Nondestructive Testing for Finding out the Displacement of Crack in Silicon Nitride Sriharsha Kurra University of Texas at El Paso, Shkurra@Miners.Utep.Edu

University of Texas at El Paso DigitalCommons@UTEP

Open Access Theses & Dissertations

2009-01-01 Nondestructive Testing For Finding Out The Displacement Of Crack In Silicon Nitride Sriharsha Kurra University of Texas at El Paso, [email protected]

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Recommended Citation Kurra, Sriharsha, "Nondestructive Testing For Finding Out The Displacement Of Crack In Silicon Nitride" (2009). Open Access Theses & Dissertations. 297. https://digitalcommons.utep.edu/open_etd/297

This is brought to you for free and open access by DigitalCommons@UTEP. It has been accepted for inclusion in Open Access Theses & Dissertations by an authorized administrator of DigitalCommons@UTEP. For more information, please contact [email protected]. NONDESTRUCTIVE TESTING FOR FINDING OUT THE DISPLACEMENT OF CRACK IN SILICON NITRIDE

SRI HARSHA KURRA

Department of Industrial Engineering

APPROVED:

Jianmei Zhang, Ph.D., Chair

Tzu-Liang (Bill) Tseng, Ph.D.

Tao Xu, Ph.D.

Patricia D. Witherspoon, Ph.D. Dean of the Graduate School

by Sri Harsha Kurra 2009

Dedication

This thesis is dedicated all my teachers and professors who have taught me till date. Special mention of Dr. C.Nagaraju who was very supportive and encouraged me to do my Masters after my Bachelors degree. I personally thank Dr. Jenny who was very supportive and helped me learn many things which I was never aware of. Can never forget the unconditional love, guidance and support given by all my family members and friends. NONDESTRUCTIVE TESTING FOR FINDING OUT THE DISPLACEMENT OF CRACK IN SILICON NITRIDE

SRI HARSHA KURRA, B.TECH

THESIS

Presented to the Faculty of the Graduate School of The University of Texas at El Paso in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

Department of Industrial Engineering THE UNIVERSITY OF TEXAS AT EL PASO August 2009 Abstract

Nondestructive testing (NDT) has become an increasingly vital factor in the effective conduct of research, development, design and manufacturing. Only with the appropriate use of nondestructive testing techniques, the benefits of advanced materials science can be fully realized. NDT has a wide range of industrial applications and various methods and techniques are employed to perform the nondestructive testing. The current work aims to demonstrate the nondestructive testing technique applied to determine the damage in silicon nitride. Ceramics are brittle materials and non destructive evaluation methods are required to assess the quality and reliability of them. A nondestructive evaluation technique has been developed to study the inspection of silicon nitride using the laser scattering method. Failure analysis is done by collecting and analyzing the data to determine the location of the damage. Nondestructive evaluation can detect the damage in the sample and give us information about the nature and the location of it. An important feature in nondestructive evaluation is that it does not cause any further damage to the sample. Failure criteria by fracture mechanics is also discussed by simulating the value of stress intensity factor and comparing it with manual solution. In addition, existing NDT techniques have been reviewed and a flowchart to determine the most suitable evaluation technique based on their working mechanism and applications has been generated.

v Table of Contents

Abstract ...... v

Table of Contents ...... vi

List of Figures ...... vii

List of tables ...... ix

Chapter 1: Introduction ...... 1 1.1 Motivation of my research ...... 2 1.2 Thesis overview ...... 2 1.3 Thesis organization ...... 3 Chapter 2: Literature review on nondestructive testing ...... 4 2.1 Nondestructive testing ...... …4 2.2 Silicon nitride and NDT of silicon nitride ...... 5 2.3 Biomaterials ...... 8

Chapter 3 Background and experimental setup of laser scattering technology ...... 12 3.1 Theory of laser ...... 12 3.2 Theory and application of optical scattering ...... 12 3.3 Application of cross polarization principle to detect subsurface scattering ...... 15 3.4 Experimental setup of laser scattering system ...... 16

Chapter 4 Experimental results from optical scattering ...... 21

Chapter 5 Fracture analysis of advanced ceramics ...... 23 5.1 Failure criteria ...... 23 5.2 Simulation of fracture for advanced ceramics ...... 24 5.3 Displacement of crack in silicon nitride due to tensile loading ...... 29

Chapter 6 Discussion ...... 32

Chapter 7 Conclusions and future direction of research ...... 33

References ...... 34

Vita………………………………………………………….……………………………………37

vi List of Figures

Figure 2.1: Structure of silicon nitride ...... 7

Figure 2.2: Flowchart for NDT of biomaterials ...... 11

Figure 3.1: Polarization of light ...... 13

Figure 3.2: Difference caused by surface roughness ...... 14

Figure 3.3: Experimental setup of laser scattering system ...... 17

Figure 3.4: Linear stage ...... 18

Figure 3.5:ESP 300 three axis controller ...... 19

Figure 3.6: Nonpolarizing beam splitter ...... 19

Figure 3.7:Power meter ...... 20

Figure 4.1 (a): Optical scattering image of subsurface damage under loading of 2000N ...... 21

Figure 4.1 (b): Optical scattering image of subsurface damage under loading of 3000N ...... 21

Figure 4.1 (c): Optical scattering image of subsurface damage under loading of 4000N ...... 21

Figure 4.2: Image analysis of the damaged profile ...... 22

Figure 5.1: Location of edge crack on the sample ...... 23

Figure 5.2: Geometric modeling ...... 25

Figure 5.3: Boundary conditions ...... 25

Figure 5.4: Applying load on the boundary ...... 26

Figure 5.5: Material selection ...... 26

Figure 5.6: Boundary expressions ...... 27

Figure 5.7: Boundary integration variables ...... 27

Figure 5.8: Applying the scalar expressions ...... 28

Figure 5.9: Mesh generation ...... 28

Figure 5.10: Value of stress intensity factor ...... 29

Figure 5.11 (a): Displacement due to load of 200N/m2 ...... 30

Figure 5.11 (b): Displacement due to load of 800N/m2 ...... 30

vii Figure 5.11(c): Displacement due to load of 1200N/m2 ...... 30

viii List of Tables

Table 5.1: Displacement of crack due to loading...... 31

ix Chapter 1: Introduction

Science and technology are advancing at an increasingly rapid pace and the ways in which they interact with economy, society and environment are becoming increasingly complex [1]. Silicon is the primary semiconductor used to fabricate microchips. Traditional manufacturing processes are slicing, edge contour grinding, flattening, etching, polishing and cleaning. Some of these manufacturing processes like the lapping and grinding will lead to the introduction of surface and subsurface damage

[2]. There are many methods applicable to assess subsurface damage in silicon wafers. A few are destructive methods like the cross sectional microscopy, drop weight testing or any other method where the material to be tested is destroyed during measurement. Nondestructive testing methods like the micro raman spectroscopy, ultrasonic testing and laser scattering can be used to measure the damage on the material without the destruction or damage to the tested material. Silicon nitride has attracted considerable interest because of its excellent combination of properties like high toughness, good strength even at high temperatures, outstanding thermal shock resistance, remarkable resistance to wear, low thermal expansion, medium thermal conductivity and good chemical resistance [3]. Optical techniques have been widely applied for nondestructive measurements of surface roughness and subsurface damage. Laser scattering technique has been used to detect the surface and near surface defects in ceramics [4-5]. Laser scattering has the ability to scan the whole wafer and detect the damage of various depths across the whole material. The experimental results of the study are presented and discussed in the following chapters. Analysis on the sample can also be performed using the comsol software. Various loads are applied on the sample and the displacement of the crack with respect to the loading along the crack length has been studied using the analytical software. The existing nondestructive evaluation techniques in biomaterials have been reviewed and a flowchart has been drafted to determine the suitable evaluation techniques. Biomaterials are nonviable materials used in medical devices and they are intended to interact with a biological system. These biomaterials must be compatible with the body so that the body does not reject them. In general there are three types of biomaterials - bio inert materials like stainless steel, titanium, alumina which have the

1 minimum interaction when placed inside the human body with its surrounding tissues; bio active materials like hydroxyapatite, glass ceramic, bio glass which have significant interaction with the surrounding bones and tissues; bio resorbable materials like tricalcium phosphate, calcium oxide, calcium carbonate which when placed inside the human body dissolve and are placed by advancing tissues [6]. The major applications of biomaterials and the critical needs of testing are presented in section 2.3.

1.1 Motivation of my research

This research aims at proving that nondestructive evaluation techniques can be applied to evaluate the damage of silicon nitride by laser scattering. The location and size of the damage can be determined using the laser scattering technique. It helps researchers to accurately determine the subsurface damage in silicon nitride using the nondestructive technique. The displacement of the damage (crack) on silicon nitride due to tensile loading can be analyzed using the comsol software. The displacement of crack with respect to the loading has been calculated along the length of the crack. This can be very useful in studying the behavior of the crack propagation due to loading. Finally a study on the existing NDE techniques has been performed to frame a flowchart for a close and long follow up observation of the biomaterials which are to be implanted into the human body. This research on a whole aims at demonstrating the application of nondestructive evaluation in science and engineering.

1.2 Thesis overview

The overall objective of this research is to use the nondestructive evaluation in determining the damage in silicon nitride and to suggest that laser scattering can be successfully implemented in locating the damage and determining the size of the damage. Laser scattering experiment gives us two dimensional laser scatter intensity images. These images help us in determining the location, size and severity of subsurface defects. The defects along the crack length with respect to various loading are analyzed using the comsol software. Nondestructive evaluation techniques have been very helpful in locating and analyzing the damage in silicon nitride.

2 1.3 Thesis organization

This thesis is organized into seven chapters. Chapter 1 gives the introduction, thesis overview and thesis organization. A formal literature review on Non destructive testing has been done in chapter 2. The third chapter explains about the background and experimental setup of the laser scattering technology. Chapter 4 explains about the experimental results from optical scattering. Chapter 5 deals with the fracture analysis of ceramics. Discussion and conclusions are made in the final chapters.

3 Chapter 2: Literature Review On Nondestructive Testing

2.1 Nondestructive testing

Nondestructive testing (NDT) is an analysis technique used in scientific fields to determine the state or function of a system by comparing a known input with a measured output, without the use of invasive approaches like disassembly or failure testing. NDT saves both money and time in product evaluation, troubleshooting, and research. The physical system does not need to be sacrificed or damaged for NDT tests and such techniques are valued for saving time and money. NDT methods do not always reveal hidden defects, and skill is usually needed in interpreting the results. NDT is commonly used in forensic engineering, mechanical engineering, electrical engineering, civil engineering, systems engineering, and medicine. NDT has a wide range of industrial activity. NDT can be used to test for engine parts and frames in automobile industry. Nondestructive techniques can be used in the construction and maintenance of bridges and structures. It has a wide range of applicability with propellers, reciprocating engines, pressure vessels, storage tanks, welds, boilers, heat exchangers, inline inspection of pipes for any leakages, rail inspection, wheel inspection and in medical imaging applications. Choosing the right method and technique is an important part of the performance for any nondestructive testing. The various methods and techniques currently available are Optical microscopy, scanning electron microscopy, liquid penetrant testing, radiographic testing, ultrasonic testing, electromagnetic testing, acoustic emission testing, infrared and thermal testing, laser testing, leak detection, magnetic resonance and visual inspection. A few of the methods are explained in this chapter. Optical microscope uses visible light and a system of lenses to magnify images of small samples. The scanning electron microscope (SEM) is a type of electron microscope that images the sample surface by scanning it with a high-energy beam of electrons in a raster scan pattern. The electrons interact with the atoms that make up the sample producing signals that contain information about the sample's surface topography, composition and other properties such as electrical conductivity. Dye penetrant inspection (DPI), also called liquid penetrant inspection (LPI), is a widely applied and low-cost inspection method used to locate surface-breaking defects in all non-porous materials

4 (metals, plastics, or ceramics). LPI is used to detect casting and forging defects, cracks, and leaks in new products, and fatigue cracks on in-service components. Radiographic testing is a nondestructive testing (NDT) method of inspecting materials for hidden flaws by using the ability of short wavelength electromagnetic radiation (high energy photons) to penetrate various materials. Since the amount of radiation emerging from the opposite side of the material can be detected and measured, variations in this amount (or intensity) of radiation are used to determine thickness or composition of material.

In ultrasonic testing, very short ultrasonic pulse-waves with center frequencies ranging from 0.1- 15 MHz and occasionally up to 50 MHz are launched into materials to detect internal flaws or to characterize materials. The technique is also commonly used to determine the thickness of the test object, for example, to monitor pipe work corrosion. Electromagnetic testing is the process of inducing electric currents or magnetic fields or both inside a test object and observing the electromagnetic response. If the test is set up properly, a defect inside the test object creates a measurable response. Acoustic Emission (AE) is a naturally occurring phenomenon whereby external stimuli, such as mechanical loading, generate sources of elastic waves. AE occurs when a small surface displacement of a material is produced. This occurs due to stress waves generated when there is a rapid release of energy in a material, or on its surface. The wave generated by the AE source, or, of practical interest, in methods used to stimulate and capture AE in a controlled fashion for study and/or use in inspection, quality control, system feedback, process monitoring and others.

2.2 Silicon nitride and NDT of silicon nitride

Silicon nitride was developed in the 1960’s and 70’s in a search for fully dense, high strength and high toughness material. Silicon nitride (Si 3N4) is a hard, solid substance. It is the main component in silicon nitride ceramics, which have good shock resistance and other mechanical and thermal properties as compared to other ceramics. This material is used for structural applications at high temperatures and its application extent from vessels for chemical reactions to heat exchanger bearings, engines and gas turbine components [7-9]. It is also used in the optical and semiconductor industries

5 [10]. Silicon nitride nanotubes and nanowires have attracted much attention because of their enhanced hardness associated with their unique optical and mechanical properties [11-12]. Silicon nitride is difficult to produce as a fully dense material. This covalently bonded material does not readily sinter and cannot be heated over 1850 oC as it dissociates into silicon and nitrogen. Dense silicon nitride can only be made using methods that give bonding through indirect methods, such as small chemical additions to aid densification. These chemicals are known as sintering aids, which commonly induce a degree of liquid phase sintering.

2.2.1 Types of silicon nitride

The different types of silicon nitride are: Reaction bonded silicon nitride (BRSN) Hot pressed silicon nitride (HPSN) Sintered reaction bonded silicon nitrides (SRBSN) Sintered silicon nitride (SSN) These types result from their methods of fabrication, which governs their resulting properties and applications. Reaction bonded silicon nitride (BRSN) is made by carefully nitriding a silicon (Si) dough or compact at about 1450°C. During the reaction the Si3N4 grows in the porosity in the compact. This results in little dimensional change accompanied by an increase in density. This feature is the biggest benefit of RBSN, as it often allows parts to be made to near net shape without the need for subsequent expensive grinding operations. A consequence of this reaction is that the final product contains porosity and as such its mechanical properties are inferior to those of the other types of silicon nitride. The material is relatively cheap to produce. Hot pressed silicon nitride (HPSN) was developed in the 1960s and 1970s with the aim of allowing engineers to utilize some of the outstanding properties of, Si 3N4 which couldn't be achieved with RBSN. HPSN is made by adding a flux (usually magnesia) to a fine Si 3N4 powder and then pressing the powder in a graphite die typically at 1800°C and 40MPa of pressure. The resultant body is fully dense with excellent mechanical properties. HPSN parts tend to be expensive.

6 Sintered reaction bonded silicon nitrides (SRBSN) is a development on RBSN aimed at reducing the final porosity of the product and therefore improving its mechanical properties. This is achieved by adding sintering additives to the starting powder mix which allows the material to be sintered after the reaction–bonding stage. Although there is now a significant shrinkage, it is smaller than for SSNs and allows greater control. As with RBSN, the starting raw materials for SRBSN, principally silicon metal, are relatively cheap compared to high quality silicon nitride powders and so SRBSN is therefore cheaper to manufacture than both HPSN and SSN.

Sintered silicon nitride (SSN) covers silicon nitride materials which are densified by pressure less sintering in a nitrogen atmosphere at around 1750°C. In order to aid densification, various combinations of sintering additives such as yttrium oxide, magnesium oxide and aluminum oxide are used. Where there is an addition of an aluminum containing additive the sintered material can be classed as a sialon. Sialons are ceramic alloys based on the elements silicon, aluminum, oxygen and nitrogen and the term is often used interchangeably with SSN. SSN and sialon generally offer the best mechanical properties available for a silicon nitride and are the most widely used in industrial applications such as molten metal handling, industrial wear, metal forming, the oil and gas industries and the chemical and process industries.

2.2.2 Crystal structure of silicon nitride

There are three crystallographic structures of silicon nitride namely α, β and γ phases. The α and

β phases are the most common forms of Si 3N4, and can be produced under normal pressure condition. The γ phase can only be synthesized under high pressures and temperatures and has a hardness of 35 GPa. α phase has a trigonal structure and β phase has a hexagonal structure.

Figure 2.1: Structure of α and β silicon nitride.

7 The important advantage of Si 3N4 is the ability to tailor their microstructures and properties, by controlling the α to β phase transformation that occurs during sintering at high temperature of the mostly

α phase original Si 3N4 powders [13-15].

2.2.3 Nondestructive testing of silicon nitride

The critical flaws are located just beneath the surface. Traditional nondestructive evaluation methods like the dye penetrant inspection, x-ray radiography, computer tomography and ultrasonics are not suitable to detect the flaws in ceramics. Dye penetrant can only detect surface opening flaws and is not effective for very rough surfaces [16]. High resolution x-ray radiography and computer tomography are mainly sensitive to interior flaws and as a result of this, they are relatively insensitive to surface or near surface flaws [17]. Ultrasonics are highly sensitive to the surface or near surface region through the use of surface waves. Ultrasonic surface wave was reported capable of detecting simulated surface flaws as small as 20 micro meters. But it could not resolve the flaw size because it is much smaller than the ultrasonic wavelength [18-21]. A more sensitive and high resolution method of nondestructive evaluation was needed to characterize the materials. For this purpose an optical laser backscatter method which utilizes a low power, continuous wave laser, polarized optics and automated translation as well as rotation stages to achieve the entire inspection of the surface was developed. It provides a two dimensional optical scattering intensity image of the surface to reveal the location, size and severity of the surface and subsurface flaws. The experimental setup is described in the next chapter.

2.3 Biomaterials

A biomaterial is a nonviable material used in medical device, so it’s intended to interact with a biological system. Biomaterials must be compatible with the body so that the body does not reject them. There are three types of biomaterials - bio inert materials like stainless steel, titanium, alumina which have the minimum interaction when placed inside the human body with its surrounding tissues; bio active materials like hydroxyapatite, glass ceramic, bio glass which have an interaction with the surrounding bones and tissues; bio resorbable materials like tricalcium phosphate, calcium oxide,

8 calcium carbonate which when placed inside the human body dissolve and are placed by advancing tissues. Bio inert, bio active or bio resorbable materials are selected to carry out the non destructive testing. They are tested for parameters like cracks, crystal structure, cavities, inclusions, degree of impregnation, structure of composites, wear, composition, chemical analysis and biomaterial modeling using the available NDT methods like analytical, electromagnetic, electronic, ultrasonic, infrared and image generation before they are actually implanted inside the body [22].

2.3.1 Damage evaluation of bio materials

Damage evaluation can be carried out in the dental implants using the image generation and analysis method. A 3D finite element analysis model is developed based on the computerized tomography (CT) scan technology to investigate the load induced damage in bone tissues and implants at different stages of the healing process. Damage analysis on the FE model reveals the damage in the surrounding bone tissues and bone implant interfaces at different stages of the healing process [23]. Synchrotron radiation based spectroscopy can help in the study of micro damage to canine vertebrae [24]. Fourier transform infrared (FT-IR) microscopy and imaging techniques are utilized for analyses of micro and molecular structure of bone, cartilage and other related engineered constructs in healthy and diseased tissues [25]. Structure of ceramic scaffolds and tissue engineered bones are obtained based on two X-ray techniques namely microtomography (micro CT) and microdiffraction. MicroCT investigations provide 3D images and quantitative data like the kinetics of newly formed bone growth, replacement of resorbable scaffold by tissue engineered bone to micro resolution. Microdiffraction provides useful information on interfaces to the atomic scale [26]. Acoustic emission (AE) technique can be used in the assessment of bone cement failure [27]. By using high frequency ultrasound transducers and applying various signal processing algorithms, a 3D representation of the enamel layer and the dentine junction can be constructed for accurate characterization of cracks and lesions [28]. An attempt has been made to determine the common objectives of biomaterial testing and also the NDT technologies which can be employed to examine whether these objectives are met. The

9 methodology is explained in detail in the flowchart for NDT of biomaterials (Fig 2.2). The applicable testing technology can be determined to test the desired parameters in the biomaterial which needs to be implanted inside the body. Based on the NDT results we can determine if it is safe to implant these biomaterials. Look at the available database if any of the methods to carry out the NDT in biomaterials is not listed in the flowchart.

By following the step by step procedures provided in the flowchart, the biomaterial to be implanted can be tested, using the available NDT technologies. If the tested parameters are within the specification limits, we can conclude that the biomaterial is safe to be implanted in the body. Otherwise, the biomaterial should be rejected. If possible, the reasons for rejection should be investigated and analyzed based on the tests, recommendation for reworking could be proposed if any, and the feasibility of reworking could be evaluated. If it is feasible, rework this biomaterial and continue the testing procedures again. If not feasible, discard the biomaterial. Necessary precautions should be taken so that the rejected implant will be disposed carefully.

Fig. 2.2: Flowchart for NDT of biomaterials.

11 Chapter 3: Background And Experimental Setup Of Laser Scattering Technology

3.1 Theory of laser

A laser is a device that emits light through stimulated emission. The term laser is an acronym for light amplification by stimulated emission of radiation [29-30]. A laser consists of a gain medium inside a highly reflective optical cavity, as well as a means to supply energy to the gain medium. The gain medium is a material with properties that allow it to amplify light by stimulated emission. In its simplest form, a cavity consists of two mirrors arranged such that light bounces back and forth, each time passing through the gain medium. Typically one of the two mirrors, the output coupler, is partially transparent. The output laser beam is emitted through this mirror. Light of a specific wavelength that passes through the gain medium is amplified; the surrounding mirrors ensure that most of the light makes many passes through the gain medium, being amplified repeatedly. Part of the light that is between the mirrors, passes through the partially transparent mirror and escapes as a beam of light [31-32]. A HeNe laser is a small type of gas laser which have many industrial and scientific uses, and are often used in laboratory demonstrations of optics. The usual operating wave length of a helium-neon laser is 632.8 nm, in the red portion of the visible spectrum [33]. The gain medium in this laser is a mixture of helium and neon gases contained at low pressure in a glass envelope [34]. The energy source of the laser is provided by an electrical discharge of around 1000 volts through an anode and cathode at each end of the tube. A current of 5 to 100 mA is typical for continuous wave operation [35]. The optical cavity of the laser typically consists of a plane, high-reflecting mirror at one end of the laser tube, and a concave output coupler mirror of approximately 1% transmission at the other end. When a light is incident on a surface between two media, part of the light is reflected from the surface and part is refracted. If the surface is perfectly smooth and reflective, the incident light and the reflection angle will be numerically equal, which is called a specular reflection or else it is called as diffuse reflection or scattering [36-37].

3.2 Theory and application of optical scattering

Light scattering is used by the semiconductor, optical, and data storage industries to inspect materials for surface quality [38]. Several studies have shown that the polarization of scattered light can

12 be used to characterize and distinguish amongst different types of defects, such as particulate contaminants, surface roughness and subsurface defects [39-41]. Many optical scattering techniques have been used for evaluation and measurement of surface topography.

Total integrated scatter approach can be used to measure the surface topography and can be defines as the ratio of the total intensity of the diffusely scattered light measured by the detector to the total intensity of the reflected radiation. TIS is related to the surface roughness parameter Rq. Rq represents the standard deviation of the profile about the mean line defined by the equation

Where x is the distance along the surface, y (x) defines the height of the surface profile about the mean line and L is the sampling length. But this method is practical only for very smooth surfaces with

Rq< < λ (wavelength of light) [42-43]. An other method which can be used to measure the surface roughness is bidirectional scatter distribution function which can be defined as the surface radiance divided by the incident surface irradiance. The surface radiance is the light intensity scattered through the scatter angle per unit illuminated surface area. The incident surface radiance is the light intensity incident on the surface per unit illuminated surface area.

Figure 3.1: Polarization of light. 13

The bidirectional scatter intensity can be calculated by using the formula

where Pi is the incident light, Ps the scattered light, Pr the specularly reflected light, Ωs the illuminated surface area, θi the incident angle, θs the scatter angle and Фs the angle between the scatter direction and x axis. A uniformly illuminated nontransparent isotropic surface is assumed for this technique and so BSDF is not capable for the anisotropic surface [44].

Speckle contrast method is also used for surface analysis. When the coherent light illuminates the rough surface, the reflected beam accounts for part of the random patterns of bright and dark regions known as speckle. The speckle pattern is created by the interference of wavelets scattered from points of different heights within the illuminated area.

Figure 3.2: Difference caused by surface roughness.

In speckle contrast measurement, the average contrast, defined as the normalized standard deviation of intensity variations at the observed surface, has a strong , linear correlation with the surface roughness parameter Ra [45-47]. Roughness average Ra represents the average deviation of a surface profile about its mean line.

14 x represents the distance along the surface, y (x) defines the height of the surface profile about the mean line and L is the sampling length. The methods described above are useful to detect the surface roughness measurements and are not suitable to assess the subsurface damage. So, the polarization property can be used to separate the combined effects of surface and subsurface. Figure 3.1 shows the polarization of light, where Pi is the incident light, Ps the scattered light, Pr the specularly reflected light, Ωs the illuminated surface area, θi the incident angle, θs the scatter angle and Фs the angle between the scatter direction and x axis. Each light beam has two perpendicular components (S and P) in the plain normal to the light propagation direction. For a relatively smooth surface, the polarization of the surface scattered or reflected light will only be changed mildly from that of the illuminating beam. For the subsurface, multiple interactions occur between the light and material grain boundaries or microstructural discontinuities, thereby completely randomizing the polarization of the scattered light [48]. By properly selecting the source and detector polarization, the subsurface effects can be separated from the surface effects.

3.3 Application of cross polarization principle to detect subsurface scattering

The backscattered light from a ceramic surface is always dominated by the surface reflection and scattering. To evaluate the subsurface scattering of a ceramic component, the combined effects of the surface and subsurface scatter must be separated. The separation can be done by examining the polarization state of a polarized illumination and the detection paths. The polarization state of the surface scatter will change very mildly from that of the illuminating beam if the roughness slope on the surface is considerably small to permit only a single interaction of each photon with the surface. But for subsurface scatter, if the scatter population is sufficiently dense, multiple interactions will occur with each photon and hence completely randomizes the polarization of the scattered light. As a result, half of the subsurface scattering has a polarization perpendicular to the incident polarization and the other half has the same polarization as the incident. By using a linearly polarized light source and selecting only the cross polarized backscattered light, we can separate the subsurface scattering from those originated from the surface [49].

15 3.4 Experimental set up of laser scattering system

Based on the cross polarization detection principle, an automated laser scattering scanning system was developed for nondestructive characterization of the entire surface of a valve. The experimental arrangement of laser scattering system is illustrated in Figure 3.3 where laser scanning is performed at the same location and on each sample. A translation/rotation stage unit controls the position and orientation of the sample such that the laser beam is always focused normally on the sample surface. One optical fiber is used to deliver the incident laser beam and another optical fiber is used to bring the collected scattered light to the detector. The data acquisition program controls the motion of the stages to follow the profile of the sample surface and synchronously collects laser scattering data during the scan. A vertically polarized laser beam is directed through a polarizing beam splitter cube onto the sample surface. Light reflected from the sample surface will not undergo change in polarization and will be reflected back in the PBS and directed back to the laser. The subsurface backscattered light becomes horizontally polarized and is transmitted through the PBS onto a detector. The detector signal is processed by a power meter and recorded in the PC. The backscatter intensity is recorded at every pixel during the scan of the surface and the resulting data is composed into a 2D laser scatter intensity image according to pixel positions on the surface [50-51]. Subsurface scattering becomes stronger at regions with subsurface defects and damage. The two dimensional scattering data can be used to identify the location, size and severity of subsurface defects.

Fig 3.3: Experimental setup of laser scattering system.

A sample is placed on the stages such that the laser beam is focused normally on the surface. The arrangement of laser source, focusing lens, PBS cube, collimator lens, detector and stages is illustrated in Figure 3.7. By scanning the entire surface of the NT551 silicon nitride, a two dimensional scatter image is created and the surface/subsurface defects can be identified from the image. A wide range of apparatus is required for the experimentation. Some of the important components are table top, isolators, helium neon laser, laser mount, stages, clamp posts, rotation mounts, stages, posts, post holders, collimators, universal motion controller, power meter, detectors and lens. The table top rests on four isolators which are 28 inches in height and can carry a load of about 8000 lb. The isolators are connected to an air supply for continuous supply of pressurized air and to make sure that the table floats. The model number of the He-Ne laser used in the experiment is R-30995. It is mounted on a mount to fix conveniently on the flotation table. Specifications of the laser are Min output power: 17 mW, Polarization: 500:1, Beam Diameter: 0.98mm Laser line polarizing cube beam splitters provide efficient narrowband polarization for higher power lasers. Their extinction ratio is better than 1000:1, and they are recommended for use in pulsed

17 laser systems and for purifying polarization in multimode, high-power lasers. Cube holders are used to hold these cubes. Laser beam must always enter the prism on the side marked with a dot. This linear stage with a DC Motor (Fig 3.4) has a ultra-high resolution 20,000 cts/rev rotary encoder with index pulse for precision homing and is the recommended choice for applications requiring accurate bi-directional positioning. For tightest position control, the rotary encoder is directly mounted on the lead screw. This eliminates the majority of drive train error sources that affect other stages with indirect position read-out. A high-torque DC motor provides the highest dynamic speed control and allows for linear speeds up to 40 mm/s. An 11:4 belt reduction between the motor and the lead screw increases the available output torque, reduces the servo sensitivity and ensures 0.3 mm incremental motion capability with all Newport motion controllers and drivers. All UTS series linear stages feature all-steel construction with preloaded linear ball bearing slides. Steel has an almost 3-times greater stiffness than Aluminum, and provides the UTS stages comparable stiffness to the popular ILS series, but in a much more compact and significantly lower profile package. In addition, because the bearings, the body, the carriage and the lead screw are all made of steel, the UTS has a completely homogenized design minimizing thermal stress or thermal bending effects. The result is more consistent performance than other Aluminum stage designs.

Figure 3.4: Linear stage.

The ESP300 (Fig 3.5) is an integrated controller and driver in one chassis, which simplifies system hookup and improves reliability. The ESP300 can drive and control up to three axes of motion using any combination of DC and/or stepper motors. Each driver module will drive 2 or 4-phase stepper and brush DC servo motors at 3 A (maximum) per axis.

Figure 3.5: ESP300 three axis controller.

The ESP300 uses a 32-bit, floating point, DSP processor for high precision synchronized control.

A digital PID-FF (feed-forward) servo loop ensures precise velocity profile tracking and accurate positioning. A 1000x micro-step programmable resolution provides ultra-smooth low-speed stepper positioning capability, and 18-bit DC motor command output ensures improved stability for precision applications.

Figure 3.6: Nonpolarising beam splitter.

Laser line non-polarizing cube beam splitter (Fig 3.6)provide true 50/50 beam splitting without altering the beam polarization, with the s- and p-polarized components matched to within 3%. They exhibit virtually zero absorption for true 50/50 beam splitting. Incoming beams are both transmitted and reflected 50%, with the s and p-polarized components matched to within 3%. These beamsplitters consist of a pair of precision right-angle prisms carefully cemented together to minimize wavefront distortion. The hypotenuse of one of the prisms is coated with a multilayer all-dielectric non-polarizing beamsplitter coating optimized for specific laser lines. The four faces are antireflection coated with a multilayer dielectric coating to minimize surface reflection losses at the laser lines.

Figure 3.7: Power meter.

For applications requiring measurement of low-power light sources, Newport’s models 1931-

C/2931-C instruments (Fig 3.7) have broken the barrier of temporal measurement performance with calibrated results. This series of power/energy meters have the ability to handle repetition-rates of up to 20 kHz at a sampling rate of 250 kHz. Peak-to-peak and DC source measurements can be displayed in units of W, dBm, dB, and A. Simultaneous measurements of a variety of light sources operating at different power levels and wavelengths can be performed with our Dual-Channel 2931-C Optical Power Meter.

20 Chapter 4: Experimental Results From Optical Scattering

The following damage was observed in NT551 silicon nitride after performing the laser scattering experiment. A load of 2000N is applied on the silicon nitride sample and later tested for subsurface damage by laser scattering method. There is no significant damage due to this amount of load as shown in figure 4.1(a). A load of 3000N is applied randomly on the sample surface and it is then tested. There are deformations found due to the application of this amount of load on the subsurface as shown in figure 4.1(b). There are three layers of damage seen in this second figure. The intensity of damage in the top part of the image is high when compared with the other sections.

Figure 4.1: Optical scatter image of subsurface damage under loading of (a) 2000N and (b) 3000N.

Figure 4.1(c): Damage under loading of 4000N.

When the load is increased to 4000N the damage is severe as shown in figure 4.1(c). The damage is significantly high when more load is applied.

21 Figure 4.1(b) is then subjected to image analysis and the graph is plotted which gives the relationship between the distance and the gray value. In figure 4.2, we can observe three regions of the subsurface damage. The graph shows the width of three lines with the damage.

Figure 4.2: Image analysis of the damaged profile.

The value begins to increase till a distance of 35 pixels and then starts decreasing again. This is the data for the first damage region. The value is low at a distance of 57 pixels. The difference between these two gives us the width of the damage for the first layer. The width of damage is 57-35 = 22 or 110 µm. By adopting the similar principle, the second damage region has a width of 90-70 = 20 pixels or 100 µm and the third damage region has a width of 113-99 = 14 pixels or 70 µm.

22 Chapter 5: Fracture Analysis Of Advanced Ceramics

5.1 Failure criteria

Stress intensity factor K, is used in fracture mechanics to accurately predict the stress state or the stress intensity near the tip of the crack by remote load or residual stresses. It is useful for providing failure criterion for brittle materials. The magnitude of K depends on sample geometry, the size and location of the crack and the modal distribution of load on the materials. Stress Intensity, K, is a parameter that amplifies the magnitude of the applied stress that includes the geometrical parameter Y load type [52]. If a very sharp crack can be made in a material, the minimum value of K can be determined, which is the critical value of stress intensity required to propagate the crack. This critical value determined is referred to as the critical fracture toughness of the material. Critical fracture toughness has units of stress times the root of a distance. The units of critical fracture infer that the fracture stress of the material must be reached over some critical distance in order for the critical fracture toughness to be reached and crack propagation to occur. This intensity factor is the most often used engineering design parameter in fracture mechanics.

Fig 5.1: Location of edge crack on the sample.

The stress intensity factor predicts if a specific crack will cause the material to fracture. We can determine the stress intensity factor using the J-integral. A J-integral is a two dimensional line integral along a counterclockwise contour surrounding the crack tip. We can perform the analysis by following the systematic procedure as described below. First generate the geometry of the sample with the given dimensions. The next step is to plot the points and define the boundaries of the sample. The model geometry must also have the interior boundaries. Divide the interior boundaries into sub domains. Apply boundary conditions to the sample and generate the mesh which can be solved to determine the stress intensity factor.

23 The sample considered here has a horizontal crack of length 0.4m on the left vertical edge. The total height of the plate is 2m. Stress intensity factor is determined using the J integral. The analysis computes the three different contours traversing three different regions around the crack tip. The first contour follows the exterior boundary of the plate and the second and third contours follow the interior boundaries. To calculate the J integral, we define boundary integration variables for each contour and this creates two variables for each contour. The first variable W, contains the integrated strain energy density, while the second, denoted Tdudx, contains the traction vector times the spatial x-derivative of the deformation components. The sum of these two variables then provides the J integral value as a scalar expression variable. When calculating the J-integral, the contour normals must point outward of the region which the contour encloses. The boundary normals of the plate geometry are all pointing outward. However, some of the normals of the interior boundaries that are used for the second and third contour do not point outward of the regions that they enclose. This means that we need to define additional normals to get the correct alignment of the normals. We define these normals as boundary expressions and use them in the boundary integration variables. The procedure followed is explained with the help of some screen shots in section 5.2 under the title, simulation of fracture for advanced ceramics. Manually KIa can be derived using the equation

where σ is force/area and ‘a’ is the length of the crack and ccf is configuration correction factor which can be defined as the amount of deviation in a measurement that is accounted for in the calibration process.

5.2 Simulation of fracture for advanced ceramics

A silicon nitride sample with a width 1m has a single horizontal edge crack of length 0.4m. The total height of the plate is 2m, but due to symmetry reasons, the model only includes half of the height.

Step.1 A geometry model is created using the analysis software. The screenshot of the model is shown below (Figure 5.2).

Fig 5.2: Geometric modeling.

Step.2 Apply the point conditions and boundary conditions into the geometry. The boundary conditions are given by going into the physics menu and choosing the boundary settings in the software as shown in the Fig 5.3.

Fig 5.3: Boundary conditions.

25 Step.3 The next step we need to perform is applying the load on the boundary plane. Here we are applying load on the boundary 3.

Fig 5.4: Applying load on the boundary.

Step.4 Now apply the sub domain settings. From the physics menu chose the sub domain settings edit field. Chose the desired material from the library material. If the required material is not available in the library, input the values of the poisons ratio and young’s modulus. The procedure employed in entering these values is demonstrated in Fig 5.5.

Fig 5.5: Material selection.

26 Step.5 From the options menu chose Expression and click on Boundary expressions. Specify the expressions for the boundaries as required. Fig 5.6 shows the procedure to apply the boundary expressions.

Fig 5.6: Boundary expressions.

Now apply the boundary integration variables. From the options menu, chose integration coupling variables and click on boundary integration variables. Fig 5.7 shows the screen shot of this operation.

Fig 5.7: Boundary integration variables.

Now apply the scalar expressions by clicking on the options menu and selecting the scalar expressions from the expressions (Fig 5.8).

Fig 5.8: Applying the scalar expressions.

STEP .6 Generate the mesh by clicking on Initialize mesh button in the tool bar and refine the mesh to the required size.

Fig 5.9: Mesh generation.

Solve the design by clicking on the solve option and select solve problem. Apply the post processing function to arrive at various results .

28 5.3 Displacement of crack in silicon nitride due to tensile loading

The stress intensity factor for the model when solved by using the formula is equal to 20 x ( Π

0.4) 1/2 x 2.1= 470.819 Pa. Ccf value of 2.1 is a standard value for this type of configuration. The stress intensity factor of the modeled sample in the software is 470.697112 Pa.

Fig 5.10: Value of stress intensity factor.

The value of stress intensity factor calculated is equal to the stress intensity factor from the software analysis. This indicates that our created model is similar to the real model and the displacement analysis can be carried out. When a tensile load of 200 N/m2, 800 N/m 2 and 1200 N/m 2 are applied on the sample, there is a maximum displacement of 1.7x10 -6 m, 6.7x10 -6 m and 1x10 -5 m along the crack as shown in figure

29 5.11(a), (b) and (c) respectively. The initial position of the crack without application of tensile load is seen in figure 5.1.

Fig 5.11: (a) Displacement due to load of 200N/m 2 and (b) Displacement due to tensile load of 800N/m2.

Fig 5.11 (c): Displacement due to 1200N/m 2.

By following this procedure, we can determine the displacement of the crack due to application of different loads on the sample. The values obtained from the graph are tabulated in table 5.1.

30 Table 5.1: Displacement of crack due to loading.

Material Load (N/m 2) Displacement (m)

Silicon nitride 200 1.7x10 -6

Silicon nitride 800 6.7x10 -6

Silicon nitride 1200 1x10 -5

Due to increase in application of load, it is observed that the displacement of crack is increasing. This indicates that more load causes more displacement along the crack surface and there is a possibility that the material can lose its stability and break when the load is applied above its capacity.

31 Chapter 6: Discussion

Traditional nondestructive evaluation methods are not much effective to detect subsurface flaws with small dimensions. Ceramics are translucent to light and it is because of this property that a new laser scattering method was developed, which is capable of detecting and characterizing the flaws. For most flaws, median cracks, their subsurface scatter intensity is considerably stronger than normal dense material and therefore can easily be identified from the nondestructive evaluation data. The automated laser scattering nondestructive evaluation system was used to evaluate the NT551 silicon nitride. The experimental system scans the entire length of the surface to construct a two dimensional laser scatter intensity image of the surface, from which the location, size and severity of subsurface flaws can be easily determined. Nondestructive techniques were successfully applied to detect the damage in silicon nitride and to find the value of the displacement in silicon nitride which has an edge crack on its surface. Laser scattering was very successful in determining the damage location and size of the damage in silicon nitride. Comsol software is then used to perform various displacement analysis on the silicon nitride sample which already has a damage on it. The experiment can help in finding out any damage on the sample and the analytical software can be very useful in predicting the orientation of the crack for various loads. Finally we can know the loads at which the material tends to break along the crack and determine the failure load of the sample for a given width of crack.

32 Chapter 7: Conclusion And Future Direction Of Research

Results obtained from the laser scattering technique on subsurface damage in silicon nitride, have been encouraging. Laser scattering technique can reveal the information of the subsurface region.

This technique is an efficient and a nondestructive method to examine the subsurface damage in the entire length of the silicon nitride sample. The width of the subsurface damage was calculated based on the laser scattering images. The displacement of the crack with respect to various tensile loading was analyzed using the comsol software. We could detect the crack and also study the behavior of this crack under various loading conditions. More deep damage can be detected by using longer wavelength. So a study could be made in the future, by changing the wavelength of the laser source. Different laser source can also be used to determine if they could be more effective in detecting deeper damage, when compared with helium neon laser.

33 References

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36 Vita

Sri Harsha Kurra was born and brought up in Vijayawada, India. He received his Bachelors Degree in Production Engineering from Acharya Nagarjuna Univeristy, India. He is currently doing his

Masters in Industrial Engineering from The University Of Texas at El Paso. He attended the 25th Southern Biomedical Conference held in Florida, USA and presented his work on the application of non destructive techniques in biomaterials. He is currently working on the detection and analysis of cracks using lasers. He served as a Teaching Assistant for the laboratory course in Operations Research and worked as a Research Assistant under the supervision of Dr. Jianmei Zhang, who is an expert in the area of detection of cracks using the non destructive techniques. He attended the intensive training program in lean manufacturing conducted by the Texas Manufacturing Assistance Center (TMAC). He attended the MAES symposium held in Las Vegas during November 2008. He is an active member of the MAES student chapter and NSBE student chapter at UTEP.

Permanent address: 1319, Randolph Dr El Paso, TX, 79902

This thesis was typed by Sri Harsha Kurra.