**2.3 Surface measurement technology and devices**

The measurement of a surface is a process that obtains the height information of the surface. Surface measurement methods are divided into two classes: contact measurement, which uses a probe to measure the height data of points on the surface, and non-contact measurement, which uses light to measure. It was always believed that contact measurement could achieve higher measurement accuracy, although its efficiency was quite low and the measurement process was timeconsuming. However, thanks to the development of optical theories and technologies, the non-contact measurement technology based on white light interferometry can get extremely high level of accuracy now as well. NANOVEA ST400 (shown in **Figure 3**), an optical non-contact measurement system, is used to measure the surface micro-topography in the research of this chapter.

Because the measurement of a surface is in fact the measurement of the points on the surface, it has to be determined which points are chosen to be measured. This

**Figure 3.** *Three-dimensional non-contact surface morphometer.*

topic is related to the sampling strategy, which means how to choose a proper set of points to measure, in order to make the measurement results of these samples able to reflect the information of the entire surface. The first question is to use 2D measurement or 3D measurement.

*Raj* <sup>¼</sup> <sup>X</sup> *M*

r

Here, *Ra* and *Rq* are quite similar in reflecting the surface roughness, although *Rq* is in general more sensitive than *Ra* to the degree of surface

The normalized *Rsk*<sup>0</sup> and *Rku*<sup>0</sup> of the *j*th profile can be obtained as follows:

r

*i*¼1

*M*

*i*¼1

the sampling profile is to a Gaussian distribution. When *Rsk* > 0, the profile presents a positive peak. This indicates that the profile has more crests or the crest height is larger than the trough height. In contrast, if a profile has more troughs, or the trough height is larger than the crest height, it presents a

On the other hand, *Rku* is compared with 3. The closer it is to 3, the more approximate the sampling profile is to a Gaussian distribution. That is, the degree of dispersion of the profile data is similar to a Gaussian distribution profile. The more *Rku* is greater than 3, the smaller the degree of data dispersion is, and in contrast,

The four 3D evaluation indexes used in the chapter are surface arithmetic mean deviation *Sa*, surface square root deviation *Sq*, surface skewness *Ssk*, and surface

the more *Rku* is less than 3, the larger the degree of data dispersion is.

*Sa* <sup>¼</sup> <sup>X</sup> *M*

r

*Ssk* <sup>¼</sup> <sup>X</sup> *M*

*Sku* <sup>¼</sup> <sup>X</sup> *M*

*length* (of X and Y direction, respectively)/*sampling step*.

*i*¼1

*i*¼1

*Sq* ¼

*i*¼1

X*<sup>M</sup> i*¼1 X*<sup>N</sup> j*¼1 *Zij* 2 *=M=*N

> X *N*

*j*¼1 *Zij* 3

X *N*

*j*¼1 *Zij*

where the height of every sampling point is defined as *Zij* and the number of sampling points within the sampling area is *M* and *N*, where *M* and *N* = the *sampling*

X *N*

*j*¼1 *Zij* � � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*Z*0*ij* 3

*Z*0*ij*

According to the definition of *Rsk*, the closer it is to 0, the more approximate

*Rqj* ¼

*Surface Measurement and Evaluation of Fiber Woven Composites*

*DOI: http://dx.doi.org/10.5772/intechopen.90813*

*Rq*0*<sup>j</sup>* ¼

*Rsk*0*<sup>j</sup>* <sup>¼</sup> <sup>X</sup> *M*

*Rku*0*<sup>j</sup>* <sup>¼</sup> <sup>X</sup>

roughness.

negative peak.

**211**

For 3D measurement data:

kurtosis *Sku*, which can be calculated as follows:

*i*¼1 *Zij* � � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X*<sup>M</sup> i*¼1 *Zij* 2 *=M*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X*<sup>M</sup> i*¼1 *Z*0*ij* 2 *=M*

*= MRq*0*<sup>j</sup>*

<sup>4</sup>*= MRq*0*<sup>j</sup>*

4

�*=M* (4)

<sup>3</sup> � � (7)

� � (8)

�*=M=*N (9)

*= MNSq*<sup>3</sup> � � (11)

<sup>4</sup>*= MNSq*<sup>4</sup> � � (12)

(5)

(6)

(10)

If a 2D measurement is adopted, points in a line are measured and calculated as one data set. In this term, sampling step (the length between two adjacent sampled points), sampling length (the length of the entire sampling line), and sampling direction (the angle between the sampling line and the structure of the surface) should be determined. In most instances of 2D measurement, one line of sampling is not able to reflect the entire surface because of the measuring error and the random surface damage. Several lines should be selected and measured in order to improve the stability of the measurement results. Therefore, sampling number (the number of the sampling lines) is also to be determined.

If a 3D measurement is adopted, an array of points inside the entire surface are measured and calculated as one data set. That's to say, the sampling area is the area of the entire surface. When sampling step is determined, the points to be measured are selected. It was believed that 3D measurement was more adaptable for complex surfaces because it could get more information of the surfaces. However, the research of this chapter proved that, if the surface to be measured is obviously directional, 3D measurement will lose its advantages and 2D measurement should be adopted. On the other side, 3D measurement always means long sampling time, huge data processing work, and, thus, low efficiency.

Selecting proper sampling parameters, including sampling step, length, direction, number of 2D measurement, and sampling step of 3D measurement, is a complex work. Small step and large length and number are always related to higher measuring accuracy but low efficiency and vice versa. Proper sampling parameters balance both two sides, maintain undistorted sampling, and, on this basis, reduce sampling points.

#### **2.4 Surface evaluation technology**

The task of surface evaluation technology is to select proper statistical characteristics (defined as evaluation indexes in this chapter), which can be calculated from the measurement data of the heights of the sampling points. The following are the indexes adopted in the research of the chapter:

For 2D measurement data:

For each sampling profile *j*, its average is defined as *μ0j*, the standard deviation is *σ0j*, and the normalized height of every sampling point is *Z0ij*, and thus

$$\mu\_{0j} = \sum\_{i=1}^{M} Z\_{ij}/M \tag{1}$$

$$
\sigma\_{0j} = \sqrt{\sum\_{i=1}^{M} \left( Z\_{ij} - \mu\_{0j} \right)^2 / (M - 1)} \tag{2}
$$

$$Z\_{0\circ j} = \left(Z\_{\circ j} - \mu\_{0j}\right) / \sigma\_{0j} \tag{3}$$

where the height of every sampling point is defined as *Zij*, *j* is the *j*th profile on the fiber bundle surface, and the number of sampling points within the sampling profile is *M*, where *M* = the *sampling length*/*sampling step*.

Based on the above, the four 2D evaluation indexes used in the chapter are profile arithmetic mean error *Ra*, profile square root deviation *Rq*, profile skewness *Rsk*, and profile kurtosis *Rku*, which can be calculated as follows:

*Surface Measurement and Evaluation of Fiber Woven Composites DOI: http://dx.doi.org/10.5772/intechopen.90813*

topic is related to the sampling strategy, which means how to choose a proper set of points to measure, in order to make the measurement results of these samples able to reflect the information of the entire surface. The first question is to use 2D

*Composite and Nanocomposite Materials - From Knowledge to Industrial Applications*

If a 2D measurement is adopted, points in a line are measured and calculated as one data set. In this term, sampling step (the length between two adjacent sampled points), sampling length (the length of the entire sampling line), and sampling direction (the angle between the sampling line and the structure of the surface) should be determined. In most instances of 2D measurement, one line of sampling is not able to reflect the entire surface because of the measuring error and the random surface damage. Several lines should be selected and measured in order to improve the stability of the measurement results. Therefore, sampling number (the number

If a 3D measurement is adopted, an array of points inside the entire surface are

Selecting proper sampling parameters, including sampling step, length, direction, number of 2D measurement, and sampling step of 3D measurement, is a complex work. Small step and large length and number are always related to higher measuring accuracy but low efficiency and vice versa. Proper sampling parameters balance both two sides, maintain undistorted sampling, and, on this basis, reduce

The task of surface evaluation technology is to select proper statistical characteristics (defined as evaluation indexes in this chapter), which can be calculated from the measurement data of the heights of the sampling points. The following are

For each sampling profile *j*, its average is defined as *μ0j*, the standard deviation is

*Zij=M* (1)

*=σ*0*<sup>j</sup>* (3)

(2)

*σ0j*, and the normalized height of every sampling point is *Z0ij*, and thus

X*<sup>M</sup> i*¼1

r

*<sup>μ</sup>*0*<sup>j</sup>* <sup>¼</sup> <sup>X</sup> *M*

*Z*0*ij* ¼ *Zij* � *μ*0*<sup>j</sup>* � �

*i*¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*=*ð Þ *M* � 1

*Zij* � *μ*0*<sup>j</sup>* � �<sup>2</sup>

where the height of every sampling point is defined as *Zij*, *j* is the *j*th profile on the fiber bundle surface, and the number of sampling points within the sampling

Based on the above, the four 2D evaluation indexes used in the chapter are profile arithmetic mean error *Ra*, profile square root deviation *Rq*, profile skewness

measured and calculated as one data set. That's to say, the sampling area is the area of the entire surface. When sampling step is determined, the points to be measured are selected. It was believed that 3D measurement was more adaptable for complex surfaces because it could get more information of the surfaces. However, the research of this chapter proved that, if the surface to be measured is obviously directional, 3D measurement will lose its advantages and 2D measurement should be adopted. On the other side, 3D measurement always means long sampling time,

measurement or 3D measurement.

of the sampling lines) is also to be determined.

huge data processing work, and, thus, low efficiency.

the indexes adopted in the research of the chapter:

*σ*0*<sup>j</sup>* ¼

profile is *M*, where *M* = the *sampling length*/*sampling step*.

*Rsk*, and profile kurtosis *Rku*, which can be calculated as follows:

sampling points.

**210**

**2.4 Surface evaluation technology**

For 2D measurement data:

$$\mathbf{Ra}\_{j} = \sum\_{i=1}^{M} |\mathbf{Z}\_{ij}| / M \tag{4}$$

$$Rq\_j = \sqrt{\sum\_{i=1}^{M} Z\_{ij}^{-2}/\mathcal{M}} \tag{5}$$

Here, *Ra* and *Rq* are quite similar in reflecting the surface roughness, although *Rq* is in general more sensitive than *Ra* to the degree of surface roughness.

The normalized *Rsk*<sup>0</sup> and *Rku*<sup>0</sup> of the *j*th profile can be obtained as follows:

$$Rq\_{0\circ} = \sqrt{\sum\_{i=1}^{M} Z\_{0\circ}r\_i^2/M} \tag{6}$$

$$Rsk\_{0j} = \sum\_{i=1}^{M} Z\_{0ij}{}^{3} / \left(MRq\_{0j}{}^{3}\right) \tag{7}$$

$$Rk\mu\_{0\circ} = \sum\_{i=1}^{M} Z\_{0\circ j}{}^{4} / \left(MRq\_{0j}{}^{4}\right) \tag{8}$$

According to the definition of *Rsk*, the closer it is to 0, the more approximate the sampling profile is to a Gaussian distribution. When *Rsk* > 0, the profile presents a positive peak. This indicates that the profile has more crests or the crest height is larger than the trough height. In contrast, if a profile has more troughs, or the trough height is larger than the crest height, it presents a negative peak.

On the other hand, *Rku* is compared with 3. The closer it is to 3, the more approximate the sampling profile is to a Gaussian distribution. That is, the degree of dispersion of the profile data is similar to a Gaussian distribution profile. The more *Rku* is greater than 3, the smaller the degree of data dispersion is, and in contrast, the more *Rku* is less than 3, the larger the degree of data dispersion is.

For 3D measurement data:

The four 3D evaluation indexes used in the chapter are surface arithmetic mean deviation *Sa*, surface square root deviation *Sq*, surface skewness *Ssk*, and surface kurtosis *Sku*, which can be calculated as follows:

$$\text{Sa} = \sum\_{i=1}^{M} \sum\_{j=1}^{N} |Z\_{ij}| / \text{M} / \text{N} \tag{9}$$

$$\text{Sq} = \sqrt{\sum\_{i=1}^{M} \sum\_{j=1}^{N} Z\_{ij}^{-2} / \mathbf{M} / \mathbf{N}} \tag{10}$$

$$\text{Ssk} = \sum\_{i=1}^{M} \sum\_{j=1}^{N} Z\_{ij}^{\;\;3\;\;/} / \left(\text{MNS} q^{\text{3}}\right) \tag{11}$$

$$\text{Sk}\mu = \sum\_{i=1}^{M} \sum\_{j=1}^{N} Z\_{ij}^{\ast 4} / \left(\text{MNS}q^{4}\right) \tag{12}$$

where the height of every sampling point is defined as *Zij* and the number of sampling points within the sampling area is *M* and *N*, where *M* and *N* = the *sampling length* (of X and Y direction, respectively)/*sampling step*.

topography. That is, a 3D sampling and evaluation method may not be able to reflect the surface details of the fiber bundle. The use of one or a group of 3D evaluation indexes based on a 3D sampled data fails to reflect the damage types

matrix is weaker than that of the end surface. The most direct reflection of the machining direction is fiber damage such as fiber debonding, fiber fractures and delamination. The fiber direction scale is more notable than the machining direction scale, and the directionality of the surface topography mainly depends on the fiber orientation. On the end surface of a fiber bundle, the fiber is mainly subjected to a shear force. The main fiber damage is fiber shearing and fiber pullout. The machining

On the side surface of a fiber bundle, the bonding strength between the fiber and

*Side surface topography of a fiber bundle with a scanning track perpendicular and parallel to the fiber direction [27]. (a) Surface topography-scanning track perpendicular to the fiber direction. (b) Surface topographyscanning track parallel to the fiber direction. (c) Original profile 1, scanning track perpendicular to the fiber direction. (d) Original profile 1, scanning track parallel to the fiber direction. (e) Original profile 2, scanning track perpendicular to the fiber direction. (f) Original profile 2, scanning track parallel to the fiber direction.*

*End surface topography of a fiber bundle with a scanning track perpendicular and parallel to the machining direction [27]. (a) Surface topography-scanning track perpendicular to the machining direction. (b) Surface topography-scanning track parallel to the machining direction. (c) Original profile 1, scanning track perpendicular to the machining direction. (d) Original profile 1, scanning track parallel to the machining direction. (e) Original profile 2, scanning track perpendicular to the machining direction. (f) Original profile*

related to the fiber orientation and machining direction.

*Surface Measurement and Evaluation of Fiber Woven Composites*

*DOI: http://dx.doi.org/10.5772/intechopen.90813*

**Figure 5.**

**Figure 6.**

**213**

*2, scanning track parallel to the machining direction.*

**Figure 4.** *Definition of the processing angle of Cf/SiC [26].*

#### **2.5 Materials used as examples in the chapter**

In order to illustrate the measurement and evaluation method, several materials were measured and evaluated as examples in this chapter. The information of the materials is shown as follows:

The carbon fiber-reinforced silicon carbide ceramic matrix composite (Cf/SiC) was fabricated through chemical vapor infiltration (CVI) combined with a liquid melt infiltration process (LMI) [24]. The preform was prepared using a 3D needling method and densified using CVI to form a porous carbon/carbon (C/C) composite. Next, the porous C/C composite was converted into Cf/SiC during LMI, in which silicon carbide (SiC) matrix was formed through a reaction with carbon and melted silicon [25]. The density of the Cf/SiC composite is 1.85 g/cm<sup>3</sup> .

The fiber diameter of the material is about 7 μm, and size of the cell body is about 1.6 mm 1.6 mm.

The Cf/SiC specimens were ground with four different processing angles. For 90° processing angle, the fiber bundles are divided into side fiber bundles and end fiber bundles, according to their directions (shown in **Figure 4**).
