H. LI ET AL.

Open Access JAMP

driving force of crack growth [9] is:

(1)

Type:

µ

is the contact surface friction coefficient, P0 is

the contact pressure (Pa), S is the fretting slip amplitude

(M), K is formula constant having a length dimension

(m). Specimens of stress which fatigue crack initiation

required is

σ

f, load stress which lead to specimen’s fati-

gue crack is

σ

ff.

σ

ff is the component's fatigue strength

fretting and

σ

f is the component’s fatigue strength no

fretting. Fatigue strength in a micro component is smaller

than which without fretting, which can be seen from this

formula, and the difference between the two depends on

P0,

µ

and S, that is to say the fretting fatigue strength is

related to friction coefficient, contact pressure and slip

amplitude and so on, yet the slip amplitude is directly

related to fatigue loading. So, based on the above men-

tioned theory, the fretting fatigue contact geometry of a

riveted two aluminum specimen was studied using the

finite element method. The contact stress fields of the

inner and outer contact edges on the two specimen’s up

and down surface under different contact friction coeffi-

cient and the fatigue loads were analyzed, the influences

of the contact friction coefficient and remote stress on

crack initiation and propagation mechanism were dis-

cussed.

3. Modeling

3.1. Computational Model

The 3D finite element model of the rived aluminum spe-

cimen and its meshing result are showed in Figure 1. In

order to reduce the computational cost, only half of the

FEM model is constructed according to the symmetries

of the specimen. The model is composed of 8 parts, in-

cluding two aluminum plates, one screw bolt, one protec-

tive sleeve, two screw caps and two gaskets. In order to

further reduce the model size and computational cost, the

reducing of the meshing numbers and contact areas is →

are often adopted in the FEM simulation. Thus, we treat

the screw bolt, the protective sleeve, the screw caps and

the gaskets as an integrated section to neglect the con-

tacts between those parts. Three contacts regions are in-

vestigated in the simulations as shown in Figure 2: The

first region is the contact area between the upper protec-

tive sleeve’s lower surface and the aluminum plate I’s

upper surface; the second region is the contact area be-

tween the two aluminum plates; the third region is the

area between the lower protective sleeve’s upper surface

and the aluminum plate II’s lower surface. Among these

three regions, the stress distributions of upper and lower

surfaces of the two aluminum plates are emphatically

analyzed to evaluate the specimen’s fatigue life. The

eight-node hexahedral solid elements are employed in the

Figure 1. FEM model of the rived aluminum specimen.

Figure 2. Contact regions.

simulation, where the total element number and node

number are 10336 and 13686. The contact area of the

two aluminum plates is 219.142 mm2 with a contact

width of 4.5 mm. The hole radius and thickness are set as

5.5 mm and 6 mm, respectively. The length and width

are respective 230 mm and 60 mm. The aluminum plates’

longitudinal axis is axis X, forward direction points to

longitudinal remote end. Transverse axis is axis Y, the

screw bolt’s axis is axis Z, origin of coordinates is lo-

cated in the centre of the hole. Normal chain bar con-

straints are exerted as boundary condition in fornter of

the model (y = 0).

3.2. Mechanics of Materia l Constants

In computing object this time, expect the two aluminum

plates whose Young’s modulus E and Poisson’s ratio

µ

are 40 GPa and 0.3, all the other parts of the specimen

are C45 steels with E = 210 GPa and

µ

= 0.3. Due to the

elastic stress states of the screw bolt during its service

process, the screw bolt is regarded as an elastic material

in current simulation while the plasticity is taken into

consideration for all the other parts of the specimen. Be-

cause the analytical objects are connected components in

the fields of aviation and high speed train systems etc, so

the work temperature is really the same as environmental

temperature. Material temperatu re effect is not taken into

consideration. Material constants of every component are

showed in Table 1.

3.3. Computational Method

In order to simulate the fastening process of the screw

bolt, the FEM model with a clearance of d between the

spaces of the two gaskets and the aluminum plate’s