Mechanical Engineering and Materials Science
MEMS, MS 321
Rice University, P.O. Box 1892
Houston, TX 77251-1892
phone: (713) 348-3609
fax: (713) 348-5423
office: 224 Mechanical Engineering Building
Deformation, Polarization and Fracture of Ferroelectric Ceramics
Ferroelectric ceramics are becoming widely employed materials for actuators and sensors. As such, prediction of device performance and reliability are important technological problems. Due to both linear and non-linear coupling of the mechanical and electrical fields, adequate non-linear ferroelectric constitutive laws have yet to be developed. New phenomenological constitutive laws for ferroelectric/ferroelastic switching need to be developed and compared to experimental observations.
The development of self consistent models for describing the non-linear switching behavior of ferroelectrics serves as a useful guide to proposing new phenomenological laws. Concepts and models for the description and evolution of the switching surface in stress and electric field space, the associated increments of remanent strain and polarization and the effects of transforming linear properties must still be understood, tested, and included in a phenomenological constitutive law. Once acceptable constitutive laws are developed there exists an abundance of boundary value problems to be solved, including predicting the performance of actuators or sensors and determining the fields and poling patterns near crack tips and metal electrodes. Furthermore, the toughness of ferroelectric ceramics under the added influence of applied electric field needs to be investigated further.
The current state of theory for fracture of materials in the presence of electric fields is unsatisfactory. Aside from the lack of a constitutive law for ferroelectric switching which would be required for determining the fields around a crack tip, even the linear piezoelectric theory is incomplete. Recently a theory has been proposed which splits the total energy release rate into an electrical and mechanical part, and the mechanical part has been used to fit experimental measurements of fracture loads in the presence of electric fields. The question is, where does the electrical energy go? In order to attain a complete energetic picture of electromechanical fracture the boundary value problem must be posed in a more consistent fashion with the appropriate (non-zero) traction and electric displacement boundary conditions on the crack faces. Once this is accomplished, a cohesive zone model which relates tractions and surface charges to potential and displacement jumps across the crack surfaces will be useful in accounting for the energetics of the fracture process. Furthermore, once a constitutive law is formulated, the toughness of ferroelectric materials can also be examined with the "transformation toughening" mechanism of domain switching using the steady state crack growth model described in the next section.
Embedded Process Zone Models for Fracture of Rate Dependant Materials
Epoxies (usually with reinforcing rubber particles) are being considered as an alternative to spot welding for joining sheet metal in the auto industry. Understanding the mechanisms that control the toughness of these materials is an important engineering problem. Epoxy adhesives exhibit both increases and decreases in fracture toughness with increases in crack velocity depending on the material system and mechanism of failure ahead of the crack tip, e.g. void growth or crazing. The model being used to investigate the toughness of these material systems employs a steady state formulation with a cohesive fracture surface. The bulk material is able to deform plastically and a cohesive surface on the crack plane controls crack propagation. Both the bulk material and the cohesive zone constitutive laws can be rate dependent. The steady state toughness of the material is then computed as a function of both the bulk and cohesive zone properties. Improvement of the cohesive zone models will come from micromechanics models for the processes occurring ahead of the crack tip. For polymers and epoxies modeling of crazing and void growth are useful.
Also, metals loaded at high strain rates also exhibit a crack velocity dependent toughness. For this material inertia can become an important factor which can be easily treated in the steady state formulation. When the metal fails by a ductile mechanism it is possible to use a rate dependent Gurson model for the cohesive surface. Along these lines it is not necessary to limit the cohesive zone to a one dimensional constitutive law, instead one can utilize the full multiaxial predictive capabilities of the Gurson model. This will allow the model to account for the actual triaxial stress states that will occur ahead of the crack tip.
"Continuum thermodyanmics of ferroelectric domain evolution: Theory, finite element implementation and application to domain wall pinning ", with Yu Su, Journal of the Mechanics and Physics of Solids, 55, pp. 280-305, (2007).
"Effects of in-plane electric fields on the toughening behavior of ferroelectric ceramics ", with J. Wang, Journal of Mechanics of Materials and Structures, preprint, (2007).
"Domain switch toughening in polycrystalline ferroelectrics ", with J. Wang, Journal of Materials Research, 21, pp. 13-20, (2006).
"Constraint Effects in Adhesive Joint Fracture ", with T. Pardoen, T. Ferracin and F. Delannay, Journal of the Mechanics and Physics of Solids, 53, pp. 1951-1983, (2005).
"Electrostatic Forces and Stored Energy for Deformable Dielectric Materials ", with R.M. McMeeking, Journal of Applied Mechanics , 72, pp. 581-590, (2005).
"Energetically Consistent Boundary Conditions for Electromechanical Fracture", International Journal of Solids and Structures, 41, pp. 6291-6315, (2004).
"Micro-electromechanical Determination of the Possible Remanent Strain and Polarization States in Polycrystalline Ferroelectrics and the Implications for Phenomenological Constitutive Theories ", with J. Wang and J. Sheng, Journal of Intelligent Materials Systems and Structures, 15, pp. 513-525, (2004).
"Non-linear Constitutive Modeling of Ferroelectrics ", Current Opinion in Solid State and Materials Science, 8, pp. 59-69, (2004).
"On the Fracture Toughness of Ferroelectric Ceramics with Electric Field Applied Parallel to the Crack Front ", with Jianxin Wang, Acta Materialia, 52, pp. 3435-3446, (2004).
"On the Fracture Toughness Anisotropy of Mechanically Poled Ferroelectric Ceramics ", International Journal of Fracture, 126, pp. 1-16, (2004).
"In-Plane Complex Potentials for a Special Class of Materials with Degenerate Piezoelectric Properties ", International Journal of Solids and Structures, 41, pp. 695-715, (2004).
"On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials ", Journal of Applied Mechanics, 70, pp. 470-478, (2003).
"On the Fracture Toughness of Ferroelastic Materials ", Journal of the Mechanics and Physics of Solids, 51/8, pp. 1347-1369, (2003).
"On the determination of the cohesive zone properties of an adhesive layer from the analysis of the wedge-peel test",with T. Ferracin, F. Delannay and T. Pardoen, International Journal of Solids and Structures, 40, pp. 2889-2904, (2003).
"Fully Coupled, Multi-Axial, Symmetric Constitutive Laws for Polycrystalline Ferroelectric Ceramics", Journal of the Mechanics and Physics of Solids, 50/1, pp. 127-152, (2002).
"Uncoupled, Asymptotic Mode III and Mode E Crack Tip Solutions in Non-Linear Ferroelectric Materials", Engineering Fracture Mechanics, 69/1, pp. 13-23, (2002).
"A New Finite Element Formulation for Electromechanical Boundary Value Problems", International Journal for Numerical Methods in Engineering, 55, pp. 613-628 (2002).
"A Phenomenological Multi-axial Constitutive Law for Switching in Polycrystalline Ferroelectric Ceramics", with R.M. McMeeking, International Journal of Engineering Science, 40, pp. 1553-1577 (2002).
"Curvature-induced Polarization in Carbon Nanoshells", with T. Dumitrica and B.I. Yakobson, Chemical Physics Letters, 360, pp. 182-188 (2002).
"Crack Velocity Dependent Toughness in Rate Dependent Materials", with T. Pardoen and J. W. Hutchinson, Mechanics of Materials, 32, pp. 663-678, (2000).
"Micromechanical Simulation of the Failure of Fiber Reinforced Composites", with I. J. Beyerlein and R. M. McMeeking, Journal of the Mechanics and Physics of Solids, 48/3, pp. 621-648, (2000).
"A Phenomenological Constitutive Law for Ferroelastic Switching and a Resulting Asymptotic Crack Tip Solution", with R. M. McMeeking, Journal of Intelligent Material Systems and Structures, 10, pp. 155-163, (1999).
"A Constitutive Model for Ferroelectric Polycrystals", with J. E. Huber, N. A. Fleck and R. M. McMeeking, Journal of the Mechanics and Physics of Solids, 47/8, pp. 1663-97, (1999).
"A Shear-Lag Model for Failure Simulations of Unidirectional Fiber Composites Including Matrix Stiffness", with I. J. Beyerlein, Mechanics of Materials, 31/5, pp.331-350, (1999).
"Stress Concentrations in Composites with Interface Sliding, Matrix Stiffness, and Uneven Fiber Spacing Using Shear Lag Theory", with R.M. McMeeking, International Journal of Solids and Structures, 36/28, pp. 4333-4361, (1999).
"An Improved Shear Lag Model for Broken Fibers in Composite Materials", with M.A. McGlockton and R.M. McMeeking, Journal of Composite Materials, 33/7, pp. 667-680, (1999).
"A Shear Lag Model for a Broken Fiber Embedded in a Composite with a Ductile Matrix", with R.M. McMeeking, Composites Science and Technology, 59/3, pp. 447-457, (1999).
"A Self-Consistent Constitutive Model for Switching in Polycrystalline Barium Titanate", with R. M. McMeeking, Ferroelectrics, 255, pp. 13-34, (2001).
"Modeling Fracture in Ferroelastic Ceramics", Fracture Mechanics of Ceramics 14 and 15, edited by K.H. White et al. (2003).
"Micro-Electromechanically Informed Phenomenological Constitutive Models for Ferroelectrics", with J. Wang and J. Sheng, Proceedings of the SPIE, 5053, (2003).
"A New Finite Element Formulation for Electromechanics", Proceedings of the SPIE, 4699, pp. 31-39, (2002).
"Asymptotic Mode III and Mode E Crack Tip Solutions in Ferroelectric Materials", Proceedings of the ICF10, (2001).
"Shear Lag Modelling of Thermal Stresses in Unidirectional Composites", Proceedings of the ICF10, (2001).
"Crack Velocity Dependent Toughness in Rate Dependent Materials", Proceedings of the ICF10, (2001).
"Predictive Fracture Model for Steady-State Failure of Adhesively-Bonded Joints with Extensive Plastic Yielding", with T. Ferracin, J.Y. Sener, F. Delannay and T. Pardoen, Proceedings of the ICF10, (2001).
"Symmetric Constitutive Laws for Ploycrystalline Ferroelectric Ceramics", Proceedings of the SPIE, 4333, pp. 271-278, (2001).
"Modeling of Fracture in Ferroelectric Ceramics", with R. M. McMeeking, Proceedings of the SPIE, 3992, pp. 176-184, (2000).
"A Self Consistent Model for Switching in Polycrystalline Ferroelectrics: Electrical Polarization Only", with R. M. McMeeking, Proceedings of the SPIE, 3667, pp. 172-180, (1999).
"Annihilation Radii for Dislocations Intercepting a Free Surface with Application to Heteroepitaxial Thin Film Growth", with M. Chang, S. K. Mathis and G. E. Beltz, in III-V and IV-IV Materials and Processing Challenges for Highly Integrated Microelectronics and Optoelectronics (edited by S. A. Ringel, E. A. Fitzgerald, I. Adesida, and D. C. Houghton), Materials Research Society Symposium Proceedings, 535, pp. 9-14 (1999).
"A Network Model for the Plastic Compaction of Monodispersed Spherical Powder", with G. Deutschmann and R. M. McMeeking, Proceedings of the AIChE PTF Topical Conference on Advanced Technologies for Particle Processing, Miami Beach, Florida, November 15-20, (1998).