02 - *Ductile MaterialsBrittle MaterialsStatic Strength Monotonic Elongation

02 - *Subscriptsu = Ultimatey = Yieldf = Fractureel = Elastic Limitpl = Proportional Limitt = tensionc = CompressionSut and Syt are generally presented in handbooksStatic Strength Nomenclature

02 - *In the linear range (below the Proportional Limit):s = E e t = G gStatic Strength and Stiffness: Hookes lawE = Youngs Modulus (slope)G = Shear ModulusEng. StressEng. StrainHookes LawRelation: E, G and n

02 - *True Stress and StrainTrue Strain (Logarithmic Strain)True StressFor small (infinitesimal) deformation, the true stress and true strain are approximately the same as the engineering stress and engineering strain.In a true stress-strain diagram, the true stress continually increases all the way to fracture. The true fracture stress sf is always greater than the true ultimate stress su, regardless of what type of material. Stress-Strain Curve

02 - *True Stress and Strain A Numerical Result

Chart1

0.0010.0009995003

0.0020.0019980027

0.0040.0039920213

0.0080.0079681696

0.010.0099503309

0.0150.0148886125

0.020.0198026273

0.0250.0246926126

0.030.0295588022

0.0350.0344014267

0.040.0392207132

0.0450.0440168854

0.050.0487901642

0.0550.0535407669

0.060.0582689081

0.0650.0629747992

0.070.0676586485

0.0750.0723206616

0.080.0769610411

0.0850.081579987

0.090.0861776962

Engineering Strain

Logarithmic Strain

Deformation (%)

Strain

Engineering and True Strains

Sheet1

%(l-li)/lln(li/l)

0.10.0010.0009995003

0.20.0020.0019980027

0.40.0040.0039920213

0.80.0080.0079681696

10.010.0099503309

1.50.0150.0148886125

20.020.0198026273

2.50.0250.0246926126

30.030.0295588022

3.50.0350.0344014267

40.040.0392207132

4.50.0450.0440168854

50.050.0487901642

5.50.0550.0535407669

60.060.0582689081

6.50.0650.0629747992

70.070.0676586485

7.50.0750.0723206616

80.080.0769610411

8.50.0850.081579987

90.090.0861776962

Sheet1

Engineering Strain

Logarithmic Strain

Deformation (%)

Strain

Engineering and True Strain

Sheet2

Sheet3

02 - *True Stress and Strain: Data Examples

02 - *d0dididuSy is increasedPu is almost not changedE is not changedDuctility is decreasedWork Hardening or Cold Working

02 - *Temperature Effect: Strength and Stiffness

02 - *Creep is a phenomenon that the strain increases even under a constant load, when the part is under the load for long periods of time. Temperature Effect: Creep and RelaxationThis is a typical curve obtained from constant stress/temperature test.Creep Deformation1st stage2nd stage3rd stageTime, tCreepCreep is most pronounced at high temperatures even when the stress level is below the yield strength. It may also occur at room temperatures when the stress level is close to the yield strength.Stage1st stage: Decreasing creep rate (de/dt ) due to strain hardening. 2nd stage: Constant creep rate caused by the annealing effect.3rd stage: Considerable reduction of cross-sectional area, with true stress being increase. Higher creep rate eventually leads to fracture.

02 - *The strength of ductile metallic materials is dependent on several parameters.

1. Load Direction (Tensile or compressive) 2. Strain Rate (Slow or Fast)3. Temperature (Hot or Cold)4. Load History (Monotonic or Cyclic)5. Fabrication Process (Self Study)Metals are complex materials when used throughout their total response envelope.Fortunately their elastic properties are most commonly used.Summary