PSI - Issue 13

Taro Suemasu et al. / Procedia Structural Integrity 13 (2018) 1088–1092 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1090

3

Fig. 2 Shape and dimension of the thin-film specimen (unit: μ m)

Fig. 1 Microstructure of the specimen

Fig. 3 Schematic of the thin-film specimen and round bar jig

The fatigue crack shapes were quantified using the SEM images, and the coordinates of the crack shape were obtained, with the pre-crack tip as the origin coordinate. The coordinates of the fatigue crack shape were displaced by the amount of displacement when shear stresses of ±150 MPa were applied to the thin-film specimen, and the location where the fatigue crack surfaces contacted was investigated. The amount of fatigue crack displacement under the shear stress can be calculated using Eq. (1) [Westergaard (1939)].       3 4 2 2 0      a x u Here, u is the amount of the displacement in the direction parallel to the crack at distance x from the center of the crack, a is the crack half-length, G is the transverse elastic modulus, and ν is the Poisson’s ratio . We assumed that the contact surface is a semi-infinite plate subjected to equally distributed pressure, the maximum shear stress is obtained from the stress distribution at this time, and the pressure acting on the contact surface is obtained by using the von Mises yield criterion. As the yield strength σ Y of the JIS-SUS 430 cold-rolled material is higher than that of a non-processed material, we assumed that the yield strength σ Y under the contact pressure is 1 GPa, which is considerably higher than that of the normal JIS-SUS430. In addition, it is assumed that the material will yield and a stress more than the yield strength (1 GPa) will not be applied by the pressure. Thus, the material is assumed to be an elastic – perfectly plastic material. Based on the pressure acting on the contact surface and the contact width, the load generated on the contact surface per unit thickness is determined, and the amount of decrease of the Mode II stress intensity factor K II ’ is calculated u sing Eq. (2) [Paris et al. (1965)]. 4 1 G (1)

Q

a b a b  

Q

a b a b  

K

K

(2)

,

   , '

   , '

a

a





Here, Q is the load per unit thickness generated on the contact surface by contact, a is the crack half-length, and b is the distance from the center of the crack to the point where Q acts. Suffixes A and B after K II ’ are used to clarify the tip of the crack. The crack tip on the side closest to the point where load Q acts is designated as A, and that on the farthest side is designated as B.