# Analysis of Debonding Failures of the Screen and Case during Tablet Drop

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory and Methodology

#### 2.1. Cohesive Zone Model

#### 2.2. Tiebreak Contact

## 3. Debonding Failure Simulations

#### 3.1. Finite Element Model

#### 3.2. Definition of the Cohesive Zone Model and Tiebreak Contact

#### 3.2.1. Definition of the Cohesive Zone Model

#### 3.2.2. Definition of Tiebreak Contact

#### 3.3. Definition of the Model Material

^{3}[34].

#### 3.4. Contact Algorithm and Other Definitions

^{2}in the y-negative direction, and use ELFORM with the value 19 to define the cohesive elements with 4-point integration. A stiffness hourglass control is added to parts with large deformations to ensure the calculation’s validity.

#### 3.5. Results and Discussions

## 4. Analysis of Influential Factors

#### 4.1. The Effect of Different Radii of Rounded Corners on Debonding

^{2}, which is 2.2% of the total area of the cohesive elements of the Air model with R = 6 mm, and the effect of T can be ignored. The area of the deleted cohesive elements S increases and then decreases, with the maximum and minimum of S achieved when the radius of the Air model’s rounded corners is R = 10 mm and R = 6 mm, respectively. S is primarily responsible for the variation in t. As a result, the t trend is consistent with S. When the Air model’s rounded corner radii are R = 10 mm and R = 6 mm, the maximum and minimum of t are obtained, and the maximum of t is 1.2 times the minimum. It can be concluded that when the rounded corner radius of the Air model R = 10 mm, t is the largest, which is 1.2 times the t of the Air model with R = 6 mm; thus, the Air model’s rounded corner radius should not be designed to be near 10 mm.

#### 4.2. Effect of Dropping with Different Positions on Debonding in the XY Plane

^{2}, the maximum t is 1, and all cohesive elements are deleted. The minimum of t is 0.377 times the maximum of t. Under the same conditions, it can be concluded that the Air model with α = 45° has the smallest t, which is 0.377 times the t for α = 0° and α = 90°. As a result, when using mobile phones or tablets, it is critical to avoid dropping the device at an angle of 0° or 90° between the long side of the mobile phones or tablets and the floor.

#### 4.3. Effect of Various Materials of Outer Case on Debonding

#### 4.4. Effect of Debonding on Different Strain Rates of PC/ABS

^{−2}s

^{−1}, 10

^{−3}s

^{−1}, and 10

^{−4}s

^{−1}, respectively, and the characteristic points were entered into the *MAT_PIECEWISE_LINEAR_PLASTICITY material model, which was used to determine the strain rate of PC/ABS. t characterizes the effect of different PC/ABS strain rates on the debonding between the outer case and outer glass of the Air model.

^{−2}s

^{−1}to 10

^{−4}s

^{−1}. The total area of deleted cohesive elements S follows the same trend as the t-transformation, with the maximum and minimum obtained at strain rates of 10

^{−3}s

^{−1}and 10

^{−4}s

^{−1}, respectively, with a difference of 0.004 between the t-maximum and t-minimum, indicating that the strain rate has a relatively small effect on t.

## 5. Conclusions

- (1)
- Different Air model rounded corner radii and PC/ABS strain rates have less effect on debonding between the outer case and outer glass of the Air model; t has a maximum difference of 0.004 for the PC/ABS strain rate from 10
^{−2}s^{−1}to 10^{−4}s^{−1}, and t has a maximum difference of 0.076 for the increase in R from 6 mm to 12 mm. - (2)
- The Air model drops in the XY plane at various angles, and different outer case materials have a greater effect on the debonding of the Air model’s outer case and outer glass. When the Air model is dropped at α = 45°, t is the smallest, 0.377 times that of the Air model dropped at α = 0° or α = 90°; when the Air model’s outer case material is glass, t is the smallest, 0.48 times that of the Air model with an aluminum alloy outer case.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Air model enhanced view [9].

**Figure 4.**(

**a**) Air finite element model; (

**b**) Definition of the outer glass local coordinate system XZ; (

**c**) Local refinement of the rounded corners of the outer case.

**Figure 5.**Definition of accelerometer (65 mm above Apple™ logo) [9].

**Figure 6.**(

**a**) Cohesive element simulating cracking; (

**b**) Cohesive element inserted between the outer glass and outer case.

**Figure 7.**Failure modes from a 1.8 m Air drop onto steel. Damage includes plastic deformation and partial glass debonding: (

**a**) Experiment [9], (

**b**) Cohesive zone model, and (

**c**) Tiebreak contact.

**Figure 8.**The cohesive zone model, the tiebreak contact, and the experimental resultant acceleration time course curves [9].

**Figure 10.**The acceleration time course curves for the Air model with different grid sizes for the cohesive zone model [9].

**Figure 11.**The acceleration time course curves for the Air model with different grid sizes for the tiebreak contact [9].

**Figure 12.**Displacement clouds of Air at (

**a**) 0.50 ms, (

**b**) 0.60 ms, (

**c**) 0.80 ms, and (

**d**) 1.00 ms for the outer glass and outer case along the z-direction.

**Figure 15.**The Air model in the XY plane, free fall, and the angle of the floor are (

**a**) α = 45°, (

**b**) α = 90°, and (

**c**) α = 0°.

**Figure 17.**Combination curves of the Air model with different materials used for the outer case, T, S, and t.

**Figure 18.**Stress–strain curves of PC/ABS at different strain rates [49].

**Table 1.**Element type, average element size, and the number of elements for each component of the Air.

Components | Element Type | Element Average Size (mm) | Element Number | |
---|---|---|---|---|

Outer case | Impactor Corner | SOLID | 0.975 | 36,885 |

Main Case | 1.5 | |||

Outer glass | Impactor Corner | SOLID | 0.975 | 18,499 |

Main Glass | 1.5 | |||

PCB | TSHELL | 3.375 | 1260 | |

Batteries | SOLID | 3.375 | 2016 | |

LCD metal tray | TSHELL | 3.0 | 4015 | |

LCD plastic surround | SHELL | 1.5 | 6984 | |

LCD glass | SOLID | 1.5 | 13,200 | |

Speaker(s) | SOLID | 3.0 | 198 | |

Rigid floor | SHELL | 4.5 | 16,198 | |

Accelerometer | - | - | - | |

Total | - | - | 99,255 |

Components | Materials Model | Density (kg/m^{3}) | Youngs’ Modulus (GPa) | Poisson’s Ratio | Yield Stress (Mpa) |
---|---|---|---|---|---|

Outer case | MAT098 | 2700 [37] | 70.2 [37] | 0.33 | - |

PCB | MAT024 | 2700 | 70.2 | 0.34 | 156.3 [37] |

Batteries | MAT024 | 2700 | 70.2 | 0.33 | 156.3 |

LCD matel tray | MAT001 | 7800 | 210.0 | 0.33 | - |

LCD plastic surround | MAT024 | 1150 [36] | 2.2 | 0.44 | 57.77 [35] |

LCD glass | MAT001 | 2500 [38] | 72.0 [38] | 0.22 | - |

Speaker(s) | MAT024 | 2700 | 70.2 | 0.34 | 156.3 |

Outer glass | MAT001 | 2500 | 72.0 | 0.22 | - |

Rigid floor | MAT020 | 7800 | 210.0 | 0.33 | - |

Materials | Friction Coefficient |
---|---|

Aluminum Alloy–Aluminum Alloy | 0.40 [40] |

Aluminum Alloy–Steel | 0.17 [43] |

Glass–Glass | 0.20 [42] |

Glass–Steel | 0.13 [42] |

Aluminum Alloy–Glass | 0.25 [41] |

**Table 4.**The area of deleted cohesive elements and total area of cohesive elements for the Air model with different radii of rounded corners.

The Radius of Corner R (mm) | Total Area of Cohesive Element T (mm^{2}) | The Area of Deleted Cohesive Element S (mm^{2}) | t |
---|---|---|---|

6 | 3738.1 | 1410.8 | 0.377 |

8 | 3717.5 | 1434.9 | 0.386 |

10 | 3690.0 | 1672.6 | 0.453 |

12 | 3655.7 | 1507.7 | 0.412 |

**Table 5.**The area of deleted cohesive elements and total area of cohesive elements for different drop angles of the Air model.

Different Drop Angles α (°) | Total Area of Cohesive Element T (mm ^{2}) | The Area of Deleted Cohesive Element S (mm^{2}) | t |
---|---|---|---|

0° | 3738.1 | 3738.1 | 1.000 |

45° | 3738.1 | 1410.8 | 0.377 |

90° | 3738.1 | 3738.1 | 1.000 |

Materials of the Outer Case | Material Models | Density (kg/m ^{3}) | Youngs’ Modulus (GPa) | Poisson’s Ratio | Yield Stress (Mpa) |
---|---|---|---|---|---|

Aluminum Alloy | MAT98 | 2700 [37] | 70.2 [37] | 0.33 [9] | - |

Glass | MAT24 | 2500 [38] | 72.0 [38] | 0.22 [9] | 143.2 [45] |

Stainless Steel | MAT24 | 7930 [47] | 196.0 [47] | 0.33 [47] | 263.0 [48] |

**Table 7.**The area of deleted cohesive elements and the total area of cohesive elements for the Air model with different materials used for the outer case.

Materials of the Outer Case | Total Area of Cohesive Element T (mm ^{2}) | The area of Deleted Cohesive Element S (mm^{2}) | t |
---|---|---|---|

Aluminum Alloy | 3738.1 | 1410.8 | 0.377 |

Glass | 3738.1 | 666.1 | 0.178 |

Stainless Steel | 3738.1 | 808.7 | 0.216 |

**Table 8.**The area of deleted cohesive elements and the total area of cohesive elements for the PC/ABS with different strain rates.

The Strain Rate of PC/ABS (s^{−1}) | Total Area of Cohesive Element T (mm ^{2}) | The Area of Deleted Cohesive Element S (mm^{2}) | t |
---|---|---|---|

10^{−2} | 3738.1 | 1403.0 | 0.375 |

10^{−3} | 3738.1 | 1408.5 | 0.376 |

10^{−4} | 3738.1 | 1392.0 | 0.372 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Z.; Jin, X.; Wang, D.; Ma, F.
Analysis of Debonding Failures of the Screen and Case during Tablet Drop. *Sustainability* **2023**, *15*, 13475.
https://doi.org/10.3390/su151813475

**AMA Style**

Zhu Z, Jin X, Wang D, Ma F.
Analysis of Debonding Failures of the Screen and Case during Tablet Drop. *Sustainability*. 2023; 15(18):13475.
https://doi.org/10.3390/su151813475

**Chicago/Turabian Style**

Zhu, Zhengtao, Xiaoming Jin, Di Wang, and Fangping Ma.
2023. "Analysis of Debonding Failures of the Screen and Case during Tablet Drop" *Sustainability* 15, no. 18: 13475.
https://doi.org/10.3390/su151813475