PSI - Issue 32

Valery Vasiliev et al. / Procedia Structural Integrity 32 (2021) 124–130 Vasiliev and Lurie/ Structural Integrity Procedia 00 (2019) 000–000

129

6

1 1 / c s   and the value of the limiting stresses  . In particular, CFRP plates with

specific value of the parameter

14 x E GPa  ,

170.5 x MPa s  ,

were considered. Tensile strength -

elastic constants

75.2

E 

GPa

y

1150 . The samples are 30 mm wide and 1.5 mm thick. Cracks with lengths of 3, 6, 9, and 12 mm were applied to the longitudinal edges of the tensile specimens. For a plate with a crack 3 mm long, the limiting stress 690 MPa   was obtained experimentally, which corresponds to the stress concentration coefficient 0 / 1.67 y y k s    . Using the constructed dependence 0  on the parameter  , we also find the parameter / 0.27. s c    Further, a prediction of the fracture load is given for plates containing cracks of a different length. For example, for a plate with a crack length of 6 mm with the found value of the parameter s , we have, / 22.2 c s    which also corresponds to 2.2 y k  and to the limiting stress 0 523 MPa   . The corresponding experimental value is 0 549 MPa   . All the results obtained for plates with cracks of various lengths were compared with the experimental values of the ultimate stresses. The high accuracy of the proposed concept has been confirmed. 4. Result and conclutions It is shown that the parameter for a particular material is a constant value and, along with the tensile strength, can be considered as a fracture parameter, giving a high accuracy forecast for the strength of the plates with cracks. In general the concept of stress concentration make it possible to predict thae failure for the brittle isotropic and orthotropic plates with cracks Mode I and also proportional limit load for the plastic materials, which was also confirmed by experiment. As the main result, we show that identified values of the length scale parameters allows us to predict the maximum failure loads for the materials samples with different length of cracks. Therefore, we show that the length scale parameter of gradient models can be treated as the shape independent material constant that controls the material fracture. We believe that the failure analysis of the structures with non-smooth geometry can be performed by using finite element simulations within SGET involving the failure criteria formulated in terms of the local stresses (Cauchy stresses). Presented approach can be treated as some type of the alternative to the classical LEFM among other known theories (theory of critical distances, cohesive zone models, Bazant theory of size effect, etc.). It is seems that the main advantages of this approach is the possibility of the mesh-independent assessments for the material fracture and the caption of size effects. Acknowledgements This work was supported by the Russian Foundation forBasicResearch (projectNo. 19-01-00355) References Aifantis E. C., 2014. On non-singular gradela crack fields. Theoretical and Applied Mechanics Letters 4 (5), 051005. Askes H., Aifantis E. C., 2011. Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results. International Journal of Solids and Structures 48 (13), 1962–1990. Carpinteri A., Paggi M., 2009. Asymptotic analysis in Linear Elasticity: From the pioneering studies by Wieghardt and Irwin until today. Eng. Fract. Mech. 76, 1771–1784. Gourgiotis P., Georgiadis H., 2009. Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity. Journal of the Mechanics and Physics of Solids 57 (11), 1898–1920. Lazar M., Polyzos D., 2015. On non-singular crack fields in helmholtz type enriched elasticity theories. International Journal of Solids and Structures 62, 1–7. Lurie S., Belov P., 2014. Gradient effects in fracture mechanics for nano-structured materials. Eng. Fract. Mech. 130, 3-11. Lurie S., Volkov-Bogorodskiy D., Moiseev E., Kholomeeva A., 2019. Radial multipliers in solutions of the Helmholtz equations. Integral Transforms Special Funct. 30, 254–263. Lurie S.A., Volkov-Bogorodsky D.B., Vasiliev V.V., 2019. A New Approach to Non-Singular Plane Cracks Theory in Gradient Elasticity. Mathematical and Computational Applications 24(4), 93. Rabotnov Yu.N., 1969. Creep problems in structural members. In.: North-Holland Publ. Co. Amsterdam/London, pp. 822. y s  MPa