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| Calculation of singular stress near the vertex of angularly heterogeneous material notch by the stress function method |
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Abstract The singular stress field around the notch tip of angularly heterogeneous material will initiate crack and cause structural failure, and its calculation is quite challenging. Here an innovative new method combing the finite element analysis with the stress function is presented to determine the complete singular stress field in the angularly heterogeneous material V-notched structure. Firstly, the stress singularity orders of notches in angular heterogeneous materials are obtained basing on the singularity characteristic analysis. Then, the governing equation and the compatibility equation for angularly heterogeneous material is transformed into the ordinary differential equation by introducing a stress function expressed by the Williams asymptotic expansion. The expression of stress function is obtained by solving the built ordinary differential equation. Furthermore, the coefficients in the stress function asymptotic expansion are determined from the known finite element stress results. Finally, the asymptotic stress field near the notch tip of angularly heterogeneous material is reconstructed. The effects of the selected number of finite element nodes, characteristic distances, and truncation terms on the calculation results of stress intensity factors are respectively examined. The stress intensity factor forms a horizontal line with the number of selected finite element nodes which means that the value remains stable. It shows that the selection of finite element nodes does not affect the stability of the calculational results. When the number of truncation terms is small, the stress intensity factors gradually change with the increase of the characteristic distance. However, when the number of truncated terms is approaching to five to six, the stress intensity factors remain stable with the increase of the characteristic distance.
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Received: 22 May 2025
Published: 27 October 2025
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2025, Vol. 46 
