A new model of metal plasticity and fracture with pressure and Lode dependence

doi:10.1016/J.IJPLAS.2007.09.004

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A new model of metal plasticity and fracture with pressure and Lode dependence

Journal Article•DOI•

A new model of metal plasticity and fracture with pressure and Lode dependence

Yuanli Bai¹, Tomasz Wierzbicki¹•Institutions (1)

Massachusetts Institute of Technology¹

01 Jun 2008-International Journal of Plasticity (Pergamon)-Vol. 24, Iss: 6, pp 1071-1096

TL;DR: In this paper, a 3D asymmetric fracture locus, in the space of equivalent fracture strain, stress triaxiality and the Lode angle parameter, is proposed.

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About: This article is published in International Journal of Plasticity.The article was published on 2008-06-01. It has received 1351 citations till now. The article focuses on the topics: Plasticity & Hydrostatic pressure.

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Journal Article•DOI•

Application of extended Mohr–Coulomb criterion to ductile fracture

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Yuanli Bai¹, Yuanli Bai², Tomasz Wierzbicki¹•Institutions (2)

Massachusetts Institute of Technology¹, General Electric²

01 Jan 2010-International Journal of Fracture

TL;DR: In this article, the Mohr-Coulomb (M-C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids.

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Abstract: The Mohr–Coulomb (M–C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids. This criterion has been extensively used in rock and soil mechanics as it correctly accounts for the effects of hydrostatic pressure as well as the Lode angle parameter. It turns out that these two parameters, which are critical for characterizing fracture of geo-materials, also control fracture of ductile metals (Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins et al. 1980). The local form of the M–C criterion is transformed/extended to the spherical coordinate system, where the axes are the equivalent strain to fracture $${\bar \varepsilon_f}$$ , the stress triaxiality η, and the normalized Lode angle parameter $${\bar \theta}$$ . For a proportional loading, the fracture surface is shown to be an asymmetric function of $${\bar \theta}$$ . A detailed parametric study is performed to demonstrate the effect of model parameters on the fracture locus. It was found that the M–C fracture locus predicts almost exactly the exponential decay of the material ductility with stress triaxiality, which is in accord with theoretical analysis of Rice and Tracey (1969) and the empirical equation of Hancock and Mackenzie (1976), Johnson and Cook (1985). The M–C criterion also predicts a form of Lode angle dependence which is close to parabolic. Test results of two materials, 2024-T351 aluminum alloy and TRIP RA-K40/70 (TRIP690) high strength steel sheets, are used to calibrate and validate the proposed M–C fracture model. Another advantage of the M–C fracture model is that it predicts uniquely the orientation of the fracture surface. It is shown that the direction cosines of the unit normal vector to the fracture surface are functions of the “friction” coefficient in the M–C criterion. The phenomenological and physical sound M–C criterion has a great potential to be used as an engineering tool for predicting ductile fracture.

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937 citations

Cites background or methods from "A new model of metal plasticity and..."

...An approach of parameter optimization using Matlab code was described in reference ( Bai and Wierzbicki 2008 )....
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...In parallel with the “physically based” models of ductile fracture, a number of empirical fracture models have earned a permanent place in the literature (Cockcroft and Latham 1968; Hancock and Mackenzie 1976; Wilkins et al. 1980; Johnson and Cook 1985; Bao and Wierzbicki 2004; Wierzbicki and Xue 2005; Bai and Wierzbicki 2008 )....
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...Recent experimental results ( Bai and Wierzbicki 2008; Yang et al. 2009; Gao et al. 2009) have shown that both the hydrostatic pressure and Lode angle parameter should be taken into account in metal plasticity....
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...It turns out that these two parameters, which are critical for characterizing fracture of geo-materials, also control fracture of ductile metals ( Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins et al. 1980)....
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...tension (test No. 1), axial-symmetric compression (test No. 6) and plane strain (test No. 4) experiments should be compared with each other, as described by Bai and Wierzbicki (2008) ....
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Journal Article•DOI•

Ductile fracture: Experiments and computations

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Heng Li¹, Heng Li², Mingwang Fu², Jian Lu², H. Yang¹ - Show less +1 more•Institutions (2)

Northwestern Polytechnical University¹, Hong Kong Polytechnic University²

01 Feb 2011-International Journal of Plasticity

TL;DR: In this paper, several criteria under the categories of uncoupled damage and coupled damage were investigated to determine their reliability in ductile failure prediction in metal plastic deformation, including the continuum damage mechanics (CDM)-based Lemaitre model and the Gurson-Tvergaard-Needleman (GTN) model, and the two categories of criteria were coded into finite element models based on the unconditional stress integration algorithm in the VUMAT/ABAQUS platform.

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432 citations

Journal Article•DOI•

New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals

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Yanshan Lou¹, Hoon Huh¹, S. J. Lim¹, Keunhwan Pack¹•Institutions (1)

KAIST¹

01 Dec 2012-International Journal of Solids and Structures

TL;DR: In this paper, a new ductile fracture criterion is proposed to model fracture behavior of sheet metals for nucleation, growth and shear coalescence of voids during plastic deformation.

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388 citations

Journal Article•DOI•

A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects

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Michael J. Borden¹, Thomas J. R. Hughes², Chad M. Landis², Amin Anvari², Isaac J. Lee² - Show less +1 more•Institutions (2)

North Carolina State University¹, University of Texas at Austin²

01 Dec 2016-Computer Methods in Applied Mechanics and Engineering

TL;DR: In this paper, a cubic degradation function was proposed to provide a stress-strain response prior to crack initiation, which more closely approximates linear elastic behavior, and a derivation of the governing equations in terms of a general energy potential from balance laws that describe the kinematics of both the body and phase-field.

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383 citations

Additional excerpts

...It is of note that the failure behavior at low triaxiality levels has received renewed interest due to the fact that the GTN model does not perform well in this regime, (Bao and Wierzbicki [7], Bai and Wierzbicki [5, 6], Halton et al. [20])....
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...It is of note that the failure behavior at low triaxiality levels has received renewed interest due to the fact that the GTN model does not perform well in this regime, (Bao and Wierzbicki [7], Bai and Wierzbicki [5, 6], Halton et al....
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Journal Article•DOI•

Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities

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Dirk Mohr¹, Dirk Mohr², Stephane J. Marcadet¹, Stephane J. Marcadet²•Institutions (2)

Massachusetts Institute of Technology¹, École Polytechnique²

15 Aug 2015-International Journal of Solids and Structures

TL;DR: In this paper, a phenomenological fracture initiation model for metals is developed for predicting ductile fracture in industrial practice based on the assumption that the onset of fracture is imminent with the formation of a primary or secondary band of localization.

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369 citations

Cites background or methods or result from "A new model of metal plasticity and..."

...Bai and Wierzbicki (2010), Luo and Wierzbicki (2010), Beese et al....
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...It is worth noting that without any shear localization analysis results at their disposal, Stoughton and Yoon (2011) and Bai and Wierzbicki (2010) had already correctly hypothesized on the existence of a Mohr– Coulomb type of criterion for predicting the onset of ductile fracture....
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...Bai and Wierzbicki (2008)). However, as clearly demonstrated by Benzerga et al. (2012), this approach is in strong contradiction with the results from unit cell coalescence analysis for non-radial loading paths....
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...…approach to evaluating a phenomenological fracture initiation model for proportional loading based on experimental data with stress state history variations in the plastic range would be to postulate that the model holds true for the average stress state history (e.g. Bai and Wierzbicki (2008))....
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...The derivation of the so-called modified Mohr–Coulomb (MMC) model (Bai and Wierzbicki, 2010) is mathematically similar to the HC model, but it is usually used as inconsistent model. As opposed to the isotropic hardening law provided by Eq. (12), Bai and Wierzbicki (2010) made use of a rather unconventional stress triaxiality and Lode angle dependent hardening rule...
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References

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Journal Article•DOI•

Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures

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Gordon R. Johnson¹, William H. Cook²•Institutions (2)

Honeywell¹, Eglin Air Force Base²

01 Jan 1985-Engineering Fracture Mechanics

TL;DR: In this paper, a cumulative-damage fracture model is introduced which expresses the strain to fracture as a function of the strain rate, temperature and pressure, and the model is evaluated by comparing computed results with cylinder impact tests and biaxial (torsion-tension) tests.

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4,744 citations

Journal Article•DOI•

On the ductile enlargement of voids in triaxial stress fields

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James R. Rice¹, D.M. Tracey²•Institutions (2)

Brown University¹, Massachusetts Institute of Technology²

01 Jun 1969-Journal of The Mechanics and Physics of Solids

TL;DR: In this article, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material.

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Abstract: The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. First, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and subjected to a remotely uniform stress and strain rate field. Then an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material. Growth is studied in some detail for the case of a remote tensile extension field with superposed hydrostatic stresses. The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. Some related results are discussed, including the long cylindrical void considered by F.A. McClintock (1968, J. appl. Mech . 35 , 363), and an approximate relation is given to describe growth of a spherical void in a general remote field. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension.

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4,156 citations

Book•

Introduction to the mechanics of a continuous medium

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Lawrence E. Malvern

01 Jan 1969

TL;DR: In this article, the authors propose a linearized theory of elasticity for tensors, which they call Linearized Theory of Elasticity (LTHE), which is based on tensors and elasticity.

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Abstract: 1. Vectors and Tensors. 2. Strain and Deformation. 3. General Principles. 4. Constitutive Equations. 5. Fluid Mechanics. 6. Linearized Theory of Elasticity. Appendix I: Tensors. Appendix II: Orthogonal Curvilinear.

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3,658 citations