3. Modeling A#

3.1. Characteristics of modeling#

_images/1000078A00000BFD0000182FBFEF0C26825DC3D2.svg

\(A\mathrm{=}\mathit{N4}\), \(B\mathrm{=}\mathit{N5}\), \(C\mathrm{=}\mathit{N13}\), \(D\mathrm{=}\mathit{N12}\).

3.2. Characteristics of the mesh#

Number of knots: 13

Number of meshes and types: 2 QUAD8 meshes, 6 SEG3 meshes.

3.3. Tested sizes and results#

Identification

Reference Type

Reference

Tolerance ( \(\text{\%}\) )

\({\sigma }_{\mathit{zz}}\) \(t\mathrm{=}\mathrm{60s}\)

ANALYTIQUE

4.0792E8

0.1

\({\epsilon }_{\gamma }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{60s}\)

ANALYTIQUE

3.9604E-3

0.1

\({\epsilon }_{\alpha }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{60s}\)

ANALYTIQUE

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{th}}\) \(t\mathrm{=}60s\)

ANALYTIQUE

-6.0E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{meca}}\) \(t\mathrm{=}60s\)

ANALYTIQUE

-2.59208E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{plas}}\) \(t\mathrm{=}60s\)

ANALYTIQUE

-1.9802E-3

0.1

\({\sigma }_{\mathit{zz}}\) \(t\mathrm{=}\mathrm{89s}\)

ANALYTIQUE

7.0684E8

0.80

\({\epsilon }_{\gamma }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{89s}\)

ANALYTIQUE

3.9604E-3

0.1

\({\epsilon }_{\alpha }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{89s}\)

ANALYTIQUE

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{th}}\) \(t=89s\)

ANALYTIQUE

-7.49460E-3

0.5

\({\epsilon }_{\mathit{xx}}^{\mathit{meca}}\) \(t=89s\)

ANALYTIQUE

-3.04046E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{plas}}\) \(t=89s\)

ANALYTIQUE

-1.9802E-3

0.3

\({\sigma }_{\mathit{zz}}\) \(t\mathrm{=}\mathrm{112s}\)

ANALYTIQUE

9.4392E8

0.1

\({\epsilon }_{\gamma }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{112s}\)

ANALYTIQUE

0.1

\({\epsilon }_{\alpha }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{112s}\)

ANALYTIQUE

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{th}}\) \(t\mathrm{=}112s\)

ANALYTIQUE

-8.68E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{meca}}\) \(t\mathrm{=}112s\)

ANALYTIQUE

-3.39608E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{plas}}\) \(t\mathrm{=}112s\)

ANALYTIQUE

-1.9802E-3

0.1

\({\sigma }_{\mathit{zz}}\) \(t\mathrm{=}\mathrm{176s}\)

ANALYTIQUE

12.101E8

0.1

\({\epsilon }_{\gamma }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{176s}\)

ANALYTIQUE

0.1

\({\epsilon }_{\alpha }^{\mathit{eff}}\) \(t\mathrm{=}\mathrm{176s}\)

ANALYTIQUE

5.068921E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{th}}\) \(t\mathrm{=}176s\)

ANALYTIQUE

-1.508E-2

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{meca}}\) \(t\mathrm{=}176s\)

ANALYTIQUE

-6.3298E-3

0.1

\({\epsilon }_{\mathit{xx}}^{\mathit{plas}}\) \(t\mathrm{=}176s\)

ANALYTIQUE

-4.51465E-3

0.1

3.4. notes#

In this modeling:

\({\epsilon }_{\mathit{zz}}^{\mathit{pt}}(T,Z)=0\)

The error on \({\sigma }_{\mathit{zz}}\) at 89 seconds is in fact due to the error made in the numerical description of metallurgical transformation which is, at this moment, approximately \(56\text{\%}\).