Designing curing conditions in order to analyse the influence of process-induced stresses upon some mechanical properties of carbon / epoxy laminates at constant T_g and degree of cure

Abstract

In the aim to study of the effects of process-induced stresses upon some mechanical properties of simple stacking sequence composite laminates, three different cure cycles were designed. This was achieved on the basis of a cure kinetics modelling. A minimum number of curing parameters were modified in order to restrain changes in material physical properties. Those latter were determined from the molecular network of the thermosetting matrix to the fibres volume fraction and thermal expansion of the laminated plates. The level of process-induced stresses generated by the three cure cycles was assessed by measuring the out-of-plane deflection on unsymmetrical laminated strips. Manufactured laminates were submitted to a set of tensile tests in order to determine the changes in their mechanical properties due to the different curing conditions. All the mechanical tests were followed by acoustic emission. This has enabled to distinguish the occurrence of the various damaging processes with respect to curing conditions and therefore process-induced stresses. Lastly, process-induced stresses on a micromechanical level were theoretically determined. This determination has enabled a first analysis of the effects of process-induced stresses upon mechanical properties to be settled.

Process-induced stresses: a brief overview of background

A huge quantity of research work has been performed since the end of the 1970’s on the subject of process-induced (or residual) stresses in polymeric matrix composite materials. Numerous aspects of the process-induced stresses have been and are still studied. For thermosetting matrix composite, one of the very first overview of the various treated issues can be found in reference [1]. A larger review paper including original results is given in ref. [2] still for thermosetting matrix composites. More recently (in 2006) some authors have published a concise compilation of the various aspects of residual stresses focussing thermoplastic matrix composites [3–5].

In a few words, it can be noted that authors have devoted their work to:

• implementing the modelling of the development of process-induced stresses [6–19];

• implementing the computation of process-induced stresses [20–28];

• measuring process-induced strains [29–41]

• integrating in the computation of process-induced stresses, the interactions between the manufactured composite part and tooling [28, 42–49].

A concise literature survey shows that the effects of process-induced stresses upon laminates and laminated structures dimensional stability emerges as the main issue. Nevertheless, as regards thermosetting matrix composites, process-induced stresses have some other consequences such as:

• changes in physical properties (i.e. crosslinked molecular network structure, glass transition temperature, moisture uptake, etc.) [50, 51];

• development of fibre waviness [52];

• generation of matrix and transverse plies cracking (with the very first thermosetting matrix used in composites) [56];

• modifications of mechanical properties (i.e. moduli, ultimate strengths, fracture behaviour, etc.).

Study frame and aims

Process-induced stresses and their influence upon laminates’ mechanical properties

The changes in mechanical properties of laminates stemming from process-induced stresses in thermosetting matrix composites have been definitely less studied than the issue of thermal stability. A few authors have focussed their work on the effects of residual stresses upon mechanical characteristics of polymeric matrix laminates (on a micromechanical and on a macromechanical level) and laminated structural parts [53–64, 74]. They are either using theoretical approaches (and finite element modelling) or experimental studies.

In theoretical approaches, it is frequently hypothesized that the process-induced stresses levels are known or can be easily computed from classical laminated plates theory using a given a temperature difference ΔT (or ΔT + cooling rate). In these cases, mechanical failure criteria—e.g. quadratic criterion with residual stresses, maximum strain criterion with residual stresses as made in ref. [54], maximum stress failure criterion at the microscale [63, 64, 74]—or energy release rate (G_IC, as proposed in ref. [55]) are formulated integrating residual stresses or strains terms.

Concerning the experimental point, in most cases, studies consist in manufacturing laminates or laminated parts in order to get materials undergoing various residual stress levels [58] and to analyse how their mechanical properties are affected or how the state of residual stresses can be locally modified [61]. In spite of very interesting results the ways the changes in process-induced stresses levels are obtained are far from being without any repercussions upon physical characteristics of matrices. In other words, it appear that different levels of process-induced stresses (for a given laminate) are generally obtained by modifying the curing conditions and more precisely the temperature difference between the curing dwell and room temperature or by submitting the materials to some post-curing stages. Therefore, most of these studies were conducted on batches of laminates for which matrix degree of cure α_c and T_g (glass transition temperature) differs from one to another. Thus, not only the process-induced stresses are modified but also matrix properties. This is increasing the difficulty to perform a clear assessment of the solely effects of process-induced stresses. For this reason, we have decided to settle a study in which those two characteristics will remain steady.

Aims

Assuming that the properties of a composite, namely its matrix modulus, remain constant while the level of residual stresses is modified for the purpose of a theoretical study is one “rather easy thing”. Performing the same kind of study from an experimental point of view is a completely different problem. Numerous difficulties are arising from the fact that when it is wanted to get laminates with various residual stresses levels, the ways used to generate these levels of stresses induce some other changes in material properties (i.e., matrix degree of cure, T_g, etc.).

In this study, our aim was to settle an analysis of the effects of process-induced stresses upon some mechanical properties of [0°₁₆], [90°₁₆], [±45°₄]_s laminates. This analysis was made at constant degree of cure α_c and matrix glass transition temperature T_g, while for a given kind of laminate (e.g. a [90°₁₆] laminate) the level of process-induced stresses changes from one manufacturing set to another. In addition special efforts were made to get completely void-free laminates in order to be certain that the ‘potential’ modifications recorded on mechanical properties are exclusively due to process-induced stresses.

To this end and as shown below, the temperature route of the cure cycles was modified—on the basis of a preliminary cure kinetics study—as shown in Fig. 2, while respecting the following constrained functions:

• matrix degree of cure α_c measured by DSC: 97% ≤ α_c ≤ 99%

• matrix glass transition temperature T_g measured by DSC: 150°C ≤ T_g ≤ 154°C

• fibre volume fraction V _f % maximum allowed change for laminates having identical stacking sequences: ΔV _f % = ± 0.2%

• void content V_v% (volume fraction): V _v  = 0% (totally void-free laminates)

Manufacturing conditions and physical characterisation of laminates

Material and manufacturing process

All investigations in this study were performed with a composite initially consisting (prior to curing) of continuous carbon fibre unidirectional prepreg tape. The trade reference of this Hexcel-Composites France prepreg is T2H-EH24 34%.

It is made of Tenax HTA carbon fibres preimpregnated with EH25 epoxy resin itself containing a thermoplastic polymer in some extents. The unidirectional prepreg tape initial fibres volume fraction is V _f  = 60%. The prepreg ply average thickness is of 0.125 mm. HTA Tenax carbon fibres density is: ρ_f = 1,770 kg.m⁻³, while the EH25 resin density (once cured) is ρ_m = 1,330 kg.m⁻³.

All the laminates under study here were manufactured under vacuum bagging (see Fig. 1) and autoclave-cured under pressure. In this work, the release agent used was solely the ETFE Film (denoted by 2b in Fig. 1).

Fig. 1

Manufacturing condition: vacuum bagging products

Determination of curing conditions

A preliminary work (started in 1992) based on the cure kinetics of Hexcel T2H-EH25 carbon/epoxy material [66, 67] (Fig. 2) has enabled three different cure cycles to be defined (Fig. 3). These cure cycles are equivalents in terms of matrix degree of cure α_c glass transition temperature T_g and fibre volume fraction V _f % (for thin laminates), but they generate changes in residual stresses levels [66]. As shown in Fig. 3, only the curing dwell temperature and duration were modified. This means that the expected changes in residual curing stresses level will be generated by the different cooling steps (i.e. temperature differences of 180, 160 or 140°C). Consequently, three values of ΔT (with ΔT = room T°-curing dwell T°) will be used for the computation of residual curing stresses: 180, 160 and 140°C. It is important to mention that the second cure cycle (Fig. 3) with a 120 min curing dwell at 180°C, is the one recommended by the prepreg manufacturer (denoted by mrcc for: manufacturer recommended cure cycle) for ‘thin laminates’.

Fig. 2

Isoconversion temperature / time abacus—degree of cure as functions of curing dwell duration and curing dwell temperature [65, 66]

Fig. 3

The three cure cycles used for manufacturing laminates undergoing different levels of process-induced stresses

One other solution to manufacture laminates undergoing different levels of process-induced stresses could consist in modifying the cooling rate between the curing dwell and room temperatures. It has not been selected for two reasons. Firstly, even if viscoelastic effects can be easily modelled, they remain somewhat difficult to control during cooling using a closed-loop monitored autoclave. Secondly, these viscoelastic effects are not as high as it could be required to produce changes in residual stresses [48]. This is limitation is due to the heating and cooling capacities of our laboratory autoclave which are lying between 0.2 up and 5°C/min.

It should be mentioned that as shown in Fig. 3, temperature was the only parameter modified. Cure cycles the pressure paths remained unchanged from one cure cycle to another provided the adjustment to the durations.

Manufactured laminates and basic characterisation of physical properties

Basic physical properties

After curing the laminates physical properties (i.e. matrix degree of cure α_c, glass transition temperature T_g and fibre volume fraction (V _f %) were determined by differential scanning calorimetry (DSC) on at least 3 samples cut out from [0°₁₆] laminates. DSC tests consisted in submitting samples (average mass ≈ 20 mg) to a 20°C/min heating ramp from −40°C up to 300°C while recording the heat flows.

The matrix glass transition temperature T_g was also determined by thermomechanical analysis (TMA) on coupons cut out from [0°₁₆] and [90°₁₆] laminates (see Table 1) by submitting these samples to a 5°C/min temperature ramp from 25° up to 250°C. These TMA experiments also enable the longitudinal α_l and the transverse α_t coefficients of thermal expansion of unidirectional laminates (U.D.) ply to be determined.

Table 1 Physical characteristics measured after curing either by DSC (α_c, T_g) or TMA (T_g, α₁ α_t)

Fibre volume fraction (V _f %) values were obtained by resin dissolution (experiments preformed according European standard E.N. 2564 with an absolute error of ± 1%). Since V _f % is depending on the laminate’s stacking sequence, resin dissolution experiments were performed on unidirectional [0°₁₆] and symmetrical laminates and also on unsymmetrical [0°₂/90°₂] laminated strips used for the experimental determination of residual curing stresses (see Table 2).

Table 2 Laminates fibre volume fractions V _f % and thickness h measured after curing depending on cure cycle and stacking sequence

As a summary of Tables 1 and 2 results, it can be said that this physical characterisation campaign clearly shows the equivalence between the three cure cycles, since laminates’ matrix degree of cure α_c remains constant and T_g values lie between the allowed limits. Furthermore, if one considers laminates which have the same stacking sequence, curing these laminates at 160, 180 or 200°C does not induce any changes in V _f %. Consequently, none of the changes that could be detected in their mechanical behaviour will be due to a modification of their physical characteristics.

Dynamic mechanical analysis: main mechanical relaxation activation energy

Despite Table 1 α_c and T_g results that show the equivalences between the three temperature paths, it still can be argued that using such different curing routes may result in some modifications of the three-dimensional crosslinked network of the EH25 epoxy matrix.

Several authors [68–70] have studied relationships between the structure of three-dimensional molecular networks of thermosetting matrices and their mechanical and physical properties. In particular, Crawford et al. [69] have shown how the α main mechanical relaxation—maximum peak temperature and magnitude and half-high wideness—was influenced by changes in the crosslinking density characterised by $\overline {{M_C}}$ the average molecular mass between crosslinks.

Consequently and in order to perform an extra study of the equivalence between the three cure cycles, some mechanical dynamical analyses were conducted on [90°₄] cured samples on a DMTA at 0.1, 0.2, 1, 2, 5, 10 and 20 Hz (for dynamic force). [90°₄] samples were heated between 30°C up to 300°C at a rate of 1°C/min. An example of obtained results is shown in Fig. 4. The transverse tensile storage modulus E₂′ (or E_t′) and the loss factor angle tg(δ are plotted as functions of temperature and frequency.

Fig. 4

DMTA: changes in E₂’ storage modulus and tg(δ loss factor angle a functions of temperature and frequency. Example of results obtained on a [90°₄] cured 120 min. at 180°C

As shown by J.G. Gerard [70] the activation energy E_α (in kJ.mol⁻¹) of the main mechanical relaxation can be determined from DMTA tests using:

$$ \ln \left( {\frac{f}{{{f_0}}} = \frac{{{E_\alpha }}}{R} \cdot \left[ {\frac{1}{{{T_m}}} - \frac{1}{{{T_0}}}} \right]} \right) $$

(1)

where f is the frequency (in Hz); f ₀ , reference frequency (1 Hz); R universal gas constant; T _m , temperature at maximum of a peak (in K) (see Fig. 4) and T ₀ , reference temperature (in K). The reference temperature was taken as the temperature for which the maximum change in E′₂ was recorded. Here T ₀  = 180°C. Equation 1 enables the activation energy of the main mechanical relaxation E_α to be determined. The results are plotted in Fig. 5. In terms of orders of magnitude the E_α values remain relatively close to those given in ref. [70]. Among the set of tested samples, the largest change in E_α recorded is of 78 kJ.mol⁻¹ (i.e. a 15% change) between samples cured for 480 min. at 160°C and those cured for 120 min. at 180°C (mrcc).

Fig. 5

Determination of the main mechanical relaxation (activation energy Eα. ln(f) plotted as a function of inverse of temperature (1/T) at which the maximum peak occurs. Laminates cured at, ⋄ {160°C, 480 min.}, □ {180°C, 120 min.} and ∆ {200°C, 40 min.}

Consequently, all the obtained results enable to say that for a given stacking sequence solely the process-induced stresses will be modified from one cure cycle to another.

Levels of process-induced stresses

Experimental determination

The main aim here was to show that the 3 cure cycles (see Fig. 3) were effectively able to generate different levels of process-induced stresses in the various manufactured laminates.

At that point it should be mentioned that throughout this study, the in-plane dimensions of the manufactured laminates were kept constant in order to avoid any changes in the level of process-induced stresses stemming from the interactions between the mould and the parts. Effectively, it has been shown that the transverse shear stresses (perpendicular to laminate plane) induced by mould/part interactions are depending on laminates initial in-plane dimensions [43, 45, 48].

A very simple method was used to show that the cure cycles are able to generate different process-induced stresses levels. It has consisted in measuring the out-of-plane deflection of unsymmetrical [0°₂/90°₂] laminated strips. This was achieved owing to a profile projector. For a 200 × 20 mm laminated strip, the relative error in the maximum deflection value V _max , is of 2.1%, versus 0.1% in the laminated strip length L and 0.9% on the laminate thickness h. (see Fig. 6). Once cumulated, those relative errors result in a whole relative error of 6.5% in curvature k_ox (mm⁻¹) value. In all cases, the out-of-plane deflection measurements were performed within 2 h after the cure cycle end, in order to avoid any changes in V _max due to moisture absorption generating stress relaxation. Three kind of unsymmetrical [0°₂/90°₂] laminated strips were manufactured with the following initial in-plane dimensions: 100 × 10 mm, 150 × 15 mm and 200 × 20 mm with sets of 5 laminates for each one of these dimensions. It has been shown that the out-of-plane deflection observed at room temperature after curing is not only depending on the laminate in-plane dimensions, but also, for unsymmetrical laminated strips, on their bottom ply orientation (ply in contact with the releasing agent placed on the mould surface—Fig. 1) [46]. In consequences, it should be mentioned that for all [0°₂/90°₂] laminated strips under study here, their 0° ply was placed as the bottom ply, i.e. in contact with ETFE release film see Fig. 1. The obtained results are plotted in Fig. 7. They show that changing curing dwell temperature and duration results in creating different levels of out-of-plane deflection measured here by the main curvature k_ox (1/mm) (Fig. 6 and Eq. 2).

$$ {k_{ox}} = \frac{1}{{{R_{ox}}}}\;{\hbox{with}}\;{R_{ox}} = \frac{{{L^2}}}{{8 \cdot {V_{\max }}}} + \frac{{{V_{\max }}}}{2} $$

(2)

Fig. 6

Out-of-plane deflection of unsymmetrical laminated strips at room temperature after curing

Fig. 7

Curvature of unsymmetrical [0°₂/90°₂] laminated strips, measured after curing at room temperature and as functions of curing conditions and length. Length / width ratio always equal to 10

Mechanical characterisation: Influence of process-induced stresses?

Foreword

Tensile tests have been performed on an 8561 INSTRON according to conditions described in European standards EN 2561 and EN 2597. An exception has been made about the displacement speed of the INSTRON moving crosshead. A 0.5 mm/min speed was used instead of a 2 mm/min speed recommended in the standards. Lowering the crosshead displacement speed enables to make a more accurate distinction between the acoustic events happening during a tensile test. The various events occurring during tensile tests such as matrix cracking, interlaminar delamination, fibres breakage, etc., were recorded owing to an acoustic emission device. The acoustic emission device is schematised in Fig. 8. The tensile test samples were all equipped with four piezoelectric sensors. Two of them are located near the sample end-tabs in order to eliminate noise signals coming from end-tabs and INSTRON jaws.

Fig. 8

Acoustic emission device used during all tensile tests

Acoustic emission: Background

Acoustic emission has been used for several year to assess the different events occurring during the mechanical testing of composites [71, 72]. All damaging mechanisms, for which the propagation ends to cause the fracture of a composite part, generate sounds, noises, elastic waves or acoustic emission. The results obtained by M Benzeggagh [71] are concerning glass/epoxy woven laminates tested in bending. Those of O. Siron [72] on carbon/epoxy are synthesised in Fig. 9. A special attention must be paid to O. Siron results because they were obtained during tensile tests performed on carbon/epoxy laminates autoclave cured. This corresponds to the kind of material and mechanical tests performed in this work. In this work on acoustic emission the magnitude values given in Fig. 9 will be taken as reference for correlating acoustic signals and damaging process.

Fig. 9

Synthesis of refs. [71, 72] results: correlation between the magnitude of acoustic signals (in dB) and kind of damages in a carbon/epoxy composite laminate

Mechanical behaviour of [0°₁₆] laminates

Mechanical tests were performed on samples cut out from [0°₁₆] laminates cured according to each one of the three cure cycles. Figure 10 shows the typical behaviour of [0°₁₆] samples during a tensile test depending on their curing temperature. The left side of Fig. 10 is a plot of the strain versus stress curves, while the right side exhibits the acoustic emission results. The acoustic emission diagrams show both the magnitude of the acoustic signals (in dB) and the energy released by the sample during the tensile test. Magnitude and energy are plotted versus the tensile load applied to the laminated sample. Even if it remains somewhat difficult to notice any difference in the elastic behaviour (i.e. longitudinal tensile moduli E_xx), it can be seen that the longitudinal ultimate tensile strength (denoted by σ ^ult._xx ) depends on the curing dwell temperature. To make mechanical behaviour more explicit, a synthesis table is included in Fig. 10. This table gives moduli E_xx and σ ^ult._xx average values depending on curing dwell temperature and duration. It shows that the average σ ^ult._xx of [0°₁₆] laminates cured 20 min at 200°C is about 17% higher than the average σ ^ult._xx of [0°₁₆] laminates cured 480 min at 160°C. The changes recorded in E_xx between the two cure cycles (160 and 200°C) are lower than 6.5%. One must bear in mind that modulus measurement uncertainty is only about 0.46%.

Fig. 10

Results of tensile tests and acoustic emission on [0°₁₆] samples. The table gives moduli E_xx and ultimate tensile strengths σ ^ult_xx average values depending on curing dwell temperature and duration

Concerning acoustic emission, only the results relative to laminates cured 480 min at 160°C and 40 min at 200°C are reported on the right side of Fig. 10. From the very beginning of the tensile tests the magnitude of acoustic signals increases quickly to reach the level of 70dB. Whatever the cure cycle was, 70dB signals were recorded for a tensile stress of about 180 MPa. The first signals for which the magnitude reaches 90dB (fibre fracture) appear for a 550 MPa tensile stress and this again whatever the cure cycle. Nevertheless, the samples cured for 480 min. at 160°C exhibit a more intense acoustic activity—in terms of signals higher than 90dB—than those cured for 20 min. at 200°C. As shown in Fig. 9, signals laying between 70 and 80 dB can be associated to both fibre/matrix debonding and matrix cracking and 90 dB (or higher) signals to carbon fibres breakage.

Mechanical behaviour of [90°₁₆] laminates

As it was made for [0°₁₆] laminates, the main parameters of the tensile behaviour of [90°₁₆] are synthesised in the table included in Fig. 11. Finally, acoustic emission results are reported in Fig. 11 right side. The transverse tensile modulus E_yy do not seems to depend on curing temperature. The average changes in E_yy between the laminates cured at 160°C and those cured at 200°C do not exceed 2%. The transverse ultimate tensile strength σ ^ult._yy is more sensitive to different cure cycles. A 19% increase in σ ^ult._yy is recorded between laminates cured for 480 min at 160 and those cured for 40 min at 200°C (Table included in Fig. 11).

Fig. 11

Results of tensile tests and acoustic emission on [90°₁₆] samples. The table gives moduli E_yy and ultimate tensile strengths σ ^ult_yy average values depending on curing dwell temperature and duration

Whatever the cure cycle is, all the acoustic signals remain below 60dB. As expected, this shows that [90°₁₆] samples failure occurs without any fibre breakage and in addition without any fibre/matrix debonding if it is hypothesised that 65dB corresponds to this phenomenon (according to Fig. 9 results [71, 72]).

As a summary, the transverse ultimate tensile strength σ ^ult._yy appears to be higher for laminates cured at 200°C than for those cured at 160°C while the residual stresses (from a micromechanical point of view) should be lower in laminates cured at 160°C than in those cured at 200°C.

An explanation could be found in refs. [63, 64, 73] on a micromechanical level. Effectively, as shown in ref. [73], when the critical normal stress on fibre/matrix interface is small, the ultimate tensile strength of [90°_n] laminates increases together with the level of residual curing stresses. This is what it can be seen with our results on [90°₁₆] laminates which confirm the conclusions of the purely analytical modelling of T. Ishikawa on off-axis strength of U.D. laminates [73].

L.E. Asp et al. [64] have also studied (by finite elements) the effects of residual stresses upon the transverse tensile behaviour of glass/epoxy composites on a micromechanical level. Using a dilatational energy density criterion, these authors showed that under certain modelling conditions (choice of the representative volume element) and for sufficiently high fibre volume fractions (i.e. at least V _f  = 60%), the presence of residual stresses induced an increase in laminate transverse ultimate tensile strength. Owing to the dilatational energy density criterion used, it was shown that under transverse tensile loading matrix crack initiated at fibres poles perpendicular to load direction.

More recently, some authors [63] have been performed a micromechanical study of residual stresses—through a theoretical study (done by 2D finite elements) and using the maximum principal stress failure criterion—on a micromechanical unit cell. For a unit cell (the representative volume element was a single fibre surrounded by a square of matrix) submitted to a tensile load (i.e. a transverse tensile load on a U.D. ply), the increases in the level of residual stresses resulted in postponing the occurrence of failure. Thus the U.D. composite exhibited a growing ultimate transverse tensile strength. This phenomenon was attributed to an increase in the compressive residual stress state in the matrix surrounding the fibre [63]. Once again, as with T. Ishikawa conclusions, these theoretical results seem to correspond to what is experimentally observed here. Nevertheless, in L.G. Zhao [63] and Y. Zhang [74] work, when the unit cell undergoes residual stresses, the external tensile loading (⊥ to fibre axis) initiates a damage located at fibre/matrix interface (debonding) which propagates into the matrix (cracking) when the external loading is sufficiently high. In absence of residual stresses the site of this damage remains located in the matrix [63]. Now, from an experimental point of view if any fibre/matrix debonding had took place some acoustic signals higher than 65dB would have been recorded. However acoustic emission diagrams (Fig. 11) do not exhibit any signal equal to or higher than 65dB the magnitude at which fibre/matrix debonding occurs!

Mechanical behaviour of [±45°₄]_s laminates

As shown by results reported in the table located in Fig. 12 (left side), shear modulus and ultimate strength are higher for laminates cured at 160°C than for those cured at 200°C. In that case, the mechanical response of the [±45°₄]_s samples is dominated by shear effects (τ_xy shear stress in principal material coordinates—see ref. [1]) and, as shown by the stress versus strain curves in Fig.12, large inelastic strains.

Fig. 12

Results of tensile tests and acoustic emission on [45°₄]_s samples. The table gives moduli G_xy and ultimate strengths τ ^ult_xy average values depending on curing dwell temperature and duration

As expected and shown in the right side of Fig. 12 the laminate failure occurs without any fibre breakage, since none of the acoustic signals reaches and goes beyond 90dB. Let’s now assume (as previously made) that for our laminates a 65dB magnitude [71, 72] effectively corresponds to fibre/matrix debonding. In that case, for laminates cured at 160°C or at 200°C, the very first fibre/matrix debondings occur respectively for a 105 and a 90 MPa mechanical tensile stress (Fig. 12 right side). Consequently, this shows that angle-ply tensile test is the loading case for which the influence of residual curing stresses upon the laminates ultimate strength appears the more clearly. Indeed, increasing the residual stress level at +45°/−45° interfaces by changing the curing conditions results in a weakening of [±45°₄]_s laminates, as shown by the experimental results (Fig. 12).

Furthermore, referring to Fig. 9, enables to see that acoustic signals for which the magnitude is higher than 80dB correspond to the propagation of delamination between consecutive plies. As shown in Fig. 12, the very first signals exhibiting a 80dB magnitude were recorded for tensile stress of 125 MPa for laminates cured at 160°C versus 90 MPa for those cured at 200°C.

On a micromechanical level, to our knowledge only L.G. Zhao et al. have studied the effects of residual stresses upon the shear behaviour of a unit cell by finite elements [63]. Our experimental results perfectly meet their conclusions: residual stresses play a detrimental role for shear loading (ultimate shear strength).

Synthesis of main results and comparison between ultimate tensile strengths and a failure criterion

Micromechanical level

The results obtained during the mechanical tests are synthesised in Table 3 for a composite unidirectional ply.

Table 3 Synthesis of mechanical characteristics of a unidirectional ply as a function of curing conditions

• Longitudinal tensile behaviour: the ply ultimate tensile strength slightly increases (σ ^ult._xx +17%) when increasing the level of residual stresses (see “Process-induced stresses on a micromechanical level” section and Fig. 15).

• Transverse tensile behaviour: the ply ultimate tensile strength increase when increasing the level of residual stresses (σ ^ult._yy +14%). As theoretically shown in ref. [63] on representative volume elements of glass-epoxy composites, increasing residual stresses results in the postponement of matrix crack initiation and propagation when the composite is submitted to an external transverse tensile load.

• Shear loading: the increase of residual stresses is detrimental for the U.D. composite shear strength which decreases here by more than 30%. In that case the superposition of residual stresses (see $\sigma_{\theta \theta }^m$ Fig. 15) and external shearing load facilitates the initiation and propagation of damage along the fibre/matrix interface [63].

Acoustic emission

Figure 13 gives a summary of the main fact recorded by acoustic emission. It concerns the propagation of delamination between plies of [±45°₄]_s samples. For laminates cured for 40 min at 200°C, acoustic signals higher than 80dB synonymous of propagation of delamination appear under a tensile stress 28% lower than the stress necessary to induce the same effects in laminates cured for 480 min at 160°C.

Fig. 13

Summary of acoustic emission main fact recorded during tensile tests

Ply level: residual stresses / classical failure criterion

If it is now assumed that the properties determined on the laminates cured for 120 min at 180°C (i.e. according to mrcc) can be taken are reference ones, it is thus possible to plot a “failure envelope” under tensile loading using a common failure criterion such as Hill’s Criterion. The Hill’s criterion was settled using the properties of laminates cured fro 120 min. at 180°C (i.e. mrcc). This enables to clearly show the effects of process-induced stresses upon the ultimate tensile strength of a composite laminate (Fig. 14).

Fig. 14

Experimental ultimate tensile stresses depending on curing conditions and as a function of plies orientation compared with the Hill’s failure criterion

Determination of theoretical process-induced stresses in unidirectional laminates

Process-induced stresses on a micromechanical level

It is important to mention that the aim of these calculations on a micromechanical level has never been the set-up of one or other refined modelling. The idea is simply to get information about the distribution and the level of residual stresses in order to analyse the effects of these stresses upon mechanical behaviour of UD laminates. To this end, the computations were made according to ref. [1] modelling (see details in Appendix 1). The fibres properties (Table 4) are given according to Fig. 15 coordinates. The fibres are considered to be transversely isotropic and to have thermoelastic behaviour. The fibres transverse coefficient of thermal expansion (CTE) was determined using an inverse calculation presented in Appendix 2. The epoxy matrix properties used for that computation are also given in Table 4. It is considered that the epoxy matrix exhibits two CTE: for temperatures lower or higher than its T_g. Matrix properties were directly determined of samples made from unreinforced resin films. The matrix behaviour is considered to be thermoviscoleastical and the matrix modulus given in Appendix 3 as functions of time and temperature.

Table 4 Carbon fibre and epoxy matrix properties (z denotes fibre axis)

Fig. 15

Micromechanical modelling and distribution of theoretical process-induced stresses on a micromechanical level

The radius of the matrix cylinder R _m around a single fibre of radius R _f  = 3.5 μm (it is assumed that the fibre has an infinite length) shown in Fig. 15 was determined as a function of unidirectional composite fibre volume fraction given in Table 2 (Vf = 65.8%):

$$ {R_m} = \frac{{{R_f}}}{{\sqrt {{{V_f}}} }} $$

(3)

As shown by Fig. 15, the preponderant stresses in the micromechanical elementary representative volume are the radial σ_rr and the hoop σ_θθ stresses which are both compressive in the fibre and the radial σ_rr stress which is also compressive in the matrix. Their levels increase when increasing the curing dwell temperature. Effectively, it can be seen that the radial stress σ_rr in fibre and in matrix (at fibre interface) reach −145 MPa for laminates cured for 40 min at 200°C versus −82 MPa for those cured for 480 min at 160°C. Since the preponderant residual stresses are compressive, a better fibre / matrix adhesion can be expected. So, when these residual stresses increase, the fibre/matrix adhesion should theoretically be higher. In other words this means that the ultimate tensile strengths σ ^ult._xx and σ ^ult._yy of UD laminates should theoretically increase when increasing the level of residual stresses in UD laminates. This is what observed experimentally here and theoretically shown in refs. [63, 64].

Concluding remarks

A few experimental studies can be found in literature upon the effects of process-induced stresses (or residual stresses) on composites mechanical properties. The main problem remain that the ways used to get laminates with various level of residual stresses also induce some other modifications in composites properties (such as T_g, Vf%, …).

The present work was intended to define the ways to manufacture laminates undergoing various levels of residual stresses while keeping their physical properties constant. This enables to make sure that the changes recorded in laminates mechanical properties were not due to alteration to other properties but to residual stresses effects.

On the basis of a cure kinetics modelling, isoconversion diagrams have enable different processing (curing) conditions to be designed in order manufacture laminates undergoing different levels of process-induces stresses. A check of laminates physical properties has shown that for a given kind of laminate (stacking sequence) the three manufacturing routes did not result in changes in their physical properties.

Consequently, none of the changes recorded in their mechanical properties was attributed to modification in their physical properties (e.g., fibres volume fraction, degree of cure…). Measurements of the out-out-plane deflection of unsymmetrical laminates have shown that the three curing conditions were able to generate different levels of process-induced stresses.

Beyond the definition of processing conditions for obtaining laminates with various levels of residual stresses, mechanical tests were performed. As it has been seen in Table 3, the average ultimate tensile strength of [0°₁₆] and [90°₁₆] laminates increases when increasing the curing dwell temperature. Mechanical tests revealed that residual stresses were beneficial for transverse tensile strength of U.D. laminates—as theoretically demonstrated in refs. [63, 64]—and also for longitudinal tensile strength.

The use of acoustic emission during tensile tests has enabled to put in evidence the influence of processing conditions upon the propagation of delamination between consecutive plies in [45°₄]_s laminates. As reinforced by results stemming from theoretical studies [63, 64] it can be stated that the decreasing in the stress required to propagate the delamination is a consequence of process-induced stresses which theoretically growth when the curing temperature was increased. In that case residual stresses seem to be highly detrimental for mechanical strength.

In order to bring a complementary light to these facts, the level of process-induced stresses were determined using a simple analytic modelling in which the main difficulty lays in the determination of the transverse properties of carbon fibres. This modelling shows that increasing the curing dwell temperature while keeping a constant degree of cure (by reducing curing dwell duration) enables to generate higher levels of radial and hoop process-induced stresses on a micromechanical level in both fibres and matrix. When now comparing these elements with the results obtained during the tensile tests it can be said—since everything has been made to avoid any change in material physical properties—that on a micromechanical level the higher the process-induced stresses are, the higher the ultimate strengths will be. Effectively, this is what can be seen in Table 3.

Nevertheless, a more accurate micromechanical modelling should be made in a future work. It will take advantage of the numerous experimental results obtained here.

Appendices

Appendix 1: Relations for the calculation of process-induced stresses on a micromechanical level

Stresses in the fibre (f) are given by:

$$ \left\{ {\begin{array}{*{20}{c}} {{\sigma_{zz}} = 2 \cdot {C_{11}} \cdot {\chi_f} + \frac{{{C_{33}} \cdot {\omega_f}}}{{{C_{13}} + {G_{13}}}}} \\{{\sigma_{rr}} = {\sigma_{\theta \theta }} = \left( {{C_{11}} + {C_{12}}} \right) \cdot {\chi_f} + \frac{{{C_{13}} \cdot {\omega_f}}}{{{C_{13}} + {G_{13}}}}} \\{{\sigma_{r\theta }} = {\sigma_{rz}} = {\sigma_{\theta z}} = 0} \\\end{array} } \right. $$

(A-1)

Stresses in the matrix (m) cylinder are given by:

$$ \left\{ {\begin{array}{*{20}{c}} {{\sigma_{zz}} = 2 \cdot {\lambda_m} \cdot {\chi_m} + \frac{{\left( {{\lambda_m} + 2{\mu_m}} \right) \cdot {\omega_m}}}{{{\lambda_m} + {\mu_m}}}} \\{{\sigma_{rr}} = 2 \cdot \left( {{\lambda_m} + {\mu_m}} \right) \cdot {\chi_m} + \frac{{{\lambda_m} \cdot {\omega_m}}}{{\left( {{\lambda_m} + {\mu_m}} \right)}} - \frac{{2 \cdot {\mu_m} \cdot {\varsigma_m}}}{{R_m^2}}} \\{{\sigma_{\theta \theta }} = 2 \cdot \left( {{\lambda_m} + {\mu_m}} \right) \cdot {\chi_m} + \frac{{{\lambda_m} \cdot {\omega_m}}}{{\left( {{\lambda_m} + {\mu_m}} \right)}} + \frac{{2 \cdot {\mu_m} \cdot {\varsigma_m}}}{{R_m^2}}} \\\end{array} } \right. $$

(A-2)

With: χ _f , ω _f , constants (fibre); C _ij , G _ij , stiffness coefficients of carbon fibre; λ _m , μ _m , Lamé coefficients of matrix and χ _m , ω _m , ζ _m , constants (matrix).

For matrix: σ_rθ  = σ_θz  = σ _rz  = 0

Appendix 2: Inverse determination of carbon fibres transverse coefficient of thermal expansion (CTE)

In order to determine the transverse coefficient of thermal expansion of a carbon fibre, the unidirectional ply was divided into 2 materials. As shown in Fig. 16, its thickness h, was separated into an isotropic material made of matrix (thickness h_m) and a transversely isotropic material corresponding to carbon fibre (thickness h_f). The following equations (Eqs. A-3 to A-XX) show how aft can be thus determined, provided that Vf% is known:

Fig. 16

The unidirectional composite ply (a) and its equivalent multi-material made of a layer of matrix and a layer of carbon fibre material (b)

$$ h = {h_m} + {h_f} $$

(A-3)

Where:

$$ {h_f} = {V_f} \cdot h $$

(A-4)

And:

$$ {h_m} = \left( {1 - {V_f}} \right) \cdot h = {V_m} \cdot h $$

(A-5)

The changes in thicknesses Δh due to temperature differences are given by:

$$ \Delta h = \Delta {h_m} + \Delta {h_f} $$

(A-6)

With:

$$ \left\{ {\begin{array}{*{20}{c}} {\Delta h = {\alpha_2} \cdot h \cdot \Delta T} \\{\Delta {h_m} = {\alpha_m} \cdot {h_m} \cdot \Delta T} \\{\Delta {h_f} = \alpha_f^t \cdot {h_f} \cdot \Delta T} \\\end{array} } \right. $$

(A-7)

In Eq. (A-7): α₂, transverse CTE of unidirectional ply (cf. Table 1); α_m, CTE of matrix, α ^t_f , transverse CTE of carbon fibre.

$$ {\alpha_2} \cdot h \cdot \Delta T = {\alpha_m} \cdot {h_m} \cdot \Delta T + \alpha_f^t \cdot {h_f} \cdot \Delta T $$

(A-8)

$$ \Rightarrow \alpha_f^t = \frac{{{\alpha_2} - {\alpha_m} \cdot {V_m}}}{{{V_f}}} $$

(A-9)

Lastly, if not available, the CTE of matrix α_m can be obtained from various modelling such as the one proposed by C.C. Chamis In: Simplified composite micromechanics equations for Hygral, Thermal and Mechanical properties. SAMPE Quarterly, 15(3): 14–23 (April 1984):

$$ {\alpha_1} = \frac{{E_1^f \cdot \alpha_1^f \cdot {V_f} + {E_m} \cdot {\alpha_m} \cdot {V_m}}}{{E_1^f \cdot {V_f} + {E_m} \cdot {V_m}}} $$

(A-10)

$$ {\alpha_2} = \alpha_2^f \cdot \sqrt {{{V_f}}} + \left( {1 - \sqrt {{{V_f}}} } \right) \cdot \left( {1 + \frac{{{V_f} \cdot {\nu_m} \cdot E_1^f}}{{{E_1}}}} \right) \cdot {\alpha_m} $$

(A-11)

Where V_f is the composite fibres volume fraction, E ^f_l , the fibres longitudinal (// to axis) tensile modulus and E_l the unidirectional ply tensile modulus.

Appendix 3: Thermoviscoleastic behaviour of unreinforced matrix

The unreinforced epoxy matrix samples were cured according to mrcc (120 min. at 180°C). After curing they were submitted to an accelerated thermoviscoelastic characterisation procedure in order to get the parameters of behaviour. The matrix was considered to be isotropic and the visoelastic behaviour to be linear. This procedure has consisted in dynamical thermal mechanical analyses carried out on a Polymer Lab MKII DMTA between 30 and 280°C (ramp at 3°C/min) at 8 different frequencies: 0.03, 0.1, 0.3, 1, 2, 5 10 and 50 Hz under a uniaxial tensile loading. Static and dynamic forces were respectively set at 1 N and 0.3 N. This enables to get a master curve describing the changes in matrix modulus E(T,t) as a function of Log(a_T) (Fig. 17). Log (a_T) is itself a function of temperature T (Fig. 18). The matrix master curve was obtained by applying the time-temperature superposition principle (Eq. A-12) (see refs. [27, 70]) with 180°C taken as the reference temperature (T_R) since the largest changes in matrix storage modulus E’ were recorded at 180°C. In the process towards the building of a master curve a_T is the horizontal shift factor either given by an Arrhenius-type Eq. (A-13) or a WLF-type Eq. (A-14) depending on considered temperature:

Fig. 17

Changes in –Log(aT) as a function of temperature

Fig. 18

Master curve of the unreinforced epoxy matrix. Tensile modulus as a function of Log(a_T)

$$ E\prime \left( {{t_1},{T_1}} \right) = E\prime \left( {{t_2},{T_R}} \right) $$

(A-12)

$$ \log {a_T} = \frac{{\Delta {H_a}}}{{2,303 \cdot R}} \cdot \left( {\frac{1}{T} - \frac{1}{{{T_R}}}} \right)\quad when\quad T < {T_R} $$

(A-13)

$$ log\;{a_T} = \frac{{ - c_1^R \cdot \left( {T - {T_R}} \right)}}{{c_2^R + \left( {T - {T_R}} \right)}}\quad when\quad {\hbox{T}} > {{\hbox{T}}_{\rm{R}}} $$

(A-14)

In Eqs. (A-13) and (A-14): $\Delta {H_a}$ is activation energy, R is the universal gas constant and $c_1^R$ and $c_2^R$ are constants relatives to T _R . They can be determined from Fig. 18 experimental results.