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Part 2. Mechanical Properties od Metals

A. Tensile Testing

A. Definitions

(Load) i) Stress = (Cross Sectional Area of Sample)

Extension of Sample ii) Strain = Original Sample Length

Strain is a result of stress

iii) Elastic Modulus (Young’s Modulus)

Stress E = in Elastic Range Strain

iv) Yield Strength (YS) - the stress at which the material begins to deform permanently.

− v) Percent Elongation - ε% = llfo× 100 or lo ∆ l × 100 lo

vi) Tensile Strength (TS) or Ultimate Tensile Strength (UTS) is the maximum value of the stress reached before fracture (breaking strength) when sample is placed in tension.

vii) Compressive Strength (CS) or Ultimate Compressive Strength (UCS) is the maximum value of the stress reached before fracture when the sample is placed in compression.

NOTE: For a given material the UTS is not necessarily equal to the UCS. In fact, for ceramics

UCS>> UTS

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B. Tensile Test (Section 6.2)

G.L. sample gripped in tensile machine at its ends i) Sample: machined outreduced of material section towhose TS you wish to determine. ensure breakage occurs here

Dimensions of sample given in ASTM Standards.

Gauge length (GL): length of sample of uniform cross-section, which is used in computing sample elongation.

ii) Test (Section 6.3)

1×= 105 psi 0.692 GPa 110psi0.692GPa×=4 0.42

* 0.28

unload Stress (GPa) 0.14

load

0.1 0.2 0.3

Strain

L

1. Plot and label axes. 2. Apply load on sample 3. Go through elastic region 4. Note in elastic region: when load is removed, sample returns 4

[Props. of elastic region]

a) to original shape

b) Stress ∝ Strain

Stress = E Modulus of Elasticity (Young's Modulus),slope Strain

c) Operating range where most engineering applications are designed.

C. Characteristics of Young’s Modulus

a) Varies from material to material, but within a class of materials the modulus is nearly the same, e.g.

Material E High Density Polyethylene 1 GPa Epoxy 2.4 Nylon 2.8 Stretching Glass Fiber - Epoxy 4.5 ability Al 69 decreases Glass 69 Steel 208 Silicon Carbide 430

b) For a given material, E decreases with increasing temperature.

c) E is a measure of the rigidity or stiffness of materials important in design of engineering structures.

d) If test were done in compression, then

τ = Gγ

where τ = Shear, compressive or torsional stress γ = Shear, compressive or torsional strain G = Shear modulus

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D. Defn – Plastic deformation (Section 6.6)

- Deformation in the sample that is not recovered when the load is removed. Plastic defn results in permanent elongation of the sample.

- Important in the processing and fabrication of materials (metals, mmcs)

- Important to know boundary between elastic and plastic deformation so engineering design stays in elastic region.

E. Elastic/Plastic Boundary

Y.S. 4 3

Stress 2

1 .002 Strain

1. Measure 0.002 strain.

2. Draw line at ε = 0.002 parallel to Hooke’s Law (Elastic Region).

3. Pt. of intersection of line − and σ − ε curve then read corresponding stress, σ .

4. This is the Yield Stress (Y.S.). If you apply stress to a sample beyond Y.S., plastic defn will occur.

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F. Defn - Yield Stress

- the stress at which the material begins to deform permanently or plastically.

G. Work Hardening (paper clips experiment)

(A) (B)

(i) * Y.S. * *

elastic

Stress ε recovered Stress

0.002 Strain 0.002 Strain

plastic

- load a sample in a tensile test beyond the Y.S. to point (i) - unload sample - you will recover the elastic part of the deformation - drop line parallel to elastic region - now take unloaded plastically deformed sample and reload it (B) - Y.S. will be at 0.002 strain. Sample will follow path (i) again.

If load is removed before Y.S. in (B) strain is recovered. n Def – Note: (Y.S.)BA> (Y.S.) , so material is stronger in elastic region due to its prior deformation – This is Work Hardening.

Material 1 Material 2

* *

Stress (W.H.)> (W.H.) Stress 12

Strain Strain 8

Work Hardening is important for:

1. Processing materials – load necessary to deform material. 2. For a material deformed past the Y.S., the amount of work hardening will define the property of material in service. 3. Performance of material: e.g., corrosion Material that are not Work Hardened - corrode slower than those that are W.H..

H. Tensile Strength

Defn – Maximum Stress that a material can take.

T.S. σ *

ε

Beyond T.S. tensile sample will start necking.

Defn - Necking is the non-uniform macroscopic (visible by eye) deformation of a sample. 9

T.S. * BREAK

σ True

True ε

If neck is measured always the result will be true stress on sample. T.S. is then the σtrue where the sample breaks. Other curve called engineering stress.

Necking and Tensile Strength are not important in design.

I. Elongation

Defn - Total Elongation of a sample. The maximum strain before the material breaks. Expressed as a percent of its initial length.

σ

*

LL− % Elongation = fi× 100 Li or =×εf 100

ε ε f

- Importance: Fabrication of materials (e.g., wire drawing, sheet bending). - Elongation is a measure of the Ductility of a material. - Defn Ductility: The ability of a material to withstand tensile stress. 10

Brittle Ductile σ * *

ε