Chapter 6 Ceramics PDF

ME-515 CERAMICS Chapter -16 Mechanical Testing By Dr. Al-Montaser Bellah Al-Ajlony Fall-2024/2025 1  Overview Ceramics differ from most metals and polymers is that at room temperature...

ME-515 CERAMICS Chapter -16 Mechanical Testing By Dr. Al-Montaser Bellah Al-Ajlony Fall-2024/2025 1  Overview Ceramics differ from most metals and polymers is that at room temperature most of them are brittle. Flaws play a major, often dominating, role in the mechanical behavior of ceramics. As a result, obtaining properties such as elastic moduli is often more difficult than it would be for metals: preparing the sample can lead to the introduction of flaws. Stress–strain curves for ceramics are usually obtained using a bending test rather than a tensile test. We need only to make our ceramic into a rectangular block. The brittle behavior of ceramics gives them low fracture toughness, a property that can most conveniently be obtained from indentation testing. A key point in this chapter is that when we use ceramics in load- bearing applications we need to understand the importance of flaws and how to incorporate that into our design approach. 2  Classical view vs reallity The classical view of ceramic materials is: a) They’re brittle. b) Dislocations are not important because they don’t move. c) They are polycrystalline and fracture along grain boundaries. Once again the classical view of ceramics and many of our preconceived ideas of how they behave are not always correct. ❑ We can bend a sheet of silicon into a tube. ❑ We can bend an alumina fiber into a circle. ❑ Dislocations move ahead of crack tips, are present at heterojunctions, and can be produced in large numbers during single crystal growth. ❑ Single crystal ceramics also fracture. As seen in an Nd-doped YAG single crystal boule that fractured during growth). 3  Modern view Therefore, the modern view of ceramics is very different because: a) We may be using the ceramic as a thin film where stresses may be very high. b) Deformation at high temperatures may be important. c) In some special “new” ceramics, displacive transformations become important. 4  Stress strain curve for various materials A stress–strain (σ-ε) curve for a material in tension. The figure to the right shows se curves for three different materials at room temperature. ❑ Material I: has high Young’s modulus, high failure stress, low ductility, low toughness, and fractures without significant plastic deformation. This behavior is characteristic of many ceramics. ❑ Material II: has moderate strength, moderate ductility, deforms plastically prior to failure, and is the toughest of the three. This behavior is characteristic of many metals. ❑ Material III: has low Young’s modulus, is very ductile, has low ultimate tensile strength, and limited toughness. This behavior is characteristic of many elastomers. 5  Factors that determine strength The strength of ceramics is affected by many factors, and this complexity is illustrated in this figure. The composition and microstructure are particularly significant, and mechanical properties depend strongly on these characteristics the measured value of a mechanical property may be affected by the test method. This is particularly true in the case of hardness. 6  Effect of Microstructure The composition and microstructure are particularly significant, and mechanical properties depend strongly on these characteristics. This figure shows two specific examples that illustrate the role of microstructure on the strength of ceramics. In part A, the strength of a porous polycrystalline alumina is shown to decrease much more rapidly than its density. The reason is that pores act to concentrate stress, which is not uniform throughout the ceramic. In large grains, there can be larger flaws. The effect of grain size is generally described as shown in part B This behavior is often more complicated than that shown in Part B when we consider ceramics where the grain size is ultrafine 7  High-performance structural ceramics High-performance structural ceramics combine the traditional advantages of ceramics (chemical inertness, high-temperature capabilities, hardness) with the ability to carry a significant tensile stress. The majority of the high-performance ceramics are based on silicon nitride, silicon carbide, zirconia, or alumina. Structural ceramics come in many forms: monoliths, composites, coatings, fibers, whiskers. 8  TYPES OF TESTING Ideally, before we use a ceramic in a load-bearing application we would like to have the following information about it. ❑ Young’s modulus ❑ Average strength and Weibull modulus ❑ Toughness ❑ Crack propagation rate ❑ Cyclic fatigue resistance ❑ Creep curves ❑ Stress rupture data We would also like to know these parameters as a function of temperature, in particular over the temperature range at which our ceramic component is going to be used. 9  Metals vs Ceramics There are big differences between how metals are tested compared to ceramics. ❑ It is often difficult to do tension tests on ceramics because of the possibility of introducing flaws. ❑ Ceramics are stronger in compression than they are in tension because of how cracks propagate. ❑ For ceramics, we need to be concerned with statistics because we don’t know where the largest flaws are. Because some mechanical properties depend on how the material was tested, it is important and necessary to establish specified test methods. Standard test methods have been adopted for ceramics. In the United States, ASTM International (originally the American Society for Testing and Materials, or ASTM) is the primary organization developing standards for materials testing. ASTM Committee C-28 on Advanced Ceramics has completed several standards. 10  ELASTIC CONSTANTS The parameters that describe the elastic behavior of materials are listed. These are the four elastic constants. 1) E—Young’s modulus (also referred to as the elastic modulus) is a material constant defined by equation σ=Eε ………………….(16.1) It is therefore the slope of a (σ-ε) curve where only elastic deformation occurs. 2) ν—Poisson’s ratio is the negative ratio of the transverse strain (εT) to longitudinal strain (εL). ν = - εT / εL...…...……………(16.2) For many ceramics and glasses it is in the range 0.18–0.30. 3) µ—Shear modulus is the ratio of shear stress to shear strain. μ = τ / γ ………………………(16.3) 4) B—Bulk modulus is the ratio of stress to strain for hydrostatic compression. B = -P(ΔV/V) ………………….(16.4) 11 Tabulated data for several ceramics 12  H—Hardness ❖ H—Hardness. There are different types of hardness. The hardness of a material is its resistance to the formation of a permanent surface impression by an indenter. It is also defined as resistance of a material to deformation, scratching, and erosion. Hence, the geometry of the indenter tip and the crystal orientation (and therefore the microstructure) affect the hardness. Table 16.4 lists hardness values on the Mohs’ hardness scale. 13  EFFECT OF MICROSTRUCTURE ON ELASTIC MODULI Young’s modulus is a property that is directly related to the bonding forces between atoms. It varies as a function of temperature. In real ceramics, we have to consider the fact that we often have more than one phase present. The overall modulus is then going to be a combination of the properties of each of the phases and lie somewhere between the high- and low-modulus components. Two analytical expressions represent the upper and lower bounds for Young’s modulus. ❑ Voigt Model ❑ Reuss Model 14  Voigt, Reuss and HS Model Voigt model; Assumption: strain in each constituent is the same (iso-strain). Represents upper bound of Young’s modulus. 15  Voigt, Reuss and HS Model Reuss model; Assumption: Stress in each phase is the same (iso-stress). Represents lower bound of Young’s modulus. Hashin and Shtrikman (HS) developed a narrower, more useful, set of bounds using basic elasticity energy theorems. The HS bounds have been shown to be best for the bulk modulus and are given by: where H=4 μ2/3 or H=4 μ1/3. Young’s moduli can be obtained from B if ν is known and reasonable fits with experimental data can be obtained, as shown in Figure 16.7 for alumina–tetragonally stabilized zirconia (Al2O3–ZrO2) composites. 16  Effect of porosity If the second phase is porosity, as is often the case in polycrystalline ceramics, then intuitively we realize that there is a decrease in the elastic modulus. A pore has zero stiffness. Several relationships have been developed to account for the change in Young’s modulus with porosity, P. They are shown in Table 16.5, where the “constants” a and b are often empirically determined; Eo is the Young’s modulus of the dense material. 17  TEST TEMPERATURE Mechanical properties often show strong variations with temperature. For some mechanical properties, the change with temperature may be more abrupt than the gradual decrease in E with increasing temperature. The ductile-to-brittle transition, which occurs with decreasing temperature, is an important topic in metals. The significance of this phenomenon really came to light during World War II, when there were reports of serious fractures in some of the Liberty ships (mass-produced vessels of predominantly welded construction). One of the most striking instances of this type of fracture was the T2 tanker S.S. Schenectady built in Portland, Oregon, which suddenly broke into two sections at 10.30 p.m. on January 16, 1943. The reason was that the steel alloy used to construct the hull had undergone a ductile-to-brittle transition at a temperature of 4C. This event gave particular impetus to the study of fracture in brittle materials. 18 Brittle-to-ductile transition temperature Ceramics can exhibit both brittle-to-ductile and ductile-to-brittle types of behavior over different temperature ranges. Figure 16.8 illustrates the temperature dependence of strength for ceramics. ❑ Region A: fracture is brittle, and the fracture strain ~10 -3. There is no significant plastic deformation prior to failure, and the strength varies little with temperature. 19 Brittle-to-ductile transition temperature ❑ Region B: fracture is again brittle, but slight plastic deformation occurs prior to failure. The failure strain is usually in the region of 10 -3 to 10-2, and strength falls with increasing temperature. ❑ Region C: appreciable plastic flow occurs, with strains of the order of 10 -1 prior to failure. Also, in this region some ceramics might exhibit slight increase in strength with increasing temperature. This later behavior is rarely observed in ceramics, even in ductile polycrystalline ceramics. The critical temperatures, TAB and TBC, vary greatly for different ceramics. For polycrystalline MgO the brittle-to-ductile transition (TBC) occurs at ~1,700C (0.6 Tm). There is no plastic deformation in b-SiC below 2,000C. Talc, MoS2 and graphite all deform at room temperature. MoS2 and graphite are widely used as solid lubricants. 20  Brittle-to-ductile transition temperature The transition can be important in structural ceramics (particularly nonoxides such as silicon nitride) when they are used in high-temperature applications. Densification in these ceramics is often achieved using a second phase that forms a glass at grain boundaries and triple points. At temperatures near the glass-softening temperature, very extensive plastic flow occurs. Figure 16.9 shows (σ-ε) curves for silicon nitride at 1,400C containing different amounts of silica. For silica contents >20 wt%, macroscopic plastic deformation occurs. At high silica contents, it is believed that the glassy phase is no longer constrained at the triple points. 21  TEST ENVIRONMENT In some cases, the environment that the ceramic is exposed to is a very important consideration. For example, you often see that mechanical tests on bioceramics are performed either in vivo or in vitro. Tests performed in the body are referred to as in vivo. Tests performed outside the body, often under conditions that seek to replicate or approximate the physiological environment, are referred to as in vitro. ISO Standard 6474 for alumina bioceramics specifies a bend strength >450 MPa after testing in Ringer’s solution. Ringer’s solution is a model liquid that resembles human body fluid. 22  TESTING IN COMPRESSION AND TENSION The tensile test is the most used procedure to determine the tensile strength of a metal. However, it is not used as widely for ceramics because of their inherent brittleness. It is difficult to make the typical “dog bone”-shaped samples, where the cross-sectional area is reduced in the gauge length. We could do this with a ceramic, but the machining needed to give this shape is likely to introduce surface flaws. In many tensile test instruments, the sample under test is connected by means of a screw thread. This is often tricky to machine with a ceramic, and it may also break in the grips. Finally, because ceramics fail after only about 0.1% strain, the specimens under test must be perfectly aligned; otherwise we introduce bending stresses, which complicate things. 23  Importance of tension strength In some practical situations, we require ceramics to support a tensile load. Consider the growth of silicon single crystals by the Czochralski process, which involves pulling the crystal from the melt. The crystal is supported entirely by a narrow region called the neck, about 3 mm in diameter. It is possible to support a total crystal weight of about 200 kg. This requirement determines the maximum overall volume of a silicon boule. The diameter is controlled by our ability to produce dislocation-free crystals. Steel reinforced concrete and safety glass are two examples of where a ceramic is prestressed in compression to increase its ability to support a tensile load. 24  Tension vs Compression Stress–strain curves for metals look very similar and provide similar results whether the testing is carried out in tension or compression. Ceramics are generally stronger in compression and can tolerate high compressive loads. Some examples are given in Table 16.6. However, reliable compressive strength data are limited for ceramics. Note that the Young’s modulus is the same because the curves have the same slope. 25  Tension vs Compression One ceramic that is widely tested in compression is concrete. Concrete is a ceramic–matrix composite consisting of a mixture of stone and sand (called the aggregate) in a cement matrix. The aggregate provides the strength and the cement the workability. When concrete is used in construction it must always be loaded in compression. As shown in Figure 16.10, cracks behave differently in compression than they do in tension. 26  Tension vs Compression In compression, cracks twist out of their original orientation and propagate stably along the compression axis. The result is that the sample crushes rather than fractures. Fracture is not caused by rapid unstable crack propagation as it is in tension. In tension, we are concerned with the largest crack, the “critical flaw,” particularly if it is on the surface. In compression, the concern is the average flaw size, c av. We can estimate the compressive stress to failure by substituting cav, into equation 16.5 and using a multiplier between 10 and 15. 27 THREE-POINT AND FOUR-POINT BENDING To avoid the high expense and difficulties of performing tensile tests on ceramics, tensile strength is often determined by the bend test. There are two geometries, which are illustrated in Figure 16.11. The main advantage of the bend test, other than its lower cost, is that we use 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. 28  3-points and 4-points bending The maximum tensile stress in the surface of the beam when it breaks is called the modulus of rupture (MOR), σr. For an elastic beam, it is related to the maximum moment in the beam, M. where W is the height of the beam, and B is its thickness. For the case of bend-testing a ceramic, this equation is applicable only when the distance between the inner rollers is much greater than the specimen height. Other terms are also used including flexural strength, fracture strength, and bend strength. The bend test is also known as a flexure test; and the resistance of a beam to bending is known as its flexural rigidity. The terminology can be a little confusing, but this test is important because it is widely used and probably the most well 29  KIC FROM BEND TEST There are several techniques to determine KIc for a ceramic. The two main approaches are to use indentation or bending. In the bend test, a notch is introduced (usually using a diamond-tipped copper cutting wheel) into the tensile side of the specimen, as shown in Figure 16.13. In (a) the notch is flat (single-edged notched beam, SENB), in (b) it is chevron-shaped. The specimen is loaded, usually in a four-point bend, until it fails at FMax, and KIc is calculated. 30  KIC FROM BEND TEST For the SENB: where c is the length of the initial crack that we introduced, and ξ is a calibration factor. The advantage of the SENB test is that it is quite simple but tends to overestimate KIc because the crack is often not atomically sharp. For ceramics with very fine grain sizes, it is necessary that the notch is very narrow. For the chevron notched (CN) specimen where ξ* is a compliance function. Sometimes you see equation 16.11 written in such a way that all the geometrical terms are grouped together as a single geometric function Y*. Then we have: The value of Y* is then necessary for different specimen geometries and different notch geometries. 31  KIC FROM BEND TEST The advantage of the CN geometry is that we don’t need to worry about introducing a sharp precrack. Our original notch is made by two saw cuts to produce a triangularly shaped cross section. A crack is easily initiated at the tip of the chevron, but the increasing cross section of the crack front causes crack growth to be stable prior to failure. Further crack extension requires an increase in the applied load, and it is possible to create an atomically sharp crack before the specimen fails. Also, you can see from equation 16.11 that we don’t need to know the actual crack length. In fact, we don’t need to know any of the materials’ properties. 32  INDENTATION Measuring the hardness of a ceramic is important, and it is usually done using an indentation test. The basic idea is that a permanent surface impression is formed in the material by an indenter. We then measure the actual or projected area of the impression. The hardness is then determined by dividing the applied force, F, by this area. The processes that happen under the indenter tip can be quite complex. We often see a deviation from what is called “Hertzian” behavior, where the indentation stress is proportional to the indentation strain (Figure 16.14). 33  Region of plastic flow The deviation is due to plasticity beneath the indenter, as illustrated in Figure 16.15. Cracking can also occur on indenting and can be used as a means of determining fracture toughness. 34  Variants of indentation tests There are many different hardness tests, and each gives a different number. The common hardness tests are listed in Table 16.7, and the geometries of the impression are shown in Figure 16.16. It is possible to convert between different hardness scales, but the conversion depends on both the material and its microstructure. The most reliable data are for steels because most of the work has been done on these alloys. Detailed conversion tables for metals and alloys are available in ASTM Standard E 140, “Standard Hardness Conversion Tables for Metals.” 35 Variants of indentation tests 36  Regimes of Hardness There are different regimes of hardness based on the load used, as shown in Table 16.8. These divisions are somewhat arbitrary but commonly accepted. 37  FRACTURE TOUGHNESS FROM INDENTATION We can obtain the fracture toughness from indentation tests. The basic idea is illustrated in Figure 16.17. We get an indent and radial cracks. The hardness is then where α is a numerical factor that depends on the shape of the indenter. For a Vickers indenter, α =2. P is the load in newtons. 38  Fracture toughness from indentation The critical stress intensity factor is obtained by assuming that the applied stress intensity caused by the load is equal to the critical stress intensity for crack propagation: where ζ is a dimensionless constant, which for ceramics has an average value of 0.016 ± 0.004. The most commonly used variant, termed the indirect method, uses indentation followed by determination of the strength after indentation using bend testing. The main concern is to ensure that the crack does not grow between indentation and bend testing. Tests seem to give reproducible values for KIc. 39  ULTRASONIC TESTING The basic principle of ultrasonic testing is that the velocity of an ultrasonic wave through a material is related to its density and elastic properties. This is one example of a dynamic method for determining elastic constants, such as Young’s modulus and shear modulus. Dynamic methods are more accurate than static methods, with uncertainties of