**3. The measurement and evaluation of fiber bundle surfaces**

### **3.1 Measurement strategy and sampling direction**

When measuring fiber bundle surfaces, 2D measurement should be adopted because of the obvious directionality of the surfaces. Here we take the surface of Cf/SiC with a processing angle of 90° as an example. Owing to the directionality of the fiber bundles, different sampling directions often result in different numerical characteristics, as shown in **Figures 5** and **6**. We can see that no matter what type of measurement direction is applied, there is no influence on the 3D surface

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

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 related to the fiber orientation and machining direction.

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

#### **Figure 5.**

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

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

silicon [25]. The density of the Cf/SiC composite is 1.85 g/cm<sup>3</sup>

fiber bundles, according to their directions (shown in **Figure 4**).

**3.1 Measurement strategy and sampling direction**

**3. The measurement and evaluation of fiber bundle surfaces**

measurement direction is applied, there is no influence on the 3D surface

materials is shown as follows:

**Figure 4.**

about 1.6 mm 1.6 mm.

**212**

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

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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

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

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

When measuring fiber bundle surfaces, 2D measurement should be adopted because of the obvious directionality of the surfaces. Here we take the surface of Cf/SiC with a processing angle of 90° as an example. Owing to the directionality of the fiber bundles, different sampling directions often result in different numerical characteristics, as shown in **Figures 5** and **6**. We can see that no matter what type of

.

*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.*

#### **Figure 6.**

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

direction scale is more notable than the fiber orientation scale, and the directionality of the surface topography mainly depends on the machining direction.

On the side surface of a fiber bundle, as shown in **Figure 5(c, e)**, when the scanning track is perpendicular to the fiber direction, the profile shows damage between fibers, whereas the profiles only show single fiber damage when the scanning track is parallel to the fiber direction (**Figure 5(d, f)**), which means that the profiles cannot reflect the machining effect on the whole fiber bundle surface. The same phenomenon occurs in the end surface of a fiber bundle. When the scanning track is perpendicular to the machining direction, the profile shows the integrated influence of the processing (**Figure 6(c, e)**); however, when the scanning track is parallel to the machining direction, the profiles simply show the effect of a single grain on the surface (**Figure 6(d, f)**).

From the analysis above, it can be seen that the 2D sampling and evaluation method is more suitable for a fiber bundle scale measurement. To guarantee measurement accuracy and consider the influence of the fiber orientation and machining direction on the surface topography, the scanning track should be perpendicular to the fiber orientation on the side surface of a fiber bundle and perpendicular to the machining direction on the end surface.

According to our research, it may be reasonably inferred that, for planes which are not truly along the fibers, the influence of the fiber orientation and machining direction should be considered. When the surface is full of processing traces and the fiber orientation is so obscure, the sampling direction should be perpendicular to the machining direction. In other cases, the sampling direction should still be perpendicular to the projection direction on the vertical plane along the fiber axis. However, a definite conclusion in this regard still requires further research.

#### **3.2 Determination of sampling length and number**

The side surface of Cf/SiC with processing angle of 90° is taken as an example to illustrate the determination method of sampling length when measuring a fiber bundle surface. Since the diameters of the fibers are approximately 7 μm, a set of candidate sampling length are chosen as the integral multiple of 7 μm, namely, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, and 147 μm. In each sampling length, 1500 surface profiles are measured with a constant sampling step of 0.1 μm. And 2D surface roughness *Ra* of each profile is obtained.

decreasing and becoming steady. When the sampling length reaches to 120 μm,

*The distribution of 2D surface roughness Ra under different sampling length [24]. (a) With the sampling*

*lengths of 7,42 84 125 and 147. (b) With the sampling lengths of 119,126 133 140 and 147.*

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

to 150 and the constant sampling length 120 μm could be obtained, which is represented by *Raavg.* Under every sampling number, the measurement process repeats 50 times independently. Then the maximum relative error of every sampling number, calculated by Eq. (13), is demonstrated in **Figure 9**. It is shown that with the rise of sampling numbers, the maximum relative error would decrease dramatically. Once the number of *Ra* reaches to 70 or above, it is stable under 2%,

> *δ* ¼ *Raave* � *Raavg*

According to the analysis given above, the conclusion can be made that as long as extracting surface profiles averagely distributed on the side surface of Cf/SiC composite fiber bundle with the appropriate sampling length and sampling number, the mean value of Ra is steady and can estimate the whole surface roughness. For

*=Raave* ∗ 100% (13)

Based on the results obtained above, a speculation is proposed that the mean value of a few number of *Ra* can steadily estimate the entire surface roughness of fiber bundle. The average value of *Ra* under the changing sampling number from 10

*Raave* is stable around 1297.3 nm.

*The changing trends of σ and Raave under different sampling length [24].*

**Figure 8.**

**215**

**Figure 7.**

which is acceptable in terms of accuracy.

According to the numerical values of 1500 *Ra*, a frequency histogram is made. It can be seen that the distribution of 2D surface roughness *Ra* in every sampling length is almost of its normal distribution. The result shown in **Figure 7** is the one using normal distribution function to fit the frequency histogram. With the growth of sampling length (**Figure 8(a)**), the curves are thinner and higher. Their shapes do not change any more in the case that sampling length is more than a certain value (**Figure 8(b)**). It is known to all that normal distribution has two parameters: the mean value *μ* and the standard deviation *σ*. *μ* is the location parameter and describes the central tendency position of the normal distribution. *σ* demonstrates the discrete degree of data. The larger the *σ* is, the more decentralized the data is, leading to a fact that the curve is fatter and lower. On the contrary, the more concentrated the data is, the thinner and taller is the curve. That is to say, *Ra* is gradually convergent and concentrated while the sampling length increases.

**Figure 8** clearly shows the changing trends of standard deviation *σ* and the mean value *Raave* of 1500 2D surface roughness *Ra* under different sampling length. It can be found that with the increase of sampling length, both *σ* and *Raave* are gradually

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

**Figure 7.**

direction scale is more notable than the fiber orientation scale, and the directionality

On the side surface of a fiber bundle, as shown in **Figure 5(c, e)**, when the scanning track is perpendicular to the fiber direction, the profile shows damage between fibers, whereas the profiles only show single fiber damage when the scanning track is parallel to the fiber direction (**Figure 5(d, f)**), which means that the profiles cannot reflect the machining effect on the whole fiber bundle surface. The same phenomenon occurs in the end surface of a fiber bundle. When the scanning track is perpendicular to the machining direction, the profile shows the integrated influence of the processing (**Figure 6(c, e)**); however, when the scanning track is parallel to the machining direction, the profiles simply show the effect

From the analysis above, it can be seen that the 2D sampling and evaluation method is more suitable for a fiber bundle scale measurement. To guarantee measurement accuracy and consider the influence of the fiber orientation and machining direction on the surface topography, the scanning track should be perpendicular to the fiber orientation on the side surface of a fiber bundle and perpendicular to the

According to our research, it may be reasonably inferred that, for planes which are not truly along the fibers, the influence of the fiber orientation and machining direction should be considered. When the surface is full of processing traces and the fiber orientation is so obscure, the sampling direction should be perpendicular to the machining direction. In other cases, the sampling direction should still be perpendicular to the projection direction on the vertical plane along the fiber axis. However, a definite conclusion in this regard still requires further research.

The side surface of Cf/SiC with processing angle of 90° is taken as an example to illustrate the determination method of sampling length when measuring a fiber bundle surface. Since the diameters of the fibers are approximately 7 μm, a set of candidate sampling length are chosen as the integral multiple of 7 μm,

According to the numerical values of 1500 *Ra*, a frequency histogram is made. It

**Figure 8** clearly shows the changing trends of standard deviation *σ* and the mean value *Raave* of 1500 2D surface roughness *Ra* under different sampling length. It can be found that with the increase of sampling length, both *σ* and *Raave* are gradually

namely, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, and 147 μm. In each sampling length, 1500 surface profiles are measured with a constant sampling step of 0.1 μm. And 2D surface roughness *Ra* of each profile is

can be seen that the distribution of 2D surface roughness *Ra* in every sampling length is almost of its normal distribution. The result shown in **Figure 7** is the one using normal distribution function to fit the frequency histogram. With the growth of sampling length (**Figure 8(a)**), the curves are thinner and higher. Their shapes do not change any more in the case that sampling length is more than a certain value (**Figure 8(b)**). It is known to all that normal distribution has two parameters: the mean value *μ* and the standard deviation *σ*. *μ* is the location parameter and describes the central tendency position of the normal distribution. *σ* demonstrates the discrete degree of data. The larger the *σ* is, the more decentralized the data is, leading to a fact that the curve is fatter and lower. On the contrary, the more concentrated the data is, the thinner and taller is the curve. That is to say, *Ra* is gradually

convergent and concentrated while the sampling length increases.

of the surface topography mainly depends on the machining direction.

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of a single grain on the surface (**Figure 6(d, f)**).

**3.2 Determination of sampling length and number**

machining direction on the end surface.

obtained.

**214**

*The distribution of 2D surface roughness Ra under different sampling length [24]. (a) With the sampling lengths of 7,42 84 125 and 147. (b) With the sampling lengths of 119,126 133 140 and 147.*

**Figure 8.** *The changing trends of σ and Raave under different sampling length [24].*

decreasing and becoming steady. When the sampling length reaches to 120 μm, *Raave* is stable around 1297.3 nm.

Based on the results obtained above, a speculation is proposed that the mean value of a few number of *Ra* can steadily estimate the entire surface roughness of fiber bundle. The average value of *Ra* under the changing sampling number from 10 to 150 and the constant sampling length 120 μm could be obtained, which is represented by *Raavg.* Under every sampling number, the measurement process repeats 50 times independently. Then the maximum relative error of every sampling number, calculated by Eq. (13), is demonstrated in **Figure 9**. It is shown that with the rise of sampling numbers, the maximum relative error would decrease dramatically. Once the number of *Ra* reaches to 70 or above, it is stable under 2%, which is acceptable in terms of accuracy.

$$\delta = \left| \mathrm{Ra}\_{\mathrm{ave}} - \mathrm{Ra}\_{\mathrm{avg}} \right| / \mathrm{Ra}\_{\mathrm{ave}} \* \mathbf{100}\mathfrak{W} \tag{13}$$

According to the analysis given above, the conclusion can be made that as long as extracting surface profiles averagely distributed on the side surface of Cf/SiC composite fiber bundle with the appropriate sampling length and sampling number, the mean value of Ra is steady and can estimate the whole surface roughness. For

acceptance range of each index is obtained through Eq. (14). The sampling length and sampling number are invariable, and the sampling step is gradually increased. All measurement results are shown in **Figure 10** (side surface) and **Figure 11** (end

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What needs to be mentioned is that the data used in **Figures 10** and **11** are acquired using a sampling direction perpendicular to the fiber orientation on the side surface and the machining direction on the end surface. For each index, the upper and lower limits express the acceptance range. The measurement result that first falls out of range is marked with a red box, and the last sampling step before it is the MaxSS of this index. Combining all four indexes on each surface, the global MaxSS is 0.75 μm on a side surface and 1 μm on an end surface, which are approx-

This chapter proposes four indexes for evaluating a fiber bundle surface, namely, *Ra*, *Rq*, *Rsk*, and *Rku*. To illustrate how the four indexes can estimate the main type and degree of damage of a fiber bundle surface, the side surface and end surface of Cf/SiC with processing angle of 90° are taken as a demonstration. The surfaces of Cf/SiC were process with three machining methods: a) ground using a grinding wheel with a wheel speed of 15 m/s, grinding depth of 0.15 mm, feed rate of 4 m/min, and grain mesh size of 80#; b) polished using a 1200# sandpaper under a constant force of 5 N, spindle speed of 0.1 m/s, and sliding time of 60s; and c) friction against a ZrO2 disk under a constant force of 30 N, spindle speed of 0.5 m/s, and sliding time of 3600 s. The three different methods caused different surface topographies and damages. Therefore, a proper set of indexes should be able to

*Changing trends of four evaluation indexes with increasing sampling steps on fiber bundle side surface [27].*

surface).

**Figure 10.**

**217**

*(a) Raave, (b) Rqave, (c) Rskave, and (d) Rkuave.*

imately 1/10 of the fiber diameter.

reflect the difference of the six kinds of surfaces.

**3.4 Evaluation indexes**

**Figure 9.** *The changing trend of the maximum relative error under different number of Ra [24].*

Cf/SiC composite used in the present work, the critical sampling length is 119 μm, which is about 17 times of the fiber diameter, and sampling number is 70.

#### **3.3 Determination of sampling step**

In this section, the side surface and end surface of Cf/SiC with processing angle of 90° are taken as an example to illustrate the determination method of sampling step, under the condition that the critical sampling length is 150 μm and sampling number is 200. It is clear that using a smaller sampling step can achieve more accurate surface data, whereas a too small step may cause an unnecessary sampling time and data processing cost. A method is proposed to determine the maximum sampling step (MaxSS) that can minimize the data size under the premise of undistorted surface sampling.

We start from setting the data measured at the step of 0.05 μm as a certain type of real value *μ* of surface topography parameters. The data measured using larger steps are to be compared with the real values *μ* to determine whether they are acceptable in terms of accuracy. To set a range of acceptance, the idea of a confidence interval in probability theory is used. If the real value is *μ*, a measurement result that is acceptable based on confidence level of 1-*α* must fall into a computable interval. Based on the probability theory, when the mean value of the overall sample *μ* is known and the standard deviation *σ* is unknown, the confidence interval of the mean value *μ* with the confidence level (1 � *α*) is

$$\left[\mu - t\_{a/2}(n-1)\mathbf{S}/\sqrt{n}, \mu + t\_{a/2}(n-1)\mathbf{S}/\sqrt{n}\right] \tag{14}$$

where *S* is the standard deviation of the samples and *n* is the number of the samples.

By looking up the table-α quantile of the t-distribution, *t<sup>α</sup>=*2ð Þ *n* � 1 is available, and thus the corresponding confidence intervals are obtained. Therefore, the sampling step gradually increases until the measurement result falls out of the acceptance range at that step. This means that this step, and the steps larger than it, can no longer achieve accurate surface data. The largest permitted sampling step can be determined under each single evaluation index. Combining all indexes, the global MaxSS can be determined.

Here, *Raave*, *Rqave*, *Rskave*, and *Rkuave* on a Cf/SiC fiber bundle surface are taken as the evaluation standards. For each index, the real value is determined as the value measured based on a sampling length of 150 μm, sampling number of 200, and sampling step of 0.05 μm. In addition, *t<sup>α</sup>=*2ð Þ *n* � 1 can be found to be 2.326 when the confidence coefficient is 98%. After that, μ and S can easily be calculated. The

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acceptance range of each index is obtained through Eq. (14). The sampling length and sampling number are invariable, and the sampling step is gradually increased. All measurement results are shown in **Figure 10** (side surface) and **Figure 11** (end surface).

What needs to be mentioned is that the data used in **Figures 10** and **11** are acquired using a sampling direction perpendicular to the fiber orientation on the side surface and the machining direction on the end surface. For each index, the upper and lower limits express the acceptance range. The measurement result that first falls out of range is marked with a red box, and the last sampling step before it is the MaxSS of this index. Combining all four indexes on each surface, the global MaxSS is 0.75 μm on a side surface and 1 μm on an end surface, which are approximately 1/10 of the fiber diameter.

#### **3.4 Evaluation indexes**

Cf/SiC composite used in the present work, the critical sampling length is 119 μm,

In this section, the side surface and end surface of Cf/SiC with processing angle of 90° are taken as an example to illustrate the determination method of sampling step, under the condition that the critical sampling length is 150 μm and sampling number is 200. It is clear that using a smaller sampling step can achieve more accurate surface data, whereas a too small step may cause an unnecessary sampling time and data processing cost. A method is proposed to determine the maximum sampling step (MaxSS) that can minimize the data size under the premise of

We start from setting the data measured at the step of 0.05 μm as a certain type of real value *μ* of surface topography parameters. The data measured using larger steps are to be compared with the real values *μ* to determine whether they are acceptable in terms of accuracy. To set a range of acceptance, the idea of a confidence interval in probability theory is used. If the real value is *μ*, a measurement result that is acceptable based on confidence level of 1-*α* must fall into a computable interval. Based on the probability theory, when the mean value of the overall sample *μ* is known and the standard deviation *σ* is unknown, the confidence interval of the

where *S* is the standard deviation of the samples and *n* is the number of the

By looking up the table-α quantile of the t-distribution, *t<sup>α</sup>=*2ð Þ *n* � 1 is available, and thus the corresponding confidence intervals are obtained. Therefore, the sampling step gradually increases until the measurement result falls out of the acceptance range at that step. This means that this step, and the steps larger than it, can no longer achieve accurate surface data. The largest permitted sampling step can be determined under each single evaluation index. Combining all indexes, the global

Here, *Raave*, *Rqave*, *Rskave*, and *Rkuave* on a Cf/SiC fiber bundle surface are taken as the evaluation standards. For each index, the real value is determined as the value measured based on a sampling length of 150 μm, sampling number of 200, and sampling step of 0.05 μm. In addition, *t<sup>α</sup>=*2ð Þ *n* � 1 can be found to be 2.326 when the confidence coefficient is 98%. After that, μ and S can easily be calculated. The

*<sup>n</sup>* <sup>p</sup> , *<sup>μ</sup>* <sup>þ</sup> *<sup>t</sup><sup>α</sup>=*2ð Þ *<sup>n</sup>* � <sup>1</sup> *<sup>S</sup><sup>=</sup>* ffiffiffi *<sup>n</sup>* � � <sup>p</sup> (14)

which is about 17 times of the fiber diameter, and sampling number is 70.

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*The changing trend of the maximum relative error under different number of Ra [24].*

**3.3 Determination of sampling step**

undistorted surface sampling.

samples.

**216**

**Figure 9.**

MaxSS can be determined.

mean value *μ* with the confidence level (1 � *α*) is

*<sup>μ</sup>* � *<sup>t</sup><sup>α</sup>=*2ð Þ *<sup>n</sup>* � <sup>1</sup> *<sup>S</sup><sup>=</sup>* ffiffiffi

This chapter proposes four indexes for evaluating a fiber bundle surface, namely, *Ra*, *Rq*, *Rsk*, and *Rku*. To illustrate how the four indexes can estimate the main type and degree of damage of a fiber bundle surface, the side surface and end surface of Cf/SiC with processing angle of 90° are taken as a demonstration. The surfaces of Cf/SiC were process with three machining methods: a) ground using a grinding wheel with a wheel speed of 15 m/s, grinding depth of 0.15 mm, feed rate of 4 m/min, and grain mesh size of 80#; b) polished using a 1200# sandpaper under a constant force of 5 N, spindle speed of 0.1 m/s, and sliding time of 60s; and c) friction against a ZrO2 disk under a constant force of 30 N, spindle speed of 0.5 m/s, and sliding time of 3600 s. The three different methods caused different surface topographies and damages. Therefore, a proper set of indexes should be able to reflect the difference of the six kinds of surfaces.

#### **Figure 10.**

*Changing trends of four evaluation indexes with increasing sampling steps on fiber bundle side surface [27]. (a) Raave, (b) Rqave, (c) Rskave, and (d) Rkuave.*

ground surfaces. A conclusion can be made that *Raave* and *Rqave* are both valid in evaluating the degree of surface roughness. The rougher the surface is, the larger

damage. The less damage a surface has, the larger *Rkuave* is.

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As a comparison, *Rkuave* of either a ground side surface or a ground end surface is roughly equal to 3. That is, the height distribution approximately obeys a Gaussian distribution on both surfaces. Polishing with sandpaper or sliding against a ZrO2 disk can make the surfaces flat, thus decreasing the amount of surface damage. Meanwhile, they show larger *Rkuave* values. It is clear that the surfaces after friction turn out to have the fewest numbers of surface defects, and *Rkuave* of the friction surfaces has the biggest value among the three processing methods on both the side and end surfaces. It can be seen that *Rkuave* is related to the amount of surface

For both ground surfaces, *Rskave* is close to 0, which is consistent with their Gaussian distribution characteristic. For the surfaces polished by a sandpaper, the crests are chipped off during this processing, with the original troughs remaining, and thus it is reasonable for these two surfaces to have a larger negative *Rskave*. After friction is applied, however, their *Rskave* values reach closer to 0 again, which can be explained by the wear debris embedded into the troughs during the friction

*Raave* and *Rqave* are.

**Figure 12.**

**Figure 13.**

**219**

*Topographies of the six surfaces [27].*

*SEM images of the six surfaces [27].*

#### **Figure 11.**

*Changing trends of four evaluation indexes with increasing sampling steps on fiber bundle end surface [27]. (a) Raave, (b) Rqave, (c) Rskave, and (d) Rkuave.*


#### **Table 1.**

*Fiber bundle surface parameters of three processing methods [27].*

After measuring the six surfaces with the sampling length of 280 μm and sampling number of 200, the scanning track perpendicular to the fiber orientation and machining direction, and the sampling step of 0.5 μm, four indexes can be calculated for every surface. The results are shown in **Table 1**.

The data in **Table 1** reflect that, regardless of the surface processing method used, the side surfaces are rougher than the end surfaces, which can be indicated by all side surfaces having larger *Raave* and *Rqave* than the end surfaces. This phenomenon can be explained as follows. During the machining process, the anti-shear strength of the end surface is stronger; it is thus not easy for the fibers to be pulledout and form surface damage, and the end surface becomes smoother than the side surface. However, fiber debonding and fiber delamination are more likely to appear, leading to more damage and a rougher surface on the side surface. In addition, for both fiber orientation surfaces, *Raave* and *Rqave* of the friction-applied surfaces are the smallest, followed by sandpaper-polished surfaces, and finally

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ground surfaces. A conclusion can be made that *Raave* and *Rqave* are both valid in evaluating the degree of surface roughness. The rougher the surface is, the larger *Raave* and *Rqave* are.

As a comparison, *Rkuave* of either a ground side surface or a ground end surface is roughly equal to 3. That is, the height distribution approximately obeys a Gaussian distribution on both surfaces. Polishing with sandpaper or sliding against a ZrO2 disk can make the surfaces flat, thus decreasing the amount of surface damage. Meanwhile, they show larger *Rkuave* values. It is clear that the surfaces after friction turn out to have the fewest numbers of surface defects, and *Rkuave* of the friction surfaces has the biggest value among the three processing methods on both the side and end surfaces. It can be seen that *Rkuave* is related to the amount of surface damage. The less damage a surface has, the larger *Rkuave* is.

For both ground surfaces, *Rskave* is close to 0, which is consistent with their Gaussian distribution characteristic. For the surfaces polished by a sandpaper, the crests are chipped off during this processing, with the original troughs remaining, and thus it is reasonable for these two surfaces to have a larger negative *Rskave*. After friction is applied, however, their *Rskave* values reach closer to 0 again, which can be explained by the wear debris embedded into the troughs during the friction

**Figure 12.** *Topographies of the six surfaces [27].*

**Figure 13.** *SEM images of the six surfaces [27].*

After measuring the six surfaces with the sampling length of 280 μm and sampling number of 200, the scanning track perpendicular to the fiber orientation and machining direction, and the sampling step of 0.5 μm, four indexes can be calcu-

*Changing trends of four evaluation indexes with increasing sampling steps on fiber bundle end surface [27].*

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**Fiber bundle surface** *Raave***/μm** *Rqave***/μm** *Rskave Rkuave* Side surface, ground 1.97 0.03 2.44 0.03 0.55 0.05 3.29 0.10 Side surface, sandpaper polished 0.98 0.02 1.41 0.05 2.15 0.09 6.48 0.59 Side surface, friction 0.56 0.02 0.78 0.02 0.84 0.07 7.96 0.44 End surface, ground 1.23 0.02 1.56 0.03 0.31 0.04 3.60 0.12 End surface, sandpaper polished 0.26 0.01 0.36 0.01 1.39 0.35 12.80 0.55 End surface, friction 0.20 0.01 0.24 0.01 0.34 0.19 21.14 2.88

The data in **Table 1** reflect that, regardless of the surface processing method used, the side surfaces are rougher than the end surfaces, which can be indicated by all side surfaces having larger *Raave* and *Rqave* than the end surfaces. This phenomenon can be explained as follows. During the machining process, the anti-shear strength of the end surface is stronger; it is thus not easy for the fibers to be pulledout and form surface damage, and the end surface becomes smoother than the side surface. However, fiber debonding and fiber delamination are more likely to appear, leading to more damage and a rougher surface on the side surface. In addition, for both fiber orientation surfaces, *Raave* and *Rqave* of the friction-applied surfaces are the smallest, followed by sandpaper-polished surfaces, and finally

lated for every surface. The results are shown in **Table 1**.

*Fiber bundle surface parameters of three processing methods [27].*

**Figure 11.**

**Table 1.**

**218**

*(a) Raave, (b) Rqave, (c) Rskave, and (d) Rkuave.*

process decreasing the height of the troughs. Thus, it can be inferred that *Rskave* is able to reflect the damage type or degree of the surface. A larger negative *Rskave* value is caused by a trough-dominant surface, and a larger positive *Rskave* value is caused by a crest-dominant surface. The surface state can be inferred by combining *Rskave* and *Rkuave*.

*μ*<sup>1</sup> ¼ *μ*<sup>2</sup> (15)

*e* ¼ *θ* � *θ* (16)

<sup>2</sup> (17)

<sup>2</sup> (18)

*RE* � *<sup>N</sup>* 0, *<sup>σ</sup>*<sup>2</sup> (19)

½ � *<sup>θ</sup>*‐0*:*39*σ*, *<sup>θ</sup>* <sup>þ</sup> <sup>0</sup>*:*39*<sup>σ</sup>* (20)

Since *θ* and *θ* are independent identically distributed (IID), their difference *e*

<sup>2</sup> <sup>þ</sup> *<sup>σ</sup>*<sup>2</sup>

<sup>2</sup> <sup>þ</sup> *<sup>σ</sup>*<sup>2</sup>

*e* � *N μ*<sup>2</sup> � *μ*1, *σ*<sup>1</sup>

*e* � *N* 0, *σ*<sup>1</sup>

Based on the analysis above, for a set of measurement results obtained from different sampling steps, the Residual Errors (*RE*s) between each of them and the

For every actual engineering question, it is reasonable to find an acceptable range of *RE* according to the actual requirements of measurement. For example, if the �15% smallest *RE*s are acceptable, the acceptable measurement results fall into

When the sampling step is small enough, the measurement result is in the range above. However, if the sampling step grows larger, the measurement result will go out of the range sooner or later. The largest sampling step that holds the measurement result within the range of Eq. (20) can be defined as the MaxSS for cell body

Here we take the measurement of a cell body of the Cf/SiC with processing angle of 90° as an example. The sampling steps of 1–45 μm were adopted to measure the cell body. The measurement results of 1 μm were set as the standard values. The rest of the results were compared with the standard values to calculate the *RE*s. The acceptable ranges of measurement results are available through Eq. (20).

The changing trends of the measurement results of the four evaluation indexes under different sampling steps are illustrated in **Figure 14**. The red and blue lines refer to the boundaries of the acceptable ranges calculated from Eq. (20). It is clear

corresponding results begin to go out of the ranges. Then the MaxSS can be determined for each index. Combining the four MaxSSs together, the MaxSS is available

**4.3 Relationship between the measurement of cell body and the whole surface**

The whole surface of a WCMC consists of many cell bodies. Some cell bodies nearby each other faced the same fabrication and machining process and may perform similar surface quality. Therefore, the measurement and evaluation of a

It can also be proved that the MaxSS of a cell body is approximately equal to the

that when the sampling steps exceed a certain value (in red blocks), the

Set *e* as the difference between *θ* and *θ*,

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

*Surface Measurement and Evaluation of Fiber Woven Composites*

Combining Eqs. (16) and (17) together,

standard value *θ* are IID to Normal distribution, so

obeys Normal distribution too:

the range of

surface measurement.

and for this material, it is 7 μm.

diameter of its reinforcing fiber.

**221**

**Figure 12** shows the fiber bundle surface topographies of three processing methods. **Figure 13** shows the microscopic surface topography of six surfaces. It is clear that the values of the four proposed indexes have a strong and direct connection with the surface damage and, thus, have a good feasibility and interpretability for a surface evaluation.
