Fracture transitions in iron: Strain rate and environmental effects

Abstract

A number of recent mechanical property studies have sought to validate atomistic and multiscale models with matching experimental volumes. One such property is the ductile-brittle transition temperature (DBTT). Currently no model exists that incorporates both external and internal variables in an analytical model to address both length scales and environment. Using thermally activated parameters for dislocation plasticity, the present study attempts a small piece of this. With activation energy and activation volumes previously determined for single and polycrystalline Fe-3% Si, predictions of DBTT both with and without atmospheric hydrogen are made. These are compared with standard fracture toughness measurements similarly for samples both with and without atmospheric hydrogen. In the hydrogen-free samples, average strain rate varied by four orders of magnitude. DBTT shifts are experimentally found and predicted to increase 100 K or more with either increasing strain rate or exposure to hydrogen.

APPENDIX: DETERMINATION OF THERMALACTIVATION PARAMETERS AS DEPENDENT ON YIELD STRENGTH

Use of the yield stress in determining the effective stress and the strain rate from Eqs. (6) and (7) was invoked by choosing the selected distance from the crack tip to be the elastic–plastic boundary for convenience. This is accomplished here using a plane-strain estimate for the early stages of yielding, knowing that the same equation also applies to plane stress at the later stages. From McClintock and Irwin’s early article on plasticity at crack tips,38 the continuum representation of the strain distribution for the Mode I analogy of the Mode III result is

$${{\rm{\varepsilon }}_{\rm{p}}} = {{{{\rm{\sigma }}_{{\rm{ys}}}}} \over E}\left( {{{{R_{\rm{p}}}} \over r} - 1} \right)\,\sim\,{{{R_{\rm{p}}}} \over r}{{{{\rm{\sigma }}_{{\rm{ys}}}}} \over E}\quad ,$$

(A1)

where R_p is the plastic zone diameter, σ_ys and E are the yield strength and modulus, and r is the distance from the crack tip. Given that ${R_{\rm{p}}} = {{K_{\rm{I}}^2} \over {3{\rm{\pi \sigma }}_{{\rm{ys}}}^2}}$ using the inverse method approximation for the plastic zone size, this gives

$${{\rm{\varepsilon }}_{\rm{p}}} = {{K_{\rm{I}}^2{{\rm{\sigma }}_{{\rm{ys}}}}} \over {3{\rm{\pi \sigma }}_{{\rm{ys}}}^2Er}}\quad .$$

(A2)

This is differentiated with respect to time giving dε/dt as ${\rm{\dot \varepsilon }}$ at R_p = r to be

$${\rm{\dot \varepsilon }} = {{2{{\dot K}_{\rm{I}}}{{\rm{\sigma }}_{{\rm{ys}}}}} \over {E{K_{\rm{I}}}}}\quad ,$$

(A3)

which is Eq. (7) in the text. A value of K_I ≃ 30 MPa m^1/2 was used which approximately represented the mean value of K_I applied. Choosing a different value of K_I would only shift the curves in Figs. 6 and 7 slightly, which could be shifted back with a slight variation of Ψ₀. The results for temperature varying from 160 to 300 for the three applied stress intensity rates used are given in Table A. Values of yield strength from Fig. 3 were utilized.

TABLE A Values of strain rate versus temperature for three stress intensity rates.

A tabulation of the values at 20 K intervals for the extremes is shown in Table A.