Influence of Microcracks on Poisson’s Ratio during Plastic Deformation of Austenitic Steel

Abstract

We researched the influence of damage accumulation on the Poisson’s ratio measured by echo-pulse acoustic method during plastic deformation of 12Kh18N10T steel. On the basis of the obtained experimental data we calculated the partial contributions to the change in the Poisson’s ratio of damage accumulation and formation of the strain induced martensite phase. The characteristics of stable cracks forming near strain-induced martensite particles at small degrees of plastic strain have been analyzed by computer simulation. The theoretical dependence of the change in the Poisson’s ratio due to crack formation during plastic deformation has been constructed. A good agreement between the experimental data and theoretical calculations has been obtained.

APPENDIX

Expressions for calculation of components of tensors of mesodefects elastic stress fields [22, 23], defined in the right-hand Cartesian coordinate system Oxy, beginning of which coincides with the mesodefect center, while axis Ox is directed along the mesodefect shoulder, are written as Planar shear mesodefect.

$$\begin{gathered} {{\sigma }_{{xx}}} = D{{w}_{\tau }}\left[ {2\left( {\arctan \left[ {\frac{{x - a}}{y}} \right] - \arctan \left[ {\frac{{x + a}}{y}} \right]} \right)} \right. \\ \left. { + \,\,\frac{{y(x + a)}}{{{{{(x + a)}}^{2}} + {{y}^{2}}}} - \frac{{y(x - a)}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}}} \right], \\ \end{gathered} $$

(A1)

$${{\sigma }_{{yy}}} = D{{w}_{\tau }}y\left( {\frac{{(x - a)}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}} - \frac{{(x + a)}}{{{{{(x + a)}}^{2}} + {{y}^{2}}}}} \right),$$

(A2)

$$\begin{gathered} {{\sigma }_{{xy}}} = D{{w}_{\tau }}\left( {\frac{{{{y}^{2}}}}{{{{{(x + a)}}^{2}} + {{y}^{2}}}} - \frac{{{{y}^{2}}}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}}} \right. \\ \left. { + \,\,\frac{1}{2}\ln \left[ {\frac{{{{{(x + a)}}^{2}} + {{y}^{2}}}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}}} \right]} \right). \\ \end{gathered} $$

(A3)

Dipole of circular disclinations:

$$\begin{gathered} {{\sigma }_{{xx}}} = D{{w}_{N}}\left( {\frac{{{{y}^{2}}}}{{{{{(x + a)}}^{2}} + {{y}^{2}}}} - \frac{{{{y}^{2}}}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}}} \right. \\ \left. { + \,\,\frac{1}{2}\ln \left[ {\frac{{{{{(x + a)}}^{2}} + {{y}^{2}}}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}}} \right]} \right), \\ \end{gathered} $$

(A4)

$$\begin{gathered} {{\sigma }_{{yy}}} = D{{w}_{N}}\left( {\frac{{{{y}^{2}}}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}} - \frac{{{{y}^{2}}}}{{{{{(x + a)}}^{2}} + {{y}^{2}}}}} \right. \\ \left. { + \,\,\frac{1}{2}\ln \left[ {\frac{{{{{(x + a)}}^{2}} + {{y}^{2}}}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}}} \right]} \right), \\ \end{gathered} $$

(A5)

$${{\sigma }_{{xy}}} = D{{w}_{N}}\left( {\frac{{(x - a)y}}{{{{{(x - a)}}^{2}} + {{y}^{2}}}} - \frac{{(x + a)y}}{{{{{(x + a)}}^{2}} + {{y}^{2}}}}} \right),$$

(A6)

where w_N, w_τ are values of mesodefects strength projections w_N, w_τ on axis Ox, 2a is length of shearing mesodefect or disclination dipole.