Modeling and simulation of large-scale ductile fracture in plates and shells

Abstract The work is concerned with the modeling and simulation of large scale ductile fracture in plate and shell structures. A meshfree method – the reproducing kernel particle method (RKPM) – is used in numerical computations in order to enact dynamic crack propagation without remeshing. There are several novelties in the present approach. First, we have developed a crack surface approximation and particle split algorithm for three-dimensional through-thickness cracks. Second, to represent evolving crack surface in 3D shell structures, a 3D parametric visibility condition algorithm is proposed, which re-constructs the local connectivity map for particles near the crack tip or crack surfaces, so that the meshfree interpolation field can represent physical material separation in the computational domain. Third, the constitutive update formulas in explicit time integration by different versions of Gurson models and the rate-dependent Johnson–Cook model are implemented for 3D computations. Finally, the performance of different Gurson-type models are investigated and compared with the experimental data of large scale in-plate tear process. Numerical simulations of crack propagation in stiffened plates and shells demonstrate that the proposed method provides an effective means to simulate ductile fracture in large scale plate/shell structures with engineering accuracy.

[1]  F. Erdogan,et al.  FRACTURE OF CYLINDRICAL AND SPHERICAL SHELLS CONTAINING A CRACK , 1972 .

[2]  Bo Cerup Simonsen,et al.  Ship grounding on rock—II. Validation and application , 1997 .

[3]  A. Needleman,et al.  Analysis of the cup-cone fracture in a round tensile bar , 1984 .

[4]  T. Rabczuk,et al.  A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks , 2007 .

[5]  Viggo Tvergaard,et al.  Effect of strain-dependent cohesive zone model on predictions of crack growth resistance , 1996 .

[6]  Bo Cerup Simonsen,et al.  Experimental and numerical modelling of ductile crack propagation in large-scale shell structures , 2004 .

[7]  N. Aravas.  On the numerical integration of a class of pressure-dependent plasticity models , 1987 .

[8]  Viggo Tvergaard,et al.  Ductile shear failure or plug failure of spot welds modelled by modified Gurson model , 2010 .

[9]  J. Klepaczko,et al.  Spall fracture: Mechanical and microstructural aspects , 1999 .

[10]  T. Rabczuk,et al.  A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics , 2007 .

[11]  Shaofan Li,et al.  Recent Developments on Thermo-Mechanical Simulations of Ductile Failure by Meshfree Method , 2011 .

[12]  R. Batra,et al.  ANALYSIS OF SHEAR BANDING IN TWELVE MATERIALS , 1992 .

[13]  J. Hutchinson,et al.  Modification of the Gurson Model for shear failure , 2008 .

[14]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[15]  T. Rabczuk,et al.  A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis , 2006 .

[16]  M. Langseth,et al.  Numerical simulation of plugging failure in ballistic penetration , 2001 .

[17]  Jørgen Amdahl,et al.  On the resistance to penetration of stiffened plates, Part I – Experiments , 2009 .

[18]  Bo Cerup Simonsen,et al.  Mesh‐free simulation of ductile fracture , 2004 .

[19]  D. Agard,et al.  Microtubule nucleation by γ-tubulin complexes , 2011, Nature Reviews Molecular Cell Biology.

[20]  Shaofan Li,et al.  Meshfree simulations of spall fracture , 2011 .

[21]  Zhenyu Xue,et al.  A modified Gurson model and its application to punch-out experiments , 2009 .

[22]  Odd Sture Hopperstad,et al.  On the resistance to penetration of stiffened plates, Part II: Numerical analysis , 2009 .

[23]  Ted Belytschko,et al.  Multiple scale meshfree methods for damage fracture and localization , 1999 .

[24]  Michael Ortiz,et al.  A cohesive approach to thin-shell fracture and fragmentation , 2005 .

[25]  Shaofan Li,et al.  Meshfree simulations of plugging failures in high-speed impacts , 2010 .

[26]  G. R. Johnson,et al.  Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures , 1985 .

[27]  Viggo Tvergaard,et al.  Three dimensional analysis of dynamic ductile crack growth in a thin plate , 1996 .

[28]  Lars Pilgaard Mikkelsen.  Post-necking behaviour modelled by a gradient dependent plasticity theory , 1997 .

[29]  T. Rabczuk,et al.  Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment , 2008 .

[30]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[31]  K. L. Nielsen,et al.  Effect of a shear modified Gurson model on damage development in a FSW tensile specimen , 2009 .

[32]  Shaofan Li,et al.  Meshfree Simulations of Ductile Crack Propagations , 2005 .

[33]  A. Needleman,et al.  Void Nucleation Effects in Biaxially Stretched Sheets , 1980 .

[34]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[35]  V. Tvergaard.  Crack growth predictions by cohesive zone model for ductile fracture , 2001 .

[36]  Ted Belytschko,et al.  Dynamic Fracture of Shells Subjected to Impulsive Loads , 2009 .

[37]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[38]  E. P. Chen.  Numerical Simulation of Shear Induced Plugging in HY100 Steel Plates , 1992 .

[39]  Shaofan Li,et al.  Meshfree simulations of thermo-mechanical ductile fracture , 2006 .

[40]  Huafeng Liu,et al.  Meshfree Particle Methods , 2004 .

[41]  T. Belytschko,et al.  Crack propagation by element-free Galerkin methods , 1995 .

[42]  H. Nguyen-Xuan,et al.  A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures , 2008 .

[43]  Dong Qian,et al.  Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heat , 2008 .

[44]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .