Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

308 R.C. Østergaard, B.F. Sørensen
Table 3 The phase angle ω (in degrees) computed with different values of the mismatch parameters and β for a specimen with
thickness ratio η = 0.5
β : 0.5 0.1 0.05 0.01 0.005 0.001
α: −1/3 −1/2
−0.4 36.1 35.7 37.0 35.6 31.4
−0.3 38.9 39.6 39.9 39.2 38.5 37.1 33.4
−0.2 43.3 43.7 43.2 41.9 39.0 37.0 34.2
−0.1 47.3 47.4 45.7 43.8 36.7 37.0 33.2
0.0 51.0 50.7 47.4 44.4 33.1 33.6 27.1
Table 4 The phase angle ω (in degrees) computed with different values of the mismatch parameters and β for a specimen with
thickness ratio η = 1
β : 0.5 0.1 0.05 0.01 0.005 0.001
α: −1/3 −1/2
−0.4 42.7 43.7 42.8 41.7 38.9
−0.3 40.9 42.7 46.3 46.8 45.0 43.6 40.1
−0.2 45.2 46.8 49.5 49.5 46.6 44.7 40.4
−0.1 49.3 50.5 52.3 51.7 47.3 44.9 39.3
0.0 53.1 54.1 54.6 53.2 46.7 43.3 35.1
Table 5 The phase angle ω (in degrees) computed with different values of the mismatch parameters and β for a specimen with
thickness ratio η = 2
β : 0.5 0.1 0.05 0.01 0.005 0.001
α: −1/3 −1/2
−0.4 47.3 50.3 52.7 52.0 48.6
−0.3 41.9 44.3 51.0 53.5 54.7 53.5 49.3
−0.2 46.3 48.5 54.4 56.5 56.4 54.7 49.4
−0.1 50.5 52.5 57.7 59.2 57.7 55.4 48.7
0.0 54.6 56.3 60.7 61.6 58.4 55.3 46.5
Table 6 The phase angle ω (in degrees) computed with different values of the mismatch parameters and β for a specimen with
thickness ratio η = 4
β : 0.5 0.1 0.05 0.01 0.005 0.001
α: −1/3 −1/2
−0.4 49.3 53.8 60.7 61.8 60.1
−0.3 42.3 45.0 53.2 57.3 62.9 63.4 60.6
−0.2 46.8 49.3 56.9 60.5 64.9 64.8 60.8
−0.1 51.1 53.4 60.4 63.6 66.8 66.1 60.6
0.0 55.3 57.4 63.9 68.4 68.4 67.1 59.8
specimen ( = 1, η= 0). With ω close to 45 ◦ ,the
mode II and mode I stress intensity factor are almost
of the same magnitude.
With decreasing , the values of ω become sensitive
to η.Forlargeη values, ω increase with decreasing
. For instance, for η = 10, ω ≈ 75 ◦ for = 0.001.
Thus, for large η, the decreasing results in the crack-
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tip stress field becoming more mode II. For η → 0,
the opposite trend is found. Here, ω decreases with
decreasing , corresponding to a more mode I dominant
crack-tip stress field.
Figure 6 also includes a few results for β =−0.3.
Those results differ from those obtained for β = 0,
suggesting that the dependence of ω on β is signifi-