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Fig. 8 — ariation in threshold stress intensity range, DKth, as a function of grain size.

Fig. 9 — Comparison of fracture surface roughness in AL6XN base metal samples with various grain sizes. A — Grain size is 21 mm and crack growth rate is 1.5 · 10–10 m/cycle at arrow; B — grain size is 211 mm and crack growth rate is 1.7 · 10–10 m/cycle at arrow location.

are expected to occur as DK is reduced. This DKGS value becomes larger with in- creasing grain size. In other words, grain size will improve fatigue resistance over a larger range of DK as the grain size in- creases. The interpretation of these values is shown schematically in Fig. 10 for three materials with three different grain sizes (where d3 > d2 > d1). The corresponding DK values at which grain size effects begin to occur with decreasing DK are denoted

as DK DK3 GS

3 GS, DK > D K 2 GS 2

GS, and > DK 1 GS

DK ).




As previously explained, the plastic zone size will increase with increasing DK. As this occurs, a point will eventually be reached where the plastic zone size be- comes appreciably larger than the grain size and any improvement in fatigue resis- tance due to grain size diminishes. Thus, the fatigue curves of materials with vari- ous grain sizes will eventually coincide as DK is increased. This type of behavior is shown schematically in Fig. 10 and, more importantly, is also observed in the exper- imental data of Fig. 7. In addition, mater- ial with the largest grain size will provide improved fatigue resistance over a large range of DK. Again, this general trend is also observed in the experimental data of Fig. 7. With this background, it also be- comes clear that the various DKGS values can be positioned as shown on the schematic fatigue curve provided in Fig. 10. For example, DK3GS represents the DK value at which the fatigue curves for alloys with grain sizes of d3 and d2 will begin to deviate as DK is reduced, and DK2GS rep-

resents the DK value at which the fatigue curves for alloys with grain sizes of d2, and d1 will begin to deviate as DK is reduced. A fourth alloy with the finest grain size d4 would be needed to plot DK1GS in Fig. 10.

The calculated values of DKGS from Table 5 are plotted in Fig. 7. The separation of experimental fa- tigue curves with decreasing DK is not nearly as sharp as the schematic curves shown in Fig. 10, which makes exact deter- mination of an ex- perimental DKGS value difficult. However, there is generally good agree- ment between the DKGS values that are calculated with Equation 3 and those ob- served experimentally in Fig. 7. For exam- ple, the AL6XN samples that were heat treated to produce the two largest grain sizes (211 and 281 mm) separate from the as-received sample with a 21-mm grain size near the calculated value of DKGS = 25 MPa m. Similarly, the sample with the Fig. 10 — Schematic illustration showing the influence of grain size on fatigue crack growth rate. The curves labeled d3, d2, and d1 are for three alloys with grain sizes (d) in which d3 > d2 > d1. 281-mm grain size begins to deviate from the 211 grain size sample near the calcu- lated value of DKGS = 23 MPa m. These general trends between measured and cal- culated DKGS values are also evident for the 316L alloy. Again, the deviations in the experimental curves are very gradual, but the reasonable agreement between mea- sured and calculated DKGS values pro- vides support for the grain size mecha-


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