Abstract
A damage law for dynamic failure in brittle solids is proposed in the present note. The new evolution equation is obtained by incorporating the Grady–Glenn–Chudnovsky average fragment size expression as the microstructural length of a two-scale damage model. In this construction, the internal length of the model explicitly depends on the local strain rate and the material parameters. The capacity of the new approach to account for the strain-rate sensitivity of the tensile strength is illustrated by comparison of the predicted material and structural responses with experimental data for concrete and ceramic materials.
References
Atiezo KM, Chen W, Dascalu C (2019) Loading rate effects on dynamic failure of quasi-brittle solids: Simulations with a two-scale damage model. Theor Appl Fract Mech 100:269–280
Daphalapurkar NP, Ramesh KT, Graham-Brady L, Molinari J-F (2011) Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws. J Mech Phys Solids 59(2):297–319
Dascalu C (2018) Multiscale modeling of rapid failure in brittle solids: branching instabilities. Mech Mater 199:2765–2778
Dascalu C, Gbetchi K (2019) Dynamic evolution of damage by microcracking with heat dissipation. Int J Solids Struct 174–175:128–144
Drugan WJ (2001) Dynamic fragmentation of brittle materials: analytical mechanics-based models. J Mech Phys Solids 49:1181–1208
Erzar B (2010) Ecaillage, cratérisation et comportement en traction dynamique de bétons sous impact: approches expérimentales et modélisation. Metz, France PhD thesis
Erzar B, Forquin P (2014) Analysis and modelling of the cohesion strength of concrete at high strain-rates. Int J Solids Struct 51:2559–2574
Galvez Diaz-Rubio F, Rodriguez Perez J, Sanchez Galvez V (2002) The spalling of long bars as a reliable method of measuring the dynamic tensile strength of ceramics. Int J Impact Eng 27:161–177
Glenn LA, Chudnovsky A (1986) Strain-energy effects on dynamic fragmentation. J Appl Phys 59:1379–1380
Grady DE (1982) Local inertial effects in dynamic fragmentation. J Appl Phys 53:322–325
Grady DE (2010) Length scales and size distributions in dynamic fragmentation. Int J Fract 163:85–99
Hu G, Liu J, Graham-Brady L, Ramesh KT (2015) A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading. J Mech Phys Solids 78:269–297
Keita O, Dascalu C, François B (2014) A two-scale model for dynamic damage evolution. J Mech Phys Solids 64:170–183
Kimberley J, Ramesh KT, Daphalapurkar NP (2013) A scaling law for the dynamic strength of brittle solids. Acta Mater 61(9):3509–3521
Levy S, Molinari J-F (2010) Dynamic fragmentation of ceramics, signature of defects and scaling of fragment sizes. J Mech Phys Solids 58:12–26
Najar J (1994) Dynamic tensile fracture phenomena at wave propagation in ceramic bars. J Phys IV 4:C8-647–C8-652
Pham K, Marigo JJ (2013) From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models. Cont Mech Thermodyn 25:147–171
Swanson GD (1972) Fracture energies of ceramics. J Am Ceram Soc 55:48–49
Zhou F, Molinari JF, Ramesh KT (2006) Characteristic fragment size distributions in dynamic fragmentation. Appl Phys Lett 88:2619181–3
Zinszner JL, Erzar B, Forquin P, Buzaud E (2015) Dynamic fragmentation of an alumina ceramic subjected to shockless spalling: An experimental and numerical study. J Mech Phys Solids 85:112–127
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Dascalu, C. Dynamic Damage Law with Fragmentation Length: Strain-Rate Sensitivity of the Tensile Response. J. dynamic behavior mater. 7, 156–160 (2021). https://doi.org/10.1007/s40870-020-00262-8
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DOI: https://doi.org/10.1007/s40870-020-00262-8