Mechanical Properties of Metals

Instructor: Joshua U. OtaigbeIowa State University

Goals of this unit

• Quick survey of important metal systems

• Detailed coverage of basic mechanical properties, especially as they apply to metals

Survey of Important Metal Systems

• Ferrous Alloys

• Aluminum Alloys• Magnesium Alloys

• Titanium Alloys

• Copper Alloys• Nickel Alloys

Ferrous Alloys (based on Fe)

• Carbon and low alloy steels– 0.05 - 2.0 wt% C, <5 wt% non-C additives

• High-alloy steels– >5 wt% non-C additives– stainless steels (Cr and Ni important)– tool steels– superalloys (for high-T use)

• Cast irons (>2 wt% C, Si also important)– most forms are quite brittle

Aluminum Alloys

• Low density and corrosion resistant

• Commonly alloyed with Si, Mg, Cu– pure Al is soft but can be precipitation

hardened through alloying and heat treatment

Magnesium Alloys

• Very low density with high strength-to-weight ratio– however, is of low ductility (hcp)

Titanium Alloys

• Fairly low density and very good strength give high strength-to-weight ratio (important in aerospace)

• Quite corrosion resistant and retains strength to fairly high temperatures

• Difficult to fabricate because of low ductility (hcp)

• Quite expensive

Copper alloys

• Used in pure form for electrical conductor (but very soft)

• Often alloyed to give better strength– with Zn to give brasses– with Sn, Si, Al, Be, etc to give bronzes

Nickel Alloys

• Ni-based alloys are usually quite resistant to oxidation and temperature

• Alloyed with Cu to form monels

• Important ingredient in superalloys such as Inconel and Hastelloy

• Important ingredient in stainless steels

• Expensive

Mechanical Properties

(Materials utilized in load-bearing applications)

Goals

• 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 fatigue and creep failures

Mechanical Properties

• Most materials are subject to some force or load in use, e.g., – airplane wing

– car axle

– brick in a wall

– automobile windshield

– deck on a bridge

• Think about the kinds of loads in each case

What do we need to know?

• What are the mechanical properties of various classes of materials

• Reliability (or variability of properties)• Fracture characteristics• How microstructure affects mechanical

properties• How we can influence the development of

microstructure to tailor mechanical properties

What are mechanical properties?

• Strength (what does that really mean?)– compressive– tensile– shear

• Hardness• Ductility• Stiffness• values depend on T, and type of loading, and

always on microstructure

Stress and Strain - Review

Force

Displacement (U)Area

Lengthσ = F/A (N/m )2

ε = U/LStressStrain

0

Engineering Stress - Force/original cross sectional area

There are also shear and torsional stresses

For tensile or compressive (axial) stresses

Shear Stress and Shear Strain

γγ = ∆∆ y / z o

P s

P sA s

ττ = Ps / As

Stress - Strain Behavior

• Stress - σ = P/Ao (where Ao is the original cross sectional area)

• Strain - ε = ∆l/lo (where lo is the original length)

• Stress is in units of:– psi (pounds force per square inch)– MPa (megapascals = 106 N/m2 )

• Strain is unitless– sometimes expressed as a percentage

Tensile testing

• 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)

Standard Tensile Test

σσ engr = P / AO εε engr = ∆∆ l / l O

U T S

Tensile Testing

Elongation Necking and Failure

Elastic Deformation

• Definition– when stress and strain are proportional– Non-permanent deformation– When stress is removed, strain disappears

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

• What is happening?– small changes in interatomic spacing– bonds are stretching but not breaking

Elastic deformation and atomic displacement (reversible strain)

Modulus of Elasticity

• Slope of stress-strain curve in elastic region§ σ = (E)(ε) (Hooke’s Law)

§ E - modulus of elasticity (Young’s modulus)

σ

ε

Slope = E

Material E (MPa)Steel 20.7 x 10 4

Aluminum 6.9 x 10 4 A l 2 O3 37 x 10 4 SiC 47 x 10 4

•• The greater the modulus the “stiffer” the material

Poisson’s ratio

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

• A. They contract.• The ratio of lateral to axial strains is

called Poisson’s ratio

υ = −ε x

ε z= −

ε y

ε z

The - sign assures νwill be positive

Poisson’s ratio, νν

ν = - ε x / ε z

Poisson’s ratio, cont.

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

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

• Most metals have a ν = 0.25 to 0.35

• The maximum value ν = 0.5– (for no volume change)

Plastic Deformation

• There is a limit to how much a metal can be deformed before it will not return to its original shape when the stress is removed

• Beyond this point, stress and strain notproportional (Hooke’s law is not valid)

• Plastic deformation occurs (the “elastic limit” has been exceeded)

Plastic Deformation

• Curvature in stress-strain curve indiates the onset of plastic deformation.

• Plastic deformation corresponds to the breaking of bonds with atom neighbors and reforming bonds with new neighbors (slip).

PlasticElastic

Strain

Str

ess

Slip produces plastic deformation

• During plastic deformation, shearing

stresses cause dislocation movement resulting in slip.

• This deformation is permanent (not recovered

when stress is removed.)

Necking during extensive Plastic Deformation

“necking”

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 elastic limit

Elastic Limit and Yield Strength

• How do you know where the elastic limit is?

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

Strain

Str

ess

σ y

0.002

Elastic recovery after plastic deformation

Shackelford 7-6

Work Hardening (Strain Hardening)

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

• As each increment of plastic deformation occurs, dislocations find it harder and harder to move because of “entanglement” with ever increasing number of dislocations

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

Work Hardening (Strain Hardening)

Yield Characteristic of low-C Steels

Tensile Strength

• After yielding, stress increases to a maximum, then decreases, and eventually the material fractures

• Tensile strength is the stress at the maximum of the stress vs strain curve.

• Deformation up to this point is uniform throughout the sample

• After maximum stress, necking occurs

Specimen Geometry Changes with Plastic Deformation

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.

Tensile Strength

• Tensile strength may vary from 7,000 psito 450,000 psi (1 psi = 6895 Pa)

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

• The fracture strength is the stress at fracture

Ductility

• Measure of degree of plastic deformation that has been sustained at fracture

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

• Ductility = percent elongation

%EL =

(l f − l o )

l o

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

• Describes the combination of strength and ductility

• Total area under the stress-strain curve

• Seldom have complete stess-strain curve, so an impact test is usually used to measure toughness

Charpy Impact Test of Toughness

Summary of Mechanical Characteristics

1 Elastic Modulus

2 Yield strength (YS)

3 UTS

4 Ductility (100 * εε F)

5 Toughness

Summary of Mechanical Characteristics

Comparison of Mechanical Characteristics

Hardness

• Measure of resistance to localized deformation (a dent or scratch)

• Early tests were based on minerals (which mineral could scratch another)

• Mohs scale;– 1 (talc) to 10 (diamond)– Qualitative method

• Qualititative means use a standarized small indenter forced into the surface

Hardness Testing

Hardness and Strength

• 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

Hardness Tests

• Although the scales are quantitative, the numbers are only relative (rather than absolute values), so you should 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

• Indentors are hardened steel balls or cones of various diameters

• The hardness is determined by the difference in depth of the indentation with 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 microscopically

• Knoop is frequently used for ceramicsShow Table 6.4, Callister 2000 (summary

of hardness tests)

Summary of Standard Hardness Tests

Failure modes

• Failure by excessive deformation

• Failure by fracture– ductile fracture– brittle fracture (covered in ceramic section)

• Fatique failure (cyclic loading)

• Creep failure (high temperature)

Fracture

• Fracture can occur in any mode of loading– tensile– compressive– shear– torsion

• Modes of fracture (based on amount of local deformation)– ductile– brittle

Fracture

• Proceeds in two stages– crack formation and crack growth

• Ductile fracture– extensive plastic deformation– slow crack growth - called “stable”

• Brittle fracture– almost no plastic deformation– very rapid crack growth - called “unstable’

Ductile Fracture

• Ductile fracture is usually preferred– Presence of plastic deformation gives

“warning” of imminent failure– Large amount of strain energy is required to

induce ductile fracture

Ductile vs. brittle fracture

• Configuration of ductile fracture

Highly ductile BrittleModerately Ductile

Appearance of Fracture Zone

• Cup and cone fracture in aluminum

• Brittle fracture in mild steel

Ductile vs Brittle Fracture*

Cold - Worked Specimens

Fractured Specimens

Ductile to Brittle Transition on cooling

Fatigue failure

• Fatigue failure is fracture that occurs under cyclic loading well below the “static”strength value of the material

• Fatigue occurs in both ductile and brittle materials

• Most metallic fractures in use are fatigue failures– bridges, aircraft, all types of machinery

• Often characterized by “cycles to failure”

Failure under Cyclic Loading

Fatigue failure (S-N curve)

Improving Fatigue Resistance

Creep (High-temperature deformation)

• Continuous plastic deformation of materials subjected to a constant stress at T>0.4Tm

– Occurs at stresses well below room temperature yield strength

• Both temperature and applied stress influence creep behavior

• Alloys resistant to creep have high E and high melting T

Stages of Creep

creep rupture

Creep depends on σσ and T

Creep rate affected by changes in applied stress

Creep rate affected by changes in temperature

End of Unit 2–1 & Review

• Describe the concepts of Stress and Strain• Differentiate between Elastic and Plastic

Deformation• Quantify Elastic Properties of Materials• Describe measures of hardness• Describe different modes of failure• Explain fatigue and creep�Read Class Notes and Relevant portions

of Callister 2000 OR Shackelford 2000