ME 350 – Lecture 2 – Chapter 3. Mechanical Properties of Materials Stress‑Strain Relationships Tensile, compressive, and shear Hardness Effect of Temperature on Properties Fluid Properties Pseudoplastic and Viscoelastic Behavior of Polymers. Tensile Test.
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Mechanical Properties of Materials
Figure 3.2 Example tensile test: (1) no load; (2) uniform elongation and reduction of cross‑sectional area; (3) continued elongation, maximum load reached; (4) necking begins, load begins to decrease; and (5) fracture. If pieces are put back together as in (6), final length can be measured.
Where σ = stress, F = applied force, and A = instantaneous or initial cross-sectional area
Engineering stress: A =
True stress: A =
where e = engineering strain; ε = true strain; L = instantaneous length at any point during elongation; and Lo = original gage length
Experimentally, a higher value of “n” means that the metal can be strained further before the onset of necking
LfAf = L0A0
A test specimen has a gage length of 2.0 in and an area = 0.5 in2. During the test the specimen yields (0.2% yield pt.) under a load of 32,000 lb at a gage length of 2.0083 in. The max load of 60,000 lb is reached at a gage length = 2.60 in. Determine (a) yield strength, (b) modulus of elasticity, and (c) the tensile strength.
(a) Y =
(b) ε =
In a tensile test on a metal specimen, strain = 0.08 at a stress = 265 MPa. When the stress = 325 MPa, the strain = 0.27. Determine (a) the strength coefficient and (b) the strain-hardening exponent in the flow curve equation.
where F = applied force; A = deflection area; T = applied torque; R = tube radius; and t = tube wall thickness
where δ = deflection; b = deflection distance; α = angular deflection (rad); and L = the gauge length of the tube
In the elastic region
where G =
For most materials, G 0.4E, where E = elastic modulus
In the plastic region,
where S =
For most materials S 0.7 TS (tensile strength)
n = strain hardening exponent
In a torsion test, a torque of 5000 ft-lb is applied which causes an angular deflection = 1° on a thin-walled tubular specimen whose radius = 1.5 in, wall thickness = 0.10 in, and gage length = 2.0 in. Determine (a) the shear stress, (b) shear strain, and (c) shear modulus, assuming the specimen had not yet yielded.
In Problem 3.24, the specimen fails at a torque = 8000 ft-lb and an angular deflection = 23°. Calculate the shear strength of the metal.
F = indentation load, kg; Db = diameter of ball, mm, Di = diameter of indentation, mm
Shear Stress: Shear Rate
Two flat plates, separated by a space of 4 mm, are moving relative to each other at a velocity of 5 m/sec. The space between them is occupied by a fluid of unknown viscosity. The motion of the plates is resisted by a shear stress of 10 Pa due to the viscosity of the fluid. Assuming that the velocity gradient of the fluid is constant, determine the coefficient of viscosity of the fluid.
(a) perfectly elastic response of material to stress applied over time; (b) viscoelastic response as a function of time exhibiting material “creep” and stress–strain graph hysteresis