Anisotropic thermal-conductivity degradation in the phase-field method accounting for crack directionality

Svolos, Lampros; Mourad, Hashem Mohamed; Bronkhorst, Curt Allan; Waisman, Haim

doi:10.1016/j.engfracmech.2021.107554

Anisotropic thermal-conductivity degradation in the phase-field method accounting for crack directionality

Journal Article · Wed Jan 20 23:00:00 EST 2021 · Engineering Fracture Mechanics

DOI:https://doi.org/10.1016/j.engfracmech.2021.107554· OSTI ID:1764220

^[1]; ^[2]; Bronkhorst, Curt Allan ^[3]; Waisman, Haim ^[1]

Columbia Univ., New York, NY (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Wisconsin, Madison, WI (United States)

Dynamic loads applied to metals may lead to brittle or ductile fracture depending on the imposed strain rates, material properties, and specimen geometry. With an increase in the applied velocity, brittle to ductile failure mode transition may also be observed. Furthermore, at high strain rates, ductile fracture may be preceded by shear bands, which are narrow bands of intense plastic deformation, typically accompanied by a significant rise in temperature. Reliable models are needed to predict the response of metals subject to dynamic loads. In particular, capturing the interplay between heat conduction and crack propagation using the phase-field fracture method is still an open research field. To accurately capture the heat transfer physics across crack surfaces, damage models degrading thermal-conductivity are necessary. While isotropic thermal-conductivity degradation models were proposed, they may lead to errors as they are indifferent to crack directionality. In our current work, a new anisotropic approach is proposed in which thermal-conductivity, which depends on the phase-field gradient, is degraded solely across the crack. Here, it is shown that this approach improves the near-field approximation of temperature and heat flux compared with isotropic degradation, when taking the discontinuous crack solutions as reference. Additionally, the anisotropic degradation approach is implemented in a unified dynamic fracture model and a couple of examples demonstrate the viability of this approach.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1764220

Alternate ID(s):: OSTI ID: 1809417

Report Number(s):: LA-UR--20-26137

Journal Information:: Engineering Fracture Mechanics, Journal Name: Engineering Fracture Mechanics Journal Issue: C Vol. 245; ISSN 0013-7944

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (55)

Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen Bruggeman, D. A. G. Annalen der Physik, Vol. 416, Issue 7 https://doi.org/10.1002/andp.19354160705	journal	January 1935
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities Geuzaine, Christophe; Remacle, Jean-François International Journal for Numerical Methods in Engineering, Vol. 79, Issue 11 https://doi.org/10.1002/nme.2579	journal	September 2009
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations Miehe, C.; Welschinger, F.; Hofacker, M. International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10 https://doi.org/10.1002/nme.2861	journal	August 2010
On localization in ductile materials containing spherical voids Tvergaard, Viggo International Journal of Fracture, Vol. 18, Issue 4 https://doi.org/10.1007/BF00015686	journal	April 1982
Influence of voids on shear band instabilities under plane strain conditions Tvergaard, Viggo International Journal of Fracture, Vol. 17, Issue 4 https://doi.org/10.1007/BF00036191	journal	August 1981
Mesh insensitive formulation for initiation and growth of shear bands using mixed finite elements McAuliffe, Colin; Waisman, Haim Computational Mechanics, Vol. 51, Issue 5 https://doi.org/10.1007/s00466-012-0765-z	journal	July 2012
Numerical simulation of dynamic fracture using finite elements with embedded discontinuities Armero, Francisco; Linder, Christian International Journal of Fracture, Vol. 160, Issue 2 https://doi.org/10.1007/s10704-009-9413-9	journal	October 2009
Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling Chu, Dongyang; Li, Xiang; Liu, Zhanli International Journal of Fracture, Vol. 208, Issue 1-2 https://doi.org/10.1007/s10704-017-0220-4	journal	June 2017
Analysis of the cup-cone fracture in a round tensile bar Tvergaard, V.; Needleman, A. Acta Metallurgica, Vol. 32, Issue 1 https://doi.org/10.1016/0001-6160(84)90213-X	journal	January 1984
Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures Johnson, Gordon R.; Cook, William H. Engineering Fracture Mechanics, Vol. 21, Issue 1 https://doi.org/10.1016/0013-7944(85)90052-9	journal	January 1985
Effect of thermal conductivity on the initiation, growth and bandwidth of adiabatic shear bands Batra, R. C.; Kim, C. H. International Journal of Engineering Science, Vol. 29, Issue 8 https://doi.org/10.1016/0020-7225(91)90168-3	journal	January 1991
Modelling of adiabatic shear band development from small imperfections Merzer, A. M. Journal of the Mechanics and Physics of Solids, Vol. 30, Issue 5 https://doi.org/10.1016/0022-5096(82)90003-5	journal	October 1982
On the temperature distribution at the vicinity of dynamically propagating cracks in 4340 steel Zehnder, Alan T.; Rosakis, Ares J. Journal of the Mechanics and Physics of Solids, Vol. 39, Issue 3 https://doi.org/10.1016/0022-5096(91)90019-K	journal	January 1991
Dynamically propagating shear bands in impact-loaded prenotched plates—II. Numerical simulations Zhou, M.; Ravichandran, G.; Rosakis, A. J. Journal of the Mechanics and Physics of Solids, Vol. 44, Issue 6 https://doi.org/10.1016/0022-5096(96)00004-X	journal	June 1996
A modified Maxwell-Eucken equation for calculating the thermal conductivity of two-component solutions or mixtures Levy, F. L. International Journal of Refrigeration, Vol. 4, Issue 4 https://doi.org/10.1016/0140-7007(81)90053-0	journal	July 1981
An analysis of shear band development incorporating heat conduction Lemonds, J.; Needleman, A. Mechanics of Materials, Vol. 5, Issue 4 https://doi.org/10.1016/0167-6636(86)90040-2	journal	December 1986
On the dependence of the dynamic crack tip temperature fields in metals upon crack tip velocity and material parameters Mason, James J.; Rosakis, Ares J. Mechanics of Materials, Vol. 16, Issue 4 https://doi.org/10.1016/0167-6636(93)90009-G	journal	November 1993
Experimental/ computational evaluation of flow stress at high strain rates with application to adiabatic shear banding Nemat-Nasser, Sia; Li, Yeou-Fong; Isaacs, Jon B. Mechanics of Materials, Vol. 17, Issue 2-3 https://doi.org/10.1016/0167-6636(94)90053-1	journal	March 1994
Dynamic full field measurements of crack tip temperatures Guduru, P. R.; Zehnder, A. T.; Rosakis, A. J. Engineering Fracture Mechanics, Vol. 68, Issue 14 https://doi.org/10.1016/S0013-7944(01)00045-5	journal	September 2001
Micromechanical concept for the analysis of damage evolution in thermo-viscoelastic and quasi-brittle materials Stumpf, H.; Hackl, K. International Journal of Solids and Structures, Vol. 40, Issue 6 https://doi.org/10.1016/S0020-7683(02)00643-1	journal	March 2003
Revisiting brittle fracture as an energy minimization problem Francfort, G. A.; Marigo, J. -J. Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 8 https://doi.org/10.1016/S0022-5096(98)00034-9	journal	August 1998
Damage evolution, localization and failure of solids subjected to impact loading Bai, Y. L.; Bai, J.; Li, H. L. International Journal of Impact Engineering, Vol. 24, Issue 6-7 https://doi.org/10.1016/S0734-743X(99)00151-7	journal	July 2000
Shear localization in dynamic deformation of materials: microstructural evolution and self-organization Meyers, Marc A.; Nesterenko, Vitali F.; LaSalvia, Jerry C. Materials Science and Engineering: A, Vol. 317, Issue 1-2 https://doi.org/10.1016/S0921-5093(01)01160-1	journal	October 2001
Microstructural evolution in adiabatic shear localization in stainless steel Meyers, M. A.; Xu, Y. B.; Xue, Q. Acta Materialia, Vol. 51, Issue 5 https://doi.org/10.1016/S1359-6454(02)00526-8	journal	March 2003
Recrystallization kinetics within adiabatic shear bands Hines, J. A.; Vecchio, K. S. Acta Materialia, Vol. 45, Issue 2 https://doi.org/10.1016/S1359-6454(96)00193-0	journal	February 1997
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits Miehe, Christian; Hofacker, Martina; Welschinger, Fabian Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 45-48 https://doi.org/10.1016/j.cma.2010.04.011	journal	November 2010
A phase-field description of dynamic brittle fracture Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A. Computer Methods in Applied Mechanics and Engineering, Vol. 217-220 https://doi.org/10.1016/j.cma.2012.01.008	journal	April 2012
Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids Miehe, Christian; Schänzel, Lisa-Marie; Ulmer, Heike Computer Methods in Applied Mechanics and Engineering, Vol. 294 https://doi.org/10.1016/j.cma.2014.11.016	journal	September 2015
Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids Miehe, C.; Hofacker, M.; Schänzel, L. -M. Computer Methods in Applied Mechanics and Engineering, Vol. 294 https://doi.org/10.1016/j.cma.2014.11.017	journal	September 2015
A coupled phase field shear band model for ductile–brittle transition in notched plate impacts McAuliffe, Colin; Waisman, Haim Computer Methods in Applied Mechanics and Engineering, Vol. 305 https://doi.org/10.1016/j.cma.2016.02.018	journal	June 2016
A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects Borden, Michael J.; Hughes, Thomas J. R.; Landis, Chad M. Computer Methods in Applied Mechanics and Engineering, Vol. 312 https://doi.org/10.1016/j.cma.2016.09.005	journal	December 2016
A phase-field formulation for dynamic cohesive fracture Geelen, Rudy J. M.; Liu, Yingjie; Hu, Tianchen Computer Methods in Applied Mechanics and Engineering, Vol. 348 https://doi.org/10.1016/j.cma.2019.01.026	journal	May 2019
Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A. Computer Methods in Applied Mechanics and Engineering, Vol. 353 https://doi.org/10.1016/j.cma.2019.05.011	journal	August 2019
A comparative study of shear band tracking strategies in three-dimensional finite elements with embedded weak discontinuities Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A. Finite Elements in Analysis and Design, Vol. 155 https://doi.org/10.1016/j.finel.2018.11.001	journal	March 2019
Effect of secondary orientation on notch-tip plasticity in superalloy single crystals Sabnis, P. A.; Mazière, M.; Forest, S. International Journal of Plasticity, Vol. 28, Issue 1 https://doi.org/10.1016/j.ijplas.2011.06.003	journal	January 2012
A large-deformation gradient theory for elastic–plastic materials: Strain softening and regularization of shear bands Anand, Lallit; Aslan, Ozgur; Chester, Shawn A. International Journal of Plasticity, Vol. 30-31 https://doi.org/10.1016/j.ijplas.2011.10.002	journal	March 2012
Microstructural examination of quasi-static and dynamic shear in high-purity iron Cerreta, E. K.; Bingert, J. F.; Gray, G. T. International Journal of Plasticity, Vol. 40 https://doi.org/10.1016/j.ijplas.2012.06.005	journal	January 2013
On the Taylor–Quinney coefficient in dynamically phase transforming materials. Application to 304 stainless steel Zaera, R.; Rodríguez-Martínez, J. A.; Rittel, D. International Journal of Plasticity, Vol. 40 https://doi.org/10.1016/j.ijplas.2012.08.003	journal	January 2013
Viscoplastic constitutive theory for brittle to ductile damage in polycrystalline materials under dynamic loading Shojaei, Amir; Voyiadjis, George Z.; Tan, P. J. International Journal of Plasticity, Vol. 48 https://doi.org/10.1016/j.ijplas.2013.02.009	journal	September 2013
A fully coupled void damage and Mohr–Coulomb based ductile fracture model in the framework of a Reduced Texture Methodology Rousselier, Gilles; Luo, Meng International Journal of Plasticity, Vol. 55 https://doi.org/10.1016/j.ijplas.2013.09.002	journal	April 2014
A unified model for metal failure capturing shear banding and fracture McAuliffe, Colin; Waisman, Haim International Journal of Plasticity, Vol. 65 https://doi.org/10.1016/j.ijplas.2014.08.016	journal	February 2015
Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations Mourad, H. M.; Bronkhorst, C. A.; Livescu, V. International Journal of Plasticity, Vol. 88 https://doi.org/10.1016/j.ijplas.2016.09.009	journal	January 2017
Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses Levitas, Valery I.; Jafarzadeh, Hossein; Farrahi, Gholam Hossein International Journal of Plasticity, Vol. 111 https://doi.org/10.1016/j.ijplas.2018.07.005	journal	December 2018
Dynamic recrystallization in adiabatic shear banding: Effective-temperature model and comparison to experiments in ultrafine-grained titanium Lieou, Charles K. C.; Bronkhorst, Curt A. International Journal of Plasticity, Vol. 111 https://doi.org/10.1016/j.ijplas.2018.07.011	journal	December 2018
Strain localization and dynamic recrystallization in polycrystalline metals: Thermodynamic theory and simulation framework Lieou, Charles K. C.; Mourad, Hashem M.; Bronkhorst, Curt A. International Journal of Plasticity, Vol. 119 https://doi.org/10.1016/j.ijplas.2019.03.005	journal	August 2019
A length scale insensitive phase-field damage model for brittle fracture Wu, Jian-Ying; Nguyen, Vinh Phu Journal of the Mechanics and Physics of Solids, Vol. 119 https://doi.org/10.1016/j.jmps.2018.06.006	journal	October 2018
Thermal-conductivity degradation across cracks in coupled thermo-mechanical systems modeled by the phase-field fracture method Svolos, Lampros; Bronkhorst, Curt A.; Waisman, Haim Journal of the Mechanics and Physics of Solids, Vol. 137 https://doi.org/10.1016/j.jmps.2019.103861	journal	April 2020
Hybrid scheduling for the parallel solution of linear systems Amestoy, Patrick R.; Guermouche, Abdou; L’Excellent, Jean-Yves Parallel Computing, Vol. 32, Issue 2 https://doi.org/10.1016/j.parco.2005.07.004	journal	February 2006
Assessing predictive schemes for thermal conductivity against diamond-reinforced silver matrix composites at intermediate phase contrast Tavangar, R.; Molina, J. M.; Weber, L. Scripta Materialia, Vol. 56, Issue 5 https://doi.org/10.1016/j.scriptamat.2006.11.008	journal	March 2007
The Electrical Resistance of Binary Metallic Mixtures Landauer, Rolf Journal of Applied Physics, Vol. 23, Issue 7 https://doi.org/10.1063/1.1702301	journal	July 1952
LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium Rayleigh, Lord The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 34, Issue 211 https://doi.org/10.1080/14786449208620364	journal	December 1892
Dynamic Recrystallization as a Potential Cause for Adiabatic Shear Failure Rittel, D.; Landau, P.; Venkert, A. Physical Review Letters, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevLett.101.165501	journal	October 2008
Adiabatic Shear Failure and Dynamic Stored Energy of Cold Work Rittel, D.; Wang, Z. G.; Merzer, M. Physical Review Letters, Vol. 96, Issue 7 https://doi.org/10.1103/PhysRevLett.96.075502	journal	February 2006
Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media Gurson, A. L. Journal of Engineering Materials and Technology, Vol. 99, Issue 1 https://doi.org/10.1115/1.3443401	journal	January 1977
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling Amestoy, Patrick R.; Duff, Iain S.; L'Excellent, Jean-Yves SIAM Journal on Matrix Analysis and Applications, Vol. 23, Issue 1 https://doi.org/10.1137/S0895479899358194	journal	January 2001

Similar Records

Experiments and simulations of directionally dependent fracture along copper/sapphire interfaces

Book · Sun Aug 01 00:00:00 EDT 1999 · OSTI ID:364080

DUCTILE-PHASE TOUGHENED TUNGSTEN FOR PLASMA-FACING MATERIALS IN FUSION REACTORS

Journal Article · Mon May 01 00:00:00 EDT 2017 · International Journal of Powder Metallurgy, 53(2):53-69 · OSTI ID:1390424

Nanoindentation Stress–Strain for Fracture Analysis and Computational Modeling for Hardness and Modulus

Journal Article · Fri Jun 15 00:00:00 EDT 2018 · Journal of Materials Engineering and Performance · OSTI ID:22860466

Related Subjects

42 ENGINEERING
Anisotropic thermal-conductivity
Dynamic fracture
Phase-field method
Thermomechanical processes
Viscoplastic material

Anisotropic thermal-conductivity degradation in the phase-field method accounting for crack directionality

Citation Formats

References (55)

Similar Records

Related Subjects