and compressive surface residual stresses were noticed. Because the applications of the present study concern thin specimens with complex geometries, it was one of the objectives of the study to investigate this specific configuration. An analytical model based on the eigenstrain reconstruction method was developed [26,27]. The compatibility equations for the total strain (plastic + elastic) are first written under basic conditions of symmetry of strain tensors and homogeneity of strains and stresses along the L and T directions (assuming homogeneity of the treatment). It can then be derived, using Hooke s law to relate elastic strains and stresses, that: 1 + ε p = Az + B, (2) E where is the residual stress and ε p the plastic strain; the two constants A and B are respectively the specimen curvature and its elongation; E and are respectively Young s modulus and Poisson s ratio of the material, assumed isotropic. Eq. (2) is used twice, the first time being to determine the plastic strain from the measured residual stress profile on 9 mm thick specimens. The constants A and B are derived by writing that no load is applied on the specimen, and more precisely that the bending moment and the normal force are both equal to zero. For example, Fig. 5 displays the plastic strain profiles obtained on a 9 mm specimen laser shocked with the condition 9 GW/cm 2 9 ns 3 impacts. Once the plastic strain, called eigenstrain, is known, the assumption advocated by Alexander Korsunsky in several of his papers (e.g. [26,27]) was used. This assumption states that, for surface treatments, the eigenstrain is not likely to depend on the structure geometry, but only on the process parameters. Under this hypothesis, Eq. (2) can be used a second time on a thin specimen and fed with the plastic strain profile determined on the thick specimen treated under the same conditions. The stress profile and a new set of A and B values can thus be computed for the thin specimen. An example of this procedure, applied on 9 GW/cm 2 9 ns 3 impacts condition, is shown in Figs. 5 and 6. The residual stress profiles obtained on the thin and the thick specimens are represented. The square symbols represent the stress values measured on the thick specimen and the continuous dark line is the fitted profile satisfying compatibility and equilibrium over the cross-section. The continuous grey line corresponds to the stress profile calculated on the thin specimen from the eigenstrain profile. This stress profile satisfies compatibility and equilibrium. The circular symbol is the surface value evaluated by X-ray diffraction on the thin specimen. Although the calculated value (+258 MPa) and measured value (+100 MPa) are not equal, the trend is good and this analysis shows that strong tensile stresses may appear in thin one-sided laser peened structures coming from the important plastic strain generated, associated with the necessary balance of the stresses in the cross section. The model developed can be discussed on a number of points. First, the assumption that stress and strain fields are homogeneous along the L and T directions may not be verified at the scale of laser impacts: the size of the impacts is indeed similar to the size of the hole diameter or the X-ray spot. However, measurements were repeated at different locations on the specimen and led to a good repeatability. The hypothesis thus seems reasonable. More questionable is the assumption that the eigenstrains are the same on thick and thin specimens. Indeed the truncation made on some of the profiles such as the one presented in Fig. 5 means that after 1 mm, the compression wave produced by the plasma still had enough energy to plastify the material and, thus, that the plastic wave was reflected on the surface of the specimen opposed to the treatment. The method can be relevant only when the depth affected by the treatment does not exceed the thickness of the component. Superficial tensile residual stresses were also observed on two thick samples, shocked at 3 GW/cm 2 9 ns 1 impact and 3 GW/cm 2 9 ns 3 impacts. This fact can be explained by the value of the laser fluence: 3 GW/cm 2. For this value, the pressure of the plasma is very close to the Hugoniot yield limit. Thus the plastification may not be sufficient to erase the initial tensile residual stresses due to machining and cannot generate compressive residual stresses. Indeed, surface tensile residual stresses were measured on the untreated surface and were found to vary from +150 to +250 MPa. The observed influence of laser fluence and pulse duration is consistent with the work of Ocana et al. [10]. Pulse duration and laser fluence are involved in the formation and the duration of the plasma. They should thus play a role in the level of residual stresses by generating higher and longer-lasting shock wave pressure. It is what is indeed observed in the present study. As explained in Section 2.1, the ratio between the high and low levels of fluence and duration were chosen in order to have specimens for which the total energy delivered during one pulse remains the same. Thus, the two specimens shocked at 9 GW/cm 2 9 ns and

7 368 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Fig. 6. Influence of the thickness on the longitudinal residual stress profile and comparison with the experimental residual stresses; specimen 9 GW/cm 2 9 ns 3 impacts. 3 GW/cm 2 27 ns respectively can be compared, taking as a reference the specimen shocked with 3 GW/cm 2 9 ns, since for both of them the energy is multiplied by three. Considering one impact and averaging longitudinal and transversal directions, it was found that: - When the laser fluence is multiplied by 3, the variations of the surface stress and the maximum stress are respectively 150 MPa and 350 MPa. - When the pulse duration is multiplied by 3, the variations of the surface stress and the maximum stress are respectively 250 MPa and 300 MPa. It was also found that, for a given energy, the residual stress levels (surface or maximum) do not change much. For instance, with one impact, for 3 GW/cm 2 and 27 ns, the maximum stress is 273 MPa, and for 9 GW/cm 2 and 9 ns, it is 325 MPa. Although the physics of plasma formation is complex (i.e. the pressure pulse duration is longer than the laser pulse duration) and material constitutive behaviour is non linear, these results show that the total energy delivered by one pulse is a good indicator of the change in residual stresses. At low fluence, the contribution of the number of impacts is almost negligible. For instance, for 3 GW/cm 2 9 ns, if the specimens shocked with one impact and with three impacts are compared, the variations of the surface stress and the maximum stress are respectively 30 MPa and 10 MPa. This result is consistent with the literature. Ocana [10] noticed that an increase of the number of impacts enhances the plastified depth and also the value of the maximum stress. Other studies [6,28] established the same effect, but only for high work-hardening materials. However, at high fluence, it was found that the number of impacts influences residual stress levels. For instance, at 9 GW/cm 2 9 ns, a variation of 200 MPa and 136 MPa was found between one and three impacts, thus showing that there is still a possibility to plastify the material. The present study on Ti-17 alloy has been compared with results presented in the literature on 7075 aluminium alloy and Ti6Al4V titanium alloy [6,10]. The general relation observed between factors (fluence and number of impacts) and responses (compressive depth, surface and maximum stress) present similar trends in all the studies. 4. Work-hardening 4.1. Experimental details As explained in Section 2.2, the evolution of work-hardening was followed in a semi-quantitative way through two indicators: width of diffraction peaks and Vickers micro-hardness. Diffraction peaks were acquired according to the protocol described in Section 3.1. Their width was described by the integral width of the K 1 component extracted with a fitting by a pseudo- Voigt function taking into account the K 1 K 2 doublet according to the Rachinger assumptions. For each specimen, the 13 width values corresponding to the 13 tilt angles were averaged. This corresponds to material characteristics at a depth of about 4 m. Hardness was obtained with a Mitutoyo AVK-C1 hardness tester. No preload was exercised and a load of 5 kg for 10 s was applied. Four measures were carried out on the centre of the specimen and averaged to obtain the value attributed to the specimen. Homogeneity of the results over the treated surface (in the L and T directions) was checked. In the direction normal to the surface, a hardness gradient may exist. To estimate the depth of material that contributes to the hardness value, a formula proposed by Gao [29] for the radius of the zone that is plastified by the indenter was used: ( rc ) 3 = 1 E cot( ) (3) a 3 Y where r c is the plastic zone radius, a the print radius, E the young modulus (110 GPa), Y the yield stress (1125 MPa) and the half angle of the penetrator (74 ). The indent radius varies from 75 to 77 m. It was thus found that the information depth for hardness is about 160 m Results Table 2 summarises the variation ranges obtained after LSP treatment. It can be seen that shock peening leads to a moderate increase in hardness (16% maximum increase). The effect is more pronounced on peak width (56% maximum increase). It can be noted that the minimum values are slightly lower than reference values, but the difference is close to measurement uncertainty. In the case of hardness, the decrease may also be due to the presence of tensile residual stresses (see below, Section 4.3). Table 2 also summarises the effects of the different factors and second order interactions on work-hardening variations. It can be seen that the pulse duration is the most influential factor for

8 C. Cellard et al. / Materials Science and Engineering A 532 (2012) work-hardening as expressed by both peak width and hardness. The other factors and interactions have negligible influence on peak width. In the case of Vickers hardness, all the factors are influential and when they are increased, they also increase the hardness of the specimens. This is easy to explain for laser fluence, pulse duration and number of impacts, which transmit more energy into the material and thus produce higher plastic straining. The case of thickness is less obvious. It is probably due to the compressive residual stresses that are created by LSP that are known to increase the apparent hardness [30,31]: when thickness increases from 1 mm to 9 mm, the residual stresses are more compressive. This explanation is supported by the second order interactions thickness/fluence and thickness/duration. It can be noted that the fluence/duration interaction gives a negative hardness variation. There is no explanation at this point, but residual stresses are unlikely to play a role because this interaction has negligible influence on the residual stresses (Table 1). A plot of peak widths versus hardness (not presented here) exhibits only a weak correlation between the two quantities. This can be explained by the fact that peak widths are only related to microstructural evolutions of the material (2nd order peak broadening due to elastic anisotropy of Ti crystal is negligible in the present case), while the hardness depends on both the microstructural and the residual stress evolutions Discussion Peak width variations are not easy to interpret directly but a comparison with other situations can help. In the present study, the maximum increase in diffraction peak width is 56%. Gill et al. [32] showed an augmentation of the width by 20% after laser shock peening on Ti6Al4V. In their case the level of compressive residual stresses increased from 400 MPa to 750 MPa. This highest absolute value is similar to the highest levels obtained in the present study. They also found that the increase of peak width after a conventional shot peening treatment was about 75 80%. This may be interpreted as a stronger increase in defects density (e.g. dislocations) due to LSP in our case, and thus a higher level of cumulated plastic strain. However, the comparison is difficult because the chemical compositions and the microstructures of the two titanium alloys are different and a given amount of cumulated plastic strain may lead to different defect densities in the two cases. What can be said is that moderate work-hardening was produced during LSP treatment of Ti-17, unlike in the case of conventional shot peening. In the case of Vickers hardness measurements, a mean increase of 6% is found between the hardness mean value and the reference hardness. This value can be compared to [33] where an increase of approximately 20% on shot peened Ti6Al4V was found. This indicates that laser shock peening generates lower work-hardening, compared to conventional shot peening, which is consistent with results from the literature [11,34]. This hardening was produced by an increase of dislocation density during the process. As mentioned in Section 4.2, the diffraction peak widths are not very sensitive to macroscopic stresses. For hardness, it is well known that the residual or applied macro-stresses may influence the hardness measurements performed with a sharp or a blunt indenter [30,31]. Many studies establish a quantitative link between the two quantities as presented in a review written by Jang [35]. In the present study, the model proposed by Carlsson and Larsson [36] is used to separate the contribution of residual stresses and the contribution of work-hardening on hardness measurements. This model leads to hardness variations expressed by Eq. (4), ( ) 1 H = H 0 1 R (4) 3 y where H 0 is the stress free hardness, R is the residual stress value and y is the initial yield stress of the material. Their model was established in the case of equi-biaxial plane stress state, assumed to be homogeneous over the whole volume affected by the indenter. In the present study, the two values H 0 and y were considered as unknown and Eq. (4) was fitted by least-squares on the 16 measured hardness values and the 16 corresponding measured residual stress values. To take into account the variations of the residual stress with the depth, the average value on a layer of 160 m thickness was calculated from the measured stress profile. As explained in Section 4.1, this thickness was estimated from Gao et al. [29]. The values of H 0 and y that gave the best fit are 418 HV and 1190 MPa respectively (Table 3). They are in close agreement with the measured values of 385 HV and 1125 MPa and correspond to a difference of 8% and 5% respectively. The least-square residual was 8 HV, which corresponds to 2% of the mean value of hardness. Now that the effect of macroscopic residual stresses on hardness is shown to be described reliably with Eq. (4), it could be interesting to improve the description further by considering the influence of work-hardening. Indeed, it is classically known that hardness increases regularly with plastic strain [37]. Thus, an additional term is introduced, linear with respect to the plastic strain, leading to: H 0 H = 1 ( R /3 Y ) + ˇε p (5) This equation was used in the same way as Eq. (4), with ˇ as an additional unknown. The values of plastic strain (ε p ) were determined by integrating the plastic strain profile obtained from Eq. (2) over a depth of 160 m. Using the 16 triplets (H, R, ε p ), a multiple least-squares analysis was performed to retrieve the optimum values of H 0, y and ˇ that are shown in Table 3. It can be seen that the least square residual is decreased from 8 to 6 HV, showing a better agreement of experimental data with Eq. (4) than with Eq. (3). This is not very surprising since additional parameters in a model usually lead to a better fit of data. More interesting is the fact that the values obtained for H 0 and y with Eq. (4) are significantly closer to the reference values. In Eq. (4), the hardness of the material is correlated to the total plastic strain deduced from the residual stress profile. However, in order to describe work-hardening, the cumulated plastic strain should have been used instead. The two quantities are identical only if plastic deformation is monotonous. According to the analysis made by Ballard with the assumption that laser shock peening induces a purely uniaxial strain, plasticity occurs during the loading phase only if the pressure pulse is between P H and 2 P H. If it is larger than 2 P H then plasticity appears also during the unloading phase. For the material studied in the present paper, P H was found equal to 2.8 GPa and it was considered that the pressure pulse was unlikely to reach 5.6 GPa without producing a breakdown of the confining medium [8]. For these reasons, the total plastic strain used in Eq. (4) was assumed to be representative of the work-hardening state of the material. 5. Surface topography 5.1. Experimental details In the present study, the roughness (micro-topography) is described by two parameters: Ra and Rt according

9 370 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Table 5 Comparison of roughness evolutions with literature results. Ra ( m) Rt ( m) Present study [40] [41] Present study [40] [41] Ti-17 35CrMo Aluminium Ti-17 35CrMo Aluminium Unshocked Laser shock peened Increase after treatment (%) to ISO Standard. A Taylor Hobson Surtronic 3+ portable profilometer was used with the following parameters: -25 mm of scanned line length in order to take into account several laser spots mm cut off. - Tip radius: 5 m. - Vertical resolution: 0.1 m. The roughness is averaged on three lines along the longitudinal direction as well as the transversal direction. The profilometer was also used to determine the depth of the impacts induced by the pressure pulse (meso-topography). To do this, scans were performed along a line going from the untreated zone to the treated zone. The average of three scans was taken. An example of impacts aspect is given in Fig Results The result of roughness variation range is reported in Table 4. It can be seen that the values of Ra and Rt can be multiplied by two after laser shock peening as compared to the untreated surface. However, it should be mentioned that the maximum values of the longitudinal Ra and Rt are not found on the same specimen. The same is true for the maximum values in the longitudinal and transversal directions. Actually, no clear relation between the factors and the increase in the maximum roughness was found. This was confirmed by the mathematical analysis of the DoE: no factor or interaction was found significant on roughness evolution (Table 4). These results are consistent with the literature [38,39]. Comparisons with results found by Ballard [40] on 35CrMo4 30HRC and Peyre [41] on 7075 Aluminium (Table 5) show that on hard materials (steel and titanium) the roughness increase is moderate, while on a soft metal such as aluminium it is much higher. Globally, the roughness obtained after LSP treatment is much smaller than after conventional shot peening, as can be seen in Wagner and Lütjering [42] who obtained Ra = 2.3 m on TiAl6V4 with conventional shot peening. Depths of impact were found to vary between 4.5 m and 11.3 m with an average of 7.2 m on the 16 treatment conditions. Analysis of the DoE shows that the four factors have an influence on the depth (Table 4). Laser fluence and pulse duration have the major effects, which is easy to explain: the higher the energy delivered to the material, the deeper the impacts. Accordingly, the only significant interaction is fluence/duration as can be seen in Table 4. These two parameters both contribute to an increase in the plasma pressure and thus generate deeper impacts. These results are consistent with the work of Ocana et al. [10] who found an impact depth of 10 m approximately with shock pressure of 9 GPa on TiAl6V4. The number of impacts has a weak influence, which shows that the material is almost saturated after 2 impacts. It can be noticed that the impacts are deeper for thick specimens, which can be explained by considering that part of the energy brought by the plasma generates elastic flexion vibrations of the thin specimens. The energy used to plastify the material is thus reduced. 6. Curvature 6.1. Experimental details The curvatures of the specimens were obtained from clouds of points measured on their surface with a three-dimensional measuring machine. The specimens were scanned with a Wenzel LH54 machine with an accuracy of about 3 m. The sensor used had a sphere of 6 mm diameter on its tip in order to limit the influence of local topography perturbations due to the laser impacts. A total of 441 points were acquired along a square grid with 2.25 mm pitch and at a distance of 3.5 mm from the edges. Polynomial functions were used to fit the measured points with a least-square method using Mathematica. The curvatures in the longitudinal and transversal directions were calculated at the centre of the specimen. An example showing an important curvature on a thin specimen is presented in Fig. 8. Table 6 Summary of the responses, effects of factors and second-order interactions for the curvature of the samples. Responses Longitudinal minimum 0.02 Longitudinal maximum Transversal minimum 0.02 Transversal maximum Curvature (m 1 ) Effects Interactions Thickness 1.88 Laser fluence 1.36 Pulse duration 0.94 Number of impacts 0.84 Thickness/fluence 1.26 Thickness/duration 0.85 Thickness/impacts 0.75 Fluence/duration 0.46 Fluence/impacts 0.54 Duration/impacts 0.43 Fig. 7. Aspect of laser spot impacts on the treated surface. Measurement uncertainty 0.71

10 C. Cellard et al. / Materials Science and Engineering A 532 (2012) Fig. 8. Curvature on a thin specimen laser shocked with the highest intensity (highest fluence and duration, 3 impacts). This curvature is about 13 m Results The range of curvature variation induced by the treatment is summarised in Table 6. For thick samples, the longitudinal and transversal curvatures are low. Most of them are far below the measurement uncertainty (0.71 m 1 ) except for the sample that has been laser shocked with the highest intensity (9 GW/cm 2 27 ns 3 impacts), whose curvature is slightly higher than 0.7 m 1. On thin specimens, the highest curvature is also obtained in the most severe conditions and is about 12 m 1. No significant differences were found between the longitudinal and transversal directions, which mean that the laser scanning direction does not have any global influence. Analysis of the DoE shows that all the factors are influential (Table 6). The effect of the thickness is coherent: thicker samples are stiffer, so they exhibit less distortion than thin specimens. The effects of the laser fluence and the pulse duration are also easy to understand. They play a role in the deformation of the specimen by generating higher and longer-lasting shock wave pressure. The effect of the number of impacts is also coherent. Additional impacts induce plastification at higher depth into the material, which leads to an increase in curvature. Altogether, it can be said that laser fluence increases the level of plastic strain, the duration increases both plastic strains and depth, and the number of impacts mainly increases the plastified depth. All these phenomena produce higher curvatures. Second-order interactions are also reported in Table 4. The highest ones are fairly consistent: a given increase in laser fluence, duration and number of impacts leads to a stronger curvature change on thin specimens than on thick ones. 7. Conclusion A design of experiment study has been presented to quantify the influence of laser shock peening treatment parameters on a Ti-17 titanium alloy. The objective of the study was to be as exhaustive as possible; this explains the large number of parameters and responses that have been considered. Particular attention has been given to all the experimental aspects of the study, as acknowledged by the presentation of the numerous experimental protocols. The measurements have been performed with details, seeking to evaluate the process quantitatively and minimizing the measurement errors as far as possible. The corresponding results are briefly summarised in the following paragraphs: The study verifies the fact that there is little work-hardening when a material is laser shocked. This is confirmed by the small influence of the treatment on the observed X-ray diffraction peak widths and on hardness (once the effect of residual stresses is removed). A low influence on the roughness parameters Ra and Rt was noticed, although the spot impacts are clearly visible on the surface. Thus, laser shock peening generates a global sinking of the material surface without crushing the micro-geometric asperities. The hardness of the material is affected by the treatment. A simple analytical modification of the equation proposed by Carlsson and Larsson is presented. The proposed equation takes into account both the residual stresses and the plastic strains to evaluate the hardness. A good fit of the experimental results by the proposed equation is obtained. It is shown that the increase in hardness is slightly due to hardening effects and can be mainly attributed to the presence of compressive residual stresses. One of the relevant findings of the study is the unexpected and important tensile residual stress that is found on the surface of the one-sided laser shock peened thin samples. The considerable plastic strain imposed through the thickness of the sample followed by the equilibrium of the stresses on the cross-section leads to this repeatable result. Care should be thus taken when such a treatment is intended on parts presenting thin sections. The study thus allows a better understanding of laser shock peening thanks to the detailed analysis of the process that is presented. One of the originalities of the present work is that the treatment has been performed on a Ti-17 alloy, of interest for aeronautical industries. It brings insights to a product-process approach, allowing for a better understanding of the influence and constraints that are due to the process on the characteristics of the treated mechanical part. Acknowledgements The authors would like to thank SNECMA (SAFRAN Group) and the French Ministry of Higher Education and Research for financial support. References [1] C.S. Montross, T. Wei, L. Ye, G. Clark, Y.W. Mai, Int. J. Fatigue 24 (2002) [2] P. 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