Question

manifactoring processes

1) Sketch Engineering stress vs. Engineering strain curve and True stress vs. true strain curve from one uniaxial tension test for an engineering metals that shows power law strain hardening (e.g. aluminum or steel), within the same plot, and identify, from the curves, the material property parameters of:

Yield strength (0.2% offset)

Uniform engineering strain ultimate tensile strength (eng.)

true stress and true strain at the onset of necking

K and n from power-law fitting (the range of data used for curve fitting)

Fracture true stress and fracture true strain

Total elongation to failure

Area reduction at fracture.

(also provide expression for the parameter whenever possible).

Answer 1

Answer 2

Creating detailed stress-strain curves and calculating all the material property parameters requires actual data from a uniaxial tension test for a specific engineering metal (e.g., aluminum or steel). Since we don't have access to such data, I can provide you with a generic representation of the stress-strain curves and explain how to identify the material property parameters conceptually.

The stress-strain curves for engineering stress (σ) vs. engineering strain (ε) and true stress (σ_true) vs. true strain (ε_true) for a metal with power-law strain hardening are typically represented as follows:

1. Engineering stress vs. Engineering strain curve: In the engineering stress vs. engineering strain curve, you will see initial linear elastic behavior up to the proportional limit (proportional limit is not asked for in your question). After that, the material will undergo strain hardening (gradual increase in stress with increasing strain) until it reaches the yield point. Beyond the yield point, the material will experience necking and strain localization.

2. True stress vs. True strain curve: The true stress vs. true strain curve takes into account the actual cross-sectional area changes during deformation, and it accounts for the necking effect more accurately than the engineering stress-strain curve. The curve will show similar behavior with strain hardening and necking regions.

Now, let's identify the material property parameters:

a) Yield strength (0.2% offset): The yield strength is typically determined by the 0.2% offset method. Draw a line parallel to the elastic region of the engineering stress-strain curve, starting at 0.2% strain (0.002) on the strain axis. The point where this line intersects the stress-strain curve is the yield strength (σ_y).

b) Uniform engineering strain ultimate tensile strength (eng.): The uniform engineering strain ultimate tensile strength (σ_u) is the maximum stress reached on the engineering stress-strain curve before the onset of necking.

c) True stress and true strain at the onset of necking: The true stress and true strain at the onset of necking can be identified directly from the true stress-strain curve where the necking starts.

d) K and n from the power-law fitting: The power-law equation represents the strain hardening behavior of the material: σ = K * ε^n where σ is the true stress, ε is the true strain, K is the strength coefficient, and n is the strain-hardening exponent.

To obtain K and n, perform a power-law fitting using the stress and strain data in the strain-hardening region of the true stress-strain curve.

e) Fracture true stress and fracture true strain: The fracture true stress (σ_f) and fracture true strain (ε_f) are the stress and strain values at the point of fracture or failure.

f) Total elongation to failure: The total elongation to failure is the engineering strain at the point of fracture or failure. It is the difference between the final gauge length and the original gauge length, divided by the original gauge length.

g) Area reduction at fracture: The area reduction at fracture is the percentage decrease in cross-sectional area at the point of fracture. It can be calculated using the original area and the area at fracture.

Keep in mind that the values and shapes of the curves will vary depending on the specific metal and its properties. The steps outlined above are general concepts to identify the material property parameters from stress-strain curves. Actual data from a tensile test is required for accurate calculations and material property determination.