Brief description of the equipment/machine: A typical Universal Testing Machine is shown in Fig. 1. The one shown in figure, is a 10 kN capacity testing machine and is screw driven. While the lower cross head is fixed, the upper cross head is movable and is fitted with the transducer type ‘load cell’. This testing machine can also be used for compression, torsion, bend/flexural and for high temperature tensile tests with other accessories.


Fig. 1: Llyod testing machine in Materials Testing Lab

Typical Tensile Curve: Typical stress-strain curve for a polycrystalline metal is shown in Fig. 2. The common definitions of yield strength (S_y) and ultimate tensile strength (S_u) of ductile metals are illustrated in Fig. 2. OA is the elastic regime. Yield strength is defined as the stress value corresponding to a strain value of 0.002 (draw parallel line to OA from a strain value of 0.002 and the intersection point is A – corresponding to S_y). Point at maximum load (U), at which an unstable neck initiates, gives the ultimate tensile strength (or tensile strength) S_u. The sample fractures at F.



Fig. 2: Engineering stress-strain curve for a polycrystalline metal

Definitions and properties within elastic limit

Hooke’s law: Within elastic limit, the deformation is proportional to load, i.e., strain is proportional to stress
Young’s modulus of elasticity, E: The ratio of stress to strain below elastic limit
Offset yield strength S_y: Stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of the curve offset by strain 0.002
Resilience (U_R): The maximum energy absorbed per unit volume within elastic limit
      Modulus of resilience (U_R) = 0.5 * S_ye_y

Definitions and properties in the plastic region

Strain hardening: The relationship between stress and strain is nonlinear during plastic deformation. Like E in elastic range, strength coefficient (K), strain hardening exponent (n) and amount of strain hardening prior to test (εo) are used to characterize material in plastic range
Ultimate tensile strength (S_u): The maximum engineering stress before rupture
      S_u = P_max/A_o
Toughness (U_T): Ability to absorb energy per unit volume up to fracture
Percentage of Total Elongation at Fracture = (L_f - L_o)/L_o*100
Percentage Reduction in Area = (A_o-A_f)/A_o *100, Maximum change in cross-sectional area which has occurred during the test (A_o-A_f) expressed as a percentage of the original cross-sectional area (A_o), where A_f is the final cross-sectional area.

Nomenclature

A   Instantaneous area (mm²)
A_o   Original area of cross-section at gauge length (mm²)
A_f   Area in the neck region after failure (mm²)
E    Young’s modulus of elasticity (GPa)
e    Engineering strain
e_y    Engineering strain at yield point
e_f    Engineering strain at failure
ε    True strain
ε_o   Strain before starting the test
K    Strength coefficient (N/m², Pa)
L   Instantaneous gauge length (mm)
L_o   Original gauge length - gauge length before application of load (mm)
L_f    Gauge length after rupture of the specimen (mm)
n    Strain hardening exponent
P   Instantaneous load/force (N)
P_max   Maximum load/force (just before necking) (N)
S    Engineering stress (MPa)
S_y   Yield stress (MPa)
S_u   Ultimate tensile strength (MPa)
σ   True stress (MPa)
t    time (s)
U_R    Modulus of resilience (J/m³)
U_T    Toughness (J/m³)

Formulas

a) Engineering stress and engineering strain


b) True stress and true strain

Tensile Testing of Steel
A typical stress-strain curve for a medium carbon steel is shown in Figure -3. The elastic-plastic transition is not very well defined and occurs abruptly in what is termed a yield point phenomenon. The normal elastic extension (region OA) is terminated at a stress level known as the upper yield point (σ_u). Plastic deformation is initiated at Point ‘A’ with an actual decrease in stress. Continued deformation fluctuates slightly about some constant stress value (region BC), termed the lower yield point (σ_L). Deformation at this stage is not homogeneous. In a portion of the tensile sample where there is a stress concentration, a deformation band appears, called Lüder bands. Beyond point C, to the ultimate tensile stress at M, deformation is essentially homogeneous and thereafter necking develops, leading to normal ductile fracture at F. We will learn more about the mechanism about this phenomenon in a later lab.

Fig. 3: Schematic stress-strain curve of a mild steel showing the yield point phenomenon