Experimental and numerical nanoscale investigation of damage and fracture processes in glass

Progression of a stress corrosion crack in pure silica. The mean crack velocity measured at the micrometer scale was 30 pm/s

Cindy Lynn ROUNTREE, Silke PRADES, Daniel BONAMY, Davy DALMAS, Claude GUILLOT, Elisabeth BOUCHAUD*Coll. with Rajiv KALIA (University of Southern California, Los Angeles, USA)*

Fracture of pure silica, a “minimal” elastic material has been explored both experimentally and through numerical simulations. In both cases, the crack was shown to progress through the growth and coalescence of damage cavities ahead of the front. This mechanism was shown to be responsible for small scales non linear elastic behaviour both for ultraslow stress corrosion and dynamic fracture.

*1.2.1. – Fracture mechanism *

Stress corrosion ultraslow (average crack velocity ranging from 1 to 100 pm/s) mode I cracks in pure amorphous silica were followed with an Atomic Force Microscope (AFM) /1/, revealing the nucleation, growth and coalescence of damage cavities (see Fig. 1).

In order to investigate the precise dynamics of crack propagation, we plotted the spatio-temporal diagram showing the evolution of the various fronts: main crack front (A in Fig. 1), rear- and fore-fronts of the cavity (respectively B and C in Fig. 1). These trajectories are shown in Fig. 2. From this plot, one could measure the mean velocities of the various fronts: V_{A}≈3 pm/s, V_{C}≈8 pm/s and V_{B}≈9 pm/s for the main crack tip, the forward front and the backward front of the cavity respectively. All these velocities, including V_{A}, are significantly smaller than the crack tip velocity measured at the continuous scale, 30 pm/s.

As a matter of fact, at these small scales, the crack front does not propagate regularly, and the largest contribution to the crack velocity is due to its merging with the cavities.

Molecular Dynamics (MD) simulations of mode I dynamic fracture were also performed on an amorphous silica specimen of size (120.6 nm)^{3} composed of 110 million atoms. Three mean crack growth velocity regimes were observed, at 10, 300 and 1300 m/s. Although at much smaller scales than in the experiment, the same mechanism involving the nucleation, growth and coalescence of damage cavities was observed. It was also shown to be at the origin of a departure from linear elasticity observed in the vicinity of the crack tip.

Top experiment, mean crack speed 0.15 nm/s; Bottom simulation, 300 m/s. Both insets show the topography of the sample surface near the crack tip (thick black arrow).

Main figures show the variation of the vertical displacement with r on logarithmic scales.

Blue circles correspond to measured data while the red line corresponds to 1/r^{1/2} . The experimental and numerical profiles depart from this scaling at distances r from the crack tip smaller than 100 nm and 10nm, respectively.

1.2.2. – Departure from linear elasticity

The process zone was determined both in experiments and simulations /2/. In an elastic medium, the stress field exhibits a square root singularity at the crack tip. As long as the linear elastic stress/strain relation remains valid, one expects also a square root singularity in the components of the strain tensor, and in the out-of-plane displacement at the free surface. We have compared the surface topography in the vicinity of the crack tip as observed both in experiments and in simulations to this prediction. Fig.3 presents a height profile taken along the direction of crack propagation. Far from the crack tip, this profile is well fitted by the 1/r^{1/2} law. But the experimental profile departs from this scaling below a given value R_{c}, which sets the length of the process zone. This value was observed to be of a few hundreds of nanometers in stress corrosion, and significantly smaller, a few tens of nanometers, in dynamic fracture. As a matter of fact, R_{c} decreases with the average crack speed.

In order to prove that nanocavitation is the dominant mechanism responsible for departure from linear elasticity, we compare the extension of the region containing the cavities, ahead of the crack tip, to the extent of the non linear elastic zone size. Since AFM observations are confined to the free surface of the sample, they cannot provide such information and we resort to the MD simulations. We consider a slice of material of size r (along the direction of crack propagation) x 10nm x 120nm. We compute the cumulative porosity Φ(r) in the direction of crack propagation as the ratio between the total volume of pores embedded and the total volume of the slice. For r larger than the porous region size, one expects to observe no pores and Φ(r) decreases in 1/r, according to its definition. Departure from this law happens at 3 nm, 10 nm and 25 nm from the crack tip for velocities of 10 m/s, 300 m/s, and 1300 m/s respectively. These values are similar to the values R_{c} limiting the distance from the crack tip below which the out-of-plane deformation departs from the 1/r^{1/2} law.

.The cavitation process, involved both in stress corrosion and in dynamic fracture, finds its origin in the amorphous structure of silica, which contains silica tetrahedra connected at the corners to form rings of various sizes. At larger length scales, the density of these rings was found to fluctuate with high density areas surrounded by low density areas /3/. These low density area constitute “weaker” regions, where pores nucleate preferentially. These pores act as stress concentrators and grow under the stress imposed by the presence of the main crack to give rise to nanocavities.

REFERENCES:

[1] S. Prades, D. Bonamy, D. Dalmas, E. Bouchaud, C. Guillot., *Int. J. of Solids and Structures* **42**, 637 (2005)

[2] D. Bonamy, S. Prades, C.L. Rountree, L. Ponson, D. Dalmas, E. Bouchaud, K. Ravi-Chandar, C. Guillot, *Int. J. of Fracture* **140**, 3 (2006)

[3] C.L. Rountree, R.K. Kalia, E. Lidorikis, A. Nakano, L. Van Brutzel, P. Vashishta, *Annu. Rev. Mater. Res.* **32**, 377 (2002)

Maj : 24/11/2009 (777)

• Systèmes complexes et transition énergétique › Statistical physics in mechanics

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