A computational model for failure of ductile material under impact

Abstract In addition to an accurate mathematical representation of the material, a computational modelling method for assessing impact problems involving large plastic deformation, damage localization, fracture etc. requires a suitable discretization scheme which can simulate the relevant physical processes without introducing any numerical artifact or being unstable. In this paper, a computational framework based on Smoothed Particle Hydrodynamics (SPH) is presented for studying the deformation and failure of ductile material, steel plate, under impact loading. This provides a useful design tool to simulate penetration of the plate. Crack propagation is modelled through a pseudo spring analogy wherein the interacting particles are assumed to be connected through pseudo-springs and the interaction is continuously modified through an order-parameter based on the accumulated damage in the spring. At the onset of crack formation i.e., when the accumulated damage reaches the critical value, the spring breaks which results in termination of interaction between particles on either sides of the spring. A key feature of the computational model is that it can capture arbitrary propagating cracks without introducing any special treatment such as discontinuous enrichment, particle-splitting etc. This computational framework is used herein to study adiabatic shear plugging in metal plates when modelling penetration under impact loading by a flat-ended, cylindrical projectile. The effects of different damage criteria are discussed. Computed results are compared with the experimental observation given in the literature and the efficacy of the framework is demonstrated.

[1]  Stephen R Reid,et al.  Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics , 2009 .

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

[3]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[4]  Ted Belytschko,et al.  The splitting pinball method for contact-impact problems , 1993 .

[5]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

[6]  Tore Børvik,et al.  Observations on shear plug formation in Weldox 460 E steel plates impacted by blunt-nosed projectiles , 2001 .

[7]  Larry D. Libersky,et al.  Smooth particle hydrodynamics with strength of materials , 1991 .

[8]  Tore Børvik,et al.  Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and c , 2002 .

[9]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[10]  Mark A Fleming,et al.  Continuous meshless approximations for nonconvex bodies by diffraction and transparency , 1996 .

[11]  M. Langseth,et al.  Ballistic penetration of steel plates , 1999 .

[12]  T. Wierzbicki,et al.  On fracture locus in the equivalent strain and stress triaxiality space , 2004 .

[13]  S. Dey,et al.  Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities , 2005 .

[14]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments , 2010 .

[15]  Werner Goldsmith,et al.  Non-ideal projectile impact on targets , 1999 .

[16]  T. Belytschko,et al.  The extended/generalized finite element method: An overview of the method and its applications , 2010 .

[17]  E. W. Parkes,et al.  The permanent deformation of a cantilever struck transversely at its tip , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

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

[19]  G. M. Zhang,et al.  Modified Smoothed Particle Hydrodynamics (MSPH) basis functions for meshless methods, and their application to axisymmetric Taylor impact test , 2008, J. Comput. Phys..

[20]  Odd Sture Hopperstad,et al.  On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part II. Numerical study , 2003 .

[21]  Wing Kam Liu,et al.  Meshfree and particle methods and their applications , 2002 .

[22]  J. P. Hughes,et al.  Accuracy of SPH viscous flow models , 2008 .

[23]  Sukanta Chakraborty,et al.  Crack Propagation in Bi-Material System via Pseudo-Spring Smoothed Particle Hydrodynamics , 2014 .

[24]  Jean-Paul Vila,et al.  Renormalized Meshfree Schemes I: Consistency, Stability, and Hybrid Methods for Conservation Laws , 2008, SIAM J. Numer. Anal..

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

[26]  H. Nguyen-Xuan,et al.  A simple and robust three-dimensional cracking-particle method without enrichment , 2010 .

[27]  Werner Goldsmith,et al.  The mechanics of penetration of projectiles into targets , 1978 .

[28]  Debasish Roy,et al.  Beyond classical dynamic structural plasticity using mesh-free modelling techniques , 2015 .

[29]  R. Sedgwick,et al.  A numerical model for plugging failure , 1973 .

[30]  Hitoshi Gotoh,et al.  Enhancement of stability and accuracy of the moving particle semi-implicit method , 2011, J. Comput. Phys..

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

[32]  T. Belytschko,et al.  A three dimensional large deformation meshfree method for arbitrary evolving cracks , 2007 .

[33]  J. K. Chen,et al.  A corrective smoothed particle method for boundary value problems in heat conduction , 1999 .

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

[35]  T. Wierzbicki,et al.  Numerical study on crack propagation in high velocity perforation , 2005 .

[36]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics: A Meshfree Particle Method , 2003 .

[37]  Charles E. Anderson,et al.  Ballistic impact: the status of analytical and numerical modeling , 1988 .

[38]  Sukanta Chakraborty,et al.  A pseudo-spring based fracture model for SPH simulation of impact dynamics , 2013 .

[39]  J. Monaghan.  On the problem of penetration in particle methods , 1989 .

[40]  Sukanta Chakraborty,et al.  Prognosis for ballistic sensitivity of pre-notch in metallic beam through mesh-less computation reflecting material damage , 2015 .

[41]  J. Monaghan.  SPH without a Tensile Instability , 2000 .

[42]  Rade Vignjevic,et al.  A contact algorithm for smoothed particle hydrodynamics , 2000 .

[43]  S. Reid,et al.  Optimised form of acceleration correction algorithm within SPH-based simulations of impact mechanics , 2011 .

[44]  Ajoy Ghatak,et al.  An Introduction to Equations of State: Theory and Applications , 1986 .

[45]  R. Woodward.  The penetration of metal targets which fail by adiabatic shear plugging , 1978 .

[46]  Gui-Rong Liu,et al.  Restoring particle consistency in smoothed particle hydrodynamics , 2006 .

[47]  T. Børvik,et al.  A computational model of viscoplasticity and ductile damage for impact and penetration , 2001 .

[48]  T. Belytschko,et al.  Stable particle methods based on Lagrangian kernels , 2004 .

[49]  M. Langseth,et al.  Effect of target thickness in blunt projectile penetration of Weldox 460 E steel plates , 2003 .

[50]  Rushdie Ibne Islam,et al.  A computational framework for modelling impact induced damage in ceramic and ceramic-metal composite structures , 2017 .

[51]  C. Ruiz,et al.  Impact loading of plates — An experimental investigation , 1983 .

[52]  G. G. Corbett,et al.  Impact loading of plates and shells by free-flying projectiles: A review , 1996 .

[53]  J. Monaghan,et al.  Shock simulation by the particle method SPH , 1983 .