Use of a modified Gurson model approach for the simulation of ductile fracture by growth and coalescence of microvoids under low, medium and high stress triaxiality loadings

Recently, we applied criterion of initiation of deformation bands based on bifurcation analysis as a criterion of ductile fracture. Experience shows that this procedure yields realistic results if plastic behavior is described by deformation theory of plasticity, with corresponding stress-strain dependence — especially with transition between strain hardening stages III and IV. But it is generally known that under high stress triaxilities, fracture strain depends strongly on stress triaxiality. If deformation theory of plasticity is suitable for modeling of constitutive properties of polycrystalline metals, it should lead to good results in prediction of cavitation instability as a criterion of ductile fracture under high triaxialities as well. We present prediction of fracture strains for reactor pressure vessel steel, in comparison with experimental results. Criterion of cavitation instability based on deformation theory of plasticity predicts similar dependence of fracture strain on stress triaxiality as the classical Rice-Tracey void growth model does, but, moreover, in contrast to the Rice-Tracey model, it predicts absolute values of critical strains. Finally, important role of deformation theory of plasticity in other areas of material engineering and structural integrity analysis is shortly remembered.

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Effective potentials in nonlinear polycrystals and quadrature formulae

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0213 ◽

2017 ◽

Vol 473 (2204) ◽

pp. 20170213 ◽

Cited By ~ 9

Author(s):

Jean-Claude Michel ◽

Pierre Suquet

Keyword(s):

Order Approximation ◽

High Stress ◽

Stress Triaxiality ◽

Local Fields ◽

Field Analysis ◽

Effective Potentials ◽

Quadrature Formulae ◽

Highly Nonlinear ◽

Transformation Field Analysis ◽

High Stress Triaxiality

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471 , 20150665 ( doi:10.1098/rspa.2015.0665 )) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

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Local Approach of Fracture in the Ductile Regime and Application to VVER Materials

10th International Conference on Nuclear Engineering, Volume 1 ◽

10.1115/icone10-22710 ◽

2002 ◽

Author(s):

B. Z. Margolin ◽

V. I. Kostylev ◽

E. Keim ◽

R. Chaouadi

Keyword(s):

Finite Element ◽

Crack Resistance ◽

Ductile Fracture ◽

Finite Element Simulation ◽

Volume Fraction ◽

Stress Triaxiality ◽

Local Approach ◽

Gurson Model ◽

Element Simulation

Within the TACIS R2.06/96 project: “Surveillance Program for VVER 1000 Reactors”, sponsored by the European Commission, the local approach of fracture has been applied in the ductile regime. Two different models were applied and compared, namely Tvergaard-Needleman-Gurson versus Prometey model. The main tasks are: • perform special Local Approach experiments on smooth and notched cylindrical specimens; • predict JR-curve on the basis of the ductile fracture models; • compare two models of ductile fracture, namely, the Tvergaard-Needleman-Gurson model and the Prometey model. In this paper, the Tvergaard-Needleman-Gurson and Prometey models are briefly described. The parameters of both models were calibrated by using experimental data obtained on tensile specimens. While only smooth tensile specimens are used to calibrate the Tvergaard-Needleman-Gurson model, notched tensile in addition to smooth tensile specimens are used to calibrate the Prometey model. In the latter, standard smooth tensile specimens are used to determine the mechanical properties (the yield stress σy, the ultimate stress σu, the ultimate elongation δu, the area reduction Z) and notched cylindrical specimens to determine the strain at rupture. The numerical analysis comprises essentially two steps: • Step 1: finite element simulation of the smooth tensile specimen (determination of true stress-strain curve and critical void volume fraction for the Tvergaard-Needleman-Gurson model) and simulation of the notched cylindrical specimen up to rupture (determination of stress triaxiality for the Prometey model); • Step 2: finite element simulation of the 2T CT specimen and determination of the crack resistance behaviour in the ductile regime (J-Δa curve). It is found that both models were able to correctly predict the crack resistance behaviour of the investigated materials. The numerical and the experimental results were in very good agreement. The main difference between the two models is that the required number of calibrated parameters in the Prometey model is less than in the Tvergaard-Needleman-Gurson model but additional tests on notched specimens are required for the Prometey model.

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