skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics

Abstract

Computationally efficient methods for bridging length scales, from highly resolved micro/meso-scale models that can explicitly model crack growth, to macro-scale continuum models that are more suitable for modeling large parts, have been of interest to researchers for decades. In this work, an improved brittle damage model is presented for the simulation of dynamic fracture in continuum scale quasi-brittle metal components. Crack evolution statistics, including the number, length, and orientation of individual cracks, are extracted from high-fidelity, finite discrete element method (FDEM) simulations and used to generate effective material moduli that reflect the material’s damaged state over time. This strategy allows for the retention of small-scale physical behaviors such as crack growth and coalescence in continuum scale hydrodynamic simulations. However, the high-fidelity simulations required to generate the crack statistics are computationally expensive. Thus, steps were taken to produce a flexible constitutive model to reduce the number of costly high-fidelity simulations needed to produce accurate results. A new stress based degradation criterion is introduced for the degradation of individual material zones. This allows for the development of a heterogeneous damage distribution within the bulk material. Then a flow stress model is added to the hydrodynamic simulation to account for plasticity in quasi-brittlemore » materials. As a result, the effective moduli model can be applied to a larger range of materials. The effective moduli constitutive model is used to simulate beryllium flyer plate experiments. The results from the continuum scale simulations using statistics from a single high-fidelity simulation are found to be in excellent agreement with numerical and experimental velocity interferometer data. The same set of crack statistics are used to extrapolate the results of a higher rate flyer plate case using the effective moduli model. In conclusion, the extension of this model to higher rate cases shows promise for further reducing the number of costly high-fidelity simulations needed to generate crack statistics.« less

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [2];  [3]; ORCiD logo [2]
  1. New Mexico State Univ., Las Cruces, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. New Mexico State Univ., Las Cruces, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1603990
Alternate Identifier(s):
OSTI ID: 1776112
Report Number(s):
LA-UR-19-24826
Journal ID: ISSN 0022-5096
Grant/Contract Number:  
89233218CNA000001; 20170103DR
Resource Type:
Accepted Manuscript
Journal Name:
Journal of the Mechanics and Physics of Solids
Additional Journal Information:
Journal Volume: 138; Journal Issue: C; Journal ID: ISSN 0022-5096
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; brittle fracture; shock loading; effective elastic moduli; crack statistics; finite-discrete element method

Citation Formats

Larkin, Kevin, Rougier, Esteban, Chau, Viet Tuan, Srinivasan, Gowri, Abdelkefi, Abdessattar, and Hunter, Abigail. Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics. United States: N. p., 2020. Web. doi:10.1016/j.jmps.2020.103921.
Larkin, Kevin, Rougier, Esteban, Chau, Viet Tuan, Srinivasan, Gowri, Abdelkefi, Abdessattar, & Hunter, Abigail. Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics. United States. doi:https://doi.org/10.1016/j.jmps.2020.103921
Larkin, Kevin, Rougier, Esteban, Chau, Viet Tuan, Srinivasan, Gowri, Abdelkefi, Abdessattar, and Hunter, Abigail. Fri . "Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics". United States. doi:https://doi.org/10.1016/j.jmps.2020.103921. https://www.osti.gov/servlets/purl/1603990.
@article{osti_1603990,
title = {Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics},
author = {Larkin, Kevin and Rougier, Esteban and Chau, Viet Tuan and Srinivasan, Gowri and Abdelkefi, Abdessattar and Hunter, Abigail},
abstractNote = {Computationally efficient methods for bridging length scales, from highly resolved micro/meso-scale models that can explicitly model crack growth, to macro-scale continuum models that are more suitable for modeling large parts, have been of interest to researchers for decades. In this work, an improved brittle damage model is presented for the simulation of dynamic fracture in continuum scale quasi-brittle metal components. Crack evolution statistics, including the number, length, and orientation of individual cracks, are extracted from high-fidelity, finite discrete element method (FDEM) simulations and used to generate effective material moduli that reflect the material’s damaged state over time. This strategy allows for the retention of small-scale physical behaviors such as crack growth and coalescence in continuum scale hydrodynamic simulations. However, the high-fidelity simulations required to generate the crack statistics are computationally expensive. Thus, steps were taken to produce a flexible constitutive model to reduce the number of costly high-fidelity simulations needed to produce accurate results. A new stress based degradation criterion is introduced for the degradation of individual material zones. This allows for the development of a heterogeneous damage distribution within the bulk material. Then a flow stress model is added to the hydrodynamic simulation to account for plasticity in quasi-brittle materials. As a result, the effective moduli model can be applied to a larger range of materials. The effective moduli constitutive model is used to simulate beryllium flyer plate experiments. The results from the continuum scale simulations using statistics from a single high-fidelity simulation are found to be in excellent agreement with numerical and experimental velocity interferometer data. The same set of crack statistics are used to extrapolate the results of a higher rate flyer plate case using the effective moduli model. In conclusion, the extension of this model to higher rate cases shows promise for further reducing the number of costly high-fidelity simulations needed to generate crack statistics.},
doi = {10.1016/j.jmps.2020.103921},
journal = {Journal of the Mechanics and Physics of Solids},
number = C,
volume = 138,
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Effect of random defects on dynamic fracture in quasi-brittle materials
journal, August 2017

  • Abedi, Reza; Haber, Robert B.; Clarke, Philip L.
  • International Journal of Fracture, Vol. 208, Issue 1-2
  • DOI: 10.1007/s10704-017-0243-x

Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture
journal, December 1998


A constitutive model for the dynamic response of brittle materials
journal, April 1990

  • Addessio, Frank L.; Johnson, James N.
  • Journal of Applied Physics, Vol. 67, Issue 7
  • DOI: 10.1063/1.346090

A review on phase-field models of brittle fracture and a new fast hybrid formulation
journal, December 2014

  • Ambati, Marreddy; Gerasimov, Tymofiy; De Lorenzis, Laura
  • Computational Mechanics, Vol. 55, Issue 2
  • DOI: 10.1007/s00466-014-1109-y

The effective compliance of spatially evolving planar wing-cracks
journal, February 2018

  • Ayyagari, R. S.; Daphalapurkar, N. P.; Ramesh, K. T.
  • Journal of the Mechanics and Physics of Solids, Vol. 111
  • DOI: 10.1016/j.jmps.2017.11.016

Fracturing Rate Effect and Creep in Microplane Model for Dynamics
journal, September 2000


Influence of strain rate and temperature on the mechanical behavior of beryllium
conference, January 1998

  • Blumenthal, W. R.; Abeln, S. P.; Cannon, D. D.
  • The tenth American Physical Society topical conference on shock compression of condensed matter, AIP Conference Proceedings
  • DOI: 10.1063/1.55657

Elastic moduli of a cracked solid
journal, January 1976

  • Budiansky, Bernard; O'connell, Richard J.
  • International Journal of Solids and Structures, Vol. 12, Issue 2
  • DOI: 10.1016/0020-7683(76)90044-5

Computational modelling of impact damage in brittle materials
journal, August 1996


Dynamic Fracture of Ceramics in Armor Applications
journal, April 2007


Strain-rate dependency of the dynamic tensile strength of rock
journal, July 2003

  • Cho, Sang Ho; Ogata, Yuji; Kaneko, Katsuhiko
  • International Journal of Rock Mechanics and Mining Sciences, Vol. 40, Issue 5
  • DOI: 10.1016/S1365-1609(03)00072-8

Molecular dynamic simulations of crack propagation
journal, January 1987


Simulation of Fracture Coalescence in Granite via the Combined Finite–Discrete Element Method
journal, March 2019


Ejecta source and transport modeling in the FLAG hydrocode
journal, August 2013


Modelling of failure mode transition in ballistic penetration with a continuum model describing microcracking and flow of pulverized media
journal, January 2002

  • Gailly, Benjamin A.; Espinosa, Horacio D.
  • International Journal for Numerical Methods in Engineering, Vol. 54, Issue 3
  • DOI: 10.1002/nme.427

Fourier amplitude sensitivity test applied to dynamic combined finite‐discrete element methods–based simulations
journal, August 2018

  • Godinez, Humberto C.; Rougier, Esteban; Osthus, Dave
  • International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Issue 1
  • DOI: 10.1002/nag.2852

The Phenomena of Rupture and Flow in Solids
journal, January 1921

  • Griffith, A. A.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 221, Issue 582-593
  • DOI: 10.1098/rsta.1921.0006

The differential scheme and its application to cracked materials
journal, January 1988


Overall moduli of solids with microcracks: Load-induced anisotropy
journal, January 1983


Reduced-order modeling through machine learning and graph-theoretic approaches for brittle fracture applications
journal, February 2019


Effective Elastic Moduli of Two-Dimensional Brittle Solids With Interacting Microcracks, Part I: Basic Formulations
journal, June 1994

  • Ju, J. W.; Chen, Tsung-Muh
  • Journal of Applied Mechanics, Vol. 61, Issue 2
  • DOI: 10.1115/1.2901451

Effective Elastic Moduli of Two-Dimensional Brittle Solids With Interacting Microcracks, Part II: Evolutionary Damage Models
journal, June 1994

  • Ju, J. W.; Chen, Tsung-Muh
  • Journal of Applied Mechanics, Vol. 61, Issue 2
  • DOI: 10.1115/1.2901452

A Three-Dimensional Statistical Micromechanical Theory for Brittle Solids with Interacting Microcracks
journal, January 1992


An Improved Two-Dimensional Micromechanical Theory for Brittle Solids with Randomly Located Interacting Microcracks
journal, January 1995


Introduction to Beryllium: Uses, Regulatory History, and Disease
journal, May 2001

  • Kolanz, Marc E.
  • Applied Occupational and Environmental Hygiene, Vol. 16, Issue 5
  • DOI: 10.1080/10473220119088

Numerical simulation of ceramic composite armor subjected to ballistic impact
journal, December 2010


Effect of crack orientation statistics on effective stiffness of mircocracked solid
journal, March 2009

  • Kushch, V. I.; Sevostianov, I.; Mishnaevsky, L.
  • International Journal of Solids and Structures, Vol. 46, Issue 6
  • DOI: 10.1016/j.ijsolstr.2008.11.023

Multiscale material modeling and its application to a dynamic crack propagation problem
journal, February 2009


Elastic moduli of a cracked body
journal, May 1983

  • Margolin, L. G.
  • International Journal of Fracture, Vol. 22, Issue 1
  • DOI: 10.1007/BF00960099

Microphysical models for inelastic material response
journal, January 1984


Dynamic fracture (spalling) of metals
journal, January 1983


Predictive modeling of dynamic fracture growth in brittle materials with machine learning
journal, June 2018


A combined finite‐discrete element method in transient dynamics of fracturing solids
journal, February 1995


Calibrating the stress-time curve of a combined finite-discrete element method to a Split Hopkinson Pressure Bar experiment
journal, June 2018

  • Osthus, Dave; Godinez, Humberto C.; Rougier, Esteban
  • International Journal of Rock Mechanics and Mining Sciences, Vol. 106
  • DOI: 10.1016/j.ijrmms.2018.03.016

Model of plastic deformation for extreme loading conditions
journal, January 2003

  • Preston, Dean L.; Tonks, Davis L.; Wallace, Duane C.
  • Journal of Applied Physics, Vol. 93, Issue 1
  • DOI: 10.1063/1.1524706

Fatigue crack growth characteristics of Fe and Ni under cyclic loading using a quasi-continuum method
journal, January 2018

  • Qiu, Ren-Zheng; Lin, Yi-Chen; Fang, Te-Hua
  • Beilstein Journal of Nanotechnology, Vol. 9
  • DOI: 10.3762/bjnano.9.93

Validation of a three-dimensional Finite-Discrete Element Method using experimental results of the Split Hopkinson Pressure Bar test
journal, September 2014

  • Rougier, E.; Knight, E. E.; Broome, S. T.
  • International Journal of Rock Mechanics and Mining Sciences, Vol. 70
  • DOI: 10.1016/j.ijrmms.2014.03.011

On the Tensile Strength of Granite at High Strain Rates considering the Influence from Preexisting Cracks
journal, January 2016

  • Saadati, Mahdi; Forquin, Pascal; Weddfelt, Kenneth
  • Advances in Materials Science and Engineering, Vol. 2016
  • DOI: 10.1155/2016/6279571

Combined continuum damage-embedded discontinuity model for explicit dynamic fracture analyses of quasi-brittle materials: COMBINED CONTINUUM DAMAGE-EMBEDDED DISCONTINUITY MODEL
journal, November 2014

  • Saksala, Timo; Brancherie, Delphine; Harari, Isaac
  • International Journal for Numerical Methods in Engineering, Vol. 101, Issue 3
  • DOI: 10.1002/nme.4814

The Deformation Mechanisms in Process of Crack Propagation for Alpha Titanium with Compounding Microdefects
journal, January 2016

  • Sheng, Ying; Zeng, Xiang-guo
  • Advances in Materials Science and Engineering, Vol. 2016
  • DOI: 10.1155/2016/2156936

A meshfree method based on the peridynamic model of solid mechanics
journal, June 2005


A constitutive model for metals applicable at high‐strain rate
journal, March 1980

  • Steinberg, D. J.; Cochran, S. G.; Guinan, M. W.
  • Journal of Applied Physics, Vol. 51, Issue 3
  • DOI: 10.1063/1.327799

Quasicontinuum analysis of defects in solids
journal, June 1996


Statistically informed upscaling of damage evolution in brittle materials
journal, August 2019


Quasicontinuum simulation of brittle cracking in single-crystal material: Quasicontinuum simulation of brittle cracking in single-crystal material
journal, February 2017

  • Xu, Taolong; Fan, Jinghong; Stewart, Ross
  • Crystal Research and Technology, Vol. 52, Issue 3
  • DOI: 10.1002/crat.201600247

Review on Multi-scale Simulation Methods
journal, July 2018


New crack-tip elements for XFEM and applications to cohesive cracks
journal, January 2003

  • Zi, Goangseup; Belytschko, Ted
  • International Journal for Numerical Methods in Engineering, Vol. 57, Issue 15
  • DOI: 10.1002/nme.849

The effect of microcracks on the elastic moduli of brittle materials
journal, December 1985

  • Zimmerman, Robert W.
  • Journal of Materials Science Letters, Vol. 4, Issue 12
  • DOI: 10.1007/BF00721363

A mechanisms-based model for dynamic behavior and fracture of geomaterials
journal, December 2014

  • Zubelewicz, A.; Rougier, E.; Ostoja-Starzewski, M.
  • International Journal of Rock Mechanics and Mining Sciences, Vol. 72
  • DOI: 10.1016/j.ijrmms.2014.09.015