Craig L. Hom

Large scale bridging in brittle matrix composites

The influence of the bridging zone length on the resistance curve behavior of three brittle-matrix composites is examined. The experimental measurements are correlated with models of crack bridging (taking into account the finite specimen dimensions) and compared with the resistance curves expected when small-scale bridging conditions prevail. The results demonstrate that the resistance curves of composite materials strongly depend on both the absolute length of the bridging zone and the length of the bridging zone relative to the total crack length and the specimen width. The latter effects are due to large-scale bridging. The results suggest that the resistance curves of toughness measurements obtained from small test specimens may overestimate the true behavior and thus, caution must be exercised in interpreting some of the recently published data. The implications for future resistance curve measurements are discussed.

Plastic flow in ductile materials containing a cubic array of rigid spheres

Abstract The results of three-dimensional finite element calculations are presented for a cubic array of rigid spherical inclusions embedded in an elastic perfectly plastic matrix. The analysis examines the strengthening effect of the inclusions under macroscopic loads of uniaxial tension and pure shear. At low volume fractions, the fractional increase in strength is more modest than the volume fraction of particles, and only becomes comparable at around 40% loading. The local stress and deformation fields in the region of the inclusion are presented. The numerical results show that for volume fractions of inclusions below about 25% the surface tractions on the inclusion have the same order of magnitude as the matrix materials tensile yield stress. Volume fractions of 40% particles are necessary before the interface tractions are approximately double the yield strength.

Modeling nonlinearity in electrostrictive sonar transducers

Electrostrictive driver materials with large strain capability hold great promise for the advancement of sonar projector technology. However, the nonlinear induced strain of these materials can create acoustic distortion in transducers through higher-order harmonics. Electrostrictors also possess complicated prestress and temperature dependencies, and an elastic modulus that depends strongly on electric field. This investigation examined these issues with a nonlinear, frequency domain model for a flextensional transducer powered by an electrostrictive stacked actuator. A simple, linear lumped-parameter model of a flextensional shell and its surrounding acoustic medium were combined with a nonlinear model of the electrostrictive driver. This model accounted for the material’s nonlinear dependencies and behavior. Predictions of the device’s acoustic/electric response during operation compared favorably with experiments performed on a single element flextensional transducer. The model’s results showed that p...

Modeling electrostrictive deformable mirrors in adaptive optics systems

Adaptive optics correct light wavefront distortion caused by atmospheric turbulence or internal heating of optical components. This distortion often limits performance in ground-based astronomy, space-based earth observation and high energy laser applications. The heart of the adaptive optics system is the deformable mirror. In this study, an electromechanical model of a deformable mirror was developed as a design tool. The model consisted of a continuous, mirrored face sheet driven with multilayered, electrostrictive actuators. A fully coupled constitutive law simulated the nonlinear, electromechanical behavior of the actuators, while finite element computations determined the mirrors mechanical stiffness observed by the array. Static analysis of the mirror/actuator system related different electrical inputs to the array with the deformation of the mirrored surface. The model also examined the nonlinear influence of internal stresses on the active arrays electromechanical performance and quantified crosstalk between neighboring elements. The numerical predictions of the static version of the model agreed well with experimental measurements made on an actual mirror system. The model was also used to simulate the systems level performance of a deformable mirror correcting a thermally bloomed laser beam. The nonlinear analysis determined the commanded actuator voltages required for the phase compensation and the resulting wavefront error.

An acoustic/thermal model for self-heating in PMN sonar projectors

Dielectric hysteresis and a strong material temperature dependence uniquely couple the acoustic output and temperature of a sonar projector driven by electrostrictive Pb(Mg1/3, Nb2/3)O3 (PMN). Both the source level and the source of self-heating, i.e., dielectric hysteresis, dramatically decrease as the PMN driver heats. The final temperature delineates outstanding PMN transducers from mediocre PMN transducers, so accurate acoustic performance prediction requires accurate transducer temperature prediction. This study examined this self-heating phenomenon by combining an electro-acoustics model for a PMN flextensional transducer with a thermal finite element model. The sonar model calculated the source level and heat generation rate for the PMN driver as a function of temperature. This computed source level varied 12 dB over a 75 degrees C temperature range solely due to the temperature dependent ceramic. The heat transfer model used the computed heat rate to predict the transducers transient thermal response. The results clearly demonstrate that the transducer reached a steady-state equilibrium temperature, where the heat generated by the PMN driver balanced the heat dissipated. While the transducer model predicted a significant temperature rise, the corresponding acoustic output still surpassed the output of an equivalent Pb(Zr,Ti)O3 (PZT) transducer by 8 dB. Good agreement with experiments made on a PMN flextensional transducer validated the model.

Constitutive and failure models for relaxor ferroelectric ceramics

A non-linear constitutive model for relaxor ferroelectrics developed by Hom and Shankar is examined and verified with electromechanical experiments. This model links polarization and strain to the electric field and stress in an electrostrictive material. A set of tests were performed to study the quasi-static electrical behavior of PMN-PT-BT materials under prestress. Another set of tests investigate the effect of DC electric field on the elastic modulus of the material. The results show excellent correlation between the predicted behavior of the model and the experiments. Failure models for electrostrictive ceramic materials are presented which address the issues of actuator reliability. The constitutive model of Hom and Shankar is incorporated into a nonlinear finite element code. A new finite element technique for computing the J-Integral for cracks in electromechanical materials is developed. This technique is based on the domain integral method and computes both the mechanical and electrical contributions to the energy release rate. The finite element code and the J-Integral computation are used to study crack growth in multilayered electrostrictive ceramic actuators.

Constitutive model for relaxor ferroelectrics

This paper presents a static, temperature dependent constitutive model for polycrystalline relaxor ferroelectrics operating near their diffuse transition temperature. The model assumes that the relaxor material consists of superparaelectric, micro polar regions with a diffuse spectrum of Curie temperatures. A simple Ising model with near neighbor ion interaction represents the thermodynamics of the individual micro polar regions. A random-order dispersion of the B-site ions simulates the distribution of phase transitions. The diffuse micro polar region model predicts two important materials parameters, the saturation polarization and the density of the polar regions, as a function of temperature. A macroscopic model was constructed with these parameters to simulate dielectric and polarization response of the aggregate material. The macroscopic model also accounts for interaction between the micro polar regions. Finally, the predictions made by the model are compared with experimental data obtained by other researchers on lead magnesium niobate (PMN) relaxor ferroelectrics.

Modeling the dynamic behavior of electrostrictive actuators

This paper examines the dynamic response of electrostrictive rod actuators. A non-linear constitutive model for electrostrictors is used to obtain periodic solutions for the actuators displacement and polarization. The method accounts for both inertial forces and a non-homogeneous stress distribution in the device. Results of the analysis predict displacement distortion and power requirements for the actuators as a function of excitation frequency. Resonance behavior of the actuator and the effect of electro-mechanical coupling are investigated. Voltage control parameters for the actuators are studied to determine the optimum control scheme for minimizing distortion of the displacement output.

Modeling time-dependent behavior in relaxor ferroelectrics

A time-dependent, constitutive model is proposed for electrostrictive, relaxor ferroelectric materials. The model is based on Ising spin theory, and simulates stress, electric field and temperature dependent phase transformations in a ceramic material. The resulting model is consistent with Devonshires theory for temperature induced phase transformations, however it captures the non- linear saturation response characteristic of ferroelectrics driven by high fields. Electric hysteresis occurs when bifurcations cause the solution state to jump between stable branches. The model shows that these bifurcations depend on electric field, stress and temperature. This bifurcation approach differs significantly from phenomenological models based on phase switching. A 1D version of the constitutive model is used to predict the induced strain and polarization as a non-linear function of applied field for a Lead Magnesium Niobate-Lead Titanate-Barium Titanate ceramic. The results are compared with experiments at various temperatures.

Analysis of mechanical systems driven by electrostrictive actuators

A dynamics model of an electrostrictive ceramic actuator is integrated with a linear mechanical system. Electrostrictive ceramics have a non-linear displacement response to applied field, which creates harmonic distortion of actuators output. Traditionally, nonlinear dynamics problems are solved in the time-domain, then Fast Fourier Transforms are used to convert the solution into the more convenient frequency-domain. In this paper, a new approach is introduced separates the nonlinear, actuator from the linear structure. The structure can be represented as an impedance that constrains the actuator, and the actuator problem is solved in the frequency domain directly. The approach significantly simplifies the nonlinear problem. The actuator-mechanical system model is used to predict actuator output and distortion as a function of signal frequency. DC voltage bias is treated as a model parameter than must be tuned to optimized output while minimizing distortion. Power requirements and energy transfer to the attached structure are also examined. The problem of a flextensional underwater sonar transducer with an electrostrictive driver is examined as an example case.