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Analysis and computations of oscillating crack propagation in a heated strip

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Abstract

This paper presents a computational analysis and several simulations of an existing experiment, which deals with a quasi-static thermal crack propagation in a glass plate. The experimental observation was that a straight or oscillatory crack propagation occurred depending on the plate width and thermal loading. The goal here is to simulate this experiment with the recent numerical tool such as XFEM. First, the analysis of the settings of the experiment is developed by providing the computed energy release rate of the crack for a wide range of experiment settings parameters. Second, different crack propagations are simulated, and show a good agreement with the experimental observation of straight or oscillatory paths. Third, a study of the results given by the fracture criteria (maximum hoop stress and Local Symmetry criteria) is also presented for this particular experiment in order to evaluate their differences.

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Abbreviations

\({a, \dot{a}}\) :

Crack length and velocity

t :

Time

T :

Temperature

\({{\underline{\underline{\sigma}}}}\) :

Stress tensor

\({{\underline{\underline{\varepsilon}}}}\) :

Strain tensor

\({\mathbb{C}}\) :

Linear elastic behavior law

\({\underline{\underline{I_d}}}\) :

Identity matrix

K1, K2:

Stress intensity factors

θ c :

Crack angle

G :

Energy release rate

α :

Coefficient of thermal expansion

ρ :

Density

E :

Young’s modulus

ν :

Poisson’s ratio

k :

Thermal conductivity

D :

Thermal diffusivity

c p :

Specific heat capacity

c r :

Rayleigh wave speeds

K Ic :

Fracture toughness

G c :

Critical energy release rate

z :

Vertical position of the crack tip

T hot :

Temperature of the oven

T cold :

Temperature of the water

ΔT = T hot − T cold :

Temperature difference

V :

Dipping velocity

h :

Distance water-oven

w :

Plate width

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Authors and Affiliations

  1. Northwestern University, Theoretical and Applied Mechanics, 2145 Sheridan Road, Evanston, IL, 60208-3111, USA

    Thomas Menouillard & Ted Belytschko

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  1. Thomas Menouillard
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  2. Ted Belytschko
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Correspondence to Thomas Menouillard.

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Menouillard, T., Belytschko, T. Analysis and computations of oscillating crack propagation in a heated strip. Int J Fract 167, 57–70 (2011). https://doi.org/10.1007/s10704-010-9519-0

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