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

Abstract

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.

Creep damage model considering unilateral effect based on bimodulus theory

“…Further work need then to be done to complement this model. As mentioned in the introduction, in future research, it is necessary to combine the bimodulus creep damage constitutive model presented in this paper with some non-local models, such as gradient-enhanced approach (Challamel and Hellesland, 2013;Kiefer et al, 2018;Seupel and Kuna, 2019;Wu et al, 2014), micromorphic approach (Forest, 2009;Negi et al, 2021;Nguyen et al, 2020;Poggenpohl et al, 2021) or phase field approach (Ambati et al, 2015;Liu et al, 2021;Mozaffari and Voyiadjis, 2016), to guarantee the solution unicity.…”

“…The mesh size should be analyzed in the practical application of the above models. Some non-local continuum models have been proposed to yield mesh-objective solution and guarantee the solution unicity, such as gradientenhanced approach (Challamel and Hellesland, 2013;Kiefer et al, 2018;Seupel and Kuna, 2019;Wu et al, 2014), micromorphic approach (Forest, 2009;Negi et al, 2021;Nguyen et al, 2020;Poggenpohl et al, 2021) and phase field approach (Ambati et al, 2015;Liu et al, 2021;Mozaffari and Voyiadjis, 2016).…”

Fully integrated multi-scale modelling of damage and time-dependency in thermoplastic-based woven composites

“…This works well as long as the materials do not reach the strain softening regime, which was well verified in all the examples considered in this study. In the contrary case, the use of non-local modelling theories (Kiefer et al., 2018; Miehe et al., 2010; Peerlings et al., 1996; Pijaudier-Cabot and Bazant, 1987; Seupel and Kuna, 2019) would be necessary to objectively represent the localization phenomena beyond the strain softening onset (Bazant, 1984; De Borst et al., 1993).…”

Ductile fracture of high strength steels with morphological anisotropy, Part II: Nonlocal micromechanics-based modeling

“…In particular, several nonlocal versions of the GTN frameworks can be found in the literature, see e.g. [45,46,47,48,49,50,40,39]. The implicit gradient enhanced nonlocal formulation pioneered in [51] is employed in this work since it can be more easily integrated into a standard finite element formulation as considered in [39].…”