The Applied Stress

There is an apparent influence of the level of applied stress on the site of crack initiation for peened specimens, i.e. the higher the applied stress the closer the crack initiation is to the surface. This behaviour has been largely reported both for ferrous and non-ferrous peened metals [1-3]. The accepted explanation of surface crack initiation for shot peening treated materials is that cyclic deformation relaxes the surface residual stresses [4]. This adverse effect is known to readily take place in the low cyclic fatigue regime, where the magnitude of the applied stresses lies closely to or even above the yield strength of the cyclically loaded material. The magnitude of the plastic strain amplitude governs the extent of macro residual stress relaxation in fatigue-loaded materials, as concluded by Schulze, et al. [5]. Furthermore, concerning the evolution of compressive residual stress (CRS) during fatigue, Schütz [6] observed that steel was much more stable than aluminium, which is consistent with the general assertion that the stability of CRS depends on the hardness of the material.

As a result, the magnitude of residual stress decreases when the applied fatigue stress increases. High tensile stresses are set up at stress concentration points, such as at the root of the indentations resulting from the peening treatment, or at any other irregularity existing immediately below the surface as illustrated in Fig. 1. Consequently, fatigue cracks are initiated and propagated in surfaces without the beneficial effect of CRS. In short, the fatigue limit for surface initiation should be determined by the magnitudes of the surface residual stress and that of the stress concentration of the applied stress.

In subsurface initiation (Fig. 2), the fatigue crack forms where the outer compressive stress field is balanced by the residual tensile stress field. The transition between the compressive and tensile residual stress fields and the depth of the plastically deformed layer roughly corresponds to the crack initiation sites. Cracks, however, may occur due to inner defects (inclusions, pores, etc.). Although crack origin is located below the surface, they soon break through the surface and become relatively larger cracks. Accordingly, the fatigue life of the subsurface crack becomes equal to that of a surface crack.

Surface Stress Concentration

Some researchers like Wohlfahrt [7] have recognised that peening conditions for optimum fatigue strength should result from achieving a surface hardening as high as possible, compressive residual stresses as large as possible and with a surface roughness as low as possible. Hence, selection of the optimum conditions implemented in the fatigue stage has to be given in line with the above. From experimental work carried out [8], the use of the finest shot did provide the best fatigue performance in both 2024-T351 and 7150-T351 AA’s. It therefore, suggested that both AA’s are likely to be roughness-sensitive or surface damage-sensitive. The consistent degradation of fatigue life as peening media size increases may be due to one or more of these factors:

1. Broken or highly deformed media and embedded particles, which give rise to deeper surface penetration (table 6.1.1) and hence, more likely to cause crack nucleation by stress concentration.
2. Unevenness in the plastic deformation layer, 100% coverage with the finest shot is entirely impinged with some overlapping. Variations of the plastically deformed layer when peening with larger media size may be quantitatively greater than with smaller media.
3. The tendency of a larger media is to leave larger indentations and, thus, material around the indentation displaced a greater distance would indent to a greater depth and or induce impact extrusion of material parallel to the surface. It has been reported by many researchers [9,10] that such surface damage known as peened surface extrusion folds (PSEF) or simply folds are responsible for acceleration of the crack nucleation by the stress concentration.

With the aim of further support for these statements, a sensitivity analysis was undertaken to assess the effect of surface degradation (in terms of the surface penetration, termed h in table 1) on the fatigue resistance by using the following peening conditions: (a) S110 (shot type), 200% (coverage), 90º (incidence angle); (b) S330, 200%, 30º; (c) S330, 200%, 90º. Fatigue testing was done using a maximum stress of 300MPa under similar experimental conditions as indicated. The effect of increasing the penetration depth was found to be more detrimental on the fatigue resistance as seen in Fig. 3 (a,b). Similar findings were reported recently by Dörr et al. on peened aluminium and magnesium alloys [11] [255].

Theoretical Stress Concentration

The effect of surface roughness considered as micro-notches (dents) is introduced utilising the Navarro & Vallellano’s formulation [256], which provide a solution to a notch fatigue crack growing through the microstructure of the material. According to their work, the nominal stress in a notched member is given by “formula can not be displayed online”

where “xxxx” is the applied stress, “xxxx”    
is the distribution of the nominal stress ahead of the notch root as a function of the distance from the notch i, mapped as i=2a/D, and Zi is the fatigue notch factor given by “formula can not be displayed online”

and i=1,3,5,…
The parameters  ”xxxx”  and  “xxxx” represent in a dimensionless form the notch depth ? and the notch half width ß . The parameter D represents the distance between two successive barriers. In the case where grain boundaries are considered as being the dominant barrier, D is regarded as the grain diameter.
According to “formula can not be displayed online”, the effect of both the crack closure stress and surface roughness on the ability for a peened component to arrest cracks is given by “formula can not be displayed online”
                                        .    
From this later relationship, the boundary conditions that would enable the residual stress to compensate totally for the notch effect (roughness caused by the shot indents) on the crack arrest capacity of the peened material is given by, “formula can not be displayed online”

Application of the above equation renders the effect of roughness (notch) on the crack arrest capacity for a peened 2024-T351 AA under optimum conditions as shown in Fig. 4.
Examination under arrest conditions of the peened materials depicted in Fig. 4 revealed a discernable influence of the stress concentration on each peened material in relation to the stress required by a crack to overcome the i-th barrier in the notch zone. A more pronounced effect of Kt in the AA 2024-T351 is predicted, as shown by the lower decrease in percentage terms of the peening arrest capacity when incorporating a notch effect. The crack arrest capacity for the peened AA 2024-T351 to optimum conditions decreases rapidly as Kt increases. Strictly speaking, for a=25µm and ß=75µm, i.e. Kt= 1.33 (experimentally determined for AA 2024-T351, S110, 200%, 45º) no appreciable peening improvement is predicted, as the calculated inherent arrest capacity of the unpeened material is higher. Thus, the stress gradient associated with the dents at the first barrier (grain size) dominates over the closure stress effect. However, the stress gradient due to the notch will decrease with distance from the notch tip, and therefore, there will be a barrier further away which would either delay the growth of a crack or arrest it. This may be the reason for achieving a marginal fatigue improvement in the peened AA 2024-T351 when compared to the unpeened material, particularly at low fatigue applied stresses.

Concluding Remarks

These results support the previously experimental observations regarding the sensitivity analysis, namely, that the effect of increasing the penetration depth or varying the notch geometry was found to be detrimental to the fatigue resistance, as seen in Fig. 3(a,b).
The strain hardening effect has been intentionally neglected because: a) the induced strain hardening developed by shot peening is usually overcome by the intrinsic hardening of cyclic harden materials, b) strain hardening is commonly limited to a depth close to the free surface and c) the above results are provided as a conservative analysis.

References

[1] Starker, P., Wohlfahrt, H. and Macherauch, E.. "Subsurface crack initiation during fatigue as a result of residual stresses". Fatigue of Engineering Materials and Structures. Vol. 1, pp. 319-327. (1979).
[2] Ochi, Yasuo, Masaki, Kiyotaka, Matsumura, Takashi and Sekino, Takeshi. "Effect of shot-peening treatment on high cycle fatigue property of ductile cast iron". Int J Fatigue. Vol. 23, pp. 441-448. (2001).
[3] Jaensson, Bernt and Magnusson, Lennart. "An investigation into the influence on the fatigue strength of aluminium alloy parts of load spectrum base level and residual stresses induced by shot peening or strengthening". In: Shot Peening- Science-Technology-Application. Third International Conference on Shot Peening (ICSP-3). Germany. Eds. H. Wohlfahrt, R. Koop and O. Vohringer. Deutsche Gesellschaft fur Metallkunde e.V.: pp. 423-430. (1987).
[4] Landgraf, Ronald W and Chernenkoff, Russell A. in: Analytical and experimental methods for residual stress effects in fatigue, ASTM STP 1004, Residual stress effects on fatigue of surface processed steels, Editors R.L. Champoux, J.H. Underwood and J.A. Kapp. American Society for Testing and Materials: Philadelphia. pp. 1-12. (1988).
[5] Schulze, V., Lang, K.H., Vohringer, O. and Macherauch, E., "Relaxation of shot peening induced residual stresses in quenched and tempered steel AISI 4140 due to uniaxial cyclic deformation". In: Sixth International Conference on Shot Peening. Proceedings of the International Conference on Shot Peening (ICSP-6). California, USA. Ed. Jack Campaigne. pp. 403-415. (1996).
[6] Schütz, W. "Fatigue life improvement of high-strength materials by shot peening". In: First International Conference on Shot Peening. Proceedings of the International Conference on Shot Peening (ICSP-1). Paris. Ed. A. Niku-Lari. Pergamon press: pp. 423-433. (1981).
[7] Wohlfahrt, H. "Practial aspects of the aplication of shot peening to improve the fatigue behaviour of metals and structural components". In: Shot Peening- Science-Technology-Application. Third International Conference on Shot Peening (ICSP-3). Germany. Eds. H. Wohlfahrt, R. Koop and O. Vohringer. Deutsche Gesellschaft fur Metallkunde e.V.: pp. 563-584. (1987).
[8] José Solis Romero, Alfonso Anguiano García, "Effect of the Shot Peening Process on the Surface Changes in the 2024-T351 Aluminium Alloys", Metal Finishing News, Vol. 9, March issue (2008).
[9] Simpson, Roger S., "Development of a mathematical model for predicting the percentage fatigue life increase resulting from shot peened components, phase I." Airtech Precision Shot Peening, Inc. Flight dynamics laboratory. Air force wright aeronautical laboratories, air force systems command wright-patterson AFB, Ohio 45433. Final report for period September 1983- April 1984: pp. 1-37. (1984).
[10] Mutoh, Y., Fair, G. H., Noble, B. and Waterhouse, R. B., "The effect of residual stresses induced by shot-peening on fatigue crack propagation in two high strengh aluminium alloys". Fatigue and Fracture of Engineering Materials and Structures. Vol. 10, No. 4: pp. 261-272. (1987).
[11] Dörr, T., Hilpert, M., Beckmerhagen, P., Kiefer, A. and Wagner, L., "Influence of shot peening on fatigue performance of high-strength aluminum-and magnesium alloys". In: Shot Peening: Present and Future. The 7th Conference on Shot Peening (ICSP-7). Warsaw, Poland. Ed. Aleksander Nakonieczny. Institute of Precision Mechanics : pp. 153-160. (1999).
[12] José Solis Romero, "Crack Arrest of Controlled Shot Peening on Fatigue Damage of High Strength Aluminium Alloys (Part 1)", Metal Finishing News, Vol. 6, November issue (2005).

E-mail:
josesolis@itesm.mx

Affiliation:
SEP-DGEST-IT de
Tlalnepantla