September 11, 2013

Cornell Scientists Develop Theory for How Materials Break

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By LISA GIBSON

If you have ever broken a bone or cracked a window, aside from having bad luck, you have broken two different types of materials that break in different ways.

Prof. James Sethna, physics, and Ashivni Shekhawat Ph.D. ’13, in collaboration with Stefano Zapperi, senior researcher, Consiglio Nazionale delle Ricerche, Italy, have created a unifying theory, the continuous damage theory, to explain how all objects break.

Previously, scientists used different models for how objects fracture, or break, for different types of material.A crystalline material, such as a salt crystal, has its molecules arranged in a specific, ordered and homogeneous way. Composite materials are made out of multiple materials but, because of the combination, have different chemical or physical properties than the original materials. Bone and shell are two natural composite materials. Composite materials have less order in how they are arranged at the molecular level.

“Disorder is the key parameter to vary between these materials as you go from glass to bone, and that is one of the key findings in our work,” Shekhawat said.

According to Shekhawat, composite materials can absorb more damage and stress than brittle crystalline materials before breaking into pieces.

Before Sethna, Shekhawat and Zapperi composed their new theory, different models were used to determine how different materials would break.The trio discovered that the amount of disorder in a material controls how much distributed damage it can take before it fails, according to Shekhawat.

The amount of disorder causes differences in having the ability to absorb damage or breaking instantly.

Sethna, Shekhawat and Zapperi’s continuous damage theory allowed them to quantify the amount of damage a system could undergo before it fell apart. They could also predict the breaking point of the material.

Although composite materials are generally more able to withstand stress, the bigger the composite materials, the more brittle they become.

“If you take a material of a certain scale and it has interesting behavior, and then take a block of it twice as big in each direction, what will the new behavior look like? And what you find is that things become more brittle, more glass like, as you get bigger,” Sethna said. “That means that they get more ‘interesting,’ from our point of view, as they get smaller. Suggesting that if you build nano devices with damage in them, they will probably be described by theories like ours.”

Using the continuous damage theory, the researchers are now able to quantify how much stress a material can withstand as the size of the object changes.

During early experiments, according to Sethna, the results did not create the predicted Weibull distributions of fractures.

The Weibull distribution is a mathematical probability distribution similar to the Gaussian distribution, also known as the bell curve, used for determining class averages and grades. The Weibull distribution has a different shape than the bell curve, and the Weibull distribution curve is used by engineers to determine failure of products, including how often they will break.

The Weibull distribution can also be used to help with weather forecasting and a variety of other models.

The researchers tested the Weibull theory using another model and established that their simulation results were accurate. They also determined that the Weibull distribution only works for a system that is “big enough,” according to Sethna.

They determined that the “big enough” system needed for the Weibull distribution to work in this case had to be one that was larger than the observable universe, said Sethna.

“This is not to say that the Weibull distribution will not work for any model or real system. In fact, there are several models for which the Weibull distribution will do just fine,” Shekawat said. “However, it does bring into question the indiscriminate use of Weibull theory. Our work provides a theoretically sound criticism of the Weibull theory.”

Testing the Weibull distribution led to the new continuous damage model.

To create the new model, the researchers studied the distribution of precursor events, smaller fractures that led up to a final break.

Shekhawat said that from a small object to a large object, they could now quantify and predict the expected behavior of the strain distributions and how the distribution of precursor events would change using the new model.

The continuous damage theory is best used for moderate size objects at the micro-length scale. When measuring stress in micro-length objects, the distribution of stress behaviors is fit well by the researcher’s distribution, and not by the Weibull distribution, Sethna said.

The next step of this research is to experiment with more composite materials that contain various amounts of disorder and to measure fracture distributions in breaking objects.

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