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Stress, Strain, & Strength: An Introduction to Materials Science

What do all of these pictures have in common? Array of pictures, clockwise from top left: the leaning tower of Pisa, the armless statue of the Venus de Milo, a soda can about to be popped open, a snapped pencil, a dog chewing a bone, the cracked Liberty Bell, the Tacoma Narrows Bridge as its deck collapses, the shattered face and eroded body of the Sphinx.

The same array of images, with no text in front.

The same array of images, with the answer to what they have in common: Each is an example of how stuff breaks!

How Stuff Breaks!

Sometimes we want things to break . . .

Picture of a soda can about to be popped open.

Breaking is not always a bad thing. With soda cans, for example, we want the rim around the opening to break before anything else. Have you ever had the pull tab break off before the can opens? Don't you hate it when that happens? Think of two different explanations for this kind of soda can failure.

Sometimes we don't!

Black-and-white photo of the famous collapse of the Tacoma Narrows suspension bridge.  High winds in the area led to harmonic vibrations of the bridge, tearing it apart.  The collapse sequence was captured on film and has been studied extensively.

For obvious reasons, we want bridges to be strong and hold up to a many different environmental conditions.

For more information on the Tacoma Narrows Bridge disaster, these online references are a good place to start:

Questions & Vocabulary

Black-and-white photo of the famous collapse of the Tacoma Narrows suspension bridge.
  • How do we figure out if a structure is going to break?
  • What are different structures made out of and what are their properties?
  • What words do we use to describe these properties?
  • How do we test these properties?


Metric Prefixes
Yotta- Y 1024 1 000 000 000 000 000 000 000 000
Zetta- Z 1021 1 000 000 000 000 000 000 000
Exa- E 1018 1 000 000 000 000 000 000
Peta- P 1015 1 000 000 000 000 000
Tera- T 1012 1 000 000 000 000
Giga- G 109 1 000 000 000
Mega- M 106 1 000 000
kilo- k 103 1000
hecto- h 102 100
deka- da 101 10
deci- d 10-1 0.1
centi- c 10-2 0.01
milli- m 10-3 0.001
micro- μ 10-6 0.000 001
nano- n 10-9 0.000 000 001
pico- p 10-12 0.000 000 000 001
femto- f 10-15 0.000 000 000 000 001
atto- a 10-18 0.000 000 000 000 000 001
zepto- z 10-21 0.000 000 000 000 000 000 001
yocto- y 10-24 0.000 000 000 000 000 000 000 001

In the U.S. we use the English system, but everyone else in the world (including England!) uses the metric system. You've certainly seen some of these metric prefixes before, for example: millimeters, Gigabytes, nanoseconds.

For an interesting exercise on the magnitudes of things, try and think of different measurements for which each of the above prefixes would be convenient. Here are some references:

Is this stress??

Picture of a stressed-out student, pulling her hair, surrounded by a stack of books, two ringing phones, a computer that crashed, a spilled drink and a mile-long to-do list.  Yikes!

When you hear the word "stress," what do you usually think of?

No, this is stress!

Stress is defined as the force on a material divided by the material's cross-sectional area.  If the force is stretching the material (e.g., a weight hanging from an object), we call it <I>tensile</I> stress.  If the force is squishing the material (e.g., a weight placed on top of an object), we call it <I>compressive</I> stress.

In terms of materials science and mechanical engineering, stress is defined as the force on a material divided by the material's cross-sectional area (A in the diagram above). We can talk about different types of stress, depending on how the force is applied. For example, if the force is tending to stretch out the material (as in the diagram on the left), we call it tensile stress. If the force is tending to squish the material (as in the diagram on the right), we call it compressive stress.

More Vocabulary

What happens when you put something under stress?

Strain is defined as the change in length of a material divided by the original length of the material.  Under tension, the material may show an incremental increase in length.  Under compression, the material may show an incremental decrease in length. Illustration of incremental length changes in response to tensile and compressive stresses, and a weightlifter straining to lift the back end of an automobile.

Strain is the response of a material to stress. It is defined as the change in length of the material under stress (L' L0) divided by the original length (L0). For a material under tension, the material may show an incremental increase in length. For a material under compression, the material may show an incremental decrease in length.

One way to demonstrate strain for yourself is to use compressible packing foam (beams) or insulation (tubes). Draw regular grids on the foam (as shown below). What happens to the grid spacing as you squish, stretch and bend the foam? When you bend the foam, you can see a combination of compressive and tensile stresses on opposite sides of the bend.

Example of a foam beam with regular grid markings.

Mechanical Properties of Materials

How do mechanical engineers describe the way a material behaves when under stress? The elastic modulus and Poisson's ratio are two measures engineers use.

How do mechanical engineers describe the way a material behaves when under stress? One measurement is called the elastic modulus, and is defined as stress divided by strain. It is a measure of how much strain is produced by a given amount of stress on a material. Another measure is Poisson's ratio, which describes how a stress applied along one dimension of a material affects the other dimensions.

Here's a demonstration you can try for yourself. As one example, compare tootsie rolls vs. jolly ranchers. What's the difference? How does each respond to tensile and compressive forces? If you squish a tootsie roll, what happens to it? Materials like tootsie rolls, taffy and caramel deform plastically (change shape permanently). They also get lots wider as they are squished shorter, or narrower if they are stretched longer. How about a jolly rancher? These are brittle, so they do not deform plastically before they break by fracturing. Other materials you might try are silly putty (see Bouncy Polymer Chemistry for a recipe for making your own) and ice cubes.

Tension Test Equipment

Materials scientists and mechanical engineers use specialized test equipment, like this tension test machine, for measuring a material's response to stress.

Materials scientists and mechanical engineers use specialized test equipment, like the tension test machine in the diagram above, for measuring a material's response to stress. The test equipment can apply a large amount of force. Both the magnitude and duration of the force can be measured with precision. The diagram also shows typical responses of ductile materials under tension.

As you might guess, this type of specialized test equipment is expensive. There are much cheaper methods that you can use to measure stress and strain for your science fair project. For example, see Strength in Numbers?

Why test materials?

Another high-powered tension test machine.

Good questions to ask:

  • How do we choose materials?
  • How do we make sure that what we're making is good?
  • How do we make sure it's safe once we've built it?
  • How do we make sure it will last?

These are some of the many good reasons for carefully testing materials.

  • Research. We need accurate measurements of properties of existing materials so that engineers can choose the right material for a given project. Materials scientists developing new materials need ways to measure progress.
  • Quality control in manufacturing. Testing insures that the manufacturing process is working as expected. When materials fail quality-control testing, the cause of the defect(s) can be traced, and the problem in the manufacturing line can be fixed.
  • As-fabricated characterization of buildings/devices. When engineers design a product, they have expectations of how their design will perform (based on models and prototypes, known properties of materials, and experience). By taking an actual product fresh from the assembly line and testing it, we can measure how the design holds up in the real world.
  • Life cycle testing. Automated testing with repeated cycles of stress can yield information about how long materials can be expected to last under various envrionmental conditions.

Tension Test Results

Stress-Strain Plot for Ductile Materials

Example of a stress-strain plot for ductile material.

Here is an example of the type of data engineers use when evaluating ductile materials. The applied stress is plotted along the y-axis, and the measured strain in response to that stress is plotted along the x-axis. The definitions below will help you understand the diagram.

  • A material that can undergo large plastic deformation before fracture is called a ductile material.
  • A material that exhibits little or no plastic deformation at failure is called a brittle material.
  • The point up to which the stress and strain are linearly related is called the proportional limit.
  • The largest stress in the stress-strain curve is called the ultimate stress.
  • The stress at the point of rupture is called the fracture or rupture stress.
  • The region of the stress-strain curve in which the material returns to the undeformed stress when applied forces are removed is called the elastic region.
  • The region in which the material deforms permanently is called the plastic region.
  • The point demarcating the elastic from the plastic region is called the yield point. The stress at the yield point is called the yield stress.
  • The permanent strain when the stresses are zero is called the plastic strain.
  • The offset yield stress is a stress that would produce a plastic strain corresponding to the specified offset strain.
  • Hardness is the resistance to indentation.
  • The raising of the yield point with increasing strain is called strain hardening.
  • The sudden increase in the area of the cross-section after ultimate stress is called necking. The illustration below shows an example of necking.
Illustration of 'necking.' The material undergoes a sudden increase in cross-sectional area after ultimate stress, leading to a broken-off hourglass shape at the point of fracture.

Moments and Torques

Diagram illustrating moments and torques.  We think of 'bending' with a moment, <I>M</I>.  We think of 'twisting' with a torque, <I>T</I>.

Moments and torques are engineering-speak for the stresses we normally call "bending" and "twisting." It's still the same ideas of stress and strain that we've been talking about, and the same units of measurement. The difference is the axis of application of the stress.

You can see in the diagram that moments produce both compressive (−σ) and tensile (+σ) stresses, depending on which part of the material you examine. You can use gridded foam beams and tubes (from compressible foam packing material and pipe insulation, respectively) to visualize the effects of moments and torques for yourself. Draw the grid lines at 2–3 in intervals.

Gridded foam beams and tubes.

Ductile or Brittle?

Bent paperclip is an example of yield, shattered windshield is an example of fracture.

Materials with different properties break differently. Think back to jolly ranchers and tootsie rolls. Which is ductile and which is brittle? Think about a paper clip. Ductile or brittle? You can use it on a small stack of paper many times, and it will spring back to its original shape. But if you open a paper clip out as shown above, you deform it plastically, and it retains the new shape permanently after exceeding the yield point. How about a windshield?

How Does Stuff Break?


Pictures of rusty geared machinery, a rusty nail popping out of a piece of wood.

Metals are strong, but they corrode or rust. Paint helps protect the metal from water and air which are the ingredients of corrosion.


Pictures of a broken coil spring and a broken crank arm from a bicycle.

Repeated loading opens and closes tiny defects over and over, and eventually those defects become cracks which propagate and fracture or tear. Under repeated loading, structures ultimately fail at much lower loads than originally thought. Take a paperclip and try unfolding and refolding it in different directions (rotating vs. bending). Try cycling with different ranges of deflection and count the number of cycles needed to break the paper clip. Is there a relationship between deflection angle and number of cycles before breakage?

Plastic Man or the Man of Steel?

Pictures of plastic bottles and jars, and the Golden Gate Bridge.

Plastics are cheap, easy to shape, light, and pretty strong for their weight, but they easily soften with temperature. Their strength-to-weight ratio is not as good as steel, a popular structural material. Steel, however, is quite heavy and subject to corrosion.

What about these materials?

Pictures of a ceramic dish, aluminum soda can, concrete roadway.

Ceramic is brittle, aluminum is ductile. Concrete is usually reinforced with metal bars inside, so the total structure has mixed properties.

Putting Materials Together

How strong are different structures? What are the advantages of different shapes?

Pictures of corrugated cardboard, an aluminum soda can and steel I-beams.

Strength depends on:

  • material properties,
  • geometry (e.g., the shape of a cross-section of the material),
  • the nature and placement of support.
How do the materials in the illustration above differ in terms of material properties, geometry and support placement?

What about these structures?

Structures made of carbon fiber composites: motorcycle helmet, violin bows, hockey stick.

These products were engineered using carbon fiber composites to be light, yet very strong. How do the material properties, geometry and support placement give each product strength?

For projects that explore strength vs. geometry see:

Making Things Strong and Light

How do we make things strong and light?

  • Geometry: using smart shapes to bear heavy loads.
  • Materials: choosing the right material for the job.

It takes a combination of good materials and the right shapes.

Strength-to-weight ratio

How can we measure to see what works best?

  • We can compare different structures and materials by comparing the strength-to-weight ratio of each one to the others.
  • We take the strength of the material (a force or breaking stress) and divide by its weight to get the strength to weight ratio.

Strong and Light: Image Gallery


This gallery of images can give you inspiration for making structures that are both strong and lightweight. For a project where you can apply these ideas, see: The Leaning Tower of Pasta.

The Hong Kong and Shanghai Bank building has triangle frames around tall rods to make sure that the rods can support the building and don't buckle. Architects often play with geometry when designing buildings. Using simple shapes helps to keep the cost and weight of material down while keeping the building safe and supported.

The Hong Kong and Shanghai Bank building has triangle frames around tall rods to make sure that the rods can support the building and don't buckle.

The Eiffel Tower achieves a large strength-to-weight ratio by utilizing a truss support structure.

The Eiffel Tower

A construction crane is a tall tower with a truss frame that is designed to lift and move heavy objects. The height of the structure compared with its weight is very good in comparison to how much weight it can lift.

A construction crane

Structural plastics

Structures made from hard plastic: wheelbarrow, child's slide, step ladder.

Different materials have different properties. A lot of metals, like steel, are very strong, but also very heavy. Structural hard plastics are strong and durable, can be molded in just about any shape, and are lightweight.

Ropes and cords

Ropes, cords, cables: lifting objects with a helicopter using a cable, and a ship's hawsers.

Even simple things like ropes and cords can exhibit enormous strength for their weights. They use the fact that the materials they are made of are very strong in tension.

Superstrong: Materials and Geometry

Carbon fiber and honeycomb geometry.

Carbon fiber is another material that is strong in tension. When you combine it with a honeycomb shape, which is good in compression, you get a very strong structure.

Bicycles also get strength from both material and geometry.

Both the materials (for example, a hollow titanium or carbon fiber frame) and the geometric triangular shape of a bicycle allow it to be very strong for its low weight.

Natural Materials

Spiderwebs, an example of natural materials that are light and strong.

Spider silk has some amazing properties.

  • It feels like silk, and is as elastic as nylon.
  • It is 3× lighter than Kevlar (the strongest manmade fibers, used in bulletproof vests) and up to 30× stronger!
  • If spider silk fibers were created to have the diameter of a small pencil and spun into a web, they would be able to stop a 747 jet in mid-air (like you see in Spiderman)!

Many materials occuring in nature have very interesting properties that humans haven't been able to copy.

Wood furniture

Wood exhibits a high strength-to-weight ratio due to its cellular microstructure. The way the cells of the tree grow (in grains) helps to make the wood strong.

Amazing balsa wood structure: weighs 18 grams, but supported 990 kg before breaking.

Even different woods have different properties. Balsa wood is extremely light, for example, but when formed into the right shapes is also extremely strong. This structure made of balsa wood and super glue weighed only 18 grams but supported 990 kg before breaking!!

Bamboo and wood arch bridge.
Pictures of bamboo bridge under construction and a stand of growing bamboo.

Bamboo is another of nature's resources for building materials.

The "Stress, Strain and Strength" pages were adapted from a workshop program developed at Stanford University for 7th grade participants interested in engineering. Stanford freshmen served as program mentors. The workshop was developed by:

Professor Beth Pruitt, Mechanical Engineering, Stanford University
Tori Bailey, Ph.D. Candidate, Mechanical Engineering, Stanford University
Alex Tung, Ph.D. Candidate, Electrical Engineering, Stanford University

The developers gave their permission for these materials to be published on the Science Buddies website.

Edited by Andrew Olson, Ph.D., Science Buddies.