Fracture toughness

In materials science, fracture toughness is a property which describes the ability of a material to resist fracture, and is one of the most important properties of any material for many design applications. The linear-elastic fracture toughness of a material is determined from the stress intensity factor ( K {displaystyle K} ) at which a thin crack in the material begins to grow. It is denoted KIc and has the units of Pa m {displaystyle { ext{Pa}}{sqrt { m {m}}}} or psi i n {displaystyle { ext{psi}}{sqrt { m {in}}}} . Plastic-elastic fracture toughness is denoted by JIc, with the unit of J/cm2 or lbf-in/in2, and is a measurement of the energy required to grow a thin crack. The subscript I denotes mode I crack opening under a normal tensile stress perpendicular to the crack, since the material can be made deep enough to stand shear (mode II) or tear (mode III). Fracture toughness is a quantitative way of expressing a material's resistance to brittle fracture when a crack is present. A material with high fracture toughness may undergo ductile fracture as opposed to brittle fracture. Brittle fracture is characteristic of materials with low fracture toughness. Fracture mechanics, which leads to the concept of fracture toughness, was broadly based on the work of A. A. Griffith who, among other things, studied the behavior of cracks in brittle materials. A related concept is the work of fracture ( γ w o f {displaystyle gamma _{wof}} ) which is directly proportional to K I c 2 / E {displaystyle K_{Ic}^{2}/E} , where E {displaystyle E} is the Young's modulus of the material. Note that, in SI units, γ w o f {displaystyle gamma _{wof}} is given in J/m2. Just as the elastic properties of materials, like elastic moduli and strength, vary among material class, so too does the fracture toughness. Figure 1 graphs the fracture toughness vs. strength for various materials and materials classes. However, unlike most elastic properties, fracture toughness displays a wide variation across materials, about 4 orders of magnitude. As can be expected, metals hold the highest values of fracture toughness. Since cracks cannot easily propagate in tough materials, this makes metals highly resistant to cracking under stress and gives their stress–strain curve a large zone of plastic flow. Comparatively, engineering ceramics have a lower fracture toughness, which leads to ease of cracking, but show an exceptional improvement in the stress fracture that is attributed to their 1.5 orders of magnitude strength increase, relative to metals. Of note is the fracture toughness of composites (made by combining engineering ceramics with engineering polymers) (in the zone of engineering alloys), which greatly exceeds the individual fracture toughness of the constituent materials.