Introduction
The history of analytical approaches to studying fracture has been relatively short lived in comparison with other methods. Only beginning around the turn of this century, there has not been much time in which to do research and theoretical analysis of fracture, yet the advances made have been significant, if not the backbone of much of our advancement in this century. The work of such men as A. A. Griffith and G. R. Irwin are just a few of the people who have helped to make these advances possible. Griffith's theory of brittle fracture helps us to understand why brittle fracture occurs in a material. Likewise, as we will later see, Irwin took Griffith's work and applied it to ductile materials, which is also beneficial. Also work in the areas of fatigue and stress concentration have enabled us to make more advances as far as the uses of specific materials are concerned.
Work of Griffith
A. A. Griffith started his work in around the 1920s. At this
time, it was accepted that the theoretical strength of a material
was taken to be E/10, where E is Young's Modulus for the particular
material. He was only considering elastic, brittle materials,
in which no plastic deformation took place. However, it was observed
that the true values of critical strength was as much as 1000
times less than this predicted value, and Griffith wished to investigate
this discrepancy. He discovered that there were many microscopic
cracks in every material which were present at all times. He
hypothesized that these small cracks actually lowered the overall
strength of the material because as a load is applied to these
cracks,
stress concentration
is experienced. This stress
concentration magnifies the stresses at the crack tip, and these
cracks will grow much more quickly, thus causing the material
to fracture long before it ever reaches its theoretical strength.
It should be noted that Griffith believed that, at the crack
tips, the value of stress actually reached the theoretical maximum,
but the overall average of the stress was lowered. It should
also be noted that this phenomenon of stress concentration is
not only relegated to microscopic cracks in a material. Any void
in the material (holes that have been machined or drilled out),
corners, or hollow areas in the internal area of the material
also cause stress concentration to occur, and most times, fracture
will begin in one of these areas simply because of this phenomenon.
(fig 22.3 Reed-Hill)
From this work with stress concentration and working with elastic, brittle materials, Griffith formulated his own theory of brittle fracture, using elastic strain energy concepts. His theory described the behavior of crack propagation of an elliptical nature by considering energy methods. The equation basically states that when a crack is able to propagate enough to fracture a material, that the gain in the surface energy is equal to the loss of strain energy, and is considered to be the primary equation to describe brittle fracture.
Work of Irwin
Griffith's work was significant, however it did not include ductile materials in its consideration. Another man, G. R. Irwin, in the 1950s, began to see how the theory would apply to ductile materials. He determined that there was also a certain energy from plastic deformation that had to be added to the strain energy originally considered by Griffith in order for the theory to work for ductile materials as well, creating what is known as the strain energy release rate.
The term stress intensity is not to be confused with stress concentration work done by Griffith. The stress concentration is how the stress is amplified at a crack tip, whereas the stress intensity is used to describe the distribution of stress around a particular flaw. This term is used when investigating modes of fracture (link to part about K1c), in particular, mode I fracture, which is the most common. This term is used when computing the plane stresses and strains which exist in front of a moving crack. This value is dependent upon many things and is different for each material. Among the things which it depends on is the applied stress, the size and placement of the crack, as well as the geometry of the specimen.
Fatigue is a special kind of failure in which fracture occurs not because of an instantaneous load that is a applied, causing a crack to grow. Rather, it is because a stress is applied for some period of time in which the cracks gradually grow until they finally reach a critical level. This concept is especially important when dealing with metals because it is the single most common cause of failure in metallic structures. There has been much study done on the concept, and much has been learned since the beginning of the study of fatigue. Since much has been learned about fatigue, much has been done in the way of learning how to prevent it. For instance it is almost universally accepted that the cracks in fatigue always start on the surface of a material, so therefore, in order to prevent fatigue from occurring, one should strengthen the surface of the material, making it more difficult to fatigue.
Submitted by Sean Grealis
Virginia Tech Materials Science and Engineering
http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/anal/grealis/history.html
Last updated: 5/4/97