A microstructural approach for modelling flexural properties of long glass fibre reinforced polyamide6.6

Abstract

This paper focuses on the development and the validation of flexural modulus and flexural strength predictive models of long glass fibre reinforced polyamide 6.6 (PA66). Based on previous injection moulding optimization of 40 wt% long glass fibre PA66, a microstructure analysis was investigated on glass fibre reinforced PA66 by varying the parameters of the material (fibre length, fibre content, fibre diameter). In a first phase, analytical models established within the framework of the processing condition limits previously determined have been elaborated. These models lead to a good experimental/calculation correlation but remain limited to a mould and part design. In a second phase the flexural modulus and maximal flexural stress have been then estimated from structural models based on a five layer morphological description of the composites (local residual fibre length, local fibre content and fibre orientations). The long glass fibre PA66 composites were characterized in terms of fibre content distribution model and fibre orientation model through the part thickness. The experimental/model correlation was achieved whatever the process variability is (mould, material and processing conditions) both for the flexural modulus or flexural strength. The models have been then validated with an industrial part. Finally, a correlation between the two studied properties has been revealed depending on the nature of the composite matrix (PA66, PA6 or PP).

Keywords

Injection moulding long glass fibre polyamide flexural properties microstructure

Introduction

In recent years the increase in the use of long glass fibre thermoplastics (LFT) in many field of applications led to a development of technical and scientific investigations. Among them, the automotive sector shows a high growth of their applications for light structural parts in the replacement of metal.^1,2 Elaborated first on the base of polypropylene for the increase of stiffness and strengths, the LFT composites have found new developments with other technical matrix (polyamides, PET or polycarbonate …) in order to answer the needs of technical performances under thermo-oxidative environments for the under-the-hood applications for instance.

The LFT injection moulding induce composite structures characterized by a fibre degradation directed by the high shear stresses occurred during the plasticization and by the melt flowing through the gates or within the mould cavities,^3,4 a fibre segregation along the flow and through the thickness,^5–7 a fibre orientation directed by the melt flowing^6–9 and an interphase specific to the crystalline matrix governing the fibre/matrix linkage.⁷ These micro-structural parameters depending of the process are responsible for the mechanical properties of the LFT’s parts.^6,7,9–14

Regarding the prediction of glass fibre reinforced thermoplastic tensile properties, in the fibre direction, a simplest model based in a rule of mixture (ROM) can be used to predict the elastic properties of a composite. This model assumes that both the fibre and the matrix have a same strain and requires the only knowledge of the, respectively, fibre and matrix elastic modulii as well as the fibre volume content in the composite. In the transverse direction, the applied transverse stress is assumed equal in the fibre and the matrix the modulus is calculated from the inverse rule of mixture (IROM).¹⁵ In the case of misaligned fibres as observed in short or long fibre composites, the fibres are not oriented in the same direction through the part thickness and have not the same length. The usual ROM applied for a unidirectional reinforced composite does not give the expected accuracy.¹⁶ Cox¹⁷ have developed a model for random in-plane fibre reinforced composite. The elastic modulus is determined from a modified ROM taking into account an orientation factor and a length factor depending on fibre shape, fibre properties as well as fibre/matrix properties. Kelly and Tyson¹⁸ have shown that for very small strain within a fully elastic domain, the sliding load transfer at fibre extremities can be neglected and the stiffness is done by a modified ROM including only the orientation factor. The Halpin-Tsai equations are certainly the most common model used to predict young’s modulus in the case of fibre reinforced polymers.¹⁹ These equations are especially attractive because no experimental measurements are required. The Halpin-Tsai equations are a set of empirical relationships that enable the property of a composite material to be expressed in terms of the properties of the matrix and reinforcing phases together with their proportions and geometry. Halpin and Tsai showed that the property of a composite could be expressed in terms of the corresponding property of the matrix and the reinforcing phase associated to an empirical shape-fitting parameter depending of the fibre shape and the fibre/loading alignment.

The tensile stress prediction is more complicated to predict than young’s modulus because the material is no longer in the lower strain region, it evolved from its initial state to plastic strain, rearrangement and damage. In a composite, the failure can occur in the fibres or at the fibre-matrix interface. In the case of a slipping matrix/fibre load transfer, the Kelly Tyson’s model¹⁸ is commonly used. The model is set on fibre contribution composed both of fibre subcritical length and fibre supercritical length and matrix contribution. Thomason²⁰ suggested an experimental method called interfacial shear stress (IFSS) to estimate these matrix and fibre contributions. Equally used for long glass fibre (LGF) strength prediction, the model is in accordance with experimental values.⁶

For complex flexural load deflection where both elongation and shear stresses are combined, the finite element methods (FEMs) are generally used. The material is considered a superimposition of unidirectional reinforced layers. The best prediction comes from the analytical homogenization models allowing estimating the bulk elastic properties of the composites from a microstructural description of the moulded composites (properties of the constituent, fibre length and fibre orientation). Most of these models are based on Elshelby model or Mori Tanaka model²¹ and are generally coupled to the injection process simulation. The FEMs can be schematically represented by four main steps illustrated in Figure 1.²² These methods require important means of calculation.

Figure 1.

Schematic representation of FEM modelling steps: (1) geometrical model generation, (2) meshing, (3) periodic conditions and FEM solution and (4) effective properties calculation.²²

The aim of the present work is to develop and validate predictive models allowing the description of the flexural mechanical behaviour of long fibre reinforced polyamide 66. These models are based on the established typical structures coming from fibre content distribution through the part thickness, fibre orientation distribution and fibre length spectra data banks. Several ways are envisaged, either by developing a simplified analytical model taking into account the whole processing variables (material, process …) or by developing a more or less complex model based on the targeted part structures.

Experimentals

Materials

The materials studied are polyamides 6-6 (PA6-6 LGF Factor®) reinforced by 10 wt%, 40 wt% or 55 wt% of 12-mm long and 12-µm diameter glass fibres (FACTS GmbH). A 40-wt% of 800 µm short glass fibre (SGF) reinforced polyamide 6-6 has also been used in the study for the comparison with the LGF compounds. All the compounds (SGF or LGF) are made on the base of Technyl® A216 polyamide 6-6 matrix (Solvay, France).

These materials will be referenced LGF 10 wt%; LGF 40 wt%; LGF 55 wt% and SGF 40 wt%.

Machine and mould

The experiments were carried out on a 2000-kN clamping force injection moulding machine (DK Codim). The machine has an injection gate located in the parting line and is equipped with a standard 55-mm diameter screw.

The prototype injection mould is a rectangular plate of 300 × 120 × 3 mm. The feeding of cavity is made by a 4-mm-thick fan gate over its whole width (unidirectional flow in the longitudinal direction of the plate). This mould was specially designed so as to reproduce some geometrical discontinuities (like frontal and tangential steps) occurring on real industrial moulds and to be able to study the effects of such more or less sharp accidents on the flow mechanisms and related part properties (Figure 2).

Figure 2.

Plastic part and fan gate geometry.

Moulding conditions

The optimum moulding conditions previously determined³ to achieve the highest flexural properties in case of 40 wt% of 12-mm LGF reinforced PA6-6 injection moulding are reported in Table 1.

Table 1.

Moulding conditions for LGF PA6-6.

	Fibre content wt%	Fibre diameter µm	Init. fibre length mm	Melt temp. ℃	Vol. flow rate cm³s^–1	Mould temp. ℃
C1	11,5	12	12	280	237	100
C2	11,5	12	12	280	83	100
C3	11,5	12	12	280	83	100
C4	40	18	12	330	83	100
C5	40	12	12	330	36	100
C6	40	18	12	330	237	100
C7	40	12	12	330	83	50
C8	40	12	12	330	83	100
C9	40	12	12	310	83	50
C10	40	12	12	330	237	100
C11	40	12	12	310	83	100
C12	40	12	12	310	83	100
C13	40	12	12	330	83	100
C14	40	18	0,450	280	83	100
C15	55	12	12	330	83	100

Mechanical testing

Bending test leading to the determination of the flexural properties (strength, defined as maximum stress and modulus) were performed according to ISO 178 on a standard tensile machine (Instron) at 2 mm/min, on five samples (dimensions 60 × 25 × 3 mm) in both flow (longitudinal, 1) and transverse (2) directions before (beginning) and after (end) the geometrical discontinuities as shown in Figure 3.

Figure 3.

Location of test samples in the plate.

Melt apparent viscosity

The LGF PA6.6 melt viscosity representation is obtained during the filling stage of the cavity. The mould is instrumented by three pressure transducers located along the flow axes at 40 mm, 110 mm and 220 mm from the gate. The two first sensors situated in the non-disturbed area allow recording the pressure losses between two parallel plans, linked to the viscosity by the relation

Δ P = 2 . K . L . [\frac{Q . 2 . (2 n + 1)}{n . l . h \frac{1 + 2 n}{n}}]

(1)

and η = K . \overset{\cdot}{γ} n - 1

(2)

where

ΔP is the pressure losses h is the thickness

η is the shear viscosity K is the flow consistency

Q is the volumetric flow rate n is the flow behaviour index

L is the flow length $\overset{\cdot}{γ}$ is the shear rate

l is the flow width

However, a non-isothermal flow occurs in the case of injection moulding. The mould cooling system induces a viscosity decrease near the mould wall and a decrease of the thickness (h) due to the increase of the frozen layer. The pressure lost is represented by the Figure 4. The melt apparent viscosity is then calculated with equation (1) from the effective pressure losses (ΔP_Effective).

Figure 4.

Evolution of pressure losses between two sensors during the filling stage.

Results and discussion

Development of the analytical model

In this section, a predictive analytical model of flexural moduli and flexural strengths from the moulding conditions within a defined framework were studied. Supported by our previous studies^6,7 and the literature,^23–27 the hypothesis of a linear response between the processing conditions (melt and mould temperatures, volumetric flow rate), the material composition (initial fibre length, fibre diameter and fibre content) and flexural mechanical properties exists within a restricted process window. The Thomason’s works on the LGF reinforced polypropylene can support this hypothesis in this way on reflection, at least in the range of 10 to 40 wt% fibre content.²⁴ On this base, an empirical model of six parameters (15 conditions Table 1) can be elaborated (equation 3). In that case the material structure (residual fibre length, fibre orientation, crystallinity degree …) is implicit in the model coefficients

[P] = A 1 . P 1 + A 2 . P 2 + \dots + A i . P i + A 0

(3)

where: [P] is the mechanical property (flexural modulus or flexural strength), P_i is the variable parameter and A_i the constant.

The model coefficients are presented in Tables 2 and 3 for the flexural modulus at the beginning and the end of the part in the flow direction (direction 1) and for flexural strength in Tables 4 and 5.

Table 2.

Analytical model coefficients for flexural modulus in direction 1 at the beginning section for LGF PA66 composites.

Parameter	Mould temp.	Vol flow rate	Melt temp.	Initial fibre length	Fibre diameter	Fibre content	Constant
A_i	7.22	0.55	–21.19	–54.08	–143.22	190.42	9062.90
Variation	50; 100℃	36; 237 cm³ s^–1	280; 330℃	0.27; 12 mm	12; 18 µm	11.5; 55 wt%
Relative weight	361	113	–1059	–635	–859	8283
Level of influence	(5)	(6)	(2)	(4)	(3)	(1)
Statistic data	R²= 0.974		Standard deviation estimation: 444 MPa

Table 3.

Analytical model coefficients for flexural modulus in direction 1 at the end section for LGF PA66 composites.

Parameter	Mould temp.	Vol flow rate	Melt temp.	Initial fibre length	Fibre diameter	Fibre content	Constant
A_i	–8.28	0.10	–22.57	76.27	31.51	226.25	7368
Variation	50; 100℃	36; 237 cm³ s^–1	280; 330℃	0.27; 12 mm	12; 18 µm	11.5; 55 wt%
Relative weight	–414	21	–1128	895	189	6448
Level of influence	(4)	(6)	(2)	(3)	(5)	(1)
Statistic data	R²= 0.979		Standard deviation estimation : 473 MPa

Table 4.

Analytical model coefficients for flexural strength in direction 1 at the beginning section for LGF PA66 composites.

Parameter	Mould temp.	Vol flow rate	Melt temp.	Initial fibre length	Fibre diameter	Fibre content	Constant
A_i	–0.0061	0.0699	–0.1459	1.7781	–2.4261	4.0826	157.32
Variation	50; 100℃	36; 237 cm³ s^–1	280; 330℃	0.27; 12 mm	12; 18 µm	11.5; 55 wt%
Relative weight	–0.3	14.4	–7.3	20.9	–14.6	177.6
Level of influence	(6)	(4)	(5)	(2)	(3)	(1)
Statistic data	R²= 0.990		Standard deviation estimation : 6.3 MPa

Table 5.

Analytical model coefficients for flexural strength in direction 1 at the end section for LGF PA66 composites.

Parameter	Mould temp.	Vol flow rate	Melt temp.	Initial fibre length	Fibre diameter	Fibre content	Constant
A_i	–0.3451	0.0364	–0.4183	3.5757	–1.6001	5.9846	192.17
Variation	50; 100℃	36; 237 cm³ s^–1	280; 330℃	0.27; 12 mm	12; 18 µm	11.5; 55 wt%
Relative weight	–17.2	7.3	–20.9	41.9	–9.6	170.6
Level of influence	(4)	(6)	(3)	(2)	(5)	(1)
Statistic data	R²= 0.969		Standard deviation estimation : 16.0 MPa

Excepted for the initial fibre content governing mainly the mechanical properties of the composites, the melt temperature remains the predominant parameter on the flexural modulus. It acts on the fibre orientation during the filling stage of the cavity. The effect of the fibre length is to be taken with precaution because it is a question of comparing the long fibres and short fibres both for the modulus and for the strength. In spite of its simplicity, the calculation is completely in accordance with the experimental data as shown in the Figure 5.

Figure 5.

Comparison experimental/calculation values for flexural modulus and flexural strength PA66 LGF for different moulding or material combinations (C₁,…,C_n) at the beginning (a, c) and end (b, d) section of the part.

The use of linear regression confirms the possibility to approach the mechanical performances of the composites as already showed by other authors.²³ The models however depend on the part and gate geometries and its use remains limited to same matrix and fibre properties within a restricted processing window of the part. They do not take into account the real parameters linked to the material (matrix and fibre moduli, residual fibre length, fibre orientations, melt viscosity …) and the interactions between the parameters. The generalisation of the models is thus necessary taking into account the local micro-structure in order to be applicable to any material and to any parts.

Development of microstructural models

In previous studies,^6,28 a thorough experimental study highlighted the influence of the processing parameters, the gate design and gate location, as well as the material formulation (initial fibre length, fibre shape ratio and fibre content) on the flexural properties of LGF reinforced polyamide 6.6. In these studies, the microstructure/flexural properties relationships have been established. The obtained results permitted to consolidate those already revealed with another LGF reinforced polymer (PET Twintex® Fibre Glass Industries Inc Netherland).⁷ These various studies allowed concluding in the possibility of predicting in a simplified way but no more enough precise, the LGF composite structure evolution (inhomogeneity, anisotropy) within a definite field of the injection process (tolerances of processing conditions, flow length, gate design and location, nature of the matrix, reinforcement parameters …). With the knowledge of the final part structure, the mechanical properties can be calculated.

The first objective was to imagine and to validate a robust model describing the LGF reinforced PA66 flexural mechanical behaviour. This model is based on the typical structures previously established for the fibre weight repartition, the residual fibre length and the fibre orientation in the parts. The part structure is defined according to a five-layer configuration symmetrically distributed compared with the symmetry plane or middle plane of the part.

Young’s modulus prediction

The mechanical properties of each layer are calculated from the correspondent unidirectional composite Young’s modulus (E_L) depending on the Young’s modulus of the fibre (E_f) and of the matrix (E_m). The elastic modulus is then weighted by an orientation factor (η₀) and a residual fibre length factor (η_l) according to equation (4)²⁹

E L = E Layer = χ f η 0 η l E f + (1 - χ f) E m

(4)

where χ_f is the fibre volume fraction

η l = 1 - \frac{l c}{2 l f} with l c = r f \frac{σ rf}{τ u}

(5\ and\ 6)

η 0 = \sum_{i} a i \cos 4 θ i

(7)

where l_c is the critical fibre length (1.24 mm⁶), l_f the fibre length, r_f the fibre radius, σ_rf the fibre strength and τ_u the fibre/matrix interface shear strength (25–30 MPa¹²), a_i represents the fibre proportion doing an angle θ_i with the referent direction.

The residual fibre lengths (l_f) are thus measured for each layer (skin, intermediate and core) for each condition and the fibre length factors are then deduced. The results are summarized in Table 6.

Table 6.

Residual fibre length measurement of PA6.6 composites.

Moulding conditions	280℃	Low temp. 310℃	High temp. 330℃	330℃
Initial PA6.6 fibre weight content t_n	11.6%	40.1%	40.1%	53.7%
Skin	1.482	1.139	1.228	1.800
Intermediate	1.341	1.214	1.115	1.539
Core	2.522	1.348	1.575	2.567
Full sample	1.806	1.237	1.338	1.119
Fibre length factor η_l	0.858	0.836	0.815	0.883

The calculated modulus E_composite is then obtained from the relation

E Composite = \frac{\sum_{i = 1}^{n} W i E i}{\sum_{i = 1}^{n} W i}

(8)

For the Young’s modulus W_i = 1; for the flexural modulus $W i = e i . z_{i}^{2} + \frac{e_{i}^{3}}{12}$

Where e_i represents the layer thickness and z_i the distance from the reference axe.

Whatever the fibre content in the polyamide 6-6 injected (10 wt% to 55 wt%) and the setting injection conditions, the fibre weight repartition through the composite thicknesses can be described according to the following representation (Figure 6):

‐ Two skin layers representing about 25% of the total thickness, the relative fibre weight content (t_rskin) being constant.

Figure 6.

Fibre content profile through the part thickness: (a) influence of initial fibre weight, (b) data for the model calculation.

One skin core layer of about 20% of the total thickness describing a constant relative fibre weight content (t_rcore).

Two intermediate layers of about 15% thick each where the relative fibre weight content increases from the skin layer to the core layer fibre weight values. The average fibre weight content can be directly calculated from these two precedent values.

The model structure for the fibre weight content through the thickness is then described with these three parameters as represented in Table 7.

Table 7.

Fibre weight descriptions of the composites for calculation.

Moulding conditions	280℃	Low temp. 310℃	High temp. 330℃	330℃	Average coefficient
Initial PA6.6 fibre weight content t_n	11.6%	40.1%	40.1%	53.7%
Relative skin fibre weight content t_rskin	0.84	0.83	0.80	0.87	0.835
Relative core weight content t_rcor_e	1.23	1.11	1.23	1.15	1.18

Regarding the fibre orientation distribution, the respective thicknesses of the five oriented layers will be the same as that of the fibre weight content in so far as a good concordance exists between the orientation profiles and the fibre content profiles (Figure 7). Thus, the model will use a five-layer model symmetrically distributed compared with the symmetric plan of the part.

Figure 7.

Fibre orientation profile through the part thickness: (a) in the flow direction (1), (b) in transverse direction (2).

The comparison between the experimental measurement of the fibre orientation profile and the data used for the calculation is shown in the Figure 7, the orientation factors calculated in the flow direction η₀₍₁₎ and the transverse direction η₀₍₂₎ are summarized in Table 8.

Table 8.

Fibre orientation descriptions of the composites for calculation.

Moulding conditions		280℃	Low temp. 310℃	High temp. 330℃	330℃
PA6.6 fibre weight content		11.6%	40.1%	40.1%	53.7%
η₀₍₁₎	Skin	0.528	0.667	0.593	0.631
		±0.071	±0.097	±0.119	±0.108
	Intermediate	0.458	0.446	0.396	0.291
		±0.097	±0.191	±0.153	±0.227
	Core	0.330	0.180	0.128	0.245
		±0.084	±0.116	±0.060	±0.055
	Average	0.440	0.501	0.418	0.437
η₀₍₂₎	Skin	0.241	0.144	0.211	0.172
		±0.045	±0.076	±0.093	±0.057
	Intermediate	0.294	0.337	0.372	0.450
		±0.053	±0.166	±0.140	±0.200
	Core	0.392	0.574	0.700	0.472
		±0.087	±0.119	±0.092	±0.097
	Average	0.308	0.291	0.381	0.324

The melt viscosity influences fibre orientation through the part thickness as presented in Figure 8. The increase in melt viscosity induces an increase of skin fibre orientation in the flow direction. In the part core, the viscosity dependence is limited. The knowledge of the pressure losses during the filling stage promotes the fibre orientation in the part, at least for a same family of polymers.

Figure 8.

Influence of melt viscosity on the skin/core layer orientations in the flow direction.

Knowing the fibre weight content distribution law through the thickness (Figure 6b), the skin/core fibre orientation law linked to the melt viscosity (Figure 8) and the residual fibre length factor (η_l), the calculation of the flexural modulus becomes accessible from the equation (8). The experimental/calculation comparison of the PA6.6 composite flexural modulii is presented in Table 9. Most of calculations are in good accordance with the experimental results whatever the direction is. Considering the standard deviation of the measurements (±3% to ±6%), the calculation/experimental deviation remains acceptable, at least for the higher fibre content. Regarding the lower fibre content (10 wt%), the calculation error overtakes 20% whatever the direction is. The difference seems to come from a difference in the fibre content shape repartition through the thickness parting a lot from the conventional shape adopted (Figure 6).

Table 9.

Experimental/calculation comparison of the PA66 flexural modulus composites.

Moulding conditions		280℃	Low temp. 310℃	High temp. 330℃	330℃
PA6.6 fibre weight content		11.6%	40.1%	40.1%	53.7%
Flexural modulus (MPa): flow direction (1)	Experimental	4240	8330	8020	11450
		±150	±530	±310	±240
	Calculation	3710	8780	8016	10566
	Deviation	–25%	+5.4%	=	–7.7%
Flexural modulus (MPa): transverse direction (2)	Experimental	2928	4746	5004	7850
		±90	±430	±150	±280
	Calculation	1783	4403	5384	8524
	Deviation	–38%	–7%	+7.5%	+8.5%

Regarding the comparison with conventional methods of calculation such as laminated plate theory³⁰ or the Elshelby-Mori Tanaka micromechanical model,^31–33 the analytical microstructural model developed here offers the advantage to give a good evaluation of the composite modulus with a limited number of layers, at least in the case of not complex part shape. The laminated plate theory considering a largest number of layers (43 oriented layers), consequently a better definition of the microstructure, gives the most precise evaluation of the rigidity of the system (Figure 9). Finally, The Eshelby-Mori Tanaka model, taking into consideration both fibre orientation and fibre aspect ratio, tends to overestimate the flexural moduli (Figure 9) probably due to the high average fibre aspect ratio measured in the composites that increases the fibre/matrix interactions (Table 6). A modulus over evaluation of more than 10% was moreover already noticed for fibre shape ratio superior to 50.^22,34,35

Figure 9.

Calculated flexural modulus in the flow direction, versus the fibre weight fraction: comparison with experimental data.

Flexural strength prediction

The strength prediction is more complicated to appreciate than Young’s modulus. The strength determination is generally achieved on the basis of laminate theory where the composite is considered as a multilayer unidirectional assembly as well as the Elshelby or Mori-Tanaka models developed from the microstructure knowledge of the composite (constituent properties, shape ratio, orientation and location) and applied in the FEM. In the case of slipping fibre/matrix load transfer for tensile strength, the microstructural Kelly Tyson’s model is commonly used to predict the stress at break.¹⁸ This model distinguishes three main contributions, the subcritical and supercritical fibre length contributions and the matrix contribution (equation 9)

σ cu = [η 0 \cdot \sum_{l i 〈 l c} \frac{τ u \cdot l i \cdot χ i}{2 \cdot r f}] + [η 0 \sum_{l j 〉 l c} σ rf \cdot χ j \cdot (1 - \frac{l c}{2 . l j})] + [σ' m (1 - χ f)]

(9)

where

σ_cu is the ultimate composite stress (stress at break)

l_i and l_j are the subcritical and the supercritical fibre length to the critical fibre length l_c

χ_i and χ_j are the volume faction of li and l_j fibre lengths

σ′_m – stress supported in the matrix at composite failure strain (σ′_m = E_m*ɛ_c)

ɛ_c – strain at composite failure

The fibre strength supported by the fibre at the moment of composite failure (σ_rf) has been experimentally determined by Thomason giving a value of 1700 MPa ± 250 for a glass fibre reinforced PA66 composite.¹²

For an ideal elastic material, the flexural strength is estimated as equal to the tensile strength. For an elastic-plastic material as the LGF reinforced PA66 composite, its pseudo-plastic behaviour leads to an increase in load capacity and the ultimate flexural strength depends on both the ultimate tensile strength and post-cracking ductility.²⁸ However, the existence of a multiplicative factor of 1.9–2.6 has been shown between the flexural and the tensile strengths for glass fibre composites.²⁸ That is why, a first approximation of the composite flexural strength was able to be made taking into consideration the model developed for the tensile strength prediction (equation 9). The experimental/calculation comparison of the PA66 composite flexural strengths is presented in Table 10.

Table 10.

Experimental/calculation comparison of the PA66 flexural strength composites.

Moulding conditions		280℃	Low temp. 310℃	High temp. 330℃	330℃
PA6.6 fibre weight content		11.6%	40.1%	40.1%	53.7%
Flexural strength (MPa): flow direction (1)	Experimental	167	271	266	337
		±5	±12	±6	±9
	Calculation	91	235	205	319
	Deviation	–46%	–13%	–23%	–5
Flexural strength (MPa): transverse direction (2)	Experimental	141	175	197	241
		±3	±9	±12	±8
	Calculation	73	88	105	115
	Deviation	–48%	–49%	–47%	–52%

The flexural strength calculation underestimates systematically the experimental values all the more that the sample has a plastic behaviour (low fibre content, transverse direction) in that case, a strength ratio (Tensile strength/Estimated flexural strength) of 2 is obtained corroborating the literature value.²⁸

On the basis of this model, linear correlations are then possible to be established between flexural modulus and flexural strength whatever the configuration is: mould design (gate location or gate size), part design (rectangular plate, tensile test sample or industrial part (half of tank presented in Figure 10)), LFT definition (initial fibre content (10 wt% to 55 wt%), initial fibre length (450 µm to 12 mm, fibre diameter (12 µm to 17 µm)), processing conditions (melt and mould temperature, volumetric flow rate) or mechanical testing location (Beginning section or end section) (Figure 11). This correlation is linked to the nature of the matrix as presented in Figure 12.

Figure 10.

Industrial part (half of tank) (a) and orientation factor comparison with the rectangular plate (b).

Figure 11.

Flexural modulus/flexural strength correlation: influence of part and gate geometries, fibre shape ratio and fibre diameter (LGF 10 wt%; LGF 40 wt%; LGF 55 wt% and SGF 40 wt%).

Figure 12.

Flexural modulus/flexural strength correlation: influence of the matrix nature.

The only cases of short glass fibre PA66 and double fan gate go away from the line of correlation (Figure 11). These two particular cases show a decrease in flexural strength due to numerous fibres under the subcritical length in the first case and the presence of weld line in the second case. Thus, with the calculation of the modulus (equation 7) and limited quantity of mechanical tests on standard samples, the flexural strength becomes possible to be evaluated; the calculated values can be of use for the creep models for instance.

Conclusion

The injection moulding of LGF PA66 composites were characterized in terms of fibre content distribution and fibre orientation through the part thickness. The relative fibre rate profiles through the part thickness present a similar distribution whatever the initial fibre content is. Thus, a structural model of fibre weight distribution through the part thickness is described from the initial fibre content of the LGF PA66, the relative fibre rate in the skin, the relative fibre rate in the core and the constant skin layer and core layer thicknesses (respectively, 25% and 15% of the total part thickness). The fibre orientation profiles have been then represented in five main layers of constant thickness whatever the initial fibre content or moulding conditions is:

Two skin oriented layers 25% thick each

One core layer 20% thick

Two intermediate layers 15% thick each

The correspondent orientation factors of each layers was able to be connected to the apparent viscosity measured directly during the filling stage of the injection process from two pressure sensors placed in the cavity. Within a framework of the LGF PA66 injection process the estimation of the orientation state of the part then becomes possible.

The analytical models obtained from the injection moulding conditions varying within a determined moulding window lead to a good experimental/calculation correlation, but these models remain limited to a part geometry and mould design. Furthermore, they do not take into account the material parameters (local fibre content, residual fibre length or fibre orientations) and thus the local moduli of the composite.

The structural models are based on a five layer description of the part thickness for the local fibre content and the fibre orientation. This orientation profile can be moreover obtained from rheological melt behaviour of the composites. A very good experimental/calculation correlation is noticed as well for the flexural modulus as the flexural strength, whatever the process variability is (mould, material and processing conditions). The models have been validated with an industrial part (half of tank) moulded inside the same processing window that of the reference plate.

Finally, a linear correlation between the flexural modulus and the flexural strength appears depending on the nature of the matrix (PA66, PA6, PP) whatever the processing conditions, the mould design (gate size or gate position) or glass reinforcement characteristics (fibre length, fibre diameter, fibre content or the presence of coupling agent).

Footnotes

Acknowledgments

The authors gratefully acknowledge the support and contribution of CISIT (International Campus on Safety and Intermodality in Transportation), the Nord-Pas-de-Calais Region and the European Community (FEDER, European Funds for Regional Development) for funding of injection materials.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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