PSI - Issue 5

Smail Sahnoun et al. / Procedia Structural Integrity 5 (2017) 1065–1071 Asseya El-amiri et al./ Structural Integrity Procedia 00 (2017) 000 – 000

1067

3

a

b

1: Steel nut 2: Steel screw 3: Rust 4: Steel plate 5: Concrete slab

Fig.1.

(a) The studied structure geometry; (b) The mesh of the studied structure

The diffusion of heat into the assembly elements under the above conditions is governed by the following equation:

K

T



( T)

 

(1)

ρc

t



The temperature response of the controlled surface is calculated by the finite element method. The mesh adopted for this structure is a mesh composed of tetrahedral elements Fig.1.

3. Simulation results

To solve the problem and to calculate the surface temperature distribution of the inspected elements, we need the thermophysical properties of rust, steel and concrete. Those properties are represented in table 2.

Table2: The thermal characteristics of rust, steel and concrete.

ρ (kg/m 3 )

Materials

k (W/m.K)

C (J/kg.K)

Steel

44.5

7850

475

Rust

0.6

5242

650

Concrete

1.8

2 200

880

3.1. Study of the rust depth’s effect

To show the aptitude of thermography in the control of the assembly elements, not only in the revelation of the rust’s presence but also its depth, we considered, for the large bolt, a layer of rust of cylindrical shape whose depth varies from 1cm to 9 cm with a pitch of 1 cm as shown in Fig.2 and whose thickness e varies from 0.5cm to 1.5cm with a pitch of 0.5cm. Whereas for the medium sized bolt, we considered that the depth of the rust layer varies from 0.1 cm to 0.6 cm with a pitch of 0.1cm, and its thickness varies from 0.1cm to 0.35cm with a pitch of 0.05cm. Based on the maximum surface temperature of the bolt for each depth, we have presented in Fig.3 the temperature evolution along the axis A1A2 of the nut surface with respect to the depth of the rust for different thicknesses for both studied structures. According to Fig.3, we notice that the temperature of the heated surface of the structure studied increases when the depth of the rust layer becomes larger. It is also noted that the size of the bolts has an influence on the thermal response. In what follows, we propose a mathematical model to illustrate the relationship between the thermal response T and the depth P of the hidden rust. The thickness of the rust is taken into consideration.