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Stress-Strain Diagram For Gray Cast Iron

Figure 116.1 is a sketch of the stress-strain diagram (tension and compression) for gray cast iron. Modulus of elasticity, E = 12.5 x 10^{6}. Determine for tension and compression:

(a) The proportional limit.

(b) The modulus of resilience.

(c) percent elongation.

**The strings**:
S_{7}P_{3}A_{32} (Force - Push).
**The math**:

Pj Problem of Interest is of type *force* (push and pull). However in this case, compression is more pronounced. Hence the choice of *force-push*.

Formulas of interest:

Modulus of resilience u_{r}, is strain energy absorbed per unit volume.

u_{r} = (σ_{pl})^{1/2}/(2E)---------(1)

Proportional limit is the maximum stress a material can sustain without deviating from the law of stress-strain proportionality.

σ_{pl} is stress at proportional limit

E is modulus of elasticity.

For tension, from diagram:

σ_{pl} = 12,500 psi.

So, Modulus of resilience u_{r} = (12,500 x 12,500)/(2 x 12.5 x 10^{6})

So, Modulus of resilience u_{r} = 6.25 lb-in/in^{3}.

Percent elongation (used for ductility comparison) is strain at rupture x 100.

So from diagram, % elongation = 0.7(0.005) x 100 = 0.35

For compression, from diagram:

σ_{pl} =25,000 psi.

So, Modulus of resilience u_{r} = (25,000 x 25,000)/(2 x 12.5 x 10^{6})

So, Modulus of resilience u_{r} = 25 lb-in/in^{3}.

from diagram, % elongation = 0.065 x 100 = 6.5

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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