PSI - Issue 17

Waleed H. Alhazmi et al. / Procedia Structural Integrity 17 (2019) 292–299 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

294

3

materials. But a ductile material under static load can redistribute stress by yielding without fracture. Thus, although strain concentration factor persists, stress concentration factor (SCF) decreases markedly. The theoretical SCF for an infinite orthotropic plate containing an open circular hole, , can be calculated from the following relation (Tsangarakis, Slepetz, and Nunes 1988):

  

   +

E E

E G

(1)

T  = +

K

1 2

−



11

11

12

12

22

Where E 11 , E 22 ,  12 , and G 12 are the elastic constants for an orthotropic plate, i.e. E 11 & E 22 , are longitudinal and transverse elastic modulus respectively, and  12 , and G 12 are the principal in plane Poisson’s ratio and shear modulus respectively. It is worth to note that, in the case of isotropic plate, i.e. E = E 11 = E 22 , and G = G 12 = E /2(1+  ), will be equal the value obtain from the will known relation = 1+2(D/  ) 0.5 = 3, where D and  are the depth and the radius of the notch respectively. The inverse of isotropic finite width correction (FWC) factors for open circular hole can be written, according to (Pilkey and Pilkey 2008), as

  

   =



( 3 1 2 1

( − + −

)



(2)

FWC K K Iso T . − = 1

3

)



T Iso

.

Where  = d H /w, and K T is the finite SCF. The inverse of orthotropic FWC factor equals (Tan and Kim 1990):

  

   =



K

(

)

(3)

1

M K ) ( 6 

2

−



FWC

M

0 5

. (

− − ) 3 1

(

)

+



T

T

K

Iso

.

T Orth

&

(

)

FWC Iso 1 .

− − −

− 1 8

1 1

(4)

M

=

2

2

( ) 

Finally, SCF based on net section instead of the whole width, K Tn , can be calculated as follows:

(5)

(1 )  = − T Tn K K

3. Numerical Work Numerical techniques such as finite element methods have been used recently for performing stress analysis or for investigating the strength and failure of mechanically fastened composite joints (Kermanidis et al. 2000). A three-dimensional orthotropic-elastic finite element code was developed to calculate the stress concentration factor in orthotropic material due to the presence of a circular hole. A plate of a width of 50 mm, height (L + e ) of 150 mm, and thickness 1.2 mm having a central circular hole was used. The centre of the circular hole is located at a distance e from the end of the plate, e = L, i.e. at the middle of the plate, in the case of open-hole tension. Due to symmetry, only one-eighth of the plate was modelled in the case of open-hole tension, however, one quarter of the plate was modelled in the case of bolted joint tensile. Four-node tetrahedral elements were used. An element size small enough to accurately calculate stress concentration factors could be realized. The half or the quarter of the circular hole was located in the fine mesh region in the case of loaded hole or open-hole respectively. The 3-D mesh was generated by translating the 2-D mesh on the central plane, i.e. z = 0, along the thickness direction, i.e. z = t/2. The elastic properties of the present CFRP are shown in Table 1.