furthermore, the modulus of elasticity of several ... modulus of elasticity, or young’s modulus...

Download Furthermore, the modulus of elasticity of several ... modulus of elasticity, or Young’s modulus (E), ... For many metals and other alloys, values of Poisson’s ratio range between

If you can't read please download the document

Post on 06-Feb-2018

215 views

Category:

Documents

0 download

Embed Size (px)

TRANSCRIPT

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 1

    Tensile stressstrain 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

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 2

    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, shear strain. If the relationship between the applied shear

    stress and shear strain rate -

    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 () of

    the material. Water is an example of a Newtonian material. The following relationship defines

    viscosity:

    Elastic Properties

    The modulus of elasticity, or Youngs 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 Hookes Law: E= /

    Youngs modulus does depend on such factors as orientation of a single crystal material. For

    ceramics, the Youngs modulus depends on the level of porosity. The Youngs 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.

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 3

    Tensile strength (TS)

    It is the ability of a material to withstand tensile (stretching) loads without breaking.

    Poissons ratio

    Relates the longitudinal elastic deformation produced by a simple tensile or compressive

    stress to the lateral deformation that occurs at same time:

    = - lateral/ longitudinal

    When a tensile stress is imposed on a metal specimen, an elastic elongation and accompanying

    strain 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 x = y.

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 4

    For many metals and other alloys, values of Poissons ratio range between 0.25 and 0.35.

    Also the maximum value for is 0.50.

    For isotropic materials, shear and elastic moduli are related to each other and to

    Poissons 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. (Poissons 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.

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 5

    -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 Youngs 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.

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 6

    -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:

  • Lecture 4

    Asst. Lecturer Hasanein M Mahbuba 7

    -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.

Recommended

View more >