Tensile stress strain curves for different materials. Shows in figure below Furthermore, the modulus of elasticity of several materials effected by increasing temperature, as is shown in Figure Asst. Lecturer Hasanein M Mahbuba 1
Shear, or torsional stresses also evokes elastic behavior, Shear stress and strain are proportional to each other through the expression Where G is the shear modulus, ϒ shear strain. If the relationship between the applied shear stress and shear strain rate ϒ - is linear, we refer to that material as Newtonian. The slope of the shear stress versus the steady-state shear strain rate curve is defined as the viscosity (ɳ) of the material. Water is an example of a Newtonian material. The following relationship defines viscosity: Elastic Properties The modulus of elasticity, or Young s modulus (E), is the slope of the stress-strain curve in the elastic region. This relationship between stress and strain in the elastic region is known as Hooke s Law: E= σ/ϵ Young s modulus does depend on such factors as orientation of a single crystal material. For ceramics, the Young s modulus depends on the level of porosity. The Young s modulus of a composite depends upon the stiffness and amounts of the individual components. If a stress of 30,000 psi is applied to each material, the steel deforms elastically 0.001.; at the same stress, aluminum deforms 0.003 in./in. The elastic modulus of steel is about three times higher than that of aluminum. Asst. Lecturer Hasanein M Mahbuba 2
Tensile strength (TS) It is the ability of a material to withstand tensile (stretching) loads without breaking. Poisson s ratio Relates the longitudinal elastic deformation produced by a simple tensile or compressive stress to the lateral deformation that occurs at same time: υ = -E lateral/ E longitudinal When a tensile stress is imposed on a metal specimen, an elastic elongation and accompanying strain ϵ z result in the direction of the applied stress as shown in figure As a result of this elongation, there will be constrictions in the lateral (x and y), If the applied stress is uniaxial (only in the z direction), and the material is isotropic, then ϵ x = ϵ y. Asst. Lecturer Hasanein M Mahbuba 3
For many metals and other alloys, values of Poisson s ratio range between 0.25 and 0.35. Also the maximum value for υ is 0.50. For isotropic materials, shear and elastic moduli are related to each other and to Poisson s ratio according to In most metals G is about 0.4E; thus, if the value of one modulus is known, the other may be approximated. Example A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10 mm. Determine the magnitude of the load required to produce a 2.5 * 10-3 mm change in diameter if the deformation is entirely elastic. (Poisson s ratio for brass is 0.34, modulus of elasticity is 97 GPA). Ans 5600 N -Resilience (modulus of resilience) The area contained under the elastic portion of a stress-strain curve, is the elastic energy that a material absorbs during loading and subsequently releases when the load is removed. For linear elastic behavior: - Elasticity It is the ability of a material to deform under load and return to its original size and shape when the load is removed. Asst. Lecturer Hasanein M Mahbuba 4
-Stiffness (rigidity) It is the measure of a material's ability not to deflect under an applied load. Stiffness of a component is proportional to its Young s modulus. A component with a high modulus of elasticity will show much smaller changes in dimensions So cast iron more rigid than steel, - Plasticity This property is the exact opposite to elasticity, it is the state of a material which has been loaded beyond its elastic limit so as to cause the material to deform permanently. Under such conditions the material will not return to its original shape. Asst. Lecturer Hasanein M Mahbuba 5
-Toughness The energy absorbed by a material prior to fracture is known as tensile toughness, it is the ability of the materials to withstand bending or it is the application of shear stresses without fracture, so the rubbers and most plastic materials do not shatter, therefore they are tough. -Ductility Is the ability of a material to be permanently deformed without breaking when a force is applied. A metal that experiences very little or no plastic deformation upon fracture is termed brittle. Figure shows comparison of stress-strain of brittle and ductile materials The percent elongation %EL is the percentage of plastic strain is: Asst. Lecturer Hasanein M Mahbuba 6
-Brittleness It is the property of a material that shows little or no plastic deformation before fracture when a force is applied. Also it is opposite of ductility. - Malleability It is the ability of material to withstand deformation under compression without rupture or the ability of material allows a useful amount of plastic deformation to occur under compressive loading before fracture occurs. Such a material is required for manipulation by such processes as forging, rolling and rivet heading. Asst. Lecturer Hasanein M Mahbuba 7