A comprehensive experimental and numerical study on redistribution of residual stresses by shot peening

A comprehensive experimental and numerical study on redistribution of residual stresses by shot peening

Materials and Design 90 (2016) 478–487 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/jmad...

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Materials and Design 90 (2016) 478–487

Contents lists available at ScienceDirect

Materials and Design journal homepage: www.elsevier.com/locate/jmad

A comprehensive experimental and numerical study on redistribution of residual stresses by shot peening A.H. Mahmoudi a,⁎, A. Ghasemi a, G.H. Farrahi b, K. Sherafatnia b a b

Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 8 September 2015 Received in revised form 18 October 2015 Accepted 31 October 2015 Available online 2 November 2015 Keywords: Shot peening Residual stresses Redistribution Grinding Finite element

a b s t r a c t Shot peening is one of the most effective surface strengthening treatment technologies in which compressive residual stresses are induced beneath the specimen surface. Effects of various factors on the distribution of residual stress profile induced by shot peening have been investigated by many researchers. However, initial residual stresses are one of the important factors which affect the shot peening residual stress. This study is aimed to present comprehensive numerical and experimental study on the effect of initial residual stresses on the shot peened specimen. Initial residual stresses were induced using a four-point bending rig and grinding. Incremental center hole drilling (ICHD) technique was employed to measure residual stresses on bent, ground, shot peened, bent plus shot peened and ground plus shot peened specimens. Numerical analyses of these processes were performed to provide quantitative comparison of different combinations of residual stresses. The comparison with experimental results helped to have a better understanding on how shot peening residual stresses were redistributed. Furthermore, the surface hardness was measured for all specimens. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Shot peening is one of the most effective mechanical surface treatments generally applied to improve fatigue life of engineering components. Shot peening is carried out to postpone the crack initiation or reduce the propagation rate. In shot peening, a target is peppered using small spherical shots with a velocity of 20–100 m/s. The outcome is a compressive residual stress field beneath the surface of metallic components. Shot peening is widely used in automobile, power generation and aerospace industries [1–7]. Many studies have been carried out on the shot peening process. AlHassani [8], Hills et al. [9], and Al-Obaid [10] developed the analytical approaches to predict shot peening residual stresses. Al-Obaid [11] attempted to perform a simple numerical simulation of shot peening process. Mori et al. [12] considered the plastic deformation for both work piece and shots. In another study by Meguid et al. [13] a quarter symmetry model was presented in which both single and twin shot impacts on the target surface were considered. Boyce et al. [14] presented the quasi-static and dynamic finite element models to simulate a single shot impacting the surface. Guagliano [15] developed a finite element model with five subsequent shot impacts to relate effects of important parameters such as velocity and shot size on the residual stress and Almen intensity. Hong et al. [16,17] simulated single shot impact ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (A.H. Mahmoudi).

http://dx.doi.org/10.1016/j.matdes.2015.10.162 0264-1275/© 2015 Elsevier Ltd. All rights reserved.

model and investigated the effect of parameters such as shot diameter, impact velocity, incident angle and component material properties on the residual stresses distributions in the target. Shivpuri et al. [18] created a 3D finite element model of shot peening to investigate the effect of process parameter and surface material response on distribution of residual stress. The single shot impact model [18] was validated by comparing the measured results to previously published experimental results presented by Kobayashi et al. [19]. Meguied and his co-workers created a symmetry cell to simulate shot peening process [20]. They considered parameters such as separation distances between adjacent shots, material damping and strain rate sensitivity for target and plastic properties on shots. Majzoobi et al. [21] performed a simulation on the shot peening process using a multiimpact symmetry cell model. Frija et al. [22] developed a model to study the effect of the friction coefficient. Kim and his co-workers [23] predicted residual stress profile based on area-average approach using a symmetry cell finite element model. Also, Kim et al. [24,25] presented a three dimension finite element model using several vertical shots impacting. The effects of material damping, dynamic friction, strain rate, impact patterns and impact sequence on the residual stress profiles were also investigated. In the modeling of shot peening process by other researchers parameters such as influence of impact angle and impact pattern [26], changes of material state in the treated area [27], using combined hardening for target material model [28] have been investigated. Others have examined the application of shot peening on aluminum [29] and steel [30] plates. The severe shot peening and its effect on creating nano-structured surface was studied by Bagherifard et al.

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[31]. The surface roughness as a function of processing time and the impacting ball size was evaluated by Dai et al. [32] using the impact simulation of surface nanocrystallization and hardening process. Child et al. [33] investigated the depth of strain-hardening effects of shotpeening treatments applied to the Ni-based super alloy. The effect of shot peening on the microstructure, oxygen ingress and high-cycle fatigue properties of the titanium alloy was also examined by Thomas et al. [34]. The computational cost is also another aspect that has been considered by researchers [35]. A random positioning of shots to simulate shot peening was developed by Hassani-Gangaraj et al. [36]. Furthermore, shot peening has been used to interact with other residual stress fields such as welded samples [37], warm peened and pre-stressed rods by torsion [38], welded aluminum alloy samples [39] and combination of severe shot peening and nitriding on fatigue life [40]. Effects of various factors on the distribution of residual stress profile induced by shot peening have been investigated by many researchers. Initial residual stresses on the shot peened specimen are one of the important factors which affect the distribution of residual stresses. All mechanical processes can cause deformation that may lead to residual stresses within the engineering components. However, a comprehensive study in the literature on the effect of present initial residual stress on the shot peened specimen is still missing. This study is aimed to investigate effects of initial residual stress on the distribution of residual stress profile inducted by shot peening both experimentally and numerically. Initial residual stresses were generated using a four-point bending rig and rough grinding. Incremental center hole drilling (ICHD) measurement of residual stresses were carried out on bent, ground, shot peened, bent plus shot peened and ground plus shot peened specimens. Finite element simulations of these processes were also performed to provide a quantitative description of the effect of initial residual stresses on the redistribution and magnitude of residual stresses. The numerically predicted residual stresses were verified using experimental results. Furthermore, the surface hardness was measured for all samples. 2. Material, specimens and test procedures The material used in this study was low-alloy steel DIN 34CrNiMo6 (1.6582) with the chemical composition presented in Table 1. In order to obtain monotonic properties of the material, tension tests were carried out according to ASTM E8M [41] as shown in Fig. 1(a). A set of cyclic tension compression tests were carried out to obtain the properties required for the nonlinear isotropic/kinematic hardening model. The evolution law of this model consists of two components: a nonlinear kinematic hardening component and an isotropic hardening component, as a function of plastic deformation. The kinematic hardening component was defined by specifying test data from a stabilized cycle. On the other hand, isotropic hardening component was defined by specifying the equivalent stress defining the size of the yield surface, as a function of the equivalent plastic strain. The simplest way to achieve these data was to conduct a symmetric strain-controlled cyclic experiment. Strain-controlled low-cycle fatigue tests were applied up to the stabilized cycle on cylindrical specimens at different strain intervals of (Δε = 0.012, Δε = 0.06). The specimens were prepared according to ASTM E606 [42]. Fig. 1(b) illustrates a picture of cyclic test sample. The stabilized cycle was obtained after 4 cycles which was used in order to make a more realistic model by simulating low number of cycles. Both monotonic tension and cyclic tension-compression test were carried out using an Instron servo-hydraulic testing machine. Table 1 Chemical composition of steel grade 1.6582 used in this study (wt.%). C

Si

Mn

Ni

P

S

Cr

Mo

0.34

0.272

0.743

1.341

0.025

0.017

1.58

0.18

Fig. 1. Test samples, (a) tensile test specimen, (b) cyclic test specimen, (c) four-point bending test sample, all dimensions are in mm.

Elastic–plastic four-point bending can create a known stress field which is the best way to validate the finite element model. There are no transverse shear stresses on the cross-sections of the beam in the inner span of the bending sample due to the pure bending condition. To induce residual stresses, the beam must be loaded beyond the yield strength. Upon removal of applied moment, elastic unloading is occurred and the residual stresses formed. The tensile and compressive residual stresses are both produced on the opposite surfaces which are independent to sign of applied moment. The four-point bending process presents the following advantage over the three-point bending process: In a three-point bend, the maximum residual stress occurs only at the mid-section. However, the entire span length is subjected to a constant residual stress in the four-point bending sample [43,44]. Beam specimens were subjected to four-point bending to induce elastic–plastic deformation. Fig. 1(c) illustrates the sample that was manufactured for four-point bending test. In order to perform the experiment, a fixture was designed. The fixture consisted of fixed and movable fulcrums. The fixture with the specimen in position is shown in Fig. 2. The displacement was applied using a servo-hydraulic fatigue testing machines. The second procedure that was employed to create residual stresses was grinding. Grinding is a commonly used finishing process to produce components with desired shape, size and dimensional accuracy. During

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A.H. Mahmoudi et al. / Materials and Design 90 (2016) 478–487 Table 2 Mechanical and thermal properties of steel grade 1.6582 [50].

Fig. 2. The fixture and specimen in position, (a) front view and (b) side view.

T (c)

E (GPa)

σy (MPa)

σu(Mpa)

α (10−6 (k−1))

k (W/m·k)

cp(J/kg·k)

20 100 200 300 400 500 600 700

210 207 201 194 184 172 160 144

538 501 448 335 318 296 276 241

707 659 581 496 484 474 423 348

11.1 11.1 12.1 12.9 13.5 13.9 14.1 14.3

38 38.9 39.4 38.7 37.4 35.4 33.2 29.7

460 481 514 561 613 685 821 938

was equal to 83.1 kW/m. The material properties of the target sample at different temperature are given in Table 2, as these properties were required when simulating the grinding process. The tests were performed at room and higher temperatures as shown in Table 2. However, some material properties such as α, k and cp were obtained from [50]. All steel specimens were subjected to shot peening process with the same peening conditions. The geometry of shot peened specimen was similar to grinding specimen. An air blast machine was employed to conduct the shot peening using standard steel shots of S230. Shot peening was performed with 100% coverage. The peening intensity measured on “Almen A” strip was 12A. The Almen saturation curve is a conventional method to measure the kinetic energy transferred by shots stream. The measurement of peening intensity is performed by standard test strips (Almen strip) and a gauge (Almen gauge) in the shot peening process. Residual stress measurement of the as-treated and as-received samples was implemented by Incremental Centre Hole Drilling (ICHD) method. The ICHD measurements were performed to obtain the trend of residual stresses using an ultra-high speed drilling technique, a tungsten carbide inverted cone drill with a nominal diameter of 0.8 mm and the micro-measurement strain recorder. For strains measurement, the EA-06-031RE-120 strain gauge rosettes, with nominal gauge diameters of 2.56 mm were mounted on the surface of each specimen. ICHD measurement of residual stress was performed on single and hybrid surface treated specimens including the compression and tension bent, ground, shot peened, compression and tension bent plus shot peened and ground plus shot peened specimens.

the grinding process a large amount of energy is consumed for the material being removed which results in generation of excessive heat in the ground region. The heat naturally causes a rise in sample temperature and, therefore thermal damage and tensile residual stresses are resulted [37,45–48]. However, compressive residual stresses are induced when coolant is used during the grinding process according to [49]. A picture of specimen while grinding is illustrated in Fig. 3. Grinding specimens in the form of a rectangular cubic was manufactured with a dimension of 60 mm by 60 mm, and height of 10 mm. The grinding wheel was used by diameter of 185 mm and width 50 mm. The cut depth of each stage was namely 0.08 mm, and the specimen speed of vs= 0.034 m/s and the wheel rotational speed of ω = 2340 rpm were kept constant during grinding process. Throughout the process, dry air was used for cooling. For each specimen, five passes at the same depth of cut were performed. The grinding wheel spindle power was measured for each pass using a precision three-phase wattmeter. The measured power

Fig. 4 shows engineering and true strain–stress curves obtained from monotonic tension test at room temperature. Based on monotonic tension test, the material properties are as follows; yield stress of 538 MPa, ultimate tensile strength of 707 MPa, module of elasticity of 210 GPa. The Poisson's ratio and density were considered 0.3 and 7800 kg/m3 respectively. The results of the cycling loading tests are shown in Fig. 5.

Fig. 3. Showing experimental grinding, dry rough grinding.

Fig. 4. Strain–stress curves of material at room temperature.

3. Experiments

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with numerical and experimental results revealed that the results were independent of the input data. In this study non-linear kinematic Chaboche hardening model were chosen to describe target material's behavior and the strain rate sensitivity was not considered. However, previous studies have indicated that it can provide reliable results well corresponding with experimental tests [52]. The strain rate has not been considered to simulate the shot peening as of for all other residual stress generating procedures employed in this work. Although not considering the strain rate may influence the residual stresses induced by shot peening, it won't harm the purpose of this study which was the redistributions of residual stresses by shot peening. This was due to the fact that all shot peening processes (alone or combined) were performed without considering the strain rate and therefore the comparison is valid. Furthermore, the experimental residual stresses measurements illustrated a good agreement with those predicted by shot peening simulations. Fig. 5. Comparison of simulation and experimental true stress–strain determined in tension compression tests for εmax = 0.006 and εmax = 0.01, which are the strain intervals of Δε = 0.012, Δε = 0.02.

The specimens were manufactured to perform four-point bending test, grinding and shot peeing. The longitudinal strain was measured during the bending test using two single strain gauges that were mounted on the top and bottom surfaces of the beam samples. The strain gauges were used to validate the loading conditions of the finite element results. The beam was first loaded beyond the yield point of the material. The required load was estimated using the finite element analysis. Residual stresses were created upon unloading from the beams. The residual stress measurement was also performed on an asreceived specimen and the manufacturing stresses were found to be negligible. The residual stress measurements were performed for some samples twice to check the repeatability of the measurements. Also, micro-hardness on the surface of all specimens was measured by a diamond Vickers indenter. Force of 100 gf was applied during time of 15 s. Three micro-hardness measurements were performed for each specimen and were averaged. The scatter of the resultant data was less than 4%. The mean indentation radius of single impact was measured to be approximately 104.8 μm after shot peening using an optical microscope. Ten measurements were performed to account for measurement errors. The resultant data scattering was not more than 7%. All results will be discussed in the discussion section.

4.1. Four-point bending model The four-point bending simulation was performed to estimate the force applied to rectangular beams and also the induced residual stresses. Fig. 6(a) illustrates four-point bending model and analytical rigid loading rollers. In the figure BC refers to boundary conditions; BC (1): displacement was applied at reference points along y-direction, BC

4. Finite element analyses Three-dimensional (3D) models were developed to study initial residual stress effects on the residual stress distribution induced by shot peening process using commercial code ABAQUS [51]. Finite element simulations were created for cyclic loading, shot peening, fourpoint bending and grinding processes. An axi-symmetric finite element model was developed to simulate a low-cycle uniaxial tensioncompressive fatigue test for both strain intervals of Δε = 0.012 and Δε = 0.02. The target is modeled as a cylindrical body with a diameter of 5 mm and height of 25 mm. Four node linear brick elements (CAX4R) with reduced integration and hourglass control were employed. A periodic linear displacement was applied to one end of the cylinder and other side was completely restrained in all degrees of freedom. Fig. 5 compares the results of the finite element analyses and the experimental data on the cyclic loading in order to assess the validity of the models. It can be seen that the numerical and experimental results represent a good agreement. Moreover, in order to check model transferability, two simulations were performed applying different symmetric strain cycles (εmax = 0.006 and εmax = 0.01) while the hardening components was defined by specifying test data from εmax = 0.01 and εmax = 0.006, respectively. In both simulations the comparison

Fig. 6. (a) Assembly view of beam and analytical rigid loading rollers, all dimension in mm, (b) meshing of the model, (c) meshing of the sub-model.

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(2): Uy = 0 for the bottom edge lines, BC (3): Ux = 0 for the indicated line of the top surface, BC (4): Uz = 0 for the center node of the top surface. The bending process was performed using two steps. First, linear vertical displacement up to 10.95 mm was applied on the reference points. Then, the applied displacement was decreased linearly to zero in order to perform unloading and elastic recovery of the beam. Fine mesh was created for the central and contact regions, while coarser mesh was employed for other sections to optimize the computational cost. A central region of (12 × 12 × 1.5 mm3) was located in the center of the top surface as shown in the figure. The number of elements was 118272 C3D8R 8-node linear brick with reduced integration and hourglass control. Element size at the central area of the beam and the contact region were 0.25 × 0.25 × 0.25 mm3. This element size was selected following a convergence mesh study. The sub-modeling technique was used to create smaller model with a refine mesh which was a powerful tool to transfer residual stresses fields induced by bending process into the model to be shot peened. This technique was based on interpolation of the solution from a global model into the sub-model. In this study, the node-based sub-modeling was used which utilized a nodal results filed (including displacements and rotation) to interpolate global model results onto the sub-model nodes. A close view of middle region for beam model and finite element meshes for sub-model are illustrated in Fig. 6(b) and (c). The dimensions of sub-model were 12 × 12 × 4.62 mm3. The sub-model boundary conditions were applied to the lateral and bottom surfaces.

where ε is the percentage of heat flux entering the specimen, F ʹt the tangential force per unit width of the specimen, vw the peripheral wheel speed and Lc the geometrical contact length between wheel and specimen which was calculated from Eq. (2) where c is the depth of cut and d is the diameter of the grinding wheel. ε was calculated according to Eq. (3) where uch is the specific energy required for chip formation. It has been reported [57] that the constant value of uch is about 13.8 J/mm3 for grinding all ferrous materials. u is the energy per unit volume required for material removal which is expressed in Eq (4). ε ¼1

uch u

ð3Þ

0



F t vw cvs

ð4Þ

where vs is the specimen velocity. F tʹ is calculated from Eq. (5) where P tʹ is the power per unit length, which was measured, while grinding. 0

0

Ft ¼

Pt vw

ð5Þ

Therefore, the heat flux can be calculated form Eqs. (1)–(5) and it can be applied the elliptical heat source to the specimen surface using Eq. (6). sffiffiffiffiffiffiffiffiffiffiffiffiffiffi z2 qðzÞ ¼ q0 1  2 a

4.2. Grinding model A 3D finite element model was constructed to investigate residual stress distribution induced by grinding. The grinding was simulated using a moving source of heat along a line on the specimen surface. The moving thermal source is a conventional method to model the grinding process that has been employed by many researchers without considering the contact stresses [47,48]. Furthermore, the residual stresses measurements results showed a good agreement with those predicted which confirmed the simplifying assumption led to reasonable results. Sequentially coupled thermal-stress analysis was employed. This analysis is useful when the stress/displacement solution is dependent on a temperature field but there is no inverse dependency. A heat transfer problem was solved and the reading of the temperature solution was fed to a stress analysis [51]. The target was considered as a cubic body (12 × 12 × 4.62 mm3) which was similar to sub-model geometry, sufficiently large to avoid the effects of boundary conditions on the numerical outcomes. 161820 first-order hexahedral diffusive heat transfer elements (DC3D8) and 161820 eight-node linear brick elements (C3D8R) with reduced integration and hourglass control were used for the thermal and stress analyses, respectively. Element size of the grinding zone was 0.02 × 0.02 × 0.02 mm3. The convergence evaluation was performed to obtain the appropriate element size. The initial temperature was set to 20 °C throughout the model. Heat flux on the surfaces was applied by film conditions. The surfaces were exposed to air, which has a film coefficient of 5 W/m2 °C and a sink temperature of 20 °C according to [53]. A uniform moving rectangular heat sources and a uniform stationary heat source was solved using the heat source method by Jaeger [54] and Carslaw and Jaeger [55]. In the literature, finite element simulation of grinding process has been performed using heat sources with rectangular, triangle and elliptical distribution [47,48,56,57]. The moving heat source with elliptical distribution was used in the present simulation as it seemed a reasonable assumption. The heat flux can be calculated according to [47,57,58] by Eq. (1);

where q0 is the maximum heat entering the specimen and a is the half of contact length (2a = Lc) between the grinding wheel and the specimen. Also, Lc is equal to the length of the heat source [47,57,58]. The DFLUX subroutine was used to move the heat source across the surface of the specimen. This subroutine can be used to define a non-uniform distributed flux as a function of position and time [51]. 4.3. Shot peening model In order to simulate three-dimensional shot peening process, single and multiple shots impact models were developed. A target in the form of a cube was modeled with a dimension of 20D by 20D surface size where D was the shot diameter, and height of 4.62 mm. The dimensions were large enough that did not affect the results. Steel shots (S230) with a radius of 0.3 mm were modeled by assuming isotropic linear elastic behavior. Eight-node linear brick elements (C3D8R) with reduced integration and hourglass control were used. Initial velocity of 45 m/s along y-direction was defined on all nodes of the shots considering an impact angle of 90° as shown in Fig. 7. Penalty contact algorithm between shots and target surface was applied with no limit on shear stress, infinite elastic slip stiffness and isotropic coulomb friction coefficient of 0.2. For the boundary condition, all the nodes located at the target bottom

0

q¼ε

Lc ¼

F t vw Lc

pffiffiffiffiffiffiffi c:d

ð1Þ

ð2Þ

ð6Þ

Fig. 7. Finite element model of shot assembly.

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were restrained in all degrees of freedom. The material damping was taken into account using Rayleigh damping. Eq. (7) defines the damping where C is damping matrix, M is mass matrix, α is mass proportional coefficient, K is stiffness matrix and β is stiffness proportional coefficient according to [51]. C ¼ αM þ βK

ð7Þ

A single shot impact was simulated to estimated indentation radius (r) and specifying reliable values of mass proportional damping α. Following the convergence study, the element size at the impact region was selected to be 0.02 × 0.02 mm2. The indentation radius of 106 μm was measured from numerical results. A random impingement simulation provided the ability to achieve full coverage of the surface [29,31, 36]. Surface coverage was defined as the ratio of the treated surface area to the whole surface area, expressed in percentage. According to SAE J2277 standard [59] defines full coverage as being equivalent to 98%. Normally, the distribution of equivalent plastic strain (PEEQ) is used to estimate the surface coverage according to [29]. However, instead of calculating coverage after each impact which enhanced computational time a simple code was written in PYTHON programming language to specify the locations of shots to acquire full coverage with minimum number of shots. The number and positions of the impacts on the target surface were determined using this code. This code calculated the number of impacts required for the full coverage by using the radius of the target surface. The locations of the shots were determined using r and θ where r was the distance from the centre of the target surface and θ was the angle with respect to x-axis. Furthermore, the computational cost using the written code was dramatically reduced. Regarding radius of treated area and single indentation, 27 impacts were calculated to obtain full coverage using by the code. The radius of treated area was C = 4r. This value was selected in such a way that no more significant change in the residual stress distribution occurred by further increase in geometry sensitivity analysis. The residual stresses from bending and grinding models were mapped to the model ready for shot peening. The residual stress profile and surface coverage were extracted from the random impacts models using a post processing code written in PYTHON programming language. A circle area (C = 4r) was selected in the finite element models to determine average residual stresses at each depth along x and z directions. The surface coverage of 99.77% was calculated for shot peening model based on the method introduced Miao et al. [29].

483

To check the validity of the finite element model, the strain against time and the load against displacement were plotted with the experiments as shown in Fig. 8(a) and (b). This figure shows the strain measurements for the bending samples. It can be seen that the numerical predictions were in a very good agreement with the experimental data. Small deviations which are observed in the figure between the experimental and the numerical results were due to the small elastic deformations within the loading rig. The experimentally measured residual stresses on the top surface of bent sample were compared with the numerical results as shown in Fig. 9(a). As mentioned earlier, ICHD technique was employed to perform all the residual stresses measurements. The residual stresses components along x-direction were tensile on the B (TRS) specimen and σz was almost zero as indicated in the figure. In depth residual stresses distributions of the ground samples are depicted in Fig. 9(b). The profiles of both components of residual stresses are shown in Fig. 9. As can be seen, the experimental measurements are in good agreement with the numerical findings. The shot peening process was performed on B (CRS), B (TRS) and Gr samples in order to evaluate the effects of presence of initial residual stresses in the specimen on the shot peening residual stresses. It should be noted that the numerical and experimental residual stresses components were presented in the x-direction and z-direction (σx and σz). This was due to the fact that the residual stresses states were not equi-biaxial in most of the cases. The residual stresses induced by shot peening were measured and compared with numerical predictions as shown in Fig. 10. The residual stress state for SP sample was almost symmetric and therefore only one component was plotted. Redistribution of residual stresses in the B (TRS) and B (CRS) samples are illustrated in Fig. 11(a) and (b). Interestingly, the shot peening has wiped out all the residual stresses from bending process

5. Results and discussion All the numerical and experimental results are presented here. Abbreviated naming was used for each sample as shown in Table 3. The average nodal residual stress at each depth and over all nodes of the treated area (radius C) was determined to indicate the residual stress profiles after shot peening. Table 3 Naming convention. Abbreviated name AR B(CRS) B(TRS) Gr SP B(CRS) + SP B(TRS) + SP Gr + SP

Description As-received Bent sample (compressive residual stress on the bottom surface of the beam) Bent sample (tensile residual stress on the top surface of the beam) Ground Shot peened Bent (compressive residual stress in the bottom surface of the beam) plus shot peened Bent (tensile residual stress in the top surface of the beam) plus shot peened Ground plus shot peened

Fig. 8. (a) Strain measurements during four-point bending along x-direction (TS: top surface and BS: bottom surface), (b) load–displacement curve during four-point bending.

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higher and in Fig. 11(b) the amount of σx is lower which are the trends observed for both predicted and measured stresses. Fig. 12(a) shows the residual stresses for ground specimen after shot peening. It is clear that the numerical predictions indicated a satisfactory consistency with the experimental measurements. Again, shot peening process has eliminated all residual stresses from grinding as can be seen in the figure. There were deviations observed between predicted and measured residual stresses in the ground sample. This was due to the alteration of the microstructure for layers beneath the ground surface which was not considered in the finite element models. The deformation contours of residual stresses for half of Gr model and close view of Gr plus SP model are illustrated in Fig. 12(b) and (c), respectively. It can be observed that the tensile residual stress state in the near surface layer of treated area for B (TRS) and Gr models were converted to the compressive residual stresses for B (TRS) + SP and Gr + SP models. As the experimental measurements validated the finite element models, the comparison of residual stresses distributions are performed on the numerical predictions. In depth residual stresses of all finite element models are shown in Fig. 13. Fig. 13(a) shows the distributions of σx and Fig. 13(b) illustrates the same for σz. Study of Fig. 13 confirmed that no significant changes occurred for the stresses near surface and on the maximum compressive residual stress of the shot peening process due to presence of initial residual stresses in all shot peened models. Also, depth of the maximum compressive residual stress remained the same following shot peening in all models. Fig. 13(b) includes all the components of residual stresses along z-direction. Considering the small values of initial residual stresses for B (TRS) and B (CRS) specimens, the shot peening residual stresses (σz) were not changed dramatically. However, this was not the case for the Gr + SP residual stresses and the shot peening residual stresses were experienced considerable Fig. 9. A comparison between residual stresses induced in,(a) B (TRS) sample in two directions, (b) ground samples in two directions.

and redistributed the residual stresses quite similar to the stresses in the SP samples. It can be seen that higher amounts of errors are observed for the higher depths. However, this is due to the nature of the incremental hole drilling (ICHD) technique. In the ICHD technique the amounts of error grow as the hole goes deeper to the sample. Therefore, the measured residual stresses by this technique are more accurate near the surface. The ICHD technique owes this error partly to the fact that the sensitivity of the strain gauges attached to the surface is less as the increments go deeper. Furthermore, compatible trends are observed between the stress components along x and y axes shown in Fig. 11. This means that although the amount of stresses from FE deviated from the measured stresses, the trends are the same. In Fig. 11(a) the amount of for deeper locations within the sample, the amount of σx is

Fig. 10. Experimental and numerical residual stress distribution for SP sample.

Fig. 11. Redistribution of residual stresses by shot peening in, (a) B (TRS) samples, (b) B (CRS) samples.

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Fig. 13. Residual stresses distributions for all samples, (a) σx, (b) σz, all lines are from FE.

Fig. 12. (a) Redistribution of residual stresses by shot peening in Gr sample, (b) close view of half Gr model, (c) close view of Gr + SP model.

alteration up to almost 300 μm which is almost the location of the maximum compressive residual stresses. The plastic zone which was a result of the shot peening led to neutralize all the initial stresses prior to shot peening within this zone. Looking at the plastic strain in Fig. 14 supports this argument. Fig. 14 illustrates the plastic zone by plotting the PEEQ against the depth for all samples. It can be seen that the plastic strain decreased from a value of 0.5–0.6 at the surface to almost zero at 200 μm depth. This depth is where the alteration of the residual stresses began according to Fig. 13. For the bent samples as almost no plasticity occurred beneath the surface, the shot peening residual stresses remained unchanged up to the plastic strain depth (200 μm). However, initial stresses forced larger alterations beyond the maximum compressive residual stress point as the deformations beyond this point were elastic. This meant that the initial compressive or tensile stresses increased or decreased the compressive residual stresses respectively beyond the peak stress point. The minimum and maximum compressive layer thickness was corresponding to the B (TRS) + SP and B (CRS) + SP specimens, respectively. Effects of tensile or compressive initial stresses were severe on the tensile region of shot peening residual stresses. The tensile stresses in the B (TRS) sample caused a dramatic rise in shot peening stresses in the tensile region. In contrast, initial compressive stresses of the B (CRS)

caused the shot peening residual stresses to remain compressive up to 1000 μm depth. In the ground sample, despite the other two samples, the residual stresses profile changed direction which caused different effects on the residual stresses profile in comparison with the bent samples. In the Gr + SP sample the residual stresses profile changed direction to compressive deeper inside the specimen. It is clear that the state of initial residual stresses distributions had a significant role on the residual stresses following shot peening. Fig. 15(a) depicts all the hardness test results performed on various samples. The micro-hardness was increased by plastic deformation process. The increasing surface hardness for SP specimen is more than B

Fig. 14. Illustrating the PEEQ against the depth for all samples.

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• Any initial stress field can be wiped out by the shot peening process up to the maximum compressive residual stress point. • The presence of initial stresses can dramatically alter the shot peening residual stresses beyond the maximum compressive residual stress point. These changes were deeply dependent to the amount and direction of residual stresses. • Shot peening process can improve both stress distributions and hardness of the components with initial stresses. • Rough grinding after shot peening not only generated compressive residual stress but also increased surface hardness.

References

Fig. 15. (a) Surface hardness for all specimens, (b) in depth micro-hardness distribution.

(TRS) and B (CRS) specimens. Also, micro-hardness at the surface of B (TRS) + SP and B (CRS) + SP specimens increased slightly in comparison with SP specimen. The surface hardness for Gr sample was almost two times of AR specimen and this value was even higher following shot peening. Therefore, maximum value of micro-hardness was corresponding to Gr + SP samples. Fig. 15(b) illustrates the distribution of micro-hardness from the treated surface to the bulk material. Maximum values of micro-hardness tests were related to the surface of all treated specimens. These values were gradually decreased until it reached a constant value. Furthermore, this figure shows that the surface properties of the ground sample changed dramatically due to the high temperature created while grinding. Although the surface hardness of the ground samples were enhanced, the birth of tensile residual stresses on and beneath the surface is considered as a down side for grinding. The shot peening, however, changed the tensile residual stresses to compressive and also forced a rise in surface hardness by around 27%. 6. Concluding remarks A comprehensive numerical and experimental study was carried out to investigate the effects of the presence of initial residual stresses on the shot peening stresses in low-alloy steel specimens. Extensive finite element analyses were performed, evaluated and discussed. Experimental tests were designed to create different initial stress fields prior shot peening. Many residual stress measurements were performed. According to the results, the following conclusions can be made: • The numerical models were able to predict the induced residual stresses affected by different processes performed in this study: the experimental ICHD measurements are in good agreement with the numerical results.

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