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Abstracts of papers for

Previous issue vol. 59, no. 3 (2011)

vol. 59, no. 4 (2011)

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Contents of issue 4, vol. 59

1. P. Church, R. Pereira, P. Gould, I. Lewtas: Methodology for comparison of hydrocode modelling with experiment for Split Hopkinson Pressure Bar (SHPB) testing of soft materials
2. Ch. Maréchal, F. Bresson, G. Haugou: Development of a numerical model of the 9 mm Parabellum FMJ bullet including jacket failure
3. M. Nowak, J. Ostrowska-Maciejewska, R.B. Pęcherski, P. Szeptyński: Yield criterion accounting for the third invariant of stress tensor deviator. Part I. Proposition of the yield criterion based on the concept of influence functions
4. P. Szeptyński: Yield criterion accounting for the influence of the third invariant of stress tensor deviator. Part II: Analysis of convexity condition of the yield surface
5. P. Perzyna: Micromechanics of localized fracture phenomena in inelastic solids generated by impact-loaded adiabatic processes

P. Church, R. Pereira, P. Gould, I. Lewtas: Methodology for comparison of hydrocode modelling with experiment for Split Hopkinson Pressure Bar (SHPB) testing of soft materials

The objective of this work is to develop a technique for reliable comparison of simulations with SHPB data in order to validate material models for "soft" materials such as polymers. Comparison with an output stress-strain curve is not sufficient since there are many assumptions built into this analysis. Primarily these concern the notion that the specimen is in stress equilibrium and volume is conserved. The problem is that the choice of material model for the specimen in the simulation dictates how and when the specimen attains stress equilibrium. The main methodology is based on comparing the simulations with the raw strain gauge data on the input and output bars, which makes no assumptions about stress equilibrium. However, one has to account for the well documented Pochhammer-Chree oscillations and their effect on the specimen.

Contents

Ch. Maréchal, F. Bresson, G. Haugou: Development of a numerical model of the 9 mm Parabellum FMJ bullet including jacket failure

Even though ballistic experiments are widely accepted as the only reliable way to probe terminal effects, we demonstrate that computer simulation can be a useful alternative. Particularly, the high energy projectiles are seldom studied in the field of forensic sciences. That situation being favorable to computer simulation, a 3D finite element model of the worldwide-used 9 mm Parabellum bullet has been developed with Abaqus explicit software. A Johnson-Cook constitutive model, fed with the split Hopkinson pressure bar experimental parameters, accurately describes the materials' behavior (lead and brass). Experiments were performed with a handgun and a hard steel plate target in order to discuss the reliability of the model. Accurate predictions about bullet deformation and failure were obtained without any post- calculation adjustment of parameters.

Contents

M. Nowak, J. Ostrowska-Maciejewska, R.B. Pęcherski, P. Szeptyński: Yield criterion accounting for the third invariant of stress tensor deviator. Part I. Proposition of the yield criterion based on the concept of influence functions

A proposition of an energy-based hypothesis of material effort for isotropic materials exhibiting strength-differential (SD) effect, pressure-sensitivity and Lode angle dependence is discussed. It is a special case of a general hypothesis proposed by the authors in [11] for anisotropic bodies, based on Burzyński's concept of influence functions [2] and Rychlewski's concept of elastic energy decomposition [16]. General condition of the convexity of the yield surface is introduced, and its derivation is given in the second part of the paper. Limit condition is specified for Inconel 718 alloy, referring to the experimental results published by Iyer and Lissenden [7].

Contents

P. Szeptyński: Yield criterion accounting for the influence of the third invariant of stress tensor deviator. Part II: Analysis of convexity condition of the yield surface

General form of yield condition for isotropic and homogeneous bodies is considered in the paper. In the space of principal stresses, the limit condition is graphically represented by a proper regular surface which is assumed here to be at least of C² class. Due to Drucker's Postulate, the yield surface should be convex. General form of convexity condition of the considered surface is derived using methods of differential geometry. Parametrization of the yield surface is given, the first and the second derivatives of the position vector with respect to the chosen parameters are calculated, what enables determination of the tangent and unit normal vectors at given point, and also determination of the first and the second fundamental form of the considered surface. Finally the Gaussian and mean curvatures, which are given by the coefficients of the first and the second fundamental form as the invariants of the shape operator, are found. Convexity condition of the considered surface expressed in general in terms of the mean and Gaussian curvatures, is formulated for any form of functions determining the character of the surface.

Contents

P. Perzyna: Micromechanics of localized fracture phenomena in inelastic solids generated by impact-loaded adiabatic processes

The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of localized fracture in inelastic solids generated by impact-loaded adiabatic processes. Particular attention is focused on the proper description of a ductile mode of fracture propagating along the shear band for high impact velocities. This procedure of investigation is based on utilization the finite difference method for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic damaged polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables consists of two scalars, namely equivalent inelastic deformation and volume fraction porosity. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena and the volume fraction porosity takes into account the microdamage evolution effects. The relaxation time is used as a regularization parameter. Fracture criterion based on the evolution of microdamage is assumed.

As a numerical example we consider dynamic shear band propagation and localized fracture in an asymmetrically impact-loaded prenotched thin plate. The impact loading is simulated by a velocity boundary condition which are the results of dynamic contact problem. The separation of the projectile from the specimen, resulting from wave reflections within the projectile and the specimen, occurs in the phenomenon.

A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Shear band advance, microdamage and the development of the temperature field as a function of time have been determined. Qualitative comparison of numerical results with experimental observation data has been presented. The numerical results obtained have proven the usefulness of the thermo-elasto-viscoplastic theory in the investigation of dynamic shear band propagations and localized fracture.

Contents

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