Three-dimensional dynamic finite element analysis of shot-peening induced residual stresses

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Abstract

This investigation is devoted to the modelling and simulation of the residual stress field resulting from the shot-peening process. In this dynamic elasto-plastic analysis, single and twin spherical indentations were examined using the finite element method. The contact between the shots and the target was modelled using contact elements of the penalty function type. Attention was devoted to three related issues. The first is concerned with the effect of the shot velocity, size and shape upon the plastic zone development and growth, and unloading residual stresses. The second with the effect of the separation distance between two impinging shots upon the equivalent stress trajectories and unloading residual stresses. Finally, the study examines the effect of the strain-hardening rate of the target upon the development and the spread of the plastic zone. The results reveal the important role played by the shot and target characteristics upon the quality of the treatment, as measured by the mechanically induced residual stresses.

Introduction

Shot-peening is a cold-working process used mainly to improve the fatigue life of metallic components 1, 2, 3. The results are accomplished by bombarding the surface of the component with small spherical shots made of hardened cast-steel, conditioned cut-wire, glass or ceramic beads at a relatively high velocity (40–70 m/s). After contact between the target and the shot has ceased, a small plastic indentation is formed causing stretching of the top layers of the exposed surface. Upon unloading, the elastically stressed sub-surface layers tend to recover their original dimensions, but the continuity of the material in both zones, the elastic and the plastic, does not allow this to occur. Consequently, a compressive residual stress field followed by tensile is trapped in the bounded solid.

This surface compressive residual stress field is highly effective in preventing premature failure under conditions of cyclic loading, since fatigue generally propagates from the upper most surface of the component, and usually starts in a region which is subjected to high tensile stresses. This is indeed the motivation behind the use of the treatment in the aerospace, automotive and power generation industries. In the case of the aerospace industry, the treatment leads to a reduction in structural weight for a specified reliability level. Typically, turbine and compressor discs and the attached blades, propellers and harmonic drives, main rotor spindles and main and nose landing gear components are shot-peened. In the automotive industry, it means that relatively small low-cost components can be upgraded for conservative operation at stress levels that would represent poor practice without the treatment. Springs, gears of all types and shapes, connecting rods, cam shafts and torsion bars are examples of components that can be upgraded by the treatment. The ability to upgrade the mechanical properties of a component by shot-peening offers obvious opportunities in the correction of undersized components when, e.g., fatigue failure occurs after a product is standardized or in field service by the power generation industry.

The effectiveness of the shot-peening treatment depends to a large extent on peening intensity and peening coverage. Peening intensity is a measure of the consistency of the treatment and of the plastic dissipation of the impinging shots. Peening coverage, on the other hand, is a measure of the area covered by peening indentations. Both intensity and coverage depend on numerous variables, including: workpiece characteristics, shot characteristics, flow conditions, jet obliquity, stand-off distance and exposure time. Peening intensity is measured using the arc-height resulting from peening standard spring steel strips, known as Almen strips. Coverage, on the other hand, is typically measured using a magnifying glass. Further details concerning these variables and the techniques adopted in measuring them can be found, for example, in references: Desvignes et al. [4]and Meguid [5].

The modelling and simulation of the shot-peening process has received some attention from the scientific community. This includes the contributions made by Shaw and De Salvo [6], Meguid et al. 7, 8, 9, Khabou et al. [10]and Li et al. [11]of the process using quasistatic analysis. The dynamic modelling of a single shot was initially conducted by Johnson [12]using a pseudo-dynamic approach. In his approach, Johnson [12]took into account only the inertial properties of the shot. As a result, a relationship between the depth of the plastic zone and the shot parameters, such as radius, mass and velocity, was obtained. This relationship was later validated by Clausen [13]and Iida [14]. Edberg et al. [15]conducted dynamic three-dimensional finite element analysis of a single shot impinging viscoplastic and elastoplastic materials. Their results showed that the two material models give similar residual stress distributions.

Review of most of the existing work in this area, however, reveals a number of shortcomings. These include: (i) the selection of unrealistic or irrelevant peening parameters, (ii) the focus of attention to the peculiarities of the specific models rather than upon the relevance of the work to the process, and (iii) the use of improper and inaccurate modelling techniques. It is believed that the present study addresses these issues more carefully.

The objective of this study is therefore to evaluate the elasto-plastic dynamic indentation behaviour of a bounded solid by a single and multiple spherical shots. The effect of the separation distance and shot velocity as well as the mechanical properties of the bounded solid upon the resulting residual stress field are examined and discussed. In addition to being of importance to the shot-peening process, this study is of value to a number of related areas, such as friction and wear, ball bearing technology, abrasive erosion and surface finish.

This article is divided into 4 sections. Following this introduction, Section 2describes the finite element model used. In Section 3, we verify the finite element results and discuss the effect of the pertinent parameters upon the plastic zone developed and unloading residual stresses. Finally, in Section 4, we conclude the work.

Section snippets

Finite element modelling

Two models are considered using the commercial finite element code ANSYS 5.3. The first is concerned with a single shot and the second with twin shots, each of radius R, impinging a metallic target at normal incidence. Due to symmetry, only one-quarter of the single shot model was discretized, as depicted in Fig. 1a. The following dimensions were selected for the target: width W=7R, height H=4R and breadth B=5R. These dimensions were carefully determined as a result of numerous axisymmetric

The single-shot model

A number of preliminary runs were conducted to establish the appropriate mesh design for the model. The dynamic analysis was carried out using Newmark implicit time-integration scheme with adjustable time steps. The total integration time was tk=10 μs. As a result of these runs, the mesh given in Fig. 1b was used for the single-shot dynamic analysis.

In order to verify our model, a comparison with the earlier work of Edberg et al. [15]was conducted. The target and shot characteristics considered

Conclusions

A three-dimensional finite element model was developed to simulate the shot-peening process. Dynamic single and twin elasto-plastic spherical indentations were examined using rigid spherical shots and metallic targets. The effect of shot velocity, size and shape upon the equivalent stress trajectories, equivalent plastic strains and unloading residual stresses of a target exhibiting bilinear material behaviour is examined and discussed. The work was further extended to account for the effect of

Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Manufacturing Research Corporation (MRCO) of Ontario.

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