Properties and Testing of Fiber-Reinforced Polymers
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and Masayuki Nakada. They provide vital insights for materials scientists and engineers. Perfect for anyone in the aircraft, marine, and automobile industries.
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Inhalt
PART I Accelerated Testing Methodology (ATM)
1 INTRODUCTION
2 VISCOELASTICITY
2.1 Introduction
2.2 Concept of Viscoelastic Behavior
2.3 Concept of Time-Temperature Superposition Principle
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
3 MASTER CURVES OF VISCOELASTIC COEFFICIENTS OF MATRIX RESIN
3.1 Introduction
3.2 Master Curves of Creep Compliance Based on Modified TTSP
3.3 Simplified Determination of Long-Term Viscoelastic Behavior
3.4 Master Curve of Relaxation Modulus by DMA and Creep Tests
3.5 Conclusion
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
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
6 APPLICATION 1 OF ATM: STATIC AND FATIGUE FLEXURAL STRENGTHS OF VARIOUS FRP LAMINATES UNDER WATER ABSORPTION CONDITION
6.1 Introduction
6.2 Specimen Preparation
6.3 Experimental Procedures
6.4 Creep Compliance
6.5 Flexural Static Strength
6.6 Flexural Fatigue Strength
6.7 Conclusion
7 APPLICATION 2 OF ATM: LIFE PREDICTION OF CFRP/METAL BOLTED JOINT
7.1 Introduction
7.2 Experimental Procedures
7.3 Results and Discussion
7.4 Conclusion
PART II Advanced Accelerated Testing Methodology (Advanced ATM)
8 INTRODUCTION
9 FORMULATION OF STATIC STRENGTH OF FRP
9.1 Introduction
9.2 Formulation of Static Strength
9.3 Application of Formulation
9.4 Results and Discussion
9.5 Conclusion
10 FORMULATION OF FATIGUE STRENGTH OF FRP
10.1 Introduction
10.2 Formulation
10.3 Application of Formulation
10.4 Conclusion
11 FORMULATION OF CREEP STRENGTH OF FRP
11.1 Introduction
11.2 Formulation
11.3 Application of Formulation
11.4 Conclusion
12 APPLICATION 1 OF ADVANCED ATM: STATIC STRENGTHS IN VARIOUS LOAD DIRECTIONS OF UNIDIRECTIONAL CFRP UNDER WATER ABSORPTION CONDITION
12.1 Introduction
12.2 Experimental Procedures
12.3 Viscoelastic Behavior of Matrix Resin
12.4 Master Curves of Static Strengths for Unidirectional CFRP Laminates
12.5 Relation between Static Strengths and Viscoelasticity of Matrix Resin
12.6 Conclusion
13 APPLICATION 2 OF ADVANCED ATM: LIFE PREDICTION OF CFRP STRUCTURES BASED ON MMF/ATM METHOD
13.1 Introduction
13.2 Procedure of MMF/ATM Method
13.3 Determination of MMF/ATM Critical Parameters
13.4 Life Determination of CFRP Structures Based on MMF/ATM Method
13.5 Experimental Confirmation for OHC Static and Fatigue Strengths of CFRP QILs
13.6 Conclusion
14. APPLICATION 3 OF ADVANCED ATM: EFFECT OF MOLDING CONDITION ON STATISTICAL STATIC
AND CREEP STRENGTHS OF CFRP STRAND
14.1 Introduction
14.2 Experiments
14.3 Creep Compliance of Matrix Resin and Static Strength of CFRP Strand
14.4. Master Curves of Statistical Static and Creep Strengths of CFRP Strands
14.5 Conclusion
15 APPLICATION 4 OF ADVANCED ATM: EFFECT OF CARBON FIBER ON STATISTICAL STATIC AND CREEP STRENGTHS OF CFRP STRAND
15.1 Introduction
15.2 Molding of CFRP Strands and Testing Methods
15.3 Results and Discussion
15.4 Conclusion
PART III Integrated Accelerated Testing Methodology (Integrated ATM)
16 INTRODUCTION
17 INTEGRATED ATM
17.1 Introduction
17.2 Formulation
17.3 Application of Integrated ATM
17.4 Statistical Long-Term Life Prediction of CFRP Strand
17.5 Conclusion
18 APPLICATION 1 OF INTEGRATED ATM: STATISTICAL CREEP AND FATIGUE LIVES OF UNIDIRECTIONAL CFRP LAMINATES UNDER BENDING LOAD
18.1 Introduction
18.2 Experiments
18.3 Results an
Chapter 1
Viscoelasticity
1.1 Introduction
Thermosetting resins used as the matrix of fiber-reinforced polymers (FRPs) show viscoelastic behavior: it is nondestructive time- and temperature-dependent mechanical behavior. Furthermore, the time-temperature superposition principle (TTSP) holds for the viscoelasticity of thermosetting resins. A master curve showing the viscoelasticity of a resin over a wide range of reduced time at a reference temperature can be constructed based on the TTSP. In addition, the long-term nondestructive mechanical behavior of the resin can be predicted from this master curve.
It can be readily inferred that FRPs also show viscoelastic behavior as a result of the influence of the viscoelasticity of the matrix resin, and that the same TTSP as for the matrix resin also holds for FRP viscoelasticity. Furthermore, it can be inferred that the same TTSP as that for matrix resin holds for the static, creep, and fatigue strengths of FRP, and that master curves of these strengths can be constructed to predict the long-term degradation of these strengths.
1.2 Concept of Viscoelastic Behavior
The concept of linear viscoelastic behavior is explained using a Maxwell model with a spring and dashpot, as shown in Figure 1.1. The spring is a solid having an elastic modulus . The dashpot is a liquid having viscosity . When this Maxwell model is loaded using a constant stress , as shown in Figure 1.2a, the total strain is generated, as shown in Figure 1.2b. Creep compliance shown in Figure 1.2c is definable by the following equation:
(1.1)Figure 1.1 Maxwell model.
Figure 1.2 Creep compliance of the Maxwell model.
1.3 Concept of TTSP
Although the elastic modulus of the spring in the Maxwell model does not change with temperature, the viscosity of dashpot decreases drastically with increasing temperature, as shown in Figure 1.3. Figure 1.4 presents the creep compliance of the Maxwell model with various temperatures against time. Each creep compliance keeps a constant value of in the short time range, and each maintains a constant slope of 1 over a long time range. These creep compliances at various temperatures are superimposed on each other by a horizontal shift, as shown in Figure 1.4. The amount of horizontal shift is defined as the time-temperature shift factor , which is shown by the following equation and Figure 1.5:
(1.2)Figure 1.3 Creep compliance of the Maxwell model at various temperatures.
Figure 1.4 Superposition of creep compliances at various temperatures by shifting.
Figure 1.5 Time-temperature shift factor.
The time-temperature shift factor can be regarded as the rate of acceleration by increasing temperature.
1.4 Master Curve of Creep Compliance of Matrix Resin
The procedure to construct a master curve of creep compliance of the matrix resin based on TTSP is presented in this section. First, the creep tests are conducted at various temperatures , , and , as shown in Figure 1.6. The creep compliances against time at various temperatures are determined by substituting the measured data in Eq. (1.1), as shown on the left side of Figure 1.7.
Figure 1.6 Creep tests at various temperatures.
Figure 1.7 Creep compliance at various temperatures and the master curve.
The master curve of creep compliance against the reduced time at the reference temperature is obtainable by superimposing the creep compliances at various temperatures by horizontal shifting, as shown on the right side of Figure 1.7. The long-term creep compliance of the matrix resin can be predicted from this master curve. The amounts of horizontal shift are also obtained as the time-temperature shift factor, as shown in Figure 1.8.
Figure 1.8 Time-temperature shift factor for deformation.
1.5 Generalization of TTSP for Nondestructive Deformation Properties to Static, Creep, and Fatigue Strengths of FRPs
The most important condition for the accelerated testing methodology (ATM) proposed by the authors is the generalization of TTSP for nondestructive deformation properties to the static, creep, and fatigue strengths of FRPs. In this condition, the same TTSP as that used for the deformation of the matrix resin holds for the strengths of FRPs, as shown in Figure 1.9. Concretely, the following equation is used for the time-temperature shift factors:
(1.3)Figure 1.9 Generalization of TTSP for nondestructive deformation properties to static, creep, and fatigue strengths of FRP.
Therefore, the long-term strengths of FRPs can be predicted from their measured short-term strengths at elevated temperatures and from the time-temperature shift factor for the deformation of the matrix resin.
1.6 Master Curve of Static Strength of FRP
The procedure to construct a master curve of static strength of an FRP using the time-temperature shift factor for the matrix resin deformation is presented in this section. First, the static tests are conducted at various temperatures and strain rates , as shown in Figure 1.10a,b. The static strengths against the failure time at various temperatures are determined from the measured data, as shown on the left side of Figure 1.10c, where the failure time is defined as the period from the beginning of loading to the failure load.
Figure 1.10 How to construct the master curve of static strength.
The master curve of static strength against the reduced failure time at reference temperature is obtainable by horizontally shifting of the static strength at various temperatures, as shown on the right side of Figure 1.10c. The long-term static strength of the FRP can be predicted from this master curve. The amount of horizontal shift is the time-temperature shift factor for the matrix resin deformation.
1.7 Master Curve of Creep Strength of FRP
The procedure to construct the master curve of creep strength of FRPs using the time-temperature shift factor for the deformation of the matrix resin is shown in this section. First, the creep tests are conducted at various temperatures and constant stresses , as shown in Figure 1.11a. The creep strength against failure time at various temperatures is determined from measured data, as shown on the left side of Figure 1.11b.
Figure 1.11 How to construct the master curve of creep strength.
The master curve of creep strength against reduced failure time at the reference temperature is obtainable by shifting the creep strength horizontally at various temperatures, as shown on the right side of Figure 1.11b. The long-term creep strength of the FRP can be predicted from this master curve. The amount of horizontal shift is the time-temperature shift factor for the matrix resin deformation.
1.8 Master Curve of Fatigue Strength of FRP
The procedure used to construct the master curve of fatigue strength of FRPs using the time-temperature shift factor for the matrix resin deformation is shown in this section. First, the fatigue tests are conducted at various temperatures and various maximum stresses under a constant frequency , as shown in Figure 1.12a. The fatigue strengths against the failure time at various temperatures under a constant frequency are determined from the measured data, as shown on the left side of Figure 1.12b. The master curve of static strength in this figure can be regarded as the fatigue strength at the number of cycles to failure .
Figure 1.12 How to construct the master curve of fatigue strength.
The fatigue strength against the reduced failure time at the reference temperature under various corresponding frequencies is obtainable by shifting the fatigue strength horizontally at various temperatures, as shown on the right side of Figure 1.12c. The corresponding frequency for is obtained as shown in the following equation:
(1.4)The long-term fatigue strength against the reduced failure time at the reference temperature for an arbitrary frequency can be predicted from this figure. The amount of horizontal shift is the time-temperature shift factor for matrix resin deformation.
The master curves of fatigue strength at various numbers of cycles to failure are obtained by connecting the fatigue strength at various frequencies at the same number of cycles to failure , as shown in Figure 1.12d,e. The long-term fatigue strength against the reduced failure time at reference temperature for an arbitrary number of cycles to failure can be predicted from Figure 1.12e.
1.9 Conclusion
The concepts of viscoelasticity and TTSP were explained using the Maxwell model. The generalization of TTSP for nondestructive deformation properties of the matrix resin to static, creep, and fatigue strengths of FRPs was introduced as the most important condition for the ATM. Procedures to obtain the master curves of static, creep, and fatigue strengths of FRPs were explained. Readers who want more details related to viscoelasticity may refer to...
