1. Reference problem#

1.1. Geometry#

_images/1000059C00001C5200001C523AE60EA5EC9A169D.svg

Infinite bar with square cross section:

side \(\mathrm{2L}=\mathrm{0,10}m\)

Point coordinates (in meters):

\(A\)

\(B\)

\(C\)

\(O\)

\(x\)

0.026

0.350

0.350

0.041

0.0

\(y\)

0.026

0.350

0.350

0.041

0.0

1.2. Material properties#

(\(\mathrm{16MND5}\) steel)

\(\rho {C}_{P}=5260000{\mathrm{J.m}}^{-3}\mathrm{.}°{C}^{–1}\)

\(\lambda =33.5{\mathrm{W.m}}^{-1}\mathrm{.}°{C}^{-1}\)

Coefficient for metallurgy:

TRC « standard »

\(\mathrm{AR3}=830°C\), \(\mathrm{alpha}=-0.0306\)

\(\mathrm{MS0}=400°C\), \(\mathrm{AC1}=724°C\), \(\mathrm{AC3}=846°C\)

\({\tau }_{1}=0.034\), \({\tau }_{3}=0.034\)

Microhardness of the various metallurgical phases:

  • for \(d\mathrm{=}200.\mathit{HV}\) ferrite

  • for perlite \(d\mathrm{=}200.\mathit{HV}\)

  • for bainite \(d\mathrm{=}300.\mathit{HV}\)

  • for martensite \(d=400.\mathrm{HV}\)

  • for austenite \(d=100.\mathrm{HV}\)

1.3. Boundary conditions and loads#

\({T}_{\infty }=15°C\)

\(h=1675{\mathrm{W.m}}^{-2}\mathrm{.}°{C}^{–1}\)

1.4. Initial conditions#

\(T(x,y\mathrm{,0})=700°\mathrm{C.}\)

\(\mathrm{Zf}(x,y\mathrm{,0})=0.7\)

\(\mathrm{Zb}(x,y\mathrm{,0})=0.3\)