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transition allows to investigate at constant loading ∆K, the change in crack closure due to
microstructural change.
The results of crack closure measurements are expressed by the development of Kop over
the crack distance from the transition (Fig. 2). It is obvious that the slope of the linear
approximation is different for the two crack propagation directions (equiaxed to lamellar
and lamellar to equiaxed). The difference in the slope for the two crack propagation
directions indicates that there is a “microstructual history effect”, which affects crack
closure and therefore crack growth rate too, leading to direction depending crack
propagation rates.
K op [MPam 1/2 ]
8
7
6
5
4
3
2
m=-0,29
m=0,46
equiaxed to lamellar
lamellar to equiaxed
-6 -4 -2 0 2 4 6 8 10 12
distance from transition [mm]
Fig. 2: Variation of Kop with the change in microstructure
Derived from dislocation theory, equation 1 is valid to calculate Kop in the case of
roughness induced crack closure.
2
1/
2 3/
2 Sθ
K op = C ⋅σ
ys ⋅ K max ⋅ SH
⋅ sin Sθ
⋅ cos
(eq. 1)
2
SH, Sθ: standard deviation of height- and angle-distribution C: fitting parameter
Calculation of Kop is in good agreement with experimental values in lamellar
microstructures showing roughness induced crack closure. In the range of microstructural
transition the calculated Kop values do not fit the experimental ones. This indicates that
small volume fractions of equiaxed grains reduce the roughness induced crack closure
significantly by reducing the shear displacement of the crack tip.
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