# Surface Reflectance: An Optical Method for Multiscale Curvature Characterization of Wear on Ceramic–Metal Composites

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Selection of Surfaces

^{®}(MathWorks, Natick, MA, USA) and applied to images with Mountains Map

^{®}(Digital Surf, Besançon, FR). High pass and low pass filters are combined to create band pass filters for multiscale analyses. These multiscale analyses characterize wear topographies at different scales and elucidate differences between materials, and between α/β structures. The former is an inter-comparison of one MMC versus another. The latter is an intra-comparison of ceramics versus metal.

#### 2.1.2. Mechanical Testing by Micro-Indentation

_{C}from the length a, the length c and the Vickers hardness H

_{v}. The fracture toughness of each ceramic was determined by measuring 2a and c, which includes L

_{c}the length of the crack generated by the indentation (Figure 3):

#### 2.2. Reflectance Measurements

#### 2.2.1. Principles

**n**are the normal vectors, and ρ is the maximum surface reflectance. ρ normalizes the normals.

_{1}, K

_{2}), are the principal curvatures. These are the extreme values, maximum and minimum, of curvatures locally. Their orientations, the principal directions, are orthogonal. The principal curvatures and directions comprise the curvature tensor.

_{g}, mean curvatures H, and Mehlum curvatures K

_{Mehlum}[39]:

_{Mehlum}= g(x,y), creating a Mehlum curvature map (Figure 6). Instead of the usual heights (z), these functions, derived from gradients and calculated from reflectance measurements as described above, are used in this study to characterize the surface topographies.

#### 2.2.2. Topographic slope acquisition by reflectance transformation imaging (RTI)

#### 2.3. Quantification of the SGCLR Relevance

- Step 1. Reflectance images, described in Section 2.2.2.
- Step 2. Gradients and curvatures computation, described in Section 2.2.1.
- Step 3. Surface segmentation: images were segmented, with an algorithm in MATLAB
^{®}, according to the colors of the ceramic and metal phases. The algorithm draws shapes by following edges of color regions. The generated binary mask (Figure 9a) was imported into MountainsMap^{®}and was applied to the shapes on each map (Figure 9b,c) in order to separate the ceramic grains from the metal phase.

- Step 4. Filtering was done in MountainsMap
^{®}for multiscale decompositions, with curvatures replacing heights. Gaussian filters were applied for low pass, high pass, and band pass, to all the ceramic and metal sections of the curvature maps, with 59 cutoff wavelengths ε varying from 2.2 to 4413 µm. High pass filtering keeps higher spatial frequencies, shorter spatial wavelengths, corresponding to roughness (low cutoffs). Low pass filtering keeps low spatial frequencies, longer wavelengths (high cutoffs), corresponding to waviness and form. Band pass is calculated by applying a high pass filter on the surface at a given cutoff ε and finally a low pass filter on the filtered surface at the cutoff ε-1. - Step 5. From these topographic representations of curvatures, within color segmentations, decomposed by multiscale filtering, 3D topographic characterization parameters were calculated in MountainsMap
^{®}. A total of 75 topographic characterization parameters were studied (ISO 25178, EUR 15178N, and software modules) treating curvatures as if they are heights. - Step 6. Statistical analyses by bootstrapping [40] and analysis of variance (ANOVA) [41] were done to determine the relevance (F) of different characterization parameters for discriminating the ceramics. A relevance index (RI) is calculated from the relevance F, the 95th percentile and the 5th percentile in order to normalize values:

## 3. Results and Discussion

^{®}) is the most relevant parameter with a relevance index of 1.36 and a relevance, F, of 63. The mean density of furrows is statistically relevant for discriminating ceramic phases with Mehlum curvatures and a band pass filter at 5.4 µm.

_{Ic}(R² = 0.90) (Figure 14a). A regression analysis, based on a single bootstrap of 100 iterations, seeking the best correlation between the 3D parameters and the mechanical properties confirmed that the density of furrows for the ceramics with the Mehlum curvatures and a band pass at 5.4 µm is one of the parameters with the strongest correlation. The valley fluid retention index (Svi) for the ceramics with the Gaussian curvatures and a low pass at 19.5 µm has the strongest correlation with an R² value of 0.99, but Svi is not a good parameter for discrimination (Figure 10).

_{c}, the lower the K

_{Ic}, and the more the ceramic surface suffers damage in use, and the density of furrows is greater.

_{V}) and horizontal (F

_{T}) forces applied during tests (Equation (7)):

_{Ic}obtained from scratch testing is close to that measured by conventional mechanical testing. They performed tests on brittle materials, such as, cement paste and sandstone, for different scratch widths and depths of cut. For both materials, K

_{Ic}decreases with an increase of width which means that damage scratches are wider for a less resistant material at a given scratch depth. This is consistant with Figure 14b,c showing the furrows of more and less damaged ceramics, 2 and 3, respectively. Ceramic 2 is less crack resistant than 3, and has more pronounced furrows. The more a brittle material is crack resistant, the more it resists abrasion scratches [43].

_{Ic}and low alumina content have less furrows because they are more elastic. Moreover, SEM investigations are made at the relevant scale of 5.4 µm to justify the statistical result. Micrometer-sized scratches are observed locally which confirms the scale of 5.4 µm (Appendix B). The scratches damage less the microstructure of the ceramic grains with the highest K

_{Ic}(Appendix B). However, these are local observations (10 x 10 µm) and not observations at the grain scale (1000 × 1000 µm). These do not represent the damage of the entire grain but justify locally the furrow phenomenom. The SGCLR method then characterizes better the damage because it averages on all grains and not a particular area of a grain.

^{–6}) and $b=0.03$ (p = 0.50) (Figure 17). Because b is small, this can be approximated as $S10{z}_{metal}=1.2\cdot S10{z}_{ceramic}$ (p = 0, R² = 0.87). With the intercept at the origin, the damage is always similar in the ceramics and the metal, providing a statistically robust model for comparing damage in the ceramics and the metal. This indicates that ceramic and metal damage are co-dependent [43]. The more the ceramic is plane, i.e., with a curvature close to zero, then undamaged, the more the metal is too. The metal damage variation increases with the ceramics’ damage. As the metal is more ductile than the ceramic, its efficiency of abrasion is low [47].

_{Ic}of 0.51 and the highest alumina content (50–80%). Group B (3, 4, 5) contains the ceramics with the lowest alumina content (10–30%), the highest fracture toughness and a mean K

_{Ic}of 0.64. As scratch width decreases when fracture toughness increases at a given scratch depth [38], curvatures increase. That is why group B has higher S10z curvatures values, with a high pass filter at 1286 µm, than group A.

## 4. Conclusions

- The density of furrows for Mehlum curvatures and S10z for mean curvatures, curvatures calculated from reflectance acquisitions, quantify the wear of the ceramics and of the metal at different scales: small, i.e., high spatial frequencies for density of furrows for Mehlum curvatures, and large, i.e., low spatial frequencies for S10z for mean curvatures.
- The density of furrows for Mehlum curvatures, at a scale of 5.4 µm, is the most relevant parameter for evaluating the wear difference between the ceramics.
- The density of furrows for Mehlum curvatures, at 5.4 µm, is proportional to the number of scratches, which are indications of an elementary wear mechanism namely abrasive wear.
- Material damage is related to mechanical properties. A strong correlation exists between the density of furrows for Mehlum curvatures, at 5.4 µm, and the fracture toughness (R² = 0.90). A material with a high K
_{Ic}presents less scratches. - A strong correlation (R² = 0.87) is found between the S10z for curvatures, with a high pass filter at 1286 µm, of the metal and the ceramics, with the metal more damaged than the ceramics.
- There are no heterogeneities in the results showing any influence of the material color on the SGCLR. The SGCLR method is not sensitive to surface colors.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Abbreviations | ||||||

ANOVA | ANalysis Of VAriance | |||||

MMC | Metal matrix composite | |||||

RTI | Reflectance transformation imaging | |||||

SGCLR | Surface gradient characterization by light reflectance | |||||

Roughness parameters | ||||||

S10z | Ten point height | |||||

Sa | Arithmetic mean height | |||||

Svi | Valley fluid retention index | |||||

Mechanical parameters | ||||||

α | Ceramic phase | |||||

β | Metal phase | |||||

d | Depth of scratch | |||||

H_{v} | Hardness | |||||

K_{Ic} | Fracture toughness | |||||

L_{c} | Crack length | |||||

w | Width of scratch | |||||

RTI and curvature parameters | ||||||

ϕ | Azimuth | |||||

θ | Elevation | |||||

H | Mean curvature | |||||

K_{1} | Minimum principal curvature | |||||

K_{2} | Maximum principal curvature | |||||

K_{g} | Gaussian curvature | |||||

K_{Mehlum} | Mehlum curvature | |||||

Multiscale and statistical parameters | ||||||

ε | Cutoff length | |||||

F | Relevance |

## Appendix A

SEM Images | Mehlum Curvature Maps | Furrows Maps | |

Surface 1K _{Ic} = 0.457 MPa√m50–80% of alumina Black and cubic grains | |||

Surface 2K _{Ic} = 0.503 MPa√m50–80% of alumina Black and cubic grains | |||

Surface 3K _{Ic} = 0.682 MPa√m10–30% of alumina White and cubic grains | |||

Surface 4K _{Ic} = 0.683 MPa√m10–30% of alumina White and spherical grains | |||

Surface 5K _{Ic} = 0.553 MPa√m30–50% of alumina White and spherical grains | |||

Surface 6K _{Ic} = 0.557 MPa√m30–50% of alumina White and cubic grains |

## Appendix B

Surfaces | 1 and 2 | 5 and 6 | 3 and 4 |

Alumina content | High (50–80%) | Medium (30–50%) | Low (10–30%) |

Mean K (MPa√m)_{Ic} | 0.48 | 0.55 | 0.68 |

SEM zoom |

## References

- Le Goïc, G.; Bigerelle, M.; Samper, S.; Favrelière, H.; Pillet, M. Multiscale roughness analysis of engineering surfaces: A comparison of methods for the investigation of functional correlations. Mech. Syst. Signal Process.
**2016**, 66–67, 437–457. [Google Scholar] [CrossRef] - Brown, C.A.; Hansen, H.N.; Jiang, X.J.; Blateyron, F.; Berglund, J.; Senin, N.; Bartkowiak, T.; Dixon, B.; Le Goïc, G.; Quinsat, Y.; et al. Multiscale analyses and characterizations of surface topographies. CIRP Ann.
**2018**, 67, 839–862. [Google Scholar] [CrossRef] - Bataille, C.; Bigerelle, M. Influence des conditions d’anodisation sur les mécanismes tribologiques de Stick-Slip. In 23ème Congrès Français de Mécanique, Lille (FR); Association Française de Mécanique: Courbevoie, France, 2017. [Google Scholar]
- Van Gorp, A.; Bigerelle, M.; Najjar, D. Relationship between brightness and roughness of polypropylene abraded surfaces. Polym. Eng. Sci.
**2016**, 56, 103–117. [Google Scholar] [CrossRef] - Shu, D.J.; Gong, X.G. Curvature effect on surface diffusion: The nanotube. J. Chem. Phys.
**2001**, 114, 10922–10926. [Google Scholar] [CrossRef][Green Version] - Shen, X.; Avital, E.; Paul, G.; Rezaienia, M.A.; Wen, P.; Korakianitis, T. Experimental study of surface curvature effects on aerodynamic performance of a low Reynolds number airfoil for use in small wind turbines. J. Renew. Sustain. Energy
**2016**, 8, 053303. [Google Scholar] [CrossRef] - Golden, J.M. The Effect of Surface Curvature on the Friction Coefficient. Wear
**1978**, 48, 73–86. [Google Scholar] [CrossRef] - Fang, X.; Li, Y.; Feng, X. Curvature effect on the surface topography evolution during oxidation at small scale. J. Appl. Phys.
**2017**, 121, 125301. [Google Scholar] [CrossRef] - Bartkowiak, T.; Lehner, J.T.; Hyde, J.; Wang, Z.; Pedersen, D.B.; Hansen, H.N.; Brown, C.A. Multi-scale areal curvature analysis of fused deposition surfaces. In Proceedings of the ASPE Spring Topical Meeting on Achieving Precision Tolerances in Additive Manufacturing, Raleigh, NC, USA, 26–29 April 2015. [Google Scholar]
- Vulliez, M.; Gleason, M.; Souto-Lebel, A.; Quinsat, Y.; Lartigue, C.; Kordel, S.; Lemoine, A.; Brown, C. Multi-scale Curvature Analysis and Correlations with the Fatigue Limit on Steel Surfaces after Milling. In Proceedings of the 2nd CIRP Conference on Surface Integrity (CSI), Birmingham, UK, 28–30 May 2014; Volume 13, pp. 308–313. [Google Scholar]
- Bartkowiak, T.; Berglund, J.; Brown, C.A. Establishing functional correlations between multiscale areal curvatures and coefficients of friction for machined surfaces. Surf. Topogr. Metrol. Prop.
**2018**, 6, 034002. [Google Scholar] [CrossRef] - Bartkowiak, T.; Brown, C. Multi-scale curvature tensor analysis of machined surfaces. Arch. Mech. Technol. Mater.
**2016**, 36, 44–50. [Google Scholar] [CrossRef][Green Version] - Maleki, I.; Wolski, M.; Woloszynski, T.; Podsiadlo, P.; Stachowiak, G. A Comparison of Multiscale Surface Curvature Characterization Methods for Tribological Surfaces. Tribol. Online
**2019**, 14, 8–17. [Google Scholar] [CrossRef][Green Version] - Bigerelle, M.; Nianga, J.M.; Najjar, D.; Iost, A.; Hubert, C.; Kubiak, K.J. Roughness signature of tribological contact calculated by a new method of peaks curvature radius estimation on fractal surfaces. Tribol. Int.
**2013**, 65, 235–247. [Google Scholar] [CrossRef][Green Version] - Malzbender, T.; Gelb, D.; Wolters, H. Polynomial texture maps. In Proceedings of the ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA, 12–17 August 2001; pp. 519–528. [Google Scholar]
- Shipulski, E.M.; Brown, C.A. A scale-based model of reflectivity. Fractals
**1994**, 2, 413–416. [Google Scholar] [CrossRef] - Everton, S.; Hirsch, M.; Stravroulakis, P.; Leach, R.; Clare, A. Review of in-situ process monitoring and in-situ metrology for metal additive manufacturing. Mater. Des.
**2016**, 95, 431–445. [Google Scholar] [CrossRef] - Davaajav, N.; Sukigara, S. Surface Characterization of Cashmere Fabrics Using Optical and Transient Thermal Properties. J. Fash. Technol. Text. Eng.
**2018**, 6. [Google Scholar] [CrossRef] - Lindqvist, M.; Evertsson, M.; Chenje, T.; Radziszewski, P. Influence of particle size on wear rate in compressive crushing. Miner. Eng.
**2006**, 19, 1328–1335. [Google Scholar] [CrossRef] - Jensen, L.R.D.; Friis, H.; Fundal, E.; Møller, P.; Brockhoff, P.B.; Jespersen, M. Influence of quartz particles on wear in vertical roller mills. Part I: Quartz concentration. Miner. Eng.
**2010**, 23, 390–398. [Google Scholar] [CrossRef] - Jensen, L.R.D.; Fundal, E.; Møller, P.; Jespersen, M. Wear mechanism of abrasion resistant wear parts in raw material vertical roller mills. Wear
**2011**, 271, 2707–2719. [Google Scholar] [CrossRef] - Lindqvist, M.; Evertsson, C.M. Liner wear in jaw crushers. Miner. Eng.
**2003**, 16, 1–12. [Google Scholar] [CrossRef] - Cleary, P.W.; Sinnott, M.D. Simulation of particle flows and breakage in crushers using DEM: Part 1-Compression crushers. Miner. Eng.
**2015**, 74, 178–197. [Google Scholar] [CrossRef] - Lindqvist, M.; Evertsson, C.M. Development of wear model for cone crushers. Wear
**2006**, 261, 435–442. [Google Scholar] [CrossRef] - Archard, J.F. Contact and Rubbing of Flat Surfaces. J. Appl. Phys.
**1953**, 24, 981–988. [Google Scholar] [CrossRef] - Jiang, X.; Ye, P. Analysis and study of the crushing mechanism of the MPS vertical roller mill. In Proceedings of the 2nd International Conference on Mechanic Automation and Control, Hohhot, China, 15–17 July 2011; pp. 1029–1032. [Google Scholar]
- Evans, A.G.; Charles, E.A. Fracture Toughness Determinations by Indentation. J. Am. Ceram. Soc.
**1976**, 59, 371–372. [Google Scholar] [CrossRef] - Castro, Y.; Pitard, G.; Le Goïc, G.; Brost, V.; Mansouri, A.; Pamart, A.; Vallet, J.-M.; De Luca, L. A new method for calibration of the spatial distribution of light positions in free-form RTI acquisitions. In Optics for Arts, Architecture, and Archaeology VII; International Society for Optics and Photonics: Bellingham, WA, USA, 2019. [Google Scholar]
- Degrigny, C.; Piqué, F.; Papiashvili, N.; Guery, J.; Mansouri, A.; Le Goïc, G.; Detalle, V.; Martos-Levif, D.; Mounier, A.; Wefers, S.; et al. Technical study of Germolles’ wall paintings: The input of imaging techniques. Virtual Archaeol. Rev.
**2016**, 7, 1–8. [Google Scholar] [CrossRef][Green Version] - Pitard, G.; Le Goïc, G.; Mansouri, A.; Favrelière, H.; Desage, S.-F.; Samper, S.; Pillet, M. Discrete Modal Decomposition: A new approach for the reflectance modeling and rendering of real surfaces. Mach. Vis. Appl.
**2017**, 28, 607–621. [Google Scholar] [CrossRef] - Pitard, G.; Le Goïc, G.; Mansouri, A.; Favrelière, H.; Pillet, M.; George, S.; Hardeberg, J. Robust Anomaly Detection Using Reflectance Transformation Imaging for Surface Quality Inspection. Image Anal.
**2017**, 10269, 550–561. [Google Scholar] - Nurit, M.; Castro, Y.; Zendagui, A.; Le Goïc, G.; Favreliere, H.; Mansouri, A. High dynamic range reflectance transformation imaging: An adaptive multi-light approach for visual surface quality assessment. In Fourteenth International Conference on Quality Control. by Artificial Vision; International Society for Optics and Photonics: Bellingham, WA, USA, 2019. [Google Scholar]
- Le Goïc, G. Qualité Géométrique & Aspect des Surfaces: Approches Locales et Globales. Ph.D. Thesis, Université de Grenoble, Grenoble, French, 2012. [Google Scholar]
- Malzbender, T.; Gelb, D.G. Apparatus for and Method of Enhancing Shape Perception with Parametric Texture Maps; US Patent Office: Alexandria, VA, USA, 2000.
- Gautron, P.; Krivanek, J.; Pattanaik, S.; Bouatouch, K. A Novel Hemispherical Basis for Accurate and Efficient Rendering. Render. Tech.
**2004**, 321–330. [Google Scholar] [CrossRef] - Pitard, G.; Le Goïc, G.; Favrelière, H.; Samper, S.; Desage, S.-F.; Pillet, M. Discrete Modal Decomposition for surface appearance modelling and rendering. In Optical Measurement Systems for Industrial Inspection IX; International Society for Optics and Photonics: Bellingham, WA, USA, 2015. [Google Scholar]
- Woodham, R.J. Photometric Method For Determining Surface Orientation From Multiple Images. Opt. Eng.
**1980**, 19, 139–144. [Google Scholar] [CrossRef] - MacDonald, L.W. Visualising an Egyptian Artefact in 3D: Comparing RTI with Laser Scanning. In Proceedings of the International Conference on Electronic Visualisation and the Arts (EVA), London, UK, 6–8 July 2011. [Google Scholar]
- Mehlum, E.; Tarrou, C. Invariant smoothness measures for surfaces. Adv. Comput. Math.
**1998**, 8, 49–63. [Google Scholar] [CrossRef] - Efron, B.; Tibshirani, R. An Introduction to the Bootstrap. In Chapman Hall/CRC Monographs on Statistics and Applied Probability; CRC: Boca Raton, FL, USA, 1994. [Google Scholar]
- Deltombe, R.; Kubiak, K.J.; Bigerelle, M. How to select the most relevant 3D roughness parameters of a surface: Relevance of 3D roughness parameters. Scanning
**2014**, 36, 150–160. [Google Scholar] [CrossRef][Green Version] - Akono, A.-T.; Ulm, F.-J. Scratch test model for the determination of fracture toughness. Eng. Fract. Mech.
**2011**, 78, 334–342. [Google Scholar] [CrossRef] - Gahr, K.-H.Z. Wear by hard particles. Tribol. Int.
**1998**, 31, 587–596. [Google Scholar] [CrossRef] - Joshi, P.; Séquin, C. Energy Minimizers for Curvature-Based Surface Functionals. Comput. Aided Des. Appl.
**2007**, 4, 607–617. [Google Scholar] [CrossRef] - Griffith, A.A. The Phenomena of Rupture and Flow. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
**1921**, 221, 163–198. [Google Scholar] - Francfort, G.A.; Marigo, J.-J. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids
**1998**, 46, 1319–1342. [Google Scholar] [CrossRef] - Torrance, A.A. Modelling abrasive wear. Wear
**2005**, 258, 281–293. [Google Scholar] [CrossRef]

**Figure 1.**Rendering of Y-gradients (slopes) of a measurement on surface from material 3 (Section 2.2) (5140 × 4797 µm).

**Figure 2.**Images of (

**a**) material 2 with black, cubic grains, and (

**b**) material 5 with white, spherical grains. Both are 5140 × 4797 µm.

**Figure 5.**Rendering of a normal map (gradients or slopes) of a measurement of surface from material 3 (

**a**). The direction of the vector is indicated by the color mix, where Red = X, Green = Y and Blue = Z (

**b**).

**Figure 7.**Reflectance images at ϕ = 215°. Θ = 80° (

**a**), θ = 57.5° (

**b**), θ = 35° (

**c**), and reflectance halfsphere (

**d**).

**Figure 9.**Segmentation of the surface 3, Y-gradient map. The binary mask was generated with a MATLAB

^{®}algorithm (

**a**), and ceramic (

**b**) and metal (

**c**) phases were obtained after application of the mask (MountainsMap

^{®}).

**Figure 10.**Classification rankings by relevance indices for discrimination of the seven materials by 75 topographic parameters for 100 bootstraps.

**Figure 11.**Relevance index versus cutoff lengths for the mean density of furrows and Sa. Ceramics, Mehlum curvatures and a band pass filtering. Classification rankings by relevance indices for discrimination of the 7 materials by 75 topographic parameters for 100 bootstraps.

**Figure 12.**Mean density of furrows for all six ceramics versus multiscale cutoff lengths. Mehlum curvatures and a band pass filtering.

**Figure 13.**SEM image (

**a**), Mehlum curvature map (

**b**), and furrows map (

**c**) of a measurement of the surface 4.

**Figure 14.**Mean density of furrows versus K

_{Ic}, for ceramics, Mehlum curvatures and a band pass filtering at 5.4 µm (

**a**). Density of furrows in grains of ceramic 2 (

**b**) and ceramic 3 (

**c**), calculated from acquisition images at the same light angular position. MountainsMap

^{®}module.

**Figure 15.**Mean density of furrows vs multiscale cutoff lengths for metal, Mehlum curvatures, and a band pass filtering (

**a**). Relevance index versus cutoff lengths for the mean density of furrows for Mehlum curvatures and a band pass (blue), and S10z curvatures for mean curvatures and a high pass (red) (

**b**).

**Figure 16.**S10z vs. multiscale cutoff lengths for metal, mean curvatures and a high pass filtering (

**a**). Common scale of the ceramic and the metal phases (

**b**).

**Figure 17.**S10z curvatures of the metal vs S10z curvatures of the ceramics. Affine and linear approximations (

**a**), and linear model (

**b**). Ceramics and metal, mean curvatures, and a high pass filtering at 1286 µm.

Criteria | Surface Characteristics | Can SGCLR… |
---|---|---|

C1 | Different levels loading for the same wear mechanism | Quantify graduated morphological differences ? |

C2 | Multiscale topographical structure (fractal) | Detect different topographical scales ? |

C3 | Different wear mechanisms, abrasion versus spalling | Detect and quantify elementary physical mechanisms that are sources of gradients ? |

C4 | Composite with two materials with different topographies (metal matrix and ceramic) | Segment surfaces for determining morphological indicators discriminating zones ? |

C5 | Different surface colors | Be invariant with respect to colors ? |

Surfaces | 2a (µm) | c (µm) | H_{v} (MPa) | K_{Ic} (MPa√m) |
---|---|---|---|---|

1 | 78.9 | 88.6 | 1489 | 0.4565 |

2 | 77.8 | 83.2 | 1532 | 0.5029 |

3 | 82.0 | 67.5 | 1378 | 0.6817 |

4 | 84.9 | 68.2 | 1288 | 0.6829 |

5 | 84.1 | 76.9 | 1310 | 0.5526 |

6 | 82.7 | 76.5 | 1356 | 0.5566 |

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## Share and Cite

**MDPI and ACS Style**

Lemesle, J.; Robache, F.; Le Goic, G.; Mansouri, A.; Brown, C.A.; Bigerelle, M.
Surface Reflectance: An Optical Method for Multiscale Curvature Characterization of Wear on Ceramic–Metal Composites. *Materials* **2020**, *13*, 1024.
https://doi.org/10.3390/ma13051024

**AMA Style**

Lemesle J, Robache F, Le Goic G, Mansouri A, Brown CA, Bigerelle M.
Surface Reflectance: An Optical Method for Multiscale Curvature Characterization of Wear on Ceramic–Metal Composites. *Materials*. 2020; 13(5):1024.
https://doi.org/10.3390/ma13051024

**Chicago/Turabian Style**

Lemesle, Julie, Frederic Robache, Gaetan Le Goic, Alamin Mansouri, Christopher A. Brown, and Maxence Bigerelle.
2020. "Surface Reflectance: An Optical Method for Multiscale Curvature Characterization of Wear on Ceramic–Metal Composites" *Materials* 13, no. 5: 1024.
https://doi.org/10.3390/ma13051024