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Archive of Applied Mechanics

, Volume 88, Issue 7, pp 1105–1119 | Cite as

A multiscale model for post-peak softening response of concrete and the role of microcracks in the interfacial transition zone

  • Keerthy M. Simon
  • J. M. Chandra Kishen
Original
  • 130 Downloads

Abstract

The effect of microcracks ahead of a macrocrack on the post-peak behavior of concrete-like quasi-brittle material is studied. The critical length of a microcrack is estimated by considering a small element near the macrocrack tip and defining the critical crack opening displacement of the microcrack that exist in the interface region between the aggregate and cement paste. A fracture model is proposed to predict the post-peak response of plain concrete. This model is validated using the experimental results for normal-strength, high-strength and self-consolidating concretes available in the literature. Through a sensitivity analysis, it is observed that the elastic modulus of concrete and the fracture toughness of the interface have a substantial influence on the critical microcrack length.

Keywords

Microstructure Interfacial transition zone Concrete Fracture process zone 

List of symbols

ITZ

Interfacial transition zone

FPZ

Fracture process zone

\(\phi \)

Airy stress function

\(F_n(\theta )\)

Eigenfunctions

\(\lambda _n\)

Eigenvalue

\(\mu _{\mathrm{micro}}\)

Shear modulus corresponding to the microscale

\(\nu _{\mathrm{micro}}\)

Poisson’s ratio corresponding to the microscale

\(K_{\mathrm{Ic}}^{\mathrm{Interface}}\)

Mode I fracture toughness of interface

\(E^{\mathrm{Interface}}\)

Elastic modulus of interface

\(d_{\mathrm{c}}\)

Critical length of microcrack

\(\sigma _y\)

Tensile strength of interface

\(\delta _{\mathrm{c}}\)

Critical crack opening displacement of microcrack

\(\delta _{\mathrm{p}}\)

Crack mouth opening displacement corresponding to the peak load

\(V_{\mathrm{f}}(\mathrm{ca})\)

Volume fraction of coarse aggregate

\(V_{\mathrm{f}}(\mathrm{fa})\)

Volume fraction of fine aggregate

\(V_{\mathrm{f}}(\mathrm{m})\)

Volume fraction of mortar

\(V_{\mathrm{f}}(\mathrm{cp})\)

Volume fraction of cement paste

\(\nu _{\mathrm{eff}}\)

Poissons ratio of concrete

\(\nu _{\mathrm{m}}\)

Poissons ratio of mortar

\(E_{\mathrm{ca}}\)

Elastic modulus of coarse aggregate

\(E_{\mathrm{fa}}\)

Elastic modulus of fine aggregate

\(E_{\mathrm{m}}\)

Elastic modulus of mortar

\(E_{\mathrm{cp}}\)

Elastic modulus of cement paste

\(V_{\mathrm{f}}\)

Total volume fraction

\(m_i\)

Mass of each constituent

\(\rho _i\)

Density of each constituent

D

Depth of specimen

S

Span of the specimen

B

Thickness of the specimen

a

Crack length

\(a_{\mathrm{c}}\)

Crack length corresponding to peak load

\(d_{\mathrm{c}}\)

Critical microcrack length

\(\delta ^{\mathrm{M}}\)

Crack opening displacement corresponding to peak load

\(\delta ^{\mathrm{m}}\)

Microcrack opening displacement

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of ScienceBangaloreIndia

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