Strength of single- and double-gated injection moulded short glass fibre reinforced polycarbonate

Abstract

The effect of temperature, strain rate, moulding thickness and the mode of loading on weldline integrity of injection moulded polycarbonate (PC) reinforced with 10% and 30% by weight short glass fibres was studied. Results showed that tensile and flexural strengths of single-gated mouldings, σ_cs, increased with increasing fibre concentration, φ_f, in a linear manner, thus obeying the rule of mixtures for short fibre composites. The presence of weldlines in double-gated mouldings reduced tensile and flexural strength by as much as 70%. It was found that tensile and flexural strengths of double-gated mouldings, σ_cd, increased initially and reached a maximum before decreasing with increasing φ_f. However, for both single- and double-gated mouldings, the flexural strength values were consistently higher than tensile strength values. It was found that tensile strength of both single- and double-gated mouldings increased linearly with increasing ln(strain rate) and decreased linearly with increasing temperature. Tensile strength of single- and double-gated mouldings showed no significant variation with respect to the thickness of the moulding. The weldline integrity factor decreased with increasing fibre concentration and showed little variation with respect to temperature, strain rate and the thickness of the moulding.

Introduction

The strength of short fibre polymer composites is derived from a combination of the fibre and matrix properties and the ability to transfer stresses across the interface between the two constituents and is affected by a number of parameters, most importantly, concentration, length and orientation of the fibres as well as the degree of interfacial adhesion between the fibre and the matrix.^1–12 However, as most short fibre composites are fabricated by an injection moulding process, a major design concern is the effect that weldlines may have on the strength of the polymer matrix and its composites. Weldlines are observed in injection moulded components due to multigate moulding, existence of pins, inserts, variable wall thickness and jetting and are classified as being either cold or hot. A cold weldline is formed when two melt fronts meet head on and this type of weldline is the worst-case scenario as far as the strength of the composite is concerned. A serious reduction in strength has been reported for many polymers and their composites in the presence of cold weldlines. To this end, the present work was undertaken to examine the influence of fibre concentration, loading mode, moulding thickness, strain rate and temperature on the strength of both single- and double-gated polycarbonate (PC) reinforced with 0%, 10% and 30% by weight short glass fibres.

Experimental

Materials

PC and its composites containing 10% and 30% by weight short glass fibres were supplied by PolyOne (Polyone (UK) Ltd. Darford) in the form of pellets for injection mouldling process. The PC and its composites were dried in an air circulating oven for 4 hours at 120°C as recommended by the manufacturer prior to injection moulding process.

Injection moulding

The dried pellets were injection moulded in a Klockner Ferromatik F-60 injection moulding machine at the processing conditions listed in Table 1 to produce a series of dumb-bell-shaped test specimens. The mould used consisted of a single-gate (SG) and a double-gate (DG) cavities as illustrated in Figure 1, each of nominal dimensions 4 × 10 × 120 mm (thickness, width, and length). In the case of double-gated cavities, the two opposing melt fronts met to form a cold weldline midway along the gauge length of the specimen.

Figure 1.

Single- and double-gated cavities with nominal dimensions of 4 × 10 × 120 mm (thickness, width, and length).

Table 1.

Processing condition for injection moulded PC and PC composites.

Processing conditions	PC	PC with 10%w/w GF (glass fibre)	PC with 30%w/w GF (glass fibre)
Barrel temperature (°C)
Zone 1 (nozzle)	300	315	315
Zone 2	295	300	300
Zone 3	295	295	295
Zone 4	290	290	290
Mould temperature (°C)	80	80	80
Injection pressure (%)	95	95	95
Injection speed (%)	85	85	85
Cooling time (s)	15	15	15

PC: polycarbonate.

In addition, a series of single- and double-gated specimens were injection moulded using mould cavities similar to that illustrated in Figure 1 but with nominal dimensions 1.5 × 10 × 120 mm (thickness, width, and length).

Fibre concentration measurements

The exact weight fraction of the fibres in the injection moulded dumb-bell-shaped specimens was determined by ashing a preweighed amount of material (cut from the gauge length area) in a muffle furnace at 550°C for at least 1 hour. After cooling, the remnant was weighed and weight fraction of fibres w _f was determined. The average w _f value was within 1% of the manufacturer’s specification.

The measured weight fractions, w _f, were subsequently converted into volume fractions, φ_f, using the following relationship:

${\mathit{\varphi }}_{\mathrm{f}}=\frac{{\mathit{\rho }}_{\mathrm{c}}}{{\mathit{\rho }}_{\mathrm{f}}}{w}_{\mathrm{f}}$

1

Table 2 gives values of φ_f obtained via Equation (1), taking density of glass fibre, ρ_f, as 2540 kg m⁻³ and composite densities, ρ_c, as provided by the manufacturer.

Table 2.

Fibre concentration and the average fibre length in injection moulded dumb-bell specimens. ^a

Composites	PC 10%w/w GF	PC 30%w/w GF
%w/w fibre	9.86 ± 0.06	32.57 ± 0.254
Density (kg m−3)	1260	1430
%v/v	4.89	18.34
Average fibre length (mm)	0.295 (800)	0.210 (800)

PC: polycarbonate.

^a Values given within parentheses are the total number of fibre lengths measured.

Fibre length measurements

The ashes of fibrous material were subsequently spread on glass slides and placed on the observation stage of a microscope. Magnified fibre images were transmitted to a large screen, and the fibre images were then automatically digitised. Approximately 800 hundred fibre lengths were measured for each composite. From the fibre length distributions, the average fibre length in the moulded specimens was determined. The measured values are given in Table 2 where it can be seen that the average fibre length (L _f) in the moulded specimens decreased with increasing fibre concentration. This is attributed to a greater fibre–fibre and fibre–machine interaction as well as increase in the apparent melt viscosity causing higher bending forces on the fibres during moulding, at higher fibre concentration.

Mechanical testing

Tensile testing. The effect of strain rate and the thickness of the moulding on tensile strength of single- and double-gated mouldings was studied at 23°C using a Tinius Olsen H10KS testing machine (Tinius Olsen LTd. Redhill, Surrey, UK). The effect of strain rate was studied at crosshead speeds of 0.5, 5, 50 and 500 mm/min giving nominal strain rate values of 7.58 × 10⁻⁵, 7.58 × 10⁻⁴, 7.58 × 10⁻³ and 7.58 × 10⁻² s⁻¹, respectively. The effect of moulding thickness was studied at a constant crosshead speed of 50 mm/min.

The effect of temperature on tensile strength of single- and double-gated mouldings was studied using an Instron testing machine at a constant crosshead speed of 50 mm/min at 23, 40, 60, 80 and 120°C.

In all cases a minimum of four specimens were tested for determining an average value. The load displacement curve for each specimen was recorded using a computer data logger from which the tensile strength was calculated using the maximum load.

Flexural testing. Strength of single- and double-gated mouldings in flexure was measured using rectangular coupons cut from the gauge length of both single- and double-gated dumb-bell mouldings of 4 mm nominal thickness. Flexural tests were performed in three-point bend by flexing the coupons flat-wise (i.e. D = 4 mm, B = 10 mm) at a constant crosshead displacement rate of 50 mm/min over a span width (S) of 64 mm in the Tinius Olsen H10KS testing machine. The double-gated specimens were positioned on the rig such that weldline was at mid span, that is, under the loading nose. The flexural strength was calculated using the following equation:

$\mathrm{F}\mathrm{l}\mathrm{e}\mathrm{x}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}=\frac{3P_{\mathrm{m}\mathrm{a}\mathrm{x}}S}{2B{D}^2}$

2

where P _max is the maximum recorded load.

Results and discussion

Effect of fibre concentration and strain rate on tensile strength of single-gated mouldings

Stress–strain curves for single-gated mouldings indicated that the strength of PC composites increases as fibre concentration is increased. This behaviour was consistently observed for all single-gated mouldings over the entire crosshead speed range of 0.5–500 mm/min.

The effect of fibre volume fraction, φ_f, on the tensile strength of single-gated mouldings at crosshead displacement rates of 0.5, 5, 50 and 500 mm/min is shown in Figure 2. Results show that in all cases, tensile strength of single-gated mouldings, σ_cs, increases linearly with increasing φ_f. This behaviour suggests that the variation of σ_cs with φ_f can be modelled using the modified rule-of-mixtures equation for short fibre composites, that is

Figure 2.

Effect of fibre volume fraction, φ_f, on tensile strength of single-gated mouldings, σ_cs, at crosshead speeds of 0.5, 5, 50 and 500 mm/min.

${\mathit{\sigma }}_{\mathrm{c}\mathrm{s}}={\mathit{\eta }\mathit{\sigma }}_{\mathrm{f}}{\mathit{\varphi }}_{\mathrm{f}}+(1-{\mathit{\varphi }}_{\mathrm{f}}){\mathit{\sigma }}_{\mathrm{m}\mathrm{s}}$

3

where σ_f is tensile strength of the glass fibre and σ_ms is the tensile strength of single-gated unreinforced PC (i.e. the matrix) moulding. The parameter η is termed the overall fibre efficiency parameter for composite tensile strength, whose value depends on the length and the orientation of fibres in the moulded specimen.

A simple rearrangement of Equation (3) gives

${\mathit{\sigma }}_{\mathrm{c}\mathrm{s}}={\mathit{\sigma }}_{\mathrm{m}\mathrm{s}}+(\mathit{\eta }{\mathit{\sigma }}_{\mathrm{f}}-{\mathit{\sigma }}_{\mathrm{m}\mathrm{s}}){\mathit{\varphi }}_{\mathrm{f}}$

4

According to Equation (4), the effect of strain rate on parameter η can be determined from the slope of the linear regression lines in Figure 2. Values of η obtained in this way with σ_f = 2470 MPa are plotted in Figure 3 as a function of natural logarithm of strain rate, ln ė. According to Figure 3, η increases linearly with increasing ln ė, thus indicating that reinforcement efficiency of the fibres depends on the rate of testing and indeed fibre behave more efficiently at higher rates than they do at lower rates. The linear relationship between η and the strain rate, ė, can be expressed as

Figure 3.

Effect of strain rate on fibre efficiency parameter for tensile strength of single-gated mouldings.

$\mathit{\eta }(\dot{e})=A_{\mathrm{o}}+B_{\mathrm{o}}ln\dot{e}$

5

where A _o = 0.207 and B _o = 6.34 × 10⁻³.

The efficiency parameter η is defined as

$\mathit{\eta }={\mathit{\eta }}_{\mathrm{L}}{\mathit{\eta }}_{\mathrm{o}}$

6

where η_L is the fibre length and η_o is the fibre orientation efficiency parameters for the composite strength. The value of η_L for short fibre composites depends largely on the ratio L _c /L _f, where L _f is the average length and L _c is the critical length of the fibre, respectively. The value of L _c can be obtained from the following relationship:

$L_{\mathrm{c}}=\frac{d{\mathit{\sigma }}_{\mathrm{f}}}{2{\mathit{\tau }}_{\mathrm{m}}}$

7

Where d is the diameter of the fibre (=10 μm), σ_f is tensile strength of fibre and τ_m is shear strength of the matrix whose value in this study is assumed to be half the tensile strength of single-gated mouldings, σ_ms. Values calculated via Equation (7) are given in Table 3 as a function of crosshead speed where it can be seen that for both composites, the average length of the fibre in the single-gated mouldings is always less than the fibre critical length. According to Kelly and Tyson, ¹³ when L _f < L _c, the efficiency parameter, η_L, can be defined as

Table 3.

Fibre efficiency parameters for tensile strength of single-gated fibre reinforced PC mouldings at crosshead speeds of 0.5, 5, 50 and 500 mm/min.

Fibre volume fraction	φf = 0.049				φf = 0.184
Average fibre length (mm)	0.295				0.210
Crosshead speed (mm/min)	0.5	5	50	500	0.5	5	50	500
L c (mm)	0.435	0.420	0.403	0.377	0.435	0.420	0.403	0.377
η	0.145	0.164	0.175	0.190	0.145	0.164	0.175	0.190
ηL	0.339	0.351	0.366	0.391	0.241	0.250	0.261	0.278
ηo	0.427	0.467	0.478	0.486	0.601	0.656	0.672	0.682
θ	36.06	34.24	33.75	33.39	28.30	25.85	25.12	24.67

PC: polycarbonate.

${\mathit{\eta }}_{\mathrm{L}}=\frac{L_{\mathrm{f}}}{2L_{\mathrm{c}}}$

8

Values of η_L calculated using Equation (8) are given in Table 3 where it can be seen that η_L increases with increasing crosshead speed but decreases with increasing fibre concentration. It is also evident, that effect on η_L due to fibre concentration is much greater than that due to crosshead speed (strain rate), primarily due to the lower average fibre length in the mouldings at higher fibre concentration values. The value of η_L = 1 implies fibre length efficiency of 100% as in continuous fibre composite systems, thus values obtained here indicate reduction in tensile strength, σ_cs, because the shortness of the fibres could be as much as 76% (i.e. η_L = 0.24).

Using Equation (6), values of fibre orientation efficiency parameters η_o were calculated. Values given in Table 3 suggest that η_o is more affected by the change in fibre concentration than by crosshead speed. The observed increase in η_o with fibre concentration is primarily due to the ease at which shorter fibres can align themselves in the flow direction as compared to longer fibres. For a perfect alignment of fibres in the loading direction as in unidirectional short fibre composites, η_o = 1, thus values obtained here indicate reduction in tensile strength, σ_cs, because misalignment of the fibres could be as much as 57% (i.e. η_o = 0.43).

The effect of strain rate on tensile strength of single-gated mouldings is shown more explicitly in Figure 4, where it can be seen that tensile strength of the unreinforced PC matrix and its composites increases linearly with the natural logarithm of strain rate mouldings, ln ė. This linear relationship can be reasonably expressed as

Figure 4.

Effect of strain rate on tensile strength of single-gated mouldings, σ_cs, containing 0, 10 and 30% by weight short glass fibres.

${\mathit{\sigma }}_{\mathrm{c}\mathrm{s}}=A_1+B_1\mathrm{l}\mathrm{n}\dot{e}$

9

where values of A ₁ and B ₁ can be found in Table 4. The increase in the slope of line, B ₁, with increasing φ_f suggests that tensile strength of the single-gated composite mouldings is more rate sensitive than the matrix strength and that the degree of sensitivity increases as fibre concentration is increased.

Table 4.

Values of A _n and B _n (A _n and B _n are constants with n =1, 2, 3, 4 and 6).

	0%w/w GF	10%w/w GF	30%w/w GF
A1 (MPa)	68.20	89.25	151.23
B1	1.255	1.980	4.260
A2 (MPa)	68.12	81.05	72.72
B2	1.160	1.811	4.92
A4 (MPa)	68.66	87.88	145.91
B4 (MPa °C−1)	−0.302	−0.397	−0.660
A6 (MPa)	69.17	79.70	54.66
B6 (MPa °C−1)	−0.304	−0.373	−0.259

Effect of fibre concentration and strain rate on tensile strength of double-gated mouldings

The stress–strain curves for double-gated mouldings revealed that the presence of weldline causes significant reduction in tensile strength and elongation at failure. All double-gated mouldings failed at the weldline region, thus indicating that the weldline was weakest part of all double-gated mouldings over the entire crosshead speed range of 0.5–500 mm/min.

The effect of fibre volume fraction, φ_f, on tensile strength of double-gated mouldings (i.e. weldline strength), σ_cd, at crosshead displacement rates of 0.5, 5, 50 and 500 mm/min is shown in Figure 5. Results show that σ_cd increases initially with increasing φ_f, reaching a maximum before decreasing with further addition of fibres. As illustrated in Figure 5, variation of σ_cd with φ_f can be described reasonably well using a second-order polynomial function of the form:

Figure 5.

Effect of fibre volume fraction on tensile strength of double-gated mouldings, σ_cd, at crosshead speeds of 0.5, 5, 50 and 500 mm/min.

${\mathit{\sigma }}_{\mathrm{c}\mathrm{d}}=a_{\mathrm{o}}+a_1{\mathit{\varphi }}_{\mathrm{f}}+a_2{\mathit{\varphi }}_{\mathrm{f}}^2$

10

The polynomial functions describing the data in Figure 5 are given in Table 5. These polynomials may be used to obtain some indication of the optimum value of φ_f (i.e. φ_f,max) for achieving the maximum tensile strength in a double-gated mouldings, at a given rate. Differentiating Equation (10) with respect to φ_f gives the value of φ_f,_max as

Table 5.

Polynomial functions for tensile strengths and the optimum volume fraction of fibres for double-gated mouldings at various crosshead speeds and temperatures.

Crosshead speed (mm/min)	Polynomial function	φf,max
0.5	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=57.40+253.28{\mathit{\varphi }}_{\mathrm{f}}-2295.1{\mathit{\varphi }}_{\mathrm{f}}^2$	0.055
5	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=59.50+264.52{\mathit{\varphi }}_{\mathrm{f}}-2108.1{\mathit{\varphi }}_{\mathrm{f}}^2$	0.063
50	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=62.20+302.81{\mathit{\varphi }}_{\mathrm{f}} -2014.9{\mathit{\varphi }}_{\mathrm{f}}^2$	0.075
500	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=65.40+322.19{\mathit{\varphi }}_{\mathrm{f}} -1910.5{\mathit{\varphi }}_{\mathrm{f}}^2$	0.084
Temperatures (°C)
23	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=62.20+302.81{\mathit{\varphi }}_{\mathrm{f}} -2014.9{\mathit{\varphi }}_{\mathrm{f}}^2$	0.075
40	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=56.90+226.83{\mathit{\varphi }}_{\mathrm{f}} -1613.8{\mathit{\varphi }}_{\mathrm{f}}^2$	0.070
60	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=51.20+177.81{\mathit{\varphi }}_{\mathrm{f}}-1354.8{\mathit{\varphi }}_{\mathrm{f}}^2$	0.066
80	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=45.01+147.86{\mathit{\varphi }}_{\mathrm{f}}-1143.2{\mathit{\varphi }}_{\mathrm{f}}^2$	0.065
100	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=38.23+131.42{\mathit{\varphi }}_{\mathrm{f}}-986.85{\mathit{\varphi }}_{\mathrm{f}}^2$	0.067
120	${\mathit{\sigma }}_{\mathrm{c}\mathrm{w}\mathrm{t}}=33.02+89.29{\mathit{\varphi }}_{\mathrm{f}}-740.25{\mathit{\varphi }}_{\mathrm{f}}^2$	0.060

${\mathit{\varphi }}_{\mathrm{f},\mathrm{m}\mathrm{a}\mathrm{x}}=-\frac{1}{2}\left(\frac{a_1}{a_2}\right)$

11

Values of φ_f,max calculated via Equation (11) are given in Table 5 where it can be seen that φ_f,max is rate sensitive and its value increases with increasing strain rate.

The effect of strain rate on tensile strength of the double-gated mouldings, σ_cd, is shown in Figure 6 where it can be seen that the tensile strength of the double-gated specimens like their single-gated counterpart, σ_cs, increases linearly with the natural logarithm of strain rate mouldings, ln ė, and likewise can be expressed as:

Figure 6.

Strain rate effect on tensile strength of double-gated mouldings, σ_cd, containing 0, 10 and 30% by weight short glass fibres.

${\mathit{\sigma }}_{\mathrm{c}\mathrm{d}}=A_2+B_2\mathrm{l}\mathrm{n}\dot{e}$

12

where values of A ₂ and B ₂ can be found in Table 4. The increase in the slope of line, B ₂, with increasing φ_f suggests that tensile strength of the double-gated composite mouldings like their single-gated counterparts is more rate sensitive than the unreinforced matrix strength, and that the degree of sensitivity increases as fibre concentration is increased.

The effect of weldline in double-gated moulding on tensile strength is expressed quantitatively in terms of weldline integrity factor (WIF) defined as

$\mathrm{W}\mathrm{I}\mathrm{F}=\frac{{\mathit{\sigma }}_{\mathrm{c}\mathrm{d}}}{{\mathit{\sigma }}_{\mathrm{c}\mathrm{s}}}$

13

where σ_cs is tensile strength of single-gated moulding (i.e. unweld strength) and σ_cd is the tensile strength of the double-gated counterpart (i.e. weldline strength). Figure 7 shows that WIF decreases quite significantly with increasing fibre concentration, φ_f, while the value of WIF is 1.0 or thereabout for the unreinforced PC and it is around 0.4 for composite containing 30% by weight fibres. The observed reduction in tensile strength in the presence of weldline (i.e. WIF <1) is attributed mainly to the orientation of the fibres in the weldline region. Previous studies^1,2 using a similar mould geometry have shown that although away from the weldline region short fibres are preferentially aligned with their long axes parallel to the flow direction (i.e. the loading direction) as in single-gated mouldings, inside the weldline region they are predominantly aligned with their long axes normal to the flow direction and hence normal to the direction of the applied stress. As a result, the material within the weldline region acts as if it was not reinforced and therefore the weldline region becomes the weakest part of the double-gated mouldings. Moreover, as fibre concentration increases so does the number of fibre ends in the weldline region and this will give rise to further reduction in weldline strength with increasing fibre concentration.

Figure 7.

Effect of fibre volume fraction on weldline integrity factor, WIF, for tensile strength at crosshead speeds of 0.5, 5, 50 and 500 mm/min.

It is worth noting that while WIF is not rate sensitive at low values of φ_f, it is rate sensitive at high values of φ_f. Indeed, it is evident from Figure 7 that the value of WIF decreases with decreasing rate, thus indicating that weldline effect is more pronounced at low strain rates than it is at high strain rates.

Effect of moulding thickness on tensile strength of single- and double-gated mouldings

The effect of moulding thickness on tensile strength on single- and double-gated mouldings is shown in Figure 8. Results show that thickness of the mouldings has little effect if any on tensile strength.

Figure 8.

Effect of moulding thickness on tensile strength of single- and double-gated mouldings.

Effect of loading mode strength of single- and double-gated mouldings

Figure 9 compares the strength of single- and double-gated mouldings in tension and in flexure. Results indicate that both single- and double-gated mouldings exhibit higher strength values in flexure than in tension. However, it can be seen that the variation in flexural strength with φ_f is similar to that of tensile strength with φ_f, for both single- and double-gated mouldings.

Figure 9.

Effect of loading mode on the strength of single- and double-gated mouldings.

The linear dependence between the flexural strength of single-gated mouldings, σ_cs, and volume fraction of glass fibres, φ_f, can be expressed also by the rule-of-mixtures as Equation (4), bearing in mind that in this case, flexural strength values are used rather than tensile values. The parameter η for flexural strength of single-gated mouldings can be obtained from the slope of the linear regression line in Figure 9. Taking flexural strength of the glass fibre as 3705 MPa, one obtains a η value of 0.175 which is the same as that obtained for tensile strength of single-gated mouldings at crosshead speed of 50 mm/min.

The effect of loading mode on WIF is shown in Figure 10. Results show that while strength of both single- and double-gated mouldings are significantly affected by the mode of loading (tension versus flexure), WIF values remain almost unaffected by this change.

Figure 10.

Weldline integrity factor for tensile and flexural strengths versus volume fraction of glass fibres at crosshead speeds of 50 mm/min.

The data in Figure 10 can be reasonably expressed as

$\mathrm{W}\mathrm{I}\mathrm{F}=1-1.19{\mathit{\varphi }}_{\mathrm{f}}-11.88{\mathit{\varphi }}_{\mathrm{f}}^2$

14

According to Equation (14), the maximum value of WIF occurs at fibre volume fraction of about 5%.

Effect of temperature on tensile strength of single-gated mouldings

The effect of fibre volume fraction, φ_f, on tensile strength of single-gated moulding, σ_cs, at test temperatures ranging from 23 to 120°C is shown in Figure 11. Results show that σ_cs increases linearly with increasing φ_f over the entire temperature range studied here and therefore variation in σ_cs with increasing φ_f conforms to the rule of mixtures as given by Equation (4). It is also evident from Figure 11 that the slope of the linear regression lines decreases with increasing temperature, thus indicating that fibres become less efficient as reinforcing fillers as temperature increases. Indeed, as shown in Figure 12 values of fibre efficiency parameter, η, as calculated from the slope of the linear regression lines in Figure 11 decrease linearly with increasing temperature. The linear temperature dependence of η can be expressed as

Figure 11.

Effect of fibre volume fraction on tensile strength of single-gated mouldings, σ_cs, at 23, 40, 60, 80, 100 and 120°C.

Figure 12.

Effect of temperature on fibre efficiency parameter, η, for tensile strength of single-gated mouldings.

$\mathit{\eta }(T)=A_3-B_{3}T$

15

where A ₃ = 0.193 and B ₃ = 8.55 × 10⁻⁴ °C⁻¹.

Values of L _c, η_L and η_o as calculated using Equations (7) and (8) are presented in Table 6 as a function of temperature for the two composites. Results show that while η_o is not significantly affected by temperature, η_L decreases with increasing temperature. It is also evident that values of η_o and η_L are smaller for the composite with φ_f = 0.184 due to shorter fibre lengths.

Table 6.

Fibre efficiency parameters for tensile strength of single-gated fibre reinforced PC mouldings at 23, 40, 60, 80, 100 and 120°C.

Fibre volume fraction	φf = 0.049											φf = 0.184
Average fibre length (mm)	0.295											0.190
Temperature (°C)	23	40		60		80		100		120		23	40		60		80		100		120
L c (mm)	0.403		0.433		0.488		0.549		0.655		0.755	0.403		0.433		0.488		0.549		0.655		0.755
η	0.175		0.156		0.139		0.125		0.109		0.090	0.175		0.156		0.139		0.125		0.109		0.090
ηL	0.366		0.340		0.302		0.269		0.225		0.195	0.261		0.242		0.215		0.191		0.160		0.139
ηo	0.478		0.458		0.460		0.465		0.484		0.461	0.672		0.644		0.646		0.653		0.680		0.647

PC: polycarbonate.

The effect of temperature on σ_cs is shown more explicitly in Figure 13, where it can be seen that σ_cs decreases with increasing temperature. The effect of increasing φ_f is an upward vertical shift in σ_cs—temperature curve. The effect of temperature on σ_cs can be expressed as

Figure 13.

Effect of temperature on tensile strength of single-gated mouldings, σ_cs, containing 0, 10 and 30% by weight short glass fibres.

${\mathit{\sigma }}_{\mathrm{c}\mathrm{s}}(T)=A_4-B_{4}T$

16

where A ₄ and B ₄ are dependent upon volume fraction of fibres φ_f and their values can be found in Table 4. The slope of the lines in Figure 13 (i.e. B ₄ = dσ_cs /dT) is plotted in Figure 14 as a function of φ_f where it can be seen that variation is linear and therefore can be expressed as

Figure 14.

Effect of fibre volume fraction on dσ_ct/dT for single-gated mouldings.

$B_4=\frac{\mathrm{d}{\mathit{\sigma }}_{\mathrm{c}\mathrm{t}}}{\mathrm{d}T}=A_5+B_5{\mathit{\varphi }}_{\mathrm{f}}$

17

where A ₅ = 0.302 MPa °C⁻¹ and B ₅ = 1.952 MPa °C⁻¹.

Effect of temperature on tensile strength of double-gated mouldings

The effect of fibre volume fraction, φ_f, on tensile strength of double-gated moulding, σ_cd, at test temperatures ranging from 23 to 120°C is shown in Figure 15. Results show that over the entire temperature range studied here, σ_cd increases initially with increasing φ_f and reaches a maximum before decreasing with increasing volume fraction of fibres. As illustrated in Figure 15, variation in σ_cd with φ_f at a given temperature can be described reasonably well using the second-order polynomial function as given by Equation (10). The polynomial functions describing the data in Figure 15 are given in Table 5. As stated earlier, these polynomials may be used to obtain some indication of the optimum value of φ_f (i.e. φ_f,max) for achieving the maximum tensile strength in a double-gated mouldings. Values of φ_f,max as calculated via Equation (11) are given in Table 5 where it can be seen that φ_f,max decreases with increasing temperature.

Figure 15.

Effect of fibre volume fraction on tensile strength of double-gated mouldings, σ_cd, at 23, 40, 60, 80, 100 and 120°C.

The effect of temperature on σ_cd is shown more explicitly in Figure 16 where it can be seen that σ_cwt like σ_ct decreases linearly with increasing temperature. The effect of increasing φ_f is an upward vertical shift in σ_cd—temperature curve. The effect of temperature on σ_cd follows the same trend as σ_ct versus temperature and similarly can be expressed as

Figure 16.

Effect of temperature on tensile strength of double-gated mouldings, σ_cd, containing 0, 10 and 30% by weight short glass fibres.

${\mathit{\sigma }}_{\mathrm{c}\mathrm{d}}(T)=A_6-B_{6}T$

18

where A ₆ and B ₆ are dependent upon volume fraction of fibres φ_f and their values can be found in Table 4. The slope of the lines in Figure 16 (i.e. B ₆ = dσ_cd/dT) is plotted in Figure 14 as a function of φ_f.

Figure 17 shows the effect of fibre volume fraction on WIF over the entire temperature range 23–120°C. It can be seen that WIF decreases with increasing φ_f and as illustrated in Figure 18, it shows little variation with respect to temperature at a fixed φ_f value.

Figure 17.

Effect of fibre volume fraction on weldline integrity factor (WIF) for tensile strength at 23, 40, 60, 80, 100 and 120°C.

Figure 18.

Effect of temperature on weldline integrity factor (WIF) for tensile strength of composite mouldings containing 0, 10 and 30% by weight short glass fibres.

Conclusions

The following conclusions were drawn based on the experimental results obtained in this work:

• Tensile and flexural strength values of single-gated fibre reinforced PC mouldings increased linearly with increasing volume fraction of fibres, φ_f. The linear dependence obeyed the rule of mixtures for short fibre composites.

• Flexural strength of single-gated PC mouldings was consistently higher than tensile strength value. However, the overall efficiency parameter for composite strength was not affected by the change in the loading mode.

• Tensile strength of single-gated PC mouldings increased linearly with natural logarithm of strain rate and decreased linearly with increasing temperature. The overall efficiency parameter for tensile strength increased with increasing rate but decreased with increasing temperature.

• Tensile strength of single-gated PC mouldings was not affected by the thickness of the moulding.

• Tensile strength of double-gated fibre reinforced PC mouldings increased initially with increasing φ_f but decreased as φ_f exceeded. This behaviour was observed over the entire temperature range and strain rate used in this study and can be described reasonably well by a series of second-order polynomial functions.

• Tensile strength of double-gated PC mouldings increased linearly with natural logarithm of strain rate and decreased linearly with increasing temperature.

• Flexural strength of double-gated PC mouldings was consistent than the tensile strength values.

• WIF was independent of loading mode and the thickness of the moulding.

• WIF decreased with increasing φ_f but was independent of temperature.

• WIF was independent of strain rate at low φ_f but was strain rate dependent at high φ_f.