MSE 2100 Module 6

Modulus of elasticity

Constant of proportionality for Hooke's Law, E (GPa or psi)^6

True/False: Necking can occur with compressive loadings

False

Modulus of resilience, dimensions

J/m^3 (Pa) or in.-lbf/in^3

Plastic deformation

Permanent, nonrecoverable

Engineering strain concept

Ratio of change in length over initial length of specimen

What is the constant of proportionality used to relate shear stress and shear strain?

The shear modulus, G

Shear strain

The tangent of the strain angle theta

True/False: All deformation prior to the point of tensile strength is uniform throughout the narrow region.

True

True/False: Ceramics and metals have similar values of the modulus of elasticity.

True

True/False: Most engineering materials are characterized by isotropic polycrystallinity.

True

True/False: Strain is sometimes expressed as a percentage.

True

True/False: When a load is released after plastic deformation, some of the total deformation is recovered as elastic strain.

True

For isotropic materials, a minimum of __ constants must be given in order to fully characterize elastic properties.

Two

Tension

Uniaxial loading applied to long axis of specimen in opposite directions, causing specimen to "stretch"

What two entities provide quantitative expressions of ductility?

%EL and %RA

What are the two primary reasons for which knowledge of material ductility is important?

1) Indicates to designer degree of plastic deformation prior to fracture 2) Specifies the degree of allowable deformation during fabrication operations

Why are hardness tests the most common?

1) Simple and inexpensive 2) Nondestructive - small indentation is only deformation 3) Other mechanical properties may be estimated from hardness data

Why are the Rockwell tests so common?

1) Simple to perform 2) No special skills required

In which two cases are compressive stress-strain tests used?

1) When a material's behavior under large & permanent strains is desired 2) When the material is brittle in tension

The numbers on the Mohs scale ranged from values of _ to _.

1, 10

What is the range of values of yield strength from low-strength aluminum to high-strength steel?

35 MPa (5000 psi) to 1400 MPa (200,000 psi)

Brittle materials have an approximate fracture strain of up to __%

5

What is the typical range of tensile stress values from aluminum to high-strength steel?

50 MPa to 3000 MPa

What is the Mohs scale?

A qualitative, somewhat arbitrary hardness indexing scheme

Torsion

A variation of pure shear in which the structural member is twisted.

Toughness

Ability of a material to absorb energy and plastically deform before fracturing

Why is fracture toughness an important consideration for structural materials?

All materials have some quantity of defects

How is toughness depicted in the stress-strain curve?

Area under the curve up to the point of fracture

How is macroscopic elastic strain manifested on an atomic scale?

As small changes in interatomic spacing and stretching of interatomic bonds

Why are most polycrystalline materials considered isotopic?

Because of their random grain orientation

Description plastic deformation from an atomic perspective.

Breaking of bonds with original neighbors and forming new bonds with new neighbors

Lower yield point

Constant stress value about which deformation fluctuates slightly.

Torsional tests are typically performed on ___ - shaped samples.

Cylindrically

Define slip

Deformation in crystalline solids, involving the motion of disclocations

What is the relationship between Young's modulus, the shear modulus, and Poisson's ratio?

E = 2G(1 + v)

Describe elastic anisotropic behavior.

Elastic behavior varies with crystallographic direction.

Anelasticity principle

Elastic deformation continues after load application, and some finite time is required for complete recovery.

What is the difference between engineering stress and true stress?

Engineering stress uses the original cross-sectional area, and true stress uses instantaneous area

Brittle material

Exhibits little or no plastic deformation

True/False: Although tensile stress-strain tests are easier to perform, compressive tests provide more information.

False

True/False: The Rockwell tests only have one scale

False

True/False: The strain offset method can be used for materials that do not exhibit linear elastic deformation.

False.

True/False: Shear stress and shear strain have an exponential relationship.

False. Directly proportional.

True/False: If a material's tensile stress is applied and maintained, fracture will not occur.

False. Fracture will occur eventually.

True/False: A low value of E corresponds to a stiffer material.

False. High E --> stiff material

True/False: The exact position of the point of yielding on the stress-strain curve can easily be determined.

False. It is difficult.

TrueFalse: Polymers have a higher Young's modulus than metals and ceramics.

False. Lower.

When are the tangent modulus and secant modulus used?

For nonlinear elastic behavior

For most metals, is the transition from elastic to plastic deformation sudden or gradual?

Gradual

What are some materials that exhibit nonlinear elastic deformation?

Gray cast iron, concrete, many polymers

What is the most commonly performed mechanical test?

Hardness test

How does the modulus of elasticity change with increased temperature?

It decreases

For nonlinear elastic materials, how is the yield strength determined?

It is defined as the stress required to produce a certain amount of strain

What is depicted by the magnitude of the yield strength for a metal?

Its resistance to plastic deformation

Poisson's ratio relates what two entities?

Lateral and axial strains

Shear stress concept

Load F acting parallel to cross sectional area Ao

True stress

Loading force divided by the instantaneous cross-sectional area

Static loading condition

Low strain rate

Hardness

Material's resistance to localized plastic deformation (i.e. a small dent or scratch)

Describe the position of tensile strength on the stress-strain curve

Maximum point

Tensile strength

Maximum stress that can be sustained by a structure in tension

Ductility

Measures the degree of plastic deformation that has been sustained at fracture.

What is a dynamic loading condition?

One with a high strain rate

Engineering stress concept

Perpendicular load F applied to initial specimen cross-sectional area.

Upper yield point

Plastic deformation initiates with an apparent decrease in engineering stress.

Yield strength

Point of intersection between stress-strain curve and offset (usually 0.002) line that is parallel to elastic region

What is a "notch" in regards to notch toughness?

Point of stress concentration

True strain

Relates instantaneous length to original length

Fracture toughness

Resistance to fracture when a crack (or stress-concentrating defect) is present

What does the magnitude of Young's modulus indicate on an atomic level?

Resistance to separation of adjacent atoms

Torsional forces produce a ___ motion around the longitudinal axis of one end of member to other end.

Rotational

What are the five key mechanical design properties?

Stiffness, strength, hardness, ductility, and toughness

Modulus of resilience

Strain energy per unit volume required to stress a material from unloaded state up to its yield point

Toughness is a function of what two material properties?

Strength and ductility

Hooke's Law concept

Stress and strain are proportional to each other with the modulus of elasticity

Elastic deformation

Stress and strain are still proportional, I.e. Non-permanent deformation

Fracture strength

Stress at fracture

Yield stress

Stress level at which plastic deformation begins

What type of test is used for a load that is both static and uniformly applied over a given cross section?

Stress-strain

Proportional limit

Synonymous to point of yielding

Shear stress formula, dimensions

Tau = F/Ao, MPa

Sign convention for tensile vs. compressive force

Tensile (+) Compressive (-)

At which point in deformation does necking occur?

Tensile strength

What is the most commonly used hardness testing method?

The Rockwell tests

Resilience

The capacity of a material to absorb energy through elastic deformation and recover that energy upon unloading.

Yield point phenomenon

The elastic-plastic region is clearly defined and occurs suddenly

How is the point of yielding identified on a stress-strain curve?

The initial departure from linearity

What does "forgiving" mean when referring to ductile behavior?

The material may experience local deformation without fracture, should there be an error in the design stress calculation.

Tensile stress-strain tests are performed more commonly than compressive stress-strain tests because:

They are easier to perform.

Notch toughness

Toughness regarding dynamic loading conditions and when a notch is present

Engineering strain formula, units

epsilon = (li - lo)/lo, dimensionless but often in m/m or in/in

Engineering stress formula, units

sigma = F/Ao, MPa

By what kind of mechanism does plastic deformation occur in noncrystalline solids and liquids?

viscous flow