Problem 1: Determining the modulus of elasticity and the proportional limit

Condition: A tensile test on a low-carbon steel rod with a diameter of 20 mm and a gauge length of 100 mm yielded the following data:

Under a load of 33 kN, the elongation was 0.05 mm.

Under a load of 66 kN, the elongation was 0.1 mm.

The load corresponding to the proportional limit was 100 kN.

Find:

Young's modulus of elasticity E of the material.

The stress corresponding to the proportional limit σpp.

Problem 2. Determining the Yield Strength and Ultimate Tensile Strength

Condition: A mild steel specimen with a diameter of 10 mm and a gauge length of 50 mm is stretched under load. The cross-sectional area of ​​the specimen after rupture is 55 mm².

At the moment the deformation begins to noticeably increase, without increasing the load, the dynamometer read
22 kN.

The maximum load the specimen withstood was 35 kN.

Find:

Physical yield strength σy.

Ultimate tensile strength σu.

Relative area reduction ψ.

Problem 3. Relationship between Hardness and Strength

Condition: A Brinell hardness test on a steel specimen (10 mm diameter ball, 3000 kgf load) yielded an indentation 4.2 mm in diameter.

Find:

Hardness number HB.

Approximate ultimate strength σB of this steel, assuming the empirical relationship for carbon steels:
σ_u (MPa) ≈ 3.5 * HB.

Problem 4. Calculating the True Stress in the Specimen Neck

Condition: In the previous problem (Problem 2), the steel specimen experienced a load of P = 30 kN at the moment before rupture. The neck diameter (minimum diameter) at this moment was 8.5 mm.

Find: The true stress in the narrowest cross-section of the neck at the moment before rupture.

Problem 5. Impact Strength Calculation

Condition: When tested on a pendulum impact tester, a standard Menage specimen with a notch measuring 10 x 10 x 55 mm fractured at an impact energy of K = 64 J. After the test, the cross-sectional area at the notch was 80 mm².

Find: Impact Strength KCU.

Problem 6. Creep Deformation Analysis

Condition: A gas turbine blade made of a heat-resistant alloy with a length of l₀ = 150 mm at a temperature of t = 850 °C and a stress of σ = 150 MPa has elongated by Δl = 0.9 mm over a time of τ = 300 hours of operation.

Find:

Steady-state creep rate v_с.

Relative elongation over 10,000 hours of operation, assuming a constant creep rate.

Problem 7. Reading the tension diagram

Condition: there are two tension diagrams, task is to find following mechanical characteristics:

- yield strength (or conventional yield strength);

- ultimate strength;

- elastic modulus;

- relative residual elongation;

- relative area reduction;

NOTICE: the length of specimen working part equal to 10*d0.