Code_Aster Titre : SSLV322 - Fissure longitudinale semi-elliptique dé[...] Responsable : CUVILLIEZ Sam

Transcription

1 Date 19/10/2016 Page 1/12 SSLV322 - Semi-elliptic longitudinal crack emerging in skin interns of a tube under pressure Summary This test 3D into quasi-static, enters within the framework of the validation of postprocessings in linear elastic breaking process. The structure is a tube subjected to an internal pressure and presenting a semi-elliptic crack emerging in internal skin. Three modelings are considered modeling A crack with a grid (FEM), radiant quadratic grid in face of crack with elements of Barsoum. This modeling is used as reference; modeling B X-FEM, with automatic refinement of a hexahedral linear initial grid structured; modeling C X-FEM, with automatic refinement of a free tetrahedral linear grid initial. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

2 1 Problem of reference 1.1 Geometry Date 19/10/2016 Page 2/12 The structure is a hollow roll height 2 L, of interior ray R1 and of external ray R2. Rays R1 and R2 define its thickness W = R2 R1. The axis of revolution of this cylinder is defined by the vector y Cartesian reference mark ( O, x, y, z ), the centers of its two bases are the points of coordinates ( 0, L, 0) and ( 0, L, 0) (see Figure and Appears 1.1-2). The crack considered is longitudinal, semi-elliptic, and emerges in internal skin of the tube. It is localised in the plan of equation z=0, and is defined by an ellipse of center ( R1, 0, 0 ), of half main roads a and of small half centers b (see Figure 1.1-2). Figure transverse crosssection (y=0 plan) Figure longitudinal cross-section (z=0 plan containing the lips and the face of crack) The digital values of these geometrical parameters are the following ones 2 L=12 m R1=1 m R2=2 m W = R2 R1 =1 m a=0,25m b=0,2 m One thus has b/a=0,8 R2 / R1=1 b/w =0,2 1.2 Properties of material The material is elastic linear isotropic, with the following properties Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

3 1.3 Date 19/10/2016 Page 3/12 E=210 GPa ν=0,3 Boundary conditions and loadings The internal skin of the tube is subjected to a time-constant pressure and in space p=1 MPa, and the lips of the crack are also subjected to this same pressure. Ésuch an amount of data symmetry problem one models only the higher part of the tube, i.e. that contained in the half space y 0. One then indicates by face the lower surface defined by the intersection of the cylinder and the plan y=0. Displacements DY are blocked on this surface in order to model symmetry (see Figure 1.3-1). Figure condition of symmetry of the half-problem The modes of rigid body as for them are blocked by adding to the condition of symmetry the linear relation DX ( A)+ DX (B)=0, where A and B the points of coordinates indicate respectively ( R2, L, 0 ) and ( R2, L, 0 ) (see Figure 1.3-1). Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

4 2 Reference solution 2.1 Method of calculating Date 19/10/2016 Page 4/12 The reference solution is obtained with modeling A. 2.2 Sizes and results of reference One tests the value of the rate of refund of energy G at the point C coordinates ( R1, a,0 ) who on the half-model corresponds to the point where the face of crack emerges in internal skin, as well as the value of G at the point D coordinates ( R1 +b, 0,0 ) who corresponds to the major point of the face of crack (see Figure 2.2-1). Figure Position of the points C and D where the value of the rate of refund of energy is tested The values tested are expressed in J.m. Identification Type of reference Value of reference Notice The problem of reference corresponds to an quasi-analytical solution suggested in [1]. For as much, one does not choose this solution like reference. This solution remains however compared for each modeling of this CAS-test with the solution finite elements obtained, in the form of curve of evolution of G according to the curvilinear X-coordinate along the face (curve with the format xmgrace). 2.4 Bibliographical references [1] Murakami, Y. Stress Intensity Factors Handbook, Volume 2, p s.l. The Society of Material Sciences, Pergamon Near, Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

5 3 Modeling A 3.1 Characteristics of modeling Date 19/10/2016 Page 5/12 Modeling is used 3D phenomenon MECHANICS. The crack is with a grid (modeling FEM). 3.2 Characteristics of the grid The grid, radiating around the face of crack, was generated with the plugin blocfissure module smesh of Salome starting from a hexahedral healthy grid structured (see Figure and Appears 3.2-2). The elements are quadratic and the pentahedrons connected to the face of crack are elements of Barsoum (use in the command file of MODI_MAILLAGE/MODI_MAILLE/OPTION=' NOEUD_QUART'). The grid contains nodes; tetrahedrons; 6128 hexahedrons; 760 pyramids; 736 pentahedrons. Figure modeling A, fissured grid, torus in face of crack Figure modeling A, fissured grid 3.3 Sizes tested and results One tests the value of G at the points C and D (see Figure 2.2-1) produced by the operator CALC_G. In the table below, one will indicate by crown 1 the couple R_INF=0,016 m and R_SUP=0.032 m, and by crown 2 the couple R_INF=0,008 m and R_SUP=0.04 m. The values of reference are those obtained with the crown 1 and one smoothing LEGENDRE of degé 5. This is why the first 4 lines of the table below correspond to references of the type NON_REGRESSION (the first two lines correspond to the option CALC_G and the two following ones with the option CALC_K_G). For all the other lines, it is thus about a reference of the type. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

6 Date 19/10/2016 Page 6/12 Identification Type of reference Value of reference Tolerance degé 5, option CALC_G ( CGleg ) NON_REGRESSION 1.E- degé 5, option CALC_G ( CGleg ) NON_REGRESSION 1.E- degé 5, option CALC_K_G ( CGKleg ) NON_REGRESSION 1.E- degé 5, option CALC_K_G ( CGKleg ) NON_REGRESSION 1.E- crown 2, smoothing LEGENDRE of degé 5, option CALC_G ( CGleg2 ) 2.E- crown 2, smoothing LEGENDRE of degé 5, option CALC_G ( CGleg2 ) 2.E- crown 1, smoothing LAGRANGE_NO_NO, option CALC_G ( CGlagno ) 13% crown 1, smoothing LAGRANGE_NO_NO, option CALC_G ( CGlagno ) 3% crown 1, smoothing LAGRANGE_NO_NO, option CALC_K_G ( CGKlano ) 5% crown 1, smoothing LAGRANGE_NO_NO, option CALC_K_G ( CGKlano ) 3% crown 1, smoothing LAGRANGE, option CALC_G ( CGlag ) 21% crown 1, smoothing LAGRANGE, option CALC_G ( CGlag ) 6% crown 1, smoothing LAGRANGE, option CALC_K_G ( CGKlag ) crown 1, smoothing LAGRANGE, option CALC_K_G ( CGKlag ) 2% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

7 Date 19/10/2016 Page 7/12 Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

8 4 Modeling B 4.1 Characteristics of modeling Date 19/10/2016 Page 8/12 Modeling is used 3D phenomenon MECHANICS. The crack is with a grid (modeling XFEM). 4.2 Characteristics of the grid The grid is not fissured because the crack is not with a grid. One starts from a hexahedral initial healthy grid structured (see Figure 4.2-1), on which one operates loops of automatic refinement with the orders RAFF_XFEM and MACR_ADAP_MAIL. Healthy grid refined (see Figure 4.2-2) with which is carried out calculation contains nodes; 9480 tetrahedrons; hexahedrons; pyramids. Figure modeling B, longitudinal crosssection of the healthy grid refined on the level of the position of the crack Figure modeling B, initial healthy grid 4.3 Sizes tested and results One tests the value of G at the points C and D (see Figure 2.2-1) produced by the operator CALC_G. In the table below, one will indicate by crown 1 the couple R INF =0, m and R_SUP=0,01875 m, and by crown 2 the couple R_INF=0, m and R_SUP=0, m. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

9 Date 19/10/2016 Page 9/12 Identification Type of reference Value of reference Tolerance degé 5, option CALC_G ( CGleg ) 0.8% degé 5, option CALC_G ( CGleg ) degé 5, option CALC_K_G ( CGKleg ) 0.8% degé 5, option CALC_K_G ( CGKleg ) Not C - K 1 degé 5, option CALC_K_G ( CGKleg ) % Not D - K 1 degé 5, option CALC_K_G ( CGKleg ) % crown 2, smoothing LEGENDRE of degé 5, option CALC_G ( CGleg2 ) 0.6% crown 2, smoothing LEGENDRE of degé 5, option CALC_G ( CGleg2 ) Not C - K 1 crown 2, smoothing LEGENDRE of degé 5, option CALC_K_G ( CGKleg2 ) % Not D - K 1 crown 2, smoothing LEGENDRE of degé 5, option CALC_K_G ( CGKleg2 ) % crown 1, smoothing LAGRANGE, option CALC_G ( CGla15 ) 2% crown 1, smoothing LAGRANGE, option CALC_G ( CGla15 ) Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

10 5 Modeling C 5.1 Characteristics of modeling Date 19/10/2016 Page 10/12 Modeling is used 3D phenomenon MECHANICS. The crack is with a grid (modeling XFEM). 5.2 Characteristics of the grid The grid is not fissured because the crack is not with a grid. One starts from a free tetrahedral initial grid healthy (see Figure 5.2-1), on which one operates loops of automatic refinement with the orders RAFF_XFEM and MACR_ADAP_MAIL. Healthy grid refined (see Figure 5.2-2) with which is carried out calculation contains nodes; tetrahedrons. Figure modeling C, longitudinal crosssection of the healthy grid refined on the level of the position of the crack Figure modeling C, initial healthy grid 5.3 Sizes tested and results One tests the value of G at the points C and D (see Figure 2.2-1) produced by the operator CALC_G. In the table below, one will indicate by crown 1 the couple R INF =0,0125 m and R_SUP=0,025 m, and by crown 2 the couple R_INF=0,00625 m and R_SUP=0,03125 m. Identification Type of reference Value of reference Tolerance degé 5, option CALC_G ( CGleg ) 3% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

11 Date 19/10/2016 Page 11/12 degé 5, option CALC_G ( CGleg ) degé 5, option CALC_K_G ( CGKleg ) 3% degé 5, option CALC_K_G ( CGKleg ) Not C - K 1 degé 5, option CALC_K_G ( CGKleg ) % Not D - K 1 degé 5, option CALC_K_G ( CGKleg ) % crown 2, smoothing LEGENDRE of degé 5, option CALC_G ( CGleg2 ) 3% crown 2, smoothing LEGENDRE of degé 5, option CALC_G ( CGleg2 ) 3% Not C - K 1 crown 2, smoothing LEGENDRE of degé 5, option CALC_K_G ( CGKleg2 ) % Not D - K 1 crown 2, smoothing LEGENDRE of degé 5, option CALC_K_G ( CGKleg2 ) crown 1, smoothing LAGRANGE, option CALC_G ( CGla15 ) crown 1, smoothing LAGRANGE, option CALC_G ( CGla15 ) 5% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is

12 6 Date 19/10/2016 Page 12/12 Summary of the results The goal of this test is achieved to validate the calculation of the rate of refund of energy in a configuration 3D where elements of edge see a field theta not no one and a loading of Neumann not no one. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is