Issue 49

M. Hadj Miloud et alii, Frattura ed Integrità Strutturale, 49 (2019) 630-642; DOI: 10.3221/IGF-ESIS.49.57 641 C ONCLUSION n this work, an inverse identification procedure is adopted to identify f N and f C parameters of GTN damage model coupled with and without hardening laws. The model was built under the software package Abaqus. Despite the high number of parameters, the approach applied made it possible to determine them simultaneously with good accuracy. This is verified comparatively with the experimental results found in the literature. In the inverse procedure, the experimental results data are extracted from the load-diametric reduction curve of an axisymmetric notched AN2 of 12NiCr6 steel bar tensile test. After identification, we noticed that the identified GTN parameters, f C and f N , with Voce or Ludwik hardening law are similar to those of Ref [9] and approximately the same fracture point is obtained. The best fit is obtained with the work hardening law of Voce. The small difference between numerical results in the case of coupled identification and those obtained experimentally highlights the mutual interaction between the hardening and damage parameters in the mechanical behavior of the materials. Thereafter, the identified GTN parameters are used in the numerical model of tear test on a CT specimen. In order to validate them, the numerical Load-Displacement curve was compared to the experimental results performed by [30]. This comparison shows a good agreement between the experimental and the numerical results. This indicates the relevance of the developed FE model. The crack propagation is materialized numerically by the elements where the final porosity is reached. All of these elements represent the fracture facies profile. In our case, this facies corresponds to that of a CT specimen without grooves. This indicates that it is imperative to take into account the notch in numerical modeling. R EFERENCES [1] Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile media, J Eng Mater Tech, 99, pp. 2–15. DOI: 10.1115/1.3443401 . [2] Tvergaard, V. (1981). Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture, 17, pp. 389–407. DOI: 10.1007/BF00036191. [3] Tvergaard, V. (1982). On Localization in Ductile Materials Containing Spherical Voids, International Journal of Fracture, 18, pp. 237–52. DOI: 10.1007/BF00015686. [4] Tvergaard, V. and Needleman, A. (1984). Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica, 32(1), pp. 157–169. DOI: 10.1016/0001-6160(84)90213-X. [5] Hancock, J.W. and Mackenzie, A.C. (1976). On the mechanisms of ductile failure in high-strength steels subjected to multiaxial stress-states, J Mech Phys Solids, 24(2–3), pp. 147–160. DOI:10.1016/0022-5096(76)90024-7 [6] Thomason, P.F. (1990). Ductile fracture of metals. Oxford: Pergamon Press. https://trove.nla.gov.au/version/20721090 [7] Chu, C. and Needleman, A. (1980). Void nucleation effects in biaxially stretched sheets, Journal of Engineering Materials and Technology,102, pp. 249–56. DOI: 10.1115/1.3224807 . [8] Springmann, M. and Kuna, M. (2006). Determination of ductile damage parameters by local deformation fields: measurement and simulation, Arch Appl Mech, 75, pp. 775–797. DOI: 10.1007/s00419-006-0033-9 [9] Hadj Miloud, M. Imad, A. Benseddiq, N. Bachir Bouiadjra, B. Bounif, A. and Serier, B. (2013). A numerical analysis of relationship between ductility and nucleation and critical void volume fraction parameters of Gurson– Tvergaard– Needleman model, Proc IMechE Part C: J Mechanical Engineering Science, IMechE, 227(11), pp. 2634–2646. DOI: 10.1177/0954406213476232. [10] Cox, T. and Low, J.J. (1974). An investigation of the plastic fracture of AISI4340 and 18Nickel-200 grade maraging steels, Metall Trans A, 5, pp. 1457–1470. DOI: 10.1007/BF02646633. [11] Sun, D.Z., Siegele, D., Voss, B. and Schmitt, W. (1989). Application of local damage models to the numerical analysis of ductile rupture, Fatigue Fract Eng Mater, 12(3), pp. 201–212. DOI: 10.1111/j.1460-2695.1989.tb00527.x. [12] Sun, D.Z., Siegele, D., Voss, B. and Schmitt, W. (1991). Numerical prediction of ductile fracture resistance behaviour based on micromechanical models, In: JG Blauel and KH Schwalbe(eds) Defect assessment in components – fundamentals and applications (ESIS/EGF9), London: Mechanical Engineering Publications, pp. 447–458. [13] Sun, D.Z., Kienzler, R,. Voss, B. and Schmitt, W. (1992). Application of micro-mechanical models to the prediction of ductile fracture, fracture mechanics, In: SN Atluri (ed.) 22nd Symposium (II), ASTM STP 1131. Philadelphia, PA: American Society for Testing and Materials, pp. 368–378. I