Shear Stress and Stress-Strain Behavior Quiz

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What is the relationship between Brinell hardness (HB) and tensile strength for most steel alloys?

TS in MPa = 5.00 (HB)
TS in psi = 300 (HB)
TS in MPa = 3.45 (HB) (correct)
TS in psi = 500 (HB)

In the given illustrative problem of elongation computation for a piece of copper, what is the modulus of elasticity (E) for copper?

110 GPa (correct)
90 GPa
100 GPa
120 GPa

If a piece of copper is pulled in tension with a stress of 276 MPa and the deformation is entirely elastic, what will be the resultant elongation for a piece originally 305 mm long?

1.020 mm
0.765 mm (correct)
0.500 mm
0.350 mm

What is the diameter change in mm for a cylindrical brass rod with a diameter of 10 mm when subjected to a 2.5 x 10^3 mm load in an elastic deformation?

0.025 mm (A) Signup and view all the answers

When a tensile stress is applied to a cylindrical brass rod, in which direction does the rod elongate?

z-direction (B) Signup and view all the answers

In the context of material deformation, what relationship governs strain (𝜖) with stress (𝝈) according to the provided information?

𝜖 = 𝝈 / E (A) Signup and view all the answers

What is the formula for computing shear stress?

𝜏 = 𝐹 / 𝐴₀ (D) Signup and view all the answers

What is the relationship described by Hooke's Law?

Stress is proportional to strain (A) Signup and view all the answers

What does the modulus of elasticity represent?

Material's resistance to elastic deformation (C) Signup and view all the answers

What does the slope of the linear segment in a stress-strain plot correspond to?

Modulus of Elasticity (E) (B) Signup and view all the answers

In which type of deformation are stress and strain proportional?

Elastic deformation (D) Signup and view all the answers

What does shear strain represent?

The tangent of the strain angle (B) Signup and view all the answers

What is toughness defined as in materials science?

The ability to deform plastically before fracturing (D) Signup and view all the answers

In the context of toughness, what does area ABC in a stress-strain curve represent?

Toughness of a brittle material (B) Signup and view all the answers

What is the unit of measurement for toughness according to the information provided?

J/m3 (C) Signup and view all the answers

How is true stress defined in materials science?

Load divided by instantaneous cross-sectional area (A) Signup and view all the answers

What happens beyond the onset of necking in terms of true stress and strain?

They are related by true stress = stress(1 + strain) (A) Signup and view all the answers

Why must a metal display both strength and ductility to be considered tough?

To absorb energy and plastically deform before fracturing (C) Signup and view all the answers

What is the minor load value for the Rockwell hardness test?

10 kg (B) Signup and view all the answers

What is the purpose of the Brinell hardness test?

To measure the hardness of metal surfaces by forcing a hard, spherical indenter into the surface (C) Signup and view all the answers

What is the diameter of the hardened steel (or tungsten carbide) indenter used in Brinell hardness tests?

10.00 mm (C) Signup and view all the answers

What is the typical range of standard loads used in Brinell hardness tests?

500 to 3000 kg in 500-kg increments (A) Signup and view all the answers

How is the Brinell hardness number (HB) determined?

By measuring the diameter of the resulting indentation and using a chart to convert to the appropriate HB number (A) Signup and view all the answers

What is the purpose of the superficial Rockwell hardness test?

To measure the hardness of thin specimens (B) Signup and view all the answers

What is the relationship between the modulus and the elastic strain of a material?

The greater the modulus, the stiffer the material, or the smaller the elastic strain that results from the application of a given stress. (C) Signup and view all the answers

What is the purpose of the modulus as a design parameter?

The modulus is used for computing elastic deflections. (A) Signup and view all the answers

What is the relationship between shear stress, shear strain, and the shear modulus?

Shear stress and shear strain are proportional through the expression $\tau = G\gamma$. (C) Signup and view all the answers

What is the definition of Poisson's ratio?

Poisson's ratio is defined as the ratio of the lateral strain to the axial strains. (A) Signup and view all the answers

What happens to the lateral strains when a tensile stress is applied to a metal specimen?

The lateral strains (in the x and y directions) are compressive and negative. (A) Signup and view all the answers

What is the relationship between the axial strain and the lateral strains according to Poisson's ratio?

$\nu = -\epsilon_y/\epsilon_x = -\epsilon_z/\epsilon_z$ (C) Signup and view all the answers