F.M. with Finite Element analysis - Different calculation techniques + Numerical examples (ANSYS Workbench) 1/2

Transcription

1 Task 6 - Safety Review and Licensing On the Job Training on Stress Analysis F.M. with Finite Element analysis - Different calculation techniques + Numerical examples (ANSYS Workbench) 1/2 Davide Mazzini Ciro Santus Pisa (Italy) June 15 July 14, 2015

2 FM parameters with Finite Element method Content Different FE techniques ANSYS Workbench - Crack geometry element mesh preparation - K I(II,III) and J calculation - Examples ANSYS Apdl - The quarter point technique - Examples 2

3 FM parameters computed with FE Stress Intensity Factor(s)SIFs: K, K, K I II III Stress parameters Energy release rate: G Contour integral: J Energy parameters Crack Mouth Opening DisplacementCMOD Crack TipOpening Displacment CTOD Deformation parameters 3

4 Three different loading modes for a crack Fracture Mechanic parameters for the three modes Mode I: Opening Mode II: In-plane shear Mode III: Out-of-plane shear J K K E K 2G I II III 4

5 ANSYS different calculation techniques ANSYS help: u J wdy T i i ds x J KI, KII, KIII KI, KII, KIII J KI, KII, KIII (only if 2/3are zero,or ratios are known) J d da 5

6 ANSYS Apdl KCALC command ANSYS Help Quarter point technique: The mid-side node is shifted at ¼ of the element size to reproduce the displacement derivative singularity. From displacement to (elastic) K I(II,III) 6

7 ANSYS Apdl KCALC command M. Beghini, C. Santus. "An application of the weight function technique to inclined surface cracks under rolling contact fatigue, assessment and parametric analysis". Engineering Fracture Mechanics. Vol.98, pp , DOI: /j.engfracmech

8 CINT command options Mid-side nodes not shifted at ¼ Crack front (ANSYS Wb => ANSYS classic) Overlapped but distinct nodes Spiderweb mesh 8

9 CINT command options Plane elements (not for Workbench) Workbench default element thus VCCT is not available 9

10 CINT command options Postprocessing menu: only available CINT for J and CINT for K1(2,3) 10

11 CINT command options CINT,SIFS Volume (not path) integration, with the virtual load technique to distinguish K 1, K 2 and K 3 This way the SIFs are obtained as integration, rather than point displacement as KCALC A coarser mesh is enough for an accurate solution 11

12 How to introduce a crack Introduce the Fracture module into the Modeler (this feature is available only since the 14.5 ANSYS version, the current version is 16.0) 12

13 How to introduce a crack 1. It is possible to (easily) introduce a crack starting from a solid uncracked body and automatically generate the spiderweb mesh distribution at the crack front (Worth noting: this is for a semielliptical crack only) 2. Alternatively a (generic) crack front can be prepared in advance and introduced as the crack front 13

14 How to introduce a crack Mesh preparation Usually Hexahedrons are to be preferred than Tetrahedrons Here Tets are necessary for mesh continuity 14

15 Mesh preparation A strong local refinement is required The Sphere of Influence tool is recommended New local Coordinate System, both for mesh and for crack position/ orientation 15

16 Crack position and orientation The crack semi-elliptical center is coincident with Coordinate System origin point X axis has to be inward the component to be cracked and it should be perpendicular If not the crack plane is going to be perpendicular to the surface anyway The Crack is identified by its dedicated Coordinate System X-Z axes define the crack plane, thus Y is the vertical direction 16

17 Mesh and geometry parameters of the crack Buffer Zone Dir. Z Dir. X Preview of the crack to be introduced 17

18 The introduction of the crack is just a matter of mesh ANSYS Workbench 18

19 Spiderweb mesh parameters 19

20 Half-space surface crack basic example Same commands for loads and constraints 20

21 Postprocessing, K 1(2,3) and J along the crack front ANSYS Workbench Curvilinear coordinate 21

22 Contour integration results Tabular values Contours Usually the first is the less accurate, while the others show very similar results 22

23 Validation example 1 (half space) a 2mm t c 2 mm 100 MPa ( 0, i 1...5) 0 i a 2mm t c 2 mm 100 MPa 0 ANSYS Wb: K (A) 162MPa mm 5.12MPa m I K (B) 177 MPa mm 5.60MPa m I Laham'sSIFs Handbook: K (A) 165MPa mm 5.22 MPa m I I (diff.% 1.9%) K (B) 179MPa mm 5.68MPa m (diff.% 1.4%) 23

24 Validation example 2 (pipe) R i 50 mm t 10 mm a 2mm c 4mm 0 50 MPa ( i bg 0, i 1...5) ANSYS Wb: K (A) 109 MPa mm I 3.45MPa m Laham's SIFs Handbook: K (A) 112MPa mm 3.53MPa m I (diff.% 2.3%) 24

25 Exercise 1: Calculate the three SIFs. Which on is expected to be zero? Introduce an inclined crack on the specimen surface Torque M 10 N m T 45 a 1mm c 1mm 25

26 Exercise 2: Verify the ASTM standard CT specimen formula for K I B W P a a/ W K P 2 B W (1 ) I ( ) 3/2 How to manage a semi-elliptical crack for this case? 26

27 Exercise 2: Corner blends Almost straight portion of a semielliptical crack P 10 kn a 22.5 mm, W 60 mm, B 12mm K P 2 (1 ) I ( ) 699MPa mm 3/2 B W K (ANSYS) 782MPa mm I % 12% Large percentage difference 27

28 How to introduce a crack Pre-Meshed Crack 1. It is possible to (easily) introduce a crack starting from a solid uncracked body and automatically generate the spiderweb mesh distribution at the crack front (Worth noting: this is for a semielliptical crack only) 2. Alternatively a (generic) crack front can be prepared in advance and introduced as the crack front 28

29 Pre-Meshed Crack, CT specimen example A crack (almost zero angle) is initially introduced on the CAD model Almost crack geometry Notch region 29

30 Pre-Meshed Crack, CT specimen example Hexahedrons mesh is to be preferred in this case 30

31 Pre-Meshed Crack, CT specimen example Named selection: Crack front The edge is then converted into the nodes 31

32 Pre-Meshed Crack, CT specimen example Crack orientation, not crack actual shape and size The associated coordinate system is placed at one edge of the crack 32

33 Pre-Meshed Crack, CT specimen example Stress distribution Plane stress Usual (self-equilibrated) loading 33

34 Pre-Meshed Crack, inaccurate results P 10 kn a 30 mm, W 60 mm, B 12mm K P 2 B W (1 ) I ( ) 971MPa mm 3/2 K (ANSYS) 480 MPa mm I J (ANSYS) negative?? Maybe this technique is intended for future development 34