Research Papers

On the Prediction of R-Curves for Ferroelectroelastic Ceramics

[+] Author and Article Information
Sebastian Stark

Institute of Solid Mechanics,
Technische Universität Dresden,
Dresden 01062, Germany
e-mail: Sebastian.Stark@tu-dresden.de

Peter Neumeister

Fraunhofer Institute for Ceramic
Technologies and Systems,
Dresden 01277, Germany
e-mail: Peter.Neumeister@fraunhofer.ikts.de

Herbert Balke

Institute of Solid Mechanics,
Technische Universität Dresden,
Dresden 01062, Germany
e-mail: Herbert.Balke@tu-dresden.de

This definition implies that size and shape of the FPZ are dependent on the fracture mechanics model discussed. Therefore, the characteristics of the FPZ are not inherent to the material. The definition used is somewhat different than in most experimental publications, in which the FPZ is usually associated with the overall inelastic zone. Here, this is only the case if the fracture mechanics model is restricted to elasticity.

Of course, in reality, fracture is a discontinuous process being largely influenced by statistical effects (e.g., distribution of inhomogeneities, grain boundaries). Hence, some averaging over volume elements is assumed here.

The term “ferroelastic ceramic” is used here instead of “ferroelectric ceramic” in order to emphasize that only mechanical loadings without any macroscopic prepoling of the material are considered.

To the authors’ knowledge, no single crystal of PZT has been manufactured to date.

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 25, 2013; final manuscript received April 5, 2013; accepted manuscript posted May 7, 2013; published online September 16, 2013. Assoc. Editor: Chad Landis.

J. Appl. Mech 81(2), 021012 (Sep 16, 2013) (8 pages) Paper No: JAM-13-1094; doi: 10.1115/1.4024416 History: Received February 25, 2013; Revised April 05, 2013; Accepted May 07, 2013

In ferroelectroelastic ceramics, the process of fracture is accompanied by significant inelastic deformation due to domain switching. This leads to an apparent toughening of the material, which is known as R-curve behavior. A promising approach to predict R-curves is based on one parameter fracture criteria. The scope of this paper is the examination of the physical validity of these criteria for realistic material behavior. Besides a general discussion of the problem, fracture of the lead zirconate titanate ceramic PIC151 is examined. Thereby, restriction is made to purely mechanical material behavior. The results indicate that the usage of one parameter fracture criteria is questionable. This is due to a conflict between the length scale of the zone wherein the asymptotic crack tip singularity dominates in the field solution of the continuum model and the length scale associated with the fracture process zone. It is concluded that an incorporation of the fracture process into the used fracture mechanics model is necessary to capture transient fracture of ferroelectroelastic ceramics properly.

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Fig. 1

(a) Schematic of the transformation zone after some crack advance for transformation toughening ceramics (model of McMeeking and Evans [13]), and (b) schematic of the switching zone after some crack advance for ferroelastic ceramics

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Fig. 2

Fit of the material model [26] to the experimental data of Zhou [16]

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Fig. 3

Schematic of the finite element model

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Fig. 4

Crack tip stress intensity factor KI,tip versus the edge length of the smallest finite element le

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Fig. 5

Stress fields at three different distances r from the crack tip in comparison with asymptotic linear elastic crack tip fields: (a) σ11, (b) σ22, and (c) σ12




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