Yield Stress According to Swift

1.3.2

One of the disadvantages of the Ludwik equation is that at φ0 the slope is infinite. Swift's approach brings an improvement.10

Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} k_{\color{myred}f}=C\cdot\left(\varphi_{\color{myred}0}+\varphi\right)^{\color{myred}n}
Yield stresskf=475.1MPa 
Strain hardening constantC = 500MPa
Natural Strainφ0 = 0.1
Natural strainφ = 0.5
Strain hardening exponentn = 0.1
Calc 1
Yield stress according to Swift10
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} C=R_{\color{myred}m}\cdot\left(\frac en\right)^{\color{myred}n}=R_{\color{myred}m}\cdot\left(\frac{2,72}n\right)^{\color{myred}n}
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} n\approx\varphi_{\color{myred}gl}=ln(1+A_{\color{myred}gl})
Strain hardening constantC=541MPa 
Tensile strengthRm = 313MPa
Strain hardening exponentn = 0.22
Calc 2
Strain hardening constant C & strain hardening exponent n1011

The material-specific constant C can be approximately estimated using the tensile strength and uniform elongation from the tensile test.

10
Birkert, A. et al.Umformtechnische Herstellung komplexer KarosserieteileSpringer ViewegBerlin - Heidelberg2013
11
Doege, E. et. al.Fließkurvenatlas metallischer WerkstoffeHanser VerlagMünchen1986
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