HPLP100 - Calculation of the rate of refund of the energy of a plate fissured in thermoelasticity

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Alexander Ward
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1 Titre : HPLP100 - Calcul du taux de restitution de l énerg[...] Date : 20/07/2017 Page : 1/6 HPLP100 - Calculation of the rate of refund of the energy of a plate fissured in thermoelasticity Summary t is about a test in thermoelasticity for a two-dimensional problem. A fissured rectangular plate is considered and one places oneself on the assumption of the plane deformations. n modeling A, the rate of refund of energy is calculated in postprocessing by two different methods: classical calculation by the method theta, calculation by the formula of RWN starting from the coefficients of intensity of constraints and. These two calculations are carried out on 4 different crowns of integration. Their interest is to compare the values of G and of G RWN compared to the reference solution and to test the invariance of calculations compared to the various crowns of integration.

2 Titre : HPLP100 - Calcul du taux de restitution de l énerg[...] Date : 20/07/2017 Page : 2/6 1 Problem of reference 1.1 Geometry t is about a fissured rectangular plate (one represents only the quarter of the structure): Y h v u A O a C X Figure 1.1-a: Fissured rectangular plate Dimensions of this plate are the following ones: Half-height of the plate: Half-width of the plate: Half-length of the crack: 1.2 Properties of material h=200.0 mm =100.0 mm a=50.0 mm Thermal properties: Mechanical properties: Cp=0. =1.0W /m C E= MPa =0.3 = / C We are on the assumption of the plane deformations 1.3 Boundary conditions and loadings Temperature imposed in X =0. : T = C Temperature imposed in X =100 : T = C Displacement for a X, Y =0. : v=0. Displacement for 0 X, Y =H : v=0.

3 Titre : HPLP100 - Calcul du taux de restitution de l énerg[...] Date : 20/07/2017 Page : 3/6 Displacement for X =0., Y =H : u=0.

4 Titre : HPLP100 - Calcul du taux de restitution de l énerg[...] Date : 20/07/2017 Page : 4/6 2 Reference solution 2.1 Method of calculating used for the reference solution The reference solution is resulting from WLSON and YU [bib1]: E T0 F a F a en mm E en N / mm n plane deformations, the formula of RWN gives: G 2 2 that is to say numerically: G E Results of reference The results of reference are those resulting from the reference solution from WLSON and YU [bib1]: G Bibliographical references 1) The Uses of J-ntegrals in thermal stress ace problems - nternational Newspaper of Fracture (1979) WLSON and YU. 2) Qualification complementary to codes NCA/MAYA in linear thermoelasticity. Technical note DRE/STRE/LMA 84/598

5 Titre : HPLP100 - Calcul du taux de restitution de l énerg[...] Date : 20/07/2017 Page : 5/6 3 Modeling A 3.1 Characteristics of modeling There are 4 crowns defined by the order CALC_G : Crown 1: Rinf =10. Rsup=40. Crown 2: Rinf =15. Rsup=45. Crown 3: Rinf =5. Rsup=47. Crown 4: Rinf =3. Rsup=48. The bottom of crack is defined by DEF_FOND_FSS, and for each crown one carries out: a calculation of G classic (option CALC_G of CALC_G), a calculation of G by the formula of RWN starting from the coefficients of intensity of constraints and (option CALC G of CALC_G). 3.2 Characteristics of the grid Many nodes: 853 Many meshs and types: 359 meshs TRA6 and 27 meshs QUAD8 3.3 Values tested and results of modeling A The values tested are those of G obtained by the classical method and that of G RWN obtained by the formula of RWN starting from the coefficients of intensity of constraints: dentification Reference Tolerance Crown 1 G Crown 1 G RWN Crown 2 G Crown 2 G RWN Crown 3 G Crown 3 G RWN Crown 4 G Crown 4 G RWN 3.4 Remarks The digital values are stable compared to the various crowns of integration and almost identical for the two methods of calculating. Nevertheless the variation with the values of reference is about 6 with 7%, which seems high.

6 Titre : HPLP100 - Calcul du taux de restitution de l énerg[...] Date : 20/07/2017 Page : 6/6 4 Summaries of the results At the time of the first modeling, the variation with the values of reference is from 6 to 7%. The validation independent of the breaking process batch should bring brief replies on the validity of G in thermoelasticity.

Code_Aster. SDLV123 - Computation of G elastodynamic in infinite medium for a plane crack finite length

Code_Aster. SDLV123 - Computation of G elastodynamic in infinite medium for a plane crack finite length Titre : SDLV123 - Calcul de G élastodynamique en milieu i[...] Date : 27/05/2013 Page : 1/7 SDLV123 - Computation of G elastodynamic in infinite medium for a plane crack finite length Summarized It acts