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Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to AlON
Accepted Manuscript
Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON A.L. Tonge, K.T. Ramesh PII: DOI: Reference:
S0022-5096(17)30452-0 10.1016/j.jmps.2017.05.020 MPS 3126
To appear in:
Journal of the Mechanics and Physics of Solids
Received date: Accepted date:
30 May 2017 31 May 2017
Please cite this article as: A.L. Tonge, K.T. Ramesh, Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON, Journal of the Mechanics and Physics of Solids (2017), doi: 10.1016/j.jmps.2017.05.020
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
CR IP T
Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON A.L. Tonge1 Department of Mechanical Engineering Johns Hopkins University Baltimore, MD 21218 USA
AN US
K.T. Ramesh Department of Mechanical Engineering Johns Hopkins University Baltimore, MD 21218 USA
Abstract
M
A minor error was present in one equation in the original paper, “Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to AlON” and in the corresponding computational implementation. The correction is provided here. None of the primary conclusions of the original paper are affected.
ED
Keywords: Correction, microcracking, dynamic fracture, ceramic, constitutive behavior
AC
CE
PT
An inconsistency between the referenced wing crack growth model [1] and the model that was presented in both of the Tonge and Ramesh JMPS papers [2, 3] was found. In ”Multi-scale defect interactions in high-rate brittle material failure. Part I:Model formulation and application to ALON”, Equation C.1 is missing a factor of cos(φ). It should read: e e e Fw = cos(φ)2s µ σ11 cos2 (φ) + σ22 sin2 (φ) + σ12 sin(2φ) 1 e e e − (σ11 − σ22 ) sin(2φ) − σ12 cos(2φ) . (1) 2
The text of the paper and the computational implementation were both missing the factor of cos(φ). The inconsistency was corrected and all simulations supporting figures in both papers, with the exception of figure 14 in [3], were re-run 1 Currently
at Army Research Laboratory, Aberdeen, MD, USA
Preprint submitted to Elsevier
Tuesday 6th June, 2017
ACCEPTED MANUSCRIPT
CR IP T
using the corrected material model and a flaw size distribution where the flaw sizes were doubled. There were no qualitative differences and the conclusions derived from the simulations are not changed. The update did result in minor quantitative differences, however these differences are on the order of the uncertainty in the model parametrization and do not affect the conclusions.
References
[1] B. Paliwal and K.T. Ramesh. An interacting micro-crack damage model for failure of brittle materials under compression. Journal of the Mechanics and Physics of Solids, 56(3):896–923, 2008. doi: 10.1016/j.jmps.2007.06.012.
AN US
[2] Andrew L. Tonge and K.T. Ramesh. Multi-scale defect interactions in highrate brittle material failure. part I: Model formulation and application to ALON. Journal of the Mechanics and Physics of Solids, 86:117 – 149, 2016. doi: 10.1016/j.jmps.2015.10.007.
AC
CE
PT
ED
M
[3] Andrew L. Tonge and K.T. Ramesh. Multi-scale defect interactions in highrate failure of brittle materials, part II: Application to design of protection materials. Journal of the Mechanics and Physics of Solids, 86:237–258, January 2016. doi: 10.1016/j.jmps.2015.10.006.
2
Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON A.L. Tonge, K.T. Ramesh PII: DOI: Reference:
S0022-5096(17)30452-0 10.1016/j.jmps.2017.05.020 MPS 3126
To appear in:
Journal of the Mechanics and Physics of Solids
Received date: Accepted date:
30 May 2017 31 May 2017
Please cite this article as: A.L. Tonge, K.T. Ramesh, Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON, Journal of the Mechanics and Physics of Solids (2017), doi: 10.1016/j.jmps.2017.05.020
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
CR IP T
Corrigendum to: Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON A.L. Tonge1 Department of Mechanical Engineering Johns Hopkins University Baltimore, MD 21218 USA
AN US
K.T. Ramesh Department of Mechanical Engineering Johns Hopkins University Baltimore, MD 21218 USA
Abstract
M
A minor error was present in one equation in the original paper, “Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to AlON” and in the corresponding computational implementation. The correction is provided here. None of the primary conclusions of the original paper are affected.
ED
Keywords: Correction, microcracking, dynamic fracture, ceramic, constitutive behavior
AC
CE
PT
An inconsistency between the referenced wing crack growth model [1] and the model that was presented in both of the Tonge and Ramesh JMPS papers [2, 3] was found. In ”Multi-scale defect interactions in high-rate brittle material failure. Part I:Model formulation and application to ALON”, Equation C.1 is missing a factor of cos(φ). It should read: e e e Fw = cos(φ)2s µ σ11 cos2 (φ) + σ22 sin2 (φ) + σ12 sin(2φ) 1 e e e − (σ11 − σ22 ) sin(2φ) − σ12 cos(2φ) . (1) 2
The text of the paper and the computational implementation were both missing the factor of cos(φ). The inconsistency was corrected and all simulations supporting figures in both papers, with the exception of figure 14 in [3], were re-run 1 Currently
at Army Research Laboratory, Aberdeen, MD, USA
Preprint submitted to Elsevier
Tuesday 6th June, 2017
ACCEPTED MANUSCRIPT
CR IP T
using the corrected material model and a flaw size distribution where the flaw sizes were doubled. There were no qualitative differences and the conclusions derived from the simulations are not changed. The update did result in minor quantitative differences, however these differences are on the order of the uncertainty in the model parametrization and do not affect the conclusions.
References
[1] B. Paliwal and K.T. Ramesh. An interacting micro-crack damage model for failure of brittle materials under compression. Journal of the Mechanics and Physics of Solids, 56(3):896–923, 2008. doi: 10.1016/j.jmps.2007.06.012.
AN US
[2] Andrew L. Tonge and K.T. Ramesh. Multi-scale defect interactions in highrate brittle material failure. part I: Model formulation and application to ALON. Journal of the Mechanics and Physics of Solids, 86:117 – 149, 2016. doi: 10.1016/j.jmps.2015.10.007.
AC
CE
PT
ED
M
[3] Andrew L. Tonge and K.T. Ramesh. Multi-scale defect interactions in highrate failure of brittle materials, part II: Application to design of protection materials. Journal of the Mechanics and Physics of Solids, 86:237–258, January 2016. doi: 10.1016/j.jmps.2015.10.006.
2