William D. Armstrong

A directional magnetization potential based model of magnetoelastic hysteresis

The theory presented in this article successfully reproduces and explains the experimental magnetostriction and magnetization hysteresis behavior of Tb0.3Dy0.7Fe1.9. It is well known that a very large number of individual domain wall translation events combine to produce each measurable domain transformation in a macroscopic sized sample. Each individual domain wall may be expected to suffer some level of domain wall translation inhibition due to the presence of defects in the material, however, the severity of the inhibition will spatially vary. We therefore assume that the presence of defects in the material increases the directional magnetization potential of subsequent domain states within a process, and distributes nontrivial probabilities of occupation of 〈111〉 type domain states in a parameter selected, inverse exponential form familiar from the study of statistical thermodynamics. The increased magnetization potential of subsequent high magnetostriction and high magnetization states retards their ...

A General Magneto-Elastic Model of Terfenol-D Particle Actuated Composite Materials

A new theory is presented of the nonlinear multi-axial magneto-elastic behavior of magnetostrictive particle actuated composite materials. The analysis assumes a uniform external magnetic field is operating on a large number of well-distributed, crystallographically and shape parallel ellipsoidal magnetostrictive particles encased in an elastic, nonmagnetic composite matrix. Comparisons between experimental and model magnetostriction results show that the model is able to provide a quantitatively correct dependence on particulate volume fraction and longitudinal stress and quantitatively accurate magnetostriction curves for both homogenous Terfenol-D rod and magnetically ordered Terfenol-D particulate actuated epoxy matrix composites over experimentally applied field ranges.

Fully three-dimensional incremental model of magneto-elastic hysteresis in Terfenol-D

The paper presents an incremental hysteretic magneto-elastic constitutive description of pseudo-cubic ferro-magnetostrictive alloys, which may be used to predict the magneto-elastic response of these materials under quite general applied magnetic field and stress processes. These processes may include fully saturated major loop, unsaturated minor loop or more general types of magnetic field processes. Local stress and domain wall pinning non-uniformities assumed in the development of the model result in smooth and continuous hysteretic magnetization and magnetostriction curves which follow the magnetization and magnetization anhysteretics with a non-constant offset. Comparisons between model results and a set of high quality measurements show that the model is agrees well with experimental curves when the magnetization response is dominated by inhibited domain wall motion.

The time-dependent magneto-visco-elastic behavior of a magnetostrictive fiber actuated viscoelastic polymer matrix composite.

The paper develops a one-dimensional magneto-elastic model of a magnetostrictive fiber actuated polymer matrix composite material which accounts for a strong viscoelastic response in the polymer matrix. The viscoelastic behavior of the composite polymer matrix is modeled with a three parallel Maxwell element viscoelastic model, the magnetoelastic behavior of the composite fibers is modeled with an anhysteric directional potential based domain occupation theory. Example calculations are performed to identify and explain the dynamical behavior of the composite. These calculations assume that a constant stress and the oscillating magnetic field are applied in the fiber longitudinal direction. The inclusion of matrix viscosity results in an apparent hysteresis loop in the magnetization and magnetostriction curves even though the model does not include magnetoelastic hysteresis in the fibers. The apparent hysteresis is a consequence of the interaction of the time varying fiber stress caused by matrix viscosity with a multidomain state in the fiber. The small increase in fiber longitudinal compressive stress due to matrix viscosity under increasing field inhibits the occupation of domains with magnetization orientations near the fiber longitudinal [112] direction. As a consequence, the summed longitudinal magnetization and magnetostriction is reduced as compared to the decreasing field limb.

Numerical Model of a Dynamic Resonant Wall Shear Stress Sensor

A novel dynamic resonant wall shear stress sensor concept based on an oscillating sensor operating near resonance is investigated numerically. The interaction between the oscillating sensor surface and the ∞uid above it is modelled using the unsteady boundary layer equations. The simulations show that the oscillating shear stress on the sensor surface due to its motion lags the sensor’s motion and is responsible for the sensitivity of the sensor to shear stress. Over a wide range of conditions, the efiect of the oscillating shear stress is well correlated by the Hummer number, the ratio of the steady shear force caused by the outside ∞ow to the oscillating viscous force created by the sensor motion. The oscillating shear stress predicted by the ∞uid model is used in a mechanical model of the sensor to predict the sensor’s dynamic motion. The results of the mechanical model show that the additional shear force causes a reduction in the oscillation amplitude, and the reduction monotonically increases. A static calibration curve is predicted that indicates that the sensor’s amplitude decreases non-linearly with increasing shear stress. These results agree qualitatively with experimental results, and thus the model provides a rigorous basis upon which further development of the dynamic resonant sensor can be pursued.

Time-dependent behavior in a Terfenol-D actuated visco-elastic polymer matrix composite

The present paper develops a one dimensional magneto-elastic model of a magnetostrictive fiber actuated polymer matrix composite material which accounts for a strong visco-elastic response in the polymer matrix. The visco-elastic behavior of the composite polymer matrix is modeled with a three parallel Maxwell element visco-elastic model, the magneto-elastic behavior of the composite fibers is modeled with an anhysteric directional potential based domain occupation theory. Example calculations are performed to identify and explain the dynamical behavior of the composite. We observed that the increasing and decreasing limbs of the magnetization and magnetostriction loops are offset at middle levels of applied field. This offset is a consequence of the interaction of the time varying fiber stress caused by matrix viscosity with a multi-domain state in the fiber. The small increase in fiber longitudinal compressive stress due to matrix viscosity under increasing field inhibits the occupation of domains with magnetization orientations near the fiber longitudinal direction. As a consequence, the summed longitudinal magnetization and magnetostriction is reduced as compared to the decreasing field limb. This results in an apparent hysteresis loop in the magnetization and magnetostriction curves even though the model does not include magneto-elastic hysteresis in the fibers.

Mixed mode elastic-magnetostrictive wave propagation in a cubic media

A preliminary theoretical effort has provided a robust three dimensional energy based model of magnetostrictive wave propagation in a general cubic magnetostrictive material. Under high intensity impact we predict that the wave front will split between a higher velocity elastic precursor wave and a lower velocity, strongly dissipative, magnetostrictive shockwave. The wave front solution strongly depends on longitudinal pre-stress level and initial magnetization state. We may expect that a significant portion of the magnetostrictive wave deformation will be reversible under the application of well chosen field paths. In combination these technical characteristics therefore present an opportunity to develop magnetostriction based shock hyper-toughness in safety critical civil and military structures utilizing relatively shock tough magnetostrictive materials such as Terfenol-D particle based composites or homogenous Galfenol rods.

Observed dependencies of the large thermal-compressive response of a NiTi shape memory alloy fiber aluminum metal matrix composite

The present work examines how the characteristics of the large thermal-compressive response of a 20 vol. % NiTi fiber 6082-T0 composite change with variations in the value of maximum tensile strain imposed during a preceding room temperature tensile process. We observe that the self thermal compression process is shifted to higher temperatures with increasing maximum room temperature tensile strain, and that the maximal thermal compression versus temperature slope becomes larger as the maximum tensile strain is increased from 4 to 6% and then becomes smaller as the maximum tensile strain is further increased to 7%.

Degradation of Terfenol-D particle epoxy composites under low frequency cyclic magneto-mechanical loading: comparisons of matrix polymer

Magnetostrictive Terfenol-D particle actuated epoxy polymer matrix composites were prepared with polyamine and anhydride cured epoxy polymer matrices. The different matrix epoxies exhibited large differences in glass transition and creep behavior. The differences in matrix thermal-mechanical properties resulted in important differences in temperature dependant damage behavior and magneto-elastic strain output in the Terfenol-D particle actuated epoxy polymer matrix composites.

Constitutive Relationship Development, Modeling and Measurement of Heat Stressing of Micro-SMD Assembly with Sn3.9Ag0.6Cu SAC Alloy

The Creep and microstructural changes during creep behaviors of bulk and thin cast forms of Sn3.9Ag0.6Cu were compared. The processing parameters of the thin cast material was selected to result in a very fine microstructure analogous to what occurs in very small size solder electronic interconnections. We found that the thin cast material was less creep-resistant than the bulk material. A comparison of Ag element maps between as crept bulk and thin cast material showed that the relevant climb process occurs in a very different environment in the bulk material as compared to the thin cast material. In the bulk material the relevant climb process occurs within a finely dispersed IMC eutectic which covers broad areas within the material. In the thin cast material the relevant climb process occurs primarily in the beta-Sn grains which continuously surround isolated, coarse IMC particles. This resulted in the activation energy of the bulk material being larger than that for the thin cast material. Finally, it is important to note that the strength deficiency of the thin cast material was persistent, once the material is cast in thin cast form it will remain weak in comparison to the bulk material. Therefore, using data obtained from bulk material samples for the construction of thermo-mechanical models of very small scale solder interconnections is likely to result in significant, intrinsic errors. Second, the thermal-mechanical response of electronic packages was simulated using the commercial finite element code ANSYS coupled with the Garofalo model to represent the solder constitutive creep response. The measured properties for bulk and thin-cast Sn3.9Ag0.6Cu SAC alloy were used in the FE modeling. A 36 I/O micro-surface mount device (SMD) package was used as a test vehicle in this work. Moire Interferometry was used to measure the horizontal displacements in the solder joints as a result of cooling the package from 100°C to room temperature. Modeling results were found to have good agreement with moire measurements on the actual SAC packages. The bulk properties produced a better correlation with the measurement of the horizontal displacement in the solder joints than the thin-cast properties. However, the assemblies that were tested used the Sn3.8Ag0.6Cu alloy rather than the Sn3.9Ag0.6Cu alloy. It is not known if this difference is significant to the thermo-mechanical response.Copyright