Accelerated Testing Methodology for Long Term Durability of CFRP

Transcription

1 IFREMER-ONR Workshop on Durability of Composites in a Marine Environment August 23 24, 22 IFREMER Centre, Nantes, France Accelerated esting Methodology for Long erm Durability of CFRP Masayuki Nakada*, Shuhei Hara**, Yasushi Miyano* * Materials System Research Laboratory, Kanazawa Institute of echnology Ishikawa, Japan ** Graduate School, Kanazawa Institute of echnology Ishikawa, Japan

2 Necessity of accelerated testing Data collection by accelerated testing Durability design Development of high reliable structures he accelerated testing methodology (AM should be established for the prediction of long-term life of polymer composites.

3 Master curve of static strength of CFRP versus time to failure at reference temperature log σ f (t, σ f = log f A (P f N f =/2 log f B (D * t log t σ fo : Static strength at reference time determined by types of fiber and weave, volume fraction, load direction and others f A : Scatter of strength as a function of failure probability P f determined by types of fiber and weave, volume fraction, load direction and others f B : ime-temperature dependent strength determined by viscoelasticity of matrix resin D* 2

4 Formulation of static strength of CFRP based on AM he long-term static strength exposed to the actual loading where the temperature and load change with time can be shown by the following equation based on the conditions of A and B. ( t ( ', D* ', log σ f ( Pf, t ', = log σ f ( t ', + log ln ( Pf nr log α Dc t he first term shows the scale parameter for the strength at the reference temperature and the reduced reference time t. he second term shows Weibull distribution as the function of failure probability P f. (Condition A he third term shows the variation by the viscoelastic compliance D* of matrix resin which is determined by the creep compliance D c of matrix resin and temperature and load histories of CFRP. (Condition B Condition A: he failure probability is independent of temperature and load histories. Condition B: he time and temperature dependence of strength of CFRP is controlled by the viscoelasticity of matrix resin. herefore, the time-temperature superposition principle for the viscoelasticity of matrix resin holds for the strength of CFRP. 3

5 Condition A Failure probability to be independent of temperature Static (R.. Creep (R.. Static (5 o C Creep (5 o C he scatter of time and temperature dependent static strength can be shown by the following equation of Weibull distribution. f ( P σ f f A = = f σ f [ ln( P ]α σ fo : Scale parameter α: Shape parameter P f : Failure probability f Variability of tensile strength of unidirectional CFRP Ref. Christensen, R. M. and Miyano, Y., Stress intensity controlled kinetic crack growth and stress history dependent life prediction with statistical variability, International Journal of Fracture (26, 37, he shape parameter does not change with time and temperature. Weibull distribution of static strength 4

6 Condition B Strength of CFRP controlled by viscoelasticity of matrix resin Static streng gth σ (t, [MPa] he relationship between the longitudinal tensile (L and flexural (LB static strengths and transverse flexural (B static strength of unidirectional CFRP and the inverse of compliance of matrix resin (/D * are uniquely determined and these slopes are constant. It is cleared that the time and temperature dependence of static strengths L, LC and B is controlled by the viscoelasticity of matrix resin. he variation of strength of CFRP is shown by the following equation. f B = σ σ f f ( t', ( t', / D * = / Dc ( ( t', ( t', n r : Parameter determined by failure mechanism D c : Creep compliance of matrix resin t ' dσ ( ( ( ( τ ' Dc t' τ ', dτ ' ε t', D * t', d ' = = τ σ t', σ t', nr ( he viscoelastic compliance D* of matrix resin is determined by temperature and load histories. 5

7 Condition B heoretical verification of SP for CFRP strength Load direction Longitudinal tension Longitudinal compression ransverse tension Failure mechanism Cumulative damage of fiber Microbuckling of fiber Controller of time and temperature dependence Viscoelasticity of matrix resin Viscoelasticity of matrix resin ime-temperature superposition principle Yes Yes Matrix crack Failure of matrix resin Yes Longitudinal tension Longitudinal compression ransverse tension he applicability of time-temperature superposition principle for the static strength to three kinds of load direction of unidirectional CFRP is theoretically confirmed. 6

8 Objective Wet Dry log D c Dry log σ s (t, n r Wet log t (= (t=t Creep compliance D c for matrix resin log E* (/D* Static strength of CFRP versus viscoelastic compliance of matrix resin log σ f Wet Dry It can be expected that the relationship between static strength and viscoelastic compliance makes a single straight line without Dry and Wet conditions when the same failure occurs. log t (= (t=t Static strength σ f for CFRP Objective: he effects of water absorption on time and temperature dependence of static strengths of unidirectional CFRP are discussed based on AM. 7

9 Determination procedure of material parameters based on AM Matrix resin Viscoelastic tests at various times and temperatures CFRP Static tests at a constant strain rate and various temperatures D c σ f α n r Master curve of creep compliance Master curve of static strength a o ime-temperature shift factor (Accelerating rate Procedure for determination of material parameters by accelerated testing: st step Determination of a o and D c of matrix resin 2nd step Determination of σ fo, α and n r of CFRP laminates 8

10 Specimens and test methods Specimens : Unidirectional CFRP (3/25 est methods: Viscoelastic modulus and SF D c and a Longitudinal Longitudinal ransverse ransverse tensile compressive tensile compressive strength strength strength strength X X Y Y UD 9 o ransverse bending UD o Longitudinal tension UD o Longitudinal bending (with cushion UD 9 o ransverse bending UD 9 o ransverse compression 9

11 Determination of SF from tan δ for the transverse direction of unidirectional CFRP (3/25 Dry ime-temperature shift factor: ( ( ( ( G H G H G H a g + + = g g 2 g H H 2.33 log a o : ime-temperature shift factor, G: Gas constant, H: Activation energy, : emperature, : Reference temperature, g : Glass transition temperature, H: Heaviside step function Wet he master curve of loss tangent in the transverse direction of unidirectional CFRP under Dry and Wet conditions can be obtained. he time-temperature shift factor (horizontal shift factor can be determined.

12 Master curves of storage modulus for the transverse direction of unidirectional CFRP (3/25 Dry emperature shift factor: 4 i Wet b ( = b ( H( log + 4 i = i = b i i i g ( + log ( H( g b o : emperature shift factor, : emperature, : Reference temperature, g : Glass transition temperature, H: Heaviside step function, b i : material constants g g he master curve of storage modulus in the transverse direction of unidirectional CFRP under Dry and Wet conditions can be obtained. he temperature shift factor (vertical shift factor can be determined.

13 Creep compliance of matrix resin (25 resin Dry he creep compliance D c modulus E by ( t E' Dc 2 ( f π t f is calculated from storage Christensen, R. M., heory of Viscoelasticity, 2nd edition, Dover Publications, Inc., 982, pp.42. Wet he creep compliance D c for matrix resin is backcalculated from that for CFRP using the rule of mixture (approximate averaging method. Uemura, M. and Yamada, N., Elastic constants of carbon fiber reinforced plastic materials, Journal of the Society of Materials Science, Japan, 24: 56-63, 975. he creep compliance D c for matrix resin is formulated by logd c = logd c, ( t', t' + log t' mg t' + t' g mr Where, D c is creep compliance, o is reference temperature, t is reduced time at o, t o is reference reduced time at o, t g is glassy reduced time at o he creep compliance of matrix resin can be calculated based on the linear viscoelasticity and rule of mixture. he creep compliance changes with water absorption as well as time and temperature. 2

14 Static strength of unidirectional CFRP (3/25 Longitudinal direction ransverse direction he static strengths for four directions change with water absorption as well as temperature. 3

15 Master curves of static strength in the longitudinal direction of unidirectional CFRP (3/25 log σ Formulation based on AM f ( Pf, t ', = log σ ', + log ln α ( t ( P f f ( t ( ', D * ', nr log Dc t he time, temperature and water absorption dependencies of static strength of unidirectional CFRP are different with the loading direction. he static strength in the longitudinal direction can be formulated clearly based on AM. 4

16 Master curves of static strength in the transverse direction of unidirectional CFRP (3/25 log σ Formulation based on AM f ( Pf, t ', = log σ ', + log ln α ( t ( P f f ( t ( ', D * ', nr log Dc t he time, temperature and water absorption dependencies of static strength of unidirectional CFRP are different with the loading direction. he static strength in the transverse direction can be formulated clearly based on AM. 5

17 Relationship between static strength of unidirectional CFRP and viscoelastic compliance of matrix resin. log σ Formulation based on AM f ( Pf, t ', = log σ ', + log ln α ( t ( P f f ( t ( ', D * ', nr log Dc t he relationship between static strength of unidirectional CFRP and viscoelastic compliance of matrix resin makes a single straight line without Dry and Wet conditions. 6

18 Conclusions he creep compliance of matrix resin changes with water absorption as well as time and temperature. he time, temperature and water absorption dependencies of static strength of unidirectional CFRP are different with the loading direction. he relationship between static strength of unidirectional CFRP and viscoelastic compliance of matrix resin makes a single straight line without Dry and Wet conditions. he applicability of accelerated testing methodology (AM can be confirmed for static strength under Wet condition. Acknowledgements: he authors thank the Office of Naval Research for supporting this work through an ONR award with Dr. Yapa Rajapakse as the ONR Program Officer. he authors thank Professor Richard Christensen, Stanford University as the consultant of this project. hank you for your attention! 7