1. Reference problem

1.1. Geometry

1.2. Material properties

The material obeys a law of behavior in large deformations with linear isotropic work hardening and transformation plasticity. For each metallurgical phase, the work-hardening slope is given in the plane logarithmic deformation-rational stress.

and

are, respectively, the initial length and the current length of the useful part of the test piece.

and

are, respectively, the initial and current surfaces.

with

	=	calorific capacity
\(\lambda\)	=	thermal conductivity
	=	YOUNG module
\(\nu\)	=	Poisson’s ratio
	=	Characteristics relating to the austenitic phase
	=	characteristics relating to ferritic, bainitic and martensitic phases
\(\alpha\)	=	coefficient of thermal expansion
	=	deformation of the ferritic, bainitic and martensitic phases at the reference temperature, austenite being considered to be undeformed at this temperature
	=	elastic limit
	=
	=	coefficient relating to transformation plasticity
	=	function relating to transformation plasticity

The TRC used makes it possible to model a bainitic metallurgical evolution, over the entire structure, of the form:

1.3. Boundary conditions and loads

• \({u}_{Z}\mathrm{=}0\) on the \(\mathit{AB}\) side (symmetry condition).

• imposed traction (follower pressure) on face \(\mathit{CD}\):

Note:

In large deformations, it is essential to use the following pressure to take into account the current surface and not the initial surface (before deformation) .

• 

, \(\mu \mathrm{=}–5°{\mathit{C.s}}^{\mathrm{-}1}\) on the whole structure.

1.4. Initial conditions