Crack formation in 3D

Dr. Neil Canter, Contributing Editor | TLT Tech Beat July 2010

Large-scale computer simulations are determining the mechanism of crack formation in three dimensions.

KEY CONCEPTS
• Cracks are formed and propagate through materials under both shear and tension.
• Large-scale computer simulations have now shown that cracks move through materials in a helical fashion.
• As the initial crack propagates, daughter cracks are formed that get bigger over time.

Material failure is often attributed to the formation and propagation of cracks. Those that work in the lubricant industry have to deal with this problem because the formation of cracks can be caused by inadequate lubrication in a particular application.

In a previous article, crack formation was examined at low speeds in silicon, a brittle material (1). A crack moving through a silicon crystal was found to generate triangular ridges. Silicon atoms reconstruct themselves into five- and seven-member rings after a crack initially breaks the bonds.

On a three-dimensional level, cracks move through materials under different modes. Alain Karma, distinguished professor of physics at Northeastern University in Boston, Mass., says, “Cracks are often seen to propagate under both shear and tension. Antiplane shear (also known as Mode III) involves the twisting of a material out of its shape. Tension (also known as Mode I) is created when the material is pulled out of shape.”

The combination of antiplane shear and tension can be easily created by cutting a material at an angle to create a crack and pulling on it, thereby causing the initial crack to rotate as it propagates. Karma indicates that this process spans all known materials. He says, “The combination of shear and tension produces stepped fracture surfaces in glass, plastics, steel alloys and even in natural structures such as rocks. In fact, it is known that “echelon cracks” formed by this process can propagate for thousands of meters through a geological formation.”

The elongated surface markings produced by those steps also are known as lances or facets. Karma says, “The former term is used because cracks resemble the elongated markings of medieval lances.”

The composite forces that collectively lead to crack formation also are seen in biological materials such as bone. Spider silk is another example where nature might exploit inherent crack instabilities to create a material that is stronger than steel despite weak bonds.

At this point, the mechanism for how cracks propagate through three dimensions has not been determined. New work that involves the use of computer simulations has now uncovered the way cracks move through materials.

HELIX FORMATION
Karma and his co-worker, Antonio Pons, have now used large-scale computer simulations to determine the mechanism of crack formation in three dimensions. Due to the complexity in simulating this phenomenon, no computational method has been available until recently. The researchers conducted a large number of experiments using a continuum phase-field approach.

A hypothetical system was developed in which a material in the shape of a disk is embedded in a different, cylindrically shaped material such as a piece of metal, which is both pulled and twisted. Crack propagation starts at the boundary of the two different materials. The crack then radiates outward through the cylindrical material.

Karma says, “We set up the experiments in this fashion so that edge effects are minimized. The edge only becomes important when the crack hits the surface of the cylinder at the end of the simulation.”

As the crack starts to propagate, some regions of the material rotate to the left while others rotate to the right. In those regions oriented toward the axis of maximum tension, energy is released at a faster rate—leading to the generation of larger forces and faster crack propagation, thereby amplifying the helical deformation.

The researchers found that the crack propagates through materials in a helical path. Karma says, “We were surprised that the crack instability develops in this fashion.”

Figure 1 shows the evolution of a crack moving through a material. The progress of the crack is shown from the top to the bottom in this photograph. As time progresses, the initial parent crack segments into a series of rotated “daughter cracks” that will get bigger over time. The helical shape of the crack is first seen in the second image from the top.


Figure 1. The movement of a crack through a material is shown from the top to the bottom. The second to the top image first shows the helical shape of the crack which grows larger over time. (Courtesy of Northeastern University)

The researchers compared the computational analysis to experimental studies done with glass, Plexiglas and steel. Karma says, “We measured the rotation angles of facets for cracks moving through these materials by varying the ratio of the shear stress to the tension. Greater shear stress means that the crack will rotate at a higher angle.”

Data obtained from the computational approach agreed better with the experimental data in steel than in Plexiglas. Karma noted that all of the angles obtained from the computer simulations were lower than predicted by previous approximate theories.

All of the analysis was done for cracks moving through surfaces at slow speeds. Karma indicates that understanding crack movement at high speeds is much more complicated. He says, “Cracks can become very unstable at high speeds, which leads to such phenomenon as microbranching. This effect is particularly noticeable in brittle materials.”

The crack formation theory developed by the researchers should enable new materials to be developed that are better able to withstand the damaging effects of cracks. One area that Karma intends to focus on in the future is a look at biological materials such as bone. He adds, “Our hope is to facilitate the preparation of composite artificial materials that are not as susceptible to fracture when placed inside the human body.”

Additional information about this work can be found in a recent publication (2) or by contacting Karma at a.karma@neu.edu. 

REFERENCES
1. Canter, N. (2009), “Crack Formation in Brittle Materials,” TLT, 65 (2), pp. 26–27.
2. Pons, A. and Karma, A. (2010), “Helical Crack-Front Instability in Mixed-Mode Fracture,” Nature, 464 (7285), pp. 85–89.

Neil Canter heads his own consulting company, Chemical Solutions, in Willow Grove, Pa. Ideas for Tech Beat items can be sent to him at neilcanter@comcast.net.