MAE Session for Intro to Engineering

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Introduction

This session aims to demonstrate how engineers might approach the design, modeling, and testing of structures for applications in mechanical, aerospace, and other engineering disciplines.

Preparation for In-class Activities

Please download and install FreeCAD on your laptop before attending the in-person session. During our session, each team will have an opportunity to design, fabricate, test, and simulate the behavior of a tensile structure. Please bring your laptop with FreeCAD installed and a pencil to class. If you have a Mac and are having issues with installation, you might watch the video below:

How to Install FreeCAD on a Mac and Add a Sketch to an Existing Part Design

Normal Stress in an Axially Loaded Member

We use multiple terms, such as yield and ultimate tensile strength, to characterize the failure of a material under mechanical loading. For ductile and brittle materials, the ultimate tensile strength indicates the maximum normal stress a material withstands before breaking. Uniaxial, normal stress has the same units as pressure (e.g., Pa or MPa where 10⁶ Pa = 1 MPa) and is a normal force divided by cross-sectional area or

σ = F/A

where σ is the normal stress, F is a normal force, and A is a cross-sectional area. A diagram depicting uniaxial, normal loading is below:

Paper as an engineering material for this session

Common values for ultimate tensile strengths range from 1 MPa for silicone to 15 MPa for tin to 20 MPa for polypropylene to 200 MPa for copper to 450 MPa for aluminum alloys to 750 MPa for high-strength steel to 3.5 GPa for Kevlar to 5.5 GPa for carbon fiber.

For this session, we will use paper as a material to demonstrate an approach to designing, testing, and modeling mechanical structures. In prior tensile testing in our lab, we found that samples of paper used in copy machines with cross-sectional dimensions of 6 mm (width) x 0.1 mm (thickness) would typically break under a normal force of 20 N. The video below shows how we tested one of our paper samples in the lab.

Tensile Test and Estimating Ultimate Tensile Strength of a Piece of Paper

How might we estimate for the ultimate tensile strength of these cut samples of paper?

The ultimate tensile strength S_u of this sample of paper is 20 N / (0.1 mm x 6 mm) or 3.3 x 10⁷ Pa or 33 MPa. Hint: the Google search engine keeps track of units automatically (see this example).

Designing and fabricating a Structure to Withstand a Specified Load

Knowing the yield strength or ultimate tensile strength of a material facilitates predicting how much load a structure might withstand before failing under idealized conditions. For example, if we design a structure made of the paper previously described to withstand a tensile load of 15 N, we calculate a suitable cross-sectional area that would permit up to 33 MPa of stress using a re-arranged version of the formula previously provided:

A= F/σ

Thus, a cross-sectional area of 0.45 mm² (15 N/33 MPa) might support 15 N with this material having an ultimate tensile strength of 33 MPa. If we maintain the same thickness (0.1 mm) using only one sheet of paper, we might use a sample with a width of 4.5 mm. If we used two sheets of paper with total thickness of 0.2 mm, we might reduce the width of the cross section to 2.3 mm.

Designing structures for mechanical, aerospace, and other engineering structures to withstand only the anticipated load with no margin of error might save mass/weight but be risky (i.e., dangerous, catastrophic, costly, unethical). For this reason, engineers specify factors of safety to account for unknowns, aging, and uncertainty in the material properties and environmental conditions. One definition of a safety factor is the following:

Safety Factor (SF) = Stress at Failure / Design Stress

For example, if the stress at failure/yielding/breaking is 2 MPa and the design stress in the structure during its use/lifetime is 1 MPa, the safety factor would be 2. With their emphasis on reduced payloads to reduce demands for lift and thrust to enable flight, safety factors for aerospace applications range from 1.25 to 2 with a typical value being 1.5, while safety factors for other mechanical or civil applications might be 3 for automobiles or 2 for buildings.

DESIGN Tasks

Work with your team to do the following:

Specify a desired force between 21 N and 60 N, which you would like your designed specimen to withstand under tension.
Thinking like an aerospace engineer, select an appropriate safety factor and specify an appropriate width and thickness of your aerospace specimen.
Thinking like a mechanical engineer, select an appropriate safety factor and specify an appropriate width and thickness of your mechanical specimen.

The video below provides an explanation for how to approach the above tasks.

Designing a Simple Structure for Tensile Loading: Using tensile strength, a specified tensile load, and a safety factor to design a specimen with an appropriate width and thickness.

Fabrication

Design and sketch outlines of your specimens on the “dog bone” specimens your team has received. Please keep in mind that sharp edges will lead to concentrations of stress, which will lead to premature failure at lower forces. Smooth curves/outlines with large radii will prevent the buildup of concentrations in stress.
While waiting your team’s turn to use the tensile testing machine, perform FEA on your designs (see next section).
When called, bring your aerospace and mechanical specimens to the tensile testing machine.
Load the specimens to the specified force to evaluate whether or not the samples will support the specified force.
Continue loading each sample to the point at which it breaks and evaluate how close the stress at the breaking point is to what your team predicted it would be based on your selected safety factors.
Record and upload a video of your team cheering during the tensile test of your specimen. Please enter the link using this Google Sheet, which will require the use of your Rutgers Scarletmail account.

The video below provides an explanation for how to approach the above tasks.

Fabricating and testing a paper-based structure for tensile loading with an appropriate cross-sectional area.

Tensile test of a paper-based specimen consisting of 3 layers of 0.1-mm thick paper with a minimum width of approximately 8 mm.

Digital Task 1: Use FreeCAD to digitize the design of your sample

Following the YouTube video below, create your designed geometry in FreeCAD. Please download and start with this FreeCAD file/model.

If you are using a MAC, start with this first video before going to the subsequent one using a PC:

Video for Mac (same video as shown at top under installation for a Mac)

Please use this video from a PC to complete the design after having performed the initial installation.

Designing a Simple Tensile Structure in FreeCAD,

Modified dog bone produced in FreeCAD. The thickness is 0.3 mm (dimension not shown), and the minimum width at the center of the profile is 7.6 mm.

digital Task 2: Perform Finite Element Analysis Using CalculiX

Following the YouTube video below, simulate the mechanical response of your designed geometry using finite element analysis (FEA) software CalculiX available within FreeCAD. Then, upload a screenshot of your FEA to a publically available link (e.g., Wikimedia commons, your Scarletmail Google drive with public sharing permissions, Instagram, Google Photos, etc.) and post the link on our spreadsheet (requires Scarletmail access for editing).

Simulating the Stress in a Simple Tensile Structure in FreeCAD Using CalculiX
Note: We display our results using von Mises stress in the video, but max principal stress or stress in the X-direction is more akin to the normal stress we previously calculated.

Example of what you might upload to a publicly available site.
Resulting von Mises stress of a tensile structure simulated with FEA in FreeCAD and CalculiX. The maximum calculated von MIses stress is 33.6 MPa. The normal load is 75 N, the thickness is 0.3 mm, and the minimum width at the center of the profile is 7.6 mm.

Resulting normal stress in the longitudinal (x-direction) of a tensile structure simulated with FEA in FreeCAD and CalculiX. The maximum calculated stress is 33.6 MPa as shown on the left for stress ‘sxx’. The normal load is 75 N, the thickness is 0.3 mm, and the minimum width at the center of the profile is 7.6 mm.

What Have We Reviewed and Accomplished?

We have reviewed the process of designing a simple structure to withstand a specified load with safety factors appropriate for mechanical, aerospace, and other engineering applications. We calculated the cross-sectional area necessary to support specified loads, we then sketched and fabricated specimens, experimentally tested them, and digitized the design. Using FEA, we also modeled and simulated the response of the specimens to mechanical loading. We have also demonstrated the use of open-source software tools, such as FreeCAD and Calculix, to model the behavior of complex mechanical systems.

What does Success Look Like?

We would like our analytical calculations, our experimental design, and simulations to agree with each other for the tensile testing of our copy paper with an ultimate tensile strength of 33 MPa. In the case presented, we predicted that a cross section with a width of 7.6 mm and a thickness of 0.3 mm would support a tensile load of 50 N with a safety factor of 1.5 (breaking force of 75 N). When we performed the experimental tensile test, we found that the specimen broke at a tensile load greater than 90 N corresponding to a safety factor of approximately 1.9. When we simulated the behavior of our sample using FreeCAD and CalculiX, we found that the maximum stress near the center of the specimen was ~33 MPa. Thus, our analytical solution, experiment, and FEA-based simulation are in agreement with each other.

Acknowledgements

We would like to thank Milan Simonovic for putting together the experimental setup, Praj Kuntal Patel and Srijay Kavuru for testing and preparing samples for 14:650:291 Mechanics of Materials, and Ziyad Abouelenin for troubleshooting issues with using FreeCAD with a MAC. We would also like to thank Jesenia Cadena from the School of Engineering and Qingze Zou from Mechanical and Aerospace Engineering for motivating us to create this lab for the Intro to Engineering course for first-year students in the Rutgers School of Engineering.