Residual stress near single shot peening impingements determined by nanoindentation and numerical simulations

Abstract

The near-surface hardness and residual stresses resulting from a single shot peening impingement on aluminum alloy 2024-T351 were assessed by nanoindentation with spatial mapping of mechanical properties on cross sections through an impingement. For residual stress, a procedure was developed to couple nanoindentation experiments with numerical simulations for better understanding and predicting the effects of shot peening. A surface preparation method was developed that exposes the cross section of a single shot impingement for nanoindentation tests, while at the same time obtaining accurate measurements of the impingement dimensions. Starting parameters for the numerical simulation in terms of shot diameter and the shot velocity were selected to best match measurements of the impingement depth and diameter. The experimental results indicated that the greatest hardness was located at the nearest indent to the peened surface, whereas the maximum compressive residual stress was located sub-surface. When comparing experimental and numerical residual stresses, the experimental results showed a greater maximum compressive residual stress that was in closer proximity to the peened surface. Overall, residual stress fields compared between experimental and numerical results were similar, and differences could be explained in terms of the effect of strain hardening. The current work demonstrated the usefulness of coupling nanoindentation experiments with numerical simulations for evaluating the surface modifications resulting from a single shot peening impingement.

Appendices

Appendix 1

The variation in residual stresses throughout the indentation depth of influence was evaluated with numerical simulations for a shot diameter of 450 µm and a shot velocity of 54 m/s. The depth of influence d ^R was set to three times the indentation depth, d ^R = 3 × 320 = 960 nm [17].

The variation in residual stresses across d ^R was obtained by comparing the residual stresses on the indentation plane located at r = 45 µm, corresponding to σ _RS,45, with the residual stresses located at a distance from d ^R from the indentation plane, corresponding to $\sigma_{{{\text{RS,45}} - d_{{}}^{R} }}$ (view Fig. 13). Since the elements used in the numerical model were of dimensions 15 µm × 15 µm × 15 µm, $\sigma_{{{\text{RS,45}} - d_{{}}^{R} }}$ was obtained through the linear interpolation of σ _RS,45 with the residual stresses located at r = 30 µm, corresponding to σ _RS,30 (view Fig. 14).

Fig. 13

Isometric view and top view of a peening impingement

Fig. 14

a Average residual stress profiles at distances from the center of the impingement of r = 30 µm and r = 45 µm and b the corresponding variation in residual stress across the indentation depth of influence

The greatest variation in residual stress across the indentation depth of influence was calculated to be 3.23 MPa located at z = 20 µm, which corresponds to a residual stress difference with respect to σ _RS,45 of 2 %. The maximum residual stress variation, corresponding to 3.23 MPa, is significantly smaller than the minimum 95 % confidence interval obtained from the calculation of residual stress through nanoindentation, corresponding to 42.2 MPa. Therefore, the variation in residual stresses across the indentation depth of influence was considered as insignificant.

Appendix 2

A variation in shot diameter results in a modification in the peening-induced residual stresses. The residual stress profile beneath the center of an impingement resulting from a variation of 3 % in the impingement diameter can be seen in Fig. 15, where the reference impingement diameter corresponds to d = 169 µm. The variation in impingement diameter was obtained using a shot velocity of 54 m/s and shot diameters of 438 µm and 485 µm, resulting in d = 164 µm and d = 174 µm, respectively (view Table 5).

Fig. 15

The variation in residual stresses produced by an approximately 3 % change in impingement diameter from d = 169 µm: a the residual stress profiles illustrated correspond to the stresses beneath the center of the impingement (r = 0 µm); b the magnitude of residual stress variation

Table 5 Impingement diameter and corresponding shot diameter determined through numerical simulations

It can be seen that the variation in the residual stress profiles follows the same trends independently of the impingement diameter. However, the magnitude of residual stresses appears to be influenced by the diameter. The increase in magnitude of compressive residual stresses was greatest when the diameter was increased by 3 % (d = 174 µm), resulting in an average difference of −41.7 MPa between z = 110 µm and z = 220 µm. Outside of this range, the difference in residual stresses is significantly smaller, inferior to 10 MPa. Moreover, this maximum difference, corresponding to −43.0 MPa, is of similar magnitude to the minimum 95 % confidence interval from the calculation of residual stress through nanoindentation, corresponding to 42.2 MPa. For this reason, the variation in residual stresses caused by a difference of ±3 % of the impingement diameter will be assumed to be insignificant.