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Stress-Strain Plot for Ductile Materials

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.

Moments and Torques

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.

Ductile or Brittle?

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?