Bronson D. Hausmann

Case Western Reserve University, Cleveland, Ohio

Jonathan A. Salem

Glenn Research Center, Cleveland, Ohio

Effects of Aqueous Solutions on Slow Crack Growth 

of Soda-Lime-Silicate Glass

NASA/TM—2016-218907

January 2016
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Bronson D. Hausmann

Case Western Reserve University, Cleveland, Ohio

Jonathan A. Salem

Glenn Research Center, Cleveland, Ohio

Effects of Aqueous Solutions on Slow Crack Growth 

of Soda-Lime-Silicate Glass

NASA/TM—2016-218907

January 2016

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

Bronson Hausmann thanks Dr. Salem for his guidance on this project over the past 2 years. The help of several other individuals

such as Ralph Pawlik, Dan Scheiman, and Dan Gerges at Glenn Research Center has also been essential to the success of this 

work. The Human Exploration and Operations project is thanked for funding of the project.

Available from

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NASA/TM—2016-218907 1 

Effects of Aqueous Solutions on Slow Crack Growth of 

Soda-Lime-Silicate Glass 

Bronson D. Hausmann*

Case Western Reserve University 

Cleveland, Ohio 44106 

Jonathan A. Salem 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Summary 

The slow crack growth (SCG) parameters of soda-lime-silicate were measured in distilled and 

saltwater of various concentrations in order to determine if the presence of salt and the contaminate 

formation of a weak sodium film affects stress corrosion susceptibility. Past research indicates that 

solvents affect the rate of crack growth; however, the effects of salt have not been studied. The results 

indicate a small but statistically significant effect on the SCG parameters A and n at high concentrations; 

however, for typical engineering purposes, the effect can be ignored. 

Introduction 

The strength degradation of silicate glass when stressed in the presence of water is a well-known 

phenomenon. Less known are effects of common water-soluble environmental agents such as salt. A 

previous study indicates no effect of human body fluid simulant on slow crack growth (SCG) of alumina 

(Ref. 1). The effects of solvents on SCG rates of silicates were studied by Michalske and Freiman (Ref. 2) 

who demonstrated that in the presence of stress molecules having structures similar to water broke the 

silicate bond, whereas molecules lacking the shape and orbital configuration of water tended to have little 

or no effect. They concluded that the degradation mechanism is dissociative absorption of water, which 

causes the formation of silanol groups, effectively breaking the siloxane bonds (Fig. 1). This effect is of 

particular interest at damage sites in silicate glasses because the sites have residual stresses and cracks 

form or extend from these sites when external stresses are applied. If glass bonds dissociate or dissolve in 

water, any residual stresses and microcracks existing at the damage sites are relieved and blunted without 

significant damage to the aggregate material, resulting in higher strength. 

Because salt forms an ionic solution in water, it might be expected to have little effect at low 

concentrations, whereas at high concentrations (such as in seawater), the charge of the dissolved ions may 

result in the formation of a weak film of sodium, motivated by the slightly polar siloxane bonds 

(Fig. 2). It follows that lower stress levels or stress rates would provide for further inhibition of the 

saltwater’s effects by allowing increased ion infiltration at a crack site. 

To study the effect of salt on the stress corrosion susceptibility of glass, soda-lime-silicate slide plates 

were tested in four-point flexure in both distilled water and seawater simulant at progressively greater 

stress rates. The SCG parameters were estimated in accordance with ASTM International C1368. This 

report compares parameters of SCG in distilled and saltwater. 

 

*

NASA Glenn Research Center, summer intern from Case Western Reserve University. 
NASA/TM—2016-218907 2 

Symbols 

A material/environmental slow crack growth parameter 

B parameter associated with A, n, fracture toughness, crack geometry, and loading configuration 

D parameter in Table I, =10

F ratio of regression slope F statistics

KI Mode I stress intensity factor 

KIC fracture toughness 

 number of standard deviations corresponding to desired probability level 

n material/environmental slow crack growth parameter 

Q quantity in Equations (10), (12), and (14) defined in Equation (15) as Q = –ln10+1ni

SD standard deviation 

t Student’s t statistic 

v crack velocity 

Y geometry correction factor 

 slope of regression curve 

 intercept of regression curve 

f fracture strength 

i inert strength 

 applied stress rate 

 degrees of freedom 
NASA/TM—2016-218907 3 

Procedure 

Fracture strength as a function of stress rate was measured at 20 °C by using four point flexure of 

annealed soda-lime-silicate slides (23- by 1.6-mm cross section loaded between 20 and 40 mm spans) at 

rates ranging from 10–3 to 101

 MPa/s in distilled water or simulant seawater.† In order to minimize 

variation, which was usually less than 3 percent of the mean at any stress rate, the specimens were 

precracked by using a Vickers indenter at 1 kg. In addition to running tests immediately after indentation, 

a set of specimens was subject to soaking in distilled water for at least 40 h. Usually 20 specimens were 

run per environmental condition. For the purposes of parameter analysis, the inert strength (i.e., the 

strength in the absence of a corrosive environment) was determined by testing 15 specimens per condition 

in silicone oil at a rate of ~25 MPa/s. This resulted in failure in 2 to 3 s. 

Data Analysis 

The data collected were fit to the power law formulation: 

n

IC

n I

I K

K

v AK A 













    (1) 

where v is crack velocity. Constants A and n are the material and environment dependent SCG 

parameters, and KI and KIC are, respectively, the Mode I stress intensity factor and the critical stress 

intensity factor (or fracture toughness) of the material. For constant-stress-rate testing based on the power 

law formulation, the fracture strength, f, is expressed as a function of stress rate as (Ref. 3) 

    2 1 1 1        n n f i B n  (2) 

where  is the applied stress rate, i is the inert strength, and B is a parameter associated with A, n, 

fracture toughness, crack geometry, and loading configuration (see Eq. (13)). The SCG parameter n can 

be determined from a plot of log f as a function of log  with Equation (2) written as 

D

n f log log 1

1 log  



   (3) 

where 

    2 log 1

1

1 log   

  n

i B n

n

D (4) 

Once the slope  and intercept  are estimated by linear regression of Equation (3), the parameters n, 

D, B, and A, and their standard deviations SD, are estimated from (Refs. 4 and 5) 

1 1  n  (5) 

 

†

Instant Ocean Reef Crystals, Blacksburg, VA 24060; specific gravity ~1.021. 
NASA/TM—2016-218907 4 

2

  SD SDn (6) 

 D  10 (7) 

      SDD 2.3026 SD 10 (8) 

 





 



  

 



 

3 1

10

i

B (9) 

    



      

      Cov , ln10 1 3 2 ln10 1 2

ln

2 2 ˆ 2

2

2

2

ln SD SD Q SD SD B Q i (10) 

    2

2

2

3 1

2 *

2

2

10 1 3

2

B n Y

K

Y

K A IC i IC

 

 

  





 



 



 (11) 

 

   



  



 





 



    









 





 



  

 



 

Cov ,

1 3

1 3 2ln10

ln10

1 3

4 1

2

ln

2

2 2

2

2 2

2

2

2

ln *

SD Q

SD SD Q K

SD

SD

i

IC

IC

K

A (12) 

2

2

2

1 1

( 2)

2

10 (1 3 )

3 3

2

B n Y

K

Y

K A

n

IC i IC

   

 



 





 



   



 









 (13) 

   

   



  



 



   



    









 



   



   

 



 

Cov , ln

1 3

1 3 2ln10

ln ln10

1 3

3 1 1

2

ln

2

2 2

2

2 2

2

2

2

ln

IC

IC

IC

K

A

SD Q K

SD SD Q K

K

SD

SD

i

IC

 (14) 

where 

Q      i ln10 ln (15)

Cov,    log  2 SD (16) 

where log is the mean of the logs of the applied stressing rates,  Y is the geometry correction factor for 

the stress intensity factor, and the standard deviation associated with the inert strength i SDln is 

calculated in logarithmic space. Probability limits on the parameters B and A can be calculated from 
NASA/TM—2016-218907 5 

B   B tSDln B 

Lower

Upper  exp ln  and    A A A t SDln

Lower

Upper  exp ln  (17) 

by using Student’s t distribution for the degrees of freedom (DOF) and probability level desired. If the 

DOF is greater than ~40, then 

B   B SDln B 

Lower

Upper  exp ln   and A  A SDln A 

Lower

Upper  exp ln   (18) 

where  is the number of standard deviations corresponding to the probability level desired. The DOF, 

, is given by 

   

    2

2 3

2

2

4

2

2

2

2

ln 2

2

ln ln

2 2

ln

Cov , ln10 2 ln10 1

1 1 3



















  





 

 



 







 

  

 







Q SD SD Q

SD SD i

B i

B

 (19) 

and 

     

   

2

2 3

2

2

4

2 2

2

2

ln 2

2

ln

2 2

ln

ln ln

2 2

ln

Cov ,

1 3

ln10 2ln10

1 3

1

1 1 3 4 1



















  



 





 



  







 





 

  





















 





  

 







Q SD SDQ

SD SD SD

i

i

Ic

Ic

K

A K

A

 (20) 

where i  is the DOF in inert strength (number of inert strength tests minus one) and  is the DOF in 

regression (number of constant stress rate tests minus two). 

Three approaches were used to estimate the slope and intercept of Equation (3): linear regression of 

(1) the individual data points; (2) the median values; and (3) the average values. Very little difference 

resulted between the approaches, and the parameter presented correspond to regression of the individual 

data points. 
NASA/TM—2016-218907 6 

Inert and Time-Dependent Strength 

The fracture strength as a function of stress rate is plotted in Figure 3 for both median and mean 

values. Similar slopes are exhibited, with the distilled water (no soak) tests showing the least SCG and the 

40-h soak distilled water tests showing the most SCG (greatest slope). The addition of salt increases the 

SCG rate compared to distilled water. Doubling the salt concentration increased the SCG further. 

Interestingly, the long-term strengths are similar, whereas the short-term strengths (10 MPa/s) are greatest 

for the soaked specimens and those tested in saltwater, implying blunting during soaking and a weak 

passivation for salt solutions. At slower stress rates, the effect of passivation is negligible, resulting in a 

steep slope and lower n. The strength increase with soaking is confirmed by the inert strength results 

shown in Figure 3, and an improved variance is implied. This decreased variance was not observed at 

slower stress rates, implying that the effects of soaking during stress rate testing, which lasted from ~5 s 

to ~10 h, were minimal. 

To determine the significance of the slope differences of any two curves, the statistics F and t were 

calculated using (Ref. 6): 

2

2

2

1



  

SD

SD F and 

2

2

2

1

1 2

 





   

SD SD

t (21) 

The value of F proved to be insignificant in all test cases implying similar variances, and the 

DOFs of the two slopes were pooled to equal N – 4. The combined DOF was used to determine if the 

slopes were significantly statistically different via Student’s t test. 

Saltwater and distilled water do not exhibit a statistically significant difference in SCG slope; 

however, doubling the salt concentration to twice that of seawater creates a small but significant 

difference at 94 percent confidence. Soaking indented test specimens creates a significant difference in 

SCG slope at 99 percent confidence. Despite the significances, the magnitudes of the differences are 

small, especially when the effect of changes in relative humidity is considered (Ref. 4). 
NASA/TM—2016-218907 7 

It is noteworthy that the soaked specimens exhibited less scatter and higher average strength for inert 

strength tests than the freshly indented specimens (coefficient of variation (CV) = 2.5 vs. 4.6 percent), 

implying some stabilization of indentation cracks. The associated F statistic shows the difference in 

variation to be significant and indicates both a strength increase and scatter decrease for inert testing of 

glass. Because many components spend much of their lifetime at low loads in humid environments, 

presoaking test specimens might better reflect component crack growth behavior. 

The SCG parameters estimated from Equations (5), (6), (8), and (13) are summarized in Table I, and 

the crack velocity as a function of stress intensity based on the estimated parameters is shown in Figure 4. 

The velocity curves reflect the ordering of the stress rate curves. For purposes of parameter estimation, 

the fracture toughness was taken as 0.80 MPa m (Ref. 4). 

TABLE I.—REGRESSION STATISTICS AND SLOW CRACK GROWTH (SCG) PARAMETERS 

Testing environment Slope of 

regression 

curve,a

 



Intercept of 

regression 

curve,a 



SCG parameter 

n A,

m/s   n

MPa m 

B,

MPa2·s

Distilled water 

(not soaked) 0.057±0.002 1.62±0.003 16.4±0.64 1.4810–1 6.15 

Saltwater 0.061±0.003 1.63±0.005 15.5±0.76 5.9310–2 13.39 

Double-concentration 

saltwater 0.064±0.002 1.64±0.005 14.7±0.59 2.6310–2 26.74 

Distilled water 

(soaked 40 h) 0.067±0.002 1.66±0.004 13.9±0.47 1.9510–2 31.99 

a

From Equation (3) D n f log log

1

1

log  

    , where f is fracture strength,  is applied stress 

rate, 1 1   n  , and D = 10. 

 
NASA/TM—2016-218907 8 

TABLE II.—COEFFICIENT OF VARIATION (CV) IN PERCENT FOR TEST SETS 

Stress rate, 

MPa/s 

Saltwater Saltwater, 

double concentration 

Distilled water,

soak 

Distilled water, 

no soak 

6.2 4 3 2 2 

0.62 4 -- 3 2 

0.06 4 3 -- 2 

0.006 4 -- 3 3 

0.0006 4 3 3 -- 

Inert (25) 5 5 2 5 

Test Variance 

The CV for each test set is listed in Table II. The CVs are relatively low in all cases (<10 percent), 

with the saltwater data exhibiting higher variances than the distilled water. This may be due to the weak 

film being relatively unstable. No trend with decreasing stress rate can be observed, and the soaked and 

no-soak data are similar. The most apparent trend is the decreased scatter for soaked specimens tested in 

an inert environment, as discussed in the previous section. 

Conclusions 

Based on the experimental data, the effects of saltwater at ocean levels of salinity and mineral content 

have little effect on the slow crack growth rate of glass. The small decrease in the slow crack growth 

(SCG) parameter n with increasing concentration at room temperature can be ignored for engineering 

purposes. Soaking of indented specimen does create a small but significant decrease in n, and improves 

inert strength and variance. 

References 

1. Rockar E.M.; and Pletka, B.J.: Fracture Mechanics of Alumina in a Simulated Biological 

Environment. Fracture Mechanic of Ceramics, Vol. 4, R.C. Bradt, D.P.H. Hasselman, and F.F. Lange, 

eds., Plenum Press, NY, 1978, pp. 725–735. 

2. Michalske, Terry A.; and Freiman, Stephen W.: A Molecular Mechanism for Stress Corrosion in 

Vitreous Silica. J. Am. Ceram. Soc., vol. 66, no. 4, 1983, pp. 284–288. 

3. Ritter, John E.: Engineering Design and Fatigue Failure of Brittle Materials. Fracture Mechanic of 

Ceramics, Vol. 4, R.C. Bradt, D.P.H. Hasselman, and F.F. Lange, eds., Plenum Press, NY, 1978, 

pp. 661–686. 

4. Salem, J.; and Tandon, R.: Test Method Variability in Slow Crack Growth Properties of Sealing 

Glass. Int. J. Fatigue, vol. 32, 2010, pp. 557–564. 

5. Salem, J.A.; and Weaver, A.S.: Estimation and Simulation of Slow Crack Growth Parameters From 

Constant Stress Rate Data. Fracture Mechanics of Ceramics: Active Materials, Nanoscale Materials, 

Composites, Glass, and Fundamentals, Springer, New York, NY, 2005, pp. 579–596. 

6. Acheson, Duncan: Quality Control and Industrial Statistics. Fourth ed., Richard D. Irwin Inc., 

Homewood, IL, 1974, pp. 835–838.