Fracture toughness evaluation of NiAl single crystals by microcantilevers—a new continuous J-integral method

Abstract

The fracture toughness of NiAl single crystals is evaluated with a new method based on the J-integral concept. The new technique allows the measurement of continuous crack resistance curves at the microscale by continuously recording the stiffness of the microcantilevers with a nanoindenter. The experimental procedure allows the determination of the fracture toughness directly at the onset of stable crack growth. Experiments were performed on notched microcantilevers which were prepared by focused ion beam milling from NiAl single crystals. Stoichiometric NiAl crystals and NiAl crystals containing 0.14 wt% Fe were investigated in the so-called “hard” orientation. The fracture toughness was evaluated to be 6.4 ± 0.5 MPa m^1/2 for the stoichiometric sample and 7.1 ± 0.5 MPa m^1/2 for the iron containing sample, indicating that the addition of iron enhances the ductility. This effect is intensified with ongoing crack propagation where the Fe-containing sample exhibits a stronger crack resistance behavior than the stoichiometric NiAl single crystal. These findings are in good agreement with macroscopic fracture toughness measurements, and validate the new micromechanical testing approach.

APPENDIX

A(1). Data correction for the penetration of the indenter

Due to the use of a sharp wedge-type indenter, the measured data needs to be corrected for indentations made into the cantilevers. As the correction for the indentation depends on the cantilever width B which was not constant for all samples tested, several imprints were performed into a FIB-milled H-bar of variable width which is shown in Fig. A1(a). The resulting “displacement-load” and “contact stiffness-load” responses for an imprint in this bar at a width of 12.9 µm (red rectangle), which corresponds to one of the used cantilever widths in this study, are depicted in Fig. A1(b) and A1(c), respectively. It is assumed that the measured displacement is the sum of the bending displacement and the indentation into the cantilever. From those reference indentations into the bulk the indentation depth at a given load can be measured and described by a polynomial fit function. The indentation depth is then subtracted from the measured displacement in the bending experiment. Similar adjustments are needed for the correction of the stiffness. The experimentally measured harmonic stiffness S_measured is a function of the contact stiffness S_imprint due to the imprint and of the requested bending stiffness of the cantilever S_cantilever. During the indentation of the bar, the stiffness is continuously recorded and the data are again fitted. As demonstrated by Kupka and Lilleodden,27 the bending stiffness of the cantilever can be calculated by applying the model of two springs connected in series leading to the following:

$${S_{{\rm{cantilever}}}} = {{{S_{{\rm{imprint}}}} - {S_{{\rm{measured}}}}} \over {{S_{{\rm{imprint}}}}\cdot{S_{{\rm{measured}}}}}}\quad .$$

(A.1)

FIG. A1

(a) SE-micrographs of an H-bar with varying width in bulk single-crystalline NiAl before and after performing the indentations with the sharp wedge indenter; the red rectangle indicates the imprint with B = 12.9 µm for which respective curves are plotted in (b) and (c).

FIG. A2

(a) Corrected force–displacement curve and cantilever stiffness of an un-notched beam for which a SE-micrograph after testing is shown in (b).

A(2). Stiffness signal of an un-notched cantilever

To attribute a decrease in cantilever stiffness purely to crack growth and consequently a reduction in cross-section, bending experiments were performed on un-notched cantilevers. These investigations were performed on single-crystalline tungsten. The force-displacement data as well as the stiffness evolution during elastic–plastic deformation are shown in Fig. A2(a).

The stiffness stays constant throughout the whole experiment. Initially there is a linear-elastic loading segment, followed by a pronounced hardening regime. Finally, a steady-state deformation behavior after a displacement of ∼700 nm is reached, where the applied force stays constant. The SEM image in Fig. A2(b) shows the sample after testing. An imprint of the sharp wedge indenter as well as distinct slip traces are visible on the surfaces of the beam.