Issue 68

Ch. F. Markides et alii, Frattura ed Integrità Strutturale, 68 (2024) 1-18; DOI: 10.3221/IGF-ESIS.68.01

[32] Torabi, A. R., Shahbaz, S., Ayatollahi, M.R. (2023). Fracture assessment of U-notched diagonally loaded square plates additively manufactured from ABS with different raster orientations. Eng. Struct., 292, 116537. DOI: 10.1016/j. engstruct.2023.116537. [33] Bagheri, P., Torabi, A.R., Bahrami, B. (2023). A new strategy for predicting fracture of U - notched specimens made of Al - 6061 - T6 and Al - 5083 using extended finite element method, Fatigue Fract. Eng. Mater. Struct., 46(9), pp. 3404– 3416. DOI: 10.1111/ffe.14086. [34] Alshaya, A.A. (2023). A developed hybrid experimental–analytical method for thermal stress analysis of a deep U notched plate. Theor. Appl. Fract. Mech., 124, 103753. DOI: 10.1016/j.tafmec.2023.103753. [35] Kourkoulis, S.K., Markides Ch.F, Pasiou, E.D (2024). A combined analytical and numerical approach to the problem of the stress- and displacement-fields in finite strips weakened by parabolically shaped notches (under review).

A PPENDIX

The formulae for the components of the stress field at any point (r, θ ) of a strip of finite dimensions, weakened by a parabolically-shaped stress-free edge notch, assuming that it is subjected to uniform uniaxial tension σ ο , applied normally to the axis of symmetry of the notch:

       

  

2

σ α

1

θ

θ

5 θ

5 θ α

3 θ

3 θ

  

  

  

  

 

  cos sin cos









xx σ σ

sin

cos

sin

o

o

π

2 2

2

2

2

2

r 4 2

r 2

2

2

     

            2

     

r

θ

θ

r

θ

θ 2 θ 2

     

     

     

     

   ξ

 sin cos



cos sin 2 2 2

α

    

    

  2 α

ξ

c

ο

2 2

ο



log

y x

2



  2

 x y , θ tan 2

1

r

r

θ

θ

r

θ

   ξ

 sin cos



cos sin 2 2 2

α

ο

2 2

  

   

2

α

r

1

θ 2

θ 2

5 θ

5 θ α

3 θ

3 θ

  

  

  

  





   sin cos sin cos







cos

sin

α

2

2

2

2

r

4 2

r 2

     

r

θ

θ 2

r

θ

θ 2

  

  

  

  

 sin cos



 sin cos



α

α

         π 0

2 2

2 2





1

1





tan

tan

r

θ

θ

r

θ

θ

  

  

  

 

(A.1)

 

 cos sin 2 2 2

ξ

cos sin 2 2 2

ξ

 

 

ο

ο

  

     

2

ξ 2 5

θ

θ α

3 θ

      2 4 2  3 θ 1 5 θ

5 θ

  

  

  

  



 



 sin cos

cos sin

cos

sin

ο

4 2 2 r

2

2

r

   

   

  

3

2

5 α α 4 r

1 r 4 2

θ

θ α cos2 θ 1 r

α

θ

θ

  

  

  

  

 cos θ 2 2 2

 



 



 cos sin



sin θ

sin2 θ cos sin

2 2

4

2 2

2 2

r

      

      

r 2

θ

θ

r

θ

θ

  

  

  

  

 

 

cos sin

ξ

cos sin 2 2 2

ξ

ο

ο

2 2





2

2

2

2

  

     

     

     

  

r

θ

θ

r

θ

θ 2

r

θ

θ

r

θ

θ 2

  

  

  

  

  

  

  

  

   ξ

 sin cos



   ξ

 sin cos



cos sin 2 2 2

α

cos sin 2 2 2

α

ο

ο

2 2

2 2

  

   

  

  

3

2

α

1 r 4 2

θ 2

θ α sin2 θ 1 r

α

θ

θ

  

  

  

  

 cos θ 2 2 2





 cos sin



  



 sin2 θ sin co s

cos θ

r

2

4 2 2

2 2

r

   

      

     

r

θ

θ 2

r

θ

θ 2

  

     

  

     

 sin cos



 sin cos



α

α

2 2

2 2





2

2

2

2

  

     

     

  

  

 

θ 2

θ 2

r

θ

θ

r

θ

θ 2

r

θ

θ

r

  

  

  

  

  

  

   ξ

 sin cos



   ξ

s in cos 



α

cos sin 2 2 2

α

cos sin 2 2 2

 



ο

ο

2 2

2

 

16