Campbell, JC

De Vuyst, T

Djordjevic, N

Hughes, K

Vignjevic, R

Brunel University Research Archive

SMOOTHED PARTICLE HYDRODYNAMICS MODELLING OF DYNAMIC FRACTURE AND FRAGMENTATION PROBLEMS  Tom De Vuyst, Rade Vignjevic, Kevin Hughes, James C. Campbell, Nenad Djordjevic Institute of Manufacturing and Materials Structural Integrity – Dynamic Response  tom.devuyst@brunel.ac.uk Brunel University London  Outline • SPH Formulations • Constitutive Model • Modelling Failure in SPH • Applications > Electro-Magnetically driven rings > Mock Holt Experiments > Explosively driven cylinder with end cap • Conclusion and Future Work   02 February 2017 A study of the ballistic limit of AA2024-T351 sheets impacted by compact steel projectiles 2 Brunel University London  Introduction To study dynamic fracture and fragmentation problems a numerical method must be capable of dealing with: > Crack formation and propagation. > Crack branching and crack joining, leading to fragmentation. > Large Deformations.  A meshless method such as the SPH method has the potential to do this Brunel University London  SPH Formulations Based on convolution integral   Approximation of a function   Approximation of the gradient of a function  Brunel University London  SPH Formulations Normalised kernels to ensure 0-th order consistency     Higher order possible when using MLS interpolation      Brunel University London  Eulerian Kernel SPH Eulerian kernel formulation > Evaluated in current configuration (particle positions) > Particles can move within, and in and out of kernel   Brunel University London  Eulerian Kernel SPH       Vignjevic, Campbell, Jaric, Powell (2009) Comp Methods Appl Mech Eng, 198, 2403-2411    Conservation Equations  Continuous Discretised (Eulerian SPH, moving reference frame)     Brunel University London  Total Lagrangian Kernel SPH Total Lagrangian kernel formulation > Gradients evaluated using initial particle positions > Neighbourhood is fixed   Brunel University London  Total Lagrangian Kernel SPH       Vignjevic, Reveles, Campbell (2006) Comput Model Eng Sci, 14 (3), 181-198    Conservation Equations  Continuous Discretised (TL SPH, reference configuration)     Brunel University London  Constitutive Model Modified Johnson-Cook (with equation of state) Brunel University London  Constitutive Model Lemaitre Damage Model:                                                            Failure when critical damage is reached Brunel University London  Modelling Failure     Randles P.W., Libersky L.D., Smoothed Particle Hydrodynamics: Some recent     improvements and applications. Comput. Methods Appl. Mech. Engrg. 139, 1996.      ‘Stress to zero concept’ – Upon failure a particle will be prevented from transferring tensile loads by setting its stress to zero.  Equivalent to basic failure models implemented in FE codes, but mass and momentum conserved.     Brunel University London  Modelling Failure Problem – Treatment of Fracture Solution – Particle visibility criterion > Truncated cone > Invisible particles are removed from neighbourhood         De Vuyst, Vignjevic, International Journal of Fracture, 2013  Brunel University London  Fragment Calculation Post Processing Calculation Same fragment if Ι xj – xi I < C * Δx with 1.2 ≤ C ≤ 1.5 Output Data:  > Fragment Number > Mass > Centre of Gravity > Velocity Brunel University London  Electromagnetically driven rings Zhang, Ravi-Chandar (2006) Int J Fract, 142, 183-217  AA6061-O rings  1.0x0.5mm cross section, radius 15.25mm   Brunel University London  Electromagnetically driven rings Zhang, Ravi-Chandar (2006) Int J Fract, 142, 183-217  Observations: > Number of fragments > Number of necks > Time of first fracture > Bending and rotation  Brunel University London  EM driven ring model Brunel University London  EM driven ring model Number of Fragments Brunel University London  Mock-Holt Experiments  Experimental setup Model            Fragment types Brunel University London  Mock-Holt Experiments Brunel University London  Mock-Holt Experiments Brunel University London  Conclusion and Future work SPH method has been successfully used to model high strain rate fracture and fragmentation problems  Model can be used as starting point to validate more physically based constitutive models  Ability to predict failure of brittle materials can be investigated 02 February 2017 22 

Smoothed particle hydrodynamics modelling of dynamic fracture and fragmentation problems

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Smoothed particle hydrodynamics modelling of dynamic fracture and fragmentation problems

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