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Research Papers

Rate-Dependent Scaling of Dynamic Tensile Strength of Quasibrittle Structures

[+] Author and Article Information
Jia-Liang Le

Department of Civil, Environmental,
and Geo- Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: jle@umn.edu

Jan Eliáš, Josef Květoň

Faculty of Civil Engineering,
Brno University of Technology,
Brno 602 00, Czechia

Anna Gorgogianni, Joshua Vievering

Department of Civil, Environmental,
and Geo- Engineering,
University of Minnesota,
Minneapolis, MN 55455

1Corresponding author.

Manuscript received October 11, 2017; final manuscript received November 12, 2017; published online December 11, 2017. Editor: Yonggang Huang.

J. Appl. Mech 85(2), 021003 (Dec 11, 2017) (12 pages) Paper No: JAM-17-1568; doi: 10.1115/1.4038496 History: Received October 11, 2017; Revised November 12, 2017

This paper investigates the effect of strain rate on the scaling behavior of dynamic tensile strength of quasibrittle structures. The theoretical framework is anchored by a rate-dependent finite weakest link model. The model involves a rate-dependent length scale, which captures the transition from localized damage to diffused damage with an increasing strain rate. As a result, the model predicts a rate- and size-dependent probability distribution function of the nominal tensile strength. The transitional behavior of the strength distribution directly leads to the rate and size effects on the mean and standard deviation of the tensile strength. The model is verified by a series of stochastic discrete element simulations of dynamic fracture of aluminum nitride specimens. The simulations involve a set of geometrically similar specimens of various sizes subjected to a number of different strain rates. Both random microstructure geometry and fracture properties are considered in these simulations. The simulated damage pattern indicates that an increase in the strain rate results in a more diffusive cracking pattern, which supports the theoretical formulation. The simulated rate and size effects on the mean and standard deviation of the nominal tensile strength agree well with the predictions by the rate-dependent finite weakest link model.

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Figures

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Fig. 1

A rectangular specimen loaded by a prescribed strain rate: (a) schematic of the specimen and (b) weakest link model representation

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Fig. 2

Modeling of strength distribution of one RVE: (a) hierarchical model of a static RVE and (b) fiber-bundle model of a RVE under high strain-rate loading

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Fig. 3

Representation of discrete element model: (a) domain discretization and (b) Voronoi body and facet

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Fig. 4

A typical realization of the random field h(x)

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Fig. 5

Simulated average nominal stress–strain curves for different specimens sizes and strain rates

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Fig. 6

Simulated damage patterns of specimens of D = 400 μm at peak load

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Fig. 7

Simulated mean size effect curves of nominal strength at different strain rates and the optimum fits by the rate-dependent finite weakest link model

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Fig. 8

Strain rate effect on the RVE size

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Fig. 9

Influence of strain rate on the statistical parameters of P1N)

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Fig. 10

Simulated size effects on the standard deviation of nominal strength at different strain rates and its comparison with the rate-dependent finite weakest link model

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