Reference problem ===================== Geometry --------- .. image:: images/1000168E000069D500005966367497FAFD3DF499.svg :width: 425 :height: 359 .. _RefImage_1000168E000069D500005966367497FAFD3DF499.svg: 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. .. image:: images/10000FD0000018B400001516CAF383453F89AD98.svg :width: 425 :height: 359 .. _RefImage_10000FD0000018B400001516CAF383453F89AD98.svg: .. image:: images/Object_1.svg :width: 425 :height: 359 .. _RefImage_Object_1.svg: and .. image:: images/Object_2.svg :width: 425 :height: 359 .. _RefImage_Object_2.svg: are, respectively, the initial length and the current length of the useful part of the test piece. .. image:: images/Object_3.svg :width: 425 :height: 359 .. _RefImage_Object_3.svg: and .. image:: images/Object_4.svg :width: 425 :height: 359 .. _RefImage_Object_4.svg: are, respectively, the initial and current surfaces. .. image:: images/Object_5.svg :width: 425 :height: 359 .. _RefImage_Object_5.svg: with +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|calorific capacity | + .. image:: images/Object_6.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |:math:`\lambda` |=|thermal conductivity | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|YOUNG module | + .. image:: images/Object_7.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |:math:`\nu` |=|Poisson's ratio | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|Characteristics relating to the austenitic phase | + .. image:: images/Object_8.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|characteristics relating to ferritic, bainitic and martensitic phases | + .. image:: images/Object_9.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |:math:`\alpha` |=|coefficient of thermal expansion | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|deformation of the ferritic, bainitic and martensitic phases | + .. image:: images/Object_10.svg + + + | :width: 425 | | at the reference temperature, austenite being considered to be undeformed at this temperature | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|elastic limit | + .. image:: images/Object_11.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=| | + .. image:: images/Object_12.svg + + .. image:: images/Object_13.svg + | :width: 317 | | :width: 425 | + :height: 270 + + :height: 359 + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|coefficient relating to transformation plasticity | + .. image:: images/Object_14.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |=|function relating to transformation plasticity | + .. image:: images/Object_15.svg + + + | :width: 425 | | | + :height: 359 + + + | | | | + + + + | | | | +------------------------------------------------------------------------------------+-+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ The TRC used makes it possible to model a bainitic metallurgical evolution, over the entire structure, of the form: .. image:: images/Object_16.svg :width: 425 :height: 359 .. _RefImage_Object_16.svg: Boundary conditions and loads ------------------------------------- * :math:`{u}_{Z}\mathrm{=}0` on the :math:`\mathit{AB}` side (symmetry condition). * imposed traction (follower pressure) on face :math:`\mathit{CD}`: .. image:: images/Object_18.svg :width: 425 :height: 359 .. _RefImage_Object_18.svg: **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) .* * .. image:: images/Object_19.svg :width: 425 :height: 359 .. _RefImage_Object_19.svg: , :math:`\mu \mathrm{=}–5°{\mathit{C.s}}^{\mathrm{-}1}` on the whole structure. Initial conditions -------------------- .. image:: images/Object_21.svg :width: 425 :height: 359 .. _RefImage_Object_21.svg: