materials engineering chapter 6
useful linear elastic relationships
** deflection is dependent on material geometric and loading parameters **materials with large elastic moduli deform less
Lateral Strain equation
**delta D/d0
stress-strain relationship
- in elastic region equal changes will yield the same change in stress - in plastic region changes in stress may produce a greater change in strain
Modulus of Elasticity
--The ratio of stress to strain when deformation is totally elastic; also a measure of the stiffness of a material. -- for tensile and compression loading, slope of linear elastic region of curve is modulus of elasticity.
with increasing temp....
--ductility increases --elastic modulus tensile and yield strength decrease
Variability of material properties
--test method --fabrication procedure --operator bias --apparatus calibration --inhomogeneties *** material property is defined by average value whereas mag. of scatter is expressed in standard deviation
Rockwell Hardness Test
--the most widely used hardness test, -- hardness determined by an indentation or penetration produced by a static load.
Elastic deformation (strain)
-a material that is stressed first goes into elastic -non pernamnet deformation -elastic def means proportional relationship between stress and strain (linear) - gen valid @ small deformations
Necking in the stress-strain curve refers to
. large reduction in cross-section in a localized region --acts as stress concentrator
Bi-axial tension
2 directions
Ductility
A measure of a material's ability to undergo appreciable plastic deformation before fracture; it may be expressed as percent elongation (%EL) or percent reduction in area (%RA) from a tensile test.
Torsion Equation
Aka SHEAR
Poisson's Ratio
For elastic deformation, the negative ratio of lateral and axial strains that result from an applied axial stress.
engineering strain
The change in gauge length of a specimen (in the direction of an applied stress) divided by its original gauge length.
Tensile strain
The extension per unit length, a dimensionless quantity
true stress
The instantaneous applied load divided by the instantaneous cross-sectional area of a specimen.
engineering stress
The instantaneous load applied to a specimen divided by its cross-sectional area before any deformation.
true strain εt
The natural logarithm of the instantaneous length divided by the original length. Numerically, it is essentially equivalent to the engineering strain for strains up to about 0.1.
Young modulus
The ratio of stress to strain for a given material, providing Hooke's law is obeyed.
yield strength
The stress required to produce a very slight yet specified amount of plastic strain; a strain offset of 0.002 is commonly used. -- transition from elastic to plastic is gradual
Anelasticity
Time-dependent elastic (nonpermanent) deformation.
hydrostatic compression
all direction
Measure of Toughness
area under stress-strain curve amount of energy absorbed before fracture
linear elastic properties
bonds stretch during force application
brittle vs ductile fracture
brittle = small toughness ductile= large toughness
influence on bonding forces
elastic modulus depends on interatomic bonding - modulus proportional to slope of interatomic force vs separation curve
Design/Safety Factors
for ductile materials, safe( working) stress is dependent on yield strengthened factor of safety
Knoop and Vickers Microindentation Hardness Test
light loads and small indenters use these techniques
Hardness vs Strength
linear graph for some metals
hardness
materials resistance to localized plastic deformation
Elastic recovery after plastic deformation
occurs if load is released
shear strain
occurs with a change in orientation of adjacent molecules as a result of these molecules slipping past each other ***dimensionless
plastic deformation
permanent deformation caused by strain when stress exceeds a certain value -bonds stretch and become displaced... remain displaced
Brinell Hardness Test
testing metals and nonmetals of low to medium hardness. uses a ball that is pressed into material and basis calculations on the diameters of ball and indentation.
modulus of resilience
the area under the elastic portion of the stress-strain diagram -energy absorbed during fracture of a material (elastic deformation) -energy recovered when load released
yielding
the onset of plastic deformation
tensile strength
the resistance of a material to breaking under tension --max stress engineering stress-strain curve
yield, tensile strength, and ductility are similar in that
they are sensitive to any prior deformation, impurities, or heat treatment **modulus of elasticity is insensitive