WELDING RESEARCH

# A

B

Fig. 7 — Applied da/dN-DK curves for various grain sizes. A — 316L; B — AL6XN.

Table 4 — Summary of DK Levels below Which Crack Closure Was Observed

Grain Size (mm)

DK below which closure was observed, (MPa√m)

24 –3.3 103 –12.8 147 –21.6

21 –2.4 211 –26.3 281 –29.7

316L Stainless Steel No closure observed 7 · 10 2 · 10 AL6XN Stainless Steel No closure observed 3 · 10 6 · 10 –10 –9 –10 –10

316L–As received

24 –3.3

316L–Annealed 45 min.

103 –12.8

316L–Annealed 5 h

147 –21.6

AL6XN–As received

21 –2.4

AL6XN–Annealed 45 min

211 –26.3

AL6XN–Annealed 5 h

281 –29.7

320-C

8

306-M

239-C

13

227-C

15

397-M

10

282-C

23

275-C

25

## Table 5 — Summary of Grain Sizes and Calculated Yield Strengths

for 316L Stainless Steel

Sample

d (mm)

s_{ys (MPa) }

M-Measured C-Calculated

DK below Which Grain Size Effects Are Expected,MPa√m

to changing their path. The expected re- sult would be a tortuous crack path, as ob- served experimentally in this study.

Equation 1 can be used with known s_{ys }values to estimate the DK value below which these grain size effects are expected to occur. This value of DK is denoted at DK_{GS }for reference. By setting the plastic zone size (given by Equation 1) equal to the grain size, the DK value below which grain size ef- fects are expected to occur is given as

1

DK

GS

=s

ys

^{Ø }d ^{ø}2 Œœ

Œ0 0 3 3 œ . ß º (2)

Where d is the grain size. There was in- sufficient material available to directly de- termine the yield strength of all the sam- ples as a function of grain size. However, knowledge of the yield strength of the as- received 316L and AL6XN provide two useful data points. In addition, Hall-Petch parameters established for the 316L alloy

permit a good estimate of the yield strength as a function of grain size for this alloy. Priddle (Ref. 21) previously estab- lished the influence of grain size on yield strength with the following Hall-Petch equation for 316L stainless steel:

s

ys

s o = +

k

d d

(3)

in which s_{o = 163 MPa and kd = 0.77 }MPa m. Equation 3 produces very good agreement between calculated (320 MPa) and measured (306 MPa) s_{ys values for }316L in the as-received condition (5% error). Although no Hall-Petch relation was available in the literature for AL6XN, Equation 3 can be used to at least estimate the expected change in yield strength with grain size for AL6XN. Here, it is assumed that the incremental change in s_{ys with d }is similar to 316L (i.e., the k_{d constant in }Equation 3 is identical), and that the net variation in s_{ys can be accounted for by the }

s_{o term in Equation 3. With this assump- }tion, the s_{o term in Equation 3 can be de- }termined so that agreement is found be- tween the starting grain size (d = 21 mm) and yield strength (s_{ys = 397 MPa) of }AL6XN. A s_{o value of 229 MPa provides }this agreement. Thus, the following two Hall-Petch equations were used to deter- mine yield strength as a function grain size

s

ys

= 163 +

0.77 d

(4)

for 316L stainless steel

s

ys

= 229 +

0.77 d

(5)

for AL6XN stainless steel

w h e r e d i s i n m m . T a b l e 5 s u m m a r i z e s s y s v a l u e s c a l c u l a t e d f o r e a c h g r a i n s i z e f each alloy. Also shown in the table are the DK_{GS values below which grain size effects }o r