Application Note | Rock Mechanics Testing

Microindentation and Fracture of Mineral Rock

Hardness, Young’s Modulus, and Fracture Threshold Loads of Biotite, Feldspar, and Quartz in Granite

Bucket-wheel excavator in a mine

Research & Experimental Testing

Duanjie Li, Jonathan Thomas & Pierre Leroux

Visual Design & Editorial

Andrew Shore

Introduction

Rock mechanics is the study of the mechanical behavior of rock masses and is applied in mining, drilling, reservoir production, and civil construction industries. Advanced instrumentation with precise measurement of mechanical properties allows for part and procedure improvement within these industries. Successful quality control procedures are ensured by understanding rock mechanics at the micro scale.

Microindentation for Research and Quality Control

Microindentation is a crucial tool used for rock mechanics related studies. These techniques advance excavation techniques by providing further understanding of rock mass properties. Microindentation is used to improve drill heads which improve mining procedures. Microindentation has been used to study chalk and powder formation from minerals. Microindentation studies can include hardness, Young’s modulus, creep, stress-strain, fracture toughness, and compression with a single instrument.

Measurement Objective

In this application the NANOVEA mechanical tester measures the Vickers hardness (Hv), Young’s modulus, and fracture toughness of a mineral rock sample. The rock is made up of biotite, feldspar and quartz which form the standard granite composite. Each is tested separately.

NANOVEA PB1000 Large Platform

Mechanical Tester

Nanoindenter and scratch tester platform NANOVEA PB1000 with nano and micro modules

Test Conditions

Vickers indenter above the granite rock sample on the mechanical tester stage
Close-up of the granite sample with dark biotite, white feldspar and grey quartz grains

Fig. 1: Sample of rock used for testing.

The following set of conditions was used:

Hardness parameterAll samples
Maximum force2 N
Loading rate4 N/min
Creep5 seconds
Computation methodOliver & Pharr
Indenter typeVickers diamond

Table 1: Hardness test parameters.

Fracture toughness parameterBiotiteFeldspar and quartz
Maximum force20 N25 N
Loading rate75 N/min75 N/min
Creep0 seconds0 seconds
Computation methodOliver & PharrOliver & Pharr
Indenter typeVickers diamondVickers diamond

Table 2: Fracture toughness test parameters.

Results and Discussion

This section includes a summary table that compares the main numerical results for the different samples, followed by the full result listings, including each indentation performed, accompanied by micrographs of the indentation, when available. These full results present the measured values of Hardness and Young’s modulus as the penetration depth (Δd) with their averages and standard deviations. It should be considered that large variation in the results can occur in the case that the surface roughness is in the same size range as the indentation.

Summary of Main Numerical Results

MineralHardness (Vickers)Hardness (GPa)Young’s modulus (GPa)Depth (µm)
Biotite94.68 ± 10.801.00 ± 0.1129.31 ± 4.979.98 ± 0.57
Feldspar850.82 ± 48.009.00 ± 0.5175.58 ± 2.334.15 ± 0.03
Quartz1258.58 ± 31.0613.32 ± 0.3399.32 ± 3.273.56 ± 0.05

Table 3a: Summary of hardness results.

MineralFracture Point 1 (N)Fracture Point 2 (N)Fracture Point 3 (N)Fracture Point 4 (N)
Biotite3.24 ± 0.709.05 ± 0.4714.93 ± 0.2716.80 ± 0.83
Feldspar2.28 ± 0.7716.62 ± 2.3921.62 ± 1.1323.45 ± 0.56
Quartz1.93 ± 0.575.83 ± 0.587.47 ± 0.1121.38 ± 1.12

Table 3b: Summary of fracture threshold loads.

Biotite: Detailed Hardness Results

TestHardness (Vickers)Hardness (GPa)Young’s modulus (GPa)Depth (µm)
1104.891.1133.019.44
294.251.0034.669.85
3108.681.1530.459.32
483.090.8822.9310.68
582.490.8725.4910.58
Average94.681.0029.319.98
Std deviation10.800.114.970.57

Table 4: Detailed hardness results of biotite.

Load versus depth curve of a 2 N Vickers microindentation on biotite
Fig. 2: Load-depth curve of a hardness test on biotite (2 N).

Biotite: Detailed Fracture Toughness Results

TestFracture Point 1 (N)Fracture Point 2 (N)Fracture Point 3 (N)Fracture Point 4 (N)
13.658.6014.9516.02
23.649.0215.1816.72
32.439.5314.6516.67
Average3.249.0514.9316.80
Std deviation0.700.470.270.83

Table 5: Fracture threshold loads of biotite.

Load versus depth curve of a 20 N Vickers indentation on biotite, with steps where fractures occur
Fig. 3: Load-depth curve of a fracture test on biotite (20 N).

Feldspar: Detailed Hardness Results

TestHardness (Vickers)Hardness (GPa)Young’s modulus (GPa)Depth (µm)
1900.949.5375.264.10
2763.468.0879.814.19
3887.949.4072.824.16
4850.489.0074.344.17
5851.289.0175.644.16
Average850.829.0075.584.15
Std deviation48.000.512.330.03

Table 6: Detailed hardness results of feldspar.

Load versus depth curve of a 2 N Vickers microindentation on feldspar
Fig. 4: Load-depth curve of a hardness test on feldspar (2 N).

Feldspar: Detailed Fracture Toughness Results

Note: Fracture Points 3 and 4 are the overall structural fracture points while the other fracture points are local points of fracture.
TestFracture Point 1 (N)Fracture Point 2 (N)Fracture Point 3 (N)Fracture Point 4 (N)
12.9819.3422.6723.80
22.4015.6721.7623.74
31.4514.8420.4222.81
Average2.2816.6221.6223.45
Std deviation0.772.391.130.56

Table 7: Fracture threshold loads of feldspar.

Load versus depth curve of a 25 N Vickers indentation on feldspar, with steps where fractures occur
Fig. 5: Load-depth curve of a fracture test on feldspar (25 N).

Quartz: Detailed Hardness Results

TestHardness (Vickers)Hardness (GPa)Young’s modulus (GPa)Depth (µm)
11286.3213.61103.663.50
21286.9313.62102.303.52
31251.0113.2497.743.58
41266.0713.4098.263.56
51202.5812.7394.623.64
Average1258.5813.3299.323.56
Std deviation31.060.333.270.05

Table 8: Detailed hardness results of quartz.

Load versus depth curve of a 2 N Vickers microindentation on quartz
Fig. 6: Load-depth curve of a hardness test on quartz (2 N).

Quartz: Detailed Fracture Toughness Results

Note: Fracture Point 4 is the overall structural fracture point while the other fracture points are local points of fracture.
TestFracture Point 1 (N)Fracture Point 2 (N)Fracture Point 3 (N)Fracture Point 4 (N)
12.525.24–20.78
21.896.397.5522.67
31.395.857.3920.68
Average1.935.837.4721.38
Std deviation0.570.580.111.12

Table 9: Fracture threshold loads of quartz.

Load versus depth curve of a 25 N Vickers indentation on quartz, with steps where fractures occur
Fig. 7: Load-depth curve of a fracture test on quartz (25 N).

Conclusion

The NANOVEA mechanical tester demonstrates reproducibility and precise indentation results on the hard surface of mineral rock. Hardness and Young’s modulus of each material forming the granite was measured directly from depth versus load curves. The rough surface meant testing at higher loads that may have caused micro cracking. Micro cracking would explain some of the variations seen in measurements. Cracks were not perceivable through standard microscopy observation because of a rough sample surface. Therefore, it is not possible to calculate traditional fracture toughness numbers that require crack length measurements. Instead, we used the system to detect initiation of cracks through the dislocations in the depth versus load curves while increasing loads.

Fracture threshold loads were reported at loads where failures occurred. Unlike traditional fracture toughness tests that simply measure crack length, a load is obtained at which threshold fracture starts. Additionally, the controlled and closely monitored environment allows the measurement of hardness to use as a quantitative value for comparing a variety of samples.

Frequently Asked Questions About Microindentation of Rock

Why use microindentation in rock mechanics?

Rock mechanics is applied in mining, drilling, reservoir production and civil construction. Microindentation advances excavation techniques by revealing rock mass properties at the micro scale, helps improve drill heads, and has been used to study chalk and powder formation from minerals.

What can microindentation measure on a rock sample?

Hardness, Young’s modulus, creep, stress-strain, fracture toughness and compression, all with a single instrument. Here each mineral of a granite sample (biotite, feldspar and quartz) was tested separately.

How hard are biotite, feldspar and quartz?

At 2 N, biotite measured 94.68 ± 10.80 HV (1.00 GPa), feldspar 850.82 ± 48.00 HV (9.00 GPa) and quartz 1258.58 ± 31.06 HV (13.32 GPa), with Young’s moduli of 29.31, 75.58 and 99.32 GPa.

How is fracture measured when cracks cannot be seen?

The rough surface made cracks imperceptible under standard microscopy, so crack-length fracture toughness could not be calculated. Instead, crack initiation was detected from the steps in the depth versus load curve as the load increased, and the fracture threshold loads were reported.

What fracture threshold loads did the minerals show?

The overall structural fracture occurred at about 16.80 N for biotite, 21.62 to 23.45 N for feldspar and 21.38 N for quartz, after earlier local fractures starting at 3.24, 2.28 and 1.93 N.

Which test conditions were used?

A Vickers diamond indenter with Oliver and Pharr analysis: hardness at 2 N, 4 N/min with 5 s creep; fracture at 20 N for biotite and 25 N for feldspar and quartz, at 75 N/min with no creep.

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