Modelling of dynamic damage and failure in aluminium alloys

Abstract A physically based damage and failure model, applicable to orthotropic metals is proposed in this paper. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Klepaczko [1] , has been adopted as the basis for the model. This assumption makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model [2–6] , which was used within the overall constitutive model to describe material behaviour in the plastic regime. A shock equation of state [7] was coupled with the rest of the constitutive model to allow for modelling of shock wave propagation in the material. The new model was implemented in DYNA3D [8] and coupled with our in-house non-linear transient SPH code, MCM (Meshless Continuum Mechanics). Parameters for the new constitutive model, i.e. parameters for the plasticity model and the damage model, were derived on the basis of the uniaxial tensile tests and Taylor anvil tests. The subject of investigation is a polycrystalline aluminium alloy AA7010, whose orthotropy is a consequence of meso-scale phase distribution, or grain morphology. Tensile tests were performed for the range of temperatures between 223.15 K and 473.15 K, and strain rates between 6.4 × 10 −4  s −1 and 6.4 × 10 2  s −1 . In order to validate the new damage model, a numerical simulation of Taylor anvil tests has been performed for AA7010, using a single stage gas gun at velocity of 200 m/s. The numerical analysis clearly demonstrates the ability of this new model to predict experimentally observed damage and failure.

[1]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[2]  U. F. Kocks,et al.  A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable , 1988 .

[3]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—II. Computational aspects , 1987 .

[4]  C. Truesdell,et al.  The Non-Linear Field Theories of Mechanics , 1965 .

[5]  K. Saanouni,et al.  On the Anelastic Flow with Damage , 1994 .

[6]  Whirley.  DYNA3D: A nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics , 1993 .

[7]  George Z. Voyiadjis,et al.  Microstructural based models for bcc and fcc metals with temperature and strain rate dependency , 2005 .

[8]  Egidio Rizzi,et al.  On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate , 2001 .

[9]  Youssef Hammi.  Simulation numérique de l'endommagement dans les procédés de mise en forme , 2000 .

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

[11]  George Z. Voyiadjis,et al.  A coupled anisotropic damage model for the inelastic response of composite materials , 2000 .

[12]  S. R. Chen,et al.  The mechanical threshold stress constitutive-strength model description of HY-100 steel , 2000 .

[13]  J. Gilman,et al.  Dynamic fracture by spallation in metals , 1970 .

[14]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1989 .

[15]  Y. Y. Zhu,et al.  A fully coupled elasto-visco-plastic damage theory for anisotropic materials , 1995 .

[16]  R. Hill.  The mathematical theory of plasticity , 1950 .

[17]  S. R. Chen,et al.  Mechanical properties and constitutive relations for molybdenum under high-rate deformation , 1998 .

[18]  P. G. Partridge,et al.  Subzero tensile properties of 7010 aluminium alloy and Ti-6A1-4V and IMI550 titanium alloys in sheet form , 1984 .

[19]  J. Klepaczko,et al.  Numerical study of spalling in an aluminum alloy 7020-T6 , 1999 .

[20]  B. Banerjee,et al.  AN EXTENDED MECHANICAL THRESHOLD STRESS PLASTICITY MODEL: MODELING 6061-T6 ALUMINUM ALLOY , 2008 .

[21]  Howard L. Schreyer,et al.  A thermodynamically consistent framework for theories of elastoplasticity coupled with damage , 1994 .

[22]  C. L. Chow,et al.  An anisotropic theory of elasticity for continuum damage mechanics , 1987 .

[23]  J. R. Klepaczko,et al.  Dynamic Crack Initiation, Some Experimental Methods and Modelling , 1990 .

[24]  George Z. Voyiadjis,et al.  A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals , 2006 .

[25]  G. T. Gray,et al.  Influence of grain size on the constitutive response and substructure evolution of MONEL 400 , 1999 .

[26]  Douglas J. Bammann,et al.  Modeling Temperature and Strain Rate Dependent Large Deformations of Metals , 1990 .

[27]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[28]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[29]  S. N. Zhurkov.  Kinetic concept of the strength of solids , 1965, International journal of fracture mechanics.

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

[31]  A. Rosakis,et al.  A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals , 2000 .

[32]  V. Tvergaard.  Material failure by void coalescence in localized shear bands , 1982 .

[33]  D. Krajcinovic,et al.  Some fundamental issues in rate theory of damage-elastoplasticity , 1995 .

[34]  G. Gray,et al.  Constitutive behavior of tantalum and tantalum-tungsten alloys , 1996 .

[35]  B. M. Butcher,et al.  A criterion for the time dependence of dynamic fracture , 1968 .

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

[37]  Dean L. Preston,et al.  Model of plastic deformation for extreme loading conditions , 2003 .