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STUDY OF AUXETIC COMPOSITES MADE

WITH MULTILAYERED ORTHOGONAL

STRUCTURAL REINFORCEMENT

JIANG Lili

Ph.D

The Hong Kong Polytechnic University

2017

II

THE HONG KONG POLYTECHNIC UNIVERSITY

INSTITUTE OF TEXTILES AND CLOTHING

STUDY OF AUXETIC COMPOSITES MADE

WITH MULTILAYERED ORTHOGONAL

STRUCTURAL REINFORCEMENT

JIANG Lili

A thesis submitted in partial fulfilment of the requirements for the

degree of Doctor of Philosophy

January 2017

To My Family,

For their Love and Support

I

Abstract

As good candidates for being used as energy absorption materials, polymeric foams

have been widely used in the cushioning, packaging and impact protection areas due

to their characteristics of large plastic deformation, inelastic energy conversion and

moderate reactive force. But at the same time, the plastic deformation, collapse of cell

walls and internal fracture can easily cause the damage and failure of foams. There

are ways that are commonly used to improve the mechanical properties of foams like

filling the chopped fibers and small particles to the plain foams. However, the

continuous long fibers and integral structural reinforcements are seldom used for

mechanical enhancement due to the increase of foam weight and the difficulties in

manufacturing. Therefore, the light-weight plastic tubes and high-performance yarns

are proposed and selected as the reinforcement materials to enhance the plain foams

without decreasing the strength to weight ratio. Meanwhile, the negative Poisson’s

ratio effect will be achieved by creative structure design of reinforcements, which

would further enhance the mechanical properties of foams under compression and

impact loading.

Optimal synchronistic effect could be achieved by structure design and material

selection to maximum the peculiarities of each constituent material in composite. The

structure for the developed composite in this study is multilayered orthogonal auxetic

structure and the component materials are rigid ABS open tubes, high-strength low-

extension polyester yarns and flexible open cell polyurethane foam. The newly

II

manufactured composite materials were named “auxetic composites made with

multilayered orthogonal structural reinforcements”.

Auxetic composites are non-conventional materials with negative Poisson’s ratio

(NPR). They have been receiving great attentions due to special properties and large

application potentials. In this research, novel kinds of auxetic composites were

proposed and fabricated via an injecting and foaming techniques by using multilayer

auxetic orthogonal structure as reinforcements and flexible open-cell polyurethane

foams as matrix. The NPR effect and mechanical behavior of the composites under

static and dynamic compression tests were investigated using experimental and

numerical methods.

The quasi-static compression results showed that auxetic composites exhibited

obvious NPR effect and behaved more like damping materials with a big range of

deformation strain. Fiber pull-out tests demonstrated that strong interfacial bonding

between the reinforcements and matrix could ensure the desired deformation of

structural reinforcements and auxetic effect of the composite. The low-velocity drop-

weight impact results revealed that the mechanical responses of composites including

the impact contact force, impact stress as well as energy absorbed were strain rate

sensitive. The cross-sections shape and dimension of ABS tubes could seriously

influence the mechanical responses of auxetic composites.

A three-dimensional finite element model about low-velocity impact on the auxetic

composites was achieved by using in Ansys/Ls Dyna Explicit codes. Good agreement

in the overall trends of stress strain curves for the FEM and experimental results were

III

found. The deformation process of composites in the simulation was captured and

compared with experimental to explore the damage mechanisms of materials. It was

concluded that the auxetic composite had good energy absorption capacities and could

be used individually or served as filling materials in sandwich materials under

different compression conditions.

Keywords:

Multilayered orthogonal, Negative Poisson’s ratio, Quasi-static compression, Low-

velocity impact, Energy absorption, Strain rate, Finite Element model.

IV

List of Publications

Academic Journal Papers:

1. Lili Jiang, Bohong Gu, Hong Hu. Auxetic composite made with multilayer

orthogonal structural reinforcement. Composite Structures 2016; 135:23-29.

2 Lili Jiang, Hong Hu. Low-velocity impact response of multilayer orthogonal

structural composite with auxetic effect. Composite Structures 2017; 169:62-68.

3 Lili Jiang, Hong Hu. Finite element modeling of multilayer orthogonal auxetic

composites under low-velocity impact. Materials 2017; 10(8):908.

International Conferences Papers:

1. Hong Hu, Lili Jiang. A study of auxetic composite with the three-dimensional

orthogonal structural reinforcement. 17th U.S. National Congress on Theoretical and

Applied Mechanics. Michigan State University. June 15-20, 2014 at Michigan, United

States.

2. Hong Hu, Lili Jiang, Zhou Lin, Xu Kun. Three-dimensional textile structural

composites with negative Poisson’s ratio. 17th European Conference on Composite

Materials. 26-30 June, 2016 at Munich, Germany.

3. Lili Jiang, Hong Hu. Low-velocity impact response of multilayer orthogonal

structural composite with auxetic effect. 2nd International Conference on Mechanics

of Composites. 11-14 July, 2016 at Porto, Portugal.

http://dx.doi.org/10.1016/j.compstruct.2016.10.018

V

Acknowledgements

Three years of PhD study life are coming to an end. I feel so grateful to all the people

that I have met and known, who’ve ever been loving, supporting and helped me

during this precious period of time.

Firstly, I would like to express my sincere appreciation to Prof. Hu Hong, who is my

chief supervisor in the PhD study. Your kindly guidance, creative instructs and

fatherhood care makes me achieve this thesis. Meantime, I want to thank our

Department - the Institute of Textile and Clothing for providing me the opportunity as

well the PhD scholarship to study here. And all the colleagues and friends at our

university and in my life, I want to say thank you and I love you all.

Secondly, I would like to thank Prof. Gu Bohong and Prof. Sun Baozhong, who were

the master supervisors when I was in Donghua University and continuously helped

me a lot in the PhD study. Your strict scientific attitudes and abundant research skills

helped me build solid research basis.

Thirdly, I have to express my deep gratitude to my external examiner, Prof. Li Wei at

Donghua University and Prof. Raul Fangueiro at the University of Minho and my

internal examiner Prof. Xu Bingang at ITC PolyU. Your precious suggestions and

revision made the thesis better.

VI

Special thanks to my husband Dr. Liu Fengwei, my daughter Liu Sichen, my parents

and parents in law, my sister and brother. Your endless love and support keep me

going thus far.

Finally, I would like to express my special acknowledgement to Research Grants

Council of Hong Kong Special Administrative Region Government for providing the

funding support in the form of a GRF project (No.515812).

VII

Table of Contents Abstract ..................................................................................................................... I

List of Publications ............................................................................................... IV

Acknowledgements ................................................................................................. V

List of Figures ........................................................................................................ XI

List of Tables ...................................................................................................... XVI

Chapter 1 Introduction ........................................................................................... 1

1.1 Research Background .................................................................................... 1

1.2 Research Objectives ....................................................................................... 2

1.3 Research Methodology ................................................................................... 4

1.4 Significance and Values ................................................................................. 6

1.5 Thesis Outline ................................................................................................. 7

1.6 Reference ......................................................................................................... 9

Chapter 2 Literature Review ............................................................................... 12

2.1 Introduction ...................................................................................................... 12

2.2 Energy Absorption Materials ......................................................................... 12

2.2.1 Introduction ............................................................................................................ 12

2.2.2 Main Features ......................................................................................................... 13

2.2.3 Polyurethane Foams ............................................................................................... 13

2.3 Auxetic materials ............................................................................................. 15

2.3.1 Introduction ............................................................................................................ 15

2.3.2 Microstructures and Models ................................................................................... 16

2.3.3 Unique Properties ................................................................................................... 23

2.3.4 Auxetic Composites ................................................................................................ 27

VIII

2.4 Low-velocity Impact Tests .............................................................................. 28

2.4.1 Introduction ............................................................................................................ 28

2.4.2 Testing Approaches and Related Physical Quantities ............................................ 29

2.4.3 Impact on Foams and Foam-cored Composites ..................................................... 30

2.5 Chapter Summary ........................................................................................... 32

2.6 Reference .......................................................................................................... 32

Chapter 3 Structure Design and Composites Fabrication ................................ 45

3.1 Introduction ...................................................................................................... 45

3.2 Structure Design .............................................................................................. 47

3.3 Composites Fabrication ................................................................................... 51

3.4 Chapter Summary ........................................................................................... 54

3.5 Reference .......................................................................................................... 55

Chapter 4 Mechanical Responses of Auxetic Composites Under

Quasi-static Compression and Low-velocity Impact Tests ................................ 58

4.1 Introduction ...................................................................................................... 58

4.2 Quasi-static Compression Tests...................................................................... 58

4.2.1 Introduction ............................................................................................................ 58

4.2.2 The NPR Effect ...................................................................................................... 60

4.2.3 Static Compression Behavior Analysis .................................................................. 64

4.3 Low-velocity Drop-weight Impact Tests ........................................................ 68

4.3.1 Introduction ............................................................................................................ 68

4.3.2 Samples and Conditions ......................................................................................... 68

4.3.3 Results and Discussion ........................................................................................... 70

4.4 Chapter Summary ........................................................................................... 83

IX

4.5 Reference .......................................................................................................... 85

Chapter 5 The Mechanical Responses of Improved Auxetic

Composites with Different Tube Cross-sections ................................................ 87

5.1 Introduction ...................................................................................................... 87

5.2 Samples with Different Tubes Cross-section ................................................. 87

5.3 Mechanical Responses under Quasi-static Compression ............................. 93

5.3.1 Conditions for Quasi-static Compression ............................................................... 93

5.3.2 Quasi-static Compression Results .......................................................................... 94

5.4 Mechanical Responses under Low-velocity Impact ................................... 102

5.5 Chapter Summary ......................................................................................... 126

5.6 Reference ........................................................................................................ 128

Chapter 6 Finite Element Modelling of Auxetic Composites

under Low-velocity Impact ................................................................................ 129

6.1 Introduction .................................................................................................... 129

6.1.1 Ansys/LS Dyna ..................................................................................................... 129

6.1.2 FE Modelling on Impact of Foams and Foam-filled Composites ........................ 130

6.2 Building the FE Models ................................................................................. 132

6.2.1 Geometric Modelling and Specifications ............................................................. 132

6.2.2 Material Modelling ............................................................................................... 141

6.2.3 Contact and Constraints ........................................................................................ 144

6.3 Simulation Results ......................................................................................... 144

6.3.1 Deformation Process and Auxetic Effect ............................................................. 144

6.3.2 Poisson’s Ratio versus Compressive Strain Curves ............................................. 148

6.3.3 Contact Stress versus Compressive Strain Curves ............................................... 151

6.4 Chapter Summary ......................................................................................... 156

X

Chapter 7 Conclusions and Future Work ........................................................ 160

7.1 Conclusions ..................................................................................................... 160

7.2 Limitations and Recommendations for Future Work ............................... 162

7.3 Reference ........................................................................................................ 163

Appendix I Keywords for FE Model in Ls Dyna .............................................. 164

XI

List of Figures

Figure 2.1 Re-entrant honeycomb structure

Figure 2.2 3D re-entrant structure

Figure 2.3 (a) Double-arrow head, (b) star-shaped, (c) sinusoidal ligament structure

Figure 2.4 Rotating structure opening up under stretch

Figure 2.5 (a) Rotating squares, (b) rotating triangles, (c) rotating rectangles structure

Figure 2.6 Nodule and fibril structure (a) normal state, (b) under stretch

Figure 2.7 Schematics for a generalized 3D tethered nodule, showing: (a) a central

nodule connected to eight others via corner fibril

Figure 2.8 Chiral honeycombs (a) Formed with the same chiral units, (b) Formed

with symmetrical chiral units

Figure 2.9 The idealized networks of the (a) intact version and (b) cur version with

the unit cells shaded

Figure 2.10 The deformation of circle holes structure under compression

Figure 2.11 Indentation resistance

Figure 2.12 (a) Anticlastic curvature, (b) Synclastic curvature

Figure 2.13 Permeability of auxetic honeycomb

Figure 3.1 3D auxetic orthogonal structure: (a) 3D view; (b) y-z cross-section; (c) x-z

cross-section; (d) contraction in x direction under compression.

Figure 3.2 (a) 2D hexagonal honeycomb, (b) rectangular honeycomb, (c) re-entrant

honeycomb

Figure 3.3 Making of multilayered auxetic orthogonal structure: (a) schematic

diagram of stainless mold; (b) multilayered auxetic orthogonal structure fixed in mold

Figure 3.4 Samples produced: (a) auxetic composite; (b) pure polyurethane foam; (c)

non-auxetic composite

Figure 3.5 States of the ABS open tubes during compression: (a) original state; (b)

collapse occurred

Figure 4.1 Quasi-static compressive test of auxetic composite

XII

Figure 4.2 Lateral deformation of composites under compression: (a) auxetic

composite (compression strain: 42.39%); (b) non-auxetic composite (compression

strain: 23.42%)

Figure 4.3 Poisson’s ratio of auxetic composite as a function of compression strain

Figure 4.4 Geometric model: (a) initial state; (b) under compression; (c) repeating unit

Figure 4.5 Compression curves for pure foam, auxetic composite and non-auxetic

composite: (a) stress versus strain; (b) specific stress versus strain

Figure 4.6 Picture of Instron® 9250 impact tester and samples fixed on the anvil

Figure 4.7 Comparison of force-displacement curves among different materials: (1)

PU foam, (2) Auxetic Composite, (3) Non-auxetic Composite under different

compression velocities: (a) static, (b) 1 m/s, (c) 2 m/s, (d) 3 m/s

Figure 4.8 Contact stress and energy absorbed versus compressive strain curves of

three materials under different velocities: (1) Quasi-static, (2) 1 m/s, (3) 2 m/s, (4) 3

m/s

Figure 4.9 Schematic illustration of filament and tube pull-out tests from the foam

block

Figure 4.10 The pictures of reinforcements after being pulled out of the foam: (1)

polyester filaments, (2) ABS tube

Figure 4.11 Fracture occurred in the PU foam after the impact velocity of: (1) 2 m/s,

(2) 3 m/s

Figure. 5.1 Pictures for the samples of foam, auxetic composites and non-auxetic

composites: (a) Foam, (b) AU_R, (c) AU_S, (d) AU_R34, (e) NA_R, (f) NA_S, (g)

NA_R34

Figure. 5.2 Picture of Polyurethane foam with open cells

Figure 5.3 The quasi static compression setup Instron 5566

Figure 5.4 Mechanical responses of different materials under quasi-static compression:

(1) Compressive Force - Compressive Displacement curves, (2) Compressive Stress-

Compressive Strain curves, (3) Energy Absorption - Compressive Displacement

XIII

curves, (4) Specific Energy - Compressive Strain curves, (5) Compressive Force -

Energy Absorption curves

Figure 5.5 Poisson’s ratio versus compressive strain curves for the sample of AU_S

under static compression

Figure 5.6 The deformation pictures for the sample AU_S at different compressive

strain: (a) 0, (b) 2.68 %, (c) 7.36 %, (d) 12.71 %, (e) 20.74 %, (f) 26.42 %, (g)

34.78 %, (h) 40.47 % ,(i) 47.16 %, (j) 49.83 %

Figure 5.7 King Design Drop-weight impact testing system

Figure 5.8 The contact acceleration versus time curves for the sample of AU_S at the

impact height of 265 mm

Figure 5.9 The velocity and displacement versus time curves for the sample of AU_S

under the impact height of 265 mm

Figure 5.10 The Impact Response of Composite AU_R under different velocities: (1)

Contact Force - Time curves, (2) Contact Force - Displacement curves, (3) Contact

Energy - Displacement curves.

Figure 5.11 The Impact Response of Composite AU_S under different velocities: (1)


Energy - Displacement curves

Figure 5.12 The Impact Response of Composite AU_R34 under different velocities:

(1) Contact Force - Time curves, (2) Contact Force - Displacement curves, (3)

Contact Energy - Displacement curves

Figure 5.13 The Impact Response of Composite NA_R under different velocities: (1)



Figure 5.14 The Impact Response of Composite NA_S under different velocities: (1)



XIV

Figure 5.15 The Impact Response of Composite NA_R34 under different velocities:

(1) Contact Force - Time curves, (2) Contact Force - Displacement curves, (3)

Contact Energy - Displacement curves

Figure 5.16 The impact results comparison of different materials under the impact

height of 115 mm (impact velocity = 1.5013 m/s): (1) Contact Force - Displacement

curves, (2) Contact Energy - Displacement curves
















Figure 6.1 The 3D Finite Element Model for the auxetic composite with round ABS

tubes: (a) the whole composite, (b) the whole reinforcement

Figure 6.2 The diagram for (a) the auxetic reinforcement, (b) the auxetic composite

from the front view, the repeating unit cell were marked in red

Figure 6.3 The diagram for (a) the auxetic reinforcement, (b) the auxetic composite

from the top view (1) and side view (2)

Figure 6.4 The small FE model for the auxetic composite with round ABS tubes

XV

Figure 6.5 The FE models with different-size meshes: (a) element length=0.2mm; (b)

element length=0.4mm

Figure 6.6 The Poisson’s ratio versus compressive strain curves for FE models with

different element sizes (0.2mm and 0.4mm)

Figure 6.7 The FE models: (a) composite; (b) ABS tubes; (c) polyester yarns

Figure 6.8 The extended compressive stress strain curve for foam in FE model

Figure 6.9 The tensile stress strain curves for polyester yarns (three testing results)

Figure 6.10 The impact deformation process and stress distribution of auxetic

composite at different compressive strains under an impact velocity of 2.67 m/s: (a) 0,

(b) 5.60 %, (c) 11.86 %, (d) 17.61 %, (e) 23.20 %, (f) 28.45 %, (g) 33.09 %, (h)

35.08 %

Figure 6.11 Poisson’s ratio versus compressive strain curves for FE impact simulation

and quasi-static compression test

Figure 6.12 Contact stress versus compressive strain curves from FEM and

Experimental: (a) impact velocity=1.50 m/s; (b) impact velocity=2.05 m/s; (c) impact

velocity=2.67 m/s

Figure 6.13 Contact stress versus compressive strain curves: (a) FE simulation; (b)

Experimental

XVI

List of Tables

Table 3.1 Material parameters for polyester filaments and ABS tubes

Table 3.2 Density for different materials

Table 3.3 Volume fraction of polyester yarns and ABS tubes and foam for auxetic and

non-auxetic composite

Table. 4.1 Dynamic compressive results of foam and composites [means (S.D.)], n=3

Table 5.1 General technical indicators of Cst-1076 A/B PU foam

Table 5.2 The peak contact force, maximum displacement, energy absorption and

strain rate of six samples under six different impact height. [means (S.D.)], n=3

Table 6.1 Comparison between the experimental and FEM results

Chapter 1

1

Chapter 1

Introduction

1.1 Research Background

Compared with conventional materials, which usually undergo small elastic

deformation and are required to have certain strength and stiffness under some

specified loads, the energy absorbing materials mostly suffer from intense impact

loading. So the deformation and damage of energy absorbing materials involves the

big strain, strain rate effect, strain hardening effect and various different deformation

modes. The energy absorbing materials used for impact protection generally hold the

characteristics of large plastic deformation, inelastic energy conversion, restricted and

constant reactive force, light weight and high energy-absorption capacity [1]. Owning

all above mentioned features, the open-cell polyurethane (PU) foam has become a

good candidate for being used as energy absorption material due to its superior energy

absorbing capability including large strain and moderate contact stress. However,

plastic deformation, collapse of cell walls and internal fracture can easily cause

fatigue even failure of the PU foams. Generally, parameters like foam density,

open/closed cell content, cell size and shape, etc. are adjusted to improve the

mechanical properties of foams [2,3]. Chopped fibers [4] and micro/nano-sized

particles [5] are also filled to increase the stiffness and plateau stress of plain foams.

But the continuous long fibers and integral structural reinforcements are seldom used

for mechanical enhancement in case the big increase of foam weight. While,

Chapter 1

2

compared with the chopped fibers, long fibers as reinforcements will increase the

integrity and avoid the easy fracture and delamination of the composites. Therefore,

the multilayered orthogonal structures with light-weight and high-strength materials

are proposed and designed as the reinforcements to enhance the PU foam without

decreasing the strength to weight ratio [6]. Meanwhile, the negative Poisson’s ratio

(NPR) effect will be achieved by suitable structure arrangement of reinforcements,

which would further enhance the mechanical properties of foams under compression

and impact loading. In this research, the developed composite with the multilayered

orthogonal structural reinforcement and NPR effect is called “auxetic composite”. In

recent years, the auxetic materials have been drawing various interests due to their

counterintuitive deformation behavior and improved mechanical properties, like

enhanced shear resistance [7-9], increased indentation resistance [10-15] and higher

fracture toughness [7-8,16-17]. These feature advantages have made auxetic materials

suitable for many potential applications such as automobile [18], aerospace and

defense [19], sport protecting equipment, where energy absorption can be one of the

highly required properties. Hence, the novel multilayered orthogonal auxetic

composites should be designed and fabricated as excellent energy absorbers, which

could be used individually or served as filling materials in composites under different

loading conditions.

1.2 Research Objectives

This research is aimed at systematically developing, fabricating and characterizing a

kind of novel multilayered orthogonal structural composite with negative Poisson’s

Chapter 1

3

ratio, analyzing the mechanism of deformation which leads to NPR effect and

identifying the applications of auxetic composite in energy absorption and impact

protection areas. The specific objectives are presented as follows:

(1) To design and optimize the reinforcement structure for auxetic composite, to

predict the value of Poisson’s ratio in relation to compressive strain of composite in

theoretical;

(2) To fabricate auxetic composites made with the multilayer orthogonal structural

reinforcements and polyurethane foam matrix by using hand operated molding

method, to prepare the composite samples in accordance with the international

standard for the next step experimental testing;

(3) To conduct the experimental investigations on quasi-static and low-velocity

impact compression of auxetic composite and analyse its strain rate sensitivity, to

obtain the deformation process and auxetic behavior of the composite, to reveal the

mechanisms of being auxetic;

(4) To develop the improved auxetic composites with more flexible and rebounded

polyurethane foam, to discuss the mechanical behavior and deformation mechanisms

of all composites under different velocity compression, to study the effect of tube

cross-sections on the mechanical responses of the auxetic composites;

(5) To build the macroscopic finite element models and simulate the mechanical

responses of auxetic composites under low-velocity impact compression, to reveal the

relationship between the mechanical responses and deformation mechanism, to

validate the FEM results with experimental.

Chapter 1

4

1.3 Research Methodology

To achieve above listed objectives, the following methods will be employed:

(1) To design the reinforcement structure for auxetic composites and optimize various

parameters.

Various geometrical structures and models that could produce the NPR effect were

collected, classified and analyzed in literature review. The auxetic structure with

alternately arranged weft and warp yarns is selected because it can concentrate under

impact loading along the thickness direction, and consequently improve the impact

resistance.

In order to optimize the orthogonal structure of the reinforcement, a simplified 2D

geometric model will be established to calculate the relation between the value of

Poisson’s ratio and compressive strain. Optimized parameters including the diameters

of materials, space, numbers of the weft and warp yarn layers will be determined

according to the manufacturing precision as well the maximum value of negative

Poisson’s ratio.

(2) To select right materials for reinforcements and fabricate the auxetic

reinforcements and composites.

Rigid ABS tubes and high strength polyester yarns are selected to be used as the

reinforcement materials. The compressible PU foam is used as the matrix of

composites to solidify and integrate the reinforcement and let the composite structure

concentrate under impact loading. A set of stainless steel mould will be manufactured

according to the designed size and parameters of the composite samples. The

Chapter 1

5

multilayered reinforcements will be braided in the mould and then compound with the

PU foam using hand injection molding technique to make sure that the auxetic

composites are of good quality with sufficient permeation and high consistency.

(3) To conduct experimental study on auxetic composites under both quasi-static

compression and dynamic impact loadings.

The auxetic composites produced above will be firstly tested under quasi-static

compression in the fabric thickness direction using universal testing machine to

examine their auxetic effect and static compressive behavior. Then the experimental

study will be extended to the impact tests. A free drop testing device will be used to

test all auxetic composites with different amounts of impacting energies. The testing

results including the contact force and energy absorbed in function of displacement

will be measured. The influences of constituent material properties, reinforcement

structures and negative Poisson’s ratios on the impact behavior of auxetic composites

will be systematically studied based on the testing results.

(4) To develop the improved auxetic composites with rebounded polyurethane foam

and thicker reinforcements and study the effect of tube cross-sections on the

mechanical responses of the auxetic composites.

The improved auxetic and non-auxetic composites with flexible rebounded

polyurethane foam and more layers reinforcement structures will be fabricated. Three

different cross-sections for the ABS tubes including circle, square and rectangle will

be adopted for comparison. The mechanical responses and deformation mechanisms

of all composites under various strain-rates compression tests will be discussed and

Chapter 1

6

compared. The strain rate dependency of composites and the effect of tube cross-

section on the mechanical responses of composites will be investigated as well.

(5) To simulate the mechanical behavior of the auxetic composites under low-velocity

impact using finite element method.

A 3D Finite Element model of auxetic composite with round tubes will be established

in Ansys/Dyna software. The mechanical responses of FE model under three different

velocities impact will be simulated. The simulation results including the Poisson’s

ratio and the contact stress curves for auxetic composite will be obtained and

compared with that of experimental. The impact process of the composite will be

captured and used for optimizing auxetic structure. The optimized parameters will be

adopted to predetermine the structure for the composites with required Poisson’s ratio

and the new auxetic composites with improved the impact resistance and energy

absorption will be fabricated. Applications of these auxetic composites will be

explored.

1.4 Significance and Values

This research mainly focuses on developing, manufacturing, experimental testing and

finite element modeling a novel kind of auxetic composite for energy absorption and

impact protection. The significance and values of the research are embodied as

follows:

(1) This study provides direct insights into the design and fabrication of novel auxetic

composites by optimal structure designing and suitable materials arrangement. The

Chapter 1

7

development of multilayer integrally reinforced composites fill the gap of continuous

and long reinforcements in foam enhancement.

(2) Experimental investigations on the mechanical behavior of auxetic composites

under quasi-static compression and impact loads have been conducted, which will

provide a basic understanding of the relationships between the deformation of auxetic

composites and the damage features.

(3) Numerical simulation method has been adopted to verify the experimental testing

results of auxetic composites under low-velocity impact. The verified finite element

modeling in ANSYS/DYNA including geometry model, material model, contact,

constraints and etc. could be used to optimize the structure and parameters design of

auxetic composite and predict its mechanical response theoretically.

(4) In practical areas, the newly developed composites with negative Poisson’s ratio

will enable broader applications in damping and impact protection including

automobile, aerospace and defense, civil engineering and sport equipment, etc. due to

their enhanced mechanical properties. The study would also provide a new method to

fabricate the auxetic composites using simple and effective manufacturing techniques.

(5) Generally speaking, the study of multilayered orthogonal auxetic composites can

be very significant for both fundamental research and engineering applications.

1.5 Thesis Outline

Chapter 1 briefly introduces the research background of studying multilayer

orthogonal structural auxetic composites. The research objectives, methodologies,

significance and values are presented.

Chapter 1

8

Chapter 2 firstly reviews the main features of energy absorption materials, then the

classifications and applications of polyurethane foams, geometric structures and

unique properties of auxetic materials are introduced. Lastly, the impact testing

approaches, related physical quantities and experimental and numerical simulation

results are elaborated and discussed.

Chapter 3 firstly designs and optimizes the multilayer orthogonal structures for the

reinforcement of the auxetic composite, the parameters like the radius of the tubes and

space between the tubes are determined to achieve a big NPR value. Then, the auxetic

and non-auxetic composites are both manufactured by injecting foam formulation into

the reinforcements in the predetermined box. The samples are finally cut and prepared

well in accordance with the international standard for the next step experimental

testing.

Chapter 4 studies the quasi-static compressive behavior and NPR effect of auxetic

composites.

It is proved that the auxetic composite and pure foam have similar mechanical

properties in specific density under quasi-static compression. The auxetic composite

behaves more like a damping material with a big range of deformation strain, while

the non-auxetic composite behaves more like a stiffer material with a small range of

deformation strain. By the follows, the dynamic impact compression tests of three

materials are conducted and analyzed. The impact results and the damage mechanisms

of three materials are investigated. Their strain rate dependency is also revealed.

Chapter 1

9

Chapter 5 fabricates improved auxetic and non-auxetic composites with flexible

rebounded polyurethane foam and more layers reinforcement structures. Three

different cross-sections for the ABS tubes are adopted for comparison. The

mechanical responses and deformation mechanisms of all composites under various

strain-rates compression tests are compared and discussed. The effect of tube cross-

section on the mechanical responses of the auxetic and non-auxetic composites is also

investigated.

Chapter 6 builds a simplified Finite Element model to represent the auxetic

composites with round tubes. Ansys/Dyna software is used for calculating the

mechanical responses of FE model under three different impact velocities. The

simulation results including the Poisson’s ratio and the contact stress curves for

auxetic composite are obtained and compared with that of experimental.

Chapter 7 presents general conclusions and limitations of this study, and gives

suggestions for future work.

1.6 Reference

[1] Lu GX, Yu TX. Energy absorption of structures and materials. Woodhead

Publishing 2003; Chapter 1.

[2] Klempner D, Sendijarevic V. Polymeric foams and foam technology. Hanser

Publishers, Munich 2004; Chapter 3.

[3] Kreter PE. Polyurethane foam physical properties as a function of foam density. J

Cell Plast 1985;21(5):306-10.

[4] Shen HB, Steven N. Mechanical characterization of short fiber reinforced phenolic

http://www.amazon.com/s/ref=dp_byline_sr_book_2?ie=UTF8&text=Daniel+Klempner&search-alias=books&field-author=Daniel+Klempner&sort=relevancerankhttp://www.amazon.com/vahid-Sendijarevic/e/B00IQI63M2/ref=dp_byline_cont_book_1http://www.sciencedirect.com/science/article/pii/S1359835X03001362

Chapter 1

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foam. Composites Part A 2003;34(9):899-90.

[5] Das D. Reinforcement of syntactic foam with silicon carbide nanoparticles.

Florida Atlantic University 2011.

[6] Jiang LL, Gu BH, Hu H. Auxetic composite made with multilayer orthogonal

structural reinforcement. Compos Struct 2016;135:23-29.

[7] Evans KE, Alderson A. Auxetic Materials: functional materials and structures

from lateral thinking! Adv Mater 2000;12(9):617-28.

[8] Choi JB, Lakes RS. Nonlinear properties of polymer cellular materials with a

negative Poisson’s ratio, J Mater Sci 1992;27(19):4678-84.

[9] Alderson A. A triumph of lateral thought. Chem Ind 1999;17:384-91.

[10] Alderson KL, Pickles AP, Neale PJ, Evans KE. Auxetic polyethylene: the effect

of a negative Poisson’s ratio on hardness. Acta Metall Mater 1994;42(7):2261-6.

[11] Alderson KL, Fitzgerald AF, Evans KE. The strain dependent indentation

resilience of auxetic microporous polyethylene. J Mat Sci 2000;35(16):4039-47.

[12] Choi JB, Lakes RS. Fracture toughness of re-entrant foam materials with a

negative Poisson’s ratio: experiment and analysis. Int J Fracture 1996;80(1):73-83.

[13] Ma ZD, Bian H, Hulbert GM, Rostam-Abadi KBF. Functionally-graded NPR

(Negative Poisson’s Ratio) material for a blast-protective deflector. MICHIGAN

UNIV ANN ARBOR 2010:1-12.

[14] Liu Q. Literature review: materials with negative Poisson’s ratios and potential

applications to aerospace and defense. Defense Science and Technology Organization,

Victoria, Australia, August 2006.

https://www.google.com.hk/search?tbo=p&tbm=bks&q=inauthor:%22Debdutta+Das%22&source=gbs_metadata_r&cad=2

Chapter 1

11

[15] Lakes RS. Foam structures with a negative Poisson's ratio. Science

1987;235(4792):1038-40.

[16] Chan N, Evans. Microscopic examination of the microstructure and deformation

of conventional and auxetic foams. J Mater Sci 1997;32(21):5725-36.

[17] Webber RS, Alderson KL, Evans KE. Novel variations in the microstructure of

the auxetic microporous ultra-high molecular weight polyethylene. Part 1: Processing

and microstructure. Polym Eng Sci 2000;40(8):1894-905.

[18] Liu YP, Hu H, Lam J K C, Liu S. Negative Poisson’s ratio weft-knitted fabrics.

Text Res J 2010;80(9):856-63.

[19] Hu H, Wang ZY, Liu S. Development of auxetic fabrics using flat knitting

technology. Text Res J 2011;81(14):1493-502.

Chapter 2

12

Chapter 2

Literature Review

2.1 Introduction

This section firstly reviews the main features of energy absorption materials

compared with conventional materials. Then the classifications and applications of

polyurethane foams, geometric structures and unique properties of auxetic materials

are introduced. Lastly, the impact testing approaches, related physical quantities and

experimental and numerical simulation results are elaborated and discussed.

2.2 Energy Absorption Materials

2.2.1 Introduction

The research on and the development of energy absorbing materials which will

dissipate kinetic energy during various velocities impact and repeated dynamic

loading has been receiving much attention since 1970s [1-2]. The commonly used

materials for energy absorption include metal and alloy, plastic and fiber reinforced

plastic, polymeric foam, paperboard and wood etc. [3]. The major applications of

these materials are in the fields of aerospace, vehicles, sport, packaging and so on.

The materials using for energy absorption generally hold some unique features which

are different with conventional materials.

Chapter 2

13

2.2.2 Main Features

Conventional materials that are used in civil engineering and machineries usually

undergo small elastic deformation and are required to have certain strength and

stiffness under some specified load. Failure tends to occur due to fatigue, corrosion

and degradation of materials after a long time. Different with conventional materials,

the energy absorbing materials usually suffer from intense impact loading. So the

deformation and damage of these materials involve the big strain, strain rate effect,

strain hardening effect and various different deformation modes. The energy

absorbing materials used for impact protection like helmet lining and sport protection

equipments generally hold the characteristics of large plastic deformation, inelastic

energy conversion, restricted and constant reactive force, light weight and high

energy-absorption capacity [3]. Owning all above mentioned features, polymeric

foams have been widely used as energy absorbers in the application of packaging,

damping and structural components in different areas.

2.2.3 Polyurethane Foams

Polyurethane was firstly made by Bayer Company in 1937 [4,5]. As one of the most

widely used polymeric foams, the polyurethane (PU) foams have been applied in

different areas such as transportation, furniture, packaging and construction industry

and their consumptions are increasing day by day due to excellent properties like light

weight, high specific strength, good thermal insulation, low cost and fast fabrication

[6]. PU foams could be classified as flexible, semi-rigid and rigid foams depending on

their chemical composition, the degree of crystallinity and cross-linking [6]. As

Chapter 2

14

described in the standard DIN 7726, flexible PU foams should have low resistance to

an applied load and most of them are open cell, permeable to air and reversible

deformable [6]. While rigid foams have relatively high compressive modulus and they

are commonly used as the sandwich structure core material. Polyurethanes are

produced by reacting isocyanates with polyols in the presence of some catalyst or by

activation with ultraviolet light [7]. The type and quantity of isocyanates and polyols

as well the surfactants and blowing agents could highly influence the properties of

polyurethane foams [6]. PU foams could also be categorized as open cell and closed

cell foams depending on the microstructure of foams. The closed cell foams are most

suitable for thermal insulation and they are generally rigid. While open cell foams are

best suit for seating and bedding cushions, acoustical insulation and among other uses.

They are usually flexible [8].

PU foam is a good candidate for being used as energy absorption material due to its

superior energy absorbing capability including large strain and moderate contact

stress. However, plastic deformation, collapse of cell walls and internal fracture can

easily cause fatigue even failure of the PU foams. Generally, parameters like foam

density, open/closed cell content, cell size and shape, etc. are adjusted to improve the

mechanical properties of foams [9,10]. Chopped fibers [11] and micro/nano-sized

particles [12] are also added to increase the stiffness and plateau stress of plain foams.

However, the continuous long fibers and integral structural reinforcements are seldom

selected for mechanical enhancement in case the big increase of foam weight and thus

decrease of specific strength and specific energy absorption. In this research,

https://en.wikipedia.org/wiki/Polyol

Chapter 2

15

multilayered orthogonal structural materials with light-weight and high mechanical

properties are designed as the reinforcements to enhance the PU foam without

decreasing the strength to weight ratio [13]. Meanwhile, the negative Poisson’s ratio

(NPR) effect will be achieved by suitable structure arrangement of the reinforcement,

which further enhanced the mechanical performance of foams under compression and

impact effectively. NPR, namely “auxetic”, means that materials will expand

transversely when pulled longitudinally or contract transversely when compressed

longitudinally [14]. With the combination of structural reinforcement and matrix foam

as well as the unique auxetic effect, the newly developed composite is named “auxetic

composite”. This multilayered orthogonal structural auxetic composite could be

regarded as a kind of reinforced PU foam with auxetic effect which could be used

individually or served as the core materials of the sandwich structures.

2.3 Auxetic materials

2.3.1 Introduction

Most materials, such as a rubber band, contract laterally when stretched in the

longitudinal direction. These materials are called positive Poisson’s ratios materials.

In contrast, auxetic materials (materials with negative Poisson’s ratio, NPR) expand in

the transverse and/or thickness direction when subjected to tensile stretch in the

longitudinal direction and shrink when compressed along a perpendicular direction. In

recent years, auxetic materials have gained various interests due to their

counterintuitive behavior under deformation and improved mechanical properties,

including shear resistance [15-17], indentation resistance [18-23] and fracture

Chapter 2

16

toughness [15-16, 24-25]. These special features have made auxetic materials very

attractive for many potential applications such as automobile [26], aerospace and

defense [27], sport equipment, where impact protection can be one of the highly

required properties.

The word ‘auxetics’ was first proposed by Evans to name the materials with negative

Poisson’s ratio, which has been commonly used now [28].

Auxetic materials have been studied for more than two decades. Since the first auxetic

polyurethane foam with re-entrant structure was made by Lakes in 1987 [23], a

number of auxetic materials have been proposed and fabricated ranging from

macroscopic and micro-structural levels to molecular level including auxetic

polymeric foams and micro-porous polymers [20-28], auxetic fibers [25,29-30] and

fabrics [26,27,31,32], auxetic honeycombs [33] and composites [34-37], etc.

Improved properties such as shear resistance [16-17], indentation resistance [18-19]

and fracture toughness [16,20] could be found for auxetic materials compared with

the corresponding common materials.

2.3.2 Microstructures and Models

2.3.2.1 Re-entrant Microstructures

Re-entrant structure is one of the most classic and common auxetic structures in

materials design. As shown in Fig.2.1, auxetic structure in the form of 2D re-entrant

honeycomb was firstly proposed by Gibson in 1982 [38]. The honeycomb combined

by 2D re-entrant hexagons could be deformed by hinging of the diagonal ribs under

an applied uni-axial load. The negative Poisson’s ratio effect is achieved by rotating

Chapter 2

17

the diagonal ribs to the horizontal direction and expanding the structure transversely.

In 1995, Choi and Lakes proposed the 3D isotropic re-entrant foam structure as shown

in Fig.2.2 [39]. The Poisson’s ratio was predicted to approach -1 in an idealized re-

entrant model.

Figure 2.1 Re-entrant honeycomb structure [38] (Reproduced with permission of The

Royal Society)

Figure 2.2 3D re-entrant structure [39] (Reproduced with permission of SAGE)

There are many other re-entrant structures with similar deformation mechanism

producing auxetic effect, like double arrow-head structure, star-shaped structure and

sinusoidal ligament structure (see Fig.2.3). The rib flexure and hinging of arrowheads

Chapter 2

18

and stars in opening and closing under uni-axial loading leads to the auxetic behavior

of materials [40-41], while the auxetic effect of sinusoidal ligament structure comes

from the opening up of re-entrant cells into near-rectangular cells [42].

(a) (b) (c)

Figure 2.3 (a) Double-arrow head [40]* (Reproduced with permission of 1997 IEEE),

(b) star-shaped [41] (Reproduced with permission of Springer), (c) sinusoidal

ligament structure [42] (Reproduced with permission of American Society of Medical

Engineers)

*In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of The Hong Kong Polytechnic University's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink.

2.3.2.2 Rotating Squares, Rectangles and Triangles Models

Grima et al. first found rotating structure in inorganic crystalline materials like

zeolites [43]. The structure is based on the arrangement of some geometric units

connected at selected vertices. The auxetic effect is achieved by the rotation of units

in opening up under some uni-axial stretch. (see Fig.2.4). Then Grima also proposed

similar structures like rotating squares, rotating triangles, rotating rectangles (Fig.2.5)

[44-50]. The model of different sized rigid rectangles [51] was also proposed to

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Chapter 2

19

represent the properties of various systems including silicates, zeolites and liquid-

crystalline polymers. It was also shown that such systems could exhibit auxetic

behavior which is scale independent when stretching in some particular directions,

while the Poisson’s ratio’s value was dependent on the shape, size and relationship of

different rectangles [52].

Figure 2.4 Rotating structure opening up under stretch [43] (Reproduced with

permission of Springer)

(a) (b) (c)

Figure 2.5 (a) Rotating squares [43] (Reproduced with permission of Springer), (b)

rotating triangles [44] (Reproduced with permission of Springer), (c) rotating

rectangles structure [45]

Chapter 2

20

2.3.2.3 Nodule and Fibril Microstructures

Nodule and fibril structure was initially reported in a 2D model for auxetic micro-

porous polymer by Caddock and Evans (Fig.2.6) [53-54]. The auxetic effect was

achieved by the translation of nodules stretched by connecting fibrils when loaded.

The Poisson’s ratio of expanded PTFE varies with the tensile strain and can attain as

large as -12. Other polymers like polypropylene and polyester fibers [55-56] could

also be processed with similar nodule and fibril structure and obtain obvious auxetic

effect. 2D nodule fibril analytical model was built by Alderson A and Evans KE to

reveal the relations between the mechanical properties of materials and geometric

parameters [57-58]. Besides, the 3D nodule and fibril model (Fig.2.7) could also be

applied to more materials including micro-porous polymers, body centered cubic

metals, foams and etc. Research showed that 3D hexagonal nodule and fibril models

exhibit more evident auxetic effect than equivalent 2D model [59-60].

Figure 2.6 Nodule and fibril structure (a) normal state, (b) under stretch [53-54]

(Reproduced with permission of IOP Publishing)

Chapter 2

21

Figure 2.7 Schematics for a generalized 3D tethered nodule, showing: (a) a central

nodule connected to eight others via corner fibril [60]. (With the permission from

Springer)

2.3.2.4 Chiral Models

As illustrated in Fig.2.8, chiral models are formed by connecting of chiral units, in

which the chiral units are composed of straight ligaments and central rigid nodes

which are circles, rectangles or other various geometries. The auxetic effects are

gained by wrapping or unwrapping of the ligaments around the nodes under an

applied force. Theoretical and experimental investigation on 2D chiral honeycomb

was conducted by Prall and Lakes as shown in Fig.2.8 (a), the Poisson’s ratio of the

chiral model under in-plane deformations was measured to be around -1 [61]. The

auxeticity of chiral and anti-chiral models and relations to the lattice have also been

studied by many other researchers in reference [61-67].

Based on this basic chiral structure, a new kind of structure named as ‘meta-chiral’

has been developed by Grima [68]. As shown in Fig.2.8 (b), the structure is formed by

connecting the symmetric blocks where the node in each unit is a rectangle. It was

Chapter 2

22

proved that the auxetic effects of chiral models are dependent on the node shape and

the ligaments length.

(a) (b)

Figure 2.8 Chiral honeycombs (a) Formed with the same chiral units [61]

(Reproduced with permission of Elsevier), (b) Formed with symmetrical chiral units

[68] (Reproduced with permission of John Wiley and Sons)

2.3.2.5 Other Structures

Other structures and models that give rise to auxetic behavior are also under

investigation including angle-ply laminates with sandwich-like stacking achieving

auxetic effect [69], double-arrow ‘hard’ block and spring ‘soft’ segment model for

copolymers [70], missing rib model proposed by Smith (Fig.2.9) [71] and the circle

holes structure (Fig.2.10) realized its auxetic effect under compression due to the

elastic instability of materials [72].

Chapter 2

23

(a) (b)

Figure 2.9 The idealized networks of the (a) intact version and (b) cur version

with the unit cells shaded [71] (With the permission from Elsevier)

Figure 2.10 The deformation of circle holes structure under compression [72]

(Reproduced with permission of John Wiley and Sons)

2.3.3 Unique Properties

2.3.3.1 Mechanical Properties

The mechanical properties of auxetic materials are totally different from the

equivalent non-auxetic materials. Research showed that the auxetic foams usually

have lower Young’s modulus than conventional foams [73-76]. In reference [77], for

example, the compressive Young’s modulus of auxetic foams is only a half of that for

Chapter 2

24

conventional counterpart at small deformation. But to the contrary, the shear modulus

of auxetic foams is much higher than that of conventional ones. This result can be

explained by the relations among shear modulus G, Poisson’s ratio ν, Young’s

modulus E and bulk modulus K. For isotropic materials, they are related in the

equation: E = 2G (1+ν) = 3K (1− 2ν). From the equations, it could be found that for

most common materials, the Young’s modulus E is at least twice higher than the shear

modulus G. While for the newly manufactured materials with negative Poisson’s ratio,

the shear modulus G increases and the bulk modulus K decreases, which means the

material are difficult to shear but easy to deform volumetrically.

Compared with most conventional materials, the auxetic materials may also own

increased fracture toughness. The fracture toughness of auxetic foams was studied as

a function of permanent volumetric compression ratio [20]. The toughness is increase

by 80%, 130% and 160% with the volumetric compression ratios of 2.0, 2.5, 3.0 than

that of conventional foams. The auxetic materials may also have enhanced crack

resistance. The crack in materials expands and closes up when the materials are pulled

apart due to the auxetic effect.

2.3.3.2 Indentation Behavior

Hardness of auxetic materials can be increased due to the auxetic effect. When the

auxetic materials get impacted and compressed in the vertical direction, they will

contract laterally (see Fig.2.11), which means the material ‘flows’ into the vicinity of

the impact point under impact [15]. The material becomes denser and harder near the

impact point. The indentation resistance of auxetic UHMWPE was found to be 2.5

Chapter 2

25

times than that of conventional counterpart [29]. This phenomenon was also found in

other auxetic materials, such as auxetic fiber-reinforced composites [29,78].

Figure 2.11 Indentation resistance [15] (Reproduced with permission of John Wiley

and Sons)

2.3.3.3 Synclastic Curvature

When conventional materials are subjected to an out-of-plane bending force, they

show saddle shape (Fig.2.12 a) because of the perpendicular shrinkage. While for

auxetic materials, they may exhibit dome shape (Fig.2.12 b) because the

perpendicular direction has the same curve trend with the bending direction, i.e.,

synclastic curvature [15]. Therefore, synclastic curvature will make auxetic materials

better fit into curve surface.

Figure 2.12 (a) Anticlastic curvature, (b) Synclastic curvature [15] (Reproduced with

permission of John Wiley and Sons)

Chapter 2

26

2.3.3.4 Variable Permeability

The permeability of auxetic materials is better than conventional materials due to their

unique pore-opening properties (Fig.2.13). The pore size becomes bigger in both axial

and perpendicular directions under stretch. This characteristic makes auxetic materials

suitable for filtering because it can improve the filtration efficiency and increase the

pressure during filtering due to the pores shrink. In addition, the smart drug release

could be designed by building the relationship between the pore size and applied

strain [79]. The variable permeability of auxetic honeycomb has been studied. It was

found the variable permeability of material could be evidently improved from both

macro and nano scales [80].

-

Figure 2.13 Permeability of auxetic honeycomb [79] (Reproduced with permission of

John Wiley and Sons)

Chapter 2

27

2.3.3.5 Energy Absorption

Superior energy absorption properties like ultrasonic, acoustic and damping were

found for auxetic materials. In reference [81], it was reported that auxetic foams had

better sound absorption capacity than conventional foams at low frequencies. The

cyclic compression tests showed the damping capacity of auxetic foams was 10 times

higher than that of the corresponding conventional foams [82-83]. Sound absorption

[82,84,85] and crashworthiness [82,85,86] of auxetic materials were also found to be

enhanced in comparison with the conventional materials.

2.3.4 Auxetic Composites

As a particular kind of auxetic materials, auxetic composites have received great

attention in recent years. Alderson et al. [34] had reported that auxetic composite

materials could be fabricated mainly by two approaches, either by specially designing

the structural configurations with conventional components or by filling auxetic

reinforcements in composites.

2.3.4.1 Angle-ply Laminates

The first approach was to produce the fiber-reinforced composite laminates by using

conventional fiber materials [34,87-89]. The route was to design the angle-ply

laminates by using pre-preg which gives specific stacking sequences to produce

auxetic effect. In these composite laminates, negative in-plane or out-plane Poisson’s

ratios could be achieved. However, the requirement for the auxetic composite

laminates was that the ply materials better to be highly anisotropic [34], which

Chapter 2

28

indicated that carbon fiber/epoxy resin [89-90] was more suitable choice than others

[91], and this limited the selection of materials and consequently reduced the

possibility of enhancing the mechanical properties of composite materials.

2.3.4.2 Composites using Auxetic Reinforcements

The second approach was to use auxetic reinforcements. The auxetic fibers [30]

embedded in the composite as the reinforcement would prevent the occurring of fiber

pullout because the fiber would get fatter when stretched, leading to self-locking of

auxetic fibers into the matrix. Composite using two-layer woven fabric made of

double-helix yarns as inherently auxetic phase was manufactured to be auxetic with

an approximate Poisson’s ratio of -0.1 [92]. While the shortcoming is the matrix

silicone rubber gel seriously constrained the strongly auxetic property of double-helix

yarn with Poisson’s ratio of -2.1. Hou et al. [35] suggested another kind of composite

structure with isotropic NPR values by randomly including re-entrant triangle

elements into a matrix. The Poisson’s ratio of the composite structure could be

tailored by changing the geometries of inclusions and properties of components [36]

and high difference in stiffness of the inclusions and the matrix material was a

condition to obtain NPR of the composite [37].

2.4 Low-velocity Impact Tests

2.4.1 Introduction

The quasi-static loadings are generally first conducted to investigate the mechanical

responses of materials because the experimental set-up is simpler than that for the

Chapter 2

29

impact tests and it is relatively easier to observe the detailed deformation process of

the materials. However, lots of materials properties are much dependent on the strain

rates. Understanding the impact resistance of the composite materials requires to

quantify the exact value of some mechanical response such as the contact force and

impact energy absorption as the material deforms. Hence, to check if the auxetic

composites are suitable for being used as energy absorbers under dynamic loading

conditions, further study on the low-velocity impact responses of composites should

be conducted.

2.4.2 Testing Approaches and Related Physical Quantities

For strain rates lower than 102 s-1, which could be defined as low velocity impact

range, the impact tests could be conducted by means of drop hammer or pendulum

[93]. For the case of drop hammer, a predetermined mass is lifted to a certain height

and then released to impact on a sample which is placed at the base anvil of the

machine. The maximum impact velocity is governed by the initial height of the

hammer. Usually, an accelerator is attached onto the impact mass to measure the

instant acceleration of the drop hammer during the impact process. A displacement

transducer is used to record the movement of the impactor. When pendulums are used

for impact test, the swinging arms should be designed to be long enough to minimize

the radial movement at the impact face and the impact face could translate only. In

both above low velocity impact methods, the velocity of the striker is not a constant, it

varies with the impact process. The strain rate that will be mentioned in this research

is to calculate as dividing the biggest impact velocity by the thickness of samples.

Chapter 2

30

For the strain rate in the range of 102 -104 s-1, the split Hopkinson pressure bar system

is usually adopted for impact testing [94-95]. Gas guns are extensively used for the

impact test ranging from 100 m/s to 800 m/s [96]. There are several other techniques

are available for the dynamic loading tests, such as explosives and Talor anvil tests

[97], which will not be elaborated in the text.

Some physical quantities are of great importance to record during the impact process

for analyzing the mechanical features of the impacted materials. They are the contact

force versus time, the contact force and the absorbed energy versus impactor

displacement, the velocity of impactor versus time, the absorbed energy/impact

energy ratio, the contact force versus energy, the residual force versus impactor

displacement and the residual force versus impact energy.

There are also critical values of some physical quantities for revealing the damage

mechanisms and impact resistance of materials. Two characteristic forces are: the first

damage force and the maximum force. Two characteristic displacements are: the

displacement at peak force and the maximum displacement during the impact. Two

characteristic energies are: the maximum impact energy and the final absorbed energy

[98-99].

2.4.3 Impact on Foams and Foam-cored Composites

The quasi-static compressive and dynamic impact properties of foams and foam-cored

sandwich panels have been studied by many researchers with experimental and

numerical methods [100-107]. The low velocity impact response of rigid PU foam at

velocities from 2 m/s to 4 m/s was studied by V.P.W. Shim [100]. The effects of

Chapter 2

31

impact velocity and impactor geometry on the energy absorption were studied.

Similar study on the impact behavior of aluminum syntactic foams was conducted by

Castro G et al. In the reference [101], failure mechanisms of foams were interpreted

from impact load versus displacement curves and examination of impacted aluminum

syntactic foam plates. Results showed that the aluminum syntactic foam has better

compression strength and energy absorption than conventional aluminum foams, but

poorer than steel syntactic foam. In order to improve the energy absorption and low

velocity impact resistance, GQ Zhang et al. [102] fabricated the PU foam filled

pyramidal lattice core sandwich panels and studied their quasi-static compression and

low velocity impact properties. A synergistic effect was found based on the

compression results. During the impact tests, the contact time between the impactor

and the sandwich panels was shorter and the impact peak force of foam filled

specimens was a little higher than that of unfilled specimens. The significant

improvement of auxetic foams in dissipating energy compared to non-auxetic and iso-

density foams at every number of cycles and loading levels has been proved by

Bezazi and Scarpa [108]. In reference [109], finite element model for an auxetic-cored

sandwich panel was built and compared to that of an Aluminum foam-cored sandwich

panel. Higher energy absorption for the auxetic-cored panel under velocity from 380

m/s to 600 m/s was identified and contributed to the local densification of materials

due to the NPR effect. The quasi-static compressive behavior [110] and dynamic

crushing [46-47] of auxetic PU foams and conventional non-auxetic foams were also

Chapter 2

32

studied by Scarpa et al. Their comparative results showed a distinctive improvement

of mechanical characteristics for auxetic foams including energy absorption.

2.5 Chapter Summary

In this chapter, energy absorption materials were firstly reviewed on their main

features like large plastic deformation, restricted and constant reactive force, light

weight and high energy absorption capacity compared with conventional materials.

As one of the most widely used polymeric foams and energy absorption materials,

polyurethane foam was then reviewed on its classifications and applications. The

developed auxetic composites in this study could be regarded as a kind of reinforced

PU foam with auxetic effect. Hence, the auxetic materials especially the auxetic

composites following above had been reviewed on geometric structures and unique

properties. To check whether the auxetic composites are suitable for being used as

energy absorbers under impact loading, studying on the mechanical responses of

composites under impact tests is necessary. Therefore, the impact testing approaches,

related physical quantities and experimental and numerical simulation results had

been elaborated and discussed finally.

2.6 Reference

[1] Johnson W, Reid SR. Metallic energy dissipating systems. ASME Appl Mech Rev.

1978;31(3):277-88.

[2] Johnson W, Reid SR. Update to: Metallic energy dissipating systems. ASME Appl

Mech Rev Update 1986;39,315-19.

Chapter 2

33

[3] Lu GX, Yu TX. Energy absorption of structures and materials. Woodhead

Publishing 2003; Chapter 1.

[4] DE 728981, IG Farben, published in 1937.

[5] Bayer O. Das Di-Isocyanat-Polyaddition sverfahren (Polyurethane) [The

diisocyanate polyaddition process (Polyurethanes)]. Angewandte Chemie

1947; 59:257–72.

[6] Oertel G. Polyurethane Handbook. 2nd Edition. Hanser Publishers 1994.

[7] Soto M, Sebastián R M, Marquet J. Photochemical Activation of Extremely Weak

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Copyright Undertaking · 2020. 6. 29. · structure for the developed composite in this study is multilayered orthogonal auxetic structure and the component materials are rigid ABS