In this study, a smoothed particle hydrodynamics (SPH) method for analyzing fatigue crack propagation was developed. In the simulation program, a crack is modeled to propagate virtually in particles based on the linear fracture mechanics and the Paris-Erdogan Law. This is realized by removal of one particle per analysis cycle. The SPH simulation in the case of the half elliptical surface crack propagation has given a smooth crack shape history, which is similar to the fatigue test result.
AshariS.E. and MohammadiS., Delamination analysis of composites by new orthotropic biomaterial extended finite element method, Int J Num Meth Engng86 (2011), 1507–1543.
3.
BelytschkoT. and BlackT., Elastic crack growth in finite elements with minimal remeshing, Int J Num Meth Eng45(5) (1999), 601–620.
4.
BelytschkoT.GuL. and LuY., Fracture and crack growth by element free Galerkin methods, Modelling Simul Mater Sci Eng2 (1994), 519.
5.
BelytschkoT.LuY.Y. and GuL., Element-free Galerkin methods, Int J Num Meth Engng37(2) (1994), 229–256.
6.
BelytschkoT.LuY.Y. and GuL., Crack propagation by element-free Galerkin methods, Eng Fra Mech51(2) (1995), 295–315.
7.
BrownW F Jr and J.ESrawley, Plane strain crack toughness testing of high strength metallic materials, ASTM STP410 (1966), 12.
8.
ChoppD.L. and SukumarN., Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method, Int J Engng Sci41(8) (2003), 845–869.
9.
ColomboD., An implicit geometrical approach to level sets update for 3D nonplanar X-FEM crack propagation, Comp Meth Appl Mech Engng237–240 (2012), 39–50.
10.
ColomboD. and MassinP., Fast and robust level set update for 3D non-planar X-FEM crack propagation modelling, Comp Meth Appl Mech Engng200(25–28) (2011), 2160–2180.
11.
FishJ.MarkolefasS.GuttalR. and NayakP., On adaptive multilevel superposition of finite element meshes, Appl Num Math14 (1994), 135–164.
12.
GéniautS.MassinP. and MoësN., A stable 3d contact formulation for cracks using X-FEM, Euro J Comp Mech16(2) (2007), 259–275.
13.
GravouilA.MoësN. and BelytschkoT., Non-planar 3D crack growth by the extended finite element and level sets-Part II: Level set update, Int J Num Meth Engng53 (2002), 2569–2586.
14.
IrwinG.R., Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics24 (1957), 361–364.
15.
Japan Ship Technology Research Association, Ship research summary report. SR169, 1979, pp. 137–147 (in Japanese).
16.
KikuchiM.TakahashiM.WadaY. and LiY., Fatigue crack growth simulation using S-version FEM: 2nd report, study on interaction of two parallel cracks, Transactions of the JSME A74(745) (2008), 1243–1248 (in Japanese).
17.
KikuchiM.WadaY.TakahashiM. and LiY., Fatlgue crack growth simulation using S-version FEM, Advanced Materials Research33(37) (2008), 133–138.
18.
KikuchiM.WadaY.UtsunomiyaA. and SuyamaH., Fatlgue crack growth simulation using S-version FEM: 3rd report, fatigue of 3D surface crack, Transactions of the JSME A75(755) (2009), 142–148 (in Japanese).
19.
LorentzE., A mixed interface finite element for cohesive zone models, Comp Meth Appl Mech Engng198(2) (2008), 302–317.
20.
L.B.Lucy, A numerical approach to the testing of the fission hypothesis, Astronom J8 (1977), 1013–1024.
21.
MaedaK.TanakaS. and TakeiT., Bifurcation and unification of fatigue cracks by X-FEM, in: 30th CMD Conference JSME No. 327, 2017 (in Japanese).
22.
MassinP.FertéG. and MoëtN., 3D crack propagation with XFEM cohesive elements, Transactions SMiRT-23 472, 2015.
23.
MoësN.DolbowJ. and BelytschkoT., A fine element method for crack growth without remeshing, Int J Num Meth Engng46(1) (1999), 131–150.
24.
MoësN.GravouilA. and BelytschkoT., Non-planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model, Int J Num Meth Engng53 (2002), 2549–2568.
NagashimaT. and SawadaM., Two-dimensional crack analyses by XFEM using crack tip elements, Transactions of the JSME A78(796) (2012), 1642–1655(in Japanese).
27.
NishiokaT.LeeH.WonY. and FujimotoT., Evaluation of fatigue crack growth behavior in materials with lubricating oil holes, Journal of the JIME47(5) (2012), 89–94 (in Japanese).
28.
ParisP. and ErdoganF., A critical analysis of crack propagation laws, Journal of basic engineering, Transactions of the American Society of Mechanical Engineers85(4) (1963), 528–534.
29.
ShiJ.ChoppD.LuaJ.SukumarN. and BelytschkoT., Abaqus implementation of extended finite element method using a levet representation of threedimensional fatigue crack growth and life predictions, Eng Fract Mech77 (2010), 2840–2863.
30.
SukumarN.ChoppD.L.BéchetE. and MoësN., Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method, Int J Numer Meth Eng76(5) (2008), 727–748.
31.
SukumarN.ChoppD.L. and MoranB., Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, Engng Fra Mech70(1) (2003), 29–48.
32.
SukumarN.HuangZ.Y.PrévostJ.-H. and SuoZ., Partition of unity enrichment for bimaterial interface cracks, Int J Num Meth Engng59 (2004), 1075–1102.
33.
YagawaG. and FurukawaT., Recent developments of free mesh method, Int J Num Meth Engng47(8) (2000), 1419–1443.
34.
YagawaG. and YamadaT., Free mesh method: A new mew mesh-less finite element meshes, Computational Mechanics18(6) (1996), 383–386.