An Experimental and Numerical Study of the Dynamic ...

Proceedings of the ASME 2013 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems InterPACK2013 July 16-18, 2013, Burlingame, CA, USA

IPACK2013-73292

AN EXPERIMENTAL AND NUMERICAL STUDY OF THE DYNAMIC FRACTURE OF GLASS

Liang Xue Binghamton University Binghamton, NY, USA 1

Da Yu Binghamton University Binghamton, NY, USA

Yuling Niu Binghamton Unversiy Binghamton, NY, USA

Hohyung Lee Binghamton University Binghamton, NY, USA

Satish Chaparala Corning Incorporated Corning, NY, USA

Seungbae Park Binghamton University Binghamton, NY, USA

ABSTRACT The needs of glass to resist the scratches, drops impact, and bump from everyday use lead to the importance of investigation of the glass fracture under dynamic impact loading. The strength of the glass under dynamic fracture conditions is significantly larger than that under quasi-static loading. There are several theoretic models. In this study, an accumulated damage model is implemented. The relation among the stress, loading rate, contact time and the fracture is investigated. The effect of impact area, impact energy and impact momentum on the glass fracture has been proved to further improve the dynamic fracture criterion of glass. For the experimental studies, the Digital Image Correlation (DIC) method enables one to obtain the first principal strain of the glass during the impact process. Moreover, the FEA model is developed in ANSYS/LS-DYNA™.

smartphones, tablets, PCs, and TVs from everyday wear and tear. The glass has to survive the impacts from everyday use and this has led to the investigation of the glass response under impact loading [1]. Under quasi-static loading, glass fractures due to the growth of a single dominant crack. However, under dynamic loading, many flaws may initiate inside the glass and glass may fracture before one single growing crack reaches the critical level. Consequently, the strength of the glass under dynamic fracture conditions is significantly larger than that under quasistatic loading [2]. The physical process is extremely complex, and there are several theoretic models proposed by former researchers. The glass failure prediction model developed by Beason models the effects of time-dependent stresses in terms of „equivalent‟ maximum principal tensile stresses S60 of 60 seconds duration [3]:

KEYWORDS Dynamic fracture, Glass, Digital Image Correlation (DIC), Finite element analysis (FEA)

tf

2

1/16

S60 = *∫ σ(t)16 dt/60+ 0

(1)

This failure prediction model of glass strength is fundamentally flawed and unrealistic because it implies that the probability of failure is effectively independent of the load at the time of failure [4]. Tuler and Butcher proposed a criterion for dynamic fracture due to damage accumulation that, in effect, anticipated the form deduced from mechanistic modeling [5]:

INTRODUCTION Glass, with appropriate composition, and when engineered to enhance its strength using methods like thermal tempering, chemical tempering such as ion-exchange process, can potentially have a wide variety of applications in daily life. One of several applications is its use as cover glass to protect the 1

2

Currently with Apple Inc., Cupertino, California, USA. Address all correspondence to this author. Email: [email protected].

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Copyright © 2013 by ASME

where AF (expressed in MPa/ms) is the loading rate; A and n are constants depending on material and test conditions; σc is critical stress to failure. The ratio (VC/V0) represents the severity of damage. Based on the theory, we can find that the fracture criterion is related to the applied stress, the loading rate and the constants depending on the material which are the objects we will study. Similar studies have been done in the past by several researchers [8-13]. However, all the results presented in the literature are related to the laminated or thick glass, instead of one thin layer of glass used to protect the displays for smartphones, tablets, PCs, and TVs nowadays. In this study, the relation among the stress, loading rate, contact time and the fracture of a thin glass is investigated. An accumulated damage model is implemented and assumes that fracture is not instantaneous, but requires a finite time for the crack initiation. The effect of impact area, impact energy and impact momentum on the glass fracture will be proved to further improve the dynamic fracture criterion of glass.

tc

∫ (σ − σ0 )λ dt = C 0

(2)

where, λ and C are constants, σ0 is the threshold stress and tc is the time to failure. This is a general criterion which assumes that fracture is not instantaneous, but requires a finite time for the crackinitiation. As shown in the Fig. 1, the time to failure will be shorter with greater stress. This criterion is found to be in a good agreement with experiment results in the case of aluminum alloy.

FIGURE 1. PULSE OF IMPACT LOADING UNDER DIFFERENT AMPLITUDES

A slight modification of the original Tuler and Butcher‟s equation is suggested by Freund [6]: tc

β

σ(t) − 1) dt = C1 (3) σw 0 where σw is the threshold stress for the cumulated damage, and C1 and β are constants. Bouzid [7] introduced a parameter of damage D given by the relationship: V0 D = 1 − = 1 − 1/Vv (4) Vi where V0 is the threshold volume below which there is no visible damage formation; Vi is the volume where the cumulative stresses provoke the crack formation; VC is the critical volume (at failure); Vv (= Vi/V0 ） is called the normalized volume affected by impact. ∫ (

FIGURE2. GLASS IMPACT TEST SETUP

EXPERIMENTAL STUDY For the experimental studies, the steel balls with different diameters impact the thin glass panels (365 mm×241×0.71mm) attached to a rigid metallic frame from different heights (different potential energy). Glass impact test setup is shown in Fig. 2. The high-speed camera is applied for the direct visualization of the whole impact process. The Digital Image Correlation (DIC) method enables one to obtain the out-ofplane deformation and first principal strain of the glass during the impact process. Digital image correlation is a full field optical measurement technique of which both the in-plane and out-of-plane deformations and strains can be computed by comparing the pictures of the target object at initial and deformed stages (see Fig. 3). Compared with using strain gauge, the non-contact method gives whole field results with higher resolution and a smaller data collection area.

The critical normalized volume of fracture is therefore expressed as: −1/n+1 VC A = [1 − (σC − σ0 )n+1 ] (5) V0 AF



Previous study shows that this kind of bending mode by the centrally concentrated load boundary condition should be applied for the glass which is thin or when the impact is slow. For this case, fracture starts from the side opposite to the impact, and cracks radially propagate from the impact point [14]. So, the camera will be set up in the back of the glass to catch the data on the side opposite to the impact point. Besides, the humidity has a huge influence on the fracture of glass fracture [15-20]. In this study, the humidity of environment is monitored and the value is between 30% and 35%.

FIGURE 4. OUT-OF-PLANE DEFORMATION RESULTS OBTAINED BY DIC

0.5J 1J 1.5J 2J

Out-of-plane deformation with 2inch ball(mm)

10 8 6 4 2 0 -2 -4 0

5

10

15

20

25

30

Time(ms) FIGURE 3. HIGH-SPEED DIGITAL IMAGE CORRELATION

FIGURE.5 OUT-OF-PLANE DEFORMATION RESULTS WITH 2-IN BALL AT DIFFERENT ENERGIES

RESULT AND ANALYSIS

TABLE 1. THE MAXIMUM DEFORMATION AND THE TIME TO THE MAXIMUM DEFORMATION WITH 2-IN BALL AT DIFFERENT ENERGIES

Effect of the Energy A 2-inch steel ball is used to perform the impact test for 17.5-inch (diagonal length) glass under different potential energy conditions. Time history results of impact responses can be easily obtained at any point of interest. In this work, the center of impact area is the point of interest where the maximum deformation occurs (Fig. 4). As the potential energy increases, the maximum out-of-plane deformation and first principal strain increases accordingly (See Fig. 5, 6 and Tab. 1, 2). Additionally, the results show excellent repeatability.

Drop Energy (J)

Time to Max. Max. deformation deformation (ms) (mm)

0.5

7.57

6.42

1.0

6.80

7.93

1.5

6.30

8.96

2.0

5.87

9.67



Out-of-plane deformation with 2 inch ball at 1J(mm)

First principal strain with 2inch ball(%)

0.5 0.4 0.3 0.2 0.1 0.0 -0.1 0

5

10

15

20

25

30

Time(ms)

10 Deformation 1st principal strain

0.5

8 0.4 6 0.3

4

0.2

2

0.1

0

0.0

-2 -4

-0.1 0

5

10

15

20

25

First principal strain with 2 inch ball at 1J(%)

0.5J 1J 1.5J 2J

0.6

30

Time(ms)

FIGURE. 6. FIRST PRINCIPAL STRAIN RESULTS WITH 2-IN BALL AT DIFFERENT ENERGIES

FIGURE.7 THE FIRST PRINCIPAL STRAIN AND OUT-OFPLANE DEFORMATION RESULTS FOR 2-IN BALL AT 1 J

TABLE 2. THE MAXIMUM FIRST PRINCIPAL STRAIN AND THE TIME TO THE MAXIMUM FIRST PRINCIPAL STRAIN WITH 2-IN BALL AT DIFFERENT ENERGIES

Drop Energy (J) 0.5 1.0

Time to Max. first principal strain (ms) 6.73 6.33

Max. First principal strain (%) 0.38 0.40

1.5 2.0

5.20 5.37

0.49 0.60

Assuming a linear elastic behavior of the glass until fracture and a plane stress condition, the stress can be easily derived from the maximum strain recorded in the measurement. From the Tab. 2 and Tab. 3, it shows that the dynamic fracture is not only related to the failure stress. The thin glass will not be broken with 2-inch ball at 2 J, although the stress can reach to 450.05 MPa which is higher than the failure stress induced by higher drop energies. This is because the time to failure is getting shorter with higher drop energies. And the loading rate increases with higher drop energies. It shows that the dynamic fracture is closely related to the fracture time, which is similar to other researchers‟ conclusions.

From Fig. 7, the phenomenon could be found that the first principal strain increases quickly, then keeps steady and increases rapidly again to reach the maximum value. The reason is probably when the ball just hit the glass, the glass will deform larger locally. Consequently, the strain value increases quickly at first.

1.8 First Principal strain with 2inch ball at 4J(%)

1.6

Dynamic Fracture analysis Dynamic Fracture Data In this work, the glass (0.71 mm in thickness) will initially fail at around 2.5 J with 2-inch ball. We can get the first principal strain and out-of-plane deformation results when the glass fail based on DIC results. The fracture principal strain is easily achieved as the first principal strain value will increase suddenly when the glass fails (circled location in Fig. 8). Then the corresponding out-of-plane deformation value can be obtained (Fig. 9).The fracture data that is discussed in the paper is the average value of three experimental results.

1.4 1.2 1.0

Failure point

0.8 0.6 0.4 0.2 0.0 -0.2 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time(ms)

FIGURE 8. THE FIRST PRINCIPAL STRAIN WITH 2-IN BALL AT 4 J



Out-of-plane deformation with 2 inch ball at 4J(mm)

12

probably because of the production process of the glass. This tempered glass which is widely used in the display industry has a layer with high compressive stress. This compression acts as a sort of “armor,” making the glass exceptionally tough and damage resistant. It stops the glass from breaking on flaws due to the surface defects. The dimension of each picture is around 85×85 mm. The SEM images illustrate this phenomenon in detail. The location shown in Fig. 11 is about 40 mm away from the hitting point. The side (layer 4) which is hit by the ball suffers large compressive stress, so it has many flaws. Additionally, layer 1 whose thickness is around 50 um is the compression layer. And layer 2 and layer 3 show the glass structure due to the ion exchange.

10 8 6 4 2 0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time(ms)

FIGURE 9. OUT-OF-PLANE DEFORMATION WITH 2-IN BALL AT 4 J TABLE 3. THE FRACTURE DATA WITH 2-IN BALL AT DIFFERENT ENERGIES

Drop energy

J

Time to failure

ms

4.37

4.1

3.57

3.2

3

Failure deformation

mm

9.62

9.87

10.37

10.75

11.05

Failure strain

%

0.51

0.59

0.57

0.58

0.68

2.5

3

4

5

6

Failure stress

MPa 382.54 442.55 427.55 435.05 510.05

Loading Rate

GPa/s 87.54 107.94 119.76 135.95 170.02

Besides, using energy as the key parameter in impact testing is limited, since it does not account for the time spent in contact during the impact event. It is encouraged to find a simple metric related to time to illustrate the dynamic fracture. It proposes momentum change as such a parameter, as momentum change is linearly related to the maximum deformation of the glass due to the transfer of momentum into the flexure of the glass [21].

(a)

(b)

(c)

(d)

FIGURE10. THE CLOSEUP VIEW OF DYNAMIC FRACTURE ZONE

Effect of the Size of the Ball Three steel balls of different size (1 in, 1.75 in and 2 in) are used to investigate the effect of impact ball size on the dynamic responses of glass panel during impact under same 1 J potential energy. It is clearly shown in Fig. 12 that larger steel ball leads to higher glass deformation due to the higher momentum change. However, the strain results show the different trends (See Fig. 13). For 1-inch ball, the ball will detach from the glass quickly compared with larger size balls. Then the first peak of principal strain has a larger value and shorter contact time. While for the larger size balls, the ball will continue traveling and then rebound together with the glass. Then it induces the larger strain value. But the 1.75-inch ball will have

Dynamic Fracture Zone The glass will split into long strip debris under dynamic impact loading. Initially, the glass around the hit point will crack because of the large compressive stress (Fig. 10(a)). Then the wave propagates from the hit point to the boundary and rebounds quickly, and then the crack length increases (Fig. 10 (b), (c)). Finally, the whole glass breaks into long strip debris instead of netlike or treelike shape (Fig. 10 (d)). It is



larger strain results and shorter contact time as it has a smaller contact area.

First principal strain at 1J(%)

The glass fails at 2 J with 1.75-in steel ball (See Fig. 14). The time to the failure is 4.5 ms and failure stress is 435.05 MPa. The loading rate is 96.68 GPa/s.

1inch 1.75inch 2inch

0.5 0.4 0.3 0.2 0.1 0.0 -0.1 0

5

10

15

20

25

Time(ms) FIGURE 13. THE FIRST PRINCIPAL STRAIN RESULTS FOR DIFFERENT SIZE BALLS AT 1J

Out-of-plane deformation for 1.75inch ball (mm)

Out-of-plane deformation at 1J(mm)

9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4

1inch 1.75inch 2inch

10

0.6

8

0.5

6

0.4

4

0.3

2

0.2

0

0.1 0

1

2

3

4

5

First principal strain for 1.75inch ball(%)

FIGURE 11. SEM MICROGRAPH OF FRACTURE SURFACE

Time(mm)

FIGURE 14. THE FRACTURE DATA WITH 1.75-IN BALL AT 2 J

0

5

10

15

20

25

FEA VERIFICATION The FEA model is built using ANSYS/LS-DYNA. Due to symmetry, only a quarter of the glass (365×241×0.71 mm, 15-inch glass) and steel ball are modeled. This model consists of glass, tape, and steel ball (see Fig. 15). The bottom surface of tape is constrained in all DOF and Tied Surface to Surface contact (TDSS) is defined to connect glass panel to tape. Auto Surface to Surface contact (ASTS) is defined between steel ball surface and glass panel surface to simulate their interaction during the impact. Impact velocity is applied to the steel ball and gravity field is applied to the whole system.

Time(ms) FIGURE 12. THE OUT-OF-PLANE DEFORMATION RESULTS FOR DIFFERENT SIZE BALLS AT 1 J

As the steel ball size increases, the momentum change for steel ball increases, which explains the longer time for the large size steel ball to detach from the glass panel after impact. It has the same conclusion as other researchers‟ results. The momentum change accounts for the time spent in contact with the glass and the contact area [22].



0.7

Sim. Exp.

0.6 First principal strain with 2 inch ball at 2J (%)

FIGURE 15. DETAIL OF FEA MODEL AND BOUNDARY

CONDITIONS

0.2 0.1 0.0 5

10

15

20

25

30

Time(ms)

FIGURE 17. CORRESPONDING STRAIN RESPONSE COMPARISONS BETWEEN EXPERIMENT AND FEA MODELS WITH 2-IN BALL AT 2 J 7

Poisson‟s ratio 0.21 0.29 0.49

Exp. Sim.

6

Out-of-plane deformation for 1 inch ball at 1J (%)

Glass Steel ball Tape

0.3

0

TABLE 4. MATERIAL PROPERTIES

Elastic Modulus (GPa) 71.7 200 0.0016

0.4

-0.1

Linear elastic material properties are applied to all components (Tab. 4). Solid164 element is used for the tape, steel ball and glass in ANSYS/LS-DYNA.

Density （kg/m3） 2440 8000 840

0.5

As the following graphs (Fig. 16--Fig. 21) show, good correlation is obtained in the displacement and strain results. The energy loss by elastic wave propagation might be responsible for the expanding mismatch between experiment and finite element simulations. The validated FEA models will be used in fracture model to obtain the strain response.

5 4 3 2 1 0 -1 -2 -3 0

5

10

15

Time(ms)

8 6

0.4

4

0.3

First Principal strain for 1inch ball at 1J (%)

Out-of-plane deformation with 2 inch ball at 2J (mm)

FIGURE18. CORRESPONDING DISPLACEMENT RESPONSE COMPARISONS BETWEEN EXPERIMENT AND FEA MODELS WITH 1-IN BALL AT 1 J

Sim. Exp.

10

2 0 -2 -4 0

5

10

15

20

25

30

Time(ms)

Exp. Sim.

0.2 0.1 0.0 -0.1 0

FIGURE 16. CORRESPONDING DISPLACEMENT RESPONSE COMPARISONS BETWEEN EXPERIMENT AND FEA MODELS WITH 2-IN BALL AT 2 J

5

10

15

Time(ms)

FIGURE 19. CORRESPONDING STRAIN RESPONSE COMPARISONS BETWEEN EXPERIMENT AND FEA MODELS WITH 1-IN BALL AT 1 J



Out-of-plane deformation for 1.75inch at 1J (mm)

It shows that the dynamic fracture is strongly related to the fracture time. It proposes momentum change as a parameter to illustrate the dynamic fracture. 4. The glass will split into long strip debris under dynamic impact loading. Because the layer with high compressive stress of the glass stops the glass from breaking at flaws due to the surface defects. 5. From the SEM micrographs, the glass has a similar fracture surface as regular glass. While one more mist zone is obtained in our case, it is probably because of the production process of the glass. 6. As the steel ball size increases, the momentum change for steel ball increases, which explains the longer time for the large size steel ball to detach from the glass panel after impact. 7. The tests whereby the glass is impacted by the projectiles with different shape and different material need to be performed to figure out how these influence the fracture of the glass. Moreover, how the dimension of glass influences the strength of glass is another interesting topic.

Exp. Sim.

8 6 4 2 0 -2 -4 0

5

10

15

20

Time(ms)

FIGURE 20. CORRESPONDING DISPLACEMENT RESPONSE COMPARISONS BETWEEN EXPERIMENT AND FEA MODELS WITH 1.75-IN BALL AT 1 J 0.6 0.5 First Principal strain for 1.75inch balla at 1J (%)

ACKNOWLEDGMENTS The authors appreciate the financial support from Corning Incorporated. The authors are thankful to Ms. Lu Yuan at the Surface and Interface Laboratory, Department of Mechanical Engineering, Binghamton University, for her help with SEM.

Exp. Sim.

0.4 0.3 0.2

REFERENCES [1] Abrate, S., 1991. “Impact on laminated composite materials, ” Appl. Mech. Rev. 44(4): 155–89. [2] Freund, L. B., 1998. Dynamic fracture mechanics. Cambridge University Press, Cambridge, Great Britain, p. 509. [3] Beason, W. L., and Morgan, J.R., 1984. “Glass Failure Prediction Model,” Journal of Structural Engineering, ASCE, 110 (2), pp.197-212. [4] Reid, S. G., “Model errors in the failure prediction model of glass strength,” 8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, PMC2000-139. [5] Tuler, F. R., Butcher, B. M., 1968. “A criterion for the time dependence of dynamic fracture,” Int J. Fract Mech; 4:431. [6] Freund, L. B., 1993. Dynamic fracture mechanics. Cambridge University Press, Cambridge, Great Britain, p. 518. [7] Bouzid, S., Nyoungue, A., 2001. “Fracture criterion for glass under impact loading,” International Journal of Impact Engineering, 25, 831-845. [8] Kumar, P., and Shukla, A., 2011. “Dynamic response of glass panels subjected to shock loading,” Journal of Non_Crystalline Solids. [9] Woodward, R. L., Baxter, B. J., Pattie, S. D., and McCarthy, P., 1991. “Impact fragmentation of brittle materials,” J. Pys, C3, pp. 259–64. [10] Jalham, I. S., Alsaed, O., 2011. “The Effect of Glass Plate

0.1 0.0 -0.1 0

5

10

15

20

Time(ms)

FIGURE 21. CORRESPONDING STRAIN RESPONSE COMPARISONS BETWEEN EXPERIMENT AND FEA MODELS WITH 1.75-IN BALLS AT 1 J

CONCLUSION AND FUTURE WORK 1. The capability of DIC optical technique used in glass product development is demonstrated. Normally, a strain gauge is used to do this kind of analysis and this new technique would provide additional advantages. Among the advantages are noncontact of the specimen, ability to calculate strain measurements directly and the ability to capture the dynamic impact response at a very high frequency. Also, high resolution over a small area is possible due to DIC techniques. 2. The DIC is used to measure the deflection and strain during the ball drop impact test on the glass panels. Excellent correlation in maximum deformation was obtained between the measurements and predictions. 3. The time to failure gets shorter with higher drop energies. The loading rate increases with higher drop energies.



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