ASTM C1678-07

Fracture mirror size analysis is a powerful tool for analyzing glass and ceramic fractures. Fracture mirrors are telltale fractographic markings in brittle materials that surround a fracture origin as discussed in Practices C 1256 and C 1322. Fig. 1 shows a schematic with key features identified. Fig. 2 shows an example in glass. The fracture mirror region is very smooth and highly reflective in glasses, hence the name “fracture mirror.” In fact, high magnification microscopy reveals that, even within the mirror region in glasses, there are very fine features and escalating roughness as the crack advances away from the origin. These are submicrometer in size and hence are not discernable with an optical microscope. Early investigators interpreted fracture mirrors as having discrete boundaries including a “mirror-mist” boundary and also a “mist-hackle” boundary in glasses. These were also termed “inner mirror” or “outer mirror” boundaries, respectively. It is now known that there are no discrete boundaries corresponding to specific changes in the fractographic features. Surface roughness increases gradually from well within the fracture mirror to beyond the apparent boundaries. The boundaries were a matter of interpretation, the resolving power of the microscope, and the mode of viewing. In very weak specimens, the mirror may be larger than the specimen or component and the boundaries will not be present.

Figs. 3-5 show examples in ceramics. In polycrystalline ceramics, the qualifier “relatively” as in “relatively smooth” must be used, since there is an inherent roughness from the microstructure even in the area immediately surrounding the origin. In coarse-grained or porous ceramics, it may be impossible to identify a mirror boundary. In polycrystalline ceramics, it is highly unlikely that a mirror-mist boundary can be detected due to the inherent roughness created by the crack-microstructure interactions, even within the mirror. The word “systematic” in the definition for “mirror-hackle boundary in polycrystalline ceramics” requires some elaboration. Mirror boundary hackle lines are velocity hackle lines created after the radiating crack reaches terminal velocity. However, premature, isolated hackle can in some instances be generated well within a ceramic fracture mirror. It should be disregarded when judging the mirror boundary. Wake hackle from an isolated obstacle inside the mirror (such as a large grain or agglomerate) can trigger early “premature” hackle lines. Steps in scratches or grinding flaws can trigger hackle lines that emanate from the origin itself. Sometimes the microstructure of polycrystalline ceramics creates severe judgment problems in ceramic matrix composites (particulate, whisker, or platelet) or self-reinforced ceramics whereby elongated and interlocking grains impart greater fracture resistance. Mirrors may be plainly evident at low magnifications, but accurate assessment of their size can be difficult. The mirror region itself may be somewhat bumpy; therefore, some judgment as to what is a mirror boundary is necessary.

Fracture mirrors are circular in some loading conditions such as tension specimens with internal origins, or they are nearly semicircular for surface origins in tensile specimens, or if the mirrors are small in bend specimens. Their shapes can vary and be elongated or even incomplete in some directions if the fracture mirrors are in stress gradients. Fracture mirrors may be quarter circles if they form from corner origins in a specimen or component. Fracture mirrors only form in moderate to high local stress conditions. Weak specimens may not exhibit full or even partial mirror boundaries, since the crack may not achieve sufficient velocity within the confines of the specimen.

Fracture mirrors not only bring one’s attention to an origin, but also give information about the magnitude of the stress at the origin that caused fracture and their distribution. The fracture mirror size and the stress at fracture are empirically correlated by Eq 1:

where:
σ	=	stress at the origin (MPa or ksi),
R	=	fracture mirror radius (m or in),
A	=	fracture mirror constant (MPa√m or ksi√in).

Equation 1 is hereafter referred to as the “empirical stress – fracture mirror size relationship,” or “stress-mirror size relationship” for short. A review of the history of Eq 1, and fracture mirror analysis in general, may be found in Refs 1 and 2.

A, the “fracture mirror constant” (sometimes also known as the “mirror constant”) has units of stress intensity (MPa√m or ksi√in) and is considered by many to be a material property. As shown in Figs. 1 and 2, it is possible to discern separate mist and hackle regions and the apparent boundaries between them in glasses. Each has a corresponding mirror constant, A. The most common notation is to refer to the mirror-mist boundary as the inner mirror boundary, and its mirror constant is designated A_i. The mist-hackle boundary is referred to as the outer mirror boundary, and its mirror constant is designated A_o. The mirror-mist boundary is usually not perceivable in polycrystalline ceramics. Usually, only the mirror-hackle boundary is measured and only an A_o for the mirror-hackle boundary is calculated. A more fundamental relationship than Eq 1 may be based on the stress intensity factors (K_I) at the mirror-mist or mist-hackle boundaries, but Eq 1 is more practical and simpler to use.

The size predictions based on Eq 1 and the A values, or alternatively stress intensity factors, match very closely for the limiting cases of small mirrors in tension specimens. This is also true for small semicircular mirrors centered on surface flaws in strong flexure specimens. So, at least for some special mirror cases, A should be directly related to a more fundamental parameter based on stress intensity factors.

The size of the fracture mirrors in laboratory test specimen fractures may be used in conjunction with known fracture mirror constants to verify the stress at fracture was as expected. The fracture mirror sizes and known stresses from laboratory test specimens may also be used to compute fracture mirror constants, A.

The size of the fracture mirrors in components may be used in conjunction with known fracture mirror constants to estimate the stress in the component at the origin. Practice C 1322 has a comprehensive list of fracture mirror constants for a variety of ceramics and glasses.

Note—(a) shows the whole fracture surface and the fracture mirror (arrow) which is centered on a surface flaw. (b) is a close-up of the fracture mirror which is elongated slightly into the interior due to the flexural stress gradient.

FIG. 2 Optical Micrographs of a Fracture Mirror in a Fused Silica Glass Rod Broken in Flexure at 122 MPa Maximum Stress on the Bottom.

Note—Notice how clear the mirror is in the low power images in (a) and (b). The mirror boundary (arrows in c) is where systematic new hackle forms and there is an obvious roughness difference compared to the roughness inside the mirror region.

FIG. 3 Silicon Carbide Tension Strength Specimen (371 MPa) with a Mirror Centered on a Compositional Inhomogeneity Flaw.

Note— The mirror boundary is difficult to delineate in this material. (a) shows the uncoated fracture surface of a 2.8 mm thick flexural strength specimen that fractured at 486 MPa. Vicinal illumination brings out the markings. (b) shows a mirror-hackle boundary where systematic new hackle is detected (small white arrows) as compared to the roughness inside the mirror. The marked circle is elongated somewhat into the depth due to the stress gradient. The radius in the direction along the bottom surface (a region of constant stress) was 345 mm.

FIG. 4 A Fracture Mirror in a Fine-Grained 3 Mol % Yttria-Stabilized Tetragonal Zirconia Polycrystal (3Y-TZP).

Note—The mirror is incomplete into the bend stress gradient, but the mirror sides can be used to construct boundary arcs in (c) [(b) and (c) are close-ups of (a)]. Radii are measured in the direction of constant stress along the bottom.

FIG. 5 Silicon Nitride Bend Bar with a Knoop Surface Crack in a Silicon Nitride (449 MPa).