PSI - Issue 66

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

150

3

* of crack propagation as

Combination of Eq. (1) and Eq. (2) for r = r C gives the criterion predicting the angle θ

follows

*

16







(3)

*  

* 3cos 1

*  

sin

2 sin cos 

0.

K

K

xx T r c

  

I

II

3

2

where r C is the size of the fracture process zone. Due to the fact that the plane of action of maximum tangential stresses is the main area, there are no shear stresses in it. Therefore, the size of the fracture process zone in this direction can be determined for a crack of mode I as it was given by Pokrovskii and Matvienko (2023a, 2023b)

2

 



2

(1 2 )  

K

(4)

,

r



I с

Т      

с

2

Y

zz

where σ Y is the yield stress, K Ic is the fracture toughness, μ is Poisson’s ratio . Combination of Eq. (3) and Eq. (4) gives the MTS criterion predicting the angle θ * of crack propagation and reflecting the effect of two-dimensional constraint parameters in three-dimensional solids, namely, the nonsingular T xx - and T zz -stress     * * I * * с Y I II 16(1 2 ) sin 3cos 1 sin cos 0. 3 2 xx zz K K T K Т             (5) 3. Results and discussion The proposed approach is implemented in the case of a tensile plate ( W = H =100 mm) with an inclined crack of the length 100 mm. To analyze the effect of the crack inclined angle on the crack propagation angle, calculations were carried out for the plate thickness B=10 mm and inclined angles α = 30°, 45°, and 60° (Fig. 1). The fracture toughness is assumed to be 50 MPa‧m 1/2 and the yield stress is 400 MPa. The angle θ* of the crack propagation was determined using the proposed MTS fracture criterion taking into account two-dimensional constraint parameters and the MTS criterion including only the Т xx -stress. The predicted results of the crack propagation angle are summarized in Table 1. The values of the stress intensity factor and components of the T-stress correspond to the failure stress which was calculated according to Pokrovskii and Matvienko (2023b). The crack propagation angle θ* is negative for considered M TS criteria. It can be seen that as the inclined crack angle α increases , T-stresses increase. A similar conclusion was obtained by Matvienko et al. (2013) for T-stresses in a diametrically compressed disk with a central through inclined crack. The most important conclusion is that there is a negligible effect of the T zz -stress on the crack propagation angle. This effect can be explained by the fact that the stress state for the plate thickness under consideration is close to the plane stress conditions. Ϭ

2l

α

2 H

2W

Ϭ

Fig. 1. A tensile plate with a through-thickness inclined crack.