Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain

Linse, Thomas; Hütter, Geralf; Kuna, Meinhard

doi:10.1016/j.engfracmech.2012.07.004

Cited by 43 publications

(18 citation statements)

References 44 publications

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“…10,11 The principle of these approaches is to introduce a spatial coupling term in the constitutive equation so as to redistribute the strain and damage fields and to avoid pathological localization. Different variables can be chosen as regularised variable; this includes the plastic strain tensor, 7 the volume variation, 12 the hydrostatic plastic strain, 13 the equivalent plastic strain, 12,14 and the damage variable. 15 Another problem observed in ductile damage simulation is the volumetric locking, which results from plastic quasiincompressibility.…”

Section: Introductionmentioning

confidence: 99%

Ductile damage modelling with locking‐free regularised GTN model

Zhang

Lorentz²,

Besson

2018

Numerical Meth Engineering

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The major goal of this work is to develop a robust modelling strategy for the simulation of ductile damage development including crack initiation and subsequent propagation. For that purpose, a Gurson-type model is used. This model class, as many other damage models, leads to significant material softening and must be used within a large deformation framework due to the ductile character of the materials. This leads to 2 main difficulties that should be dealt with carefully: mesh dependency and volumetric locking. In this work, a logarithmic finite strain framework is adopted in which the Gurson-Tvergaard-Needleman constitutive law is reformulated. Then a nonlocal formulation with regularisation of hardening variable is applied so as to solve mesh dependency and strain localization problem. In addition, the nonlocal model is combined with mixed "displacement-pressure-volume variation" elements to avoid volumetric locking. Thereby, a mesh-independent and locking-free finite strain framework suitable for the modelling of ductile rupture is established. Attention is paid to mathematical properties and numerical performance of the model. Finally, the model parameters are identified on an experimental database for a nuclear piping steel. Simulations of standard test specimens (notched tensile bars and compact tension and single edge notched tensile cracked specimens) are performed and compared to experimental results. KEYWORDSductile damage, GTN model, mesh dependency, mixed finite element, nonlocal regularisation, volumetric locking

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Section: Introductionmentioning

confidence: 99%

Ductile damage modelling with locking‐free regularised GTN model

Zhang

Lorentz²,

Besson

2018

Numerical Meth Engineering

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“…According to the findings, a refinement of the mesh be≤L/4 is applied in the critical zones for all upcoming simulations. This requirement towards the discretization has already been proposed by Linse et al. (2012) and Seupel et al.…”

Section: Experimental Methods and Fe Modelsmentioning

confidence: 97%

“…The part Δafail is the true distance measured from the FE node former positioned at the initial crack tip (node B) to the front of total material degradation (D≥Dc) along the ligament. From literature it is known that the first total failure of an element will occur in a small distance ahead from the initial crack tip if gradient-enhanced damage models are used (Linse et al., 2012; Simone et al., 2003). This leads to kinks of the simulated R-curve at the transition from pure blunting to crack growth.…”

Section: Experimental Methods and Fe Modelsmentioning

confidence: 99%

A gradient-enhanced damage model motivated by engineering approaches to ductile failure of steels

Seupel

Kuna

2019

International Journal of Damage Mechanics

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Material models for ductile damage, crack initiation, and crack growth are of high interest, e.g. for metal forming simulations. Empirical engineering approaches are often applied, but the numerical results are sensitive to the discretization if no method is utilized to prevent ill-posedness of the underlying boundary value problem due to strain softening. In order to face this issue, an empirical damage model is equipped with a gradient-enhancement which introduces an additional length scale parameter. Until the initiation of damage, the material is modeled with standard von Mises plasticity. Damage initiation is taken into account by an uncoupled failure indicator. After damage initiation, material degradation is assumed to be driven by a non-local quantity, which depends on plastic deformation and stress triaxiality. During damage evolution, the macroscopic material behavior becomes dependent on hydrostatic stress, which is motivated by well known void growth and coalescence mechanisms. A calibration strategy is developed to determine the parameters of strain hardening, damage initiation, and damage evolution as well as the internal length step-by-step. The proposed model is calibrated to experimental data of a pressure vessel steel. Reasonable predictions of smooth and notched tensile tests as well as a small punch test show the validity of the model for loadings from moderate to high stress triaxialities.

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“…the models by Chen and Yuan (2002); Zhang et al (2018), and (iii) implicit gradient type, see e.g. the developments by Ramaswamy and Aravas (1998); Reusch et al (2003b,a);Håkansson et al (2006); Reusch et al (2008); Linse et al (2012); Hütter et al (2013); Hütter et al (2014); Zybell et al (2014). The integral and implicit gradient types are found to be largely equivalent and referred to being strongly nonlocal while explicit gradient type can be considered as being weakly nonlocal (Peerlings et al, 2001).…”

Section: Introductionmentioning

confidence: 93%

“…The implicit gradient type is employed in this work since it can be more easily integrated into a standard finite element implementation in comparison with the integral type (Peerlings et al, 1996). In the implicit gradient type, either the porosity (Ramaswamy and Aravas, 1998;Håkansson et al, 2006), the effective porosity (considered in the GTN model after applying the void expansion acceleration) (Reusch et al, 2003b(Reusch et al, ,a, 2008, or the volumetric equivalent plastic strain (Linse et al, 2012;Hütter et al, 2013;Hütter et al, 2014;Zybell et al, 2014) is generally chosen as a nonlocal variable.…”

Section: Introductionmentioning

confidence: 99%

A nonlocal approach of ductile failure incorporating void growth, internal necking, and shear dominated coalescence mechanisms

Nguyễn

Pardoen²,

Noels

2020

Journal of the Mechanics and Physics of Solids

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An advanced modeling framework is developed for predicting the failure of ductile materials relying on micromechanics, physical ingredients, and robust numerical methods. The approach is based on a hyperelastic finite strain multi-surface constitutive model with multiple nonlocal variables. The three distinct nonlocal solutions for the expansion of voids embedded in an elastoplastic matrix are considered: a void growth phase governed by the Gurson-Tvergaard-Needleman yield surface, a void necking coalescence phase governed by a heuristic extension of the Thomason yield surface based on the maximum principal stress, and a competing void shearing coalescence phase triggered by the maximum shear stress. The first solution considers the diffused plastic deformation around the voids while the last two solutions correspond to a state of plastic localization between neighboring voids. This combination captures the Lode variable and shear effects, which play important roles in dictating the damage evolution rates. The implicit nonlocal formulation with multiple nonlocal variables, including the volumetric and deviatoric parts of the plastic strain, and the mean equivalent plastic strain of the matrix, regularizes the problem of the loss of solution uniqueness when material softening occurs whatever the localization mechanism. The predictive capability of the proposed model is demonstrated through different numerical simulations in which complex failure patterns such as slant and cup-cone of respectively plane strain and axisymmetric samples under tensile loading conditions develop.

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Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain

Cited by 43 publications

References 44 publications

Ductile damage modelling with locking‐free regularised GTN model

Ductile damage modelling with locking‐free regularised GTN model

A gradient-enhanced damage model motivated by engineering approaches to ductile failure of steels

A nonlocal approach of ductile failure incorporating void growth, internal necking, and shear dominated coalescence mechanisms

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