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Dissertation Abstract: Auxetic Structure

Chapter 1: Introduction

This chapter introduces the term 'auxetic materials' and observes the main characteristics of these substances. To increase the readers' knowledge about the term as well as explain the nature of auxetics, the author briefly refers to the history of their discovery, qualities, and behavior. It is necessary to know that the term 'auxetic' has Greek roots and is used to define a matter or substance that tends to expand or become larger. For the first time, auxetic behavior was detected in the structure of aluminum. In particular, the honeycomb structure of this material was changed demonstrating auxetic qualities. i.e., expansion in a lateral side, that occurred in response to the applied load. A few years later, scientists introduced to the world an artificially created material, a microporous polyethylene, which was called the auxetic.

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The introductory chapter reveals that the auxetics are the materials that have a negative Poisson's ratio. In contrast, conventional materials are characterized by a positive Poisson's ratio. The equation that displays the Poisson's ratio is v = - [-?trans / ?longitudinal]. It depicts the relation between the power that a particular material endures and the level of its deformation that occurs as a result of the applied force, for example, compression or strain. Conventional materials have a positive Poisson's coefficient because they reveal the signs of deformation in the direction that is perpendicular to the direction of the applied force. In other words, when one side becomes longer or larger, the other one becomes thinner. Unlike conventional materials, auxetics tend to become thicker in the lateral direction, thus displaying greater resistance to the action of the outer stimuli. This behavior of the auxetic materials presumes a better capacity to absorb energy while being compared to conventional materials. Specifically, the energy goes inwards, increasing the shear stiffness of auxetics. These qualities are stipulated by the molecular structure that is geometrically close to square, rectangle, triangle, hexagon, or octagon.

Moreover, a negative Poisson's ratio of auxetic materials correlates with other variables of elasticity, such as Young's modulus (E), shear modulus (G), and bulk modulus (K). Young's modulus (E) is a dimension that expresses the relation between the stress and its impact on a certain substance in terms of the increase of its length. Simply put, it is the coefficient of the matter's elasticity that measures its ability to strain. Bulk modulus (K) is a coefficient that reveals the substance's capability to resist volumetric stresses. Typically, it means taking into account the three-dimensional impact (x, y, z) while estimating the ability of the material to resist this multi-directional stress. Moreover, shear modulus (G) measures the matter's resistance to shifting under the action of the applied force. The relationship between these interdependent components of elasticity is expressed with the equations below.

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The auxetics can be either organic or non-organic. In nature, the examples of such materials are cow and salamander skin. Nevertheless, the auxetic materials are mostly synthesized artificially, in particular, by using the method of additive manufacturing. The fact is that the manufacture of these materials is rather pricy; therefore, it is more feasible to use the mixture of auxetics and conventional matters, which is done by using the additive manufacturing technique.

The introductory chapter ends with a brief review of the thesis structure. It reveals the purpose of this paper that is to collect more empirical knowledge about the nature of auxetics and their positive qualities, which can be used to facilitate and improve people's life. Moreover, it reveals the objectives of the survey: auxetic properties and behavior, re-entrant structure, and in particular, the honeycomb macrostructure of H13 steel that is used as a tested material for this study. To be more precise, this thesis aims to explore the auxetic behavior of H13 steel in the conditions of the applied tensile and compression loads.

Chapter 2: Literature Review

This chapter observes and discusses the types of auxetic materials, their structure, properties, and applications. In particular, there are auxetic cellular solids that have the re-entrant structure of their cells, which allows them to resist compression and strain. Another kind of auxetics is honeycomb-structured materials that have a negative Poisson ratio due to their construction. Moreover, there are auxetic composites that are created from the mixture of fibers and some matrix materials that typically have a star-shaped structure. In addition, auxetics also include microporous polymers. The most famous is ultra-high molecular weight polyethylene (UHMWPE). It is one of the first auxetic materials that were created artificially. Similar to other auxetics, the principle of UHMWPE auxetic behavior is based on its structure. It consists of filaments and nodules. In the event of stress, the rotation power forces nodules to twist up to 90 degrees, which creates more volume, thus demonstrating a negative Posson's ratio of this matter. Another type is molecular auxetics that gains the corresponding behavior by bonding hydrogen or changing the molecular structure to rotating rods, which increases in volume due to rotation power once the material with the corresponding structure endures tension.

Besides, this chapter accentuates an important peculiarity that auxetic materials of both kinds, those that exist in nature and those that are made artificially, have a significant role in biology. For example, some types of skin and bones display auxetic behavior. Moreover, modern artificial blood vessels are designed to have a nodule and fiber structure to resist blood pressure, which decreases the likelihood of cardiovascular diseases.

Finally, there are isotropic and anisotropic auxetic materials. The first kind expands in both directions (x and y) when they are stressed. The second expands only in one direction. Nonetheless, both reactions depend on and require a specific structure of materials. Apart from the above-described structures of the auxetics, one should distinguish such constructions as polymeric and chiral structures that stipulate the auxetic behavior of matters.

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Observing the properties of auxetic materials, it is necessary to accentuate their shear resistance, which is stipulated by the ability to consume energy while changing the structure. The relation between shear modulus and the other 3 components of elasticity is presented in the following equations: G = 3K (1 - 2)/2(1 + v), E = 2G (1+ ?) = 3K (1- 2?). Besides, this chapter reveals that it is scientifically proven that auxetics have greater indent resistance than conventional matters. This ability depends on the hardness of the material, which is presented with the following formula: H? [E/ (1-v2)] ?. This equation reveals the relations between the Poisson's ratio, Young's modulus, and hardness. Besides, an indentation can be measured by P (pressure) with the help of this formula: P = hE/2a (1-v2). In a word, the auxetics have a greater ability to resist shear and indention compared to the conventional materials. This beneficial quality is stipulated by the ability of these matters to absorb energy inward. It becomes possible due to the distribution of energy within the inner structure of the auxetic material. In this regard, the properties of the sandwich-structured auxetic matters include the greater capacity to absorb energy compared to simple auxetics.

Taking into account the above-discussed auxetic properties, this chapter points to numerous useful applications of auxetics. For example, they are used in the manufacturing of seals, rivets, and gaskets. Besides, since the auxetics are light with high stiffness and stress resistance, they are utilized as materials for automobiles and aircraft. What is more, the structure of auxetic materials allows them to consume much energy that is obtained from the outer stimuli and directed inwards, which means that these matters are effective shock and sound absorbers.

Considering the important benefits of the auxetic properties, it is not surprising that scientists work on developing various ways of the artificial production of the auxetics. This chapter introduces such ways of manufacturing as compression molding, sintering, flow molding, extrusion, and transfer molding. Sintering and extrusion are considered to be the most feasible techniques because they are relatively cheap and easy to perform. Therefore, for example, the manufacturing of polyethylene is done using these methods.

Chapter 3: Problem Statement

This chapter is dedicated to the statement of the research question. Specifically, considering that the auxetics have a negative Poisson's ratio, they are characterized with the appropriate behavior. For example, shear and indentation resistances, expansion in one or several directions are results of forces, compression, or strain. The research is aimed at verifying these properties of the auxetic behavior through applying them to the creo simulation tool.

Chapter 4: Design Methodology

This chapter describes the steps of surveying the research question. Besides, it provides detailed information regarding the tools utilized in this study. The author uses the computer program Pro/Engineer to construct a simulation of the predicted auxetic behavior. This program creates a three-dimensional image of the material that will be created by implementing additive manufacturing in the DMD machine. The first step, which is the computer simulation of manufacturing, is conducted to verify that the predictions are valid. It is necessary to clarify that the verification is possible because this program allows observing and exploring the volumetric loads that the matter endures. To begin with, the author of the experiment draws a two-dimensional image of the auxetic material, creating a typical re-entrant structure.

Chapter 5: Simulation of Auxetic Model

This chapter describes the steps of creating the simulation of an auxetic model. To begin with, it accentuates that the author uses the latest Creo 2.0 software that replaces the Pro/Engineer program at the actual stage of simulation. The material that is used is H13 steel. The properties of this chemical element are added to Creo 2.0 software manually to assure that all necessary variables are taken into account. Thereafter, these properties are assigned to the already existing re-entrant structure.

The next step of the simulation is the definition of the degree of freedom. It is an important part because it is connected to the ratio of load, which should also comply with the characteristics of the chosen material. In this case, the model was fixated at one side and released at the other; the free side was the actual place that endured the loads. Further, the author distinguishes the kind of load that will be applied to the chosen material. In this experiment, the only load that will affect the matter is the force load.

The next step is to choose the type of analysis that is the most suitable for this research. Creo 2.0 contains three kinds of analysis, which are dynamic, static, and thermal. Static analysis is defined as the most appropriate because it measures the relations between the applied loads and respective strains, deformations, and stresses. The author inputs the corresponding setting in Creo 2.0 software. Moreover, to monitor the process of simulation, the corresponding setting is applied in the program. It reveals that static analysis is conducted successfully. The next stage described in this chapter is the observation of results. It is aimed at identifying the changes that occur as a result of the applied force. These changes include stresses, strains, and shear. At this phase of the experiment, visual observation of the auxetic material displays that, exactly as it is suggested, the matter becomes thicker in a lateral direction.

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This chapter demonstrates the practical application of the obtained knowledge about the auxetic behavior of materials. It contains visual evidence that the structure plays a vital role in the discussed auxetic properties. Specifically, the first two re-entrant structures are proven to be ineffective in terms of expanding in the y-plane. Nevertheless, after the necessary changes are made, the experiment shows positive results that can be detected visually while observing the results of the simulation. What is more, visual analysis of results reveals that the model demonstrates a different response to power in various parts. In particular, the lateral direction that was expanded initially contained the ribs that were joined in a way that created peak and trough regions. The simulation displays that the peaks of structure endured lesser changes than its troughs under the applied tensile and compression loads. It can be detected visually that the lateral ends that were v-shaped at the beginning of the experiment formed almost straight lines from both sides after the force was applied. It means that the discussed structure has a negative Poisson's ratio both at peaks and troughs, but the value of this auxetic behavior is different for these regions as it was described above. Besides, this experiment depicts that the structure displays auxetic properties in response to both tensile and compression loads.

Chapter 6: Fabrication of Auxetic Structure

This chapter describes the stages, approaches, and tools that are utilized to create auxetic structures. First and foremost, it introduces the direct metal deposition (DMD) machine which fabricates auxetic materials applying the additive manufacturing technique. The model simulated in CAD software is brought to the DMD machine to create the actual structure based on the simulated one. To transfer the necessary information from CAD software to DMD, the author of the experiment uses NC language.

Thereafter, DMD utilizes the metallic powder to create three-dimensional parts by the information that is passed from CAD. The laser of DMD melts the powder and creates the needed detail layer by layer. The necessary structure of the simulation model is achieved by this additive technique. It presumes adding layer after layer with the proper time intervals that comply with the time needed for the melted metal powder to cool down and solidify before the next layer is added to its surface. In addition to the time variable, the temperature is a vital factor that greatly affects the results of additive manufacturing. Therefore, DMD allows the controller to monitor the temperature in different parts of the machine as well as at different manufacturing stages. Besides, it also takes the probes of the produced material to detect and observe the interim results. According to this information, the real-time controller can test the properties of the material and define if they comply with the initially set instructions.

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This chapter depicts that to create the needed part in DMD, the author uses metallic powder (H13 steel) with shield gas (CO2). The identified issue with additive manufacturing is the insufficient temperature of the laser that prevented the correct melting of the powder. Undoubtedly, it negatively affected the process of manufacturing, complicating the composition of the proper microstructure of the matter. Therefore, to accomplish the desired results, the temperature set by the NC program was increased from 700 to 1000 watts. Besides, the 3D model turned to have somewhat different measurements from those that were initially set in CAD. This change is connected with the peculiarity of laser work and the required shape of the structure. This peculiarity stipulated the difference between the results obtained in simulation and the outcomes of the actual experiment.

Chapter 7: Experimental Procedure

This chapter describes the methods and tools that are used for the part of the experiment that presumes the application of loads to the produced 3D model. To conduct the survey, the author uses tensile and compression loads, which are implemented with the help of the Instron 8801 machine. Even though this machine is typically utilized for dynamic kinds of tests, it is also suitable for static analysis of any matter. To assure the safety of an operator, it has protective shields that prevent the fragments apart from getting outside the frames of the machine.

The auxetic structure that was created by DMD using additive manufacturing has been tested four times by the Instron 8801 machine. All the performed tests were aimed at defining the Poisson's ratio and its plausible variations in different parts of the produced model. To measure the number of changes, the dial gauge was used. It helped identify the impact of both tensile and compression loads by detecting the change in the length and shape of the lateral side. The obtained measurements were included in the table. The appropriate visuals were added to Chapter 7 and Appendix to let readers comprehend the process and outcomes of this experiment.

Chapter 8: Results and Discussion

This chapter is aimed at introducing the results of the conducted experiment and interpreting the findings, linking empirical knowledge to the corresponding theoretical concepts. The results were measured at one side of the model; however, given that the changes occurred in both directions, the obtained results were multiplied.

The experiment displays that auxetic behavior starts after the applied load becomes greater than 3.1 kN. Starting with this measure, a negative Poisson's ratio grows. Nevertheless, this process stops when the applied force reaches 21.6 kN. What is more, it is detected that inflection occurs when the stress reaches 19 MPa.

It is appropriate to accentuate that the results obtained by using simulation software regarding the difference of the auxetic behaviors between troughs and peaks of the manufactured part comply with the data received using the real-life experiment. Both regions display auxetic behavior, but troughs have greater authenticity than peaks. Besides, it is identified that the Poisson's ratio remains almost the same when the load reaches 27 MPa. Therefore, it is assumed that this measure is the maximum load under which the manufactured material demonstrates auxetic behavior in response to stress. Furthermore, enduring compression, the peak region of the lateral side expresses the biggest negative Poisson's ratio (-0.378585) when the load is 7.95. In addition, in the troughs, the biggest negative Poisson's ratio (-0.5681) has been fixated when the applied force has reached 6.9MPa.

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The interpretation of the above-revealed results suggests that H13 steel manifests the auxetic behavior under the applied tensile and compression loads. Specifically, it displays the negative Poisson's ratio that continues to increase simultaneously with the growth of the applied force. At the same time, this capacity is limited by the load frames. For example, auxetic behavior occurs neither under small loads nor when the applied force becomes high. Therefore, it is possible to deduce that the auxetic behavior of this material has load limits, which were presented in the numbers above.

The difference between the results of computer simulation and the actual results of the experiment is that simulation expresses the same Poison's ratio under all loads. In contrast, the actual experiment reveals that this measurement differs depending on the load. This peculiarity is stipulated by the above-mentioned change of dimensions that were created by DMD and varied from the initial characteristics set in the NC program.

Chapter 9: Conclusions

This chapter summarizes the findings. Specifically, it has been proven that the honeycomb structure of steel displays considerable auxetic behavior. Moreover, it is identified that the auxetic structure of a part demonstrates the different values of the Poisson's ratio in its peak and trough regions. In particular, the peaks are less perceptive to loads; therefore, these areas express less prominent auxetic behavior compared to troughs. In other words, the lateral expansion is greater at trough regions. Given these findings, it is presumed that trough areas have greater freedom for movement because, initially, their structure is unconstrained.

In terms of production, it is proven that DMD can successfully perform the described additive manufacturing to create the auxetic materials by electron beam melting. Considering the obtained results, the author suggests that further research should be directed at surveying the peculiarities of the auxetic behavior under tensile and compression loads for 3D structures (x, y, z). It is assumed that such a model will allow conducting impact and hardness testing. Besides, identifying the objectives for future research, it is necessary to accentuate the appropriateness of measuring the geometric dimensions (width and length) of the ribs in the auxetic structure. This approach should help detect if the geometric characteristics of ribs affect the level of the auxetic behavior. In other words, to enhance the knowledge about the auxetic properties, it should be explored whether different ribs express the different values of the Poisson's ratio.

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