Name Lauren Wagner Section 09 Date 3 17 22 Instructor Lodhi E Mech 316 LAB 4 Prediction of Yielding For General States of Stress OBJECTIVE To be able to predict the yielding of general states of stress from the max shear stress theory MSST and the distortion energy theory DET of a thin walled specimen PROCEDURE First measure and record the outer diameter and then the wall thickness of the aluminum 6061 T6 Then insert the longer section of the end plug into each end of the tube Next place the specimen with plugs into the torsion machine and bring the grips together Lastly tighten the grips until the specimen is engaged Then measure and record the gauge length of the specimen defined in this situation as the distance between the machine s grips Next we rotate the hand crank until a small initial torque is then indicated on the gauge The corresponding angular displacement will be set equal to zero Then while continuing to twist the specimen by 4 degree increments until the relative angular displacement is equal to 40 degrees We can record the angle and torque values Lastly we unload the specimen and remove it from the machine DATA AND RESULTS Table 1 Specimen Dimensions Outer Diameter O D Wall Thickness t Gauge length L0 25 08 mm 3 16 mm 508 mm Torque in lbs Torque N m Angle of Twist rads 0 230 550 1000 1420 1900 2230 2400 2520 2545 2610 0 25 9863844 62 141354 112 98428 160 4376776 214 670132 251 9549444 271 162272 284 7203856 287 5449926 294 8889708 0 0 06981317 0 13962634 0 20943951 0 27925268 0 34906585 0 41887902 0 488692191 0 558505361 0 628318531 0 698131701 ANALYSIS OF DATA Plot torque versus angle of twist Determine the offset angle of twist corresponding to the 0 2 offset shear strain from ro L0 where is in radians Draw the 0 2 line and graphically determine the offset yield torque Convert this torque to a shear yield strength using equation 4 5 Redraw the MSST and DET yield envelopes Be sure they are properly scaled and labeled Also indicate the two possible loading paths Tabulate the two theoretical and one experimental measures of yield strength in shear determined in this lab Method DET MSST Experimental Shear Yield Strength MPA 159 35 138 120 55 DISCUSSION 1 Based on this experiment explain which theoretical shear yield strength seems to be more accurate for your results MSST is more accurate to our results This is because looking at the data the MSST is very closely related to the experimental and the DET is not This means that the MSST is more restricted so it has less allowable yield strength than the DET would which is more accurate with our experimental yield strength 2 Postulate why a thin walled tube was used in this experiment as opposed to a solid bar Use illustrations of the shear stress distribution to support your argument With the thin walled tube the shear stress force is more uniformly distributed rather than if a solid bar was used it would not be uniformly distributed CONCLUSION We can see that the MSST is more restricted and have less allowable yield strength than the DET theoretical shear yield strength both are close to the experimental value