PSI - Issue 52

Feifei Ren et al. / Procedia Structural Integrity 52 (2024) 730–739 Author name / Structural Integrity Procedia 00 (2023) 000–000

734

5

In this section, the IM7 / 8552 unidirectional carbon fiber prepreg from Hexcel is employed as a representative example, with a ply thickness of 0.125 mm. The temperature-dependent properties of the IM7 / 8552 material are presented in Table 1. Since temperature-dependent material properties are essential input parameters for the SAFE

Table 1. The IM7 / 8552 mechanical properties for the unidirectional lamina. Temperature E 11 [GPa] E 22 = E 33 [GPa] G 23 [GPa]

3 ]

G 12 = G 13 [GPa]

v 12 = v 13

v 23

ρ [kg / m

Room

171.42

9.08

3.974

5.29

0.32

0.5

1590

model, the tensile tests were conducted to determine how these properties vary with temperature. These tests serve to elucidate the manner in which these properties fluctuate in response to temperature variations. By comprehending the changes exhibited by material properties under varying temperature conditions, the SAFE model can provide the relationship of group velocity and temperature. The experiments were carried out using an Instron Hydraulic 250 KN machine equipped with a chamber, in accordance with the requirements specified in established standards cdi (2018, 2017). The tests were performed over a temperature range of [ − 50 ◦ C : 5 ◦ C : 100 ◦ C], covering the typical operating temperatures of aircraft. The temperature-dependent properties of E 22 and G 12 of the IM7 / 8552 material are fitted using the following Equations:

= α E 22

T T ref

E 22 E 22 ref

(12)

+ β E 22

= α G 12

T T ref

G 12 G 12 ref

(13)

+ β G 12

where E 22 ref and G 12 ref represent the values of E 22 and G 12 at reference temperature T ref . For this research, the reference temperature T ref is set as the room temperature of 20 ◦ C. According to the results presented in Ren et al. (2023), the coe ffi cients of the fitted curve are determined as α E 22 = − 0 . 03872, β E 22 = 1 . 06, and α G 12 = − 0 . 05306, β E 22 = 1 . 01. These coe ffi cients are derived from the curve fitting analysis and provide insights into the relationship between the material properties and temperature changes. In this research, certain assumptions are made regarding the temperature dependence of other material properties. These assumptions are based on experimental findings and conclusions from previous studies. It has been observed that certain plate properties exhibit minimal variations with temperature, specifically, the density ρ plate and Poisson’s ratio v 12 = v 13 are not significantly a ff ected by temperature Saad et al. (2014); Yule et al. (2021). In this research, The assumption is also made that v 23 remains constant. Additionally, E 11 , which is primarily influenced by the sti ff ness of the fibers, is expected to remain relatively stable with temperature variations Pinto et al. (2016). The longitudinal Poisson’s ratio remains almost constant throughout the temperatures considered in the study, the value v 12 = v 13 = 0 . 32 is used, and v 23 is also assumed constant in this research. By employing the equation G 23 = E 33 2(1 + v 23 ) , the G 23 can be approximately calculated by G 23 G 23 ref = E 33 E 33 ref .

4. Results and discussion

4.1. The Temperature E ff ect on the Group Velocity

The theoretical results establish the relationship between group velocity with the frequencies and thicknesses, form ing the basis for the sensitivity analysis of guided wave signals in panels of varying thicknesses. The dispersion curve