Stress vs. Strain Curve

1. Professor Julie A. Young
Thomas Nelson Community College
Mechanical Properties of Materials
Derived from the Stress vs. Strain Curve

2. Introduction

Material selection is an important step in product development.
In a mechanical engineering sense, we select a material based on:
Strength
Stiffness
Ductility
These properties dictates how a material responds to applied loads and
forces.
But how are mechanical material properties determined?

3. Learning Objectives:
Given a material sample, explain how the uniaxial tensile test
is conducted to determine mechanical properties of a
material and how the plot of stress vs. strain is generated.
Given a stress vs. strain curve for a material (either one that
yields or does not yield), identify the Proportional Limit,
Elastic Limit, Yield Strength and Ultimate Strength, calculate
the Modulus of Elasticity and the percent elongation. State
whether the material is brittle or ductile.

4. Uniaxial Tensile Test
•One of the simplest and more effective tests.
•Places a constant force on an material.

5. The Material Test Sample
A cylindrical material sample of the
material is used.
Two marks are scribed on the material a
precise distance apart. This is called the
gage length. (L
o
)
The sample is placed in the machine and a
force is applied in tension.
.

Tension



Gage Length,
L
o

6. Test Data
• Force is applied.
• The length
between the gage
marks is measured
and the difference
between the
measurement and
the gage length is
recorded,
elongation.
• Graph of Force
vs. Elongation.
Force vs. Elongation
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090
Elongation (in.)

7. Independence on Sample Size
The graph generated is dependent on the sample size:
A 6-inch diameter sample would behave differently than a
0.5-inch sample.
The data is normalized to eliminate the size factor.

8. Engineering Stress-Strain Curve
Pt. O - Origin
Pt. A - Proportional Limit
Pt. B – Elastic Limit
Pt. C – Yield Strength
Pt. D – Ultimate Strength
Pt. E – Breaking Point

9. Additional Properties from the Stress-
Strain Curve
•Modulus of Elasticity – the slope of the stress-strain curve in
the linear region
•Percent Elongation –

if less than 5%, the material is brittle,
if more than 5%, the material is ductile
%100
0
0
´
-
=
L
LL
f

10. Conclusion
Mechanical properties of materials are determined from the
stress-strain curve.
We choose a material based on the following mechanical
properties:
Strength (Yield and Ultimate)
Stiffness (Modulus of Elasticity)
Ductility (Percent Elongation)