1 332 Laboratories 1. 2 Computational Exercises 1 FEA of a Cantilever Beam... 1 Experimental Laboratory: Tensile Testing of Materials...

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1 1 332 Laboratories Contents Laboratories 1 2 Computational Exercises 1 FEA of a Cantilever Beam Experimental Laboratory: Tensile Testing of Materials Computational Exercises 332 Computational Lab #1: Finite Element Analysis of a Cantilever Beam MAT SCI 332 FEA Report Guidelines Compile the team s work into a single report. Your report should contain: (a) A brief introduction. (b) The work of each individual student as a separate section. You can work together on the finite element analysis, but write up the work for your component individually and combine work with labmates later. (c) A conclusion for the project as a whole. I am looking for accuracy and deliberation in your modeling and thoughtful consideration of the results. I am not concerned with formatting or the length of your report particularly, but as for any report you write, readability, good citation sourcing, informative figure presentation, and conciseness are valued. Broadly, the body of the report should include the following: (a) The problem definition: geometry, materials properties, loads and boundary conditions. (b) Discretization: Element type and mesh parameters. (c) The results: Provide the results as a function of parameter values and discretization, as required. Show relevant results displacement or stresses and make sure to note which stress values you are showing. Note how your results change as the parameters or mesh changes. Hint - well-constructed figures are very important to a good report. You may want to carefully design your figures so that that they are efficient at conveying relevant information. Note that the Abaqus/CAE viewport can be exported as an image by selecting File Print. Submit an electronic copy of your report, as well as your Abaqus files (.cae and.odb files), by uploading them to CANVAS the date that they are due. The embodiment of stresses and strains in a cantilever beam is well known from solid mechanics. A simple theory used to explain this behavior is Euler-Bernoulli beam theory, or E-B theory, a model that does not account for large or plastic deformation, transverse shear strain or Poisson contraction. In this exercise, you will use finite element analysis (FEA) to model a rectangular cantilever beam under an end load. You will use Abaqus explore the stresses and strains present in the beam, compare them to E-B theory, and use engineering principles to adapt the cantilever design. Objectives Explore basic FEA modeling (defining loads, boundary conditions, and meshes) using Abaqus. Use computational solvers to calculate and subsequently visualize stress and displacement fields. Compare computational and analytical results, noting the strengths and weaknesses of each. Use your results to adapt the cantilever design to achieve a performance tolerance. Directions below. Model a cantilever beam loaded on its free end by a shear traction T z, as shown in Figure2.1, 1

2 FEA of a Cantilever Beam 2 COMPUTATIONAL EXERCISES z y x T z 0 h L b Figure 2.1: A cantilever beam fixed at one end. The beam is made of Al 6070-T6 with Young s modulus E = 80 GPa, Poisson s ratio ν = 0.33, and yield strengthσ y = 69 MPa. Its dimensions are length L = 150 mm, height h = 10 mm and base b = 50 mm. The beam is uniformly loaded with a stress of T z = 0.50 MPa on the free end. We will model the cantilever beam to be fixed to the wall at one end (displacements of nodes at x = 0 are u = 0). We define our origin as the point at the beam s centroid and the interface with the wall. These parameters are summarized below: L = 150 mm h = 10 mm b = 50 mm E = 80 GPa ν = 0.33 σ y = 69 MPa T z = 0.5 MPa u 1 (x = 0) = u 2 (x = 0) = u 3 (x = 0) = 0 Refer to the walk-through provided in class to construct your model and perform the computational analysis. Don t hesitate to ask questions if you get stuck. Address the following question in your report: (a) Describe (using words and figures) theu 2 and u 3 displacement fields present in the deformed beam. Explain the sources of the features of thesefields. (b) Describe (using words and figures) theσ xx and von Mises (σ) stress fields present in the deformed beam. Explain the similarities and differences between these fields. Do you expect this beam to yield? (c) Plot and discuss the FEA-computed and the Euler-Bernoulli displacement as a function of distance from the fixed end (x-direction). The beam deflection in thez-direction as a function of distance is δ z (x) = wheref z is the force applied along thez-axis of the beam andi = bh3 12 F z 6EI (3L x)x2, (2.1) is the second moment of inertia. (d) Plot and discuss the FEA-computed and the Euler-Bernoulli axial stresses (σ xx, ors 11 in Abaqus) in the tensile region in thex-direction. Theσ xx stress at the topmost yz-face of the beam is: wherez = bh2 6 is the section modulus. σ xx (x) = F z(l x), (2.2) Z (e) Referring to your previous two plots, identify any major deviations between the FEA results and the results from Euler-Bernoulli theory. Identify two possible sources reasons for any derivations you may see. Hint: Both E-B theory and your FEA model may have shortcomings. 2

3 FEA of a Cantilever Beam 2 COMPUTATIONAL EXERCISES (f) Assume that the the tip displacement you find for this beam,δ z (L), is smaller than you can tolerate in your application, but the beam itself is too heavy. Based on your FEA results, construction a new model in which 50% of the Al 6070-T6 is replaced with polystyrene (E = 3 GPa,ν = 0.35), but such that the bending stiffness (K = Tz δ z(l) ) reduces only by 25% compared to the all-al beam. Hints: Look at the von Mises stress field. Where can you tolerate a more compliant material? Also, it is very easy to copy and modify an Abaqus model! 3

4 Experimental Laboratory: Tensile Testing of Materials 2 COMPUTATIONAL EXERCISES Experimental Laboratory: Tensile Testing of Materials Both the mechanical testing and the lab report will be completed in pairs. Your partner should be the same partner as your FEM lab partner because you will need to use the data collected here for one of the questions on the Stress Concentration FEM assignment. Goals Gain experience with tensile testing of metals and polymers Determine mechanical properties from stress strain curves Determine the effect of defects on the mechanical behavior of metals. Use experimentally determined data to create FE models Materials Each pair of students will perform tension tests on one of the following metals, plus a polymer (Lexan) sample: Steel 1018 Steel 4130 (hot rolled, annealed) (Supplier of metal samples: Laboratory Devices Company) Tensile Testing Tensile tests will be performed using a Sintech 20G tensile testing apparatus in the Central Laboratory for Materials Mechanical Testing (CLaMMP), Cook Hall Room You MUST wear safety glasses! Prior to testing, measure and record the gauge length, gauge width, and sample thickness of all the samples to be tested. If the sample has a drilled hole, measure the diameter of the hole. Select the appropriate test method from the Method menu. Load tensile specimen into sample grips (first the top, then the bottom) and tighten, making sure the sample is as vertical as possible. If necessary, reduce load to 0 N by moving the crosshead (black wheel on the handset. CW is tension. CCW is compression). Start test. You will be prompted to enter the specimen dimensions here. Observe the sample deforming during the test. The software will collect a force vs. crosshead extension curve. At the end of the test, the data will be exported as a.txt file to the MSE 332 folder under Exports. Please bring a USB drive to get the data from the computer. If your sample necked during testing, be sure to measure the cross section of the neck after testing. Lab Report Instructions (a) Briefly (no more than a paragraph or two) describe the experimental setup. This should include materials tested, defect geometry, test conditions, etc. (b) Using the Load vs. Extension generated during the lab, plot both engineering and true stress vs. strain curves for each of the two samples you tested and each of the as-received samples (no hole in the center) given. Are there any regions where you cannot calculate part of the stress vs. strain curves? Why or why not? (c) Calculate the Young s Modulus, tensile yield strength, ultimate tensile strength, and strain to failure for each of the samples. Provide a brief description of how you determined these values. For the as-received steel sample label these values on the stress-strain curve. (d) How do the values calculated in Question 3 compare to the values reported in literature for the asreceived steel sample and the polymer sample (be sure to cite here)? Calculate the % error and comment on why the values are the same or different. (e) Do you observe necking in any of the samples? Why or why not? 4

5 Experimental Laboratory: Tensile Testing of Materials 2 COMPUTATIONAL EXERCISES (f) What is the reduction of area (%) in the neck of the sample? Based on this data is there any additional information you can plot on the engineering/true stress vs. strain curves? (g) Describe the failure mechanisms for each of your samples. (h) Compare the stress vs. strain behavior for the as-received steel sample and the steel sample with a defect. Are there any similarities? Differences? (i) Repeat Question 8 for the as-received polymer sample and the polymer sample with a defect. (j) Compare the behavior of the as-received steel sample to that of the polymer sample. How are they the same or different? Why? (k) What is the chemical composition of the steel samples your group tested? Why were each of the alloying elements added to the major constituent (strengthening, ductility, corrosion resistance, etc.)? Feel free to draw from the class notes, textbook, or other literature for this, but be sure to cite appropriately. (l) What are some potential applications of this alloy and how are the mechanical properties relevant to these applications? Which property(ies) is(are) most important for the particular application? (m) Compare the stress vs. strain curve and relevant mechanical properties of the steel sample with a defect that your group tested with that of another group. Here, you might choose to look at the effect of material. You may use the stress vs. strain curves and data generated by the other group provided that you cite appropriately or you may do these calculations yourself. A couple of reminders Please use SI units. Label all graphs, figures, and tables appropriately (title, legend, axes, units, etc.). Please cite any sources used for this assignment. Please include captions for figures. Please upload your final reports to Canvas as a.pdf file. If you use MATLAB or another similar software to calculate things, upload those files as well. 5

Bending Load & Calibration Module

Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of