1. Simulation of Waterjet Erosion
Using ANSYS/LS-DYNA
And Smoothed Particle Hydrodynamics (SPH)
Mike Valant
ME 8364
Steve Groothuis

2. Smoothed Particle Hydrodynamics
Matter is represented by particles of fixed mass
Conservation equations are expressed as inter-particle forces
Mechanical equations are expressed as the summation of interpolants (interpolation equations), using a kernel function W with a smoothing function h.

3. Smoothed Particle Hydrodynamics Integration Cycle
Bucket Sort

4. Abrasive Waterjet Erosion Process
Erosion Testing Machine

5. Abrasive Waterjet Erosion Process
45° from normal
0° from normal
Monolithic Erosion Test Samples

6. Abrasive Waterjet Erosion Process
Multilayered Erosion Test Samples

7. Abrasive Waterjet Erosion Process
Erosion is a micro-scale process which occurs over long periods of time
The cumulative effect of erosion is the sum of millions of high-speed microscopic impacts
A true model of abrasive waterjet erosion would include millions of micro-scale events integrated over a time scale many orders of magnitude larger than that of each individual event.
Therefore, for this model, several approximations and adjustments are made

8. Abrasive Waterjet Erosion Model
Abrasive Waterjet – SPH Particles
1.25mm diameter Quartz Sand
Density – 2.65 g/cc
Elastic Modulus – 70 GPa
Compressive Yield Strength – 1100MPa
Poisson’s Ratio – 0.17
Shear Modulus – 31 GPa
Material model - *MAT_ELASTIC_PLASTIC_HYDRO
Equation of State - Gruneisen

9. Abrasive Waterjet Erosion Model
Workpiece – Lagrangian Elements
6061 T6511 Aluminum
Density – g/cc
Elastic Modulus – 68.9 GPa
Yield Strength – 276MPa
Ultimate Tensile Strength – 310 MPa
Poisson’s Ratio – 0.33
Shear Modulus – 27 GPa
Material Model - *MAT_PLASTIC_KINEMATIC

10. Abrasive Waterjet Erosion Model
Model Dimensions
Jet Diameter – 4cm
Jet Length – 15cm
Jet Speed – 3000 km/s (1% of speed of light!)
Jet angles from normal - 1°, 22.5°, 45°, 67.5°
Workpiece length and width – 12cm
Workpiece layer thickness – 3mm
Number of layers - 5

11. Abrasive Waterjet Erosion Model
Sample code - ANSYS
/PREP7 !
! ELEMENT DEFINITION
ET,1,SOLID164
KEYOPT,1,1,1 ! = 0,1 (Constant stress solid element)
! = 2 (Fully integrated selectively-reduced solid)
KEYOPT,1,5,0 ! = 0 (LAGRANGIAN), =1 (1PT ALE)
! = 1 ALE (Arbitrary Lagrangian-Eulerian)
ET,2,MESH200 ! Not solved element
KEYOPT,2,1,6 ! 4-node meshing element
! GEOMETRIC PARAMETERS
PI = acos(-1) ! definition of pi
RCYL = 2 ! jet radius [cm] changed from 2
HCYL = ! jet column height [cm]
XBLOCK = 12 ! workpiece width [cm]
YBLOCK = 12 ! workpiece length [cm]
NUMLAYER = 5 ! number of workpiece layers
AVGBLOCK=(XBLOCK+YBLOCK)/2 ! AVERAGE NUMBER FOR MESHING
ZBLOCK = 0.3 ! workpiece LAYER height [cm]
ZTOTAL = ZBLOCK*NUMLAYER ! total height of workpiece
RCYL2 = 2*RCYL ! jet radius on workpiece [cm] --- changed from 2*rcyl
IANG = ! jet angle from normal [deg] !

12. Abrasive Waterjet Erosion Model
Sample code - ANSYS
! BASE BLOCK !
RECT,0,XBLOCK,0,YBLOCK ! MAKE RECTANGLE
MSHKEY,1 ! NOT free meshing
TYPE,2
MAT,WPIECE2
ESIZE,AVGBLOCK/WPIECEMESH
AMESH,ALL
! BUILD LAYER 1
ALLSEL
TYPE,1 ! SELECT 3D ELEMENT TYPE
MAT,WPIECE1
EXTOPT,ESIZE,1,0, ! Val1 (1) sets the number of element divisions in the direction of volume generation or volume sweep.
! Val2 sets the spacing ratio (bias) in the direction of volume generation (zero calls default, uniform spacing=1)
VEXT,ALL, , ,0,0,ZBLOCK,,,,

13. Abrasive Waterjet Erosion Model
Sample code - ANSYS !
! SOLID MESHING FOR WATERJET !
MSHAPE,0,3D
SMRT,MCYL ! Overall element size level for meshing. The level value controls the fineness of the mesh.
! is finest mesh, 10 is coarsest
! SPH CYLINDER
MAT,WJET
VSWEEP,NUMLAYER+1
ALLSEL $ CMSE,ALL
MODMSH,DETACH
! COMPONENT DEFINITION FOR WATERJET PLUS DELETE WATERJET ELEMENTS
ESEL,S,MAT,,WJET
NSLE,S,1
CM,SPHNODES,NODE
EDEL,ALL

14. Abrasive Waterjet Erosion Model
Sample code - ANSYS !
! GATHER CONSTRAINED NODE DATA
nsel,s,loc,z,0 ! select all nodes on z0 plane
n1=0 ! set n1 to 0
cn=ndinqr(0,13) ! return number of selected entities
*dim,cnodes,,cn,1 ! define a FORTRAN-like array with cn rows, one column, and one plane (default one plane)
*do,indx,1,cn ! do loop, counter indx, start from 1 and go to cn
n1=ndnext(n1) ! n1 now equals next selected node having a node number greater than n1, where n1 started at 0
cnodes(indx,1)=n1 ! value of cnodes at row (indx) equals n1
*enddo ! end of do loop
cmin=cnodes(1,1) ! cmin equals the first node in cnodes
cmax=cnodes(cn,1) ! cmax equals the last node in cnodes
allsel $ cmse,all ! reselect all
! GATHER SPH NODE DATA
CMSE,S,SPHNODES
N1=0
SPHN=NDINQR(0,13)
*DIM,SNODES,,SPHN,4 ! define a FORTRAN-like array with SPHN rows, four columns, and one plane (default one plane)
*DO,INDX,1,SPHN ! do loop, counter indx, start from 1 and go to SPHN
N1=NDNEXT(N1)
SNODES(INDX,1)=N1 ! NODE NUMBER
SNODES(INDX,2)=NX(N1) ! X-CCORDINATE
SNODES(INDX,3)=NY(N1) ! Y-COORDINATE
SNODES(INDX,4)=NZ(N1) ! Z-COORDINATE
*ENDDO
SMIN=SNODES(1,1)
SMAX=SNODES(SPHN,1)

15. Abrasive Waterjet Erosion Model
Sample code - ANSYS !
! EXPORT DATA TO WJBORE.K
*VWRITE
('*KEYWORD')
('$ cm micros GPa')
('*TITLE')
*VWRITE,TVELO,IANG
('Waterjet Boring: Particle Speed :',G8.2,'km/s at',G8.2,'deg')
('*CONTROL_TERMINATION')
*VWRITE,ENDTIM
%10.6f
('*CONTROL_TIMESTEP') ! timestep scale factor TSSFAC is usually from .67 to .9, not .2
(' ')
('*CONTROL_SHELL')
(' ')
('*CONTROL_DAMPING')
(' ')

16. Abrasive Waterjet Erosion Model
Sample code – LS-DYNA
*MAT_PLASTIC_KINEMATIC
*MAT_ELASTIC_PLASTIC_HYDRO
*EOS_GRUNEISEN
*MAT_ADD_EROSION

17. Abrasive Waterjet Erosion Model
Early solution with plastic deformation but no erosion model
Material and jet are plotted as a cross-section
Maximum plastic strain is over 100%

18. Abrasive Waterjet Erosion Model
Impact angle 67.5° from Normal
Model Geometry

19. Abrasive Waterjet Erosion Model
Impact angle 67.5° from Normal
Reverse Elevated View – Von Mises Stress

20. Abrasive Waterjet Erosion Model
Impact angle 67.5° from Normal
Side View – Von Mises Stress

21. Abrasive Waterjet Erosion Model
Impact angle 67.5° from Normal
Bottom View – Plastic Strain

22. Abrasive Waterjet Erosion Model
Impact angle 67.5° from Normal
Top View, Jet Not Shown – Plastic Strain

23. Abrasive Waterjet Erosion Model
Impact angle 45° from Normal
Model Geometry

24. Abrasive Waterjet Erosion Model
Impact angle 45° from Normal
Elevated View – No Fringe Levels

25. Abrasive Waterjet Erosion Model
Impact angle 45° from Normal
Side View – No Fringe Levels

26. Abrasive Waterjet Erosion Model
Impact angle 45° from Normal
Top View – Plastic Strain

27. Abrasive Waterjet Erosion Model
Impact angle 22.5° from Normal
Model Geometry

28. Abrasive Waterjet Erosion Model
Impact angle 22.5° from Normal
Elevated View – No Fringe Levels

29. Abrasive Waterjet Erosion Model
Impact angle 22.5° from Normal
Elevated View – Von Mises Stress

30. Abrasive Waterjet Erosion Model
Impact angle 22.5° from Normal
Elevated Side View, Cross-Section – Plastic Strain

31. Abrasive Waterjet Erosion Model
Impact angle 1° from Normal
Model Geometry

32. Abrasive Waterjet Erosion Model
Impact angle 1° from Normal
Elevated View – No Fringe Levels

33. Abrasive Waterjet Erosion Model
Impact angle 1° from Normal
Elevated View – Von Mises Stress

34. Abrasive Waterjet Erosion Model
Impact angle 1° from Normal
Elevated View, Cross-Section – Plastic Strain

35. Abrasive Waterjet Erosion Model
Impact angle 1° from Normal
Side View, Cross Section – Plastic Strain

36. Abrasive Waterjet Erosion Model
Impact angle 1° from Normal
Side View, Cross Section – Plastic Strain
Note Shape of Deformation

37. Model Correlation, AKA “Goodness”
Some of the major overall effects of abrasive waterjet erosion are present in this model:
The impact and erosion patterns on the workpiece surface are similar in shape to the erosion patterns seen in experiments.
A decrease in impact angle (relative to normal) results in an increase in the erosion rate. This is true for very high-speed abrasive waterjets.
The erosion shape in cross-section is similar to the shape seen in experiments.

38. Future Work
There are many parts of the model which can be improved or augmented:
Model geometry should equal experimental geometry.
Abrasive waterjet speed should be closer to the experimental speed.
If possible, a finer mesh for the workpiece and for the waterjet should be employed. Also a much longer waterjet is desirable.
The waterjet mesh should be more uniform to enhance SPH solution stability.
Artificial particle penetration and contact instability issues should be addressed.
The waterjet particle distribution can be improved by using a Gaussian-distributed mesh to more accurately represent the true particle distribution in a typical waterjet.
Materials of different properties can be used for different workpiece layers to simulate laser-deposited hard coatings.

39. THANK YOU
Many thanks go to Steve Groothuis, without whom this project would not have been possible.
Thanks must also go to Dr. Kovacevic for encouraging me to enroll in this class.
Finally, thank you for being a good audience!