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2024 | Book

Multiscale Buckling Modes in the Mechanics of Fiber-Reinforced Plastics

Authors: Vitaly Paimushin, Andris K. Chate, Sergey Kholmogorov, Maksim Makarov, Ruslan Gazizullin

Publisher: Springer Nature Switzerland

Book Series : Advanced Structured Materials

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About this book

This book is a useful source of knowledge for engineers and scientists in the field of mechanics of deformation and destruction of composite materials.

In Chapter 1 three-dimensional equations of elasticity theory composed for the case of finite displacements and deformations of solids have been analyzed. It is found that the generally accepted simplifications known in the literature and carried out for the case of small deformations result in equations that are considered to be absolutely correct and consistent in all scientific and educational literature on mechanics of deformable solid bodies. However, this conclusion is not sufficiently well-founded as confirmed by formulation and solution of problems on the basis of generally accepted equations for determining both the stress-strain state (SSS) and the critical loads and buckling modes. In Chapter 2 the theoretical and experimental methods for determining the mechanical characteristics of fiber-reinforced plastics (FRPs) based on tensile and compression tests of flat specimens with [0]s , [±90]s, and [±45]2s lay-ups are analyzed. For FRPs with [±45]2s lay-ups, relations are derived for determining the components of lamina strains and stresses in the orthotropy axes of FRP monolayer in terms of axial strains and Poisson ratios of specimens measured in experiments. In Chapter 3 the structure of a unidirectional fibre composite of two types ELUR-P carbon fibre based on KhT-118 cold-curing binder and HSE 180 REM prepreg based on hot-curing binder has been studied. The diameters of fibres and fibre bundles (filaments) of both types of composites have been measured. Based on the results of the analysis of the composite material structure, a refined formulation of the linearised problems of a refined statement of linearized problems on flat internal multiscale buckling modes of a rigid lamina with either fibers or a fiber bundle is presented taking into account their interaction with an epoxy matrix. In Chapter 4 for shells of a layered structure based on the Timoshenko’s model, taking into account the transverse compression used for each layer, two versions of two-dimensional equations are constructed that describe geometrically nonlinear deformation with arbitrary displacements and small deformations. The formulation of a linear problem on the initial (subcritical) stress-strain state of a test specimen from a unidirectional fibrous composite with the [900]s structure during tension-compression tests with shear is given. A numerical method for solving the formulated problem is developed, which is based on the reduction of the original problem to a system of integro-algebraic equations and the search for their numerical solution by the finite sum method. In Chapter 5 conclusions were done and directions for further research have been identified.

Table of Contents

Frontmatter
Chapter 1. Geometric Nonlinearity and Stability Problems in Mechanics of Deformable Solids
Abstract
Three-dimensional equations of elasticity theory composed for the case of finite displacements and deformations of solids have been analyzed. It is found that the generally accepted simplifications known in the literature and carried out for the case of small deformations result in equations that are considered to be absolutely correct and consistent in all scientific and educational literature on mechanics of deformable solid bodies.
Vitaly Paimushin, Andris K. Chate, Sergey Kholmogorov, Maksim Makarov, Ruslan Gazizullin
Chapter 2. Stress–Strain State of Fiber-Reinforced Plastic Specimens with [±45]2s Lay-Ups in Tensile and Compression Tests
Abstract
The theoretical and experimental methods for determining the mechanical characteristics of fiber-reinforced plastics (FRPs) based on tensile and compression tests of flat specimens with [0]s, [±90]s, and [±45]2s lay-ups are analyzed.
Vitaly Paimushin, Andris K. Chate, Sergey Kholmogorov, Maksim Makarov, Ruslan Gazizullin
Chapter 3. Flat Internal Buckling Modes of Structural Elements of Fiber-Reinforced Plastic Specimens with a [±45°]2s Lay-Up in Tensile and Compression Tests
Vitaly Paimushin, Andris K. Chate, Sergey Kholmogorov, Maksim Makarov, Ruslan Gazizullin
Chapter 4. Tension–Compression and Shear of Plane Test Specimens from Laminated Composites with the [90°]s Structure
Abstract
For shells of a layered structure based on the Timoshenko’s model, taking into account the transverse compression used for each layer, two versions of two-dimensional equations are constructed that describe geometrically nonlinear deformation with arbitrary displacements and small deformations.
Vitaly Paimushin, Andris K. Chate, Sergey Kholmogorov, Maksim Makarov, Ruslan Gazizullin
Chapter 5. Experimental Studies of the Mechanisms of Formation of Residual Strain in Fibrous Composites Under Cyclic Loading
Abstract
On the example of a unidirectional fibrous composite made from ELUR-P unidirectional carbon fiber reinforced plastic and KhT-118 cold curing binder, tests of test specimens with for \([ \pm 45^{^\circ } ]\) lay-up for cyclic tension were carried out. It is shown that in each loading cycle, a change in the mechanical properties of the material occurs, associated with the restructuring of its microstructure due to the implementation of different-scale buckling forms leading, in particular, to degradation of the material, a change in the secant modulus of elasticity, and stabilization of the magnitude of the strain increment. For various, significantly different loading rates, experimental dependences on the cycle number of the values of the secant moduli of elasticity at the stages of loading and unloading, which differ most from each other in the initial cycles, are obtained. It has been established that under cyclic tension, the loading and unloading branches do not coincide, forming a hysteresis loop.
Vitaly Paimushin, Andris K. Chate, Sergey Kholmogorov, Maksim Makarov, Ruslan Gazizullin
Metadata
Title
Multiscale Buckling Modes in the Mechanics of Fiber-Reinforced Plastics
Authors
Vitaly Paimushin
Andris K. Chate
Sergey Kholmogorov
Maksim Makarov
Ruslan Gazizullin
Copyright Year
2024
Electronic ISBN
978-3-031-48216-8
Print ISBN
978-3-031-48215-1
DOI
https://doi.org/10.1007/978-3-031-48216-8

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