Apple iPhone 6 Plastic Deformation Analysis

5/18/2018 Apple iPhone 6 Plastic Deformation Analysis

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Finite Element Analysis of the iPhone 6s

Resistance to Permanent Deformation

Compiled by: Devon Cates, Dan Cho, Cody Crone

Submitted to: Professor I. Smid

The Pennsylvania State University

December 4th, 2014


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Abstract

With the recent release of the iPhone 6 there have been user claims and consumer speculation

that the new phone has the potential to undergo irreversible, plastic deformation under relatively

low stresses. To theoretically evaluate the force needed to permanently deform the phone, an

accurate three-dimensional model has been created using SolidWorks CAD software.

Incrementally increasing bending forces were applied to the phone utilizing SolidWorks Finite

Element Analysis (FEA) capability, with multiple iterations for each load at varying node

quantities to converge upon accurate results. The maximum stress and deformation for each load

case were documented and compared to the yield strengths of the materials incorporated in the

iPhone 6 to determine at what point permanent deformation will occur.


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Introduction

The iPhone 6 incorporates the thinnest wall thickness to date in a phone released by Apple Inc.

While it may be aesthetically pleasing to consumers, there have been concerns about its

structural integrity. The iPhone body consists of an alloy with material properties similar to

6061-T4 aluminum [2]. Corning Gorilla Glass [3], upgraded from previous iPhones, has been

integrated into the construction of the phones screen. While the strengths of these materials,

which make up a vast majority of the iPhones structure, are considerably high for their weight,

the overall thinness of the device may lead to yielding under forces not substantially greater than

those experienced during everyday operation.

Approach & Formulation

To test at what point the iPhone 6 experiences permanent deformation, an analysis using the

Finite Element Method has been conducted. The first step in approaching this problem was to

find in-depth dimensioned schematics (SeeFigure 1) of the iPhone 6. The source used to acquire

these drawings is found below in the references section [1]. After obtaining the required

schematics a dimensionally accurate mock version of the device was modeled on computer-aided

design software; in this case Solidworks was utilized.

Figure 1. iPhone 6 Schematics


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For simplicity, the internal electrical components of the iPhone 6 were not included in the CAD

model. It is assumed that the contribution to the overall structural integrity of the model from

these components is negligible because they are small and generally not designed to withstand

large forces. However, the volume rocker, volume adjustment, and sleep/wake button cavities in

the aluminum body of the phone were included in the model because they could be the sight of

stress concentrations and therefore could have an impact on the phones integrity. The home

button feature on the glass screen was also included for this reason. The wall thickness of the

model was set to an approximately average value determined by the varying wall geometry of

the actual iPhone 6 shown inFigure 2.

After extensively modeling the

phone, the next challenge was to

determine where the phone should

be constrained and where the

force(s) should be applied to run

the Finite Element simulation. The

two most applicable situations are

as follows: let the phone be

constrained on the top and bottom

with an applied load directly in the

middle of the body, or let the

phone be constrained directly in

the middle with an applied load on

the top and bottom. These are

common situations, and both could

be encountered by a typically consumer. Figure 3. Illustrates the load/constraint configuration

that was chosen for this study. For clarity, green arrows represent fixed geometric constraints,

and purple arrows represent the force applied over the area shown.

Figure 2. iPhone 6 Aluminum Body


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Figure 3.Forces and Constraints on the Model

A static FEA was performed using the governing equation shown inFigure 4. This is a simple

yet useful method for calculating the effects of static loads on isotropic materials. A tetrahedral

mesh was used to discretize the body into a series of nodes and elements, each with its own

stiffness equation (defined in Figure 4). Referencing Figure 4, K represents the stiffness

matrix, which is derived from material parameters of the object in question and is assumed to be

constant throughout. x represents the displacement of a particular node which is elicited by

F, the force at that node. These equations are solved simultaneously using linear algebra in the

form shown in Figure 5, where [ ] represents matrix notation and { } represents vector

notation.

Figure 4. Spring Element Stiffness Equation

[K] {x} = {F}


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Finite Element Analysis Methodology

SolidWorks 2014 CAE Simulation software was used in the Finite Element portion of this study.

The meshed part (seeFigure 5) consisted of basic tetrahedral elements, with an average element

number approaching 18,000 for final-iteration runs (See Figure 6). Material properties for the

aluminum alloy (yield strength = 227.5 MPa) body and Gorilla Glass (yield strength !800 MPa)

screen were obtained from sources [2] and [3] respectively. Because the strength of the

aluminum is lower than that of the Gorilla Glass, it was the first component to plastically deform

under loading and was used as a metric for determining whether permanent damage to the device

had occurred at a given load (see Table 1 under Results and Discussion). CPU time for one

meaningful simulation run was approximately 10 minutes on a 64-bit DELL Optiplex 7010

computer with 8.0 GB of RAM. Mesh iterations were made until the maximum stress (shown in

Figure 6) and maximum displacement (not shown) remained at approximately (+/- 0.2%)

constant values.

Figure 5. Mesh With Loads and Geometric Constraints


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Figure 6. Result Accuracy vs. Number of Mesh Elements

The main design assumptions/approximations that were made during the modeling process are

detailed in the Approach and Formulation section of this report (see Figure 7 for illustration).

Additionally, minor features such as the camera, flash housing, speakers, headphone jack and

charge port were not included because they are not located in areas of high force/displacement.

All relevant dimensions match Apple Inc. nominal values for the iPhone 6 according to

schematics from reference [1]. It is understood that the Finite Element Method is not currently

capable of generating results that match experimental data with 100% accuracy, but the stress

and displacement values achieved in this analysis lie within a plausible and meaningful range. It

is also understood that the simplifications made to remain within time/resource constraints have

sacrificed some of the accuracy of the results. With more time and/or better computers/software,

the accuracy of the results would likely be marginally improved.

Figure 7. Cutaway Showing Cavities for Volume and Sleep/Wake Buttons


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Results and Discussion

In order to generate results with the highest level of accuracy possible, the iPhone 6 model

underwent several Finite Element simulations with incrementally increasing loads (shown in

Table 1). The purpose of these simulations was to ascertain the minimum load that would elicitplastic deformation in the device. In Table 1it is shown that starting from 116.1 N, the aluminum

body of the iPhone 6 will exhibit plastic deformation under the load/constraint configuration

illustrated inFigures 5 & 3.

Load

[N]

Number of

Iterations

Max. Displacement

[mm]

Max. Stress

[MPa]

Yield Strength

[MPa]

Plastic

Deformation?

100 5 0.5879 179.8 227.5 No

105 5 0.6743 205.9 227.5 No

110 5 0.7065 215.8 227.5 No

115 5 0.7386 225.5 227.5 No

116 5 0.745 227.4 227.5 No

116.1 5 0.7456 227.6 227.5 Yes

200 5 1.176 359.6 227.5 Yes

300 5 1.764 538.8 227.5 Yes

400 5 2.042 655.3 227.5 Yes

500 5 2.52 722 227.5 Yes

As evidenced in Table 1, the Finite Element model behaved as expected. The iPhone 6 was

hypothesized to be permanently deformed under relatively low forces due to its overall wall

thinness, low moment of inertia in the bending direction, insubstantial material properties, and

abundance of geometric features that could result in stress concentration. The maximum stress

was located at the volume button cavities (shown in Figure 8), as expected. This is because these

features include small radii in the filleted corners, and are more likely to experience increased

stress at these areas. Therefore, these areas will be the first to experience plastic deformation,

Table 1. Simulation Results


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although a small amount of deformation here would not present a serious risk of compromising

the functionality of the device.

Figure 8. Stress Concentrations Around Button Cavities

Although the maximum stress was located at the volume buttons, the maximum displacement

(shown in red) was located in the center of the model where the load was applied (seeFigure 9).

This has been verified by numerous physical tests on iPhone 6 bending that can be found on the

Internet, and thus the results achieved in this analysis were again observed to be accurate at least

in terms of overall mechanical and geometric behavior. The advantage of the Finite Element

Method in this application is its ability to locate and quantify specific amounts of deformation in

any given area with a relatively high amount of precision compared to physical testing.


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Figure 9. Displacement Gradient

Conclusions

This study illustrates the compromises that Apple Inc. designers and engineers have had to make

during the conceptualization and development of the iPhone 6. Due to rapid advancements in

microprocessor and energy storage technology resulting in the ability to produce smaller yet

equally or more powerful versions of these components, the demand has increased for thinner

and sleeker smart devices. If anything can be learned from this analysis, it is that perhaps more

research should be done in developing stronger alloys that are more capable of retaining

structural rigidity at thinner dimensions. For the time being, however, the load necessary for

plastic deformation established in this analysis falls outside of the range of regular and intended

operating conditions and should not be a cause for concern for the average consumer.


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Improvements and suggestions for future work

Problems were encountered throughout the entire process of the project. These problems

happened before the modeling even began, some of them were easy fixes, but others caused

exacerbated issues. One of the first FEA problems was trying to incorporate all of the internal

wall features of the actual iPhone housing; for simplicity these were incorporated into an average

thickness value applied to the entire housing. Resource capabilities created setbacks in terms of

the softwares ability to mesh intricate features. The complexity of assembly caused several

meshing problems. The idea of the assembly was to get the phone to deform around a stress

concentration point, such as the lock button or volume rocker, as observed in physical bend

testing. Assembling all the external features and glass worked well until meshing; problems were

run into where the mated components came into contact. Despite all of the setbacks a completemodel was successfully obtained. Looking at this from a cost-benefit analysis standpoint this has

the potential to save numerous technician man-hours in experimental design, conduction, and

analysis. Physically testing iPhones as many times as a model can be run to obtain accurate

results is not feasible or cost effective.

There are numerous variables that could be incorporated into future work that would have the

potential to drastically impact the results of the simulation. One variable that would notably

impact the behavior of the phone is temperature. This product is marketed worldwide, and most

of the materials found in the product have a temperature dependence. Where the constraints and

forces are applied would also have a large impact on the results of the simulation. If resources

allowed, multiple and exact forces and constraints could have been placed on the model to

simulate various load scenarios that could occur in day to day usage.


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Distribution of Work

Devon Cates:

" Drafted/reviewed/edited final written report

" Created multiple CAD model designs/iterations

" Composed relevant images

" Spearheaded incompatible mesh troubleshooting

" Determined geometric features to include/ignore

Cody Crone:

" Researched Material Properties

" Created slideshow for final presentation

"

Aided in CAD model development and troubleshooting" Performed cost-benefit analysis

" Suggested improvements for future work

Dan Cho:

" Completed and documented FEA testing and results analysis

" Performed sensitivity analysis concerning mesh iterations

" Made improvements to load and constraint applications

" Composed relevant images

" Provided CAD modeling consultation


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References

* Solidworks 2014 was the modeling software used to create and analyze the three dimensional

model.

[1] "BulletTrain BulletBlog by JakeE: Apple IPhone 6 & IPhone 6 Plus Dimensional Drawings

Schematics."BulletTrain BulletBlog by JakeE: Apple IPhone 6 & IPhone 6 Plus Dimensional

Drawings Schematics. N.p., n.d. Web. 02 Dec. 2014.

[2]Redditor Explains Why the Aluminum IPhone 6 Bends and the Plastic Note 3 Doesn't -

GSMArena Blog." GSMArena Blog Redditor Explains Why the Aluminum IPhone 6 Bends and

the Plastic Note 3 Doesnt Comments. N.p., n.d. Web. 02 Dec. 2014.

[3] Incorporated, Corning. Corning Gorilla Glass(n.d.): n. pag. Web.

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