1. Mechanical & Aerospace Engineering West Virginia University Elastic Properties of Materials, Tensile Test Xingbo Liu

2. Mechanical & Aerospace Engineering West Virginia University Tensile Test

3. Mechanical & Aerospace Engineering West Virginia University

4. Mechanical & Aerospace Engineering West Virginia University Engineering Stress:  E = F/A 0 Engineering Strain:  E = (L-L 0 )/L =  L / L Hook’s Law:  E = E  E  = G  Generalized Hook’s Law:  x =  x /E -  y /E-  z /E  y =  y /E -  x /E-  z /E  z =  z /E -  y /E-  x /E

5. Mechanical & Aerospace Engineering West Virginia University Tensile Test Typical F vs  L plots of linear and nonlinear materials under tensile loading

6. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) Typical F/A 0 vs  L/L 0 plots of linear and nonlinear materials under tensile loading

7. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d)

8. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) Proportionality Limit: Last point where stress and strain are linearlyrelated. (Point a.) Elastic Limit: Last point from which after removal of load, there is no permanent strain. (Point b.) Yield Point: Technically the same as the elastic limit but usually associated with the gross onset of permanent strain. Many materials do not exhibit a clearly defined yield point and so this point is often taken to correspond to a certain offset of strain. Point c is the yield point for 0.2% (0.002 strain) offset

9. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) Yield Strength: Stress at yield point,  y. Tensile Strength: Sometimes called the Ultimate Tensile Strength (UTS) and is the maximum stress reached during the loading. Point d. Material Toughness: The area under the elastic and the plastic portion of the stress-strain curve. It is the total energy required to stress the material to the point of fracture

10. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) Elongation:(Plastic) strain after fracture, or tensile ductility. The broken pieces are put together and measured, and  f = (L-L 0 )/L 0. Reduction of Area:The maximum decrease in cross-sectional area. RA = (A - A 0 )/A 0 Resilience:The ability of a material to absorb energy when deformed elastically and to return it when unloaded.

11. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) True Stress:  T = F/A = F(  E +1)/A 0 True Strain:  T = ln (L/L 0 ) = ln (  E +1)

12. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) Comparison of engineering and true stress-strain curves

13. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) At Maximum Load: Eliminating Fmax yields

14. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) True Fracture Stress: The load at fracture divided by the cross- sectional area at fracture. True Fracture Strain:The true fracture strain e f is the true strain based on the original area A 0 and the area after fracture A f

15. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) True Uniform Strain: True strain based only on the strain up to maximum load. It may be calculated from either the specimen cross-sectional area Au or the gage length Lu at maximum load. The uniform strain is often useful in estimating the formability of metals from the results of a tension test.

16. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) – Work Hardening * n is the strain-hardening exponent K is the strength coefficient

17. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) – Work Hardening Log/log plot of true stress-strain curve

18. Mechanical & Aerospace Engineering West Virginia University Tensile Test (Cont’d) – Work Hardening Various forms of power curve  =K*  n

19. Mechanical & Aerospace Engineering West Virginia University Values for n and K for metals at room temperature MetalConditionnK, psi 0,05% C steelAnnealed0,2677000 SAE 4340 steelAnnealed0,1593000 0,60% C steelQuenched and tempered 1000 o F0,10228000 0,60% C steelQuenched and tempered 1300 o F0,19178000 CopperAnnealed0,5446400 70/30 brassAnnealed0,49130000