Lab Manual for Engrd 202, Virtual Torsion Experiment. Aluminum module

Transcription

1 Lab Manal for Engrd 202, Virtal Torsion Experiment Alminm modle Introdction In this modle, o will perform data redction and analsis for circlar cross section alminm samples. B plotting the torqe vs. twist data for alminm and performing analses of the data o can infer relations between sample geometr, strength and stiffness. Seeing how the samples deform and fail will also help o to better nderstand material behavior nder torsional loading. From the torqe twist crve o can find qantities sch as ield torqe (for dctile materials), ltimate torqe (for brittle materials), maximm torqe, stiffness, and material properties sch as shear strength and shear modls. If o need, o can review the theor for data redction and analsis for circlar samples b going throgh the chalk-talks on basic theor and on testing of engineered materials. Procedre Select three data sets for alminm. Each of the alminm tests were performed sing the same material, machined to different lengths, and inner and oter diameters. These geometries are labeled geometries 1-4 in the tables linked nder Test Data. Yo will find the nominal dimensions for each geometr in the tables linked nder Test Data. The actal, measred dimensions for each sample (which ma differ from the nominal dimensions) are listed at the top of each individal data file. Data files are named according to the following convention: Material_Geometr_Repeat.***, where the stars are in place of the file tpe extension (For example AL_1_2.txt wold be the text file containing data for the second test on an alminm sample made sing geometr 1). Select one data set each from geometries 1, 2 and 3 of the alminm tests (Yo ma se an data set within a particlar geometr since there are repeats of nominall identical samples). Plot the torqe-twist crves for each data set; contine or analsis b completing tables 1 and 2, then proceed to answering the qestions below and to writing or lab report. Step-b-step directions for completing the data and comparison sheets, (tables 1 and 2) are given at the end of the modle 1

2 Lab Report Yor lab report shold inclde the completed data sheets, graphs and a brief discssion of the lab procedre. The report shold also provide answers to the qestions below and an other discssion, observations or comments o wish to inclde. Qestions 1. For the alminm tests, compare the elastic stiffness, k sample, from geometries 2 and 3 to that for geometr 1. Do the relative vales (i.e. ratios of k sample from one geometr to the other) agree with theor? 2. Compare torqe at first ield, T, for alminm geometries 2 and 3. Repeat for geometries 1 and 2. When are the vales different? Do the relative vales of T agree with theor? 3. Calclate the shear modls, G, and shear ield stress, τ, for the alminm samples. Compare these to the reference vales for these materials. Discss an discrepancies between or measred vales and the reference vales. Do o notice an trend in the G vales for alminm as the sample dimensions change? Sggest a wa to improve the measrement of G. 4. Review the virtal test for the alminm and comment on the deformation of the sample dring the test. If o were to replace this circlar sample with a sqare sample of same length and polar moment of inertia, what difference wold it make in the deformation? Step b step instrctions for completing Tables 1 and 2 for a given data set and Sample ID a) Select the data file and open it. Yo ma choose to se a text file (.txt) or an Excel file (.xls). The Matlab GUI (VL_1_v10.m) ses the.txt files b) Enter the sample ID, material and the dimensions of the test sample on table 1. Use the information given in the header of the text file or Excel file. If o choose to se the Matlab program, this information will be displaed on the GUI. c) Calclate J (polar moment of inertia) and enter this vale on row 3 of table 1. 2

3 d) Plot the torqe vs. twist for the sample. For this prpose, o ma choose to se the Matlab GUI. In the Excel files the plots are provided to o. Yo ma refer to Hints for graphing in case of an difficlt in plotting the data. e) Now, plot the torqe vs. twist crve in the linear region. Find the stiffness (slope of the torqe-twist crve). Denote this vale as k total engineered materials). Enter this vale in row 4 of table 1. f) Calclate the sample stiffness, k sample, the total stiffness (slide 5 of chalk talk on (slide 6, 7 of the chalk talk on engineered materials). Using this vale of stiffness, calclate shear modls for the sample and enter this vale in row 5 of table 1. g) Calclate the shear modls, G, sing the relation given in slide 7 of the chalk talk on engineered materials. Enter this vale in row 6 of table 1. h) Calclate the ield torqe (or ltimate torqe for brittle materials) and the maximm torqe (refer to slide 9 of the chalk talk on engineered materials) and enter these vales into row 7 and 8 of table 1. i) Now, calclate ield strength or ltimate strength (refer to slide 10 of the chalk talk on engineered materials) and enter these vales in row 9 of table 1. j) Look at the broken sample and comment on the tpe of fractre. Write or comments in row 10 of table1. k) Follow this procedre for three of the for alminm samples. Then transfer the data over to table 2 and complete the sggested comparisons. 3

4 Table 1. Circlar sample dimensions ID of the test sample sed* Dimensions (mm) GL: OD: ID: GL: OD: ID: GL: OD: ID: J** 4 ( m ) k total (N-m/rad) k sample *** (N-m/rad) G (N/m 2 ) T or T # (N-m) T max (N-m) τ or τ # (N/m 2 ) Fractre Description *Data file name **To convert mm 4 to m 4, mltipl b ***Corrected for machine compliance # T and τ for dctile materials, T and τ for brittle materials. 4

5 Table 2.Comparison sheet (Circlar samples) Specimen ID of test sample sed Material AL 2024-T3 AL 2024-T3 AL 2024-T3 Reference material properties## Nominal dimensions G τ GL: 88.9 mm OD: 12.7 mm ID: 0.0 mm G τ GL: 88.9 mm OD: 12.7 mm ID: mm G τ GL: 44.5 mm OD: 12.7 mm ID: mm Measred size GL: OD: ID: GL: OD: ID: GL: OD: ID: J (m 4 ) Torsional stiffness, k sample (N-m/rad) T or T * (N-m) Length ratio L #1 1 L #1 L #2 L #1 L #3 L #1 Polar moment of inertia ratio J #1 1 J #1 J #2 J #1 J #3 J #1 Stiffness Ratio k #1 1 k #1 k #2 k #1 k #3 k #1 T ratio T #1 1 T #1 T #2 T #1 T #3 T #1 ##Yo can find these vales in man mechanics of materials textbook. A qick web reference is 5

6 Trke tibiotarss modle Introdction In this modle, o will perform data redction and analsis for trke tibiotarss bones. The are not circlar in cross section and so the analsis for bones is different from the circlar samples. In the analsis, o will approximate the bone as a hollow circlar cross section. Yo will se the dimensions of the circlar cross section to estimate the stiffness, shear modls and strength of the bone. Yo will plot the torqe vs. twist crve and std it to examine the behavior of bone nder torsional loading. From this plot o will determine whole bone ltimate torqe and stiffness. Based on these vales, o will dedce bone material properties sch as shear strength and shear modls. Yo ma note that each individal bone behaves slightl different. Details of the sample geometr, as defined in slides 6 and 7 of the chalk talk on trke bone, are provided along with each data file. For review refer to the chalk talk on trke bone. To nderstand the calclations for cross sectional area and polar moment of inertia, refer to slide 7 of the chalk talk on trke bone. Procedre Select one data set from the wet trke bone test data and one from the dr trke bone test data. The measred dimensions for each bone sample are listed at the top of the text and Excel data files. This information is displaed in the Matlab GUI as well. Date files are named according to the following convention: Material_Tpe_Repeat.***, where the stars are in place of the file tpe extension. For example trkebone_wet_3.xls wold be the Excel file containing data for the test performed on wet trke sample 3. Plot the torqe-twist crves for the data set; contine or analsis b completing tables 3 and 4, then proceed to answering the qestions below and to writing or lab report. Step-bstep directions for completing the data sheets, (tables 3 and 4) are given at the end of the modle. Lab Report Yor lab report shold inclde the completed data sheets, graphs and a brief discssion of the lab procedre. The report shold also provide answers to the qestions below and an other discssion, observations or comments o wish to inclde. 6

7 Qestions and data analsis for trke tibiotarss: 1. Find the shear modls, G, and the shear strength, τ. 2. Using or textbooks and other resorces, find a different material (or materials) with similar G vales to the wet trke bone. Do o think that this material can be sed as an artificial bone? 3. Describe in words what the fractre srfaces look like. Do all the bones break exactl in the same wa? 4. Sppose o want to breed sper trkes that were twice the mass of normal trkes. Do o think the tibiotarss bone wold be thicker and or bigger in diameter (2 r 0 )? If so, b how mch wold these increase to doble the torsional load carring capacit of the wet bone? 5. Compare the reslts o got for the dr trke bone to those for the wet trke bone. How do the ltimate torqe T, the bone stiffness, the shear modls and shear strength differ? Step b step instrctions for completing Tables 3 and 4 for a given sample ID a) Select the data file and open it. Yo ma choose to se a text file (.txt) or an Excel file (.xls). The Matlab GUI (VL_1_v10.m) ses the.txt files. b) Enter the sample ID, material and the dimensions of the test sample on table 3. Use the information given in the header of the text file or Excel file. If o choose to se the Matlab program, this information will be displaed on the GUI. c) Calclate the area and polar moment of inertia of the eqivalent circlar cross section. Refer to slides 6 and 7 of the chalk talk on trke bone for details. Enter these vales in rows 2 and 3 of table 4. d) Plot the torqe vs. twist for the sample. For this prpose, o ma choose to se the Matlab GUI. In the Excel files the plots are provided to o. Yo ma refer to Hints for graphing in case of an difficlt in plotting the data. e) From the plot, find the ltimate torqe T. Fill this vale in row 4, table 4. f) Now, plot the torqe-twist crve in the linear region. Find the sample stiffness (eqal to the slope of the line). Denote this vale as k total, the total stiffness (slide 8 of the chalk talk on trke bone). Note that o ma assme k total k, since the test machine is sample almost infinitel stiffer than the bone sample. Enter this vale in row 5, table 4. 7

8 g) Now sing formlas given in slides 9 and 10 of the chalk talk on trke bone, calclate the shear modls and shear strength for the bone. Enter these vales in rows 6 and 7 of table 4. 8

9 Sample ID* Table 3. Bone sample dimensions Gage length (mm) Sample dimension (mm) *Data file name r 0 r i r 0 r i Sample ID Area (m 2 ) Table 4. Measred and calclated data for trke bone J (Polar moment of inertia) (m 4 ) Ultimate Torqe,T (N-m) Measred Stiffness, k sample (N-m/rad) Shear modls, G (N/ m 2 ) Shear strength, τ (N/m 2 ) 9