Enhancement of mechanical properties of polypropylene by blending with styrene-(ethylene-butylene)-styrene tri-block copolymer

2.1 Preparation of samples

The homopolymer of isotactic PP, Moplen HP 400R (density 0.90 g/cm³, melt flow index 25 g/10 min at 230°C/2.16 kg, differential scanning calorimetry (DSC) melting peak T_m=170°C at a heating rate of 10°C/min) was purchased from LyondellBasell Ind. (Ludwigshafen, Germany).

The impact modifier, Kraton G1652 [a linear poly(styrene-b-(ethylene-co-butylene)-b-styrene) block copolymer with a styrene content of 29%, density of 0.91 g/cm³, melt flow index of 5 g/10 min at 230°C/5 kg and number average molecular weight M_n=79100] was supplied by Kraton Polymers (Wesseling, Germany).

To prepare a PP/SEBS blend with the elastomer concentration of 12 wt%, the components were blended in a Prism Eurolab-16 co-rotating twin-screw extruder (Thermo Scientific, Hvidovre, Denmark) at 200°C, with speed of 300 rpm and a feed rate of 2 kg/h. Dumbbell specimens for tensile tests (ASTM standard D-638) with cross-sectional areas of 9.8 mm×3.8 mm were molded by using the injection-molding machine, Ferromatic K110/S60–2K (Ferromatik A/S, Humlebeak, Denmark). To compare mechanical properties of neat PP and the PP/SEBS blend, PP specimens were manufactured following the same route.

Specimens for impact tests in the form of parallelepipeds with length 100 mm, width 9.8 mm and thickness 3.8 mm were cut from dumbbell specimens.

As the polymers used in preparation of the samples are identical to those employed in [18–20], our choice of SEBS content is based on the results of previous investigations, which reveal that this concentration is close to optimal from the standpoints of stiffness-toughness balance and distribution of SEBS inclusions in the PP matrix. Although this study is confined to the experimental and theoretical analysis of the mechanical behavior of PP and the PP/SEBS blend, its results are compared with observations in X-ray diffraction [18], DSC [18, 20], atomic force microscopy (AFM) [18–20] and dielectric spectroscopy [20] tests.

2.2 Mechanical tests

Tests were performed a few days after preparation of the samples, to avoid the effect of physical aging of PP on the mechanical response.

2.2.1 Impact tests

Impact tests were conducted by means of an Instron CEAST 9050 impact tester (Instron, Bucks, UK) equipped with a DAS 8000 Junior data-acquisition system, with a frequency of 1000 kHz and a 50 J instrumented hammer. Each test was repeated five times on new samples.

Observations in impact tests are reported in Figures 1 and 2. In Figure 1, force f is presented as a function of displacement d, and in Figure 2, specific dissipated energy W [the area below the f(d) curve in Figure 1] is plotted vs. time t. Except for a narrow region close to the origin in Figure 1 (with d<4 mm, where the graphs reflect self-oscillations of samples), the curves demonstrate good reproducibility: discrepancies between diagrams measured on different specimens are <3%.

Figure 1

Force f vs. displacement d. Symbols: experimental data in impact tests on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•).

Figure 2

Specific dissipated energy W vs. time t. Symbols: experimental data in impact tests on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•).

According to these figures, blending of PP with 12 wt% of SEBS leads to substantial enhancement of its impact resistance: the ultimate displacement d_max increases by a factor of three and the ultimate dissipated energy W_max grows by a factor of two.

The presence of the impact modifier results in qualitative changes in the shape of the force-displacement diagram: instead of the rapid decay in the f characteristic for brittle fracture, a monotonically decreasing branch of f(d) appears in the post-yield interval of deformation, whereas the yield region widens dramatically. Our results are in agreement with those reported in [14], where it was found that the slope of the decreasing branch of the force-displacement diagram increases with strain rate (and reaches infinity for brittle fracture).

2.2.2 Tensile tests

Uniaxial tensile tests were conducted by means of a universal testing machine Instron-5568 (Instron, Bucks, UK) equipped with an optical extensometer. Tensile force was measured by a 5 kN load cell. Engineering stress σ was determined as the ratio of axial force to cross-sectional area of each specimen in the undeformed state.

The experimental program involved three series of tests: (i) tensile tests with various cross-head speeds δ ranging from 1 to 400 mm/min, (ii) relaxation tests with various strains ε in the interval between 0.01 and 0.15 and (iii) cyclic tests with a mixed program (10 cycles of oscillations between a fixed maximum strain ε_max and the zero minimum stress) with ε_max ranging from 0.05 and 0.15. Each test was performed on a new specimen and repeated twice. Observations reveal good reproducibility of measurements: deviations between stresses measured on different specimens did not exceed 3%.

The first series consisted of four tensile tests with maximum strain ε_max=0.2 and cross-head speeds δ=1, 10, 100 and 400 mm/min (corresponding to strain rates e=2.2×10^-4, 2.2×10^-3, 2.2×10^-2 and 8.8×10^-2 s^-1). Observations in these tests are depicted in Figures 3 and 4, where engineering stress σ is plotted vs. tensile strain ε. According to these figures, at each cross-head speed δ, stress increased with strain in the sub-yield region of deformation, reached its maximum value σ_y at the yield point and decreased weakly with strain in the post-yield region of deformation. The growth of strain rate e resulted in an increase in σ, whereas blending of PP with SEBS induced a decrease in stress. The yield strain ε_y was weakly affected by strain rate and composition and remained close to ε_y=0.1 for all specimens.

Figure 3

Stress σ vs. strain ε. Circles: experimental data on neat polypropylene (PP) in tensile tests with various strain rates e s^-1 (○– e=2.2×10^-4; • – e=2.2×10^-3; * – e=2.2×10^-2; ⋆– e=8.8×10^-4). Solid lines: results of numerical simulation.

Figure 4

Stress σ vs. strain ε. Circles: experimental data on polypropylene (PP)/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend in tensile tests with various strain rates e s^-1 (○– e=2.2×10^-4; • – e=2.2×10^-3; * – e=2.2×10^-2; ⋆– e=8.8×10^-4). Solid lines: results of numerical simulation.

To assess the effect of blending on the strength of PP, yield stress σ_y is plotted vs. strain rate e in Figure 5. The experimental data are approximated by the function:

Figure 5

Yield stress σ_y vs. strain rate e. Symbols: treatment of observations in tensile tests on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•). Solid lines: approximation of the data by Eq. (1) with σy0=36.7,σy1=3.56 (PP), σy0=29.2,σy1=2.40 (PP/SEBS).

(1)σy=σy0+σy1log e (1)

where log=log₁₀, and coefficients σy0 and σy1 are found by the least-squares technique. Figure 5 shows that Eq. (1) correctly describes the observations: the coefficient of determination R² equals 0.955 for neat PP and 0.995 for the PP/SEBS blend. According to this figure, the slope of the σ_y (log e) curve for neat PP exceeds that for the PP/SEBS blend by 48%, which implies that the decay in yield stress due to blending becomes more pronounced at higher strain rates.

The other series of experiments involved six relaxation tests with strains ε=0.01, 0.03, 0.06, 0.09, 0.12 and 0.15. In each test, a specimen was stretched with a constant strain rate e=2.2×10^-2 s^-1 to the required strain. Afterwards, a decrease in stress was monitored as a function of time while the strain was kept constant. Following the protocol ASTM E–328 for short-term relaxation tests, the duration of relaxation tests t_rel=20 min was chosen. Experimental data in relaxation tests are reported in Figure 6. Following common practice, the semi-logarithmic plots are employed, where stress σ is depicted vs. logarithm of relaxation time τ=t-t₀ with t₀ standing for the instant when relaxation starts. Figure 6 shows that the growth of strain ε results in an increase in the slope of relaxation diagrams (which means that the time-dependent response is strongly nonlinear). The increase is rather pronounced when ε lies in the sub-yield interval of deformations, but it weakens when strain ε exceeds yield strain ε_y.

Figure 6

Stress σ vs. relaxation time τ. Symbols: experimental data on (A) neat polypropylene (PP) and (B) PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend in relaxation tests with various strains ε (○– ε=0.01; • – ε=0.03; * – ε=0.06; ⋆ – ε=0.09; ◊ – ε=0.12; Δ – ε=0.15).

The third series of tests consisted of three cyclic tests with a mixed deformation program (oscillations between a maximum strain ε_max and a minimum stress σ_min) with ε_max=0.05, 0.10 and 0.15 and σ_min=1 MPa. Each test involved n=10 cycles of loading–retraction with constant strain rate e=2.2×10^-2 s^-1. Observations are reported in Figure 7, where stress σ is plotted vs. strain ε. To avoid overlapping of experimental data, only the data along the first loading, retraction and reloading paths are presented. Figure 7 demonstrates that the growth of maximum strain ε_max induces a pronounced increase in residual strain (estimated as the strain under retraction down to zero stress) and a substantial increase in hysteresis energy (evaluated as the area between subsequent unloading and retraction paths of each stress–strain diagram).

Figure 7

Stress σ vs. strain ε. Symbols: experimental data on (A) neat polypropylene (PP) (A) and (B) PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend in tensile tests (⋆) and cyclic tests with various maximum strains ε_max (○– ε_max=0.15; • – ε_max=0.10; * – ε_max=0.05) and σ_min=1 MPa. Solid lines: results of numerical simulation.

To assess damage accumulation under cyclic loading, maximum stress per cycle σ_max and minimum strain per cycle ε_min are plotted vs. number of cycles n in Figures 8 and 9. The experimental data are approximated by the equations:

Figure 8

Maximum stress per cycle σ_max vs. number of cycles n. Symbols: experimental data on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•) in cyclic tests with various maximum strains ε_max. Solid lines: approximation of the data by Eq. (2) with σmax0=25.4,σmax1=2.82 (PP), σmax0=22.7,σmax1=2.54 (PP/SEBS) at ε_max=0.05, σmax0=29.0,σmax1=3.73 (PP), σmax0=24.9,σmax1=3.31 (PP/SEBS) at ε_max=0.10, σmax0=28.4,σmax1=4.16 (PP), σmax0=24.5,σmax1=3.35 (PP/SEBS) at ε_max=0.15.

Figure 9

Minimum strain per cycle ε_min vs. number of cycles n. Symbols: experimental data on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•) in cyclic tests with various maximum strains ε_max. Solid lines: approximation of the data by Eq. (2) with εmin0=0.0087,εmin1=0.084 (PP), εmin0=0.0048,εmin1=0.085 (PP/SEBS) at ε_max=0.05, εmin0=0.033,εmin1=0.016 (PP), εmin0=0.0028,εmin1=0.016 (PP/SEBS) at ε_max=0.10, εmin0=0.069,εmin1=0.022 (PP), εmin0=0.065,εmin1=0.022 (PP/SEBS) at ε_max=0.15.

(2)σmax=σmax0−σmax1log n,εmin=εmin0+εmin1 log n (2)

with coefficients calculated by the least-squares method. Figures 8 and 9 show good agreement between the observations and their fits by Eq. (2). For neat PP, coefficient R²=0.984, 0.985 and 0.949 and 0.999, 0.993 and 0.989 for σ_max and ε_min in tests with ε_max=0.15, 0.10 and 0.05, respectively. For the PP/SEBS blend, the corresponding values of R² read 0.999, 0.990 and 0.953 and 0.979, 0.994 and 0.983. Maximum stress per cycle σ_max for neat PP exceeds that for the PP/SEBS blend (in accordance with the data depicted in Figure 5) and their ratio is independent of the number of cycles n. Minimum strain per cycle ε_min for the PP/SEBS blend is lower than that for neat PP, which means that blending of PP with SEBS results in a pronounced decay (25% at ε_max=0.05) in residual strain under cyclic deformation.

Maximum strain ε_max=0.2 in tensile tests was chosen close to the necking strain for neat PP (Figure 3 shows that necking of a sample stretched with a cross-head speed δ=400 mm/min starts in the close vicinity of ε_max). The interval of strains for relaxation tests covers the entire region of strains under consideration. Minimum stress σ_min=1 MPa for cyclic tests was chosen instead of σ_min=0, to avoid buckling of samples under retraction. Strain rate e=2.2×10^-2 s^-1 was selected as the maximum strain rate at which strains ε in relaxation tests and maximum strains ε_max in cyclic tests are correctly reproduced (with relative errors <1%) by the testing machine.

The following conclusions are drawn from observations: (i) under high-speed (impact) tests, blending of PP with SEBS (with a modest concentration 12 wt% of the impact modifier) results in a strong increase in strain to break (by a factor of 3) and a substantial growth of dissipated energy (by a factor of 2) and (ii) under low-speed tests, the presence of SEBS leads to a reduction in strength (σ_y decreases by 17%), a decay in slopes of relaxation curves and a noticeable decrease in residual strains under cyclic deformation. The latter result is in agreement with observations reported in [4] on blends of PP with ethylene-octene copolymer.

3.1 Relaxation tests

To find material constants in the stress-strain relations, we begin from the analysis of observations in relaxation tests.

According to the model, a decrease in stress σ with time τ observed in uniaxial tensile relaxation tests is described by the equation:

(3)σ(τ)=σ0[1-κ∫0∞f(v)(1-exp(-Γ(v)τ)dv] (3)

where σ₀ stands for stress at the instant τ=0 when relaxation starts, and dimensional parameter κ denotes concentration of temporary chains: ratio of the number of temporary chains to the entire number of temporary and permanent chains per unit volume of the equivalent network. Dummy variable v denotes dimensionless activation energy for separation of active chains, and the function f(v) stands for distribution of meso-domains with various activation energies. With reference to the random energy model, the quasi-Gaussian expression is adopted for this function:

(4)f(v)=f0exp[-v2/(2∑2)](v≥0) (4)

where Σ is a measure of heterogeneity of the equivalent network, and coefficient f₀ is found from the normalization condition ∫0∞f(v) dv=1. The rate of rearrangement Γ(v) is given by:

(5)Γ(v)=γ exp(-Av) (5)

where γ stands for relaxation rate and the dimensionless coefficient A characterizes nonlinearity of the time-dependent response. This quantity equals unity in the interval of the linear viscoelastic response and decreases linearly with strain ε at which relaxation tests are performed:

(6)A=A0-A1 ε (6)

with A⁰=1. Eqs. (3)–(6) involve four material constants: A¹, γ, κ and Σ. To find these quantities, we fit the observations reported in Figure 6. Each set of experimental data is matched separately. First, we approximate observations in relaxation tests with ε=0.01 (for which we set A=1) and calculate parameters γ, κ and Σ that ensure the best fit of the experimental data (γ and σ are determined by the method of nonlinear regression, and κ is found by the least-squares technique). The integral in Eq. (3) is evaluated by the Simpson method with M=100 points and step Δv=0.25. Afterwards, we fix these coefficients (their values are listed in Table 1) and approximate each relaxation diagram at ε=0.03, 0.06, 0.09, 0.12 and 0.15 by means of Eqs. (3)–(6) with the only adjustable parameter A.

Figure 10 demonstrates that the model describes adequately the experimental data: the maximum discrepancy between the observations and the results of simulation does not exceed 3%. To avoid overlapping of data, only relaxation curves at ε=0.01, 0.03 and 0.15 are presented. However, the same accuracy of fitting is reached for relaxation diagrams with ε=0.06, 0.09 and 0.12.

Figure 10

Stress σ vs. relaxation time τ. Symbols: experimental data on (A) neat polypropylene (PP) and (B) PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend in relaxation tests with various strains ε (○– ε=0.01; • – ε=0.03; Δ – ε=0.15). Solid lines: results of numerical simulation.

The effect of strain ε on parameter A is illustrated in Figure 11, where the data are approximated by Eq. (6) with the coefficient of determination R²=0.714 for neat PP and 0.754 for the PP/SEBS blend. The following conclusions are drawn from Table 1 and Figure 11: (i) the presence of SEBS does not affect practically coefficients A, κ and Σ and (ii) blending of PP with the impact modifier induces a decrease in relaxation rate γ by 40%.

Figure 11

Parameter A vs. strain ε. Symbols: treatment of observations in relaxation tests on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•). Solid lines: approximation of the data by Eq. (6) with A⁰=0.94, A¹=1.52 (PP) and A⁰=0.94, A¹=1.50 (PP/SEBS).

3.2 Tensile tests

We proceed with matching experimental data in tensile tests with various strain rates e. The viscoelastoplastic behavior of the equivalent medium under uniaxial tension is described by the equation:

(7)σ(t)=E(1-φ(t))[εe(t)-κ ∫0∞f(v) Z(t, v) dv] (7)

where elastic strain ε_e reads:

(8)εe=ε-εpa-εpc (8)

and ε_pa and ε_pc denote plastic strains in amorphous and crystalline regions, respectively. The rate of plastic strain in the crystalline phase is proportional to the rate of strain under macro-deformation:

(9)dεpc/dt=φ(t)dε/dt (9)

where the coefficient of proportionality φ obeys the equation:

(10)dφ/dt=a[1-φ(t)]2 dε/dt (10)

The rate of plastic strain in the amorphous phase is governed by the equation:

(11)dεpa/dt=S[εe(t)-κ∫0∞f(v) Z(t, v) dv-R εpa(t)]dε/dt (11)

The function Z(t,v) in Eqs. (7), (11) obeys the equation:

(12)∂Z/∂t(t,v)=Γ[εe(t)-Z(t,v)] (12)

where Γ is given by Eqs. (5) and (6). Eqs. (7)–(12) with initial conditions ε_pa(0)=0, ε_pc(0)=0, φ(0)=0 and Z(0, v)=0 involve four material constants: E stands for the Young’s modulus, a denotes the rate of plastic flow in the crystalline phase, S characterizes the rate of plastic flow in the amorphous phase and R is a dimensionless measure of interchain interaction.

To find these quantities, we approximate the stress-strain diagrams reported in Figures 3 and 4. Each set of experimental data is fitted separately under the additional assumption that R=1 (which means that moduli coincide in the expressions for the strain energy density and the energy of interchain interaction).

We start with the analysis of observations in tensile tests with strain rate e=2.2×10^-2 s^-1 and find E, a and S that ensure the best fit of experimental data (a and S are calculated by the nonlinear regression method and E is determined by the least-squares technique). Integration over time is performed by the Runge-Kutta method with step Δt=10^-2 s. Afterwards, we fix the Young’s moduli E (listed in Table 1) and approximate stress-strain diagrams in tensile tests with the other strain rates by means of two parameters, a and S, only.

Figures 3 and 4 show good agreement between the experimental data and the results of numerical analysis. The effect of strain rate e on rates of plastic flow a and S is illustrated in Figure 12. The data are approximated by the equations:

Figure 12

Parameters a, S vs. strain rate e. Symbols: treatment of observations in tensile tests on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•). Solid lines: approximation of the data by Eq. (13) with a⁰=9.06, a¹=0.27, S⁰=8.62, S¹=4.29 (PP), a⁰=9.56, a¹=0.25, S⁰=10.9, S¹=4.36 (PP/SEBS).

(13)a=a0+a1 log e,   S=S0-S1 log e (13)

with coefficients calculated by the least-squares method. The accuracy of fitting is evaluated by the coefficient R² which equals 0.988 (PP) and 0.942 (PP/SEBS) for coefficient a and 0.699 (PP) and 0.957 (PP/SEBS) for parameter S.

The following conclusions are drawn from Table 1 and Figure 12: (i) blending of PP with SEBS leads to a decrease in the Young’s modulus E by 12% and an increase in rates of plastic flow in the amorphous phase (S grows by 26%) and the crystalline phase (a increases by 6%) and (ii) acceleration of plastic flow under tension is practically independent of the rate of stretching e.

3.3 Cyclic tests

Finally, we approximate the stress-strain diagrams under stretching, retraction and reloading in cyclic tests with various maximum strains ε_max.

The mechanical response of the equivalent medium under cyclic loading is described by Eqs. (7)–(12), where parameters a, R and S adopt different values a_j, R_j and S_j under tension (j=1), retraction (j=2) and reloading (j=3). The quantities a₁=a, R₁=1 and S₁=S are taken from the analysis of observations in tensile tests (Figures 3 and 4). The coefficients a₂, R₂ and S₂ and a₃, R₃=1 and S₃ are calculated from the best-fit condition by matching observations under retraction and reloading, respectively (Figure 7).

Results of numerical simulation are depicted in Figure 7, which reveals that the model describes correctly the experimental data: the maximum discrepancy between the observations and the results of simulation is <3%.

The effect of plastic strain ε_p=ε_pa+ε_pc at the instant when retraction starts on a₂, R₂ and S₂ is illustrated in Figure 13. The data are approximated by the equations:

Figure 13

Parameters a₂, R₂, S₂ vs. plastic strain ε_p. Symbols: treatment of observations under retraction on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•). Solid lines: approximation of the data by Eq. (13) with a20=3.82,a21=1.74,R20=0.39,R21=9.98,S20=1.30,S21=1.06 (PP), a20=2.79,a21=1.87,R20=0.45,R21=10.0,S20=1.35,S21=0.92 (PP/SEBS).

(14)a2=a20+a21  εp,  logR2=R20-R21 εp,  log S2=S20-S21 εp (14)

with coefficients calculated by the least squares method. The accuracy of fitting is characterized by the coefficient R², which reads 0.939, 0.986 and 0.966 (PP) and 0.951, 0.989 and 0.922 (PP/SEBS) for a₂, R₂ and S₂, respectively.

Parameters a₃ and S₃ are plotted vs. stress increment Δσ=σ_max-σ_min in Figure 14, where the data are matched by the equations:

Figure 14

Coefficients a₃, S₃ vs. stress increment Δσ. Symbols: treatment of observations under reloading on neat polypropylene (PP) (○) and PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend (•). Solid lines: approximation of the data by Eq. (15) with a30=-34.2,a31=1.39, (PP), S30=9.20,S31=-0.30a30=-66.6,a31=0.45, (PP/SEBS).

(15)a3=a30+a13Δσ,        logS3=S30−S31Δσ (15)

with coefficients determined by the least-squares technique. The coefficient of determination R² equals 0.999, 0.997 (PP) and 0.727, 0.712 (PP/SEBS) for a₃ and S₃, respectively.

The following conclusions are drawn from Figures 13 and 14: (i) under retraction, blending of PP with SEBS results in slowing down of plastic flow in the crystalline phase (a₂ decreases by 37%) and weak acceleration of plastic flow in the amorphous phase (S₂ increases by 5%); these changes are not affected by ε_max and (ii) under reloading, due to the presence of the impact modifier, the rate of plastic strain in the crystalline phase a₃ grows by several times, whereas the rate of plastic strain in the amorphous phase S₃ decreases by an order of magnitude.

To verify Eqs. (14) and (15), numerical integration of the stress–strain relations is conducted for cyclic tests with maximum strains ε_max=0.04, 0.08, 0.12 and 0.16 that differ from those used in the experimental investigation. Results of simulation are reported in Figure 15, which shows that the model predicts physically plausible mechanical responses (without overshoots on the stress-strain diagrams).

Figure 15

Stress σ vs. strain ε. Symbols: results of numerical simulation for (A) neat polypropylene (PP) and (B) PP/styrene-(ethylene-butylene)-styrene copolymer (SEBS) blend in cyclic tests with various maximum strains ε_max (○– ε_max=0.16; • – ε_max=0.12; * – ε_max=0.08; ⋆ – ε_max=0.04) and σ_min=1 MPa.