PSI - Issue 66

Yu.G. Matvienko et al. / Procedia Structural Integrity 66 (2024) 148–152 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

151

4

Table 1. The effect of the inclined angle on the crack propagation angle.

MTS criterion including only the Т xx -stress

MTS criterion including Т xx - and Т zz -stress

K I , MPa ∙ m 1/2

K II , MPa ∙ m 1/2

T xx , MPa -176 -161 -130

Ϭ frac , MPa 138

K I , MPa ∙ m 1/2

K II , MPa ∙ m 1/2

T xx , MPa -227 -194 -148

T zz , MPa -151 -104 -56,1

Ϭ frac , MPa 159

α, о

θ * , о

θ * , о

30 45 60

42,2 38,5 25,9

20,6 32,8 38,2

-31,8 -43,9 -53,5

55,6 42,1 27,0

27,0 35,5 39,4

-26,9 -40,3 -51,6

167 225

181 231

The effect of the plate thickness on the crack path in the case of the inclined crack angle of 30° is also analyzed (Table 2). The plate thickness is taken to be 10, 40, and 100 mm. In contrast to the MTS criterion including only the Т xx -stress, the crack propagation angle is significantly dependent on the thickness in the case of the MTS criterion including two-dimensional constraint parameters, namely, the nonsingular T xx - and T zz -stress. The effect of the thickness can be explained by the following. The increase in the plate thickness leads to changing the stress state from plane stress to plane strain. Therefore, there is a significant change in the T zz -stress with a negligible change in the T xx -stress, thereby and, as a result, changing the crack propagation angle.

Table 2. The effect of plate thickness on the crack propagation angle.

MTS criterion including only the Т xx -stress

MTS criterion including Т xx - and Т zz -stress

2 t , mm

K I , MPa ∙ m 1/2

K II , MPa ∙ m 1/2

T xx , MPa -176 -178 -179

Ϭ frac ,М Па

K I , MPa ∙ m 1/2

K II , MPa ∙ m 1/2

T xx , MPa -227 -194 -190

T zz , MPa -151 -105 -76,2

Ϭ frac , MPa

θ * , о

θ * , о

10 40

42,2 48,7 48,4

20,6 23,4 23,8

-31,8 -31,4 -32,0

138 139 137

55,6 53,2 51,4

27,0 25,5 25,3

-26,9 -29,1 -30,4

159 151 145

100

4. Conclusions The following conclusions can be drawn.

In the case of the asymptotic elastic stress field according to Williams, the nonsingular T xx - and T zz -stresses characterize two-dimensional constraint in the transverse ( Т xx ) and longitudinal ( Т zz ) directions along the crack front in three-dimensional solids. Two-dimensional constraint parameters in the transverse (Тxx) and longitudinal (Тzz) directions along the crack front in three-dimensional solids are employed to predict crack paths under a mixed-mode I/II loading conditions. The fracture criterion and the crack path prediction for a mixed-mode crack are based on the maximum tangential stress which should be equal to the local strength in the fracture process zone ahead of the crack front. The proposed MTS criterion is implemented in the case of a tensile plate with an inclined crack. The crack propagation angle is negative for considered MTS criteria, and besides as the inclined crack angle increases, T-stresses increase. There is a negligible effect of the T zz -stress on the crack propagation angle, because the stress state for the plate thickness under consideration is close to the plane stress conditions. The effect of the plate thickness on the crack path is also estimated. In contrast to the MTS criterion including only the Т xx -stress, the crack propagation angle is significantly dependent on the thickness in the case of the MTS criterion including two-dimensional constraint parameters, namely, the nonsingular T xx - and T zz -stress. The increase in the plate thickness leads to changing the stress state from plane stress to plane strain. Therefore, a significant change in the T zz -stress with a negligible change in the T xx -stress is observed, thereby and, as a result, changing the crack propagation angle.