Fundamentals of Ceramic Materials 2024-2025 PDF

FUNDAMENTALS of CERAMIC MATERIALS Prof.Dr. Filiz Şahin 2024-2025 Fall Mechanical Properties of Ceramic Materials 2  Introduction – Elastic Deformation 1. Initial 2. Small load 3. Unload...

FUNDAMENTALS of CERAMIC MATERIALS Prof.Dr. Filiz Şahin 2024-2025 Fall Mechanical Properties of Ceramic Materials 2  Introduction – Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial d F F Linear- elastic Elastic means reversible! Non-Linear- elastic d 3 Introduction – Plastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared delastic + plastic dplastic F F Plastic means permanent! linear linear elastic elastic d dplastic 4  Introduction – Stress-Strain Curve Material I: High Young’s modulus (E) High failure stress Low ductility Low toughness No significant plastic deformation Ø Common for many ceramics Material II: Material III: Moderate strength Low E Moderate ductility, Very ductile Deforms plastically prior to failure Low ultimate tensile strength The toughest of the three Ø Common for many elastomers Ø Common for many metals 5  Introduction – Stress-Strain Curve Deformation of … Ceramics: Critical elasticity: ~ 0.01% Plasticity: ~0% Metals: Critical elasticity: ~ 1 - 2 % Plasticity: up to 50 - 100 % PMMA*: Critical elasticity: ~ several % Plasticity: up to several 100 % Stress * Polymethylmethacrylate (acrylic glass) Trade Name „Plexiglas“ 6 Strain  Introduction – Elastic Constants § Modulus of elasticity (Young’s modlulus, E) § Poisson’s ratio (ν or μ) § Bulk modulus (stress to strain for hydrostatic compression) § Shear modulus (ratio of shear stress to shear strain) These constants are related directly to bonding forces between atoms, in real ceramics they are affected by microstructure, e.g., porosity and the presence of second phases. 7  Introduction – Modulus of Elasticity (Young’s Modulus) Modulus of Elasticity, E: à slope of the stress-strain curve in elastic region (also known as Young's modulus) Hooke's Law: s=Ee F s E e Linear- 2 factors affect the E F elastic 1. Bond strength simple tension 2. Temperature test 8  Introduction – Modulus of Elasticity (Young’s Modulus) At ambient and intermediate temperatures for short term loading, most ceramics behave elastically with no plastic deformation up to fracture (Brittle fracture) Most ceramic materials undergo plastic deformation at high temperature. Even at room temperature ceramics such as LiF, NaCl, and MgO undergo plastic deformation, especially under sustained loading. These ceramics all have NaCl structure, which has cubic symmetry and thus has many slip systems available for plastic deformation by dislocation movement. The magnitude of the elastic modulus is determined by the strength of the atomic bonds in the material. The stronger the atomic bonding, the greater the stress required to increase the inter atomic spacing, and thus the greater the value of the modulus of elasticity. Ceramics with weak ionic bonding have low E values (E for NaCl: 44.2 GPa) Ceramics with strong covalent bonding have high E values (E for diamond: 1035 GPa) 9  Introduction – Modulus of Elasticity (Young’s Modulus) Stress Silica glass-fiber: tensile deformations Strain lead to an increase in stiffness. This is related to the rotation of the (SiO4)4- tetrahedra, giving an increase in stiffness once the rotation has occurred. 10 T > 1800°C Plastic deformation occurs Also found in many covalent ceramics, such as Si3N4, at high temperatures. The inelasticity is caused by viscous flow of a glassy phase, which is often present in the grain boundaries of these materials 11  Measurement of Modulus of Elasticity Ultrasonic testing A dynamic method for determining elastic constants (Young’s modulus and shear modulus). Dynamic methods are more accurate than static methods 12 Measurement of Modulus of Elasticity 13  Poisson’s Ratio (ν or μ) Relates the longitudinal elastic deformation produced by a simple tensile or compressive stress to the lateral deformation that occurs simultaneously. ν = -εlateral / εlongitudinal For many ceramics, ν is ~ 0.18-0.30 14  Strength Theoretical strength can be defined as the tensile stress required to break atomic bonds and pull a structure apart. The theoretical strength for ceramic materials typically ranges from one-tenth to one-fifth of the elastic modulus. However, the theoretical strength of a ceramic material has not been achieved. This is due to the presence of fabrication flaws and structural flaws in the material, which result in stress concentration and fracture at a load well below the theoretical strength. 15  Strength However, it is evident that the severity of strength reduction is affected by a combination of factors: The shape of a pore The presence of cracks or grain boundary adjacent to a pore The distance between pores and between a pore and the surface The size and shape of an inclusion The differences in elastic moduli and coefficients of thermal expansion between the inclusion and the matrix 16  Strength Measurements Tensile strength is not common for ceramics--applied for metals Bending strength-3 point bending or 4 point bending Compressive Strength- mostly for concrete. Surface preparation of ceramics is important in strength testing that involves tensile stresses. Imperfections such as cracks, pores, large grains, or even scratches may lead to stress concentration and crack growth from these origins. Therefore, well-polished surfaces are required for less scattered data. In compressive stresses however, such imperfections do not play important roles since cracks or crack-like imperfections tend to be closed under these stresses. 17  3-Point Bending Strength Measurement The loading rate is usually between 0.5 mm/min and 1.0 mm/min σ = 3LF/(2bd²) in 3-point testof rectangular specimen L – specimen length; F – loading force; b – specimen width; d – specimen thickness ASTM C1161 18  4-Point Bending Strength Measurement σ = 3Fa/(bd²) in 4-point testof rectangular specimen L – specimen length; F – loading force; b – specimen width; d – specimen thickness; a -distance between the supporting and loading pins; 19 3- and 4-Point Bending Strength Measurement The main advantage of the bend test, other than its lower cost, due to simple sample geometries. The specimens have either a rectangular or cylindrical geometry. The four-point bend test is preferred because an extended region with constant bending moment exists between the inner rollers. 20 Bending Strength 21 Compressive Strength 22  Hardness Hardness is a material's resistance to permanent deformation. Hardness is a function of – the crystal structure, – crystal defects, – bond type, – fractional density, – grain size, – purity of the ceramic. External variables that may affect hardness are; – temperature, – the presence of reactive species, e.g. acids, alkalis, or even water in some cases. 23  Hardness Indentation test is used. Cracking can also occur on indenting à determining fracture toughness 24  Hardness Vickers hardness is a common method for ceramics 25  Hardness Usually the measured value of hardness is load-dependent. Especially at low loads the measured values of microhardness tend to increase. This reflects an effect of a ratio of the impression size to a characteristic microstructural dimension such as grain size, pore size and distribution, inclusions, and the range of residual stresses. The microhardness also depends on the relationship of surface properties vs bulk properties and on environmental interactions. At high loads, such as several kg, the measured hardness of ceramics decrease due to the fracture of the material under the indenter. 26 Stiffness and Hardness 27  Fracture Mechanics Measured fracture strength stress concentrator or stress raiser § Macroscopic internal discontinuities (e.g., voids), sharp corners, 28 notches in large structure –> stress concentrator or stress raiser  Fracture Mechanics Cracks always exist under normal conditions at the surface and within the interior of a body of material. 29 Fracture Mechanics 30  Fracture Mechanics The maximum stress at crack tip (σm) Assumption: crack (surface crack with a length of "a") is similar to an elliptical hole through a plate, and is oriented perpendicular to the applied stress (σ0), maximum stress occurs at the crack tip 31  Fracture Mechanics – The maximum stress at crack tip The maximum stress at crack tip (σm) For long microcracks that has a small tip radius of curvature, the factor (a/ρt)1/2 will be very large à σm = many times of σ0 σm /σ0 = stress concentration factor (Kt) A measure of the degree to which an external stress is amplified at the tip of a crack. 32  Fracture Mechanics – Critical stress for crack propagation All brittle materials contain cracks and flaws with a variety of sizes, geometries, and orientations. When the magnitude of a tensile stress at the tip of one of these flaws exceeds the value of this critical stress, a crack forms, propagates, and results in fracture. Critical stress (σc) required for crack propagation in a brittle material: 33  Fracture Mechanics – Fracture Toughness Measure of a material’s resistance to brittle fracture when a crack is present. Unit of Kc: MPa·m1/2 Y: dimensionless parameter or function that depends on both crack and specimen sizes and geometries, as well as the manner of load application (Y =1 or Y = ~1.1) and σc: failure stress § This is the stress intensity factor at which the crack will propagate and lead to fracture. It is also referred to as fracture toughness. § The higher the fracture toughness, the more difficult it is to initiate and propagate a crack. As the crack size increases, the failure stress drops. To achieve a design failure stress, it must be possible to detect and prevent any cracks larger than a certain size. 34  Fracture Mechanics – Fracture Toughness Thickness of specimen is important! § For relatively thin specimens: Kc depends on specimen thickness § When specimen thickness >>> crack dimensions, Kc becomes independent of thickness; under these conditions a condition of plane strain exists. When a load operates on a crack in the manner represented in figure, there is no strain component perpendicular to the front and back faces. Kc value for this thick specimen is known as plane strain fracture toughness or fracture toughness (KIC or K1c ) plate of infinite width having a 35 through-thickness crack  Fracture Mechanics - 3 modes of crack surface displacement Mode I, opening or tensile mode I in KIC denotes mode I Most commonly encountered Mode III, tearing mode Mode II, sliding mode Mode 1.If the load applied perpendicular to crack. Mode 2. and 3. when the load applied tangentially to the fracture. 36 Fracture Mechanics – Fracture Toughness (KIc) Kıc for brittle materials 96% of relative density using SPS at 1850 °C. The results showed that HfB2 and ZrB2 diffuses mutually to form (Zr,Hf)B2 solid solution, which enhances the fracture toughness of the material (HZ20S: 8.7 MPa·m0.5) when compared with H20S (5.2 MPa·m0.5) and Z20S (5.7 MPa·m0.5). The reinforcement of CNT (as HZ20S6C) and has led towards achieving the toughest ceramic (10.2 MPa·m0.5) in HfB2- ZrB2 system. Nisar, A.; Balani, K. Phase and Microstructural Correlation of Spark Plasma Sintered HfB2-ZrB2 Based Ultra-High Temperature Ceramic Composites. Coatings 2017, 7, 110. 49  Toughening Mechanisms – Factors contributing the fracture toughness of composite a) Volume fraction of reinforcement à b) Strength of the matrix/reinforcement interface. In fiber-reinforced composites a strong interface can lead to transfer of the stress from the matrix to the fibers; weak interface can lead to debonding and crack deflection à c) Young’s modulus of matrix and reinforcement. If a matrix is reinforced with high modulus, high strength fibers then more of the stress can be carried by the fibers. 50  Toughening Mechanisms – Transformation Toughening Phase transformation in ZrO2. Transformation toughening can lead to an improvement in both toughness and strength (preferred toughening mechanism) Manufacturing of partially stabilized zirconia Add about 10% MgO Sinter in the cubic phase to 1800 C Lower temperature (quench to room temp.) and heat treat (age- above 1400 C) to nucleate small precipitates of t-phase These are growing below the critical size for t-m transformation Cool to room temperature Remaining c-phase has no time to 51 transform  Toughening Mechanisms – Transformation Toughening PSZ is a transformation-toughened material; Microcrack and Induced-stress may be two explanations for the toughening in partially stabilized zirconia. The Microcrack explanation depends upon difference in the thermal expansion between the cubic phase particle and monoclinic (or tetragonal)-phase particles in the PSZ. CTE for the monoclinic form is 6.5-6/° C up to 1200° C, 10.5-6/° C for cubic form is. This deference creates microcracks that dissipate the energy of propagating cracks 52  Toughening Mechanisms – Transformation Toughening After sintering at 1800°C an Mg-PSZ Microstructures annealing stage at 1400°C is introduced: -After 4-5 hours tetragonal precipitates, grow by conventional diffusion processes as coherent spheroids along {001} cube planes -Below a well defined critical size of about 200 nm the t-particles remain tetragonal down to room temperature!!!! - Optimum microstructures contains about 25% - 30% by volume of tetragonal phase in cubic matrix. Toughening Mechanisms – Transformation Toughening 1. The stresses concentrated at the crack tip transform the surrounding tetragonal ZrO 2 inclusions to the monoclinic crack polymorph. The transformation absorbs fracture energy and slows down crack propagation. tetragonal ZrO2 inclusion “ transformed to monoclinic structure stress orientation around the crack tip transformation zone Lense-shaped tetragonal inclusions in a matrix (black) of cubic zirconia (A. 200 nm Heuer).  Toughening Mechanisms – Transformation Toughening 2. Microcracking around the transformed inclusions: The volume stresses resulting from the tetragona- monoclinic transformation delocalize also the stresses from the crack tip volume of the tetragonal zirconia inclusion crack volume after transformation to monoclinic stresses due to the volume increase microfracture due to the volume stresses Penetration depth 3. Crack deflection due to volume stresses: The deflection of cracks increases the crack surface.The stress releave per unit penetration is, therefore, larger then for an inclusion free zirconia. crack  Toughening Mechanisms – Transformation Toughening 100nm Initially tetragonal zirconia inclusion in a cubic zirconia matrix, which are completely transformed to the monoclinic structure. The bands within the Monoclinic inclusions are twin lamellae.  Toughening Mechanisms – Transformation Toughening § Zirconia-toughened alumina (ZTA), which contains 10–20 vol% of fine ZrO2, particles. § At high temperatures ZrO2 is tetragonal (t) and at low temperatures it is monoclinic (m). On cooling, t à m transformation may occur in ZrO2. § This transformation (not time dependent, very rapid) is accompanied by an increase in volume of about 3%. This volume change produces stresses in the Al2O3 matrix around the transformed particle leading to microcracking. § These microcracks increase the toughness of the ceramic by their ability to deflect and branch a propagating crack. Control of the extent of the microcracking determines the increase in toughness. If microcracking becomes extensive, strength will decrease! 57  Toughening Mechanisms – Transformation Toughening Several conditions are required for transformation toughening to occur. First, the matrix and zirconia should not react to form a new phase. Second, the dispersed zirconia phase should not be soluble in the matrix and vice versa. In addition, the following parameters must be optimized to maximize toughening: 1. the particle size of the zirconia, 2. the stabilizing phase concentration, 3. the particle size distribution, and 4. the particle-matrix thermal expansion mismatch. Unstabilized particles that are, larger than a critical size will transform spontaneously during cooling whereas particles that are too small will not transform, even under stress. The critical particle size for ZTA is 0.6 µm. (particle size of ZrO2 is 1.25 µm) 58 Toughening Mechanisms – The Effect of Different Toughening Mechanisms 59 References 60 Glass and Glass-Ceramics  Introduction – Definition of Glass § Glass is an amorphous solid material (no arrangement on a scale larger than a few times the size of atom groups). https://www.sciencedirect.com/science/article/pii/B9781845699314000076 https://www.sas.upenn.edu/~milester/courses/chem101/LSChem101/LSPages/LSfigures174.ht ml  Introduction – Definition of Glass § The term glass classically refers to any noncrystalline solid, which is formed by cooling from the melt. § Some glasses do not have to be formed by rapid melt cooling. ü For instance, sol-gel glasses are prepared by using organic-precursors or solutions prepared at low temperature. The solution is either poured into a mold then allowed to gel or is diluted and applied to a substrate by spinning, dipping, spraying or electrophoresis. § It possesses no sharp melting point and definite chemical formula.  Glass – Amorphous Solid § Surface crystallization can occur § No volume crystallization XRD of lead-silicate glass.  Introduction – Definition of Glass § Traditional glasses are made of inorganic materials like silica, sand, sodium and calcium carbonates, feldspars, borates, and phosphates. These inorganic materials form metallic oxides as they are melted together. § The glass composition is not limited to inorganic materials. There are many examples of organic glasses (Organic glasses consist of carbon-carbon chains which are so entangled that rapid cooling of the melt prevents reorientation into crystalline regions).  Introduction – Definition of Glass A metastable solid with no long-range atomic order (short-range atomic order) § The material has a less stable state when it is in the form of glass and it reaches a more stable state by crystallization. Ø Glasses are metastable with respect to their stable crystalline phase Ø Atoms can rearrange to for more stable state given enough time and thermal energy  Properties of Glass Amorphous (i.e. SRO) Brittle Transparent / Translucent Can absorb, transmit and reflect light Good electrical insulator Unaffected by air, water, acid or chemical reagents (but HF is an exception) High compressive strength  Properties of Glass Mechanically Strong- Glass has great inherent strength and is weakened only by surface imperfections. Hard Surface- Glass resists scratches and abrasions Chemical corrosion resistance- Glass is affected by a few chemicals. It resists most industrial and food acids. Heat Absorbent- Glass retains heat, rather than conducts it. Glass absorbs heat better than a metal. Optical Properties- Glass reflects, bends, transmits and absorbs light with great accuracy. Volume vs Temperature § Volume of the material decreases as if the melt is being cooled with a steady cooling rate along the ab line. § If the cooling is slow enough and there is nuclei in the melt then the liquid crystallizes at temperature Tf, with a sudden change in volume given with bc. § As the cooling goes on, the crystalline material follows the cd line. § If the cooling rate is high enough, crystallization does not occur at Tf and the volume of the supercooled liquid decreases along be.  Glass Transition Temperature (Tg) Tg: Glass transition temperature. At Tg, the volume-temperature curve continues almost parallel to the curve of the crystalline material and demonstrates a change in gradient. Hence the material can be referred as glass only below Tg. Viscosity of the material at Tg is very high ~ 1012 Pa·s (In the glass- transition interval, viscosity increases from about 108 to 1012 Pa·s)  Volume vs Temperature § A material is a supercooled liquid in the temperature range between Tg and Tf. Its volume will decrease along the vertical arrow until it comes to the be line, if the glass is held at temperature just below Tg. § In the glass transition region, other properties of the material also change which are time dependent. This effect is named as stabilization. § Supercooled liquid cannot reach a more stable state without crystallization. Hence, there are no time-dependent changes above Tg. § The material has a less stable state when it is in the form of glass and it reaches a more stable state by crystallization. Hence, properties of glasses depend on the cooling rate to a certain degree especially in the temperature range near Tg due to stabilization effects.  Structural Theories of Glass Formation 1) Early structural theories § Tammann (1925), investigated the formation and constitution of glasses and regarded them as strongly undercooled liquids. § Tammann studied the thermodynamics of glass structures. 2) Goldschmidt’s theory-radius ratio criterion § Goldschmidt derived empirical rules about glass formation. § Goldschmidt stated that the ratio of atomic radii of the cations and anions controls the formation of glass. § According to Goldschmidt theory, glass formation is only possible if the CN = 4 for all the glass forming oxides. § This criterion was first agreed for SiO2, P2O5 and later it was understood that the theory was also true for GeO2 and BeF2. § Theory lacks the appreciation of the bonding type and assumes that glass-forming oxides are assumed to be purely ionic due to the radius ratio of the ions and CN but later it is understood that most of the glass forming oxides such as SiO2 have covalent character. CN: coordination number  Structural Theories of Glass Formation 3) Zachariasen’s random network theory § The random network theory proposed by W. H. Zachariasen for the structure of oxide glasses is very important. § The random network theory characterizes “the glass network as an infinitely large unit cell containing an infinite number of atoms, which does not have any periodicity”. § The theory and the requirement for a material to form glass infers that the structures should be disordered and open structures are more likely to give rise to such disorder, because the coordination polyhedral need not share edges and faces. Edge and face sharing induce crystalline order. (Zachariasen, 1932)  Structural Theories of Glass Formation 3) Zachariasen’s random network theory Zachariasen formulated a set of rules for glass formation: 1. An oxygen atom is linked to not more than two glass-forming atoms, 2. The CN of the glass-forming atoms, which are cations, is small: 3 or 4, 3. The oxygen polyhedra share corners with each other, not edges or faces, 4. The polyhedra are linked in a three-dimensional network (at least 3 corners are shared) Same type of oxygen polyhedra of low CN exists in both crystalline and glassy states since they have similar energies. As the bond angle of A-O-A varies in the network structure, crystalline structure loses its periodicity. Long-range columbic interactions force edge and face sharing of the oxygen polyhedra in highly ionic materials and hence these compounds are not good glass formers such as MgO, Al2O3 and TiO2. Only applies to most (not all) oxide glass (Zachariasen, 1932) Highlights the importance of network topology  Structural Theories of Glass Formation 3) Zachariasen’s random network theory Zachariasen categorized the cations in a glass structure according to their role in the glass network 1) Network-formers: Si4+, B3+, P5+, Ge4+, As3+, Be2+, where CN is 3 or 4. 2) Network-modifiers: Na+ , K+ , Ca2+, Ba2+, where CN ≥ 6. 3) Intermediates: reinforce (CN=4) or loosen the network further (CN is 6 to 8). Ø SiO2, B2O3, P2O5 GeO2, As2S3 and BeF2 are network formers.  Structural Theories of Glass Formation 3) Zachariasen’s random network theory Ø Short-range order is preserved Ø Long-range order is disrupted by changing bond angle (mainly) and bond length Ø Structure lacks symmetry and is usually isotropic The glass network can be defined as a corner sharing Crystalline Glass oxygen polyhedra, which does Zachariasen’s Random Network not have periodicity. Theory (1932)  Structural Theories of Glass Formation Network-modifiers: Na+ , K+ , Ca2+, Ba2+, where CN ≥ 6: § As Na2O is added into the SiO2 structure, it breaks the Si-O-Si linkages by cutting the oxygen bridges and forms Si-O- terminations à structure is depolymerized or modified. § The oxygen bonds in the network, Si-O-Si linkages, are known as bridging oxygens. § The oxygen bonds, in the Si-O- linkages are known as non-bridging oxygens. SiO2 à network former Na2O à network modifier  Structural Theories of Glass Formation Intermediates: reinforce (CN=4) or loosen the network further (CN is 6 to 8). § Al2O3 does not form glass. § In aluminosilicate crystals the CN of Al =4 and CN of O =2. Hence, aluminosilicate crystals obey the Zachariasen’s rules and form glasses. These oxides are known as intermediates or conditional glass formers. § Intermediate oxides do not form glass by themselves but act like glass formers if they are combined with others. § Aluminosilicate, aluminoborate and aluminophosphate glasses are examples for intermediate oxides.  Structural Theories of Glass Formation 4) Dietzel and field strength Dietzel classified elements according to their field strength (Fs). This considers the forces (attraction / repulsion) between cations and anions in the glass. 5) Kinetic theory of glass formation