3.22 | Spring 2008 | Graduate

Mechanical Behavior of Materials


Role of Water in Accelerated Fracture of Fiber Optic Glass - Problem Set 5

(b) Michalske [1] predicted that water molecules assisted bond breaking in silica long before it was observed directly in atomistic simulations. In his 1984 paper, Fig. 6 is a little hard to understand at first. Make this the inset in a larger figure that shows a macroscopic crack, the direction of loading to open that crack in Mode I, and the direction of propagation of that crack.

Below is a larger figure that shows the macroscopic crack. The figure 6 is the one from Michalske’s 1984 paper. It is an atomic view of the crack front separating severed from intact bonds.

The direction of loading during mode 1 is normal to the crack faces.


Portion of image removed due to copyright restrictions. Please see Fig. 6 in [1].


(c) Explain chemically assisted fracture so that anyone in 3.22 would understand it, using Michalske’s Fig. 7 type graphics [1] to illustrate the interaction of water with silica at the molecular level.


Image removed due to copyright restrictions. Please see Fig. 7 in [1].


The diagram above shows an example of a chemically assisted fracture mechanism; in this case, how an active molecule (such as H2O or NH3) can assist the breaking of strained Si-O-Si bonds, ie. the kink on fig. 6 in question b. The steps are as follows:

  1. The initial silica surface, in the absence of applied strain.
  2. Under applied tension, silica initially responds by changing its conformation but retaining tetrahedral bond angles around the Si molecules.
  3. As the tension increases the Si-O-Si bonds elongate to form an angle of 180° around the bridging oxygens. This step is almost costless (4 kcal/mol) and has little effect on the bond reactivity.
  4. Finally, certain silicon atoms are forced to give up their tetrahedral molecular orbital configuration. In this strained state, the bridging Si-O-Si bond has a strongly increased reactivity.
  5. The Si-O-Si bond reacts with H2O and is cleaved into 2-OH terminal groups.

(d) Michalske’s argument [1] necessarily implies that the amount of chemical in the environment affects the speed of crack growth. Assume an initial, through-thickness crack of width 150 nm at the surface of a sheet of silica that is 1 cm thick. The crack is under Mode I loading. From Michalske’s Fig. 2, how long would it take for that crack to grow another 150 nm under an applied stress of 100 MPa in an environment of 100% water?


Image removed due to copyright restrictions. Please see Fig. 2 in [1].


In class we saw that the stress intensity KI in Mode I loading is calculated by

where c is the crack size and f is a factor close to unity. Using the crack size and stress values given, we get a value KI = 0.069 MPa m1/2. This value is out of the range of the data plots on the figure above, but by extrapolation we can estimate the crack propagation velocity to be 5 nm/s. It would thus take 30 s for the crack to grow another 150 nm.

(e) At a partial pressure of 50%, how many water molecules would be sitting on the initial crack faces?

Michalske [1] states that Si-O bonds are incapable of adsorbing environmental chemicals until the strain exceeds a certain critical level. We can therefore assume that at the initial stage, molecules will sit on the crack faces without any preference. At a partial pressure of 50%, half of the molecules sitting on the crack faces will be water molecules. The molar volume of an ideal gas at room temperature is Vm = 24.8 L/mol. Therefore, the number of molecules per unit area is: (Na /Vm)2/3 = 8.39*1016 /m2 where Na is the Avogadro number. On a crack surface of width 150 nm and thickness 1 cm, the number of water molecules is: 6.29*107 molecules.


[1] Michalske, T. A., and B. C. Bunker. “Slow Fracture Model Based on Silicate Fracture Models.” Journal of Applied Physics 56 (November 15, 1984): 2686-2693.


Plasticity and fracture of microelectronic thin films/lines
Effects of multidimensional defects on III-V semiconductor mechanics
Defect nucleation in crystalline metals
Role of water in accelerated fracture of fiber optic glass | Problem Set 2 | Problem Set 3 | Problem Set 5
Carbon nanotube mechanics
Superelastic and superplastic alloys
Mechanical behavior of a virus
Effects of radiation on mechanical behavior of crystalline materials

Course Info

As Taught In
Spring 2008
Learning Resource Types
Simulation Videos
Exams with Solutions
Problem Sets with Solutions