On the Brittle Fracture of Mild Steel (The 1st Report)

Abstract

In order to explain the mechanism of brittle fracture of mild steel, flow stress surface and fracture stress surface are assumed as follows;
Flow stress surface: J2=a2I21/2+A(dI1/220/dt)nes/T
Fracture stress surface:
σ11-1/2(σ33-|σ33|)=bI21/2+{B0-B1/2(σ-|σ|)}(dI1/220/dt)meU/T for σ11=Maximum principal stress σ33=Minimum principal stress ……etc
Where J2, and I2=The 2nd order invariant of stress deviator tensor, and plastic strain deviator tensor, respectively
σ=Mean of principal stresses, T=Absolute temperature
A, B0, B1, S, U, m, n, a, and b=Material constants.
S_??_170_??_180, U_??_65-75, n-m_??_0.02-0.04
(B0/A)2(dI1/220/dt)2m-2n_??_{25(Statical tension) 10(charpy impact)
dI1/220/dt=Total strain velocity, t=time
I20=The 2nd order invariant of total strain deviator tensor.
As the relation between transition temperature and r/t (r: notch radius, t: plate thickness) the following formula is obtained
A2/B02e2(S-U)Tr=(3+e-2st/r)2(1+d2)+2d(e-4st/r-9)/12(3+e-2st/r)
where A≡A(dI1/220/dt)n, B0=B0(dI1/220/dt)m d_??_{0.42(Statical tension) 0.09(charpy impact)
Tr=Transition temperature (Absolute temperature), s=Constant.
The calculated curves from this formula match very well with the experimental results by Mr. H.R. Thomas, etal., Mr. A.Boodberg, etal., and Mr. A.B.Bagsar.
The data obtained by Mr. C.W.Macgregor etal., concerning with strain velocity and transition temperature are also explained by the above formula.