Crack Paths 2012

numerical calculations of KIr, specifically k # 0.22. If the reduction of GSIF H2r is

applied in the crack deflection/branching analysis, a very good agreement with

experimental data is obtained. Figure 7 shows that the crack branches/deflects at the

angle Mp #22° for the loading force F #220 N when the additonal energy ' W (see

Eq. (2)) is starting to be greater than zero. It can be also inferred from Figure 7 that

crack bifurcation is preferred to crack deflection, because the change of the potential

energy G 3 during crack bifurcation is (slightly) greater than that corresponding to to

single crack deflection.

The key feature in the design is the high residual compressive stress in the A M Z

layer, which is present in laminate configurations with relative high material volume

ratio (i.e. VATZ/VAMZ•5). In laminate configurations with lower volume ratios the

residual stresses are lower and the inclined single penetration of the crack might be

preferred to crack bifurcation.

C O N C L U S I O N S

A semi-analytical model based on Finite Fracture Mechanics theory has been developed

to describe and predict the crack propagation (i.e. straight propagation, single deflection

or bifurcation) in layered ceramics during flexural loading. Results have been compared

with experiments in an alumina-zicronia multilayer ceramic designed with internal

residual stresses. A combined loading (thermal and mechanical) has been taken into

consideration to clarify the influence of the residual stresses on the crack path during

fracture.

The proposed fracture criterion, where the crack follows the path which maximizes

the energy released in the fracture process, can predict both the type and angle of

propagation of a crack through the interface in a layered structure. For the laminate of

study, crack bifurcation observed in experiments can be explained with the proposed

model. The key feature in the design is the high residual internal stresses in the

compressive layers which favour the propagation of the crack through the interface

between layers at an inclined angle.

A C K N O W L E D G E M E N T S

Financial support by the Austrian Federal Government and the Styrian Provincial

m b H

Government, represented by Österreichische Forschungsförderungsgesellschaft

and by Steirische Wirtschaftsförderungsgesellschaft

mbH,within the research activities

of the K2 Competence Centre on “Integrated Research in Materials, Processing and

Product Engineering”, operated by the Materials Center Leoben Forschung G m b Hin

the framework of the Austrian C O M E CTompetence.Centre Programme is gratefully

acknowledged.

The authors gratefully acknowledge also a financial support of the Czech Science

foundation under the Project No. 101/09/1821.

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