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Fracture Science on the Micro Part 1: The significance of cracking

World Cement,

Grinding research conducted at the MIT Concrete Sustainability Hub has tremendous implications for the cement industry. Its research started off with a deceptively simple investigation into the phenomenon of cracking, except MIT started off at the atomic level.

The significance of cracking

No material is immune to cracking. From cardboard to concrete, from soils to steel, all materials crack. Cracking is an incredibly important phenomenon for an engineer because of the insight that cracking provides into the properties of the materials that we use everyday, and because of the consequences of failing to heed that insight.

Regardless of size, engineers look at cracking with a critical eye. They have very specific questions that they want to answer:

  • Where do cracks come from?
  • Is the function of structure or material compromised?
  • What’s the largest crack I can tolerate?
  • How long does it take for a crack to grow?
  • If a structure or material is cracked, what is the impact on its service life?
  • How often should I be checking for cracks?

Cracking and grinding are intimately related. At the cement plant, we want our clinker to crack and we want it to fracture with as little grinding energy as possible. From a reverse engineering standpoint the same questions that engineers ask to prevent cracks are just as important to those who want to cause cracks.

Researchers have been looking at this relationship between cracking or fracture and the energy required for comminution for a very long time. They recognised long ago that size reduction is all about fracturing materials. After all, cement plants don’t crush and grind to make things larger; they crush and grind to make things smaller. In the cement industry, the size of the particles is a key parameter that helps define the rate of hydration and resulting strength development of mortars and concretes, heat generation and other related properties.

Early studies

The earliest research into cracking and fracture was conducted by Von Rittinger in the late 1800s. It seems plainly obvious now, but he discovered that the size reduction process is all about increasing surface area: the more a material was reduced in size, the greater the surface area of that material and the more energy was required. Kick carried out research about 20 years later and tied the size reduction process back to the number of size reduction stages: the more stages used, the greater the size reduction. Bond built upon that research in the 1950s and 1960s to develop correlations between particle size reduction and the energy needed to reduce a material from one particle size to a smaller particle size. Although each of these researchers had valid points, none of their research worked for all particle sizes. Later, research by Hukki tried to balance the major size reduction theorems algebraically. As important as all of these approaches were, they suffered from a major flaw: each researcher could only observe size reduction at the macro level. What they discovered was based on what they saw with the naked eye and what they could measure with the equipment they had available.

Research into cracking or fracture may have stopped there were it not for the work of Griffith in the early twentieth century. Griffith discovered that there’s a relationship between energy, crack length, and brittle fracture. That was a foundational discovery because it allowed engineers to find any one of those three variables provided they could measure or predict the other two variables. Griffith also discovered that the reason the observed toughness of a material is much lower than the theoretical or calculated toughness is because of the existence of microcracking throughout most materials. The grain size of a material is a good indication of the size of that microcracking.

Griffith related what he called the critical strain energy release rate – a property of a material – to the stress level applied and the size of a flaw ordefect in the material. His equation also uses the material’s modulus of elasticity. He clearly saw that a flaw or defect that reaches a certain characteristic length will start to fracture. That characteristic length is defined by engineers as the fracture process zone. Interestingly enough, the characteristic length varies dramatically: for fine grained ceramic materials, the length is approximately 10 µm to 1 mm, while for Arctic Ocean sea ice the length might approach 20 km. He also saw that smaller samples of a material were proportionally tougher than larger samples of that same material. That’s because the smaller sample size does not provide enough volume for a flaw or defect to reach the characteristic length needed to start the crack. Engineers and material scientists typically refer to Griffith’s work as the energy approach.

A competing approach to Griffith’s is the stress intensity approach. The stress intensity approach looks at the stress state near the tip of a sharp crack and considers three potential failure modes. Materials can be displaced through a variety of mechanisms. A common everyday example is the process of chewing. Mode I represents the jaw opening and closing as it chews food. Mode II represents the back and forth or sliding movements we use and Mode III represents the tearing action.

Researchers have long known that both the energy approach and the stress intensity approach are fundamentally related. The toughness or resistance to crack growth is determined by the energy absorbed as the crack moves forward. Simply put, there is a relationship between stress, flaw size and fracture toughness. If you know any two of those variables, then you can find the third.

Read part two of Fracture Science on the Micro here.

Written by Rick Bohan, Portland Cement Association (PCA). This is an abridged version of the full article, which appeared in the December 2013 issue of World Cement. Subscribers can view the full article by logging in.

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