# ICME Overview of Tetragonal Zirconia Polycrystals (TZP)

## Contents |

## Introduction

Tetragonal zirconia polycrystals (TZP) are ceramic materials that are known for both fracture toughness and hardness at room temperature as well as corrosion resistance at high temperatures. They also exhibit features such as ionic conductivity, low thermal conductivity, transformation toughening, and shape memory effects. That is why they are widely used in areas like the biomedical field for hip transplant and dental reconstruction, and in the nuclear field as thermal barrier coating in fuel rod claddings. However, these features of TZP ceramics destroys at lower temperatures due to low temperature degradation (LTD). The LTD occurs due to tetragonal to monoclinic martensitic phase transformation in TZP ceramics. Researchers have shown that LTD in zirconia ceramics can be mitigated by appropriate selection of alloying element and process control^{[1]}. This provides motivation for the Integrated Computational Material Engineering (ICME) overview of TZP ceramics in order to understand the information microstructure evolution, phase transformation, transformation toughening, crack nucleation and growth, void nucleation and coalescence, and total damage that occurs at different length scales.

## Multiscale Modeling Approach

The length scale for multiscale modeling of TZP can be obtained by downscaling the damage model. A reconstructed TZP dental crown is used as an example throughout the paper. As shown in Figure 1, the damage model for a reconstructed dental crown can be downscaled to the macroscale, mesoscale (polycrystal and singlecrystal), nanoscale, and electronic scale. In this paper, the constitutive models in each length scale and the bridging of information between adjacent length scales are determined.

- Macroscale

At the macroscale, a Finite Element Analysis (FEA) with crystal plasticity model and multi-stage fatigue (MSF) models can be performed in order to obtain information about macro crack growth, fatigue life, and stresses at this level. However, in order to study cracks, we need to know about crack nucleation and crack growth rate which are obtained from a lower length scale. The behavior like shape memory effects requires the model at mesoscopic level^{[2]}.

- Mesoscale (Polycrystal)

At the mesoscale, phase field study of polycrystalline zirconia can be performed. Software like COMSOL and Monte Carlo simulation can be used to perform a simulation^{[3]}. This study gives the information about internal stresses, crack nucleation, micro-crack growth, and corrosion information. Also, the effect of stress-induced transformation and shape memory effect from martensitic transformation can be studied in the polycrystalline models. However, the phase distribution, martensitic volume fraction, and stress condition on the singlecrystal should be obtained from the lower scales.

- Nanoscale (Singlecrystal)

At the nanoscale, a phase field simulation of solid-state phase transformation from tetragonal to monoclinic is performed. This allows one to incorporate single crystal deformation kinematics. The parameters such as mobility and diffusion constants are obtained from the atomic scale. Similarly, the constitutive model provides the information about crystal slips, martensitic twins, and microstructure evolution. This mesoscopic modeling is able to track the volume change, transformation toughening, and internal stresses in a tetragonal singlecrystal^{[4]}.

- Atomic scale

Using techniques like Embedded Atom Method (EAM), and Modified Embedded Atom Method (MEAM), and Molecular Dynamics (MD), the values for mobility and diffusion constants can be calculated and passed through the next level. Also, the information about high rate mechanisms can be passed to the continuum level. At this level, the alloying element plays an important role in determining the values for mobility and diffusion constant.

- Electronic scale

The electronic scale uses the Density Field Theory (DFT) to calculate elastic moduli for different crystal structures of zirconia: cubic, tetragonal, and monoclinic. Similarly, the information on interfacial energy of zirconia and elasticity calculated at this level are passed to the upper level.

## Conclusion

Thus, the ICME approach of a TZP material in multiscale level can be used to study the material behaviors of TZP ceramics and optimization of their properties like fracture toughness and strength. The study of microstructure evolution during tetragonal-to-monoclinic martensitic phase transformation has provided abundant information on the behavior of martensitic transformation in zirconia^{[4]}^{[5]}^{[6]}. Similarly, the multiscale approach can be used to develop an accurate damage model for TZP applied applications like dental crowns.

## References

- ↑ Chevalier J, Gremillard L, Virkar AV, Clarke DR. The Tetragonal-Monoclinic Transformation in Zirconia: Lessons Learned and Future Trends. J Am Ceram Soc. 2009;92:1901-20.
- ↑ Hwang SC, McMeeking RM. A finite element model of ferroelastic polycrystals. International Journal of Solids and Structures. 1999;36:1541-56.
- ↑ Chen L-Q. Phase-Fieldmodels Formicrostructureevolution. Annual Review of Materials Research. 2002;32:113-40.
- ↑
^{4.0}^{4.1}Mamivand M, Asle Zaeem M, El Kadiri H. Phase field modeling of stress-induced tetragonal-to-monoclinic transformation in zirconia and its effect on transformation toughening. Acta Mater. 2014;64:208-19. - ↑ Mamivand M, Asle Zaeem M, El Kadiri H. Shape memory effect and pseudoelasticity behavior in tetragonal zirconia polycrystals: A phase field study. Int J Plast. 2014;60:71-86.
- ↑ Mamivand M, Asle Zaeem M, El Kadiri H. Phase field modeling of tetragonal to monoclinic phase transformation at zirconium oxide. 142nd Annual Meeting and Exhibition: Linking Science and Technology for Global Solutions, TMS 2013. San Antonio, TX2013. p. 885-91.