A failure scenario of ceramic laminates with strong interfaces

Highlights

• Paper explains in detail scenario of damage mechanism of layered ceramic composite.

• The reason for crack bifurcation in the compressive layer is explained.

• The paper contributes to the better understanding of damage of ceramic laminates.

Abstract

Over the last years many researchers have put a lot of effort into designing layered structures combining different materials in order to improve low fracture toughness and mechanical reliability of ceramics. It has been proven that an effective way is to create layered ceramics with strongly bonded interfaces. Significant internal residual stresses are developed within the composite layers after the cooling process from the sintering temperature, due to the different coefficients of thermal expansion of individual composite constituents. Residual stresses can significantly change the crack behaviour. Suitable choice of material of layers and ratio between layer thicknesses can lead to higher value of the so-called apparent fracture toughness, i.e. higher resistance of the ceramic laminate to the crack propagation.

The paper deals with a description of the specific crack behaviour in the layered alumina–zirconia ceramics. Attention is devoted to the differences in the stress field description in the vicinity of the crack front. Two-dimensional and three-dimensional numerical models are developed for this purpose. The main aim is to clarify crack behaviour in the compressive layer and provide computational tools for estimation of crack behaviour in the field of strong residual stresses. The crack propagation is investigated on the basis of linear elastic fracture mechanics. Fracture parameters are computed numerically and by routines of authors. The sharp change of the crack propagation direction is estimated using the Sih’s criterion based on the strain energy density factor, and conditions for crack bifurcation are determined. Estimated crack behaviour is qualitatively in a good agreement with experimental observations.

Introduction

Ceramic materials are widely used in many engineering applications for their temperature stability, hardness, mechanical strength or chemical inertness. However, ceramics are very brittle materials; therefore they are mainly utilized under compression loading. Over the last years many researchers have been working on improving of mechanical properties of ceramics by fabricating ceramic composites materials. It was shown that material interfaces play an important role in mechanical behaviour and material properties of composite, which can cause improving of fracture toughness of the ceramic laminate. The presence of multiple constituents influences the stress distribution in the composite. Therefore, the influence of different materials and geometry combination and weak and strong material interfaces on the resulting material behaviour were studied both experimentally and theoretically, see e.g. [1], [2], [3], [4], [5], [6], [7], [8], [9] for details.

Improvement of resistance against crack propagation through a ceramic composite body can be caused by several factors; (a) presence of residual stresses developed during the fabrication of ceramics due to different coefficients of thermal expansion of constituents and cooling down from high temperatures; (b) material interfaces; (c) consuming of more fracture energy during crack deflection or/and bifurcation [10], [11], [12], [13], [14], [15], see Fig. 1. Mentioned mechanisms were proved experimentally for different layered ceramic materials with strongly bonded interfaces, see [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. In [30] a procedure for estimation of apparent fracture toughness of ceramic laminate based on generalized linear elastic fracture mechanics was published. The specific crack behaviour in the compressive layer of layered ceramics composites was the subject of several studies [31], [32], [33], [34], where procedures, derived in the frame of linear elastic fracture mechanics, for estimation of crack deflection or bifurcation were published. However, comprehensive interpretation of failure of layered ceramic composite and explanation of the role of residual stresses is still missing in the literature.

As is mentioned above, the presence of residual stresses developed during sintering process in individual layers can significantly influence the fracture behaviour of the whole composite. Compressive residual stresses can cause closure of crack, its deflection from the original direction of crack propagation, or crack bifurcation. Furthermore a crack can stay arrested at the bimaterial interface under specific conditions. These mechanisms lead to consumption of more fracture energy, and contribute to increase the (apparent) fracture toughness of the composite [2], [3], [4], [7], [8], [9], [10], [11], [12], [13], [14], [15].

The motivation of this work is to investigate and describe the specific crack behaviour and failure mechanism of ceramic laminate with special focus on crack behaviour in the compressive layer of multilayer composites. For this purpose, numerical modelling and linear elastic fracture mechanics procedures are used.

A material system based on alumina and zirconia is herein chosen. These two constituents can be taken as typical examples of convenient materials for layered ceramics. Behaviour of such kinds of laminates was experimentally studied e.g. in [20], [21], [22], [23]. Considered ceramic laminate is created by 9 layers; 5 are made of Al₂O₃/5vol.%t-ZrO₂ (alumina with tetragonal zirconia, referred as ATZ) and 4 are made of Al₂O₃/30vol.%m-ZrO₂ (alumina with monoclinic zirconia, referred as AMZ). Material characteristics are taken from the literature [20], [21] and summarized in Table 1. Table 2 shows grain sizes of the laminate components. The laminate is subjected to four-point bending (4PB) test, see Fig. 2.

The magnitude of residual stresses in the case of crack absence in the layered composite can be estimated from forces balance in individual layers. This leads to the following expressions [35]:

$${\sigma }_{\mathit{res}\text{,}\mathit{ATZ}}=\frac{{\int }_{T_{\mathit{sf}}}^{T_0}({\alpha }_{\mathit{AMZ}}-{\alpha }_{\mathit{ATZ}})\mathit{dT}}{\frac{1}{E_{\mathit{ATZ}}^{\prime }}+\frac{1}{E_{\mathit{AMZ}}^{\prime }}·\rho ·\frac{N+1}{N-1}}\text{,}{\sigma }_{\mathit{res}\text{,}\mathit{AMZ}}=-{\sigma }_{\mathit{res}\text{,}\mathit{ATZ}}·\rho ·\frac{N+1}{N-1}\text{,}$$

where $\rho =\frac{t_{\mathit{ATZ}}}{t_{\mathit{AMZ}}}$, $E_{\mathit{AMZ}}^{\prime }=\frac{E_{\mathit{AMZ}}}{1-{\nu }_{\mathit{AMZ}}}$, $E_{\mathit{ATZ}}^{\prime }=\frac{E_{\mathit{ATZ}}}{1-{\nu }_{\mathit{ATZ}}}$, T_sf [°C] is a stress free temperature, T₀ [°C] room temperature, α [10⁻⁶ K⁻¹] the coefficient of thermal expansion, N [–] the number of layers, t [mm] the thickness of layer, E [MPa] Young’s modulus and ν [–] Poisson’s ratio. Calculated values of residual stresses for the studied configurations are shown in Table 3 and are in good agreement with experimental observation [36]. Stress free temperature T_sf = 1200 °C is used in the calculations.

From Table 3, it can be noted that the compressive residual stresses in the AMZ layers are about six hundred megapascals and higher for all considered cases. These stresses are responsible for typical stepwise crack propagation, as is shown in the scheme in Fig. 2.