PSI - Issue 13

Yinghao Dong et al. / Procedia Structural Integrity 13 (2018) 1714–1719 Yinghao Dong, Xiaofan He, Yuhai Li / Structural Integrity Procedia 00 (2018) 000–000

1716

3

(a)

(b)

Fig. 1. Geometry of the cracked body (a) a surface cracked finite plate subjected to uniform tension, and (b) the cross section containing a surface crack with the surface point denoted by B and the depth point denoted by A.

(a)

(b)

Fig. 2. Finite element model (a) global mesh, (b) mesh of the cross section containing a surface crack.

were used, depending on the complexity of the part geometry. All the degrees of freedom of one plate end were constrained and uniform tensile stresses ( σ = 230 MPa) were applied to the other end. Symmetry conditions were applied to the y − z plane. The modulus of elasticity is 110 GPa and Possion’s ratio 0.3. Prior to the K I calculation, we verified the FE model from three aspects: (1) whether the J -integrals are independent of paths, (2) whether the calculated K I converges with mesh refinement, and (3) whether the e ff ect of h / W can be neglected when h / W = 3 . 0. After that, we calculated K I for surface cracked plates with W = 40 mm, t / W ranging from 0.05 to 0.5, c / a ranging from 1.0 to 5.0 and a / t ranging from 0.032 to 0.896. We used Matlab to generate the input file written in Python to establish FE models in Abaqus 6.16. More than 11,400 FE models were built and analyzed. After the FE analyses, we extracted K I , K II and K III at each node along the crack front. Results show that K II and K III are negligible compared with K I . Numerical K I results will be fitted in the next section.

3. Development of K I expressions

First, we normalized K I with the product of the analytic SIF solution for an elliptical crack embedded in an infinite body Irwin (1962) and function f 1 ( θ ):

K I

(1)

K n =

σ √ π a / Q a 2

2 θ + sin 2 θ

1 / 4

c 2 cos

f 1 ( θ )