Dear Masoud,

Many materials experience a decrease in the Young's modulus with temperature since it becomes easier to stretch the atomic bonds. For example, the temperature dependence of the elastic stiffness constants of metals is a well-known phenomenon. Particularly, according to the literature (see references below: Sutton, Kamm, Brammer, Varshni, etc.) the static elastic (or Young’s) moduli of pure Al and AA 2024 decrease linearly with temperature in the range from room temperature (RT) to 300ºC. Deviations from this linear behavior are reported close to the absolute zero and above 300ºC. Also, Wolfenden observed a highly linear decrease of the dynamic elastic modulus with temperature from RT to 475ºC, measured at high frequency (80 kHz), for pure Al and for AA 6061 reinforced with alumina (Al2O3). I myself have observed a linear decrease of the storage modulus with temperature for Al alloy 7075-T6 and 2024-T3; please, check these questions in ResearchGate:

https://www.researchgate.net/publication/257707473_Modeling_of_the_Effect_of_Temperature_Frequency_and_Phase_Transformations_on_the_Viscoelastic_Properties_of_AA_7075-T6_and_AA_2024-T3_Aluminum_Alloys?ev=prf_pub

https://www.researchgate.net/post/Does_the_Youngs_modulus_vary_with_respect_to_temperature

and these references (probably, looking at references that cite these references, you can find investigations on variations of elastic modulus of steel with temperature):

[52] Sutton, P.M., "The Variation of the Elastic Constants of Crystalline Aluminum with Temperature between 63°K and 773°K," Physical Review, Vol. 91, No. 4, 1953, pp. 816-821.

[53] Brammer, J.A., and Percival, C.M., "Elevated-Temperature Elastic Moduli of 2024-Aluminum obtained by a Laser-Pulse Technique," Experimental Mechanics, Vol. 10, No. 6, 1970, pp. 245-&.

[54] Das, T., Bandyopadhyay, S., and Blairs, S., "DSC and DMA Studies of Particulate-Reinforced Metal-Matrix Composites," Journal of Materials Science, Vol. 29, No. 21, 1994, pp. 5680-5688.

[55] Wolfenden, A., and Wolla, J.M., "Mechanical Damping and Dynamic Modulus Measurements in Alumina and Tungsten Fiber-Reinforced Aluminum Composites," Journal of Materials Science, Vol. 24, No. 9, 1989, pp. 3205-3212.

[56] Wolla, J.M., and Wolfenden, A., "Dynamic elastic modulus measurements in materials, ASTM STP 1045," Wolfenden, A. ed., ASTM, Philadelphia, USA, 1990.

[132] Kamm, G.N., and Alers, G.A., "Low‐Temperature Elastic Moduli of Aluminum," Journal of Applied Physics, Vol. 35, No. 2, 1964, pp. 327-330.

[133] Varshni, Y.P., "Temperature Dependence of the Elastic Constants," Physical Review B, Vol. 2, No. 10, 1970, pp. 3952-3958

Dear Masoud,

You can go through these papers.

1) Elevated-temperature mechanical properties of high strength structural steel S460N: Experimental study and recommendations for fire-resistance design by Xuhong Qiang

2) Mechanical properties of High and Very High Steel at elevated temperatures and after cooling down by Chrysanthos Maraveas

3) Effect of Temperature on Strength and Elastic Modulus of High-Strength Steel by Wei-yong Wang