Modelling of nucleation and void growth in dynamic pressure loading, application to spall test on tantalum

• Published in: International journal of fracture Vol. 141; no. 1-2; pp. 177 - 194
• Main Authors: Czarnota, Christophe, Mercier, Sébastien, Molinari, Alain
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.09.2006; Springer Nature B.V; Springer Verlag
• Subjects: Cavitation; Coalescing; Computer simulation; Ductile fracture; Dynamic pressure; Dynamics; Engineering Sciences; Evolution; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Material properties; Mathematical models; Mechanics; Mechanics of materials; Nucleation; Physics; Porosity; Solid mechanics; Stress concentration; Structural and continuum mechanics; Tantalum; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Voids; Nucleation; Micro-inertia; Modeling; Crack propagation; Sphere; Cavity; Ductile fracture Spall; Dynamics; Weibull distribution; Loading test(mechanics); Damaging; Dense matrix; Probabilistic approach; Spacing; Experimental study; Cavitation; Exact solution; Nucleation and growth; Tantalum; Scaling; Inertia; Ductile fracture; Porosity; Coalescence; Dynamic load; Step function
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-006-0070-y

Dynamic ductile fracture is a three stages process controlled by nucleation, growth and finally coalescence of voids. In the present work, a theoretical model, dedicated to nucleation and growth of voids during dynamic pressure loading, is developed. Initially, the material is free of voids but has potential sites for nucleation. A void nucleates from an existing site when the cavitation pressure pc is reached. A Weibull probability law is used to describe the distribution of the cavitation pressure among potential nucleation sites. During the initial growth, the effect of material properties is essentially appearing through the magnitude of pc. In the later stages, the matrix softening due to the increase of porosity has to be taken into account. In a first step, the response of a sphere made of dense matrix but containing a unique potential site, is investigated. When the applied loading is a pressure ramp, a closed form solution is derived for the evolution of the void that has nucleated from the existing site. The solution appears to be valid up to a porosity of 0.5. In a second part, the dynamic ductile fracture of a high-purity grade tantalum is simulated using the proposed model. Spall stresses for this tantalum are calculated and are in close agreement with experimental levels measured by Roy (2003, Ph.D. Thesis, Ecole Nationale Supérieure de Mécanique et d’Aéronautique, Université de Poitiers, France). Finally, a parametric study is performed to capture the influence of different parameters (mass density of the material, mean spacing between neighboring sites, distribution of nucleation sites...) on the evolution of damage.