PSI - Issue 28

R.M. Zhabbarov et al. / Procedia Structural Integrity 28 (2020) 1768–1773 Author name / Structural Integrity Procedia 00 (2019) 000–000

1773

6

reliable results we performed a series of FEM calculations for plates with different dimensions and the results of FEM calculations are given in Table 1 (hight of the plate is 10cm, width is 5cm, crack length is 2cm, load is 100kg).

Table 1. Coefficients of the Williams series expansion for the plate with the central crack obtained by FEM analysis.

Coefficients of the Williams series expansion

Coefficients of the Williams series expansion

Coefficients of the Williams series expansion













1

3/2

1 2 1 5 1

2

1

5/2

1 72.528 / a kg cm 

27.517 / 2.844 /

3 21.406 / a kg cm 

a a

kg cm

   













1 4

3

7/2

1 6

4

0.337 /

a

kg cm

 

0.919 /

kg cm

a a

kg cm

 













1

9/2

5 8 0.025 / a kg cm  11 0.087 / a kg cm  8 14 0.006 / a kg cm   1 13/2 1

1 9

11/2

7 0.965 / a kg cm 

0.340 /

kg cm

 





 





1

6

1 7 12 0.013 / a kg cm  15 0.012 / a kg cm  1

0.017 /

a

kg cm

 

10











1

15/2

17/2

13 0.046 / a kg cm 

3. Conclusions In this study coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate are obtained by the use of the finite element analysis. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give more accurate estimation of stress, strain and displacement fields and to extend the domain of validity for the Williams series expansion. The developed procedures simplify the analysis of the description of mechanical fields at a greater distance from the crack tip considerably. Acknowledgements The work was supported by Russian Foundation for Basic Research (project 19-01-00631). References Ayatollahi, M.R., Mirsayar, M.M., Dehghany, M., 2011. Experimental determination of stress field parameters in bi-material notches using photoelasticity. Materials & Design 32(10), 4901-4098. Dolgikh, V.S., Stepanova, L.V., 2020. A photoelastic and numeric study of the stress field in the vicinity of two interacting cracks: Stress intensity factors, T-stresses and higher order terms. AIP Conference Proceedings 2216, 020014. Hello, G.,Tahar, M.B., Roelandt, J.M., 2012. Analytical determination of coefficients in crack-tip stress expansions for a finite crack in an infinite plane medium. International Journal of Solids and Structures 49, 556-566. Jobin, T.M., Khaderi, S.N., Ramji, M., 2020. Experimental evaluation of the strain intensity factor at the inclusion tip using digital photoelasticity. Optics and Lasers in Engineering 126, 105855. Li, H., Guo, R., Cheng, H., 2019. Calculation of stress intensity factors of matrix crack tip in particle reinforced composites using the singular Voronoi cell finite element method. Theoretical and Applied Fracture Mechanics 101, 269-278. Karihaloo, B.L., Xiao, Q.Z., 2001. Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Eng. Fract. Mechanics 68(15), 1609-1630. Malikova, L., Vesely, V., 2014. Significance of higher-order terms of the Williams expansion for plastic zone extent estimation demonstrated on a mixed-mode geometry. Procedia Material Science 3, 1383-1388. Patil, P., Vysasarayani, C.P., Ramji, M., 2017. Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity. Optics and Lasers in Engineering 93, 182-194. Shanlong, Y., Changzheng, C., Zhongrong N., Zongjun H., 2018. Evaluation of notch stress intensity factors by the asymptotic expansion technique coupled with the finite element method. Applied Mathematical Modelling 61, 682-692. Stepanova, L.V., 2020. The algorithm for the determination of the Williams asymptotic expansion coefficients for notched semidiscs using the photoelasticity method and finite element method. AIP Conference Proceedings 2216, 020013. Stepanova, L.V., Roslyakov, P.S., 2016. Complete Williams asymptotic expansion of the stress field near the crack tip: analytical solutions, interference-optic methods and numerical experiments. AIP Conference 1785, 030029. Su, R.K.L., Feng, W.J., 2005. Accurate determination of mode I and mode II leading coefficients of the Williams expansion by finite element analysis. Finite Elements in Analysis and Design 41(11-12) 1175-1186. Vivekanandan, A., Ramesh, K., 2019. Study of interaction effects of asymmetric cracks under biaxial loading using digital photoelasticity. Theoretical and Applied Fracture Mechanics 99, 104-117.