Material resistance to crack growth and fracture is known as fracture toughness (Kc), which determines the structural integrity of brittle materials by characterizing the rate at which energy is released during fracture.
Structural defects, such as faults, microcracks, micro-voids, and inclusions, influence the apparent toughness in many ways.
Some structural defects reduce toughness by increasing the crack growth rate, while others increase resistance by blunting the crack tip by generating microplasticity and local toughening in the material structure.
Nanoindentation techniques have been widely employed to assess the fracture toughness of brittle materials with sharp tip geometries. The developed models rely on directly measuring radial cracks that form at the edge of sharp Vickers (Berkovich) or cube corner indentation marks.
Various fragile materials were examined in this article using different tip geometries and imaging approaches.
Experimental Method
The KLA Nano Indenter® G200 and iMicro nanoindenter were utilized to provide various loads for material testing. Fracture toughness was assessed by measuring fracture length with the nanoindenter's optical and scanning characteristics.
The iMicro nanoindenter, equipped with the InForce 1000 actuator, was used to test various extremely hard materials.
The G200, equipped with a high load 10 N force actuator, was also used to generate cracks in extremely hard materials requiring higher forces. Indentation and cracking were performed using the ISO 14577 constant loading rate method.
Vickers and cube corner tips were utilized for cracking. Fracture toughness was calculated using the linear elastic mechanics (LEM) equation:
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(1) |
where c is the average crack length from the center of indent, H and E are the material's hardness and Young's modulus, and Pmax is the maximum load during indentation.
The coefficient α was measured experimentally for brittle (bulk) materials and found to be approximately 0.016 for the Vickers 4-sided pyramidal indenter and 0.032 for a cube corner indenter.
KC denotes the critical value of the stress intensity factor at the fracture edge required to cause catastrophic failure under plane-strain conditions. Lower values of KC suggest a greater likelihood of catastrophic failure.
The residual impressions from the indentations were then imaged using the G200's optical microscope. High-resolution imaging is necessary for small indentation impressions with fine cracks on extremely hard materials or fragile thin films loaded at very low levels.
Instead of employing high-resolution microscopy, such as SEM, the Stiffness Mapping approach on the KLA G200 NanoVision Stage enabled the collection of the full length of small fractures, resulting in the most accurate readings.
The fracture toughness method described in this article is best suited for brittle bulk materials in which radial crack dimensions are often substantially larger than the size of the indentation mark.
The geometry of crack systems, indenter tip geometry, and material properties must all be considered. The ratio of E/H, or E/σy (where σy is the yield stress), plays a crucial role in crack geometry and indicates material brittleness (e.g., E/σy ~ 10 for brittle materials).
As materials become more ductile, such as metallic systems, E/σy approaches 100. This ratio is complex in more complex systems, such as multilayers and numerous coatings, due to the underlying impacts of substrate material qualities and residual stress throughout manufacturing operations.
In such instances, improved models or energy-based techniques are preferable.
Indentation Testing Results – Cube Corner Tip
Figure 1 depicts images generated using the scanning and stiffness mapping methods on the KLA G200 NanoVision stage. The left image was created by scanning a silica indent and describes the residual impression's surface topography and cracks migrating across the surface at each of its three corners.
The right image was created using stiffness mapping, providing a clearer view of the depression and cracks along the three edges. Stiffness mapping was also employed to predict crack length for fracture toughness calculations.
Figure 1. G200 images of a silica indent using a NanoVision stage with the scanning method (left) and the stiffness mapping method (right). Image Credit: KLA Corporation
Some shorter split fractures can be observed in the corners. The three principal cracks are caused by the constant increase in applied load during the final stages of loading. Calculations were based on primary crack lengths.
The experimental fracture toughness for a maximum load of 100 mN averaged over 10 repeated tests was 0.74 ± 0.09 MPa·m1/2. This value is consistent with the stated value for bulk fused silica, 0.79 ± 0.01 MPa·m1/2.
Using the same method, several extremely hard ceramic carbide materials were tested, and their fracture toughness values were computed.
In addition to high hardness and modulus, these materials' fracture toughness (resistance to cracking) is crucial because they can be used as tip materials for high-temperature indentation.
In Figure 2, the left set of SEM pictures reveals residual indentation impressions on these materials, employing a sharp Cube corner tip with 2-10 µm measured crack lengths.
The right figure displays the computed fractured toughness Kc and applied load for each material, including niobium carbide (NbC), sapphire, vanadium carbide (VC), titanium carbide (TiC), zirconium carbide (ZrC), and tungsten carbide (WC).
Interestingly, the single crystal WC exhibits no obvious cracking, even at stresses as high as 3 N.
Figure 2. (top) SEM images of residual impressions for six hard materials: NbC, sapphire, VC, TiC, ZrC, and WC; (bottom) calculated fracture toughness Kc and maximum applied load for the six materials. Image Credit: KLA Corporation
Indentation Testing Results – Vickers Tip
Schott BK7 (borosilicate) glass and Plexiglas (PMMA) were incised with a Vickers tip. As seen in Figure 3, lengthy radial cracks occurred along the borosilicate indentation mark edges at each of the tip's four corners.
Borosilicate's fracture toughness was reported at 0.96 ± 0.01 MPa·m1/2.
The PMMA indentation in Figure 4 (left) shows no signs of brittle cracking along the borders of the sharp Vickers tip. Plexiglas, also known as PMMA, is a transparent plastic that is shatter-resistant and often exhibits ductile behavior during deformation.
If a material is subjected to different environmental conditions, extreme changes in mechanical behavior can occur. Indentation is an excellent method for detecting such surface changes.
When the PMMA was indented in an acetone environment, cracks formed and spread from the indentation corners, demonstrating that crack formation is aided by the environment (Figure 4, right). This process is sometimes referred to as stress-corrosion cracking.
Figure 3. Indentation of borosilicate glass using a Vickers tip. Image Credit: KLA Corporation
Figure 4. Indentation of Plexiglass (PMMA) using a Vickers tip under normal conditions (left) and exposure to an acetone environment (right). Image Credit: KLA Corporation
Summary
The bulk fracture toughness of several brittle materials was assessed using KLA G200 and iMicro Nanoindenters. Fracture toughness was determined by measuring material property data using the ISO 14577 standard procedure.
The G200 NanoVision stage's imaging capacity enables crack length measurements for calculation purposes. This concept, which employs existing models or other energy dissipation methodologies, can expand the use of nanoindentation in fracture toughness measurements for more complicated structures.
KLA Instruments is proud to be a sponsor for the upcoming Structure & Fracture conference Gefüge & Bruch Tagung 2025 February 26 – 28 at Montanuniversität Leoben.
This information has been sourced, reviewed and adapted from materials provided by KLA Corporation.
For more information on this source, please visit KLA Corporation.