50
J. Hahn and W. Becker
Herein F
pred
f
means the predicted failure load whereas F
exp
f
means the experimentally obtained failure load. We assume that those combinations of material strength and
fracture toughness that minimize pred characterize the material in the best way. This
leads to the material properties σ
c = 722 MPa and G
c = 23.46 N/m. The corresponding comparison of calculated and experimentally obtained failure loads is given in Fig. 4.
Obviously, the experimental data can be reproduced in a satisfying manner.
Fig. 4. Comparison of predicted and experimental failure loads (from Mouginot/Maugis [7]).
The comparison of these material parameters with the results of other authors, however, reveals some discrepancies. The fracture toughness K Ic for boron silica glass is
given in the range between 0.7 and 0.9 MPa mm 1/2 , see e.g. [13] or [14]. From G
c on
the other hand we get a fracture toughness of 1.44 MPa mm 1/2 . Also the strength value
790 MPa is comparatively large. Petzold [15] for instance specifies the range from 30
to 90 MPa. This, however, corresponds to an effective strength with some flaws in the
material. For glass without any defect we can expect much higher theoretical strength
values [15]. According to Leguillon [16] not the effective but an ideal strength value has
to be employed within finite fracture mechanics. Beyond this potential reasons for the
deviations of the fracture toughness values might be plastic effects or friction between
indenter and the specimen. All these aspects require further investigations.
9 Conclusions
A compact analytical model for the crack generation in indentation tests with spherical
indenters has been presented. The model is based on the coupled criterion of finite fracture
mechanics. The stress field required for the stress criterion results from a superposition
of Boussinesq solutions. Under the assumption of a negligible effect of the crack on the
J. Hahn and W. Becker
Herein F
pred
f
means the predicted failure load whereas F
exp
f
means the experimentally obtained failure load. We assume that those combinations of material strength and
fracture toughness that minimize pred characterize the material in the best way. This
leads to the material properties σ
c = 722 MPa and G
c = 23.46 N/m. The corresponding comparison of calculated and experimentally obtained failure loads is given in Fig. 4.
Obviously, the experimental data can be reproduced in a satisfying manner.
Fig. 4. Comparison of predicted and experimental failure loads (from Mouginot/Maugis [7]).
The comparison of these material parameters with the results of other authors, however, reveals some discrepancies. The fracture toughness K Ic for boron silica glass is
given in the range between 0.7 and 0.9 MPa mm 1/2 , see e.g. [13] or [14]. From G
c on
the other hand we get a fracture toughness of 1.44 MPa mm 1/2 . Also the strength value
790 MPa is comparatively large. Petzold [15] for instance specifies the range from 30
to 90 MPa. This, however, corresponds to an effective strength with some flaws in the
material. For glass without any defect we can expect much higher theoretical strength
values [15]. According to Leguillon [16] not the effective but an ideal strength value has
to be employed within finite fracture mechanics. Beyond this potential reasons for the
deviations of the fracture toughness values might be plastic effects or friction between
indenter and the specimen. All these aspects require further investigations.
9 Conclusions
A compact analytical model for the crack generation in indentation tests with spherical
indenters has been presented. The model is based on the coupled criterion of finite fracture
mechanics. The stress field required for the stress criterion results from a superposition
of Boussinesq solutions. Under the assumption of a negligible effect of the crack on the