MSE 3143 Ceramic Materials Mechanical Properties of Ceramics Assoc.Prof. Dr. Emre YALAMAÇ Res.Asst. B.Şölen AKDEMİR 2017-2018 Fall 1
OUTLINE Elasticity & Strength Stress & Strain Behaviour Of Materials Young s Modulus Poisson s Ratio Strength Strength Measurements Fracture Toughness Hardness and Indentation Test Estimation of Compressive Strength Indentation Fracture Toughness Nanoindentation Method 2
ELASTICITY & STRENGTH Load Defined as Stress (s) Unit of Stress is psi(pound per sqaure inch) or MPa Deformation Strain = Strain rate (e) Strain unit is deformation cm/cm Strain type depends on bond energy, stress and temperature. Elastic Deformation: Once the forces are no longer applied, the object returns to its original shape. E= Young s modulus (=Elastic Modulus) s = E e G = Shear Modulus t = G g Volumetric Modulus of Elasticity 3
STRESS & STRAIN BEHAVIOUR OF MATERIALS a) Brittle Fracture diagram typically observed in ceramics b) Ductile Fracture diagram observed in materials that can deform plastically (with no distinct yield point) c) Ductile Fracture diagram with a yield point observed in low carbon steels. d) Stress & Strain diagram of Elastomers. Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006 4
E= YOUNG S MODULUS / ELASTIC MODULUS The magnitude of the elastic modulus is determined by the strength of the atomic bonds in the material. Calculation from the plot of stress&strain diagram E s e Atomic bond E Bonding Type E (GPa) Organic Materials 10 Weak Ionic Bond (NaCl) 44.2 Aluminium 69 Iron Nickel alloys 200 Strong Covalent Bond(Diamond) 1035 5
E= YOUNG S MODULUS / ELASTIC MODULUS In single crystalline materials, Young s Modulus value depends on crystallographic orientation. Anisotropy In single Iron crystalline: Crystallographic directions E (GPa) [111] direction 283 [100] direction 124 6
E= YOUNG S MODULUS / ELASTIC MODULUS Many materials encountered by an engineer are made up of more than one composition or phase and have elastic modulus intermediate between the moduli of the two constituent phases. E E V a a E b V b E a, E b : elastic moduli of the constituents V a, V b : volume fractions E : estimated elastic modulus of the mixture Porosity is also a factor affecting the elasticity. E E (1 1.9P 0.9P 0 2 ) E 0 : elastic modulus of nonporous material P : volume fraction of pores
E= YOUNG S MODULUS (ELASTIC MODULUS) Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
E= YOUNG S MODULUS (ELASTIC MODULUS) Effect of temperature on the elastic modulus Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
POISSON S RATIO When a tensile load is applied on the material, the length of the sample increases slightly and the thickness decreases slightly. The ratio of the thickness changes to the length changes is referred to as Poisson s ratio, ν. d / d l l For isotropic and polycrystalline ceramics, Poisson s ratio, Young s Modulus, and the shear modulus are related by E 2G(1 ) Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
POISSON S RATIO Poisson s ratio typically varies from 0.1 to 0.5. Values for various materials at room temperature are listed in table Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
Young s Modulus for Some Ceramics G
STRENGTH Yield Strength Tensile Strength Theoretical Strength Strength Fracture (Breaking) Strength Compressive Strength Flexural Strength Ultimate Strength
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 1/10 or 1/5 times of the elastic modulus. However, the theoretical strength is not available during material production or due to structural defects. Eg s th a 0 1/ 2 s th : theoretical strength E : elastic modulus a 0 : interatomic spacing g : fracture surface energy
STRENGTH Effect of Defects on Strength The presence of a defects such as a crack, pore or inclusion in a ceramic material results in stress concentration. Inglis Evans and Tappin s m s a s f c 2 Z Y 1/ 2 2Eg c Griffith 1/ 2 s f A E c g 1/ 2 Elliptic crack model
STRENGTH MEASUREMENT Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
STRENGTH MEASUREMENT Tensile Testing Ceramic materials are not generally characterized by tensile testing because of the high cost of test specimen fabrication and the requirement for extremely good allignment of the load train during testing. s t P A
Tensile Strength of Ceramics at Room Temperature
STRENGTH MEASUREMENT Compressive Strength In ceramic materials (e.g. refractory bricks and building bricks), the compression strength is usually measured. Because the compression strength of a ceramic material is usually much higher than the tensile strength. It is often beneficial to design a ceramic component so that it supports heavy loads in compression rather than tension. Residual compressive stresses are created in the material to increase the tensile strength. Example: Concrete prestressed with steel bars and safety glasses In general, compressive strength increases with decreasing grain size.
STRENGTH MEASUREMENT Compressive Strength Why the compressive strength of ceramic materials is higher than their tensile strength? Ceramic Material Ceramic Material Metallic Material
STRENGTH MEASUREMENT Compressive Strength Ceramic materials exhibit low tensile strength due to structural defects such as surface cracks, void-porosity, impurities and grain growth during production. Because pores, impurities and surface cracks are centers of stress intensity. The crack appears easily from these spots under the applied load and progress rapidly in fragile materials like ceramics. As a result, fracture occurs at low stress (load) values. However, under compressive strength, it is important to break atomic bonds instead of structural defects in ceramic materials.
STRENGTH MEASUREMENT Compressive Strength Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
STRENGTH MEASUREMENT Bend Strength (Flexure test) The bend strength is defined as the maximum tensile stress at failure and is often referred to as the modulus of rupture (MOR). S Mc I M : moment I : the moment of inertia c : distance from the neutral axis to the tensile surface Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
STRENGTH MEASUREMENT The strength characterization data for ceramics are reported in terms of MOR or bend strength. Specimens are relatively inexpensive and testing is straightforward and quick. However, there is a severe limitation on the usability of MOR data for ceramics; the measured strength will vary significantly depending on the size of the specimen tested and whether it is loaded in three-point or four-point. To understand this magnitude and reason for this variation, data generated fot hot-pressed Si 3 N 4 during the late 1970s is used. Testing Type MOR (MPa) 3-point bend testing 930 4-point bend testing 724 Uniaxial tensile testing 552? Why Which of these strengths should an engineer use? are they different?
BENDING STRENGTH 3-Point Bending: The peak stress occurs only along a single line on the surface of the test bar opposite to the point of loading. The stress decreases linearly along the length of the bar and into the thickness of the bar, reaching zero at the bottom supports and at the neutral axis, respectively. The probability of the largest flaw in the specimen being at the surface along the line of peak stress is very low. Silicon Nitride (Si 3 N 4 ) samples produced by hot isostatic pressing. 4-Point Bending: The peak stress is present over the area of the tensile face between the load points. The area and volume under peak tensile stress or near peak tensile stress is much greater for four-point bending than for three-point bending, and thus the probability of a larger flaw being exposed to high stress is increased. The 4-point bending test result is lower than the 3-point bending result.
Calculating Bending Strength Example 4-point bending is applied to a 5x5x120 mm SiC bar. The inner (inner span) spacing of the touch points is 40 mm and the outer (outer span) spacing is 80 mm. a) If the measured load at failure is 200 N, what is the bending strength of this specimen? b) Is it possible to say that the calculated bending strength is the bending strength of SiC? Why?
BIAXIAL STRENGTH In many applications, materials are subjected to multiaxial stress fields. Very few data are available for the response of ceramics to multiaxial stress fields. The illustrated sample test provides a biasing datum that has been subjected to a biaxial stress stance. The defect in the material is subjected to simultaneous tensile and shear stresses. Biaxial loading frequently occurs at the contact zone between two ceramic parts or between a ceramic and a metal part, especially during relative motion due to mechanical sliding or thermal cycling. Under certain conditions, very localized surface tension stresses are much higher than the applied load. Many engineers are not aware of this mechanism of tensile stress generation, yet it is a common cause of chipping, spalling, cracking, and fracture of ceramic components.
STRENGTH DATA Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006 continues
STRENGTH DATA Examples of strength vs. temperature for typical polycrystalline oxide ceramics. Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
STRENGTH DATA Strength versus temperature for carbide and nitride ceramics and superalloy metals. Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
FRACTURE TOUGHNESS Until now, discussions have considered strength and fracture in terms of critical flaw size. An alternative approach considers fracture in terms of crack surface displacement and the stresses at the tip of the cracks. This is the fracture mechanics approach. The stress concentration at a crack tip is denoted by the stress intensity factors K I, K II and K III. The subscripts refer to the direction of the load application according to the crack position. If the load is perpendicular to the crack, as is typically the case in a tensile or bend test as indicated by K I. Mode I is most frequently encountered for ceramic materials.. The critical stress intensity factor (K IC ) is the stress intensity factor at which the crack will propagate and lead to fracture. This is also called fracture toughness.
FRACTURE TOUGHNESS The parameters associated with Mode I stress intensity factor are: For plane strain: 2Eg 2 1 1/ 2 For plane stress: K I 2Eg K I 2 1/ For the applied stress s a and crack length 2c: K s ayc 1/ I 2
FRACTURE TOUGHNESS Fracture toughness can be found by many methods. Two common methods are bending and indentation. In the bend test, a notch is introduced, usually using a diamond-tipped copper cutting Wheel, into the tensile side of the specimen. The notch is flat but it can also be in chevron-shaped. Carter, C.B.; Norton, M.G.; Ceramic Materials: Science and Engineering, Springer, 2007
FRACTURE TOUGHNESS K ıc From Bending Strength Test 3-Point = 4-Point notations a = c Y = x P = F max L = (S 1 -S 2 ) b = B
FRACTURE TOUGHNESS Calculation of Fracture Toughness Example A Si 3 N 4 specimen with 10 mm width, 16 mm thickness and 200 mm length shall be measured for toughness with split bar test. The width of split is 100 mm and the depth is 8 mm. The internal and external discharge ranges are 60 and 120 mm respectively. If the maximum load value of the test apparatus measured during printing is 400 N, what is the toughness of the sample?
HARDNESS and INDENTATION TEST Hardness of a ceramic material is measured by an indentation test. The hardness is generally determined by dividing the applied load by the projected area. FIGURE 16.15 Plasticity under the indenter (the shaded area) causes the deviation from Hertzian behavior. FIGURE 16.14 Indentation stress versus indentation strain. Deviation from what is called Hertzian behavior. Carter, C.B.; Norton, M.G.; Ceramic Materials: Science and Engineering, Springer, 2007
HARDNESS and INDENTATION TEST Mohs Hardness Values
HARDNESS and INDENTATION TEST Carter, C.B.; Norton, M.G.; Ceramic Materials: Science and Engineering, Springer, 2007
HARDNESS and INDENTATION TEST Carter, C.B.; Norton, M.G.; Ceramic Materials: Science and Engineering, Springer, 2007
ESTIMATION OF Compressive STRENGTH Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006
INDENTATION FRACTURE TOUGHNESS K ıc from indentation test a = 2 for a Vickers indenter is dimensionless constant, which for ceramics has an average value of 0.016±0.004 Carter, C.B.; Norton, M.G.; Ceramic Materials: Science and Engineering, Springer, 2007
NANOINDENTATION METHOD Thin films and surfaces The low loads used mean that the extent of cracking is much smaller than in conventional indentation methods. Two parameters are often of most interest in nanoindentation testing: Elastic modulus Hardness Nanoindentation is a powerful technique because the shape of the load-displacement curve can be used to identify effects such as phase transformations, cracking, and film delamination during indentation. It is also important in studying the mechanical properties of nanomaterials, such as carbon nanotubes. Carter, C.B.; Norton, M.G.; Ceramic Materials: Science and Engineering, Springer, 2007
ANY QUESTIONS? 43