E-book details

Selected Problems in Mechanics of Thermosets and Unidirectional Fibre-Reinforced Thermoset Matrix Composites

Selected Problems in Mechanics of Thermosets and Unidirectional Fibre-Reinforced Thermoset Matrix Composites

Daniel Nycz, Marian Klasztorny

Ebook

The monograph formulates and solves selected issues of the theory of linear elasticity and rheology of thermosetting polymers and unidirectional monotropic fibre-reinforced thermoset matrix (UFRT) composites. The analytical modelling includes: the quasi-exact homogenization theory of UFRT composites; the inverse problem in the homogenization theory of UFRT composites; the elastic and rheological constitutive modelling of thermosetting polymers and UFRT composites (standard and inverse, uncoupled and coupled constitutive equations); experimental validation of a new rheological model for thermosets, based on the Mittag-Leffler fractional exponential generic function; and numerical validation of a new rheological model for UFRT composites, based on a single Mittag-Leffler fractional exponential generic function. Both the thermosetting polymers and UFRT composites are described by the minimum numbers of the viscoelastic constants. The monograph also presents testing, identification, validation and cognitive studies, including: experimental identification of the elastic and viscoelastic constants of representative resins; numerical identification of the elastic and viscoelastic constants of representative UFRT composites, based on the homogenization theory, the uncoupled rheological constitutive equations, and the elastic-viscoelastic correspondence principle; and simulations of selected rheological processes in the representative resin and representative UFRT composites. The formulations, analytical solutions and numerical analyses are original and unique worldwide.

Foreword 7

Preface 9

Designations 13

1. Introduction 23

2. Thermosets and UFRT composites for identification and validation tests 33

3. Elastic and rheological modelling of thermosets 35

3.1. Assumptions 35

3.2. Elastic modelling 35

3.3. Rheological modelling 37

4. Homogenization of UFRT composites 45

4.1. Assumptions, representative volume cell and compliances 45

4.2. General solutions of selected boundary problems of theory of linear elasticity 49

4.2.1. Basic equations in cylindrical coordinates 49

4.2.2. Standard constitutive equations of monotropic material in cylindrical coordinate system 50

4.2.3. Axisymmetric boundary problem 51

4.2.4. Boundary problem for disc in in-plane shear 56

4.2.5. Longitudinal shear of monotropic solid 61

4.3. Analytic solutions of selected boundary problems (Lamé-type tasks) 64

4.3.1. Longitudinal uniform tension in x1 direction 64

4.3.2. Axisymmetric transverse tension in x2x3 plane 67

4.3.3. Transverse shear in x2x3 plane 70

4.3.4. Longitudinal shear in x1r planes 75

4.4. Experimental validation 77

5. Inverse problem in homogenization theory of UFRP composites 81

5.1. General description of improved inverse problem in homogenization theory 81

5.2. Analytic solutions in inverse problem 82

5.2.1. First Lamé-type task 82

5.2.2. Second Lamé-type task 85

5.2.3. Third Lamé-type task 88

5.2.4. Fourth Lamé-type task 91

5.3. Numerical validation 92

6. Elastic and rheological modelling of homogenized UFRT composites 95

6.1. Assumptions 95

6.2. Elastic modelling 96

6.3. Rheological modelling 100

7. Complementary problems 105

7.1. Numerical integration of selected improper integrals 105

7.2. Experimental unidirectional tension creep test on thermoset 106

7.3. Identification of viscoelastic constants of thermoset 107

7.4. Determination of effective viscoelastic constants of UFRT composite 109

8. Software and preliminary numerical analyses 111

8.1. Software 111

8.2. Gauss-Legendre quadrature testing 111

8.3. Creep function analysis 112

8.4. Thermoset complex shear compliance analysis 113

9. Experimental and numerical studies 117

9.1. Identification of elastic and viscoelastic constants of selected thermosets 117

9.1.1. Epoxy resin 117

9.1.2. Polyester resin 120

9.2. Influence of fibre volume fraction on effective elastic constants of selected UFRT composites 123

9.3. Calculation of effective viscoelastic constants of selected UFRT composites 126

10. Rheological simulations 129

10.1. Constitutive equations to simulate selected rheological processes 129

10.1.1. Thermosetting polymers 129

10.1.2. UFRT composites 133

10.2. Concept of numerical study 136

10.3. Rheological simulations for epoxy resin 140

10.4. Rheological simulations for UFRT composites 146

10.4.1. Glass-epoxy UFRT composite 146

10.4.2. Carbon-epoxy UFRT composite 152

11. Final conclusions 159

References 165

Brief biographies of authors 169

  • Title: Selected Problems in Mechanics of Thermosets and Unidirectional Fibre-Reinforced Thermoset Matrix Composites
  • Author: Daniel Nycz, Marian Klasztorny
  • ISBN: 978-83-8156-602-5, 9788381566025
  • Date of issue: 2024-01-18
  • Format: Ebook
  • Item ID: e_3rzi
  • Publisher: Oficyna Wydawnicza Politechniki Warszawskiej