Fractional strain gradient plasticity and ductile fracture of metals
Abstract
We present an optimal scaling analysis based on (possibly fractional) strain-gradient plasticity. The analysis yields optimal scaling laws, in the sense of upper and lower bounds of a power-law type with matching exponents, connecting macroscopic fracture properties, such as the critical elongation at failure and the specific fracture energy, to microscopic mechanisms such as cleavage and microplasticity. We show that an optimal upper bound can be derived from an exceedingly simple test deformation that opens up a sheet of parallelepipedic voids. We also show that an optimal lower bound can be obtained by relaxing compatibility between transverse fibers, which effectively renders the analysis one-dimensional. The analysis predicts a 'gating effect' of the surface energy. Specifically, a critical surface energy arises from the analysis that marks a sharp transition between brittle and ductile behavior. When the surface energy of the material exceeds the threshold value, the macroscopic specific fracture energy is predicted to rise sharply as a power of the surface energy with an exponent defined precisely by the theory.
Copyright and License
© 2023 Elsevier Masson.
Acknowledgement
S. Conti and M. Ortiz gratefully acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060; project 441211072 - SPP 2256; and project 390685813 - GZ 2047/1 - HCM. P. Ariza gratefully acknowledges financial support from the Consejería de Economía y Conocimiento of the Junta de Andalucía, Spain, under grant number P18-RT-1485; and from Ministerio de Ciencia e Innovación, Spain under grant number PID2021-124869NB-I00.
Data Availability
Data will be made available on request.
Conflict of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional Information
Dedicated, grato animo, to Viggo Tvergaard, admired scientist, generous mentor.
Additional details
- Deutsche Forschungsgemeinschaft
- 211504053 - SFB 1060
- Deutsche Forschungsgemeinschaft
- 441211072 - SPP 2256
- Deutsche Forschungsgemeinschaft
- 390685813 - GZ 2047/1
- Junta de Andalucía
- P18-RT-1485
- Ministerio de Ciencia, Innovación y Universidades
- PID2021-124869NB-I00
- Caltech groups
- GALCIT