Applicability of image correlation techniques to characterise asymmetric refractory creep during bending tests

https://doi.org/10.1016/j.jeurceramsoc.2012.09.011Get rights and content

Abstract

The design of fibre reinforced refractory castable structures for high temperature applications requires the characterisation of the material creep behaviour. As many other heterogeneous ceramics, these materials creep faster under tensile stresses than under compressive ones because of the motion of hard particles in a soft matrix. Bending tests have been performed to characterise the creep behaviour of the considered material, and 3D digital image correlation is used to obtain strain fields after interrupted tests. The position of the neutral axis, defined here from the residual inelastic strain field, allows to highlight the asymmetry of creep and to evaluate the asymmetry ratio.

Introduction

Fibre reinforced refractory castables are suitable materials for structures undergoing high thermal exposure. Above 1200 °C creep mechanisms occur in the material even under low stresses. The creep behaviour characterisation of these materials is therefore mandatory to design such structures. As it is the case for most of the materials, the creep of ceramics can generally be divided into three steps.1 This complex behaviour is the result of many possible mechanisms1 as for examples, grain boundary sliding,2 diffusion, dislocation motion, viscous flow, cracking and cavitation or grain growth.3 The first step involves non-linear creep mostly related to micro-cracking and micro-porosity cavitation.4 A stationary creep step takes place subsequently (second step) until macro-damage occurs and accelerates the creep1 (third step).

Due to an easy processing at high temperature, bending tests are usually chosen to characterise this behaviour for refractories, involving a stress redistribution as a result of non-linear behaviour and non-uniform loading.5 Moreover heterogeneous ceramics at high temperature exhibit an asymmetric behaviour due to preferential damage4 or cavitation6, 7 in tension and/or related to the motion of hard particles in a glassy matrix8 leading the material to creep faster in tension than in compression.

Due to the difficulty to perform tension experiments at high temperature,7, 9 many works have been carried out in order to study the creep of ceramics in tension by using bending tests4, 10 in order to complete compressive characterisation data. If the experimental procedure is therefore simplified, data processing is significantly more difficult due to the non-uniform state of stress involved in the specimen. Moreover bending tests involve both tension and compression whose effects cannot be discriminated by processing the usual test data without new specific assumptions, for instance by neglecting the compressive creep11, 12 or assuming that the maximal asymptotical tension stress13 is the same as in the symmetric case.14 Most of the studies10, 11, 12, 13, 15, 16 assume a steady state creep law. For materials exhibiting a strong primary creep behaviour, this assumption is only relevant under uniaxial loading. Under bending conditions, the primary creep strongly affects the stress redistribution and cannot be neglected if the material undergoes a pronounced primary creep.

Interesting attempts have been proposed to characterise the asymmetrical creep behaviour from only bending tests. Talty and Dirks15 performed bending tests on trapezoidal cross-section beams. Depending on the orientation of the specimen (larger surface under tension or compression), the ratio between the cross section area under compression and under tension was modified. The difference between the creep of the specimen oriented within one direction or the other is then due to the asymmetric behaviour. Both tensile and compressive stationary creep characteristics were obtained through an analytical model.

The other way investigated to characterise asymmetrical creep from bending data is based on the location of the neutral axis of the beam which diverges from the mid-plane of the specimen when asymmetrical creep occurs. This effect, studied from an analytical point of view by Chuang,17 inspired some experimental studies. Wiederhorn et al.,18 then Chen and Chuang16 measured the neutral axis position by using indentations made on the specimen along two parallel lines perpendicular to the specimen length. This parameter was used as an index of the asymmetry and permitted an analytical estimation of tensile and compressive creep parameters from a single bending test.

In order to assess the location of the neutral axis, it is proposed in the present study to use 3D-Digital Image Correlation (3D-DIC) to perform full-field strain measurements. This experimental method was successfully used to characterise the behaviour of ceramics undergoing small strains. For example, elasticity and damage were studied during bending tests at room temperature.19, 20 High temperature contactless measurement data are also available in the literature. They have been obtained by 2D-DIC to measure large tensile strains using an alumina powder suspension sprayed speckle.21 Small strains can be also measured by video extensometer even at ultra-high temperature,22 but only mean strains are provided over the investigated area.

This study reports experimental results obtained using 3D-DIC method, that highlight the asymmetric creep behaviour at high temperature from a single bending experiment. Full-field strain data were measured after interrupted four-point bending tests, emphasising that the neutral axis is not located in the mid-plane of the specimen. The neutral axis is defined in this case by the location where the residual inelastic strain is zero, which differs from the zero-stress plane as will be discussed further in the paper. A faster creep in tension results in a neutral axis shifted towards the initially compressed volume.

Section snippets

Fibre reinforced refractory castable

The studied material is a commercial ultra low cement bauxite castable (Table 1) constituted of bauxite aggregates dispersed in a matrix, Fig. 1. The aggregates size is between 0.2 and 5 mm diameter, see in Fig. 2 the size distribution histogram obtained from image analysis. The matrix is not homogeneous since it is composed of small bauxite particles (diameter lower than 200 μm, Fig. 1a) and contains 8 wt.% of a calcium alumina cement, fumed silica and α-alumina.23 The castable is reinforced with

Full-field strain measurements

DIC is now a well known technique in the field of experimental mechanics24 and its principle will not be presented here. 3D-DIC at high temperature encounter different technical problems that limit its use to high strain measurements. Except in vacuum, the convective effects linked to the spatially variation of the refraction index around the specimen create image distortions that cannot be corrected yet.25 Moreover, adding an artificial controlled speckle pattern requires a coating material

Monotonic bending behaviour at 1030 °C

This section presents the behaviour of the material under four-point bending loading at high temperature. A monotonic test at 1030 °C illustrates the behaviour of the material up to failure, see Fig. 5. The material exhibits a quasi brittle behaviour even at high temperature. At 1030 °C, its apparent Young's modulus, measured in bending,31 is 6.5 GPa and the failure arises at 14 MPa. Above 8 MPa, a weak discrepancy to a linear behaviour appears due to micro-damaging and to viscoplasticity. For that

Discussion

As verified by Nazaret et al.31 the Young's modulus of refractory castables at room temperature is the same under tensile and compressive stresses. The asymmetric strain field measured in the present study is thus mainly due to creep asymmetry since no cracking is observed at 1200 °C. This is not the case at 1030 °C. However it is not straightforward that the iso-value line ɛxx = 0 measured in this study is the neutral axis, defined usually as the iso-value line σxx = 0 (axial stress component),

Conclusion

Experimental results are reported in this paper that characterise the asymmetric creep behaviour of a refractory castable at high temperature. Usual four-point bending tests were interrupted in order to carry out full-field strain measurements on the surface of the specimens. At 1030 °C, each specimen underwent cracking preventing any creep interpretation. However, if the temperature is high enough and the stress low enough to prevent cracking, the creep asymmetry can be highlighted by the

Acknowledgement

The authors gratefully acknowledge Correlated Solutions for providing Vic-3D® software. Special thanks are expressed to G. Azema and A. Pasquier for specimen preparation and experiments.

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