HSNV103 - Thermoplasticity and metallurgy in plane deformations

Transcription

1 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 1/10 HSNV103 - Thermoplasticity and metallurgy in plane deformations Summary: One treats the determination of the mechanical evolution of a right-angled parallépipède in plane deformations subjected to evolutions thermics T t and metallurgical Z t known and uniform (the metallurgical transformation is of bainitic type). The elements used are two-dimensional elements in plane deformations and the relation of behavior is the plasticity of von Mises with linear isotropic work hardening (for modeling B, one also takes account of the plasticity of transformation). The yield stress and the slope of the traction diagram depend on the temperature and the metallurgical composition. The dilation coefficient depends on the metallurgical composition. For modeling A (without plasticity of transformation), the reference solution is obtained by the analytical resolution of the problem. For modeling B (with plasticity of transformation), the reference solution is obtained by the digital resolution of the problem by using axisymmetric elements for which one imposes the condition of plane deformations. Results provided by Code_Aster are very satisfactory with errors lower than 0,5%.

2 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 2/10 1 Problem of reference 1.1 Geometry Width: a=0.05 m Height: h=0.2 m 1.2 Properties of materials 6 E y aust aust aust o Pa o s T T notons H t E t t E t t o aust 6 aust o aust aust o Pa H H T T 6 1 aust 6 1 fbm s Ho aust C Pa. C Pa 6 1 aust y fbm fbm fbm o aust 6 1 o 3 ref o fbm Pa H fbm H fbm o fbm fbm T T o ref 900 C fbm 6 1 s Pa. C Ho fbm Pa C s T T 5 10 Pa. C T fbm J.m C W.m C 5 10 Pa C fbm Pa. cp * aus = characteristics relating to the austenitic phase * fbm = characteristics relating to the phases ferritic, bainitic and martensitic fbm = thermal dilation coefficient of the phases ferritic, bainitic and martensitic aus = dilation coefficient of the austenitic phase réf fbm = deformation of the phases ferritic, bainitic and martensitic at the temperature of reference, austenite being regarded as not deformed at this temperature: translated the difference in compactness between the cubic crystallographic structures with centered faces (austenite) and cubic centered (ferrite). k

3 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 3/10 TRC to model a metallurgical evolution of bainitic type, on all the structure, of the form: si t 1 Z fbm ={0. 1=60 s t 1 si 1 t 2 2 =112 s si t 2 Law of plasticity of transformation: pt =K fbm F Z fbm Z fbm with F Z fbm =Z fbm Z Z fbm Notations: T 1 =T 1 T 2 =T Boundary conditions and loadings u Y =0 on the side AB ; u X =0 in A. T =T 0 t, = 5 C.s 1 on all the structure. The loading on the structure is due with the phenomena of thermal and metallurgical dilation constrained in the direction z by the condition of plane deformations. 1.4 Initial conditions T 0 =900 C=T ref

4 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 4/10 2 Reference solution (for modeling A) 2.1 Method of calculating used for the reference solution Before transformation, thermoelastic solution until in t 1 such as: zz = E th = y T T 0 = o y E s =76.92 C t 1 =15.38s thus for t t 1 : zz = E T T 0 Before transformation, and for t t 1, thermoelastoplastic solution such as: zz =0 and zz =R p zz y from where p xx = T E T T 0 y E RT During the transformation, one remains in load as long as th 0 and zz = E p zz T T 0 for T C th =0 T = T 0 réf fbm T 1 T 2 = C 2 t=t 2 =72.23 s there is thus a thermoelastoplastic soution with phase shift: p zz = yt, Z E [Z T T 0 Z réf fbm ] ER T, Z and for T C there is thus a thermoelastic soution with phase shift: zz = E [Z T T 0 Z réf fbm p zz t 2 ] and zz = E p zz Z T T 0 Z réf fbm After the transformation, one replastifie when: zz =R T, Z p zz y T, Z and one thus has for T C : with zz = zz E T T 0 réf fbm =0 that is to say T = C p zz = E [ réf fbm T T 0 ] y T,Z R Z,T E and zz =R T, Z p zz y T, Z

5 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 5/ Results of reference With t=16 s : p xx zz With t=60 s : p xx zz With t=72 s : p With t=112 s : With t=176 s : p zz xx zz 2.3 Bibliography 1) DONORE A.M. - WAECKEL F. - Influence of structure transformations in the elastoplastic laws of behavior Notes HI-74/93/024.

6 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 6/10 3 Modeling A 3.1 Characteristics of modeling y C D N13 N11 N12 N9 N10 N7 N6 N8 N1 N3 N4 N2 N5 A B A= N4, B=N5, C= N13, D=N Characteristics of the grid Many nodes: 13. Many meshs and types: 2 meshs QUAD8, 6 meshs SEG3.

7 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 7/10 4 Results of modeling A 4.1 Values tested One tests the structural parameters of data results: Identification Reference INST for NUME_ORDRE= ITER_GLOB for NUME_ORDRE=176 2 Identification Reference xx t=16 s t=16 s 1 t=16 s p t=16 s xx t=60 s p t=60 s t=60 s p t=72 s t=112 s 0 t=112 s p t=112 s xx t=176 s t=176 s 1 t=176 s Remarks In this modeling: pt zz T, Z =0 The error on the plastic deformation cumulated at 72 seconds comes by way of the mistake made on the digital description of the metallurgical transformation which is, at this moment, from approximately 0.5%.

8 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 8/10 5 Modeling B 5.1 Characteristics of modeling y C D N13 N11 N12 N9 N10 N7 N6 N8 N1 N3 N4 N2 N5 A B A=N4, B=N5, C= N13, D=N Characteristics of the grid Many nodes: 13. Many meshs and types: 2 meshs QUAD8, 6 meshs SEG3.

9 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 9/10 6 Results of modeling B 6.1 Values tested Identification Reference t=60 s p t=60 s yy t=89s p t=89s t=89s 13, yy t=112 s t=112 s p t=112 s yy t=176 s p t=176 s t=176 s Remarks In this modeling, one takes into account the term due to the plasticity of transformation: pt Z,T 0 when Ż 0 The reference solution is obtained by the digital resolution of the problem with axisymmetric elements for which one imposes the condition of plane deformations.

10 Titre : HSNV103 - Thermo-plasticité et métallurgie en défo[...] Date : 10/06/2011 Page : 10/10 7 Summary of the results Results found with Code_Aster are very satisfactory, with percentages of error lower than 0.5%.