A theoretical prediction framework for the construction of a fracture forming limit curve accounting for fracture pattern transition

Mu, Lin; Jia, Zhe; Ma, Ziwei; Shen, Fuhui; Sun, Yuekuo; Zang, Yong

doi:10.1016/j.ijplas.2020.102706

Cited by 46 publications

(16 citation statements)

References 72 publications

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“…an FFLC) consisting of a line with a slope equal to À1 in the coordinate system of major strain e 1 against minor strain e 2 . In later modelling work, fracture loci with a similar monotonic linear dependence between e 1 and e 2 were developed (Lee et al, 2004;Mahalle et al, 2020;Mu et al, 2020); these were consistent with the experimental results obtained in studies on a variety of sheet materials (Gu¨ler and Efe, 2018;Isik et al, 2014;Jawale et al, 2018;Lee and Wierzbicki, 2005;Soeiro et al, 2015;Song et al, 2017). In other experimental studies, however, it was found that the FFLC had a similar shape to the FLC, with the FFLC approaching the FLC as the strain path approaches the equal-biaxial strain state (Jain et al, 1999;Tasan et al, 2009).…”

Section: Introductionsupporting

confidence: 81%

A CDM-based unified viscoplastic constitutive model of FLCs and FFLCs for boron steel under hot stamping conditions

Zhang

Shi

Yardley

et al. 2022

International Journal of Damage Mechanics

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Forming limit curves (FLCs), which are constructed using the limit strains at localised necking, are the most widely used tools for the evaluation of the formability of sheet metals. Fracture forming limit curves (FFLCs) are more recently developed, complementary tools for formability evaluation which are instead constructed using the limit strains at fracture. Since the formability depends strongly on forming conditions such as strain state, temperature and strain rate, models for predicting FLCs and FFLCs are essential for the optimisation and further application of hot forming processes in which these forming conditions vary significantly with both position and time. However, no model has so far been developed to predict FFLCs either alone or in conjunction with FLCs for sheet metals such as boron steel under hot stamping conditions. In this study, a set of unified viscoplastic constitutive equations for the prediction of both FLCs and FFLCs based on continuum damage mechanics (CDM) has been formulated from a set of recently developed constitutive equations for dislocation-based hardening, in combination with two novel coupled variables characterising the accumulated damage leading to localised necking and fracture. The novel variables take into account the effects of strain state, temperature and strain rate on the formability of sheet metals. The material constants in the CDM-based constitutive equations have been calibrated using experimental data comprising true stress-true strain curves and limit strains of a 22MnB5 boron steel obtained at a range of temperatures and strain rates. Investigation of the effect of varying selected parameters in the coupled damage variables on the resulting computed FLCs and FFLCs has demonstrated the flexibility of the model in enabling curves of different shapes and numerical values to be constructed. This indicates the potential of the CDM-based constitutive model for application to other materials for warm or hot stamping processes.

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Section: Introductionsupporting

confidence: 81%

A CDM-based unified viscoplastic constitutive model of FLCs and FFLCs for boron steel under hot stamping conditions

Zhang

Shi

Yardley

et al. 2022

International Journal of Damage Mechanics

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“…Experimental determination of forming limits is laborious and expensive, and several analytical models have been developed and applied to the numerical prediction of the forming limits of diverse materials [8]. Among these models, the modified maximum force criterion (MMFC) [9] and the Marciniak-Kuczynski (MK) model [10] are widely applied [9,[11][12][13][14][15][16][17]. In addition to analytical models, the finite element (FE) simulations using accurate constitutive models are alternatives for the forming limits determination [18].…”

Section: /1mentioning

confidence: 99%

Determination of Forming Limits Based on Finite Element Simulations

Shen¹,

Chen²,

Lian³

et al. 2021

Esaform 2021

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Two categories of experiments have been performed to obtain the experimental forming limits of a ferritic stainless steel from uniaxial to equibiaxial tension, including Nakajima tests and tensile tests of flat specimens with different geometries of the central hole as well as the notched dog bone. The plasticity behavior of the investigated material is described using an evolving non-associated anisotropic plasticity model, which is calibrated based on experimental results of uniaxial tensile tests along different loading directions. A damage mechanics model is calibrated and validated based on the global force and displacement response of tensile tests. Finite element simulations of the Nakajima tests and the tensile tests of various geometries have been performed using the anisotropic material model. A novel spatio-temporal method is developed to evaluate the forming limits under different stress states by quantitatively characterizing the plastic strain distribution on the specimen surface. The forming limits have been independently determined from finite element simulation results of tensile specimens and Nakajima specimens using the spatio-temporal evaluation method. The forming limits obtained from numerical simulations of these two types of experiments are in good agreement with experimental results.

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“…Numerically, damage initiation, in this study, is defined as the onset of macroscopic softening due to damage, which must be taken into account by the numerical representation of the material behaviour. In order to consider the change of stress state during plastic deformation, the average values of the stress triaxiality η avg and the Lode-angle parameter θ avg have been used to describe the stress state for non-proportional loading paths (Wu et al 2017;Mu et al 2020).…”

Section: Extension Of Mbw Model For Non-proportional Loading Paths (Npmbw-19)mentioning

confidence: 99%

The differences of damage initiation and accumulation of DP steels: a numerical and experimental analysis

et al. 2020

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Many studies have examined the damage behaviour of dual-phase steels already. It is a topic of high interest, since understanding the mechanisms of damage during forming processes enables the production of steels with improved properties and damage tolerance. However, the focus was rarely on the comparison between representatives of this steel class, and the numerical simulation for the quantification of damage states was not thoroughly used. Therefore, this study compares the damage initiation and accumulation of two dual-phase steels (DP800 and DP1000), which are used in the automotive industry. Additionally, parameter sets of a phenomenological damage mechanics model with coupled damage evolution are calibrated for each material. The combined analysis reveals an earlier initiation of damage for the DP800, where the damage accumulation phase is prolonged. For DP1000 the damage nucleates only shortly before material failure. The material model is able to correctly predict the behaviour, while experimental analysis confirms the prediction via light optical and SEM metallography.

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A theoretical prediction framework for the construction of a fracture forming limit curve accounting for fracture pattern transition

Cited by 46 publications

References 72 publications

A CDM-based unified viscoplastic constitutive model of FLCs and FFLCs for boron steel under hot stamping conditions

A CDM-based unified viscoplastic constitutive model of FLCs and FFLCs for boron steel under hot stamping conditions

Determination of Forming Limits Based on Finite Element Simulations

The differences of damage initiation and accumulation of DP steels: a numerical and experimental analysis

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