# Fracture Toughness: Measurement, Types and Typical Values

Fracture toughness is a material property that describes the material's capacity to resist fracture when enduring a crack.

It is one of the most important properties, for it is crucial in avoiding failure in materials, which might cause devastating losses. It was estimated in 1983 by the National Institute of Science and Technology (then, the National Bureau of Standards) together with Battelle Memorial Institute that failures resulting from fracture have cost over \$119 billion annually, not to mention the effects on human lives [1].

It is critical among all design applications to take into account what is known as fracture mechanics; in other words, to take into consideration as many factors as possible that may result in failure.

## How is fracture toughness approached?

Flaws in materials are not always easy to detect, and more often than not, they are unavoidable as they may emerge during processing, manufacturing or servicing a certain material. Since it is difficult to make sure that the material is free of flaws, engineers suppose that a certain flaw exists and approach the problem using methods such as the Linear Elastic Fracture Mechanics (LEFM) method. Developed by A. A. Griffith in the 1920s, LEFM provides a means of solution for engineering problems, including the estimation of safety and life expectancy of structures with cracks.

The LEFM revolves around a parameter called the stress-intensity factor (Κ), which is a function of the loading stress, the size of existing or assumed crack, and the structural geometry [2]. This factor is a suitable way to understand the stress distribution around a crack. In mathematical terms, the stress intensity factor can be reached as follows [3]:

• Energy required to cause fracture (Gc) is a function of the stress σ, crack length α, and the elastic modulus Ε:

• Rearranging the equation gives:

• Stress intensity factor Κ of unit [MPa.m0.5] can be defined as:

• Fracture takes place when the stress intensity factor reaches a critical value Κc ; i.e:

• Κis what is known as the fracture toughness of the material:

This can be described also in relation to material thickness. As the thickness of a material changes, the states of stress around the crack change as shown in Figure 1 [4]. When the material thickness reaches a critical value, the value of the stress intensity factor Κ relatively plateaus at a critical value known as the fracture toughness Κc. In thin samples, the stress state is called plane stress, while that in thicker samples is referred to as plain strain. Plain strain characterizes more acute stress states and lower Κ values.

Figure 1 Fracture toughness as a function of material thickness. Retrieved from Ref. 4

Fracture toughness is not to be confused with fracture strength. Fracture strength – also known as tensile strength – describes the maximum stress a material can withstand before experiencing fracture. Fracture toughness, on the other hand, represents the energy required to fracture a material containing a pre-existing flaw (or crack) [5].

## Modes and types of fracture

The fracture process consists of two stages: Crack initiation and crack propagation. The propagation of a crack that would result in fracture provides information about what mode that fracture is in. According to Irwin, fracture exists in three modes [6].

Mode I fracture is also referred to as the Opening mode, within which a tensile stress acts perpendicularly to the crack plane.

Mode II fracture is also called the Sliding mode, where an in-plane shear stress acts normal to the crack front.

Mode III fracture, or the Tearing mode, is when a torsional (out-of-plane) shear stress exists parallel not only to the crack plane, but also to the crack front.

Fractures can be labelled as either ductile or brittle based on the material’s plasticity. In other words, depending on the amount of plastic deformation that a material can undertake, the characterization of fracture changes. If significant plastic deformation takes place before and during the propagation of the crack, the fracture is considered a ductile fracture. Conversely, if only deformation at the microscale takes place, the fracture would be a brittle fracture. Plastic deformation is a caution signal to an impending fracture. Yet, it is not easy to find the boundary between brittle and ductile fracture since there are several factors that can affect material deformation, including the stress state, loading rate, ambient temperature and crystal structure.

## Fracture toughness in different materials

Fracture toughness spans over a broad number of materials, showing a variation up to four orders of magnitudes. Metals and engineering alloys have the highest Κc values due to their high resistance to cracks. Engineering ceramics have a relatively lower fracture toughness despite their higher strength. Engineering polymers are also less tough when it comes to resisting cracking, yet engineering composites of ceramics and polymers show an enhancement in fracture toughness than both components. Wood, cement, concrete, glass, and plaster are downwards from the aforementioned material in Κc values. The materials with the lowest fracture toughness are types of foams and polymers. Figure 2 shows different materials on a graph relating the fracture toughness to the material strength [7].

Figure 2: Fracture Toughness vs Strength: Distribution of different materials. Retrieved from Ref. 7

## Sources

[2] Irwin, G. R. (1968) Linear Fracture Mechanics, Fracture Transition, and Fracture Control. Engineering Fracture Mechanics, 1, 241-257.
[3] Fracture Toughness (n.d.) UNSW, School of Materials Science and Engineering. Retrieved from: http://www.materials.unsw.edu.au/tutorials/online-tutorials/3-fracture-toughness