Crack tip opening displacement

LEFM (Linear elastic fracture mechanics) is not valid. This assumption was proven when a unique relationship between Crack Tip Opening Displacement (CTOD) and the J integral was established. In the case of the ductile materials, the crack faces move prior to fracture and create a blunt crack tip. This crack opening can be used as a measure of the toughness of the material. This parameter is known as Crack Tip Opening Displacement or commonly in the form of abbreviation CTOD.

Definition

There are a number of alternative definitions of Crack Tip opening displacement. The most common definition is the displacement at the original crack tip and the 90° intercept. These are equivalent if the crack blunts in a semicircle.

Relationship between K and CTOD

CTOD can be expressed in terms of K as ${\frac {K^{2}}{\sigma _{y}E}}$

In case of the small scale yielding conditions the same can be expressed as

Relationship between J-integral and CTOD

For Linear Elastic Conditions, the relationship between CTOD and G is given by Equation

between CTOD and J in the limit of Small-Scale Yielding.

Relationship between G and CTOD

Since J = G for linear elastic material behavior, these equations also describe the relationship between the G and CTOD also.

CTOD testing

Crack Tip Opening Displacement test is usually done on materials that undergoes plastic deformation prior to failure. The testing material should more or less resemble the original one though dimensions can be reduced proportionally. Loading is also done so as to resemble the actual load expected. More than 3 testing are done so as to ensure any experimental deviations are minimum. There is also an inter relationship between the dimensions of the testing material to ensure proportionality is maintained throughout The specimen is placed on the work table and a notch is created exactly at the centre. The crack should be generated such that the length of defect reaches a value of about half the depth. The load applied on the specimen is generally a three point bending load. A strain gauge is used to measure the crack opening. Crack tip plastically deforms until a critical point after which a cleavage crack is initiated which may lead to either partial or complete failure. The critical load and strain gauge measurements at the load is noted and a graph is plotted. Crack tip opening can be calculated from the length of the crack and opening at the mouth of the notch. According to material used fracture can be brittle or ductile which can be concluded from graph plotted

Laboratory measurement

Early experiments used a flat paddle-shaped gauge that was inserted into the crack; as the crack opened, the paddle gauge rotated, and an electronic signal was sent to an x–y plotter. This method was inaccurate, however, because it was difficult to reach the crack tip with the paddle gauge. Today, the displacement V at the crack mouth is measured, and the CTOD is inferred by assuming that the specimen halves are rigid and rotate about a hinge point

Application

Examination of fractured test specimens led to the observation that the crack faces had moved apart prior to fracture, due to blunting of an initially sharp crack by plastic deformation. The degree of crack blunting increased in proportion to the toughness of the material. This observation led to the opening at the crack tip being considered as a measure of fracture toughness. Today, this parameter is known as CTOD. Irwin, later postulated that crack-tip plasticity makes the crack behave as if it were slightly longer. Thus, estimation of CTOD can be done by solving for the displacement at the physical crack tip.

Advantages and disadvantages of using CTOD as a design parameter

• Advantages
  • Single parameter which takes care for the cracktip plasticity also
  • Easy to measure when compared with the similar techniques like J integral etc.
  • A fracture parameter which has more physical meaning than the rest
• Disadvantages
  • The equavalance of CTOD and J integral is proved only for non-linear materials, and not for plastic materials
  • Hard to expand the concept of CTOD for large deformation conditions
  • It is easier to calculate J-integral in case of a design process using FEM techniques