Mechanical Properties of Materials

Ability to resist bending, twisting, or stretching

Resistance to plastic deformation

Resistance to localized plastic deformation

Resistance to fracture; energy absorbed before fracture (area under the whole stress-strain curve)

Extent of ductility; strain to fracture

Measure of plastic deformation sustained at fracture; reported as %EL or %RA

Failure due to accumulated damage from repeated application of small loads

Material returns to original shape after load removal; caused by separation (stretching) of atomic bonds

Permanent change in shape/size after load removal; caused by defect (dislocation) or molecular motion

Inability of a component to perform its intended function

Separation of a component into two or more pieces

Tension, compression, shear (cortante), torsion

Standard tensile specimen; reduced central section concentrates deformation and reduces breakage at the grips

Diameter about 12.8 mm (0.5 in); reduced section at least 4x diameter (about 60 mm); gauge length about 50 mm (2 in)

Uniaxial load increased until fracture; gives elastic modulus, yield strength, UTS, and ductility; destructive

Moves crosshead at constant rate; load cell records force; extensometer records elongation

Same machine as tension but specimen shortens; useful for brittle-in-tension materials (ceramics, composites), forging, powders, foams

tau = F / A0 (load parallel to the face)

gamma = tan(theta), approximately theta for small angles

Torque on a cylinder gives pure shear; used for axles, drive shafts, drill bits

sigma = F / A0 (A0 = original cross-section area); units: Pa, MPa, psi

epsilon = (l - l0) / l0 = delta l / l0; dimensionless (mm/mm)

Original length l0 over which elongation is measured (about 50 mm)

sigma = E * epsilon (linear elastic region)

Slope of the linear elastic region; resistance to separation of adjacent atoms; decreases with increasing temperature

Stress at the end of the linear (Hookean) portion of the curve

Stress at the limit of the elastic region; start of plastic deformation

Draw a line with slope E shifted by 0.2% strain; where it intersects the curve is the yield strength

Maximum engineering stress: F_max / A0

Engineering stress at fracture

Strain at fracture

Local reduction in cross-section area after UTS; load capacity drops until fracture

Plastic deformation increases the strength of the material

After unloading past yield, the unloading line has the original E; new yield strength is where the load was removed

Properties are the same in all directions

Properties depend on orientation (example: ears on drawn cans)

%EL = (lf - l0) / l0 x 100

%RA = (A0 - Af) / A0 x 100

Energy absorbed elastically and recovered on unloading (springs); Ur = sigma_y^2 / (2E)

Energy absorbed before fracture; approx. area under the stress-strain curve

sigma_T = F / A_i (instantaneous area) = sigma(1 + epsilon)

epsilon_T = ln(l_i / l0) = ln(1 + epsilon)

sigma_T = K * epsilon_T^n (onset of plasticity to necking)

n = 1 elastic; n = 0 rigid and perfectly plastic; K and n depend on material condition

nu = - epsilon_lateral / epsilon_axial

Steel ball pressed into surface; HB = P / (pi * D * depth)

10 mm ball, 3000 kgf, 10-15 s

63 HB with a 10 mm ball, 500 kgf load, 30 s

Most popular test; preload plus applied load; no optical measurement of the indent; scales A, C, D, N

Result 64 on scale C

Square-base diamond pyramid; microindentation; HV = 1.8544 P / d^2

Result 440 at 30 kgf load

No; it is an empirical, comparative test (indentation, relatively cheap and nondestructive)

About 10^12 Pa (diamond, silicon)

About 10^11 Pa (NaCl, CsF)

About 10^11 Pa (copper, iron)

About 10^9 Pa (polyethylene)

207 GPa (30 x 10^6 psi)

69 GPa (10 x 10^6 psi)

110 GPa (16 x 10^6 psi)

107 GPa (15.5 x 10^6 psi)

407 GPa (59 x 10^6 psi)

45 GPa (6.5 x 10^6 psi)

97 GPa (14 x 10^6 psi)

Linear defect around which some atoms are misaligned

Extra half-plane of atoms; moves like a caterpillar along the slip plane

One part of the crystal slides relative to the other

Combination of edge and screw character; most dislocations are mixed

Vector describing magnitude and direction of the lattice distortion caused by a dislocation

Number of dislocations per unit volume; about 10^5 to 10^12 cm^-2 in heavily deformed metals

Plastic deformation (most important), solidification, thermal stresses, grain boundaries, irregular surfaces, oxide interfaces, irradiation

Dislocation pinned at its ends bows out under shear stress until it forms a loop; multiplies dislocations

Repel

Attract

Combination of slip plane and slip direction

FCC is more ductile (more slip systems)

tau_R = sigma cos(phi) cos(lambda)

Minimum shear stress required to initiate slip

sigma_y = tau_crss / (cos phi cos lambda)max

0.5 (at 45 and 45 degrees), so sigma_y = 2 tau_crss; slip starts on planes about 45 degrees off the load axis

Polycrystals are stronger: grain boundaries pin dislocations; slip systems change between grains; each grain is constrained by neighbors

Plastic deformation raises dislocation density; dislocations block each other; mobility drops; strength and hardness rise

Other names for strain hardening

Plastic deformation below about 0.3 of the melting temperature (in kelvin)

%CW = (A0 - Ad) / A0 x 100

Cannot exceed the material's total elongation (maximum % ductility)

Rolling, forging, drawing, cold extrusion, stamping, bending, machining, grinding

Shot peening, burnishing, cold hammering (improve wear resistance)

Strength and hardness increase; ductility decreases

Heat treatment that restores properties from before cold work via recovery and recrystallization, possibly followed by grain growth

Dislocations annihilateearrange into low-angle grain boundaries by diffusion; internal stress drops; conductivity restored; no major microstructure change

Formation of new strain-free, equiaxed grains with low dislocation density; ductility and strength return to pre-cold-work levels

Difference in internal energy between strained and unstrained material

Temperature at which recrystallization completes in 1 hour; typically 0.35-0.5 Tm (kelvin)

Lowers it

Faster in pure metals

Large grains grow at the expense of small ones to reduce grain boundary area and energy

d^n - d0^n = K t, with n usually 2 or more

Fine grains give higher strength and toughness

Stop or impede dislocation motion

Grain size reduction, solid-solution strengthening, strain hardening (also precipitation and dispersion hardening)

Grain boundaries block dislocations (a dislocation must change orientation to cross); smaller grains are stronger

sigma_y = sigma_0 + k_y d^(-1/2)

Dislocations on one plane stack at a grain boundary; leading dislocation feels tau* = n tau; larger grains hold more

Solute atoms (interstitial or substitutional) have stress fields that interact with dislocations and create energy barriers

Tension-field solutes migrate to the dislocation's compression region and compression-field solutes to its tension region

Low T: solutes immobile. High T: solutes too mobile to restrict dislocations. Strongest when mobilities are about equal

D = D0 exp(-Q / RT)

Interstitial solute atoms (C, N) clustered at a dislocation that lock it in low-carbon steel

Maximum stress needed to unlock dislocations from Cottrell atmospheres (higher than lower yield)

Plateau on a low-carbon steel curve where free dislocations move at the lower yield stress

Localized deformation bands that propagate through a sample during yield point elongation

Causes thickness irregularities in stamped low-carbon steel sheet

Add Al, V, Ti, Nb or B to tie up solutes; or prestrain above the lower yield point so stamping starts in the strain-hardening region

Yield point returns after prestraining and resting because interstitials re-lock dislocations; different from precipitation aging

Fe-31Ni-0.1C austenitic alloy: interrupted test, 3 hour wait, reload shows yield point, plateau, load drop

Fe 156, C 67, N 56, Si 111, Mn 161, Mo 190, Ni 149