Convergence Proving of the Theoretical & True Elongation Inequalities by Derivation and Analogy

Source:
By:Run Xu

DOI: https://doi.org/10.30564/jmmr.v3i1.1757

Abstract:

According to LNƐ, theoretical & true elongation of tensile, and by adopting the increasing function of formulas with the derivation and analogy methods, the elongation formula of 0<(1+ε)1/ε<e & 0<ε1/ε<1& four convergences are deduced too when ε >1 and 0<ε<1.The inequalities of LNε <ε and LN(1+ε)<ε and LN(1+ε)> LNε are deduced if ε>1 and 0<ε<1 in material dynamics. Finally the conclusions of LNε <ε and LNε<LN(1+ε)< ε are deduced together if ε>1 and 0<ε<1.

References:

[1] Liu Hongwen. Material mechanics [M], 5th Edition, Higher Education Press, 2011.1:23. [2] Xu Run. Effect of components on the structure and mechanical properties of TiAl intermetallic compounds [D], Master's Thesis of Metal Materials Engineering, Gyeongsang University, 1999:2:1-2. [3] Xu Run Hur Boyong, Lim Sugun, Kim Younwook. Tensile test of the theory of shrinkage rate and elongation of the compare and analysis [J]. Chinese Science and Technology Periodical Database (Full Version) of Natural Science, 2018, 9 (1) : 95 ~ 97.