The failure of ceramic materials is caused by the extension of small flaws. Therefore, linear-elastic fracture mechanics can be applied to describe the failure behaviour. The main problem in the application of the simple fracture mechanics relation is the existence of a rising crack growth resistance curve, which is caused by crack bridging forces behind the advancing crack tip or by transformations in front of the crack tip. The increasing crack growth resistance leads to problems in the transformation of results from specimens with macrocracks to components with natural cracks.

Fracture Mechanics of Ceramics

After twenty years of partly quiet and ten years of partly enthusiastic research into lead-free piezoceramics there are now clear prospects for transfer into applications in some areas. This mimics prior research into eliminating lead from other technologies that resulted in restricted lead use in batteries and dwindling use in other applications. A figure of merit analysis for key devices is presented and used to contrast lead-containing and lead-free piezoceramics. A number of existing applications emerge, where the usage of lead-free piezoceramics may be envisaged in the near future. A sufficient transition period to ensure reliability, however, is required. The use of lead-free piezoceramics for demanding applications with high reliability, displacements and frequency as well as a wide temperature range appears to remain in the distant future. New devices are outlined, where the figure of merit suggests skipping lead-containing piezoceramics altogether. Suggestions for the next pertinent research requirements are provided.

Transferring lead-free piezoelectric ceramics into application

Statistical Models in Engineering

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1048&context=usnavyresearch

Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization

Review of limit loads of structures containing defects

The local approach was recently proposed by Beremin and Mudry for evaluating the statistical behaviour of toughness results of materials. This approach introduces a stress parameter σ
 w
 , termed the Weibull stress, as a measure of the fracture resistance of materials instead of the conventional toughness parameters such as K
c, δ
 c
 and J
cl (critical stress intensity factor, CTOD and J-integral, respectively). The Weibull stress σ
 w
 obeys the Weibull distribution with the two parameters m and σ
 u
 (the shape and the scale parameter, respectively). The first parameter m is normally estimated to be 22 irrespective of the kind of material. In this paper a procedure for the determination of the Weibull parameters m and σ
 u
 is developed. This procedure consists of the determination of the plastic zone ahead of the crack tip, from which cleavage fracture originates, and of the maximum likelihood estimation of the parameters m and σ
 u
 based on the stress distribution in the plastic zone. Calculations using this procedure confirm that the distribution of the Weibull stress σ
 w
 is a material property independent of specimen thickness, and in particular that the shape parameter m depends on the material, e.g. m≃12 for a German reactor pressure vessel steel (20 Mn Mo Ni 5 5). Using these parameters for the distribution of the Weibull stress the size effect in fracture toughness values is predicted and an improved agreement between theory and experiments is obtained compared to the Weakest Link model.

Estimation procedure for the Weibull parameters used in the local approach

On the calculation of crack opening displacement from the stress intensity factor

The weight function method is used to calculate stress intensity factors for a semi-elliptical surface crack in a plate exposed to stress gradients.

D. Munz

Papers

Estimation procedure for the Weibull parameters used in the local approach

On the calculation of crack opening displacement from the stress intensity factor

Stress intensity factor at the surface and at the deepest point of a semi-elliptical surface crack in plates under stress gradients

Nonsymmetry in the deformation behaviour of PZT

Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium