Phase-field modeling of the interactions between an edge dislocation and an array of obstacles

Shuozhi Xu; Justin Y Cheng; Zezhou Li; Nathan A. Mara; Irene J. Beyerlein

doi:10.1016/j.cma.2021.114426

Phase-field modeling of the interactions between an edge dislocation and an array of obstacles

Shuozhi Xu, Justin Y Cheng, Zezhou Li, Nathan A. Mara, Irene J. Beyerlein

Chemical Engineering and Materials Science

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Obstacles, such as voids and precipitates, are prevalent in crystalline materials. They strengthen crystals by serving as barriers to dislocation glide. In this work, we develop a phase-field dislocation dynamics (PFDD) technique for investigating the interactions between dislocations and second-phase obstacles, which can be either voids or precipitates. The PFDD technique is constructed to account for elastic heterogeneity, elastic anisotropy, dissociation of the dislocation, and dislocation transmission across bicrystalline interfaces. Within the framework, we present a model for “pseudo-voids”, which are voids shearable by dislocations, in contrast to unphysical, unshearable voids in conventional phase-field dislocation formulations. We employ the PFDD technique to investigate the in-plane interactions between an edge dislocation and an array of nano-scale obstacles with different spacings. In this application, the interactions take place in glide planes of either a face-centered cubic (FCC) Cu or a body-centered cubic (BCC) Nb matrix, while the precipitates have a Cu_1−xNb_x composition, with x varying from 0.1 to 0.9. Our atomistic simulations find that the alloy precipitates can have an FCC, an amorphous, or a BCC phase, depending on the compositional ratio between Cu and Nb, i.e., value of x. Among all types of obstacles, the critical stresses for dislocation bypass are the highest for unshearable amorphous precipitates, followed by shearable crystalline precipitates, and then the pseudo-voids.

Original language	English (US)
Article number	114426
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	389
DOIs	https://doi.org/10.1016/j.cma.2021.114426
State	Published - Feb 1 2022

Bibliographical note

Funding Information:
We thank Dr. Yifei Zeng, Dr. Xiaoyao Peng, Mr. Wu-Rong Jian, and Ms. Ashley Roach for helpful discussions. The authors gratefully acknowledge financial support from the Department of Energy, Office of Science, Basic Energy Sciences Program, USA DE-SC0020133 . JYC is supported by DOE NNSA SSGF, USA under cooperative agreement number DE-NA0003960 . Use was made of computational facilities purchased with funds from the National Science Foundation, USA ( CNS-1725797 ) and administered by the Center for Scientific Computing (CSC), USA . The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center, USA (MRSEC; NSF DMR 1720256 ) at UC Santa Barbara. JYC, ZL, and NAM acknowledge the Minnesota Supercomputing Institute at the University of Minnesota ( http://www.msi.umn.edu ) for providing resources that contributed to the research results reported within this paper.

Funding Information:
We thank Dr. Yifei Zeng, Dr. Xiaoyao Peng, Mr. Wu-Rong Jian, and Ms. Ashley Roach for helpful discussions. The authors gratefully acknowledge financial support from the Department of Energy, Office of Science, Basic Energy Sciences Program, USADE-SC0020133. JYC is supported by DOE NNSA SSGF, USA under cooperative agreement number DE-NA0003960. Use was made of computational facilities purchased with funds from the National Science Foundation, USA (CNS-1725797) and administered by the Center for Scientific Computing (CSC), USA. The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center, USA (MRSEC; NSF DMR 1720256) at UC Santa Barbara. JYC, ZL, and NAM acknowledge the Minnesota Supercomputing Institute at the University of Minnesota (http://www.msi.umn.edu) for providing resources that contributed to the research results reported within this paper.

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Dislocation/obstacle interactions
Phase-field dislocation dynamics
Precipitate
Void

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10.1016/j.cma.2021.114426

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@article{b10c4e145f114966a370cd64eca7241b,

title = "Phase-field modeling of the interactions between an edge dislocation and an array of obstacles",

abstract = "Obstacles, such as voids and precipitates, are prevalent in crystalline materials. They strengthen crystals by serving as barriers to dislocation glide. In this work, we develop a phase-field dislocation dynamics (PFDD) technique for investigating the interactions between dislocations and second-phase obstacles, which can be either voids or precipitates. The PFDD technique is constructed to account for elastic heterogeneity, elastic anisotropy, dissociation of the dislocation, and dislocation transmission across bicrystalline interfaces. Within the framework, we present a model for “pseudo-voids”, which are voids shearable by dislocations, in contrast to unphysical, unshearable voids in conventional phase-field dislocation formulations. We employ the PFDD technique to investigate the in-plane interactions between an edge dislocation and an array of nano-scale obstacles with different spacings. In this application, the interactions take place in glide planes of either a face-centered cubic (FCC) Cu or a body-centered cubic (BCC) Nb matrix, while the precipitates have a Cu1−xNbx composition, with x varying from 0.1 to 0.9. Our atomistic simulations find that the alloy precipitates can have an FCC, an amorphous, or a BCC phase, depending on the compositional ratio between Cu and Nb, i.e., value of x. Among all types of obstacles, the critical stresses for dislocation bypass are the highest for unshearable amorphous precipitates, followed by shearable crystalline precipitates, and then the pseudo-voids.",

keywords = "Dislocation/obstacle interactions, Phase-field dislocation dynamics, Precipitate, Void",

author = "Shuozhi Xu and Cheng, {Justin Y} and Zezhou Li and Mara, {Nathan A.} and Beyerlein, {Irene J.}",

note = "Funding Information: We thank Dr. Yifei Zeng, Dr. Xiaoyao Peng, Mr. Wu-Rong Jian, and Ms. Ashley Roach for helpful discussions. The authors gratefully acknowledge financial support from the Department of Energy, Office of Science, Basic Energy Sciences Program, USA DE-SC0020133 . JYC is supported by DOE NNSA SSGF, USA under cooperative agreement number DE-NA0003960 . Use was made of computational facilities purchased with funds from the National Science Foundation, USA ( CNS-1725797 ) and administered by the Center for Scientific Computing (CSC), USA . The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center, USA (MRSEC; NSF DMR 1720256 ) at UC Santa Barbara. JYC, ZL, and NAM acknowledge the Minnesota Supercomputing Institute at the University of Minnesota ( http://www.msi.umn.edu ) for providing resources that contributed to the research results reported within this paper. Funding Information: We thank Dr. Yifei Zeng, Dr. Xiaoyao Peng, Mr. Wu-Rong Jian, and Ms. Ashley Roach for helpful discussions. The authors gratefully acknowledge financial support from the Department of Energy, Office of Science, Basic Energy Sciences Program, USADE-SC0020133. JYC is supported by DOE NNSA SSGF, USA under cooperative agreement number DE-NA0003960. Use was made of computational facilities purchased with funds from the National Science Foundation, USA (CNS-1725797) and administered by the Center for Scientific Computing (CSC), USA. The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center, USA (MRSEC; NSF DMR 1720256) at UC Santa Barbara. JYC, ZL, and NAM acknowledge the Minnesota Supercomputing Institute at the University of Minnesota (http://www.msi.umn.edu) for providing resources that contributed to the research results reported within this paper. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

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doi = "10.1016/j.cma.2021.114426",

language = "English (US)",

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T1 - Phase-field modeling of the interactions between an edge dislocation and an array of obstacles

AU - Xu, Shuozhi

AU - Cheng, Justin Y

AU - Li, Zezhou

AU - Mara, Nathan A.

AU - Beyerlein, Irene J.

N1 - Funding Information: We thank Dr. Yifei Zeng, Dr. Xiaoyao Peng, Mr. Wu-Rong Jian, and Ms. Ashley Roach for helpful discussions. The authors gratefully acknowledge financial support from the Department of Energy, Office of Science, Basic Energy Sciences Program, USA DE-SC0020133 . JYC is supported by DOE NNSA SSGF, USA under cooperative agreement number DE-NA0003960 . Use was made of computational facilities purchased with funds from the National Science Foundation, USA ( CNS-1725797 ) and administered by the Center for Scientific Computing (CSC), USA . The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center, USA (MRSEC; NSF DMR 1720256 ) at UC Santa Barbara. JYC, ZL, and NAM acknowledge the Minnesota Supercomputing Institute at the University of Minnesota ( http://www.msi.umn.edu ) for providing resources that contributed to the research results reported within this paper. Funding Information: We thank Dr. Yifei Zeng, Dr. Xiaoyao Peng, Mr. Wu-Rong Jian, and Ms. Ashley Roach for helpful discussions. The authors gratefully acknowledge financial support from the Department of Energy, Office of Science, Basic Energy Sciences Program, USADE-SC0020133. JYC is supported by DOE NNSA SSGF, USA under cooperative agreement number DE-NA0003960. Use was made of computational facilities purchased with funds from the National Science Foundation, USA (CNS-1725797) and administered by the Center for Scientific Computing (CSC), USA. The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center, USA (MRSEC; NSF DMR 1720256) at UC Santa Barbara. JYC, ZL, and NAM acknowledge the Minnesota Supercomputing Institute at the University of Minnesota (http://www.msi.umn.edu) for providing resources that contributed to the research results reported within this paper. Publisher Copyright: © 2021 Elsevier B.V.

PY - 2022/2/1

Y1 - 2022/2/1

N2 - Obstacles, such as voids and precipitates, are prevalent in crystalline materials. They strengthen crystals by serving as barriers to dislocation glide. In this work, we develop a phase-field dislocation dynamics (PFDD) technique for investigating the interactions between dislocations and second-phase obstacles, which can be either voids or precipitates. The PFDD technique is constructed to account for elastic heterogeneity, elastic anisotropy, dissociation of the dislocation, and dislocation transmission across bicrystalline interfaces. Within the framework, we present a model for “pseudo-voids”, which are voids shearable by dislocations, in contrast to unphysical, unshearable voids in conventional phase-field dislocation formulations. We employ the PFDD technique to investigate the in-plane interactions between an edge dislocation and an array of nano-scale obstacles with different spacings. In this application, the interactions take place in glide planes of either a face-centered cubic (FCC) Cu or a body-centered cubic (BCC) Nb matrix, while the precipitates have a Cu1−xNbx composition, with x varying from 0.1 to 0.9. Our atomistic simulations find that the alloy precipitates can have an FCC, an amorphous, or a BCC phase, depending on the compositional ratio between Cu and Nb, i.e., value of x. Among all types of obstacles, the critical stresses for dislocation bypass are the highest for unshearable amorphous precipitates, followed by shearable crystalline precipitates, and then the pseudo-voids.

AB - Obstacles, such as voids and precipitates, are prevalent in crystalline materials. They strengthen crystals by serving as barriers to dislocation glide. In this work, we develop a phase-field dislocation dynamics (PFDD) technique for investigating the interactions between dislocations and second-phase obstacles, which can be either voids or precipitates. The PFDD technique is constructed to account for elastic heterogeneity, elastic anisotropy, dissociation of the dislocation, and dislocation transmission across bicrystalline interfaces. Within the framework, we present a model for “pseudo-voids”, which are voids shearable by dislocations, in contrast to unphysical, unshearable voids in conventional phase-field dislocation formulations. We employ the PFDD technique to investigate the in-plane interactions between an edge dislocation and an array of nano-scale obstacles with different spacings. In this application, the interactions take place in glide planes of either a face-centered cubic (FCC) Cu or a body-centered cubic (BCC) Nb matrix, while the precipitates have a Cu1−xNbx composition, with x varying from 0.1 to 0.9. Our atomistic simulations find that the alloy precipitates can have an FCC, an amorphous, or a BCC phase, depending on the compositional ratio between Cu and Nb, i.e., value of x. Among all types of obstacles, the critical stresses for dislocation bypass are the highest for unshearable amorphous precipitates, followed by shearable crystalline precipitates, and then the pseudo-voids.

KW - Dislocation/obstacle interactions

KW - Phase-field dislocation dynamics

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KW - Void

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ER -

Phase-field modeling of the interactions between an edge dislocation and an array of obstacles

Abstract

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