Hertzian Ring Crack Initiation in Hot‐Pressed Silicon Carbides

Abstract

The use of Hertzian indentation to measure ring crack initiation force (RCIF) distributions in four hot‐pressed silicon carbide (SiC) ceramics is described. Three diamond indenter diameters were used with each SiC; the RCIF in each test was identified with the aid of an acoustic emission system; and two‐parameter Weibull RCIF distributions were determined for all 12 combinations. RCIF testing was found to be an effective discriminator of contact damage initiation and response. It consistently produced the same ranking of RCIF between the four SiCs, with all three different indenter diameters, which is noteworthy because Knoop hardness and fracture toughness measurements were only subtly different or equivalent for the four SiCs. However, because RCIF, like hardness, is a characteristic response of a target material to an applied indentation condition (e.g., a function of indenter diameter) and not a material property, the implications and possible limitations should be acknowledged when using RCIF to discriminate the target material response.

Size‐Scaling of Tensile Failure Stress in a Hot‐Pressed Silicon Carbide

“…Test Type 6 (Hertzian indentation with a 47.62 mm diameter Si 3 N 4 sphere) appears that it would also fit well to the regressed lines [i.e., ] that go through data of Test Types 1–5; however, it could not be conclusively determined that machining damage was associated with Test Type 6 Hertzian ring crack initiation. Using the Griffith criterion with a fracture toughness of 4.49 MPa√m for this SiC 13 and a crack geometry value of 1.5, a Griffith flaw size of 4.6 μm is estimated for a characteristic strength of 1400 MPa (i.e., Test Type 7) and 1.4 μm is estimated for 2500 MPa (i.e., Test Type 8). The average grain size of this SiC is 3.25 μm 13 with grain sizes in its distribution as large as 12–13 μm (A.…”

“…Using the Griffith criterion with a fracture toughness of 4.49 MPa√m for this SiC 13 and a crack geometry value of 1.5, a Griffith flaw size of 4.6 μm is estimated for a characteristic strength of 1400 MPa (i.e., Test Type 7) and 1.4 μm is estimated for 2500 MPa (i.e., Test Type 8). The average grain size of this SiC is 3.25 μm 13 with grain sizes in its distribution as large as 12–13 μm (A. A. Wereszczak, W. L. Daloz, K. T. Strong Jr., and O. M. Jadaan, unpublished data), and hence the failure stress associated with ring crack initiation of Test Types 7–8 is likely caused by the grains themselves or some “flaw” of the same scale of the SiC grains. Multiple flaw distributions are operative .…”

“…For the frictionless extreme, the classical Hertzian maximum (radial tensile) stress associated with ring crack initiation ( S RCI ) can be calculated according to the following equation 11 : where ν is the Poisson's ratio of the target, P RCI is the compressive force needed to initiate ring cracking, and z is the Hertzian contact radius. An elastic modulus of 454 GPa and a Poisson's ratio of 0.171 for the SiC were used in the calculations 13 . For the Si 3 N 4 sphere properties used in the Hertzian indentation stress calculations, the elastic modulus and Poisson's ratio were measured using a resonance ultrasound spectroscope, and found to be 312 GPa and 0.276, respectively.…”

“…An elastic modulus of 454 GPa and a Poisson's ratio of 0.171 for the SiC were used in the calculations. 13 For the Si 3 N 4 sphere properties used in the Hertzian indentation stress calculations, the elastic modulus and Poisson's ratio were measured using a resonance ultrasound spectroscope, and found to be 312 GPa and 0.276, respectively. For the infinite friction extreme, the maximum radial tensile stress was determined using the analysis of Johnson 14 for each ring crack initiation force, and the elastic properties of both the target and sphere materials.…”

Using Hertzian Indentation to Understand the Strength and Ballistic Resistance of Silicon Carbide

“…Hertzian indentation, again, offers a very attractive alternative if a reliable and trustworthy ranking procedure can be determined. Recent work comparing the Hertzian indentation responses to ballistic performance, for several silicon carbide (SiC) materials, has produced encouraging results 3 …”