Is it possible that both are correct? With a little manipulation, you may be able to get one from the other.
My Bruhn, page B1.8 shows
(E*eps)/F70=f/F70+(f/F70)^n (A)
where: eps is strain, f is stress. Rewriting (A) to (A')
eps=f/E+(F70/E)*(f/F70)^n (A')
F70 is written as "F0.7" in my Bruhn--F0.7 is the stress
when the line drawn as f=0.7E*eps intersects the material
curve f vs. eps. F70 is the same value as F0.7, but I
like F70 because it is more convenient form to write. I
don't have the Niu book, but I can guess that the formula
he uses is (the notation may be different from Niu, but
the meanings of the symbols are the same):
eps=f/E+(3/7)*(F70/E)*(f/F70)^n (B)
I think the Bruhn equation is in error. The original
Ramberg Osgood equation was written:
eps=(f/E)+K(f/E)^n (C)
the parameter F70 means the stress 'f' when the stress-
strain curve (C) intersects the line eps=f/(0.7*E), right?
So that we want to solve the following equation:
eps=F70/(0.7*E)=(F70/E)+K(F70/E)^n (D)
Solving (D) for K=(3/7)*(F70/E)^(1-n)=(3/7)*(E/F70)^(n-1)
Plugging in this expression for K into (C):
eps=f/E+(3/7)*(F70/E)*(f/F70)^n (E)--same as (B)
But if we try to find the intersection of (A') and this
F70/(0.7*E) line, then (replacing 'f' with F70):
eps=F70/(0.7*E)=(F70/E)+(F70/E)*(F70/F70)^n
F70/(0.7*E)=(F70/E)+(F70/E)=2*(F70/E)---of course this
is wrong, because 1/0.7 does not equal 2!!!
