Table of Contents
Cover
Title Page
Copyright
Preface
Chapter 1: Introduction
Chapter 2: Viscoelasticity
2.1 Introduction
2.2 Concept of Viscoelastic Behavior
2.3 Concept of Time–Temperature Superposition Principle (TTSP)
2.4 Master Curve of Creep Compliance of Matrix Resin
2.5 Generalization of TTSP for Nondestructive Deformation Properties to Static, Creep, and Fatigue Strengths of FRPs
2.6 Master Curve of Static Strength of FRP
2.7 Master Curve of Creep Strength of FRP
2.8 Master Curve of Fatigue Strength of FRP
2.9 Conclusion
Reference
Chapter 3: Master Curves of Viscoelastic Coefficients of Matrix Resin
3.1 Introduction
3.2 Master Curve of Creep Compliance Based on Modified TTSP
3.3 Simplified Determination of Long-Term Viscoelastic Behavior
3.4 Conclusion
References
Chapter 4: Nondestructive Mechanical Properties of FRP
4.1 Introduction
4.2 Role of Mixture
4.3 Mechanical and Thermal Properties of Unidirectional CFRPs, Fibers, and Matrix Resin
4.4 Master Curves of Creep Compliance of Matrix Resin
4.5 Conclusion
References
Chapter 5: Static and Fatigue Strengths of FRP
5.1 Introduction
5.2 Experimental Procedures
5.3 Results and Discussion
5.4 Applicability of TTSP
5.5 Conclusion
References
Chapter 6: Formulation of Static Strength of FRP
6.1 Introduction
6.2 Formulation of Static Strength
6.3 Application of Formulation
6.4 Results and Discussion
6.5 Conclusion
References
Chapter 7: Formulation of Fatigue Strength of FRP
7.1 Introduction
7.2 Formulation
7.3 Application of Formulation
7.4 Conclusion
References
Chapter 8: Formulation of Creep Strength of FRP
8.1 Introduction
8.2 Formulation
8.3 Application of Formulation
8.4 Conclusion
References
Chapter 9: Application 1: Static Strengths in Various Load Directions of Unidirectional CFRP Under Water Absorption Condition
9.1 Introduction
9.2 Experimental Procedures
9.3 Viscoelastic Behavior of Matrix Resin
9.4 Master Curves of Static Strengths for Unidirectional CFRP
9.5 Relation between Static Strengths and Viscoelasticity of Matrix Resin
9.6 Conclusion
References
Chapter 10: Application 2: Static and Fatigue Flexural Strengths of Various FRP Laminates Under Water Absorption Condition
10.1 Introduction
10.2 Specimen Preparation
10.3 Experimental Procedures
10.4 Creep Compliance
10.5 Flexural Static Strength
10.6 Flexural Fatigue Strength
10.7 Conclusion
References
Chapter 11: Application 3: Life Prediction of CFRP/Metal Bolted Joint
11.1 Introduction
11.2 Experimental Procedures
11.3 Results and Discussion
11.4 Conclusion
References
Chapter 12: Application 4: Life Prediction of CFRP Structures Based on MMF/ATM Method
12.1 Introduction
12.2 Procedure of MMF/ATM Method
12.3 Determination of MMF/ATM Critical Parameters
12.4 Life Determination of CFRP Structures Based on MMF/ATM Method
12.5 Experimental Confirmation for OHC Static and Fatigue Strengths of CFRP QIL
12.6 Conclusion
References
Appendix A: Effect of Physical Aging on the Creep Deformation of an Epoxy Resin
A.1 Introduction
A.2 Creep Deformation for Aged Polymers
A.3 Experimental Procedure
A.4 Results and Discussion
A.5 Conclusions
References
Appendix B: Reliable Test Method for Tensile Strength in Longitudinal Direction of Unidirectional CFRP
B.1 Introduction
B.2 Evaluation of Tensile Strength Using Post-Bonded CFRP Strand Specimen
B.3 Development of Co-Cured CFRP Strand Specimen
B.4 Conclusions
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 Necessity for accelerated testing.
Figure 1.2 Role of matrix resin on CFRP.
Chapter 2: Viscoelasticity
Figure 2.1 Maxwell model.
Figure 2.2 Creep compliance of Maxwell model.
Figure 2.3 Creep compliance of Maxwell model at various temperatures.
Figure 2.4 Superposition of creep compliances at various temperatures by shifting.
Figure 2.5 Time–temperature shift factor.
Figure 2.6 Creep tests at various temperatures.
Figure 2.7 Creep compliance at various temperatures and the master curve.
Figure 2.8 Time–temperature shift factor for deformation.
Figure 2.9 Generalization of TTSP for nondestructive deformation properties to static, creep, and fatigue strengths of FRP.
Figure 2.10 How to construct the master curve of static strength.
Figure 2.11 How to construct the master curve of creep strength.
Figure 2.12 How to construct the master curve of fatigue strength.
Chapter 3: Master Curves of Viscoelastic Coefficients of Matrix Resin
Figure 3.1 Construction of the master curve of creep compliance. (a) TTSP (only horizontal shift) and (b) TTSP (horizontal and vertical shifts).
Figure 3.2 Specimen configuration and test apparatus.
Figure 3.3 (a) Master curve of creep compliance, (b) time–temperature shift factor, and (c) temperature shift factor.
Figure 3.4 Master curves of creep compliance for epoxy resin. (a) Long-term creep, (b) medium-term creep, and (c) short-term creep.
Figure 3.5 Comparison of shift factors obtained from long-, medium-, and short-term creep compliances for epoxy resin. (a) Shift factor
obtained by only horizontal shift and (b) shift factors
and
obtained by horizontal and vertical shifts.
Figure 3.6 Comparison of master curves for creep compliance by TTSP with horizontal and vertical shifts.
Figure 3.7 Comparison of test periods between the DMA test and the conventional creep test.
Figure 3.8 Concept of formulation: (a) master curve of creep compliance, (b) time–temperature shift factor, and (c) temperature shift factor.
Figure 3.9 Automatic shifting procedure for the construction of master curve of creep compliance. (a) Original experiment data points. (b) Primary shift horizontally and vertically. (c) Refinement of shift by optimization.
Figure 3.10 Master curve of storage modulus by DMA tests.
Figure 3.11 Master curve of tan δ by DMA tests.
Figure 3.12 Time–temperature shift factor (a) and temperature shift factor (b) for storage modulus shown by open circle and loss tangent shown by red solid circle.
Figure 3.13 Master curves of creep compliance by DMA and creep tests.
Figure 3.14 Time–temperature shift factor (a) and temperature shift factor (b) for creep compliance by DMA and creep tests.
Chapter 4: Nondestructive Mechanical Properties of FRP
Figure 4.1 Two constitutive element models for determining the elastic moduli of a unidirectional FRP.
Figure 4.2 Master curves of tan δ and storage modulus for the transverse direction of a unidirectional CFRP.
Figure 4.3 Two kinds of shift factors for a unidirectional CFRP.
Figure 4.4 Master curve of creep compliance for the matrix resin.
Chapter 5: Static and Fatigue Strengths of FRP
Figure 5.1 Tensile test method for CFRP strand.
Figure 5.2 Configuration of three-point bending test. (a) Longitudinal bending and (b) transverse bending.
Figure 5.3 Master curves of σ
s
for three kinds of loading. (a) Tensile σ
s
for longitudinal direction, (b) flexural σ
s
for longitudinal direction, and (c) flexural σ
s
for transverse direction.
Figure 5.4 Time–temperature shift factors
for σ
σ
.
Figure 5.5 σ
f
–
N
f
curves for various temperatures
T
. (a) Tensile σ
f
for longitudinal direction and (b) flexural σ
f
for longitudinal direction, and (c) flexural σ
f
for transverse direction.
Figure 5.8 σ
f
–
N
f
curves (predicted from test at
f
= 2 Hz) and test data at
f
= 0.02 Hz for various temperatures
T
. (a) Tensile σ
f
for longitudinal direction, (b) flexural σ
f
for longitudinal direction, and (c) flexural σ
f
for transverse direction.
Figure 5.6 σ
f
–
curves for various reduced frequencies
f
. (a) Tensile σ
f
for longitudinal direction, (b) flexural σ
f
for longitudinal direction, and (c) flexural σ
f
for transverse direction.
Figure 5.7 Master curves σ
f
–
for various numbers of cycles to failure
N
f
. (a) Tensile σ
f
for longitudinal direction, (b) flexural σ
f
for longitudinal direction, and (c) flexural σ
f
for transverse direction.
Figure 5.9 Side view of specimens after the longitudinal bending tests. (Miyano and Nakada 2006 [1]. Reproduced with permission of Springer.)
Figure 5.10 Fracture surface of specimens after the transverse bending tests. (Miyano and Nakada 2006 [1]. Reproduced with permission of Springer.)
Chapter 6: Formulation of Static Strength of FRP
Figure 6.1 Static strength against failure time at a constant temperature
T
0
.
Figure 6.2 Configurations of specimen and test methods. (a) Bending creep test for EP resin. (b) Tensile static test for EP resin. (c) Longitudinal tensile static test for unidirectional CFRP. (d) Longitudinal bending static test for unidirectional CFRP. (e) Transverse bending static test for unidirectional CFRP.
Figure 6.3 Master curve of creep compliance for EP resin.
Figure 6.4 Horizontal and vertical shift factors for EP resin.
Figure 6.5 Formulation of master curve of creep compliance for EP resin.
Figure 6.6 Master curve of tensile static strength for EP resin.
Figure 6.7 Tensile static strength versus viscoelastic compliance for EP resin.
Figure 6.8 Stress history under constant deformation rate loading (static loading) for simplified determination of the viscoelastic compliance
D
*.
Figure 6.9 Weibull distribution of tensile static strength for EP resin.
Figure 6.10 Master curve of tensile static strength in the longitudinal direction of the unidirectional CFRP.
Figure 6.11 Master curve of flexural static strength in the longitudinal direction of the unidirectional CFRP.
Figure 6.12 Master curve of flexural static strength in the transverse direction of the unidirectional CFRP.
Figure 6.13 Tensile static strength in the longitudinal direction of the unidirectional CFRP versus the viscoelastic compliance of matrix resin.
Figure 6.15 Flexural static strength in the transverse direction of the unidirectional CFRP versus the viscoelastic compliance of matrix resin.
Figure 6.16 Weibull distribution of three kinds of static strength for the unidirectional CFRP.
Figure 6.17 Flexural static strength in the transverse direction of the unidirectional CFRP versus tensile static strength of matrix resin.
Chapter 7: Formulation of Fatigue Strength of FRP
Figure 7.1 Explanation of formulation of fatigue strength.
Figure 7.2 (a) Master curve and (b) shift factors for storage modulus in the transverse direction of unidirectional CFRP laminates.
Figure 7.3 Master curve of creep compliance for the matrix resin calculated from the storage modulus for the transverse direction of unidirectional CFRP laminates.
Figure 7.4 Weibull distributions for the strength of CFRP laminates. (a) Static strength of CFRP laminates at
T
= 25 °C. (b) Static strength of CFRP laminates for all temperatures tested. (c) Fatigue strength of CFRP laminates for all temperatures tested. (d) Fatigue strength of CFRP laminates at
T
= 25 and 80 °C.
Figure 7.5 Temperature dependence for the static strength of CFRP laminates.
Figure 7.6 Static strength of CFRP laminates versus viscoelastic compliance of matrix resin.
Figure 7.7 Fatigue strength of CFRP laminates versus number of cycles to failure at various temperatures.
Figure 7.8 Strength degradation of CFRP laminates by the number of cycles to failure at various temperatures: (a) including the data measured at all temperatures tested; (b) except the data measured at 150 °C.
Figure 7.9 Master curves for static strength of CFRP laminates.
Figure 7.10 Master curves for fatigue strength of CFRP laminates.
Chapter 8: Formulation of Creep Strength of FRP
Figure 8.1 Master curves of static and creep strength.
Figure 8.2 Failure probability against failure time under a creep loading.
Figure 8.3 Dimensionless creep compliance of matrix resin at
T
= 120 °C.
Figure 8.4 Weibull distributions of static tensile strength of CFRP strand at four temperatures.
Figure 8.5 Statistical static strength of CFRP strand against viscoelastic compliance of resin.
Figure 8.6 Failure probability against creep failure time of T300 CFRP strand.
Chapter 9: Application 1: Static Strengths in Various Load Directions of Unidirectional CFRP Under Water Absorption Condition
Figure 9.1 Master curves of loss tangent in the transverse direction of a unidirectional CFRP. (a) T300/EP and (b) T700/VE.
Figure 9.2 Master curves of storage modulus in the transverse direction of a unidirectional CFRP. (a) T300/EP and (b) T700/VE.
Figure 9.3 Shift factors of storage modulus in the transverse direction of a unidirectional CFRP. (a) T300/EP and (b) T700/VE.
Figure 9.4 Master curves of creep compliance for matrix resin calculated from the storage modulus in the transverse direction of a unidirectional CFRP. (a) T300/EP and (b) T700/VE.
Figure 9.5 Master curves of tensile and compressive strengths in the longitudinal direction of a unidirectional CFRP. (a) T300/EP and (b) T700/VE.
Figure 9.6 Master curves of tensile and compressive strengths in the transverse direction of a unidirectional CFRP. (a) T300/EP and (b) T700/VE.
Figure 9.7 Static strengths for four directions of unidirectional CFRP versus viscoelastic compliance of matrix resin. (a) T300/EP and (b) T700/VE.
Chapter 10: Application 2: Static and Fatigue Flexural Strengths of Various FRP Laminates Under Water Absorption Condition
Figure 10.1 Constitution of five kinds of FRP laminates combined with different resins and fibers. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.2 Water content versus soaking time.
Figure 10.3 Water content in resin and FRP for wet and wet + dry conditions. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.4 Configuration of three-point bending test.
Figure 10.5 Master curve of creep compliance for neat vinylester (VE) resin and shift factors.
Figure 10.6 Master curve of creep compliance for neat epoxy (EP) resin and shift factors. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.7 Master curves of flexural static strength in dry, wet, and wet + dry conditions.
Figure 10.8 Flexural static strength versus creep compliance of matrix resin in dry, wet, and wet + dry conditions. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.9 Fracture appearances of specimens after flexural static test at 25 °C in dry condition. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.10 σ
f
versus
N
f
curves at frequency 2 Hz for dry specimen. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.11 Master curves of flexural fatigue strength for (a) T300/VE, (b) T700/VE-F, (c) T700/VE-K, (d) T300/EP, and (e) E-glass/VE. (Nakada and Miyano 2009 [1]. Reproduced with permission of Elsevier.)
Figure 10.12 Photographs of the cross sections of dry and wet + dry specimens for T300/VE, T300/EP, and E-glass/VE.
Figure 10.13 Fractographs of dry and wet + dry specimens for T300/VE, T300/EP, and E-glass/VE after fatigue tests.
Chapter 11: Application 3: Life Prediction of CFRP/Metal Bolted Joint
Figure 11.1 Configuration of CFRP/metal bolted joint system.
Figure 11.2 Photograph of CFRP/metal bolted joint system.
Figure 11.3 Photograph of CFRP bolted joint system for “wet” specimen.
Figure 11.4 Master curve of creep compliance for “dry” specimen.
Figure 11.6 Master curve of creep compliance for “wet + dry” specimen.
Figure 11.7 Time–temperature shift factors for creep compliance.
Figure 11.8 Load–elongation curves under static loading for “dry” specimen.
Figure 11.9 Load–elongation curves under static loading for “wet” specimen.
Figure 11.10 Load–elongation curves under static loading for “wet + dry” specimen.
Figure 11.11 Master curve of static failure load for “dry” specimen.
Figure 11.12 Master curve of static failure load for “wet” specimen.
Figure 11.13 Master curve of static failure load for “wet + dry” specimen.
Figure 11.14 Fatigue failure load versus number of cycles to failure at frequency
f
= 5 Hz for “dry” specimen.
Figure 11.15 Fatigue failure load versus number of cycles to failure at frequency
f
= 5 Hz for “wet” specimen.
Figure 11.16 Fatigue failure load versus number of cycles to failure at frequency
f
= 5 Hz for “wet + dry” specimen.
Figure 11.17 Master curves of fatigue failure load for “dry” specimen.
Figure 11.18 Master curves of fatigue failure load for “wet” specimen.
Figure 11.19 Master curves of fatigue failure load for “wet + dry” specimen.
Figure 11.20 Prediction of fatigue failure load at frequency
f
= 0.05 Hz for “dry” specimen.
Figure 11.21 Prediction of fatigue failure load at frequency
f
= 0.05 Hz for “wet” specimen.
Figure 11.22 Fracture appearances of CFRP/metal bolted joint during static and fatigue tests.
Figure 11.23 Observation area of CFRP/metal bolted joint.
Figure 11.24 Fracture appearance in the cross section of CFRP/metal bolted joint under static and fatigue loadings.
Chapter 12: Application 4: Life Prediction of CFRP Structures Based on MMF/ATM Method
Figure 12.1 First step in the prediction procedure by the MMF/ATM method: determination of MMF/ATM critical parameters.
Figure 12.2 Second step in the prediction procedure by the MMF/ATM method: life determination of CFRP structures.
Figure 12.3 Master curves of MMF/ATM critical parameters. (a)
T
f
and
C
f
. (b)
T
m
and
C
m
.
Figure 12.4 Failure index distribution map of static load (
T
= 25 °C,
t
= 1 min).
Figure 12.5 Failure index distribution map of cyclic load (
T
= 25 °C,
f
= 2 Hz,
N
= 1 × 10
5
).
Figure 12.6 Failure indexes at the corner of open hole under static and cyclic loadings. (a) Static loading (
T
= 25 °C,
t
′ = 1 min). (b) Cyclic loading (
T
= 25 °C,
f
= 2 Hz,
N
= 1 × 10
5
).
Figure 12.7 Prediction of OHC static and fatigue strengths.
Figure 12.8 Static and cyclic compression tests for QIL CFRP laminates with a central hole.
Figure 12.9 Initial failure at the corner of hole of QIL CFRP laminates under static loading (σ = 0.95σ
s
,
T
= 25 °C,
V
= 0.1 mm/min).
Figure 12.10 Initial failure at the corner of QIL CFRP laminates under cyclic loading (σ = 0.80σ
s
,
T
= 25 °C,
f
= 2 Hz,
N
= 1 × 10
5
).
Appendix A: Effect of Physical Aging on the Creep Deformation of an Epoxy Resin
Figure A.1 Explanation of physical aging.
Figure A.2 Explanation of superpositions for creep compliance
D
c
and aging parameter β.
Figure A.3 Specimen configuration and test apparatus.
Figure A.4 Creep compliances at various temperatures for epoxy resin aged for
t
a
= 10
3
min at
T
a
= 120 °C.
Figure A.5 Master curve of creep compliance for epoxy resin aged for
t
a
= 10
3
min at
T
a
= 120 °C.
Figure A.6 Shift factors
and
for epoxy resin aged for
t
a
= 10
3
min at
T
a
= 120 °C.
Figure A.7 Master–master curves for creep compliance of epoxy resin for various aging times and aging temperatures.
Figure A.8 Aging parameter β versus aging time at various aging temperatures and the master curve at reference aging temperature
= 80 °C.
Figure A.9 Density ρ versus aging time at various aging temperatures and the master curve at reference aging temperature
= 80 °C.
Figure A.10 Aging time–temperature shift factor
for aging parameter and density.
Figure A.11 The relationship between aging parameter β and density ρ.
Appendix B: Reliable Test Method for Tensile Strength in Longitudinal Direction of Unidirectional CFRP
Figure B.1 Configuration of winding machine for resin-impregnated carbon fiber strand (CFRP strand).
Figure B.2 Configuration of post-bonded CFRP strand specimen.
Figure B.3 Universal tensile testing machine for CFRP strand specimen.
Figure B.4 Load–elongation diagrams for post-bonded CFRP strand specimen: (a) T300-3000 and (b) T800-12000.
Figure B.5 Configuration of co-cured CFRP strand specimen.
Figure B.6 Winding frame with tab (1).
Figure B.7 Hand-winding of strand to winding frame.
Figure B.8 Assembling tab (2) to winding frame before curing.
Figure B.9 Bolt fastening between tabs (1) and (2) after curing.
Figure B.10 Load–elongation diagrams for co-cured CFRP strand specimen: (a) T300-3000 and (b) T800-12000.
Figure B.11 Improvements on co-cured CFRP strand specimen: (a) without hand-winding of strand by using traverse, (b) added epoxy resin adhesion at the end of tabs, (c) cutting strands between specimens before curing, and (d) holding plates for co-cured CFRP strand specimen.
Figure B.12 Load–elongation diagrams for improved co-cured CFRP strand specimen: (a) T300-3000 and (b) T800-12000.