ch. 6 mechanical properties

hooke’s law for stress-strain

tensile stress

tensile force/applied area

shear stress

shear force/applied area

torsion

torque/polar moment of inertia

strain

change in length/original length (no units)

shear strain

∆x/y=tanθ

poisson’s ratio

dimensionless

nature of elastic forces

shear modulus

bulk modulus (K)

relationships between moduli for isotropic materials

stress-strain diagram for tensile testing

yield strength

stress at which a noticeable plastic deformation has occurred

0.2% method

tensile strength

maximum stress on engineering stress-strain curve

fracturing for metal

fracture occurs when noticeable necking starts

fracturing for polymers

fracture occurs when polymer backbone chains are aligned and about to break

percent elongation

percent reduction of area

at necking point

toughness

energy to break a unit volume of material

approximated by the area under stress-strain curve

resilience

ability of material to store energy (best stored in elastic region)

elastic strain recovery

true stress

true strain

trues stress-true strain curve

stops at yield point

strain hardening

as plastic defromation increases, metal becomes stronger

strain hardening curve fit equation

compression test

necking replaced by barreling due to friction between specimen and the platen

three point bending test

bending stress is higher, but shows greater scatter

four point bending test

bending stress is lower, but shows more consistent results

hardness

resistance to permanently indenting the surface

large hardness means resistance to plastic deformation in compression, and better wear properties

What are the standard test parameters and units for the Brinell Hardness (HB) test?

Uses a 10 mm diameter steel/tungsten carbide sphere under a 3000 kg load for 10-15 seconds; output units are BHN or kg/mm^2.

What are the major load options and indenter types used in the Rockwell Hardness test?

Major loads are 60 kg (Scale A), 100 kg (Scale B), and 150 kg (Scale C); indenters are diamond cones (A, C) or a 1/16 inch steel ball (B).

What is the general empirical relationship between hardness and yield strength (sigma_y) for metals?

Hardness is approximately equal to 2.5 to 3.0 times the yield strength (sigma_y).

What is microhardness testing, and what maximum load is typically used?

Hardness testing where indentation dimensions are comparable to microstructural features (e.g., individual grains/phases); uses loads of 200 g or less on polished surfaces.

What type of indenter and geometry are used in the Vickers Hardness test?

A square-base pyramidal diamond indenter with an angle of 136 degrees between opposite faces.

What is the formula for Vickers Hardness (HV)?

HV = (2 * P * sin(alpha / 2)) / d^2 = (1.8544 * P) / d^2, where P is load in kg and d is average diagonal length in mm.

What geometry characterizes the Knoop Hardness indenter, and why is it useful?

An elongated diamond pyramid indenter with a 7.11 to 1 major-to-minor diagonal ratio; its shallow impression makes it ideal for testing thin components.

What is the formula for Knoop Hardness (HK)?

HK = (14.228 * P) / L^2, where P is load in kg and L is the long diagonal length in mm.

What are the hardest and softest minerals on the Mohs Hardness Scale?

Softest is Talc (Mohs 1) and hardest is Diamond (Mohs 10).

Why is there notable statistical variability in measured mechanical properties like tensile strength?

Critical failure properties depend heavily on microscopic sample flaws and defects, leading to sample-to-sample scatter.

How are the sample mean (x-bar) and standard deviation (s) calculated for mechanical property data?

Mean is the sum of all x_i divided by n; standard deviation is the square root of [sum(x_i - x-bar)^2 / (n - 1)].

What is the formula for working stress (sigma_working) using a factor of safety (N)?

sigma_working = sigma_y / N, where sigma_y is yield strength and N is the safety factor (typically between 1.2 and 4).

How do you select a material to minimize elastic deformation in a load-bearing application?

Select a material with a high elastic modulus (E or G).

What defines the onset of plastic behavior in a material during a tensile or compressive test?

Plastic (permanent) deformation occurs when the uniaxial stress reaches the yield strength (sigma_y).

What is the definition of toughness in material mechanical behavior?

The total energy required to break a unit volume of material, represented by the area under the stress-strain curve up to fracture.