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Multi-length scale micromorphic process zone model

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Abstract

The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix–particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.

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Authors and Affiliations

  1. Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Campus Box 428, Boulder, CO, 80309-0428, USA

    Franck Vernerey

  2. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208-3111, USA

    Wing Kam Liu

  3. Department of Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208-3111, USA

    Brian Moran

  4. Department of Material Science and Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208-3111, USA

    Gregory Olson

Authors
  1. Franck Vernerey
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  2. Wing Kam Liu
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  3. Brian Moran
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  4. Gregory Olson
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Corresponding authors

Correspondence to Franck Vernerey or Wing Kam Liu.

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Vernerey, F., Liu, W.K., Moran, B. et al. Multi-length scale micromorphic process zone model. Comput Mech 44, 433–445 (2009). https://doi.org/10.1007/s00466-009-0382-7

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  • DOI: https://doi.org/10.1007/s00466-009-0382-7

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