Chapter 7 Mechanical Properties

Viscoelastic creep

Many polymeric materials are susceptible to time-dependent deformation when the stress level is maintained constant; such deformation is termed __________________.

Flexural Strength

Modulus of rupture, fracture strength, or bend strength; an important mechanical parameter for brittle ceramics.

Tension

One of the most common mechanical stress-strain tests is performed in _______. Can be used to ascertain several mechanical properties of materials that are important in design.

Table 7.7

Page 230 in book

Shear Strain

Related to the angle of twist.

Fracture Strength

The _________________ corresponds to the stress at fracture; ___________________ are not normally specified for engineering design purposes.

Resilience

The capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered.

Modulus of Elasticity

The constant of proportionality, E (GPa or psi); Young's modulus. This may be thought of as stiffness, or a material's resistance to elastic deformation. The magnitude of the _____________________ is a measure of the resistance to separation of the adjacent atoms, that is, the interatomic bonding forces. It is proportional to the slope of the interatomic force-separation curve at the equilibrium spacing.

Yield-Point Phenomenon

The elastic-plastic transition is very well defined and occurs abruptly in what is termed a _____________________.

Relationship of Modulus of Elasticity and Stiffness

The greater the modulus, the stiffer is the material, or the smaller is the elastic strain that results from the application of a given stress.

Yield Strength

The magnitude of the ______________ for a metal is a measure of its resistance to plastic deformation. The stress required to produce a very slight yet specified amount of plastic strain; a strain offset of 0.002 is commonly used.

Yielding

The onset of plastic deformation.

Proportional Limit

The point on a stress-strain curve at which the straight-line proportionality between stress and strain ceases.

Slip

The process by which plastic deformation is produced by dislocation motion and causes permanent deformation for metals.

Poisson's Ratio

The ratio of the lateral and axial strains; positive. Equation 7.8 See Table 7.1 in book

Hooke's Law

The relationship between engineering stress and engineering strain for elastic deformation (tension and compression). Equation 7.5

Shear Modulus

The slope of the linear elastic region of the shear stress-strain curve. See Table 7.1 in book

Modulus of Resilience

The strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. Equation 7.13a

Tensile Strength, TS (MPa or psi)

The stress at the maximum on the engineering stress-strain curve.

Stress Beyond Point M

The stress required to continue deformation past the maximum, point M, indicates the metal is weakening, but it's strength is increasing. The cross-sectional area is decreasing rapidly within the neck region, where deformation is occurring; resulting in a reduction in the load-bearing capacity of the specimen.

Elastic to Plastic

The transition from _______ to _______ is a gradual one for most metals; some curvature results at the onset of plastic deformation, which increases more rapidly with rising stress.

Anelasticity

This time-dependent elastic behavior is known as ____________, and is due to time-dependent microscopic and atomistic processes that are attendant to the deformation. For metals, the _________ component is normally small and neglected. For some polymeric materials, its magnitude is significant.

Torsion

_______ is a variation of pure shear in which a structural member is twisted in the manner of 7.1d. _________ forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end.

Toughness

___________ is a property that is indicative of a material's resistance to fracture when a crack (or other stress-concentrating defect) is present. __________ is the ability of a material to absorb energy and plastically deform before fracturing.

Notch Toughness

________________ is assessed by using an impact test.

Plastic Deformation

__________________ corresponds to the breaking of bonds with original atom neighbors and then the re-forming of bonds with new neighbors as large numbers of atoms or molecules move relative to one another.

Room-Temperature modulus of elasticity values for a number of metals, ceramics, and polymers.

Table 7.1 (page 197 in book)

Summary of Mechanical Properties

Table 7.8

Why is the stress-strain behavior of brittle ceramics not usually ascertained by a tensile test?

1. It is difficult to prepare and test specimens having the required geometry. 2. It is difficult to grip brittle materials without fracturing them. 3. Ceramics fail after only about 0.1% strain, which necessitates that tensile specimens be perfectly aligned to avoid the presence of bending stresses, which are not easily calculated.

How do polymers differ mechanically from metals and ceramic materials?

1. Metals rarely elongate plastically to more than 100% and some highly elastic polymers may experience elongations exceeding 1000% 2. The modulus for polymers is much smaller than those of metals.

Why is Porosity deleterious to flexural strength?

1. Pores reduce the cross-sectional area across which a load is applied. 2. They act as stress concentrators.

Why are hardness tests performed?

1. Simple and inexpensive 2. Test is nondestructive 3. Other mechanical properties often may be estimated from hardness data, such as tensile strength

Compressive

A ___________ force is taken to be negative, which yields a negative stress. ____________ strains computed from Equation 7.2 are also negative.

Compression Test

A ________________ is conducted in a manner similar to the tensile test, except that the force is compressive and the specimen contracts along the direction of stress. A ________________ is used when a material's behavior under large and permanent strains is desired, or when the material is brittle in tension.

Stress-Strain Test

A __________________ typically takes several minutes to perform and is destructive; that is, the test specimen is permanently deformed and usually fractured.

Brinell hardness Test

A hard, spherical indenter is forced into the surface of the metal to be tested. See Section 7.16 in the book.

Rockwell Hardness Tests

A hardness number is determined by the difference in depth of penetration resulting from the application of an initial minor load followed by a larger major load. See Section 7.16 in the book.

Ductiliity

A measure of the degree of plastic deformation that has been sustained at fracture. May be expressed quantitatively as either percent elongation or percent reduction in area.

Brittle

A metal that experiences very little or no plastic deformation upon fracture is termed _______.

Elastomers

A polymeric material that may experience large and reversible elastic deformations.

Viscoelasticity

A type of deformation exhibiting the mechanical characteristics of viscous flow and elastic deformation. See Section 7.15 in the book.

Knoop and Vickers Microindention Hardness Tests

A very small diamond indenter having pyramidal geometry is forced into the surface of the specimen. Both are well suited for measuring the hardness of small, selected specimen regions; hardness of ceramic materials are measured using these tests; the Knoop test is preferred for very brittle ceramic materials.

Relationship Between Yield, Tensile Strengths, Ductility, and Temperature

As temperature increases, the magnitudes of both yield and tensile strength decline; as temperature increases, ductility usually increases.

The Relationship Between the Modulus of Elasticity and Temperature

As temperature increases, the modulus of elasticity decreases for all but some rubber materials.

How Temperature Affects Mechanical Characteristics of Polymers

As temperature increases: 1. Elastic modulus decreases 2. Tensile strength reduces 3. Ductility increases.

Upper Yield Point

At the _________________, plastic deformation is initiated with an apparent decrease in engineering stress.

Macroscopic Deformation of Semicrystalline Polymers

At the upper yield point, a small neck forms within the gauge section of the specimen. Within this neck, the chains become oriented, which leads to localized strengthening. There is a resistance to continued deformation at this point, and specimen elongation proceeds by the propagation of this neck region along the gauge length. This tensile behavior may be contrasted to that found for ductile metals, in which once a neck has formed, all subsequent deformation is confined to within the neck region.

Isotropic

Because the grain orientation is random in most polycrystalline materials, these may be considered to be _________; inorganic ceramic glasses are also _________.

Lower Yield Point

Continued deformation fluctuates slightly about some constant stress value, termed the _________________; stress subsequently rises with increasing strain. For metals that display this effect, the yield strength is taken as the average stress that is associated with the _______________.

Elastic Deformation

Deformation in which stress and strain are proportional is called ___________________. ___________________ is non-permanent, which means that when the applied load is released, the piece returns to it's original shape.

Why do modulus values among metals, ceramics, and polymers differ?

Differences are a direct consequence of the different types of ataomic bonding that exist for the three materials.

Engineering Stress (σ)

Equation 7.1

Ductility, as percent elongation

Equation 7.11

Ductility, as percent reduction in area

Equation 7.12

Modulus of Resilience for Linear Elastic Behavior

Equation 7.13b

Modulus of Resilience for Linear Elastic Behavior, incorporating Hooke's Law

Equation 7.14

True Stress

Equation 7.15

True Strain

Equation 7.16

Conversion of Engineering Stress to True Stress

Equation 7.18a

Conversion of Engineering Strain to True Strain

Equation 7.18b

True Stress-True Strain Relationship in the Plastic Region of Deformation (To the Point of Necking)

Equation 7.19

Engineering Strain

Equation 7.2

Flexural Strength with rectangular cross section

Equation 7.20a

Flexural Strength with circular cross section

Equation 7.20b

Dependence of modulus of elasticity on volume fraction porosity

Equation 7.21

Dependence of flexural strength on volume fraction porosity

Equation 7.22

Relaxation Modulus

Equation 7.23

Creep Modulus

Equation 7.24 Decreases with increasing temperature.

Shear Stress

Equation 7.3 is a function of the applied torque

Relationship Between Shear Stress and Shear Strain for Elastic Deformation

Equation 7.7

Relationship Among Elastic Parameters

Equation 7.9

Three typically different types of stress-strain behaviors for polymeric materials

Figure 7.22

Coorrelation Between Hardness and Tensile Strength

For steel alloys, conversion of Brinell hardness to tensile strength: Equation 7.25a and Equation 7.25b in book