Before I can really describe any of this, I have to explain a few background topics.
Stress:
Stress is defined as a force per area. For example, if you have a 1 inch x 1 inch bar (cross section, length of the bar isnt important for this example) of steel and you put 4 lbs of force on it, the value of stress would be 4 lbs/square inch. If it was instead a 2 inch x 2 inch bar with a 4 lbs force (or load) on it, the value of stress would be 1 lbs/square inch.
In the previous examples the stress was axial stress, which is usually represented by the lower case greek letter sigma. Theres also shear stress, represented by the a lower case tau, but we wont worry about that.
The concept of stress is important because its under a certain stress that a material will fail, not under a specific load. So something like A36 steel, which was once used in most structural applications, fails, or yields, at 36 ksi (36000 lbs/ square inch). This means that regardless as to whether its a huge I-beam, or something like a knife, itll still fail at 36 ksi, though the actual load will be very different.
There are a few different values of stress that you should know about, which are dependent on the material being used. A side note: the terms stress and strength are frequently used interchangeably.
Yield stress This is the point at which the material begins to deform in such a manner that it wont return to its original shape when unloaded. This is whats used for calculating the loads that a building can withstand. Also called yield strength.
Ultimate stress This is the largest stress that a material can withstand. After yield stress, the material can frequently take more stress, but this is not without permanent deformation. Also called ultimate strength.
Proportional limit This is the point at which the stress stops being directly related to strain, which Ill define later. Its important to note that this point marks the limit of the linear elastic range, but theres still a region that is nonlinear elastic. In both of these regions, after the load has been removed the material will return to its original shape.
Rupture stress This is the stress that steel experiences at failure. Its important to know that rupture stress is not synonymous with ultimate stress. This is probably the least important of the stress points from a design standpoint. Also called rupture strength.
Strain:
Strain is defined as the change in length due to a load divided by the original length. For example, if a bar is originally 10 inches long and is pulled to 12 inches long, the strain would be 2 inches / 10 inches, or 0.2. Sometimes this is referred to as 20% strain instead. Note that strain is unitless.
Relation between Stress and Strain:
There are 3 ranges of the Stress vs Strain graph that Ill talk about here. Those arent the only ranges, but theyre the most relevant ones to knives.
Linear elastic This is the range for which stress is proportional to strain. In other words, stress is equal to strain multiplied by a constant. This constant is called Youngs Modulus and is denoted as E. For most structural steels E = 29,000 ksi and most steels hover around this value. Within this range, strain will go straight back to 0 once the load is removed, which is the same as saying that the material will go back to its original shape. This range extends to the proportional limit.
Nonlinear elastic For this range the stress is no longer proportional to strain. However within this range, the strain will still go back to 0 once the load is removed. This range starts at the proportional limit and ends at the yield stress.
Inelastic/Plastic In this range you will have permanent deformation, meaning even when the load is removed, strain will not go back to 0. This range is past the yield stress.
Theres a picture of a stress vs strain curve in the following article:
http://en.wikipedia.org/wiki/Yield_(engineering)
In the next installment Ill describe how the stress due to a bending moment is calculated. This is the type of stress that a knife is subjected to during a bending test.