Issue 10

G. Bolzon et alii, Frattura ed Integrità Strutturale, 10 (2009) 56-63; DOI: 10.3221/IGF-ESIS.10.07 59 Parameters governing DP constitutive law have been inferred from available experimental information gathered from conical Rockwell indentation of Al/TiB 2 , Al/ZrO 2 and Cu/Al 2 O 3 with about 40 to 50% weight metal content. Associative plasticity has been then introduced as reasonable hypothesis, so that α=β in relations (4). Poisson’s ratio has been a priori fixed due to the expected low influence of this parameter on indentation results; see [10, 14] and references therein. Then, the unknown overall material parameters to be returned by inverse analysis are: the elastic modulus E; the initial compression yield stress 0 c  ; the internal friction angle α and the hardening modulus h . Results listed in Tab. 1 concern the case of an Al/TiB 2 sample with 50% TiB 2 weight content produced by spark plasma sintering in a joint research project with Inasmet-Tecnalia (San Sebastian, Spain), partner of the KMM NoE [8]. The identified parameter values are given in terms of the average and of the standard deviation of several converged optimization solutions, which returned small similar values of ( ) opt  z starting from different initial z vectors. The scatter on the value of the internal friction angle returned by the exploited inverse analysis procedure is relatively large, nevertheless α values were found much larger than zero in all considered situations, thus indicating that hydrostatic stress component plays a significant role in controlling the mechanical response of the considered metal-ceramic composites. The accuracy of the selected material model and of the optimal parameter set obtained from the present identification procedure can be appreciated by the comparison between the experimental information and the corresponding recalculated curves, drawn in Fig. 1. Elastic modulus E [GPa] Initial yield limit in compression 0 c  [MPa] Internal friction angle Arctan(α) [°] Hardening modulus h [MPa] Al/TiB 2 57.9 (±3.7) 240.4 (±36.5) 10.7 (±4.3) 1032 (±91) Table 1 : Identified material properties after different initializations of the discrepancy minimisation algorithm for an Al/TiB 2 sample with 50% TiB 2 weight content. The results of this research work showed that the overall material properties are strongly influenced by embedded defects and local damages, as earlier observed for different material systems [6]. Classical homogenization rules and mixture laws, which do not consider micro-structural details, fail in returning reliable quantitative prediction of constitutive parameters even in the elastic range. F RACTURE P ROPERTIES he brittleness of the composite materials under investigation is mitigated by the ductility of their metal phase. In fact, during fracture processes, large plastic deformations produce metal ligaments which bridge crack surfaces as shown e.g. in Fig. 2. This image is relevant to a fracture experiment performed at the Technical University Darmstadt (TUD), partner of the KMM Network, on a Cu/Al 2 O 3 composite with interpenetrating network structure [1- 3]. Fracture can be induced in a brittle material sample to parameter identification purposes by the sharp corners of a Vickers pyramidal tip, as shown i n Fig. 3 f or the case of a pure zirconia (ZrO 2 ) specimen. Semi-empirical formulae based on linear elastic fracture mechanics (LEFM) permit to correlate the material toughness to the length of the cracks, measured from the centre of the imprint left by indentation [27, 28] which can be observed after unloading. However, experimental investigations show a systematic dependence of such estimated toughness values on the level of the applied indentation load. This result, inconsistent with LEFM assumptions, is likely originated by various error sources like the experimental difficulties in getting reliable measurement of the actual crack length and the influence of possible residual stresses, besides the existence of a crack-bridging zone at the crack tip [1, 4]. Furthermore, indentation results of brittle and quasi- brittle materials are affected by big scatters and influenced by microstructure [29, 30]. These limitations can be mitigated by an identification approach based on inverse analysis, as introduced above, comparing results gathered from the experiment and from the test simulation. Material separation during fracture propagation can be introduced in FE simulation of the indentation tests by interface elements, as shown e.g. i n Fig. 4 a n d 5. The relationship between displacement discontinuities and the cohesive tractions transmitted across the fracture surface of metal-ceramic composites can be described by relatively simple and T