The Brinell Hardness Test
The Brinell hardness test method consists of indenting the test material with a 10 mm diameter hardened steel or carbide ball subjected to a load of 3000 kg. For softer materials the load can be reduced to 1500 kg or 500 kg to avoid excessive indentation. The full load is normally applied for10 to 15 seconds in the case of iron and steel and for at least 30 seconds in the case of other metals. The diameter of the indentation left in the test material is measured with a low powered microscope. The Brinell harness number is calculated by dividing the load applied by the surface area ofthe indentation.
Yield criteria and macroscopic aspects of plastic deformation
Gross plastic deformation of a polycrystalline specimen corresponds to the comparable distortion of the individual grains by means of slip. During deformation, mechanical integrity and coherency are maintained along the grain boundaries; that is, the grain boundaries is constrained, to some degree, in the shape it may assume by its neighboring grains. Before deformation the grains are equiaxed, or have approximately the same dimension in all directions. For this particular deformation, the grains become elongated along the directions. For this particular deformation, the grains become elongated along the direction in which the specimen was extended.
True Stress and Strain
When one applies a constant tensile force the material will break after reaching the tensile strength. The material starts necking (the transverse area decreases) but the stress cannot increase beyond tensile strength. The ratio of the force to the initial area, what we normally do, is called the engineering stress. If the ratio is to the actual area (that changes with stress) one obtains the true stress.
Tensile Properties
Yield point. If the stress is too large, the strain deviates from being proportional to the stress. The point at which this happens is the yield point because there the material yields, deforming permanently (plastically). Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is called yield stress, and is an important measure of the mechanical properties of materials. In practice, the yield stress is chosen as that causing a permanent strain of 0.002 The yield stress measures the resistance to plastic deformation. The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched beyond repair, but the motion of dislocations, which involves breaking and reforming bonds. Plastic deformation is caused by the motion of dislocations. Tensile strength: When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength, and then falls as the material starts to develop a neck and it finally breaks at the fracture point. For structural applications, the yield stress is usually a more important property than the tensile strength, since once it is passed, the structure has deformed beyond acceptable limits. Ductility: The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation åmax or maximum area reduction. %EL = åmax x 100 % %AR…
Plastic deformation
When the stress is removed, the material does not return to its previous dimension but there is a permanent, irreversible deformation. In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law: σ = E ε That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. In some cases, the relationship is not linear so that E can be defined alternatively as the local slope: E = dσ/dε Shear stresses produce strains according to: τ = G γ where G is the shear modulus. Elastic moduli measure the stiffness of the material. They are related to the second derivative of the interatomic potential, or the first derivative of the force vs. inter nuclear distance. By examining these curves we can tell which material has a higher modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic. Yield criteria and macroscopic aspects of plastic…
Elastic deformation
When the stress is removed, the material returns to the dimension it had before the loadwas applied. Valid for small strains (except the case of rubbers).Deformation is reversible, non permanent
X-RAY DIFFRACTION: DETERMINATION OF CRYSTAL STRUCTURES
Diffraction occurs when a wave encounters a series of regularly spaced obstacles that (1) are capable of scattering the wave, and (2) have spacings that are comparable in magnitude to the wavelength. Furthermore, diffraction is a consequence of specific phase relationships established between two or more waves that have been scattered by the obstacles. The magnitude of the distance between two adjacent and parallel planes of atoms (i.e., the interplanar spacing ) is a function of the Miller indices (h, k, and l) as well as the lattice parameter(s). For example, for crystal structures that have cubic symmetry
Imperfections in Solids
Point Defects Vacancies and Self-Interstitials A vacancy is a lattice position that is vacant because the atom is missing. It is createdwhen the solid is formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal vibrations. An interstitial is an atom that occupies a place outside the normal lattice position. It maybe the same type of atom as the others (self interstitial) or an impurity atom. In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect. This means that the forces are not balanced in the same way as for other atoms in the solid, which results in lattice distortion around the defect A hightemperature is needed to have a high thermal concentration of vacancies. Frenkel-defect is a vacancy-interstitial pair of cations Schottky-defect is a pair of nearby cation and anion vacancies Theoretical yield point Theoretical yield is the maximum quantity of a product that could be formed in a chemical reaction if all the limiting reactant reacted to form products (distinguished from actual yield). Dislocations—Linear Defects…
Miller Indices
A system of notation is required to identify particular direction(s) or plane(s) to characterize the arrangement of atoms in a unit cell Rules for Miller Indices (Planes) 1. Determine the intercepts of the face along the crystallographic axes, in terms of unit cell dimensions. 2. Take the reciprocals 3. Clear ractions 4. Reduce to lowest terms 5. For example, if the x-, y-, and z- intercepts are 2, 1, and 3, the Miller indices are calculated as: 6. Take reciprocals: 1/2, 1/1, 1/3 7. Clear fractions (multiply by 6): 3, 6, 2 8. Reduce to lowest terms (already there) Thus, the Miller indices are 3,6,2. If a plane is parallel to an axis, its intercept is at infinity and its Miller index is zero. A generic Miller index is denoted by (hkl). A family of planes is represented by {hkl} If a plane has negative intercept, the negative number is denoted by a bar above the number. Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get 1,1,1. This…
Crystalline and Non-crystalline materials
Single Crystals Crystals can be single crystals where the whole solid is one crystal. Then it has a regular geometric structure with flat faces. Polycrystalline Materials A solid can be composed of many crystalline grains, not aligned with each other. It is called polycrystalline. The grains can be more or less aligned with respect to each other. Where they meet is called a grain boundary. Non-Crystalline Solids In amorphous solids, there is no long-range order. But amorphous does not mean random, since the distance between atoms cannot be smaller than the size of the hard spheres. Also, in many cases there is some form of short-range order. For instance, the tetragonal order of crystalline SiO2(quartz) is still apparent in amorphous SiO2 (silica glass.)
