Figure 2. Mechanical coupling between magnetostrictive coating and substrate that is exposed to a magnetic field.

The use of thermoelastic stress analysis in composite materials induced by magnetostrictive effects

Peng Yang, Rani Elhajjar, Chiu T. Law

Aluminum Substrate

Terfenol-D Epoxy Bar

Figure 1. Cantilever beam that consits of a Terfenol-D Epoxy bar mounted onto an aluminum substrate.

Strain produced by Terfenol-D [1]:

Where is the applied stress, is the modulus of the material, is the saturation magnetostrictive constant, is the saturation magnetization, and is the magnetization.

TSA in aluminum substrate [2]:

Where is the sum of principle stresses on the surface, is the reference temperature, and is the thermoelastic material constant. is the change in temperature on the substrate due to cyclic loading. At certain loading frequencies (around 3 to 15hz for metals), the material exhibits adiabatic conditions and temperature can be measured.

2. Theory

Figure 4. Temperature gradient along bottom side of cantilever sample with an applied load. Scale units is in Kelvins

Figure 5. Von Mises Stress distribution along cantilever sample as a result of mechancial loading using FEA. Units are in Psi. (Top) Isometric view. (Middle) Bottom view. (Bottom) Side view.

Figure 6. Predicted Von Mises Stress distribution along cantilever sample as a result of the magnetostrictive effect. Units are in Psi. (Top) Isometric view. (Middle) Bottom view. (Bottom) Side view.

TSA Camera

Slider Crank

Clamped SampleRubberband Connection

Power-drill Power

TSA Camera

Rubberband ConnectionClamped Sample

Figure 3. Experimental setup to test mechanical stress of the cantilever beam using TSA camera.

• TSA is able to detect stress gradients in substrate (Figure 4) in terms of temperature from the mechanical loading

• FEA results shows close correlation with the TSA system (Figure 5) in terms of stressed locations from mechanical loading

• A model was generated predicting the effect that the Terfenol D epoxy bar will have on the substrate when it is exposed to a magnetic field by replacing the magnetic strain with an equivalent thermo-induced strain (Figure 6).

4. Results/Conclusion

• Reduce noise in TSA detection system. • Run the test using a magnetic field to see how the FEA model

compares.• Replace aluminum substrate with carbon fiber composite.• Experiment with different volume fractions of Terfenol-D in the

epoxy• Experiment with different thickness of the Terfenol-D epoxy

composite.

5. Future Work

The authors would like to acknowledge the support from the UWM Research Growth Initiative (RGI) for the project.

Acknowledgements

[1] Liu, Xin’en and Zheng, Xiaojing. A nonlinear constitutive model for magnetostrictive materials. Acta Mech Sinica (2005). Vol 21, p278-285. [2] Kobayashi, Albert S. (1993) “Handbook on Experimental Mechanics, Second Edition.” Society of Experimental Mechanics. P581-599.

References

1. Introduction/DefinitionsResearch Goal: Utilize a coating made from Terfenol-D to induce stress in a composite structure that can be detected using Thermoelastic Stress Analysis (TSA)

DefinitionTSA - Thermal imaging technique which detects principal stress in a material by correlating it to temperature change

Terfenol-D - A giant magnetostrictive material that will deform its shape producing strain when exposed to a magnetic field.

Project Scope: Detecting the mechanical stresses on an aluminum cantilever beam using TSA and predict its behavior with an applied magnetic field.

Test Specimen: Terfenol-D particles embedded in epoxy mounted on an aluminum substrate (Figure 1).

Magnetic Test: A magnetic field is applied to the specimen causing the Terfenol-D embedded in epoxy to elongate and compressing the substrate releasing heat that should be detectable to the thermo-imaging camera (Figure 2). No mechanical load will be applied.

Mechanical Test: A power drill spins a slider crank mechanism at 7.6hz to induce stress in the specimen. A rubber band connection limits the displacement and the bottom of the specimen is painted black to increase emissivity of the thermo-response for the TSA camera (Figure 3). No magnetic field is applied.

3. Test Setup