The study of material science involves
investigating the relationships that exist between the structures and properties
of matter. Several specific areas, that are related to traditional physics courses,
will be isolated and studied from the material science and engineering discipline.
Further investigation of this extensive subject area is encouraged. This topic
is associated with chapter 9 of *College Physics* by Serway and Faughn.

Definitions |
material terms #1 |
stress | strain | |

Experiments |
rubber band | aluminum | concrete | terms #2 |

problems | competencies |

**Core
Component/Definitions**

__MATTER__ is divided into four categories: **solids
(crystalline and amorphous), liquids, gases, plasma, then fluids
**

Two additional groups of engineering materials are:

σ= F / A

THREE TYPES OF STRESS

•**STRAIN**

Strain (ε) is the measure of deformation in a given material. The quantification
of strain is referred to as TENSILE STRAIN which is the ratio of a change in
length (ΔL) to the original length ( L_{O} ).

ε = Δ L / L_{O}

Shear strain is the ratio of the change in horizontal distance / height. (ε
= Δx/h) , as diagramed below.

•MODULI

The ratio of stress to strain creates a modulus. For example, tensile stress
to tensile strain is termed YOUNG'S MODULUS (Y) or ELASTIC MODULUS. This quantity
is used to characterize a material under either tension or compression and only
depends on the material itself.

In equation form:

Y is measured in PASCALS (Pa) and is a constant for a given material.

example values: Iron = 100 x 10^{9} N/m^{2} Nylon = 5 x 10^{9}
N/m^{2}

An additional deformation may occur when equal and opposite forces are applied
across an objects opposite faces. This shear stress produces it own proportionality
constant referred to as SHEAR MODULUS.

We define the Shear Modulus as the shear stress divided by the shear strain.

Shear Modulus (S) is measured in Pascals (Pa). example : Iron = 40 x 10^{9}
N/m^{2}

One final deformation involves the compression of an object by applying force
at right angles to all of its faces. These forces now generate VOLUME STRESS
and VOLUME STRAIN, the ratio of change in volume to the original volume. This
new ratio is defined as BULK MODULUS (B) . Where:

Bulk Modulus (B) is also measured in Pascals (Pa). example: Iron = 90 x 10^{9}
N/m^{2}

Several
additional concepts that support the study of stress and strain are listed below.

FRACTURE - the amount of stress (tensional, compressional, or shear) on a solid
that will produce breakage of that object.

ELASTIC LIMIT - the point where a solid will return to its original shape under
a given applied force.

HOOKE’S LAW - when strain is proportional to stress a material will obey
this law.

PLASTIC REGION - an object enters this region when the material does not return
to its original shape when an applied force is removed.

DUCTILITY - when a material is drawn out in tension without fracturing. Ductile
materials are strong and plastic.

MALLEABILITY - permanently extending an object in all
directions without fracture by hammering or pressing. Materials must be
plastic, but not so dependent on strength.

TOUGHNESS - the amount of energy that a material can absorb before it fractures.

BRITTLENESS - a material that breaks with little permanent distortion. It
lacks toughness and ductility.

HARDNESS - the resistance to wear or indentation of a material.

II. Experimental Component

EXPERIMENT #1 Tensile Strength of rubber band

Record the thickness ______ (mm) and length _______ (mm) of the specimen.

Attach a mass to the rubber band to stretch it. Measure the length. Calculate
the weight of the mass hanging on the rubber band.

Add mass in small steps repeating the previous step each time.

Continue this until the rubber band breaks.

Graph stress vs strain

EXPERIMENT #2 Tensile Test of an Aluminum Cylinder.

• Make measurements of the aluminum sample recording each of the characteristics.

• Mount the sample in the tensile testing machine. Insert one end into
the load cell and the other end in the moving crosshead. (fig. 1)

• Setup the extensometer to measure
the sample elongation.

• CAUTION !! Close the protective shield door before applying any force
to the sample.

• Apply force slowly and record the values from the force gauge and the
extensometer until fracture of the sample occurs.

• Calculate the tensile stress and tensile strain. Calculate Young’s
modulus.

• If sufficient readings were obtained, graph stress versus strain and
identify the salient features of this characteristic curve.

EXPERIMENT #3 Compression Test of a Concrete sample.

• Using the pre-made concrete sample provided determine its outer dimensions
and mass. Also calculate the volume and density of the sample.

• Place the sample in the compression tester. WEAR PROTECTIVE EYEGLASSES!

• Close the bleeder valve on the hydraulic pump.

• Lower the hydraulic cylinder, using the pump handle, until contact with
the sample is made. (ensure that contact areas above and below the sample completely
cover the samples surface)

• Continue to apply pressure to the sample until fracture occurs. At the
point of fracture make note of the pressure reading on the pump gauge. (requires
two people)

• Compute the compressive stress on the sample at maximum pressure. (hint
- remember you are reading pressure in pounds per square inch (psi) and you
must convert to metric force per unit area)

• Computing the compressive strain for a concrete sample is difficult
to do accurately. State why this is so.

• Compute the force acting on the concrete sample.

1) Determine the pressure of:

- a)
a bicycle (10.0 kg) with a 62.0-kg rider. Each tire is in contact with the
ground in a shape that is 1.0 cm by 4.0 cm.

- b)
a 42-kg girl has a pair shoes that spreads her weight over 15 cm
^{2}for each shoe.

- c)
The same girl when wearing a pair of stiletto heels that allows her to put
all of her weight onto 1 cm
^{2}on each shoe.

If the girl in part c is standing on a concrete floor, what kind of stress, and how much, is created?

2) Complete the following problems from chapter 9, College Physics (Serway, Faughn)

Problems (beginning on page 295) # 1, 2, 3, 5, 6, 8 and 14.

4)
The pressure at a depth of 300m in the ocean exceeds sea-level atmospheric pressure
by 2.94 x 10^{6} Pa. By how much does the volume of a 1000cm^{3}
aluminum object contract when it is lowered to this depth?

5) The reciprocal of the bulk modulus B of a liquid is called its compressibility
k, so that k=1/B. The bulk modulus of water is 2.3 x 10^{9} Pa. (a)
Find its compressibility per atmosphere of pressure, where 1 atm = 1.013 X 10^{5}
Pa is the pressure exerted by the earth's atmosphere at sea level. (b) How much
pressure in atm is needed to compress a sample of water by 0.1% ?

COMPETENCIES for Governor's School Physics 2004-5 using College Physics by Serway and Faughn, sixth edition 2003and Material Science and Engineering by Callister, third edition
1994 |

Develop a beginning model for material science that includes the relationships that exist between the structures and properties of matter by being able to:

ENABLING OBJECTIVES

25.1 Distinguish between the three basic groupings of materials: metals, ceramics, and polymers.

25.2 State the relationship of forces for the stresses of tension, compression, and shear.

25.3 Explain the difference between stress and strain.

25.4 Calculate tensile stress and strain.

25.5 Compute Young’s modulus and explain when this is an appropriate measurement of a solid.

25.6 Calculate Bulk modulus and explain under what physical conditions you may study this factor.

25.7 Diagram and interpret a stress versus strain graph for a solid. Include elastic region, elastic limit, fracture, and plasticity zone.

25.8 Calculate Shear modulus and diagram the forces and displacements utilized in its measurement.

25.9 Describe the terms ductility, malleability, toughness, brittleness and hardness in terms of the three general groupings of materials.

last modified 1/9/05