Figure 1
In an earlier entry, we saw that bending is one of the basic loading geometries. In Figure 1, we create three-point bending in a simple beam by pushing down on the two ends and up in the middle. In this situation, imagine a chunk of cheddar cheese (or go get one!) and bend it up in the middle while bending down on the ends. If you can imagine the cheese behaving the same way the steel bar in Figure 1 behaves, the top layers will stretch and the bottom layers will be squeezed or compressed. If you are doing this with a block of cheese, it won’t take much to create a crack that is probably similar in orientation to that shown in the upper half of Figure 1. In both cases, the stretching length change happens along the long direction of the “beam” (as shown), and the crack forms perpendicular to the stretching. It is difficult for a crack to open when the material is tightly squeezed, like it is on the bottom of the beam or block of cheese. The tensile or stretching stresses along the top of the beam can more easily allow a crack to open if the stress exceeds the strength.

Figure 2
Note that if this “beam” were sitting on two supports out in the back yard and you sat on it in the middle, it would be gravity loading and the tensile stress would be on the bottom – the opposite of what is shown in Figure 1 but like the crack as oriented in Figure 2. Note the crack in Figure 2 is in a Charpy V notch bar, which was actually broken by a hammer impact going parallel to the ground! The vertical or horizontal position of the part is not really important when we talk about loading geometries. The stresses that are created in the part as a result of the interaction between the loads and the part shape are what we need to worry about.

Going back to the original beam of Figure 1, which has stretching or tensile stresses along the upper surface, any time the stress exceeds the strength, a crack can open. The crack now makes the loading even more uneven. The stresses no longer vary gradually from tensile to compressive as you go from a top to bottom surface layer. The maximum tensile stress is now experienced at the crack tip, which may be anywhere in the thickness. The original top surface layers now have a near zero stress. But the crack tip location does not experience the same level of stress as the material at the originally intact surface did. The crack tip location has a much higher stress condition due to concentration of the stresses. Most of the shape change (strain) associated with the stress is forced into the small area at the crack tip instead of being spread out along the top surface. The atoms along the crack tip are “really stressed out!”

Figure 3
We can see that the crack started out perpendicular to the length of the beam, parallel to the direction of the load application and perpendicular to the tensile stress, but then something happens. The direction of the crack changes. A technical explanation of why this happens can get complicated. But one reason is that many materials do not have the same strength in different directions. This is often the case in wrought materials. Grain orientation and the presence of weakening stringer-type inclusions are two things that can make it easier for the crack to travel along a direction parallel to the beam than it is to travel perpendicular. Think of a piece of wood. If you have to split a log, it is much easier to split it along the grain than across the grain. Figure 3 shows a “real part” rather than a test coupon, which broke due to a bending load, and it shows where the crack changed direction at least in part due to its oriented grain structure.

There is another major reason that cracks can change direction. Instead of a block of cheese, imagine in your hands a pack of cards. If you look closely while bending or flexing the pack in your hands, the edges of the cards at the ends perpendicular to the length of the bend are now forming tiny steps. This is because the cards have slid a little bit with respect to each other due to the bending. The solid part can’t slide as easily as the cards, but the same stresses are acting to make this happen in the solid parts as well. Shear stress is the technical name for this. When an intact beam is loaded in bending, the shear stresses are parallel to the length of the beam, just like in the pack of cards. Because of the restraint (steps can’t form in a solid block) the shear stresses are highest near the center of the beam thickness. Occasionally, I have seen a crack make a “hard left” turn, usually in the center half of the “height” (or thickness) of the beam, due to shear stresses “taking over.” Cracks due to shear stresses in bending are at 90 degrees to the cracks created by the tensile stresses.

Figure 4
Another situation is more common. As the crack lengthens, the stress changes dramatically. The entire remaining ligament may be in tension or compression. Now, the tensile and compressive loading-related shear stresses, which you may remember are at a 45-degree angle, can now allow a macro-scale ductile crack to form, finishing off the part that started cracking in a macro-scale brittle manner.

Figure 4 shows a round bar that was notched with a band saw to make it easier to break at a later time. The saw cut simulates the separation due to an initial macro-brittle crack due to tensile stresses. The actual crack is seen to be at an angle to the length of the round “beam.” When the stress is high enough, the remaining ligament separates due to shear stresses from compressive or tensile loading. This effect is often called a “compression hinge.”