mechanical behaviornano.engineering.iastate.edu/courses/mate271/week9.pdf · material sciences and...

Material Sciences and Engineering, MatE271 1

Material Sciences and Engineering MatE271 1Week9

Mechanical Behavior

Material Sciences and Engineering MatE271 Week 9 2

Mechanical Behavior

Application

1. Support load - Applied vs. dead weight- Static vs. dynamic

2. Controlled deformation-Small vs. large

3. Reliability

• How microstructure affects mechanical properties

• Tailored microstructure for mechanical properties



Goals for this unit (Ch. 6)

�Detailed coverage of basic mechanical properties- Describe the concepts of stress and strain

- Differentiate between elastic and plastic deformation

- Quantify elastic properties of materials

- Describe measures of hardness, ductility,

toughness and strength

- Understand fracture, fatigue and creep failures


6.1 Stress vs. Strain

load

Displacement (�L)

Area(Ao)

Length(Lo) � = P/ Ao (N/m2 )

� = �L/ Lo

Stress

Strain

Engineering Stress - load/original cross sectional area

There are also shear and torsional stresses

For tensile or compressive stresses



Stress vs. Strain: units

�Stress��F/Ao (where Ao is the original cross-sectional

area)psi (pounds force per square inch)MPa (Mega Pascals = 106 N/m2 )

�Strain� = �L/Lo (where Lo is the original length)

unitless-sometimes expressed as a percentage


x

z

y

�Ps

Lo

�y

��Ps ��s ��tan �� y �Lo

�

Shear Stress vs. Shear Strain



Application of Loads

Tension Compression


Application of Loads

Shear

Torsional



• One of the most common stress-strain

tests performed is tensile testing

• There are standards for the shape and size

and finish of test specimens

• Tensile testing equipment elongates a

specimen at a constant rate and measures:

– Load (load cell)

– Elongation (extensometer)

Tensile testing

Load cell

Gage length

Crosshead

Specimen

Grip

Grip


Tensile testing

Load cell

Gage length

Crosshead

Specimen

Grip

Grip

Stre

ss

Elastic Plastic

Yield strength

Tensile strength

Fracture

Strain



Elastic Deformation

�Definition• When stress and strain are proportional

• Non-permanent

• When stress is removed, strain disappears

• i.e. the sample returns to it’s original shape

�What is happening?• small changes in inter-atomic spacing

• bonds are stretching but not breaking


Modulus of elasticity depends on bond strength!



Modulus of Elasticity

Elastic modulus is the slope of the atom forcevs distance curve at

equilibrium spacing

• Slope of stress-strain curve in

elastic region

��= (E)(�� Hooke’s Law)

E - modulus of elasticity

(Young’s modulus)Material E (GPa)

Steel 207

Aluminum 69

Al2O3 370

SiC 470


Elastic Stress - Strain Behavior

�Shear stress and strain are also proportional to each other in the elastic region:

� = G��shear stress��shear strain G ��shear modulus

Compare to� = E�



Example Problem

�A tensile force of 2000N is applied along the axis of an aluminum cylindrical specimen (E = 70 GPa, 1 m long, radius 0.01 m). Assuming the deformation is elastic, estimate the elongation.


Poisson’s Ratio

�Q. When a specimen is elongated in one direction - what happens in the other two directions?

�A. Usually, they contract.�The ratio of lateral to axial strains is

called Poisson’s ratio

� � �

� x� z

� �

� y

� z

The - sign assures �will be positive

z



Poisson’s Ratio


Poisson’s Ratio

�Q. What is Poisson’s ratio for an isotropic material?

�A. If the properties are the same in all directions, then � = 0.25

�Most metals have a � = 0.25 to 0.35

�Admissible range -1 � � � 0.5• for no volume change � � 0.5



Poisson’s Ratio

�Shear and elastic moduli are related:

E = 2G(1+�)

�Most materials are elastically anisotropic• E varies with crystallographic direction

• most polycrystalline materials may be considered to be isotropic

�Most engineering materials are polycrystalline


Plastic Deformation� There is a limit to

how much a metalcan be deformed before it will notreturn to its originalshape when the stressis removed

� After reaching elasticlimit, deformation is plastic (in metals dislocation movement).

(in ceramics micro-cracking)

Stre

ss

Elastic Plastic

Yield strength

Tensile strength

Fracture

Strain



Plastic Deformation

� In metals: Plastic deformation corresponds to the breakingof bonds with atom neighbors and reformingbonds with new neighbors

- (dislocation motion)�Beyond Yield point,

stress is notnot proportional to strain (Hooke’s law is not valid)

PlasticElastic

Strain

Stre

ss �y


• During plastic deformation, shear stresses cause dislocation

movement resulting in slip.

• This deformation is permanent (not recovered when stress is removed.)

Slip produces plastic deformation

Check week 5 slides 20-33



Yielding and Yield Strength

�Most structures are designed such that only elastic deformation occurs when a stress is applied

�The point at which plastic deformation occurs must be known (what stress level will bend the metal permanently?)

� Phenomenon is called yielding� For metals that experience a gradual transition, the

point is called the proportional limit


Proportional Limit

�How do you know where �y is?

�By convention, a specified strain offset of 0.002 is used to identify the yield strength, �y.

PlasticElastic

Strain

Stre

ss

�y

0.0020.2%

P



Elastic recovery after plastic deformation

Strain (mm/mm)

Stre

ss (M

Pa)

Elastic Recovery


• Process of plastic deformation (slip)multiplies the number of dislocations

• As each increment of plastic deformation occurs, dislocations findit harder and harder to move because of “entanglement” with ever increasingnumber of dislocations

• Result is that yield strength increases afterplastic deformation (“strain hardening”)

Work Hardening (Strain Hardening)

Strain

Stre

ss

Yield point



Yield Point Phenomenon

� Some steels show a yield point which occurs abruptly

� Yield point is taken as the average stress of the lower yield point

� Yield points for steels vary from 5,000 to 200,000 psi!

Strain

Stre

ss

�y

UpperYield Pt.

LowerYield Pt.


Tensile Strength

� After yielding, stress increasesto a maximum, then decreases,and eventually the material

fractures� Tensile strength is the stress

at the maximum of the engineering stress vs strain curve.

� Deformation up to this point is uniformthroughout the sample

� After maximum stress, necking occurs

Stre

ss

Elastic Plastic

Yield strength

Tensile strength

Fracture

Strain



True vs. Engineering Stress and Strain• Does material actually get

weaker after TS has been

exceeded?

• No, that is an “artifact” of

using engineering stress

instead of true stress in the plot.

• X-sectional area is decreasing,

and especially after necking

starts.


True Stress and Strain

True Stress = P/A (A: is the current area)True Strain = �L/L (L:current length)

Vol= AL =Ao Lo

�true�P LAo Lo

• When strength of a metal is cited, for design purposes, the yield strength is used.

• The fracture strength is the stress at fracture



Definition - Ductility

�Measure of degree of plastic deformation that has been sustained before fracture

� If there is little plastic deformation before fracture --- called brittle

�Ductility = percent elongation

%EL �

(l f � lo )lo

x 100


Ductility



Ductility

Why is ductility important?� Specifies how much a structure will deform before

fracture� Specifies how much deformation is allowable

during fabrication�Ductility is strongly temperature dependent

– i.e., ductile-to-brittle transitions


Toughness�Capacity to absorb energy when deformed, up to

fracture�Given by area under curve�Describes the combination of strength and ductility

tougher



Charpy Impact Test of ToughnessSeldom have complete stess-strain curve, so an impact test is usually used to measure toughness


Comparison of Mechanical Characteristics



Hardness

Hardness: surface resistance to indentation

H= F/Aprojected

F

�

Ap

- Quantitative means use a small indenterforced into the surface

- Indenter: round (ball)pointed (cone or pyramid)


Hardness Tests

� There is a correlation between tensile strength

and hardness

� Hardness tests are simple and inexpensive

� Hardness tests are nondestructive (you still have a

usable sample when you are done)

�Other properties can be estimated from hardness

information.



Tensile Strength often scales with Hardness

Stre

ngth

, MPa

Hardness, BHN


Hardness Tests

�Although the scales are quantitative, the numbers are only relative (rather than absolute values)

�Only compare hardness values obtained using the same method

�Methods of testing• Rockwell Hardness

• Brinell Hardness

• Knoop and Vickers Microhardness



Rockwell Hardness

�Most common method�Indenters are hardened steel balls of various

diameters�The hardness is determined by the

difference in depth of the indentation of two different loads

�Modern instruments are automated


Brinell Hardness

�Hard, spherical indenter is forced into the surface (like for Rockwell)

�The indentor is steel or WC (tungsten carbide)

� Standard loads are used

�The load is maintained for a specified amount of time

�The diameter of the indentation is measured with a microscope



Knoop and Vickers

�Very small diamond indenter with a pyramid geometry is forced into the specimen.

�The resulting impression is measured�Knoop is frequently used for ceramics


Summary of Standard Hardness Tests

mechanical behaviornano.engineering.iastate.edu/courses/mate271/week9.pdf · material sciences and...

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