New insights into nanoindentation crack initiation in ion-exchanged sodium

aluminosilicate glass

Xiaoyu Li1, 2 , Liangbao Jiang1, 2*, Iman Mohagheghian3,4, John P. Dear3*, Lei Li1, 2 and Yue

Yan1, 2*

1Beijing Institute of Aeronautical Materials, Beijing 100095, China

2Beijing Engineering Research Center of Advanced Structural Transparencies for the Modern

Traffic System, Beijing, China

3Department of Mechanical Engineering, Imperial College London, South Kensington

Campus, London SW7 2AZ, UK

4Department of Mechanical Engineering Sciences, University of Surrey, Guildford, GU2

7XH, UK

*Corresponding authors, Tel: +86-10-62496505

liangbaojiang@hotmail.com; j.dear@imperial.ac.uk; Yue.Yan@biam.ac.cn

Abstract:

The effect of ion-exchange on the fracture behavior and the threshold load is

investigated for radial crack initiation resulting from cube-corner indentation. Both tin

and air sides of the sodium aluminosilicate float glass are considered. The threshold

load and mechanical properties are experimentally measured by nanoindentation. A

qualitative explanation of crack initiation is developed by analyzing the stresses at the

indentation site. The ion-exchanged glasses show a lower threshold load for radial

crack initiation with a cube-corner indenter than the raw glass, and this is due to a

higher crack driving stress for ion-exchanged glasses. However, the compressive

stress on the surface of the ion-exchanged glasses can inhibit the expanding of the

radial cracks. The air side always shows higher values for the threshold load than the

tin side before and after ion-exchange, which is in accordance with the calculated

crack driving stress results.

Key words: ion-exchange; threshold load; crack initiation; cube-corner

1. Introduction

Ion exchange, also known as chemical strengthening, is an effective method of

strengthening glass. During this process, glasses are immersed into molten alkali salt

bath at a temperature below the glass transition. The small host alkali ions in the

surface of the immersed glasses are exchanged for the comparatively larger alkali ions

from the molten salt bath, resulting in Compressive Stress (CS) at the glass surface 1, 2.

As the main material for fabricating the touch screen panels and windshields for

aircraft, the susceptibility of ion-exchanged glasses to damage initiation is as

important as the strength of the material. Indentation is a useful method to study the

mechanics of damage initiation under abrasive or particle impact condition 3.

Amongst the cracks formed during indentation, radial cracks are considered to be

representative of strength-controlling flaws. Most indentation fracture studies are

based on the use of the four-sided Vickers pyramid with a centerline-to-face angle of

68 or the three-sided Berkovich analogue with a centerline-to-face angle of 65.3.

However, there is an inherent size limitation when extending Vickers or Berkovich

indentation to small-volume systems. That is, below a certain threshold load, cracks

cannot be observed 4. Since the indentation associated with the load is relatively large,

the threshold loads place severe restrictions on the sample size. An approach to

overcoming the threshold load imposed length scale limitation is to increase the

acuteness of the indenter from the Vickers or the Berkovich pyramid to a cube-corner

indenter 5, 6. A cube-corner indenter, with a centerline-to-face angle of 35.3, displaces

more than 3 times the volume of the Vickers or Berkovich indenter, thus producing

greater stresses and strains in the surrounding material 7. As a result, the threshold

load for radial crack initiation with a cube-corner indenter is significantly reduced,

therefore the cube-corner indenter is more suitable to investigate the cracking

behavior on small samples or films.

The fracture behavior of glasses has been investigated in some detail 3, 7, 8, 9, 10, 11.

However, most research on glass have been based on the use of Vickers indenter 3, 8, 9

and conducted on raw glasses 7, 10, 11. The fracture behavior of ion-exchanged glasses

under ultra-low load (<10 mN) and the threshold load of ion-exchanged glasses with a

cube-corner indenter remains unclear to date. In addition, approximately 90% of all

flat glasses produced worldwide are manufactured using the float forming process 12,

which was first demonstrated by Pilkington 13. In this process, the molten glass will be

floated on a tin bath 14, 15. The molten tin diffuses into the bottom surface of the glass,

producing two chemically different sides, which are often referred to as the air and tin

sides. The difference in composition and structure between these sides can lead to

diverse properties 12, 16 and performance during crack initiation. However, this

difference in ion-exchanged sodium aluminosilicate glass remains unclear.

The research presented in this paper explores the effect of ion-exchange on the

fracture behavior and the threshold load for radial crack initiation resulting from cube-

corner indentation and the difference between the air and tin sides of the sodium

aluminosilicate float glass. An in-situ scanning probe microscopy (SPM) provided by

the indentation system is used to obtain the surface topography. A qualitative

explanation of this phenomenon is developed based on an analysis of stresses at the

indentation site.

2. Experimental procedure

2.1 Glass preparation

The glass used was a 4-mm-thick float glass which was provided by AVIC

SANXIN. The chemical composition of the glass is 67.0 wt% SiO2, 5.0 wt% Al2O3,

14.9 wt% Na2O, 9.2 wt% MgO, and 3.9 wt% K2O. The Tg of the glass sample is about

587 C. The tin side was distinguished by fluorescence obtained by irradiating with an

ultraviolet lamp. The ion-exchange process was carried out in an electric furnace at

420 °C for different times (1, 12, 24, 48 and 96 hours (h)).

2.2 Compressive stress and depth of stress layer measurements

The compressive stress (CS) and depth of stress layer (DOL) on both sides of glass

samples were measured by the surface stress meter (FSM-6000LE, ORIHARA,

Japan) which was based on the theory of photoelasticity 17,18. The photoelastic

constant (p=28.0) and the refractive index (n=1.51) was measured by a birefringence

measurement device (ABR-10A, UNIPT) and V-prism refractometer, respectively.

The systematic errors for the CS was 20 MPa, and for the DOL was 2 μm. Each

glass sample was measured at three random positions.

2.3 Nanoindentation

An indenter (TI 950 Triboindenter, Hysitron) with a full-scale capacity of 10 mN

was used for all experiments. Before performing nanoindentation on glass samples,

calibration was carried out on a standard fused silica sample.

For each glass sample, the indentation threshold load for radial cracks initiation

with a cube-corner indenter was obtained. As the crack formation was a stochastic

process, the threshold load for radial cracks initiation was defined as the load at or

above which 60% of the possible radial cracks formed to take the variability into

account 3. For each indentation load, ten indentation experiments were carried out in

random positions on the surface to find the threshold load. After indentation testing,

all the impressions were imaged using a scanning probe microscopy (SPM) provided

by the indentation system to measure the length of the radial cracks emitted from their

corners. The length of the radial cracks in the SPM images was measured using a

graphic editing software (Adobe Photoshop, USA)19, 20. Hardness and elastic modulus

were measured using a Berkovich indenter on the same instrument. The indentation

load was 9 mN for all the hardness tests.

3. Results

3.1 Compressive stress and depth of stress layer

The Compressive Stress (CS) and Depth of Stress Layer (DOL) values on air and tin

sides of the ion-exchanged specimens as a function of ion-exchange time are shown in

Fig. 1. The CS and DOL results are closed to our previous works on glass samples

with similar composition 12, 21. Some difference in DOL results may be ascribed to

different glass composition and KNO3 salt purity. The CS decreases with ion-

exchange time continuously while the DOL increases with ion-exchange time.

However, the tin side always shows higher values for the CS and lower values for the

DOL than the air side.

3.2 Threshold load

Fig. 2 shows the representative examples of load-displacement (P-h) curves obtained

at peak load of 9 mN with a cube-corner indenter (Fig. 2a) and a Berkovich indenter

(Fig. 2b), respectively. For both raw and ion-exchanged glass samples, larger

displacements at peak-load are observed for the cube-corner indenter (with a small tip

angle of 35.3°).

Fig. 3 shows typical SPM images of the nanoindents on the air side of the raw glass

and the ion-exchanged glass for 12h under different loads. The indentation

impressions become larger, and the number of radial cracks increases when the

loading force increase for both two glass specimens. The ion-exchanged glass shows

more radial cracks than the raw glass under the same indentation load. In addition, the

length of the radial cracks on the raw glass is significantly larger than that on the ion-

exchanged glass under large indentation load (Fig. 3 e and f). Fig. 4 shows typical

SPM images of nanoindents on the tin side of the raw glass and the ion-exchanged

glass for 12h under different loads. These results are similar to that on the air side.

Fig. 5 shows the probability of radial crack initiation as a function of the

indentation load for the air side of the ion-exchanged glass for 12h as a typical

illustration for the method of finding threshold load. The threshold load for cracking,

Pth, is defined as the load at or above which radial cracks form at 60% of prospective

indentation sites 3. Each point represents the average of ten indentation experiments,

or 30 radial crack formation sites. The Pth as a function of ion-exchange time is shown

in Fig. 6. The raw glass shows higher values for the Pth than the ion-exchanged

glasses. For the ion-exchanged samples, the Pth decreases with ion-exchange time

continuously. In addition, the air side always shows higher values for the Pth before

and after ion-exchange. However, the relative difference between the Pth values of the

air and tin sides decreases by increasing the ion-exchange time.

3.3 Crack length results under high indentation load

Fig. 7 shows the radial crack length (measured from the center of the indentation

impression) as a function of ion-exchange time at indentation load of 9.5 mN. The

radial crack length on the raw glass is significantly larger than that on the ion-

exchanged glasses. The radial crack length on the ion-exchanged glasses increases

with the exchange time. In addition, the radial crack length on the tin side of the raw

glass is obviously larger than that on the air side while this parameter on the tin side is

slightly lower than that on the air side after ion-exchange.

3.4 Hardness and elastic modulus results

Fig. 8 shows the hardness and elastic modulus as a function of ion-exchange time.

The hardness and elastic modulus results are in accordance with previous works with

similar glass composition16, 22. Ion-exchanged specimens show higher values for

hardness and modulus than the raw glass on both sides. The hardness decreases with

exchange time for ion-exchanged glasses while the modulus did not show the similar

trend. The tin side always shows higher values for these parameters than the air side.

4. Analysis

The aim of this section is to develop a simple analytical model for crack driving

stress in raw and ion-exchanged glasses using a cube-corner indenter. The analysis

will be used to further expand the understanding of crack initiation phenomenon on

the raw and ion-exchanged glass surfaces during nanoindentation.

The model used here is based on what was developed by Yoffe 23 for elastic

materials using a conical indenter, further discussed by Cook and Pharr 24 for

materials without surface stress using a Vickers indenter, and then be developed by

Tandon for the ion-exchanged glasses with a Vickers indenter 8. Rouxel et al. 25, 26

used Yoffe model to predict the microcracking behavior of a series of oxide glasses.

Yoshida et al. 27 estimated residual stresses around the ball indentation imprint using

Yoffe model. Sglavo and Green et al. 28, 29 modified the parameter in Yoffe model, and

calculated the residual stress field generated by Vickers’ indentation. Here, the model

is extended to the crack driving stress analysis for raw and ion-exchanged glasses

with a cube-corner indenter.

According to Yoffe model 23, a parameter B which is used to calculate radial crack

driving stress, is related to the volume displaced by the indenter 24. The displaced

volume can be equated to the volume of the contact impression during indentation 30

which, for a cube-corner indenter with a tip angle of 35.3°, is calculated as:

(1)

where P is the indentation load, H is hardness, and f stands for the densification effect

and relates to the material properties. For normal glasses (glasses with a substantial

component of network modifiers31), this value is always chosen to be f=1 (no

densification) 24. It should be pointed out that densification takes place in indentation

even in normal glass. Thus, f=1 is not exactly but approximated. As a result, for a

cube-corner indenter 24,

(2)

Substituting Eq. 1, 2 and the definition of hardness11 into Yoffe model23, the stresses

normalized with respect to the hardness during loading (Eq. 3) and unloading (during

unloading process, B is fixed at Bmax determined by P=Pmax) (Eq. 4) are expressed as

follows:

Loading: (3)

Unloading: (4)

The stresses driving different cracks during an indentation cycle will depend on the

material parameter . Fig. 9 shows the stress driving the radial crack for a

specific value of =0.126. The stress driving the radial crack increases to a

maximum at complete unloading.

For ion-exchanged glasses, the equi-biaxial stress state on the glass surface can be

represented in Cartesian coordinate as: ; all other stress components

are considered to be zero. The stress component which drives radial crack can be

translated into spherical coordinate system as 8:

(5)

For the radial crack, the stress driving force acting on ion-exchanged glass surface

can be expressed as:

Loading: (6a)

Unloading: (6b)

where the negative sign is included so that the compressive stresses naturally decrease

the crack driving force.

It can be seen that the radial crack driving stress increases to maximum values at the

end of unloading when P equals zero from Fig. 9. Thus the maximum driving stress

for radial cracks of raw and ion-exchanged glasses can be expressed as follows:

Raw glass： (7a)

Ion-exchanged glasses: (7b)

Considering the compressive stress results in Fig. 1 and elastic modulus

measurements from Fig. 8, the radial crack driving stress for raw and ion-exchanged

glasses is calculated and the results are shown in Table 1 (Note: for normal glasses, f

=1 24, 31). It should be pointed out that since the indentation depth is very small (less

than 1 μm as shown in Fig. 2) relative to the depth of stress layer (larger than 14 μm

as shown in Fig. 1), the is considered to be constant and independent of depth.

The residual stresses are also calculated by the variation of fracture toughness 4, 32.

The calculating equation is shown below:

(8)

where P is the indentation load, c is the crack length on a stressed glass surface, is

the crack length on the unstressed glass surface, is a surface correction factor which

equals 1.13 4, 32, and equals 0.057.

It was found that there can be a factor of ten discrepancy (low by a factor of 10)

when calculating surface residual stress for ion-exchanged glass with the above

equation, although it can properly predict residual stresses on thermally tempered

glasses 3, 33. Morris et al. 3 indicated that the crack geometry can be changed caused by

the large compressive stress on the glass surface, therefore the parameter which

depends on crack geometry can be altered, leading to the invalidation of this equation.

Thus, Morris et al. calibrated the value of from a comparison of independently

measured stress values and the calculated stress values, and obtained an average value

of =0.090 0.006. However, the method of Morris is based on a Vickers indenter

which can lead to different crack geometry from the cube-corner indenter used here,

and this difference can lead to different value of . By comparing the calculated

stress results and the results from the photoelastic method of 10 glass samples which

were ion-exchanged for 12 hours, an average value of =0.072 0.008 for the air

side and =0.110 0.006 for the tin side is obtained for our ion-exchanged glass

samples using a cube-corner indenter. With the new value of , the residual stresses

of other ion-exchanged glass with exchanging time for 1, 24, 48 and 96 hours are

calculated and the results are listed in Table 2. The residual stress results from

photoelastic method are also listed in Table 2 to make a comparison.

It can be seen that the calculated results are close to the results obtained using the

photoelastic method.

5. Discussion

With increases of the ion exchange time, the number of K+ ions diffusing into the

glass surface increases continuously to result in an increase of DOL, and this result is

in accordance with our previous work 21. The CS decreases with ion exchange time

which is attributed to the stress relaxation under high temperature. Stress relaxation is

roughly proportional to the stress which leads to a high relaxation rate in the near-

surface layers 8, 34. However, the extent of ion-penetration also increases with

exchange time. The combination of these two events will lead to the surface

compressive stress maximum moving inwards from the surface 8. The tin side always

holds a higher value of CS and lower value of DOL. This is due to the hindered

diffusion of K+ ions by the tin in the glass and this result is in accordance with our

previous research 12, 16.

As shown in Fig. 2, the indentation depth of cube-corner indenter is much larger

than that of the Berkovich indenter under the same indentation load which is due to a

smaller centerline-to-face angle of 35.3 for the cube-corner indenter 7. As a result,

the cube corner indenter is more suitable for the crack initiation experiment and the

Berkovich indenter is more appropriate for the hardness and elastic modulus

measurement tests. According to previous research 35, 36, the hardness and elastic

modulus results in shallow penetration depth show lower precision than that at a

deeper indentation depth. This is caused by a process called the Reverse Indentation

Size Effect (RISE) 37, 38, especially when the indentation depth is less than 200 nm.

Thus the indentation depth in our hardness and modulus tests are all larger than 200

nm to avoid the influence of RISE (Fig. 2b).

After ion exchange, the high levels of residual compressive stress present on the

strengthened glass surfaces can strongly resist the penetration of the indenter 39. As a

result, the hardness and modulus increased after ion exchange. In addition, the

increase in density caused by the wedging of larger K+ ions into the glass matrix can

also lead to a higher mechanical property on ion exchanged glass surface40. This result

is in accordance with our previous work16.

The threshold load for radial crack initiation for the raw glass is higher than that for

the ion-exchanged glasses on both air and tin sides. This result is not in agreement

with some of the previous studies using a Vickers indenter in which surface CS can

inhibit crack initiation 3, 41, 42, 43. Previous research using the Vickers indenter 9 shows

that the ion-exchanged glass with surface CS lower than 380 MPa has a lower crack

initiation load compared to the raw glass but higher initiation load with the increase of

the surface CS. The reason is ascribed to a larger size of residual stress field on the

ion-exchanged glass than that on the raw glass after indentation 9. The exchange of

larger ions to smaller ions can cause a denser glass structure and a higher residual

stress field 16, which arises from the strain mismatch of the plastically deformed zone

embedded in the surrounding elastically restraining matrix. With the increase of the

CS, the inhibiting effect to crack initiation becomes stronger, and as a result, the crack

initiation load increases for the ion-exchanged glasses 24. Despite having the CS

greater than 380 MPa in all ion-exchanged glasses used in this study (Fig 1), the

threshold load was still lower than that of the raw glass. According to previous

researchers11, 44, 45, the discrepancy between our results with the previous works come

from the different residual stress field between the Vickers and the cube-corner

indenter caused by the different centerline-to-face angle between the two indenters.

The residual elastic-plastic stress field can be modeled as a center loaded point

force acting on a circular crack, which gives rise to the residual stress-intensity factor,

46 given by,

(9)

where l is the length of the crack from the indentation corner, a is the length from the

central point of the indentation impression to the indentation corner, and is a semi-

empirical stress-field amplitude. For a Vickers indenter, 44, and for a cube-

corner indenter used here, 44, 45. Thus, the ,which is related to the radial

crack driving force 11, of the cube-corner indenter is approximately quadruple the

same parameter of the Vickers indenter. As a result, for a cube-corner indenter, a

higher CS is needed to resist the increased crack driving force.

In addition, the threshold load results are in line with the radial crack driving stress

calculated based on Yoffe model shown in Table 1. The crack driving stress for ion-

exchanged glasses are much larger than that of the raw glass on both two sides.

According to Eq. (7), the crack driving stress is a function of both elastic modulus and

CS. Introducing ion-exchange in the surface of glass here increases both the CS (Fig.

1) and elastic modulus (Fig. 8b). The suppression effect for crack initiation caused by

CS (in Eq. 7) however, has only a minor influence on reducing the load to crack

initiation compared to the acceleration effect caused by increased modulus. The

threshold load on the air side is always larger than that on the tin side. According to

the calculations (Table 1), this is also caused by the higher modulus on the tin side. In

addition, it is reported that the tin side shows significant larger flaws than the air side

under fractographic analysis, and this is due to contact damage by the rollers in the

float glass process47. This can also lead to a lower value of the Pth on the tin-side.

For ion-exchanged specimens, the load required to cause crack initiation decreases

with exchange time which is due to the decreasing of CS. The surface CS can prevent

ingress of moisture to the incipient crack tips 48 which can prevent crack initiation.

With similar modulus, the threshold load for radial crack initiation for ion-exchanged

glasses decreases with CS. However, this is not reflected in the calculated driving

stress for radial crack initiation in Table 1 (i.e. relatively similar driving forces for all

ion-exchange glasses), suggesting the contribution of additional effects.

The radial crack length in the raw glass is larger than that on the ion-exchanged

glasses under same indentation load which can be attributed to the suppression effect

of surface CS 49, 50. The CS has a minor influence on reducing the load for crack

initiation but a large influence on suppressing the expanding of radial cracks which

means that the CS can reduce susceptibility to further strength degradation during

service. The surface CS decreases with exchange time which leads to an increase of

the radial crack length on ion-exchanged glasses. The radial crack length on the tin

side of the raw glass is obviously larger than that on the air side. This phenomenon

can be ascribed to a lower concentration of Si-O-Si bridging oxygen (BO) 51, 52 and a

larger number of defects on the tin side 35, 53. In contrast, the radial crack length on the

tin side of the ion-exchanged glasses is slightly shorter than that on the air side, and

this is attributed to the larger surface CS on the tin side.

6. Conclusions

The threshold load for radial crack initiation with a cube-corner indenter on raw

glass is higher than that on the ion-exchanged glasses which is caused by a higher

crack driving stress for ion-exchanged glasses. The suppression effect for crack

initiation caused by CS has only a minor influence on reducing the threshold load

compared to the acceleration effect caused by increased modulus. The threshold load

in ion-exchanged glass decreases with exchange time which is attributed to the

decrease of CS. The air side always shows higher threshold load values than the tin

side which is also caused by the higher modulus on the tin side and the results are in

accordance with the calculated crack driving stresses. The CS on the surface of the

ion-exchanged glasses can inhibit the expansion of the radial cracks. The surface CS

decreases with exchange time which leads to an increase of the radial crack length in

ion-exchanged glasses with longer exchange time. The radial crack length on the tin

side of the raw glass is obviously larger than that on the air side which is due to a

lower concentration of Si-O-Si bridging oxygen (BO) and a larger number of defects

on the tin side. The difference of radial crack length between the two sides decreases

after ion-exchange and is attributed to the larger suppression effect of CS on the tin

side.

Acknowledgements

The authors thank Y. P. Jing (JMT Glass) for the technical support and useful

discussions. The research is part of a collaboration between Imperial College London

and Beijing Institute of Aeronautical Materials.

Fund

This work is supported by The National Natural Science Foundation of China (Grant

No. 51402273).

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Figure Captions:

Fig. 1 Effect of ion-exchange time on: (a) Compressive stress, (b) Depth of stress

layer, with fitted dashed curves for air (black) and tin (red) sides.

Fig.2 Load versus indentation depth in one indentation cycle for: (a) Cube-corner

indenter, (b) Berkovich indenter, for both raw and ion-exchanged glass samples.

Fig. 3 Typical SPM images of nanoindents on the air side of the raw glass and ion-

exchanged glass for 12 h under different loads.

Fig. 4 Typical SPM images of nanoindents on the tin side of the raw glass and ion-

exchanged glass for 12 h under different loads.

Fig. 5 Plot of the probability of radial crack initiation as a function of indentation load

for the air side of the ion-exchanged glass for 12h.

Fig. 6 Threshold indentation load versus ion-exchange time, with fitted dashed curves

for air (black) and tin (red) sides.

Fig. 7 Radial crack length versus ion-exchange time at indentation load of 9.5 mN,

with fitted dashed curves for ion-exchanged air (black) and tin (red) sides.

Fig. 8 Effect of ion-exchange time on: (a) Hardness, (b) Elastic modulus with fitted

dashed curves, for ion-exchanged air (black) and tin (red) sides.

Fig. 9 Stress driving the radial crack during an indentation cycle, versus normalized

indentation load, for a specific value of .

Table 1 The radial crack driving stress for raw and ion-exchanged glasses with

different exchange times

Ion-exchange time (h)Radial crack driving stress (GPa)

Air side Tin side

0 14.87 15.58

1 16.71 16.76

12 16.38 16.55

24 16.31 16.42

48 16.26 16.54

96 16.49 16.59

Table 2 Calculated residual stresses and residual stresses from photoelastic method

Ion-exchange time

(h)

Calculated residual stress

(MPa)

Residual stress from

Photoelastic method (MPa)

Air side Tin side Air side Tin side

1 -782 -809 -747 -770

12 -704 -725 -710 -718

24 -666 -725 -690 -706

48 -629 -673 -640 -657

96 -558 -551 -555 -590