New crack generation phenomena by crack collision in 10 mm thick tempered glass

Abstract

High speed photography by Caustics method using Cranz–Schardin camera was used to study crack propagation and divergence in thermally tempered glass. Tempered 10 mm thick glass plates were used as a specimen. New crack generation by two crack collision was observed. Regarding the presence/absence of new cracks, the dependence of the two cracks on the collision angle was confirmed. Considering that it is based on the synthesis of stress 𝜎_CR generated at the crack tip, tensile stress necessary for the generation of new cracks could be created.

Keywords

New crack generation crack collision caustics method 10 mm thick tempered glass

1. Introduction

Tempered glass has been widely used and is recognized as a safety glass, because of its highly strength as compared with ordinally float glass and fragmentation phenomenon when fractured. As the fragmentation phenomenon in tempered glass is caused by the new crack generation of crack divergence and propagation, especially the divergence phenomenon has a very important meaning, because fragmentation is caused by repeated crack divergence and propagation. The distance from crack divergence to re-divergence is very short as a major feature of fracture in tempered glass. It is known that crack in glass propagates to the normal direction with the maximum applied tensile stress based on the normal stress law (Normalspannungs-gesetz) [12].

Hara et al. has been discussed the divergence of glass using the energy release rate G proposed by Irwin [13]. The schematic diagram is shown in Fig. 1. The crack propagation velocity can be expressed as a function of the energy release rate G. The crack begins to propagate rapidly when a certain value G ₀ exceeded, and eventually reaches the terminal velocity. After that, if the fracture energy increases, the crack continues to propagate, and the phenomenon of new crack generation or crack divergence will be created. The values of the fracture energy G ₀ that the crack begins to propagate rapidly in the figure, the G _M that the crack velocity is reached to the terminal velocity, and the G _B that the crack diverges are shown in the case of an ordinary flat glass. If the conventional flat glass is not strengthened, the general terminal velocity is reported at 1500–1540 m/s [16]. The authors reported that even in the case of tempered glass, it was about 1500 m/s, and there was a dependence on surface compressive stress [8]. Also, two results after crack divergence have been reported that the fracture velocity V does not decrease [12] and decreases [1].

Fig. 1.

Relation between crack velocity and energy release rate G.

Griffith [6] thought that crack would start to propagate when the following conditions were met: $\begin{eqnarray}\partial (U_{1}-U_{2})/\partial c=0\ldots .\end{eqnarray}$ (1) Here, U ₁ was the elastic strain energy, U ₂ the crack generation energy and c the crack length. It is considered that (U ₁–U ₂) being satisfied the equation (1) corresponds to G _O, and the fracture mirror surface seen at the fracture origin is formed between G _M and G _B. The following relational expression, $\begin{eqnarray}G=K^{2}/E\ldots\end{eqnarray}$ (2) holds between the energy release rate G, the stress intensity factor K, and Young modulus E.

Although crack propagation phenomenon is very important for researching the fragmentation mechanism in tempered glass, its analysis is not easy. Because the crack propagation in tempered glass is very high-speed phenomenon at fracture. The following two methods have been generally proposed as observing crack propagation. One is fractography analysis which is observed from the rib marks and Walner lines generated in the thickness direction of the glass fragment. Another is the analysis used by high-speed camera which observes of the propagating crack front and the fracture pattern after crack propagation. Since no special equipment is required, many analyses using the former method have been performed. For example, Aoki et al. [2] reported that crack reached a divergence in a catastrophic change through the mirror-mist-hackle state, after propagating in a certain distance, the crack has a re-divergence in a re-catastrophic change through the mirror-mist-hackle state. Also, fractography observation has become a powerful analytical tool for researching the fracture origin [18] and the crack propagated direction [17]. Takatsu et al. [22] reported crack propagation in tempered glass was affected by the local residual stress, and this analysis was performed by the rib-mark observation.

Authors have mainly investigated the crack propagation phenomenon in tempered glass by the latter method using Cranz-Schadin type high-speed camera [19]. Namely, crack velocity in tempered glass was about 1500 m/s [8], and crack connection phenomenon [20,21] which could be explained [7] by introducing the concept of stress 𝜎_CR [3] created at the propagating crack tip being observed in zone-tempered glass.

By observing the crack divergence phenomenon of 3.5 mm thick tempered glass [4], it was reported that there were also type of branching divergence as shown in Fig. 2 and which was stated by Oka [14] in the vascular divergence, adding bifurcation divergence as shown in Fig. 3 which traditionally known. Namely, there were three types of new crack generation called bifurcation, blanching and secondary crack [10] which generated with a time delay in tempered glass. It is also said that the propagating crack will stop when it collides with the preceding crack. No new crack generation other than divergence and secondary cracks has been reported so far.

Fig. 2.

Branching divergence.

Fig. 3.

Bifurcation divergence.

Caustics method [9,15] is widely known as a method for measuring the dynamic stress intensity factor from the size of the shadow spot generated at the tip of the crack. It was reported [5] that may be possible to estimate the conventional high velocity crack propagation in more detail by technique adding the shadow spot information generated in front of the propagating crack. The generation of cracks and their propagation direction could be estimated accurately using by observation of shadow spot by Caustics method.

Investing the precise crack generation adding the technique of shadow spot information by Caustics method, new crack generation was focused in this study, adding crack propagation and propagating direction after divergence. New crack generation phenomenon which was different from the crack divergence generation and secondary crack could be observed in tempered glass.

2. Experiment

2.1. Specimens

Ordinary tempered glass that has passed the British standards BS-5282 and the Japanese standards JIS R3206 was used as a specimen. The specimen used was 900 × 400 × 10 (mm) in size, and was an ordinary soda-lime-silicate glass. Both glass substrate and tempered glass were produced by Central Glass Co. Ltd. Refer to another report [4] for chemical composition of soda-lime-silicate glass.

2.2. Test equipment and method

An in-laboratory constructed Cranz–Schardin-type camera was used for high-speed photography. Refer to another reports [5,9] for the details of the principle of the Caustics method and the experimental.

2.3. Analysis method

Conventionally, a technique of sensitized development (ASA 200 → 800) has been used in order to make photographs clear. Photographs were captured with a film scanner 400-SCN024 made by Sanwa Supply Inc. and were analyzed by clarifying using image processing software [5]. The image quality of photographs could be improved significantly, compared with the conventional method of sensitized development.

Furthermore, black and white were reversed and analyzed for making the state of shadow spots and crack propagation as clear as possible in many photographs. Namely, it should be noted that shadow spots and propagated cracks are shown in white.

3. Results and discussion

3.1. New type of crack generation

It was reported that observation of crack propagating direction by Caustics method can be gotten with higher reliability than that by the general high-speed photography [5]. Taking advantage of this feature, the crack propagation phenomenon in tempered glass can be observed in detail. An example is shown in Fig. 4. As high-speed photographs taken at 5 μs intervals from Fig. 4(a) to Fig. 4(c), Fig. 4(b) corresponds to 5 μs before and Fig. 4(c) to 10 μs before based on Fig. 4(a).

Fig. 4.

Photographs of crack generation after collision by 5 μs-period observation.

Focusing on the crack of the circled region A in Fig. 4(c), a new crack was seemed to generate from the two cracks’ collision point, and it propagated after that. Looking at Fig. 4(b) which being 5 μs before, one shadow spot could be observed. Looking at Fig. 4(a) which being 5 μs also before, the two cracks could be observed propagating in the direction of collision point. Namely, it could be observed that a two cracks’ collision, a new crack generation and propagation in the different direction from two cracks.

Just one new crack generation was not observed, but also observed 3 cracks in Fig. 4. In addition to the above-mentioned new crack generation of the crack A, new crack generations by two crack’s collisions were observed in the circled region B and the region C. However, the collision state and the propagation were different. An increase of shadow spot diameter could be observed with propagating of the crack A, and a similar phenomenon was observed in the crack B which was not as extreme as the crack A. Also, next divergence phenomenon could be observed with propagating of the new crack C.

Table 1 shows summarized process of two crack collision and a new crack generation. Although the three cracks observed in Fig. 4 had different timings, it was common that two cracks were collided and new cracks which propagated in a direction completely different from the propagated direction of two cracks.

Table 1

Summary of the new generated three cracks shown in Fig. 4

	New crack A	New crack B	New crack C
Fig. 4(c)
Crack(s)	Approach	None	Adjacent
Shadow spot(s)	2	None	2
Fig. 4(b)
Crack(s)	Collision	None	Propagation
Shadow spot(s)	1	1	2
Fig. 4(a)
Crack(s)	Propagation	Propagation	Propagation
Shadow spot(s)	1	1	2

The crack propagation phenomenon in tempered glass is extremely complex [6,22]. The initial crack propagation is different which depends on the condition of the stress field at the fracture origin point, fracture method and fracture energy etc. For example, the number of cracks at fracture origin, the condition of divergence generation and divergence phenomenon after propagation are each different. There is almost no the same fracture pattern in tempered glass made in same product conditions. It can be considered as a peculiar phenomenon which occurred as a result of overlapping some conditions in a special sample. Therefore, observations were also made on different sample of tempered glass with a thickness of 10 mm. New crack generated by two cracks’ collision were observed even in another sample as shown in Fig. 5. Thus, it could be presumed that new crack generation phenomenon by two cracks’ collision was not a peculiar phenomenon seen in a specific sample.

Fig. 5.

Photograph of new crack generation by collision for another specimen.

Fig. 6.

Stop propagation of late arrived crack.

It is said that the preceding crack becomes an obstacle and late arrived crack stops when a late arrived crack collided with a preceding crack as shown in Fig. 6, and cracks by divergence and secondary crack were thought as a new crack generation in tempered glass. Few papers have reported that the generation of new crack by two cracks’ collision. As crack in tempered glass propagates at high speed of about 1500 m/s [8], it is presumed that the matching probability of two crack collision point can be extremely small. It could be observed, however, that two cracks collided even at high speeds of about 1500 m/s, and one crack propagated from the collided point, as shown in Fig. 7. Namely, a different type of new crack generation which previously unknown was observed, adding to the type of bifurcation divergence, branching divergence and secondary crack generation. However, the crack propagation was observed to be similar in ordinary tempered glass, even if the crack was caused by the two cracks’ collision.

Fig. 7.

New crack generation by two cracks' collision.

3.2. A new crack generation mechanism due to two cracks’ collision

It is presumed that this result was not a peculiar phenomenon observed in a specific sample, the new crack generation mechanism can be estimated by combining the results. Table 1 shows summary of the new generated three cracks shown in Fig. 4. The flow of a new crack generation mechanism is as follows, based on the results in Table 1.

Generation of two cracks by each divergence (two small sizes of shadow spots).

Propagation of two cracks (growth of each shadow spot).

Approaching of two cracks (existence of two shadow spots).

Further approaching of two cracks (partly overlapping of shadow spots).

Collision of two cracks (one shadow spot).

New crack generation (very small size of shadow spot).

Propagating of the new crack (growth of shadow spot).

Considering the case where two cracks that propagate in the direction of collision occur, two small shadow spots are observed at the each tip of the two cracks at this time. Propagating of two cracks, both of the two shadow spots grow large. It is in good agreement with the conventional observation results [5] that each crack has a small shadow spot immediately after divergence and shadow spot grows large with crack propagation.

Figure 8 shows that two cracks of the crack 1 and the crack 2 are approaching each other. Two shadow spots are observed at each of the two approaching cracks. Each principal stress direction of two cracks is different, because of these two cracks having different propagation directions. The two cracks propagate without affecting each other, because of two large shadow spots being observed. Each of the two cracks can be thought to propagate independently.

Fig. 8.

Model of two cracks’ approaching and the shadow spots.

Figure 9 shows a flow of the two approaching cracks, the generation of new crack and its growth. It is inferred that the two stress fields which created at the tips of two cracks were made overlapping gradually, when the two cracks get closer as shown in Fig. 9(a). Stress synthesis would be done gradually by overlapping of stresses 𝜎_CR which existed at propagating two crack tips. It seemed that a stress field was not made of complete stress synthesis, but each stress field at two propagating cracks also existed, because two shadow spots could be observed in this time.

Fig. 9.

Model of new crack generation mechanism.

Figure 9(b) shows the more proximity of two cracks. As there was completely one shadow spot in this state, it is inferred that the stress field changed to the stress field common to the two propagated cracks. This means that two stress fields at the tip of two cracks were combined by further approaching. Although, no new cracks were observed at this time, it is presumed that sufficient stress could be created to generate a new crack, because, subsequent crack propagation could be seen in the direction of shadow spot generation [5].

After that, the new crack which propagated in a direction completely different from the propagation direction of the two cracks before the collision, was generated. Figure 9(c) shows that shadow spot of small size grew larger with the new crack propagation. Although, the knowledge about the generation of new crack was completely different from the conventional one, the growth of shadow spot with the propagation of crack was consistent with conventional findings. Even in this new crack, it was in good agreement with the phenomenon observed in the past that the shadow spot of crack propagating start was small and it grows with the crack propagation.

Large residual stress exists even just before the crack collision in tempered glass. The collision phenomenon of two cracks could not be explained by the only conventional concept, because each crack propagates based on the normal stress law. However, the collision phenomenon of two cracks and the new crack generation could be explained by introducing the idea of stress 𝜎_CR which created at the tip of propagating crack. The sum of the maximum principal stress 𝜎₁ and the stress 𝜎_CR has an effect to the crack propagation [3,7]. As the stress field is different from the residual stress 𝜎₁ alone, the crack can be propagated straight using the stress of 𝜎_CR. New crack generation phenomenon by two cracks’ collision can be explained by using this concept of 𝜎_CR, similar to explaining two cracks’ connection phenomenon [20,21] in zone-tempered glass.

3.3. No new crack generation

In some cases, the generation of new crack was not observed as shown in Fig. 10, despite observing the two cracks’ collision. Figure 10(a) shows the state before of two cracks’ collision. It was not observed the new crack generation after 5 μs as shown in Fig. 10(b). No new crack was observed even in Fig. 10(c) after 10 seconds, despite the fact that the surrounding cracks have propagated considerably. It could be judged that no new crack was generated, because it is the timing corresponding to the occurrence of the so-called secondary crack generated with a time delay. Namely, it could be observed that there are two cases of new crack generation and non-crack generation, even when two cracks collided.

Fig. 10.

Photographs of non-crack generation after two cracks’ collision by 5 μs-period observation.

3.4. Effect of collision angle

It is possible to create the tensile stress required to generate the new type of crack, considering that two stress fields by 𝜎_CR created at the tip of the propagating cracks will be combined. If crack propagation follows normal stress law and the stress created by the stress 𝜎_CR of the two cracks will be combined, it can be inferred that the combined stress 𝜎_col is expressed by Eq. (3) in relation to the collision angle shown in Fig. 11. $\begin{eqnarray}\displaystyle {\sigma}_{\text{col}}={\sigma}_{\text{CR1}}\cos {\theta}_{1}+{\sigma}_{\text{CR2}}\cos {\theta}_{2}\ldots . & & \displaystyle\end{eqnarray}$ (3)

Here, 𝜎_CR1 is the stress generated at the tip of the crack 1, and 𝜎_CR2 is the stress generated at the tip of the crack 2. Collision angle was defined that the direction of propagation of the new crack when a new crack is generated, and the direction of propagation of surrounding cracks when no new cracks are observed.

Figure 12 shows an example of collision angle measurement when a new crack was generated. Since the collision angles in this case were 60° and 40°, the combined stress 𝜎_col is obtained from Eq. (4). $\begin{eqnarray}\displaystyle {\sigma}_{\text{col}}\text{} & =\text{} & \displaystyle {\sigma}_{\text{CR1}}\cos {\theta}_{1}+{\sigma}_{\text{CR2}}\cos {\theta}_{2}\nonumber\\ \displaystyle \text{} & =\text{} & \displaystyle {\sigma}_{\text{CR1}}\cos 60+{\sigma}_{\text{CR2}}\cos 40\nonumber\\ \displaystyle \text{} & =\text{} & \displaystyle 0.50{\sigma}_{\text{CR1}}+0.77{\sigma}_{\text{CR2}}\ldots .\end{eqnarray}$ (4)

It can be considered that the two stresses 𝜎_CR generated at the crack tips are almost equal, because the two cracks propagate at the nearby same speed in tempered glass manufactured to comply with JIS R 3206. As a result, Eq. (4) is calculated to 1. 27𝜎_CR. This means that a tensile stress corresponding to 1.27 times of the stress 𝜎_CR at the tip of propagating crack is created. The value of stress 𝜎_CR in 5 mm thick zone-tempered glass was reported [3], however, it is a value for partially tempered glass manufactured under certain conditions. There are still many unclear points about the stress value 𝜎_CR of 10 mm thick tempered glass, the combined stress 𝜎_col should be not described as a specific numerical value, but is represented with 𝜎_CR.

Fig. 11.

Measurement of collision angle for new crack generation.

Fig. 12.

Example of the new crack generation and the collision angle.

Figure 13 shows the results of this measurement regarding new crack generation in two specimens of 10 mm tempered glass. The vertical axis is the value 𝜎_col calculated from the above Eq. (4), and the horizontal axis is the collision angle (𝜃₁ + 𝜃₂). The generation of 5 new cracks was observed after the collision in this study. Otherwise, two cases were observed in which no new cracks were generated in spite of two crack collision. A strong correlation could be found between the value 𝜎_col and the collision angle (𝜃₁ + 𝜃₂) as clear from Fig. 12. Also, new cracks were observed when the collision angle was acute, and showed a tendency of not being generated in the case of obtuse angle.

Fig. 13.

Relation of stress 𝜎_Col and collision angle (𝜃₁ + 𝜃₂) for new crack generation.

The above results show that a new crack will be generated when the value of the combined stress 𝜎_col is large, and will not be generated when the value of the combined stress 𝜎_col is small. Namely, it means the combined stress 𝜎_col obtained from Eq. (3) will be valid. This relationship supports the existence of the stress 𝜎_CR and also indicates the stresses of two propagating crack may be combined. These results mean that combined stress 𝜎_col create tensile stress in the glass for new crack generation, there is stress field inducibility for new crack generation, and Eq. (3) appears to be significant. However, the detailed examination will be a topic for future research.

4. Conclusions

New crack generation phenomenon in a 10 mm thick tempered glass was investigated using the Caustic method. As a result, the following findings were obtained:

(1) A new type of cracks generated after the two cracks’ collision could be observed.

(2) It was observed that two shadow spots became one according to the proximity of the crack, and a new crack propagated in the direction of the shadow spot.

(3) On the other hand, even when it was clear that two cracks collided, there was a case where new crack was not generated.

(4) The collision angle dependence of the two cracks was observed. Namely, new crack generation was observed when the collision angle of the two cracks was acute, and there was a tendency not to generate when it was obtuse.

(5) New crack generation phenomenon can be considered to be based on the synthesis of 𝜎_CR, however, a detailed examination of its validity is a topic for future research.

Footnotes

Acknowledgements

The author is grateful to Professor Emeritus A. Toshimitsu Yokobori, Jr of Tohoku University, Professor Emeritus Kiyoshi Takahashi, the late Mr. Haruo Komatsu and Mr. Toshio Mada of Kyushu University for making suggestions and performing experiments, as well as to Central Glass Company Ltd. for providing glass specimens.

Conflict of interest

None to report.

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