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A comparison of Gurson and Cocks–Ashby porosity kinetics and degradation functions

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Abstract

Effects of porosity play a key role in ductile fracture and many modern metals are less than fully dense with a finite porosity created either unintentionally (as in additively manufactured or powder processed materials) or intentionally (as in metallic meta-materials and foams). This study compares the Gurson and Cocks–Ashby models’ predictions of porosity evolution (kinetics) and material degradation against unit cell simulations of a strain-rate dependent material under varying triaxiality. Previous comparisons do not address varying triaxiality and direct comparisons between the Gurson and Cocks–Ashby models are limited. This study also uses triaxiality, flow stress, strain rate, and strain-rate sensitivity from unit cell simulations as inputs to each model to give an accurate depiction of the models’ performance under complex evolving loading and material states. A fitting procedure for porosity evolution is also shown. This study shows the overall predictive power of the Gurson model over the Cocks–Ashby model. It also highlights the accuracy of the Cocks–Ashby porosity evolution model and Cocks–Ashby degradation function when each model is calibrated independently.

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Acknowledgements

The author would like to thank Nathan Barton for his input and discussions regarding poro-plasticity modeling and Lawrence Livermore National Laboratory’s Visiting Scientists and Professionals program.

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  1. Department of Mechanical Engineering, Marquette University, Haggerty Hall, Room 225, 1515 W Wisconsin Ave, Milwaukee, WI, 53233, USA

    John A. Moore & Andrew Frasca

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  1. John A. Moore
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  2. Andrew Frasca
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Correspondence to John A. Moore.

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Appendix

Appendix

1.1 A1: Calibrated degradation function parameters

See Table 2 and Table 3 for calibrated degradation function parameters.

Table 2 Cocks–Ashby degradation function parameters
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Table 3 Phenomenological and Gurson degradation function parameters
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1.2 A2: Abaqus user MPC subroutine

figure a

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Moore, J.A., Frasca, A. A comparison of Gurson and Cocks–Ashby porosity kinetics and degradation functions. Int J Fract 229, 253–268 (2021). https://doi.org/10.1007/s10704-021-00539-6

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  • DOI: https://doi.org/10.1007/s10704-021-00539-6

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