**3. Tensile deformation**

The sample specimens were cut into a dumbbell shape having a gauge length of 10 mm. The tensile strain was calculated from the ratio of the increment of the length between the clamps to the initial gauge length. The tensile stress was determined by dividing the tensile load by the initial cross section. The stress–strain

*Tensile Properties in β-Modified Isotactic Polypropylene DOI: http://dx.doi.org/10.5772/intechopen.83348*

curves at room temperature were measured at a constant crosshead speed of 20 mm/min.

**Figure 4a** shows the overall stress–strain curves for all the samples with various *β*-phase contents at the same crystallinity. The ultimate tensile elongation markedly increases with increasing the *β*-phase content, and the *β*-iPP (PP98) has higher drawability than *α*-iPP (PP0). The *β*-iPP is elongated more gradually with ambiguous necking as compared to *α*-iPP, which is elongated with obvious necking.

As seen in **Figure 4b**, the initial elastic strain domain is surprisingly insensitive to the change in the composition of the crystalline phase at a fixed crystallinity. Thus, Young's modulus was constant and completely independent of the *β*-phase content (see **Figure 5**). This phenomenon is responsible for the strain concentration in the amorphous region [24] because the amorphous phase in iPP is rubberlike at room temperature and the mechanical modulus of the amorphous phase is considerably lower than those of *α*- and *β*-phase crystals. Consequently, before yielding, the deformation of the semicrystalline polymers is dominated by the deformation of the amorphous phase, indicating that the initial elastic region depends mainly on the crystallinity.

The elasticity limits where the actual stress-strain curves for the *β*-modified iPP samples are deviated from the linear elastic behavior were around 0.1 strain as shown in **Figure 4b**. The deviation may be due to the onset of microscopic plastic

**Figure 4.**

**2.3 Crystalline morphology**

**Figure 3.**

tion spots corresponding to 65.3 nm.

and *β*-phase peak near 0.0625 nm�<sup>1</sup>

were about 14 and 16 nm.

**3. Tensile deformation**

**76**

The small angle X-ray scattering (SAXS) measurement was performed with a point-focusing optics and a one-dimensional position-sensitive proportional counter (PSPC) with an effective length of 10 cm. The CuKα radiation supplied by a MAC Science M18X generator operating at 40 kV and 30 mA was used throughout. The distance between the sample and PSPC was about 40 cm. The geometry was further checked using a chicken tendon collagen, which gives a set of sharp diffrac-

*Lorentz-corrected SAXS patterns of iPP samples having different* β*-contents with a fixed crystallinity.*

*Polypropylene - Polymerization and Characterization of Mechanical and Thermal Properties*

From the volume fraction of the crystals *χV*, and SAXS long period *Lp*, the lamellar crystal thickness *Lc* and amorphous layer thickness *La* can be determined,

**Figure 3** shows the Lorentz-corrected SAXS intensities plotted against magnitude of scattering vector *s* (= 2/*λ* sin*θ*) where 2*θ* is the scattering angle and *λ* is the X-ray wavelength (= 0.1542 nm). The maximum point in the SAXS curves yields the average long period. The *s* value of *α*-PP (or PP0) was around 0.07 nm�<sup>1</sup>

period *Lp* of *β*-iPP is greater than that of *α*-iPP. The iPP samples with both modifications have two SAXS peaks corresponding to the *α*-phase peak near 0.072 nm�<sup>1</sup>

samples with the *α*- and *β*-spherulites coexist but no co-crystallization of *α*-phase and *β*-phase crystals takes place. The specific long periods for *α*-phase and *β*-phase

The sample specimens were cut into a dumbbell shape having a gauge length of 10 mm. The tensile strain was calculated from the ratio of the increment of the length between the clamps to the initial gauge length. The tensile stress was determined by dividing the tensile load by the initial cross section. The stress–strain

*Lc* ¼ *χVLp, La* ¼ ð Þ 1 � *χ<sup>V</sup> Lp* (8)

. This strongly suggests that the modified iPP

, and

, indicating that the long

assuming a two-phase model, from the following relationship:

the *s value* of *β*-iPP (or PP98) was around 0.0625 nm�<sup>1</sup>

*Stress-strain curves of iPP samples having different β-contents with a fixed crystallinity. (a) Overall curves and (b) their magnification in the initial strains.*

**Figure 5.** *Yield stress and Young's modulus plotted against the* β*-contents for the* β*-nucleated iPP.*

deformation resulting from the lower packing density of the *β*-phase. The main differences in the stress-strain curves exist in the yield region. In this region, the macroscopic structural transformation from a spherulitic structure to microfibrils takes place.

The yield process was found to become broader as the *β*-phase content increases, and the yield stress linearly decreases with increasing *β*-phase content (see **- Figure 5**). This is relevant to the early and more gradual activation of plastic processes in the *β*-phase as compared to *α*-phase because of the higher molecular mobility in the *β*-phase at the same temperature. This demonstrates that the plastic behavior is much more sensitive to the nature of the crystalline phase. In addition, the yield peak in the stress–strain curves broadens, and the neck region is more ambiguous as the *β*-phase increases. As mentioned before, the *β*-phase crystals have a lower cohesive force than the *α*-phase crystals, which is also reflected by their lower melting temperature and lower density. The lower cohesive force leads to easier slipping of the lamellar chains, resulting in a lower yield stress. Furthermore, as shown in **Figure 6**, the yield energy, which is defined as the energy dissipated for yielding to take place, linearly increases with increasing *β*-phase content, and all data almost fall on the solid line, which can be calculated according to the simple mixture law as follows:

$$U\_Y = \phi\_\beta U\_{\beta Y} + \left(\mathbf{1} - \phi\_\beta\right) \ U\_{aY} \tag{9}$$

PP98 sample deformed up to the post-yielding region (see **Figure 7e**), and they are scarcely oriented even in the initial necking region. In contrast to PP98, PP0 exhibits the reflections of the *α*-phase concentrated in the perpendicular direction to the elongation even in the post-yielding and necking regions. This pattern is almost the same as the typical profile of the iPP specimens at the final failure point, indicating that *α*-iPP attains the final *c*-axis orientation of crystals after yielding. In addition, it should be noted here that there is no clear difference in the orientation pattern at the final failure point between PP98 and PP0. The strain induced *β* ! *α* transition on tensile drawing has been reported by several authors [25–29]. In the present work, there is no evidence for the occurrence of a *β* ! *α* transition as seen in **Figure 7f**, but the final orientation morphology of PP98 appears to be the same as that of PP0. The reflections showing the attainable final orientation exist between 14 and 16°, suggesting the assignment of smectic form as demonstrated by

*Small angle X-ray diffraction patterns of* α*- and* β*-iPP samples: (a) original* α*-iPP, (b) stretched* α*-iPP at a strain of 0.4 (neck region), (c) stretched* α*-iPP at the failure point, (d) original* β*-iPP, (e) stretched* β*-iPP at a*

*Polypropylene*

According to our previous studies [30, 31] concerning the yield behavior of typical spherulitic polymers such as PE and *α*-iPP, several lamellae tend to cluster into bundles with tie molecules, where these are separated from one another by the amorphous regions and the lamellar clusters constituting of spherulites act as deformation units. The lamellar clusters are bridged by the inter-cluster or

intercrystalline links, as proposed by Keith-Padden et al. [32], thus acting as stress transmitters. The stacked lamellae or lamellar clusters are fragmented into cluster units or blocks at the yield point, resulting in a stress drop. Beyond the yield point, the plastic deformation involves the rotation of the cluster units and the sliding of stacked lamellae inside each cluster units, and the fragmented cluster units are rearranged into microfibrils in the necking region [33]. The continuous structural transformation corresponds to the neck propagation. In the case of *β*-spherulitic iPP

Turner-Jones et al. [12] and Shi et al. [8].

*strain of 0.8 (neck region), and (f) stretched* β*-iPP at the failure point.*

**Figure 7.**

*Tensile Properties in*

*DOI:*  *β-Modified*

*http://dx.doi.org/10.5772/intechopen.83348*

 *Isotactic* 

**79**

**4. Deformation of isolated spherulites**

Here *UY* is the yield energy (resilience), which was estimated from the area under the stress-strain plot from the origin to the stress drop, and *Uβ<sup>Y</sup>* and *Uα<sup>Y</sup>* are the yield energies of *β*-iPP and *α*-iPP, respectively.

To obtain better insights into the plastic behavior of the crystalline component, the WAXD experiments were carried out at room temperature during tensile tests. The direction of the incident beam was perpendicular to the plate surface of the specimens. **Figure 7** shows the WAXD patterns of *α*-iPP (PP0) and *β*-iPP (PP98). The WAXD patterns of the undrawn specimens of PP0 and PP98 are shown in **Figures 7a** and **d**, respectively. The patterns of iPP0 stretched at a strain of 0.4 and PP98 stretched at a strain of 0.8, in which both stretched samples are in the postyielding region, are shown in **Figures 7b** and **e**, respectively, and those of both specimens at the final failure point are shown in **Figures 7c** and **f**, respectively. The Debye rings of the (300) and (030) reflections of the *β*-phase crystals remain in the

**Figure 6.** *Yield energy (resilience) plotted against the* β*-contents for the* β*-nucleated iPP.*

*Tensile Properties in β-Modified Isotactic Polypropylene DOI: http://dx.doi.org/10.5772/intechopen.83348*

**Figure 7.**

deformation resulting from the lower packing density of the *β*-phase. The main differences in the stress-strain curves exist in the yield region. In this region, the macroscopic structural transformation from a spherulitic structure to microfibrils

*Polypropylene - Polymerization and Characterization of Mechanical and Thermal Properties*

The yield process was found to become broader as the *β*-phase content

line, which can be calculated according to the simple mixture law as follows:

yield energies of *β*-iPP and *α*-iPP, respectively.

*Yield energy (resilience) plotted against the* β*-contents for the* β*-nucleated iPP.*

*UY* ¼ *ϕβUβ<sup>Y</sup>* þ 1 � *ϕβ*

Here *UY* is the yield energy (resilience), which was estimated from the area under the stress-strain plot from the origin to the stress drop, and *Uβ<sup>Y</sup>* and *Uα<sup>Y</sup>* are the

To obtain better insights into the plastic behavior of the crystalline component, the WAXD experiments were carried out at room temperature during tensile tests. The direction of the incident beam was perpendicular to the plate surface of the specimens. **Figure 7** shows the WAXD patterns of *α*-iPP (PP0) and *β*-iPP (PP98). The WAXD patterns of the undrawn specimens of PP0 and PP98 are shown in **Figures 7a** and **d**, respectively. The patterns of iPP0 stretched at a strain of 0.4 and PP98 stretched at a strain of 0.8, in which both stretched samples are in the postyielding region, are shown in **Figures 7b** and **e**, respectively, and those of both specimens at the final failure point are shown in **Figures 7c** and **f**, respectively. The Debye rings of the (300) and (030) reflections of the *β*-phase crystals remain in the

*Uα<sup>Y</sup>* (9)

increases, and the yield stress linearly decreases with increasing *β*-phase content (see **- Figure 5**). This is relevant to the early and more gradual activation of plastic processes in the *β*-phase as compared to *α*-phase because of the higher molecular mobility in the *β*-phase at the same temperature. This demonstrates that the plastic behavior is much more sensitive to the nature of the crystalline phase. In addition, the yield peak in the stress–strain curves broadens, and the neck region is more ambiguous as the *β*-phase increases. As mentioned before, the *β*-phase crystals have a lower cohesive force than the *α*-phase crystals, which is also reflected by their lower melting temperature and lower density. The lower cohesive force leads to easier slipping of the lamellar chains, resulting in a lower yield stress. Furthermore, as shown in **Figure 6**, the yield energy, which is defined as the energy dissipated for yielding to take place, linearly increases with increasing *β*-phase content, and all data almost fall on the solid

takes place.

**Figure 6.**

**78**

*Small angle X-ray diffraction patterns of* α*- and* β*-iPP samples: (a) original* α*-iPP, (b) stretched* α*-iPP at a strain of 0.4 (neck region), (c) stretched* α*-iPP at the failure point, (d) original* β*-iPP, (e) stretched* β*-iPP at a strain of 0.8 (neck region), and (f) stretched* β*-iPP at the failure point.*

PP98 sample deformed up to the post-yielding region (see **Figure 7e**), and they are scarcely oriented even in the initial necking region. In contrast to PP98, PP0 exhibits the reflections of the *α*-phase concentrated in the perpendicular direction to the elongation even in the post-yielding and necking regions. This pattern is almost the same as the typical profile of the iPP specimens at the final failure point, indicating that *α*-iPP attains the final *c*-axis orientation of crystals after yielding. In addition, it should be noted here that there is no clear difference in the orientation pattern at the final failure point between PP98 and PP0. The strain induced *β* ! *α* transition on tensile drawing has been reported by several authors [25–29]. In the present work, there is no evidence for the occurrence of a *β* ! *α* transition as seen in **Figure 7f**, but the final orientation morphology of PP98 appears to be the same as that of PP0. The reflections showing the attainable final orientation exist between 14 and 16°, suggesting the assignment of smectic form as demonstrated by Turner-Jones et al. [12] and Shi et al. [8].
