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…
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:…
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…
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,…
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…
Metallic Crystal Structures
Important properties of the unit cells are - The type of atoms and their radii R. - Cell dimensions (side a in cubic cells, side of base a and height c in HCP) in terms of R. - n, number of atoms per unit cell. For an atom that is shared with m adjacent unit cells, we only count a fraction of the atom,…
