Lesson 2. Strength of materials Sections 1.4 – 1.6. Today’s lesson will cover:. The Stress/Strain diagram aka curve Elasticity, Plasticity and Creep (what may happen to a specimen of material under a constant load, not some scary guy you just passed in the hallway on the way to class…)
Strength of materials
Sections 1.4 – 1.6
The Stress/Strain diagram aka curve
Elasticity, Plasticity and Creep (what may happen to a specimen of material under a constant load, not some scary guy you just passed in the hallway on the way to class…)
Linear elasticity, Hooke’s Law, and Poisson’s Ratio
To the document reader!
Watch this on your own (it is on the wiki space home page)
Unwrap them but don’t eat them (yet)
Standard size specimens, e.g., L = 2” and d = 0.505”
Load is applied and gradually increased
Elongation is measured
Since dimensions of specimen are known, we can calculate stress and strain from the load and elongation, respectively:
Then, we can plot stress vs. strain and determine various mechanical properties and types of behavior of the material.
“Nominal” vs. “true” stress and strain
In the top chart, the stress (load) never exceeds the proportional limit
The material “snaps” back once load removed. It behaves elastically.
In the bottom chart, the stress exceeds A. When load is removed, it doesn’t “snap” all the way back. There is a residual strain.
“E” is called the elastic limit. Below that stress, completely elastic. Above, only partially elastic.
The “plasticity” of a material describes how much of its deformation remains after a load is removed.
A type of strain that is time-dependent.
Sometimes (usually at high temperatures), materials will continue to elongate—develop more strain—with the passage of time.
Example—a wire sagging
Example—turbine blades in jet engines “Creeping”
This version of Hooke’s Law applies only to longitudinal stresses and strains developed in simple tension or compression
Note: material must be homogeneous and isotropic. Also, Poisson’s Ratio is constant only in the linearly elastic region. Ordinary materials will have a positive Poisson’s Ratio
Hooke’s Law describes the linearly elastic region of the stress-strain curve:
E is the “Modulus of Elasticity” or “Young’s Modulus”, and is a physical property of the material (not of its shape).
When a specimen is elongated, it contracts in the dimension normal to the load. This is called lateral contraction. The ratio of the change in lateral strain to normal strain is Poisson’s Ratio:
Poisson’s ratio is another physical property of a material
You’re given a table of loads and elongations as well as dimensions of specimen. Need to plot the stress-strain curve, and determine:
Modulus of Elasticity
Yield stress at 0.1% offset (see page 42)
Percent elongation in 2.00 inches
Percent reduction in cross-sectional area
(see page 43 for last two)
Linear region: occurs between zero load and the proportional limit. Stress vs. strain is proportional here.
Proportional limit: stress at which the relationship between stress and strain is no longer proportional. Strain increases faster than stress.
Yield Stress: Stress at which the plastic region of the stress-strain curve begins.
Ultimate stress: stress at which specimen begins to “neck”. The highest load applied to the specimen during the test occurs at the ultimate stress.
Plastic region: part of curve where specimen deforms without an increase in applied load
Strain Hardening: area of curve where material undergoes changes to its crystalline structure. Increased loading is required to increase deformation.
Necking: the narrowing of the test specimen after the ultimate stress that culminates in fracture.
E = Modulus of Elasticity: stress over strain; the slope of the curve in the linear region.
ν = Poisson’s Ratio (Greek lowercase “Nu”); negative 1 times lateral strain over axial strain
HW#1 due Monday (check your answers against those in back of the book after solving each problem)
Quiz on Monday—review lesson slides!
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Have a good weekend!