Abstract
ASTM F75 implants distort due to residual stress released after finishing machining operations, causing implants to fail quality requirements. Previous work has shown that a shot blasting cleaning process could be the source of this distortion. Finite element analysis (FEA) is conducted to predict stress and Almen strip arc heights for experimental comparison. 2D and 3D single impact models and 3D multiple impact models are created. 3D multiple impact models with plastically deforming shot are shown to accurately predict the stress state and distortion. For shot with hardness similar to the implants, distortion creating stress magnitudes are induced, with the greatest fluctuations in stress coming from shot velocity. The depth of the predicted compressive stress layer ranges from 0.23 to 0.6 mm.
Introduction
ASTM F75 femoral knee implants tend to distort unpredictably due to the release of residual stresses after being removed from investment casting, with one of the causes qualitatively assessed as a shot blasting process [1]. In a recent study, two rectilinear ASTM F75 parts measuring approximately 80 × 24 × 2.3 mm3 were bolted together and put through the same shot blasting process as the ASTM F75 femoral knee implants [2]. When removed and un-bolted, all parts distorted by approximately 20% of their thickness indicating that a compressive stress had been induced. Using fundamental elasticity theory, the stress induced from the shot blasting process can be estimated [2]. Owing to the potential for loosening in-service, femoral implants have very tight tolerances and therefore out of tolerance implants are scrapped or reworked thus increasing production's environmental and business costs [3]. With the usage of femoral knee implants in the United States set to grow by 143% from 2015 to 2050 [4], the motivation of this research is to determine how to reduce the volume of scrapped implants.
Shot blasting is the process of firing a stream of high velocity metallic or ceramic balls, called the ‘shot’, at the surface of a metallic component to clean it [5]. For the ASTM F75 femoral knee implants, a centrifugal drum accelerates a stainless-steel shot while they are tumbled on a belt, removing any excess shell material leftover from the investment casting process. The shot's velocity is not a controlled parameter and is limited to the size and rotational speed of the drum. Therefore, predicting the intensity of the blasting process is challenging to determine. The same process is also commonly referred to as shot peening when the intention is not to clean the surface, but to induce a compressive layer of residual stress. The impact of this stream causes plastic deformation on the surface of the workpiece. The plastic deformation forms a protective compressive layer of stress and work hardens the surface, thus improving its service life due to the increased crack growth resistance [6]. However, it will also cause the workpiece to distort if a material layer is removed from the surface due to a rebalancing of the residual stress [7]. For this research, the shot blasting process is referred to as shot peening to avoid confusion with studies available in the literature.
Finite element analysis (FEA) has been used extensively in the literature to numerically approximate residual stress magnitudes in shot-peened workpieces. However, few studies focus on relating the method to a complex shaped industrial product, a shot of similar hardness to the workpiece and a plastically deforming shot. An accurate assessment of the residual stress state in the workpiece will give insight into how process parameters can be altered to a level where deformation will not occur.
Maximum specified chemical composition of ASTM F75 (%, mass/mass) [8].
Shot peening residual stress and FEA simulation
Energy transformation during impact
Figure 1 presents an impact model between a solid sphere and a solid structure represented as the workpiece in the shot peening process. The initial impact energy is expressed as the Newtonian kinetic energy Ei (Equation 1), where m is the mass of an individual shot and vi is the initial velocity at which the shot travels.
Illustration indicating a single shot striking the surface of a workpiece, adapted from [9]. Plastic deformation of the shot will also occur if hardness is of similar value to the workpiece.
Shot velocity
As described in section ‘Energy transformation during impact’, shot velocity is of utmost importance in determining the plastic deformation of the workpiece and, ultimately, the intensity of the shot peening process. Thus, accurately predicting the shot velocity from the acceleration source is key to having a stable process with repeatable results. The shot is accelerated using compressed air through a blasting nozzle or a centrifugal drum [7]. In the case of ASTM F75 femoral knee implants, the shot is accelerated by a centrifugal drum.
Kirk [11] provides an analytical calculation for estimating shot velocity in a centrifugal drum process (Equation 3). The equation solves the shot velocity Vs by inputting the known process parameters: n revolutions per second of the drum, r radius of the drum, L length of the blade. Figure 2 presents a diagram of the process.
Centrifugal drum acceleration of shot, adapted from [11].
Residual stress in shot peened materials
After the impact of the shot, a layer of compressive stress is formed on the surface of the workpiece, with a balancing tensile stress layer beneath that, as illustrated in Figure 3. When referring to the residual stress in a shot-peened part, it is usually considered to be the transverse stress acting parallel to the surface, as this is the stress that aids in the prevention of crack initiation [12] – see Equation (4). Schiffner and Droste gen. Helling [13] identified that the residual stress state could be described by two phenomena: Hertzian Pressure and Plastic Stretching.
Schematic showing the plastic deformation of the workpiece in tension (left) and the resulting residual stress profile for a single stress component σxx (right). For the results presented in this study, ‘residual stress’ is implied to be the stress component σxx.
Plastic deformation of the workpiece will continue until the elastic energy of deformation is restituted, and the shot will rebound. When the shot impacts, it will plastically stretch the material around it, yielding the surface of the workpiece in tension. In order to retain equilibrium once the elastic deformation has been released, compressive residual stress will form on the surface region [14]; a schematic of this phenomenon is shown in Figure 3.
Residual stress-induced shape changes
The Almen strip test gives a clear description of how residual stress-induced shape changes occur in shot-peened workpieces. An Almen strip is a rectangular strip of material that is fixed at both longitudinal ends and subjected to a shot-peening treatment. When the shot-peened workpiece is in a balanced stress state, there is a compressive surface layer on both sides, with a tensile balancing layer throughout the bulk of the workpiece – see Figure 4(a). The tensile stress layer acting over the cross-sectional area of the tensile region of the workpiece introduces a tensile force F. If a compressive force –F/2 acting at one side of the strip is not present to balance the tensile force, then the workpiece is in an unbalanced state of stress – see Figure 4(b). The unbalanced state will rebalance, causing one side to compress and the other to stretch, leading to bending of the strip. This unbalanced stress state can arise by removing the compressive layer on one side of the workpiece, by only shot peening on one side or by uneven exposure to the shot stream. This simple analogy occurs in the production of the femoral components where the articulating surfaces are machined, thereby removing a compressively stressed layer which can lead to femoral distortion.
Residual stress-induced bending in an Almen strip, adapted from [2] (a) shows a cross-section of a sample in balanced stress state, with compressive surface stress and core tensile stress magnitudes (b) shows the same cross-section, but with one of the compressive surface layers removed, which results in distortion, quantified by ‘h', the ‘Almen Strip arc height’.
Guagliano [15] introduces the relationship between the induced level of compressive residual stress magnitude and the induced bending height of the strip h, referred to as the Almen strip arc height. Equations (5 and 6) are fundamental elastic formulae for calculating force and bending moment, where σres is the induced compressive residual stress magnitude from the impacting shots and y is the compressive stress layer depth. Equation (7) highlights that once the workpiece is released from clamping, it will bend and stretch until it reaches a state of equilibrium. The stress released during this process is subtracted from the induced stress to give the final magnitude of residual stress. Equation (8) describes how to obtain the arc height as a function of induced bending moment, material geometry and material properties. An FEA simulation combined with the analytical expression for arc height can be compared to experimentally measured heights.
Residual stress in ASTM F75 femoral knee implants
Typical ASTM F75 femoral knee implants are shown in Figure 5, which shows experimentally determined residual stress magnitudes in a femoral [16]. The shape is relatively complex, and due to the difficulty of machining the component and the amount of material to be removed, it is cast to a near-net shape. The investment casting process can induce residual stress magnitudes as well as the post-processing procedures, including: Mould removal; Casting cut off; Heat treatments; and Shot blasting [3]. As discussed in section ‘Residual stress-induced shape changes’ and observed in Figure 5, the shot blasting process used to remove the investment casting shell forms a compressive residual stress layer on the surface of the femoral [1]. During subsequent machining, the stress will rebalance, leading to distortion.
Residual stress σxx (MPa), of an ASTM F75 femoral knee implants before and after a shot blasting process taken by contour method [16].
Shot peening FEA
Numerous studies have been conducted to research the effect that the shot peening process has on the residual stress state. The studies fall into two main categories: 2D axisymmetric models and 3D models. 2D axisymmetric models are efficient to create and analyse but lack the advantage that 3D models have in simulating the impact of multiple shots and non-symmetric behaviour.
2D axisymmetric modelling
Most early studies focusing on shot peening used 2D models and had limitations in that they did not thoroughly study effects that are now commonplace, such as including friction [13] and damping [17]. However, observations were made of how the impact should be modelled more correctly by using strain-rate sensitive material models [13], including frictional effects [17], and that isotropic and kinematic hardening models affect the final residual stress state [18]. Kim et al. [19] conducted a comprehensive study on implementing a 2D model, concluding that the effects of penalty contact stiffness, damping, friction, element size, plasticity model and shot plasticity should all be considered to achieve an accurate 2D model.
3D modelling
Meguid et al. [20,21] conducted early work on 3D FEA analysis of the shot peening process. The work incorporated friction, showing that a friction coefficient µ ≥ 0.25 is needed to achieve stable residual stress distribution and that a material damping factor ξ = 0.5 is enough to dampen oscillations in the model. The damping factor aids in significantly improving computation time by dissipating the energy in the model faster. The effect of strain rate is also concluded to play a role in determining the residual stress and the effect of work hardening of the shot with unconditioned deformable shots reducing residual stress magnitudes.
The ability to study multiple shot impacts has been incorporated into studies showing that multiple impacts will introduce a uniform stress profile [21-23]. Therefore, the number of shot impacts should also be considered and calibrated from experiments.
Recent studies have tried to relate multiple shot models with non-symmetric impact patterns to the Almen strip arc height [24-28]. This method attempts to capture the actual shot peening process by simulating a random pattern of coverage that occurs in a physical shot peening process. The resulting average residual stress is extracted from these models and input into an analytical expression (see Equation 8). Alternatively, the residual stress state is input into an implicit FEA simulation to determine the arc height h. Experimental arc height comparison is considered the most accurate method of determining the severity of residual stress induced shape changes due to a combination of several process parameters that can lead to the same residual stress profile [13]. Furthermore, there are difficulties in measuring experimental residual stress levels of some materials, including ASTM F75 [1,3].
Numerical simulation in Abaqus®
Material model
As noted in the literature [13,21], strain rate sensitivity should be included in the plasticity model of the workpiece material. The model chosen for this analysis is the Johnson-Cook (JC) plasticity model [29] due to its ease of dealing with high strain rates and dynamic simulations. The model formulates the Von Mises flow stress 
as per Equation (9), where 
is the equivalent plastic strain, 
is the equivalent plastic strain rate, with C and 
being strain rate sensitivity coefficients. The strain-rate sensitivity is incorporated by defining the evolution of plastic strain by Equations (10 and 11), where R is a ratio of the strain rate yield stress to the static yield stress.
In a significant amount of conducted studies, the shot is considered to be a rigid body. However, for shot peening ASTM F75 castings, the shot used is typically SUS304 (250–350 Hv) which has a similar hardness to ASTM F75 (310–350 Hv) [1]. This must be accounted for in the simulation as the shot will also deform during the process.
The JC parameters of ASTM F75 are calibrated from work-hardening data in the literature [3] with the resulting strain-rate sensitive curves presented in Figure 6. The material parameters are given in Table 2 with the data for SUS304 taken from the literature [30].
JC true stress – true strain curves for ASTM F75 calibrated from [3].
Geometry and meshing
2D axisymmetric
The 2D axisymmetric model is limited to a single impact with a shot radius of 0.4 mm used to replicate the process used for ASTM F75 femorals [1]. The model predicts the effect of a single shot striking a cylindrical workpiece with a radius of 3 mm and a height of 3 mm. This geometry was chosen based on the literature advice [19], with no geometrical effects at this size found to affect the final residual stress state. The model contains a finer meshed impact region at its centre to ensure accurate stress resolution. The impact region is surrounded by a larger boundary region and infinite boundaries at the extremities. These boundaries act as stabilisers to not reflect elastic waves after impact and reach a stable solution [31]. A representation of the model is presented in Figure 7.
Geometry of 2D axisymmetric model. Image on the left gives 3D view, while image on the right shows a cross sectional view.
The shot and workpiece were meshed with CAX3R and CAX4R axisymmetric reduced integrated linear elements. The infinite elements boundaries are of type CINAX4. Mesh convergence was conducted, and an element size of 0.01 mm was used, agreeing with similar values found in the literature [19]. The workpiece is fully constrained at its base, while the shot is constrained along its impingement angle, which is normal to the surface.
A penalty contact model was implemented between the shot and the workpiece. The shot is chosen as the master surface, with the workpiece being the slave surface. A damping coefficient ξ = 0.5 and a friction coefficient µ = 0.3 are used based on a trial-and-error selection and advice from [17,19], with stable results showing at those values.
3D model
The 3D model depicted in Figure 8 can predict the effect of a single impact and multiple shot impacts. The model uses a rectangular workpiece that contains another rectangular impact region at its centre; a rectangular workpiece was used for the simplicity of meshing. The infinite boundaries fit the same purpose of the axisymmetric model described in section ‘2D axisymmetric’. The same penalty contact, damping coefficient and friction coefficient as the axisymmetric model was used.
Geometry of 3D model including 20 randomised shots and impact region at the centre of the model.
The workpiece is meshed with a bias along the depth of the workpiece in the z-direction to create layers in the model. The layers are used to average the residual stress magnitudes at specific depths as the stress state in the impact region is not symmetric with multiple impacts. C3D8R reduced integrated linear quadrilateral elements were used for meshing the workpiece and shots, while CIN3D8 infinite elements were used at the boundaries. For the single-shot model, an element size of 0.01 mm was used, but some distorted elements can occur at this element size when there is a large deformation due to multiple impacts. Further mesh convergence studies found no distorted elements occurred in the impact region at an element size of 7 µm, with this element size used for modelling the multiple impact model.
The order in which the shots impact was randomised to replicate the actual shot peening process, with the impact pattern represented in Figure 9. The number of random shots used is based on an exponential coverage function provided in the literature [11] that approximates >99% peening coverage at 60 m.s−1, with the impact dent area used based on the single impact model. The random 3D coordinates were generated by Equations (12–14). A random number between 0 and 1 was generated by the rand() function in Microsoft Excel® and multiplied by the length and breadth of the impact region shown in Figure 8 to create the x and y coordinates. The z coordinates are spaced at intervals of 0.1 mm. The coordinates were generated once and used for simulating all velocities of the shot.
Pattern of 20 randomised shots on the impact region (left) and deformed surface layer induced by this pattern (right).
Residual stress
Single impact
Residual stress
Figure 10(a) compares residual stress profiles for a single impact in the 2D and 3D deformable model at 60 m.s−1. The results show the 2D model having a larger compressive stress depth and maximum magnitude. The compressive stress profile starts with a tensile stress at the surface of the workpiece that transitions into a compressively stressed region, see Figure 11. Sanjurjo et al. [31] highlighted this behaviour in other literature but is not present in a physical shot peening process where compressive surface stress is typically observed.
Residual stress profiles acting in the x-direction for: (a) 2D and 3D single impact at a shot velocity of 60 m.s−1 and (b) 3D single impact model at velocities of 20–100 m.s−1. Predicted residual stress magnitudes acting in the x-direction, S11 (Pa), in shot and workpiece of 3D single impact model at a shot velocity of 60 m.s−1.
The residual stress profile results in Figure 10(b) show an increasing compressive residual stress depth for an increasing velocity, but the maximum residual stress value increases up to 60 m.s−1 and decreases after that. This phenomenon is expected to be caused by increased levels of plastic deformation above 60 m.s−1, making the compressive stress act over a greater area and correlates with previously published research [32].
An example of the residual stress in the 3D model with a deformable shot at 60 m.s−1 is given in Figure 11, highlighting the deformation of both the shot and the workpiece during impact. The residual stress in the shot is due to the plastic deformation of the used deformable shot. The shots are used repeatedly in the physical peening process and will condition to work harden with use. The effect of the deformation and conditioning of the shot requires further investigation and is not included as part of this study.
Dent geometry
The dent geometries for a 2D and 3D single-shot impact at 60 m.s−1 are shown in Figure 12(a). The greater dent size is also reflected in the residual stress profiles in Figure 10(a), where the depth of residual stress increases with the depth of the indents. An approximately linear relationship between dent depth or diameter and shot velocity is observed in the results shown in Figure 12(b).
(a) Dent geometry of 2D and 3D single impact model at 60 m.s−1 and (b) impact dent depth and diameter for 2D and 3D single impact model at velocities of 20–100 m.s−1.
Multiple impact
The residual stress state in the impact region of the 3D multiple shot model is shown in Figure 13, with a non-symmetric stress state observed compared to the single-shot model in Figure 11. Some areas of tensile stress are observed at ridges formed by the random impact pattern. However, most of the surface contains compressive stress magnitudes, unlike the single-shot model with tensile surface stress magnitudes acting over the impact area.
Magnitude of residual stress acting in the x-direction, S11 (Pa), of the entire impact region (left) and of a cross-sectional cut along the x–z plane (right) at a shot velocity of 60 m.s−1.
The averaged residual stress results in Figure 14(a) show both a larger residual stress depth and maximum magnitude compared to the 3D single-shot model. Furthermore, unlike the single-shot results in Figure 10(b), the maximum compressive stress magnitude increases with an increasing velocity. This shows that multiple impacts in the same region change the residual stress profile with an increasing velocity and cause the maximum compressive stress to also increase.
Residual stress profiles acting in the x-direction for: (a) 3D single and multiple shot models at 60 m.s−1 and (b) 3D multiple impact model at velocities of 20–100 m.s−1.
Figure 15 displays the non-symmetric deformation in the z-direction (U3) of the first workpiece layer showing how the random coverage distribution forms a ridged surface.
Displacement in the z-direction (U3 (m)) of the workpiece surface impact region indicating areas of varying deformation.
Model verification
Residual stress
Figure 16 compares residual stress profiles of the different FEA models at a shot velocity of 60 m.s−1 to the experimental values taken by X-Ray Diffraction (XRD) and centre hole drilling (CHD) method as part of earlier published research [1]. The multiple impact model shows close agreement with the experimental finding of the XRD surface measurements and hole-drilling method for surface stress, maximum stress and compressive stress depth. Both the 2D and 3D single-shot models are comparable to the residual stress profile taken by the hole drilling method, with the maximum residual stress and depth in a similar range. However, these methods fail to predict the surface residual stress magnitude calculated from XRD measurements, which is likely due to the presence of tensile stress magnitudes at the surface as indicated in Figure 11. Clearly, this is a limitation of using a single impact model.
Comparison of 2D single, 3D single and 3D multiple impact models at a shot velocity of 60 m.s−1 with experimental values found in the literature [1] via centre hole drilling (CHD) and X-Ray Diffraction (XRD).
Almen strip arc height
To verify the FEA results with the residual stress state in ASTM F75 femoral knee implants, the results are compared with Almen strip arc height results taken from previously published experimental measurements [2]. The arc height is measured by extracting the average residual stress in the compressively stressed zone σres and the depth of the compressively stressed region y from the residual stress profiles and calculating the resulting arc height h from Equation (8).
σres is calculated by integrating a curve fitted function of the residual profile over the depth of the compressively stressed region according to the method provided in the literature [33]. An example of the extraction method for the 3D single-shot impact is shown in Figure 17.
Example extraction of σres for the 3D multiple impact model at 60 m.s−1 by calculating the integral of the curve fit.
Figure 18 presents the arc heights at different velocities for the different modelling methods. From the results of the 3D multiple shot model in Figure 18 the shot velocity vi of the shot blasting process can be estimated by solving a second-order polynomial curve fit of the data in Equation (15) with an input of the experimental arc height h.
Calculated Almen strip arc heights using Equation (8) and FEA predicted stress distributions for 2D single, 3D single and 3D multiple impact models at shot velocities of 20–100 m.s−1. The average arc height of results found in [2] is 0.5 mm.
Inputting the experimental arc height of 0.5 mm from [2] into Equation (15), the estimated shot velocity is ∼54 m.s−1. Figure 19 shows that the updated shot velocity estimate of 54 m.s−1 gives a better approximation of the experimental residual stress profile from [1] as this profile is approximately half way between the FEA results of 40–60 m.s−1.
Residual stress profile of 3D multiple impact model at velocities of 20–100 m.s−1 compared with experimental values found in previously published work [1] determined from centre hole drilling (CHD) measurements.
Shot peening process
The shot peening process for ASTM F75 has a significant amount of variability in the process parameters, including; shot velocity from the centrifugal drum, shot to shot contact, workpiece to workpiece contact on the conveyor belt, shot impact coverage, shot and workpiece material interaction, presence of ceramic casting shell, and shot conditioning and hardening. Furthermore, variability in the FEA approximation is present due to material calibration, numerical accuracy in Abaqus Explicit®, random shot distribution and stress averaging. Considering the plethora of variability in the process, the results indicate a reliable method for the industry to approximate the shot peening process using controlled parameters and relating it to experimental Almen strip results. Using the experimental findings, the shot velocity can also be approximated to control the rotational speed of the shot peening centrifugal drum. This method can also be applied to a shot peening process that uses compressed air to accelerate the shot.
Results in Figure 14(b) show that the stainless-steel shot of similar hardness to ASTM F75 can induce significant residual stress in the femoral that may lead to distortion when the residual layer is removed by machining. Furthermore, the depth of these layers range from 0.225 to 0.65 mm at velocities of 20–100 m.s−1. The hardening induced by the shot peening process and the depth at which the residual stress layer acts agree with findings found in the literature [34], where it was observed that before the parts are machined to specification, there is increased hardness at the surface and that the machining depth can range from 0.1 to 2 mm. Given the predicted depths of residual stress, this machining cut can fully or partially remove the residual stress layer. As explained in section ‘Residual stress-induced shape changes’, the femoral will have to rebalance and distort if this layer is removed. Results show that for an Almen strip of ASTM F75, reducing the shot's velocity can greatly reduce the level of residual stress and distortion. This suggests that a shot peening process with a reduced shot velocity for an extended period, may help in reducing the levels of distortion.
Further experimental work can correlate with the FEA results, such as microscopic measurement of the dent geometry and further Almen strip tests. This can help further approximate the shot's velocity from the centrifugal drum and having an accurate approximation of the shot velocity will give improved control over the process.
The most accurate method of predicting the process for industrial applications is the 3D multiple impact model that requires more pre-processing, run-time and post-processing than the 2D and 3D single impact models. This can be considered a drawback for industrial applications where time might be a constraint. The 2D single impact results roughly follow the experimental data, and with careful consideration and an applied tolerance to the result, this method could quickly indicate the severity of the shot peening process. Further work in FEA modelling can be conducted relating the analytical expression (Equation 8) with an FEA model of an Almen strip. Residual stress states can be extracted from the impact region and imported to a strip of material that is constrained at both ends. Upon release of the constraints, the residual stress will rebalance and approximate an Almen strip test. As with the experimental work completed in this area [2], the Almen strip analysis can be used as a good indicator for the likely distortion in more complex parts such as the femoral.
Conclusion
The research conducted in this paper focused on predicting residual stress and resulting Almen strip arc height by FEA and compared these results to the experimental findings found as part of the work in the literature [1-3,16]. An accurate approximation of these results enables industrial practice to measure the intensity of the shot blasting process and adjust process parameters. Adjustment of process parameters may reduce unwanted distortion due to the release of residual stress induced by the process. The following conclusions are made:
FEA methods present in the literature are suitable for predicting the residual stress state in ASTM F75 Almen strips resulting from typical industrial shot blasting processes. 3D multiple shot models with randomised shot impacts should be used for more accurate approximations. Analytical calculation of Almen strip arc height from FEA stress predictions is a viable method for use in industry to compare with experimental results. The shot blasting process for ASTM F75 femoral knee implants induces a significant amount of residual stress even with a shot of similar hardness. A clear option to help reduce femoral distortion is a small reduction in the shot velocity. After the investment casting process, the machining of ASTM F75 femoral knee implants will fully or partially remove the induced residual stress layer, thereby causing a rebalancing of stress and part distortion. Experimental correlation of impact dents and coverage rates are needed to estimate the intensity of the process with greater accuracy
The method presented in this paper is achievable to be implemented in industry and shows that modern methods in FEA simulation of the shot peening process are accurate enough to apply to an industrial product.
Footnotes
Acknowledgements
The authors wish to express sincere thanks to Dr Brian Conroy for his valuable insight and knowledge of the research.
Disclosure statement
No potential conflict of interest was reported by the author(s).