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