COMSOL Modeling and Tensile Loading of Aluminum Material ...
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COMSOL Modeling and Tensile Loading of Aluminum Material Test Samples Joseph L. Palladino, Ph.D. Trinity College, Dept. of Engineering, 300 Summit St., Hartford, CT 06106, USA Axial Strain Transverse Strain 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 -0.001 -0.0008 -0.0006 -0.0004 -0.0002 0 Axial Load [lb] Axial Strain, Transverse Strain 0 500 1000 1500 2000 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 Axial Strain Transverse Strain Introduction Material test samples are commonly subjected to tensile testing, with an extensometer used to measure changes in length of the material to deter- mine strain. Lacking an extensometer, strain gages were used to measure axial and transverse strain, with the location and magnitudes of strain guided by a COMSOL finite element model. Test samples were loaded with an Instron tensile test machine (model 5500R), and model strains were vali- dated by comparison with measured strains in both the axial and transverse directions for different aluminum alloys. COMSOL Multiphysics Model A three dimensional Solid Mechanics model was built, with the test sample profile geometry drawn using a CAD program (Ashlar-Vellum Graphite) and imported using the COMSOL CAD Import Module. The profile was extruded into a 3D bar and modeled as homogeneous, linearly elastic 6061 or 7075 aluminum. One end of each test sample was defined as a fixed constraint boundary. Loads were applied to the other end using a parametric sweep and keeping the material in its linearly elastic range (up to 2000 lb for 6061 and 4000 lb for 7075). An extra fine physics-controlled mesh was generated and a stationary analysis was performed using default solver settings. Model Verification Material test samples were fabricated from 6061 and 7075 aluminum bar stock and strain gages were mounted at the midpoint of the test section in the axial and transverse directions. Strain gages were general purpose Vishay Micro-Measurements CEA-13-240UZ-120 and were installed using standard techniques. Gages were wired as quarter-bridge Wheatstone circuits using a Vishay P3 Strain Indicator and Recorder. Loads were applied with the Instron test machine and axial and transverse strains were recorded. Results The following figure shows the first principal strain for 6061 aluminum with an applied load of 600 lb. COMSOL model strain predictions were within +/-1.5% of measured strains. The test sample’s elastic modulus measured using a linear regression of all measured longitudinal stresses and strains was found to be within 2% of literature values, and the Poisson ratio was within 2.5%. Similar results were found for the 7075 alloy. Conclusions References Despite its simplicity, this COMSOL model was useful in predicting and visu- alizing experimental stresses and strains, especially the stress concentra- tions between the grip regions at the test sample ends and at the narrower test region. Model results guided placement of the strain gages. The model permits visualization of phenomena such as Saint-Venant’s principle, whereby the difference between the effects of two different but statically equivalent loads becomes very small at sufficiently large distances from the load . This approach allows measurement of the elastic modulus and Pois- son ratio for unknown material alloys. Close agreement between theory, model, and experiment validates the model, giving students confidence in this approach before moving on to more complex finite element models [1] Fung, Y.C., A First Course in Continuum Mechanics (2ed), Prentice-Hall, Englewood Cliffs, NJ, 1977. [2] Davis, J.R., ed., Metals Handbook Desk Edition (2ed), ASM International, Materials Park, OH, 1998. [3] Student Manual for Strain Gage Technology, Bulletin 309E, Vishay Measurements Group, Raleigh, NC, 1992. [4] Model P3 Strain Indicator and Recorder, instruction manual, Vishay Micro-Measurements, Raleigh, NC, 2005. [5] Saint-Venant, A.J.C.B., Memoire sur la Torsion des Prismes, Mem. Divers Savaants, 14:233-560, 1855. Axial Strain Axial Stress [psi] 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0 5000 10000 15000 20000 25000 30000 Left: First principal strain for a 6061 aluminum test sample with a 600 lb tensile load. The test section width for this particular sample was 0.6 in., giving a test section stress of 8000 psi and first principal strain of 0.0008. Right: Modeled first and second principal strain contours for a 6061 sample with a 600 lb load, showing complex local strains near the test sample grip ends and a uniform central test region Test sample profile geometry drawn in Graphite, then imported into COMSOL with CAD Import Module. Units are in inches. COMSOL extra fine mesh of material test sample, yielding 2,192 tetra- hedral elements with 13,368 degrees of freedom. Left: Elastic modulus, E, calculated from a linear regression of measured axial stress and strain for a 6061 test sample. Measured E was 9.785 x 10 6 ksi, which compares well to the literature value of 10.0 x 10 6 ksi. Right: The Poisson ratio, ν, calculated from a linear regression of measured transverse strain and axial strain for a 6061 test sample. Measured ν was 0.3217, which compares well to the literature value of 0.33. Axial stress calculated from a COMSOL model of a uniform bar of aluminum of width b subjected to an axial point load. Results show that stress is not uniform near the applied load, but becomes so at a distance b from the load (red curve), demonstrating Saint-Venant's principle. Measured axial and transverse strains for a 6061 test sample with load range 0-2000 lb, showing a high degree of linearity. COMSOL Model Equations Excerpt from the Proceedings of the 2018 COMSOL Conference in Boston
Transcript of COMSOL Modeling and Tensile Loading of Aluminum Material ...
COMSOL Modeling and Tensile Loading of Aluminum Material Test SamplesJoseph L. Palladino, Ph.D.
Trinity College, Dept. of Engineering, 300 Summit St., Hartford, CT 06106, USA
Axial Strain
Tran
sver
se S
trai
n
0 0.0005 0.001 0.0015 0.002 0.0025 0.003-0.001
-0.0008
-0.0006
-0.0004
-0.0002
0
Axial Load [lb]
Axi
al S
trai
n, T
rans
vers
e St
rain
0 500 1000 1500 2000-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
Axial StrainTransverse Strain
IntroductionMaterial test samples are commonly subjected to tensile testing, with an extensometer used to measure changes in length of the material to deter-mine strain. Lacking an extensometer, strain gages were used to measure axial and transverse strain, with the location and magnitudes of strain guided by a COMSOL �nite element model. Test samples were loaded with an Instron tensile test machine (model 5500R), and model strains were vali-dated by comparison with measured strains in both the axial and transverse directions for di�erent aluminum alloys.
COMSOL Multiphysics ModelA three dimensional Solid Mechanics model was built, with the test sample pro�le geometry drawn using a CAD program (Ashlar-Vellum Graphite) and imported using the COMSOL CAD Import Module. The pro�le was extruded into a 3D bar and modeled as homogeneous, linearly elastic 6061 or 7075 aluminum. One end of each test sample was de�ned as a �xed constraint boundary. Loads were applied to the other end using a parametric sweep and keeping the material in its linearly elastic range (up to 2000 lb for 6061 and 4000 lb for 7075). An extra �ne physics-controlled mesh was generated and a stationary analysis was performed using default solver settings.
Model Veri�cation
Material test samples were fabricated from 6061 and 7075 aluminum bar stock and strain gages were mounted at the midpoint of the test section in the axial and transverse directions. Strain gages were general purpose Vishay Micro-Measurements CEA-13-240UZ-120 and were installed using standard techniques. Gages were wired as quarter-bridge Wheatstone circuits using a Vishay P3 Strain Indicator and Recorder. Loads were applied with the Instron test machine and axial and transverse strains were recorded.
ResultsThe following �gure shows the �rst principal strain for 6061 aluminum with an applied load of 600 lb. COMSOL model strain predictions were within +/-1.5% of measured strains. The test sample’s elastic modulus measured using a linear regression of all measured longitudinal stresses and strains was found to be within 2% of literature values, and the Poisson ratio was within 2.5%. Similar results were found for the 7075 alloy.
Conclusions
References
Despite its simplicity, this COMSOL model was useful in predicting and visu-alizing experimental stresses and strains, especially the stress concentra-tions between the grip regions at the test sample ends and at the narrower test region. Model results guided placement of the strain gages. The model permits visualization of phenomena such as Saint-Venant’s principle, whereby the di�erence between the e�ects of two di�erent but statically equivalent loads becomes very small at su�ciently large distances from the load . This approach allows measurement of the elastic modulus and Pois-son ratio for unknown material alloys. Close agreement between theory, model, and experiment validates the model, giving students con�dence in this approach before moving on to more complex �nite element models
[1] Fung, Y.C., A First Course in Continuum Mechanics (2ed), Prentice-Hall, Englewood Cli�s, NJ, 1977.[2] Davis, J.R., ed., Metals Handbook Desk Edition (2ed), ASM International, Materials Park, OH, 1998.[3] Student Manual for Strain Gage Technology, Bulletin 309E, Vishay Measurements Group, Raleigh, NC, 1992.[4] Model P3 Strain Indicator and Recorder, instruction manual, Vishay Micro-Measurements, Raleigh, NC, 2005.[5] Saint-Venant, A.J.C.B., Memoire sur la Torsion des Prismes, Mem. Divers Savaants, 14:233-560, 1855.
Axial Strain
Axi
al S
tres
s [p
si]
0 0.0005 0.001 0.0015 0.002 0.0025 0.0030
5000
10000
15000
20000
25000
30000
Left: First principal strain for a 6061 aluminum test sample with a 600 lb tensile load. The test section width for this particular sample was 0.6 in., giving a test section stress of 8000 psi and �rst principal strain of 0.0008.Right: Modeled �rst and second principal strain contours for a 6061 sample with a 600 lb load, showing complex local strains near the test sample grip ends and a uniform central test region
Test sample pro�le geometry drawn in Graphite, then imported into COMSOL with CAD Import Module. Units are in inches. COMSOL extra �ne mesh of material test sample, yielding 2,192 tetra-hedral elements with 13,368 degrees of freedom.
Left: Elastic modulus, E, calculated from a linear regression of measured axial stress and strain for a 6061 test sample. Measured E was 9.785 x 106 ksi, which compares well to the literature value of 10.0 x 106 ksi.Right: The Poisson ratio, ν, calculated from a linear regression of measured transverse strain and axial strain for a 6061 test sample. Measured ν was 0.3217, which compares well to the literature value of 0.33.
Axial stress calculated from a COMSOL model of a uniform bar of aluminum of width b subjected to an axial point load. Results show that stress is not uniform near the applied load, but becomes so at a distance b from the load (red curve), demonstrating Saint-Venant's principle.
Measured axial and transverse strains for a 6061 test sample with load range 0-2000 lb, showing a high degree of linearity.
COMSOL Model Equations
Excerpt from the Proceedings of the 2018 COMSOL Conference in Boston
