Definition of Strain Rate
Mathematic Definition
Rough Definition – not accurate due to how to define L0
JLR test example –10 strain rate (as target) In all JLR tests, date in yellow boxes are measured directly -Axial Displacement: cross head movement -Axial Strain: strain measured from strain gauge -Axial Force: measured from load cell mounted on the bottom end Time
Axial Displacement Axial Strain
Axial Force
Sec
mm
N
0.03108724 0.03125 0.031412762 0.031575523 0.031738281 0.031901043 0.032063805 0.032226563 0.032389324 0.032552086 0.032714844 0.032877605 0.033040367 0.033203125 0.033365887 0.033528648 0.033691406 0.033854168 0.03401693
mm/mm 0.018267632 0.020750424 0.022842733 0.026037276 0.031506021 0.039343044 0.048848432 0.05900741 0.069636345 0.081659116 0.0961366 0.11325382 0.13198851 0.15108865 0.17000243 0.18891421 0.20818344 0.22781435 0.2478011
-0.13904959 -0.13900094 -0.13892902 -0.13882883 -0.13869627 -0.13852914 -0.13832693 -0.13809007 -0.13781752 -0.13750821 -0.13716608 -0.13680129 -0.13642316 -0.13603288 -0.13562763 -0.13520944 -0.1347858 -0.13436165 -0.13393448
Eng Strain mm/mm
7.5742359 19.97122 34.887718 52.184269 71.222878 90.449989 107.61268 120.55981 128.36293 132.06245 134.00871 136.14685 139.25072 143.73012 150.95399 163.99083 186.45239 218.90036 256.10992
0 4.865E-05 0.00012057 0.00022076 0.00035332 0.00052045 0.00072266 0.00095952 0.00123207 0.00154138 0.00188351 0.0022483 0.00262643 0.00301671 0.00342196 0.00384015 0.00426379 0.00468794 0.00511511
Eng Stress MPa 0.209100759 0.551342383 0.963139837 1.440643046 1.966238981 2.497038862 2.970846619 3.328276035 3.543695563 3.645827639 3.699557738 3.758585039 3.844273098 3.967935201 4.167363463 4.52726949 5.147362304 6.043148395 7.070386965
True ε mm/mm 0 4.86488E-05 0.000120563 0.000220736 0.000353258 0.000520315 0.000722399 0.00095906 0.001231312 0.001540193 0.001881738 0.002245776 0.002622987 0.003012169 0.003416118 0.003832795 0.004254726 0.004676986 0.005102072
JLR test example –10 strain rate (as target) In accurate definition or calculation: •Plot axial vs time and its tangent is cross head velocity - blue dots: velocity is 168.39mm/s (red circle) •Plot engineering strain vs time and its tangent is mathematic definition (accurate strain rate) – purple dots: strain rate is 10.3 (red circle). So, the claimed test strain rate is 10 •One can also plot true strain vs time and get so-called true strain rate – 8.9936 Time
Axial Displacement Axial Strain
Axial Force
Sec
mm
N
0.03108724 0.03125 0.031412762 0.031575523 0.031738281 0.031901043 0.032063805 0.032226563 0.032389324 0.032552086 0.032714844 0.032877605 0.033040367 0.033203125 0.033365887 0.033528648 0.033691406 0.033854168 0.03401693
mm/mm 0.018267632 0.020750424 0.022842733 0.026037276 0.031506021 0.039343044 0.048848432 0.05900741 0.069636345 0.081659116 0.0961366 0.11325382 0.13198851 0.15108865 0.17000243 0.18891421 0.20818344 0.22781435 0.2478011
-0.13904959 -0.13900094 -0.13892902 -0.13882883 -0.13869627 -0.13852914 -0.13832693 -0.13809007 -0.13781752 -0.13750821 -0.13716608 -0.13680129 -0.13642316 -0.13603288 -0.13562763 -0.13520944 -0.1347858 -0.13436165 -0.13393448
Eng Strain mm/mm
7.5742359 19.97122 34.887718 52.184269 71.222878 90.449989 107.61268 120.55981 128.36293 132.06245 134.00871 136.14685 139.25072 143.73012 150.95399 163.99083 186.45239 218.90036 256.10992
0 4.865E-05 0.00012057 0.00022076 0.00035332 0.00052045 0.00072266 0.00095952 0.00123207 0.00154138 0.00188351 0.0022483 0.00262643 0.00301671 0.00342196 0.00384015 0.00426379 0.00468794 0.00511511
Eng. strain vs time
Eng Stress MPa 0.209100759 0.551342383 0.963139837 1.440643046 1.966238981 2.497038862 2.970846619 3.328276035 3.543695563 3.645827639 3.699557738 3.758585039 3.844273098 3.967935201 4.167363463 4.52726949 5.147362304 6.043148395 7.070386965
True ε mm/mm 0 4.86488E-05 0.000120563 0.000220736 0.000353258 0.000520315 0.000722399 0.00095906 0.001231312 0.001540193 0.001881738 0.002245776 0.002622987 0.003012169 0.003416118 0.003832795 0.004254726 0.004676986 0.005102072
In rough definition or calculation: velocity is 168mm/s, then the strain rate will depend on how you define L0 •Strain gauge is 10mm in all the tests, so 16.8 rate (168/10) if you use this as L0 •The straight line part of the sample is 12mm, so 14 rate (168/14) if you use this as L0 •One may argue that this sample has large radii, therefore, there is some contribution of deformation from that part. Then L0 would be bigger, say 16mm, then 10 rate can be claimed
True strain vs time
JLR test example –10 strain rate (as target) •Interesting thing is that the rates in different calculations are similar •In strain vs time, you can see the curve is not perfect straight, there is a slop in the start
Slop at start
Bochen’s test example ABC-XYZ_25C_500rate… (sent by Zhicun) –500 strain rate (as claimed) In accurate definition or calculation: •Plot strain vs time, the tangent is 1400 rate Test Data Displacement(mm) Load(N) 0 0 0 0 0.000841297 772.635498 0.001682595 1482.178833 0.002523892 2065.59082 0.00336519 2484.563477 0.004206487 2764.868896 0.005047785 2942.521484 0.005889082 3053.5354 0.00673038 3133.425293 0.007571677 3202.203857 0.008412975 3261.765381 0.009254272 3312.976563 0.01009557 3356.704346 0.010936867 3393.814941 0.011778164 3425.175537 0.012619463 3451.652588 0.01346076 3474.112793 0.014302057 3493.422852 0.015143354 3510.449463
Engineering Engineering Stress(MPa) 0 0 0 0 0.000701081 161.9780884 0.001402162 310.7293091 0.002103244 433.0379028 0.002804325 520.8728638 0.003505406 579.637085 0.004206487 616.8807983 0.004907568 640.1541748 0.00560865 656.9025879 0.006309731 671.3215332 0.007010812 683.8082275 0.007711893 694.5443726 0.008412975 703.7116089 0.009114056 711.4915771 0.009815137 718.0661621 0.010516219 723.6168823 0.0112173 728.3255615 0.011918381 732.3737793 0.012619462 735.9432983
Engineering Strain
Time (ms) 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 0.0055 0.006 0.0065 0.007 0.0075 0.008 0.0085 0.009 0.0095
DeformationLoad (mm) (N) 0 0 3.68E-05 14.76 7.35E-05 29.52 0.00011 44.28 0.000147 59.05 0.000184 73.81 0.000221 88.57 0.000257 103.3 0.000294 118.1 0.000331 132.9 0.000368 147.6 0.000404 162.4 0.000441 177.1 0.000478 191.9 0.000515 206.7 0.000552 221.4 0.000588 236.2 0.000625 250.9 0.000662 265.7 0.000699 280.5
Velocity (mm/s) 0 228.89609 228.58447 228.58447 228.89583 228.58617 228.89583 228.58447 228.89754 228.58447 228.89583 228.58447 228.89754 228.58447 228.89438 228.58592 228.89609 228.58447 228.89583 228.58617
Acceleration (g) 0 0.226800799 0.455786914 0.671581209 0.886464119 1.125987768 1.384359837 1.645738482 1.906636596 2.178980112 2.474361897 2.785333157 3.068914175 3.463713169 3.912172079 4.232405663 4.576045036 4.949243546 5.281404495 5.604303837
Time s 0 5E-07 1E-06 1.5E-06 2E-06 2.5E-06 3E-06 3.5E-06 4E-06 4.5E-06 5E-06 5.5E-06 6E-06 6.5E-06 7E-06 7.5E-06 8E-06 8.5E-06 9E-06 9.5E-06
标距应变 0 3.07E-05 6.13E-05 9.19E-05 0.000123 0.000153 0.000184 0.000214 0.000245 0.000276 0.000306 0.000337 0.000368 0.000398 0.000429 0.00046 0.00049 0.000521 0.000552 0.000582
Strain rate = 0.1/(0.07/1000)=1428
Need Bochen to explain the test measurement