USE OF MODEL FREE KINETIC LIFETIME VALUES TO EVALUATE MECHANICAL PERFORMANCE OF A HIGH TEMPERATURE POLYIMIDE COMPOSITE

J.R. Williamson, C.Semprimoschnig, P. Simon-Boutemen, L. Levan, M. van Eesbeek

TEC-QEM, ESTEC, ESA, Postbus 299,2200 AG, Noordwijk zh, The Netherlands, +31 715 656334, Jason.williamson@esa.int,

ABSTRACT

Lifetime predictions for a high temperature Ube Industries composite were made using thermogravimetric analysis (TGA) and advance model free kinetics (AMFK). These techniques provide a prediction for the isothermal times and temperatures required to obtain a certain level of degradation of the polymer in terms of mass loss. In the case of carbon fibre composites the majority of the degradation is from the resin. This data on its own provides an indication of the survivability of the material at a given temperature however it does not provide a link to changes in other important properties such as the mechanical performance. However if it is assumed that the mechanism for mass loss is the primary degradation mechanism then the AMFK data can be utilised to make predictions of the times to achieve a certain mass loss at higher, accelerated temperatures with respect to the lifetime temperatures. These values can then be utilised to develop temperature programmes for mechanical test samples which equate to a known mass loss and therefore a lifetime datapoint. Coupled with the measurement of any changes in the mechanical properties of the material following exposure a prediction can then be made for a given time-temperature frame. This script presents an outline of the work performed as well as results from the mechanical test campaign. It goes on to evaluate the lifetime estimates and compare them with predictions derived by applying a TTS (time-temperature superposition) evaluation.

1 INTRODUCTION

1.1 Background

A number of current, and future ESA missions (Venus Express, Solar Orbiter, BepiColombo) are to encounter high temperature environments. Whilst thermal management and design will address some of this the need for materials able to withstand higher temperatures is a fundamental necessity for a successful mission outcome . One of the areas for consideration is in the use of composite materials able to withstand high temperatures without significant loss of performance. The material investigated in this script is a phenylethynyl termindated imide composite capable of elevated temperature operation (300°C) for long periods.

1.2 Materials

The material is an Ube industries PETI-plate composite panel, grade HA-10. The panel is a 10 ply plain weave carbon fibre composite approximately 2mm thick. The resin is a phenylethynyl termindated imide. These materials were originally developed under NASA’s high speed civil transport (HSCT) programme in the late 1990’s. Since then ongoing development has raised operating temperatures to above 300°C by increasing the glass transition temperature[1][2][3]. The resin has a low melt viscosity that allows it to flow well under low pressure at elevated temperatures as well as good melt stability allowing it to infiltrate carbon fibre structures. The formation chemistry involves the reaction of 2,3,3’,4’-biphenyl tetracarboxylic dianhydride (a-BPDA), a mixture of two aromatic diamines; 1,3-bis(4-aminophenoxy) benzene and 1,3-diaminobenzene and phenylethynyl phthalic anhydride (PEPA) as an end-capping agent[3].

Fig. 1: Composition of 330°C PETI resin[3]

1.2 Model Free Kinetics

Lifetime predictions have been derived from a model free kinetics (MFK) iso-conversional approach developed by Vyazovkin [4]. This utilises a model-free kinetic analysis to establish Arrhenius parameters thus enabling kinetic predictions based upon the effect of variables such as temperature, pressure and concentration on the reaction rate.

Thermal decomposition of a solid material such as a polymer involves the chemical breakdown of the material, transportation and removal from the specimen. All of these processes will be kinetically driven and therefore have a minimum activation energy (Ea) required to allow the reaction to initiate.

Arrhenius developed a relationship for the reaction rate based upon the reaction temperature (T) and activation energy for simple order reactions:

−=

RT

EATk aexp)(

where k(T) is the temperature dependent rate constant, A is a pre-exponential factor, R is the universal gas constant, t is time and, α is the degree of conversion or extent of reaction.

From the Arrhenius equation, it can be seen that the reaction rate and hence time to completion is dependent on both the activation energy of the reaction and the temperature. This fact forms the basis for analysis and prediction of isothermal reaction rates utilising non-isothermal linear heating programs.

Solid state kinetics can be generalised to an equation form which takes into account the dependence of the reaction rate on the extent of reaction:

( ) ( )ααfTk

dt

d =

where .f(α) is the reaction model – a function describing the dependence of reaction rate on the extent of reaction. The reaction model f(α) for solid state reactions such as mass loss is often empirically based. For isothermal conditions this equation can be expressed in its integral form; g(α):

( ) ( )∫ =≡α

αα

α0 )(

1tTkd

fg

For non-isothermal conditions, time dependence can be eliminated from the equation by introducing a constant heating rate:

dt

d

dT

d αβ

α 1=

where:

dt

dT=β

thus the integral can now take the form of:

( ) ( )∫∫ =≡T

dTTkdf

g00

1

)(

1α

βα

αα

and introducing the Arrhenius equation by substituting for k(T) gives:

( ) ∫

−=T

a dTRT

EAg

0exp

βα

This equation provides the global reaction kinetics from three pieces of information; the reaction model and the two Arrhenius parameters. These three items are sometimes referred to as the kinetic triplet[1]. The time required to achieve any particular extent of reaction can be determined for any chosen value of temperature under isothermal conditions by rearranging equation (3) or, for any chosen heating rate β by rearranging equation (7). Further these values can be obtained as a function of conversion without any knowledge of the specific reactions or the various kinetic processes taking place hence its “model-free” title.

Kinetic predictions such as time to reach a specified conversion or reaction rate at some reference temperature cannot be directly made by equations (2) and (3)[4] since activation energy will vary with the extent of reaction. This can be resolved by assuming the partial kinetic triplets remain the same when changing temperature. Using this assumption equation (3) and equation (7) can be equated with a given conversion. Simultaneously solving these two equations yields[1]:

dTRT

E

RT

Et

T

−

−= ∫ α

αα

α

β 0

0

exp.

exp

1

where Tα is an experimental value of temperature which corresponds to a given conversion at the heating rate β. From equation (8) the time at which a given conversion will be reached at an arbitrary temperature T0 can be determined. Similarly other temperature-conversion-heating rate functions can be established without a knowledge of either the reaction model or the pre-exponential factor.

(1)

(4)

(5)

(7)

(8)

(2)

(6)

(3)

2 PROCEDURE

2.1 TGA and AMFK

Specimens were analysed using thermogravimetric analysis (TGA). TGA was carried out with a Mettler-Toledo TGA/SDTA851e operating with the STARe software using a heating programme from 25°C up to 1000°C at different ramp rates ranging from 2°C.min-1 up to 50°C.min-1. The furnace was continuously purged with nitrogen gas at a flow rate of 70ml.min-1. Buoyancy and baseline corrections were made using an equivalent empty pan run using the same method. All tests were performed in accordance with ISO specification 11358[5].

Five different heating rates and a single isothermal test were performed to enable kinetic modelling and lifetime prediction for the polyimide composite using the STARe model free kinetics analysis module. Where appropriate the thermogram obtained from one of the heating rates was discarded if necessary to facilitate analysis. All of the resultant thermograms were normalised with respect to sample mass and plotted against sample temperature.

Analysis of the results was conducted on the resultant normalised mass loss-temperature curves. The derivative of each curve was first obtained to identify suitable analysis limits, the curves were cut to this frame (or no frame was utilised), then the conversion curves were derived for each heating rate across these limits. Using the conversion curves the activation energy was determined as a function of the conversion using Vyazovkin’s model free kinetics approach[4]. From the activation energy function time-temperature-mass loss curves were determined.

An advanced MFK (AMFK) technique was used. AMFK utilises a differential approach for prediction of the activation energy function compared to an integral approach for the MFK analysis. The AMFK technique generally results in improved lifetime predictions particularly at low conversion values. A number of isothermal runs were conducted at 500°C.

2.2 Mechanical Testing

Two types of mechanical tests were performed on exposed samples; interlaminar shear tests (ILS) and three point bend flexural tests. ILS tests (see Fig. 2) were performed in accordance with [6] and three point bend tests (see Fig. 3) were done using the Class IV specimens of [7].

Fig. 2. Interlaminar shear test

Fig. 3. Three point bend test

3 RESULTS AND DISCUSSION

The TGA data and the resulting AMFK iso-conversion predictions are shown in Fig. 4 and Fig. 5. From the model isothermal predictions were made for the two exposure temperatures (see Fig. 6 and Fig. 7). In addition to the thermal analysis and mechanical tests performed the mass of the test samples was accurately monitored and their correlation with the predictions can also be seen in Fig. 7. A very good correlation was obtained at 350°C and for the 395°C test temperature the predictions were slightly lower than the measured values. Despite this difference the correlation was considered sufficiently good for the prediction to be accepted. The difference is possibly associated with the presence of vacuum with the 395°C whereas the 350°C campaign was performed under nitrogen. The latter more closely matches the TGA conditions. The atmospheres differed because the remaining TEC-QEM high temperature vacuum facilities were unavailable and therefore the 350°C exposure campaign was performed in a standard nitrogen purged oven.

Step -10.5518 % -4.1595 mg

%

0

20

40

60

80

100

°C100 200 300 400 500 600 700 800

Activation Energy

kJmol̂ -1

0

200

400

%-5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

%

60

70

80

90

100

min0 200 400 600 800 1000 1200 1400 1600 1800 2000

JRW TGA PETI plate BC MFK v1-2a 13.08.2009 11:06:57

Fig. 4. TGA data and AMFK prediction for the activation energy function

At each test point mechanical test samples were removed from the environmental chambers for evaluation. The test results are presented in Table 1 and Table 2 along with the exposure durations. Utilising the mechanical data, exposure durations and determining the mass loss at these particular points enables the generation of a set of isopleths to be generated. The resulting isopleths are shown in Fig. 8. Assuming that the degradation of the mechanical properties tracks the mass loss then the isopleths in Fig. 8 can be used to generate empirically the properties of a material for a range of temperature/time couplets. An initial trial of this has been performed using the 350°C and 395°C temperatures (see Fig. 8). From Fig. 8 sets of temperature time durations which should correspond to a respective mechanical performance can be empirically derived. These results would then be based on a single - or in this case dual – dataset. Fig. 9 - Fig. 14 show the original and shifted results based upon these assumptions for various mechanical properties.

Activation Energy

kJmol̂ -1

0

200

400

%20 40 60 80

h

10 4̂

10 3̂

10 2̂

10 1̂

10 0̂

10^-1

°C300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490

alpha(100%)

alpha(80%)

alpha(60%)

alpha(40%)

alpha(30%)

alpha(20%)alpha(15%)alpha(10%)

alpha(5%)

alpha(1%)

STARe SW 9.20Lab: METTLER

Fig. 5. AMFK analysis

0 5000 10000 15000 200000

2

4

6

Heraeus (350°C) HITES (395°C) AMFK 350°C AMFK 395°C

Mas

s Lo

ss (

%)

Time (hours)

Fig. 6. Correlation of AMFK predictions with mass loss measurements

0 600 12000

1

2 Heraeus (350°C) HITES (395°C) AMFK 350°C AMFK 395°C

Mas

s Lo

ss (

%)

Time (hours)

Fig. 7: Detailed view of AMFK/mass loss correlation

Activation Energy

kJmol̂ -1

0

100

200

300

400

500

%20 40 60 80

HITES TP3

HITES TP2

HITES TP1

Heraeus TP3

Heraues TP2

Heraeus TP1

h

10 5̂

10 4̂

10 3̂

10 2̂

10 1̂

10 0̂

°C300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490

STARe SW 9.20Lab: METTLER

Fig. 8. AMFK Isopleths corresponding to the Heraeus and HITES test points.

Table 1. Mechanical data after exposure to 350°C

Time (h) τmax (MPa) SD Fmax (N) SD Ef (GPa) SD F (N) @

1.5xh0 SD

Control 0 66.59 2.89 354.85 24.94 55.1 1.3 137.76 7.13

TP1 573.7 58.06 4.77 291.82 12.37 54.0 2.1 143.29 4.57

TP2 485.0 56.4 4.15 280.69 3.73 52.3 0.5 141.92 3.88

TP3 470.3 50.5 2.18 244.19 11.45 51.2 2.2 130.64 6.78

Table 2. Mechanical data after exposure to 395°C/10-5mbar vacuum

Time (h) τmax (MPa) SD Fmax (N) SD Ef (GPa) SD F (N) @

1.5xh0 SD

Control 0 66.59 2.89 354.85 24.94 55134 1268 137.76 7.13

TP1 573.7 37.73 3.26 243.95 28.42 50904 2570 129.71 6.18

TP2 485.0 35.66 3.28 184.6 19.31 54692 665 124.53 2.36

TP3 470.3 35.42 1.59 151.1 10.43 50222 3015 122.81 5.12

200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

300

400

350°C 395°C

Fai

lure

Loa

d (N

)

Time (hours)

Fig. 9. Failure loads after exposure to 350°C and 395°C

1 10 100 1000 10000 1000000

50

100

150

200

250

300

350

400

350°C 395°C Fmax using AMFK time estimate

Fai

lure

Loa

d (N

)

Time (hours)

Fig. 10. Shifted Failure loads as per the AMFK isopleth

200 400 600 800 1000 1200 1400 1600 1800 20000

20

40

60

80

100

395°C 350°C

Fle

xura

l Mod

ulus

(G

Pa)

Time (hours)

Fig. 11. Flexural moduli after exposure to 350°C and 395°C

1 10 100 1000 10000 1000000

20

40

60

80

100

350°C 395°C Flexural modulus using AMFK time estimate

Fle

xura

l Mod

ulus

(G

Pa)

Time (hours)

Fig. 12. Shifted modulii loads as per the AMFK isopleth

200 400 600 800 1000 1200 1400 1600 1800 20000

20

40

60

80

100

350°C 395°C

ILS

(M

Pa)

Time (hours)

Fig. 13. ILS strengths after exposure to 350°C and 395°C

1 10 100 1000 10000 1000000

20

40

60

80

100

350°C 395°C ILS using AMFK time estimate

ILS

(M

Pa)

Time (hours)

Fig. 14. Shifted ILS strengths as per the AMFK isopleth

Evaluation of the shifted data given in Fig. 9 - Fig. 14 suggests that some correlation exists between the mass loss and the change in mechanical performance however with only two data sets for evaluation the empirical trends are not sufficiently clear for a high level of confidence in utilising this approach for long term performance. For instance the trends in the failure loads (Fig. 9 and Fig. 10) can be extrapolated using the isopleths to derive a general trend however a much more acceptable trend could also be obtained using some form of time-temperature superposition (TTS) approach where the 395°C data is shifted along the time scale to around 2000 hours. Further the shifts on the temperatures utilised to date provide estimates out to 18.3 years at 350°C making verification difficult. Similar comments can also be made for the flexural modulus and the interlaminar shear strength.

Since the shifts based on mass loss calculations alone do not generate a good correlation when considered in terms of their mechanical performance it seems clear that the changes in mechanical performance are not solely driven by mechanisms which evolve mass as a by-product suggesting that additional chemical or physical effects take place within the composite to influence the mechanical properties. These effects do not always result in a significant mass loss and therefore cannot be estimated by this approach.

A comparison of the empirical predictions using an AMFK approach and a TTS approach for the failure loads are shown in Fig. 15 where it can be seen that the 18.3 year life estimate differs significantly from the 105 day estimate obtained if a TTS approach is utilised. From this data it can be seen that the use of equivalency from the AMFK mass-loss isopleths does not transpose directly for use as acceleration factors for other properties such as mechanical degradation. The primary reason for this is likely to be the lack of any direct relationship between the level of mass loss

observed and the mechanical properties of the composite.

1 10 100 1000 10000 1000000

50

100

150

200

250

300

350

400

350°C 395°C Fmax using AMFK time estimate Fmax using TTS estimate

Fai

lure

Loa

d (N

)

Time (hours)

Fig. 15. Comparison of AMFK and TTS shift effects using Failure load data.

(a)

(b)

Fig. 16. Damage formation following exposure to 395°C/10-5mbar vacuum, (a) before, (b) after.

A brief SEM evaluation was performed on reference and aged specimens. Fig. 16 shows the formation of

surface cracks in the PETI material following thermal exposure. It seems likely that the formation of this damage following thermal exposure is what causes the decrease in mechanical performance.

4 CONCLUSIONS

Evaluation of the data provided a useful investigation indicating the changes in mechanical performance as well as the TGA response of the polyimide composite material. However utilising model free kinetic predictions to extrapolate lifetimes was unsuccessful. Despite this it is possible to perform a TTS analysis on the failure load data and, with additional test temperatures master-curves could be derived for the materials performance.

5 REFERENCES [1] Connell J.W. etal., High Temperature Transfer

Moulding Resins: Preliminary Composite Properties of PETI-375, NASA Technical Reports Server, http://ntrs.nasa.gov/search.jsp, 2004.

[2] Connell J.W. etal., High Temperature Transfer Moulding Resins: Status of PETI-298 and PETI-330, NASA Technical Reports Server, http://ntrs.nasa.gov/search.jsp, 2003.

[3] Pater R.H., Curto P.A., Advanced Materials For Space Applications, NASA Technical Reports Server, http://ntrs.nasa.gov/search.jsp, 2005.

[4] Vyazovkin S., Wight C.A., Kinetics in Solids, Annu. Rev.Phys. Chem 1997 48:125-49.

[5] ISO Specification 11358, Plastics – Thermogravimetry (TG) of Polymers – General Principles, International Standards Organisation, 1997

[6] ISO Specification 14130, Fibre-reinforced plastic composites – Determination of apparent interlaminar shear strength by short-beam method, International Standards Organisation, 1997

[7] ISO Specification 14125, Fibre-reinforced plastic composites – Determination of flexural properties, International Standards Organisation, 1998