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What is a Tearing Resistance Curve (R Curve)?


A tearing resistance curve, or R-curve, represents a material's resistance to progressive crack extension (this implies that a material's fracture toughness can change with crack extension). Hence, a tearing resistance curve is a plot of fracture toughness against crack extension (e.g.: J vs Δa or CTOD vs Δa, where Δa is crack extension (see FAQ: What is a fracture toughness test?). An example is shown below.

Tearing resistance curves are only of use if a material exhibits stable tearing behaviour, and cannot be generated beyond the onset of a brittle fracture event. Stable tearing in metals occurs predominantly by the process of microvoid coalescence. In this process, material within the crack tip plastic zone deforms plastically, forming microvoids ahead of the crack tip. Linking of these voids with the crack tip results in crack extension.

In many ductile, work hardening materials, the size of the plastic zone at the crack tip increases as the crack extends. Hence, each successive unit of crack extension requires more energy than the preceding unit of extension ( order to further increase the plastic zone size). Thus, the resistance of the material to crack extension increases with crack extension. This type of behaviour is known as a 'rising R-curve'. Of course, there is a limit to this increase in toughness, and hence all R-curves eventually flatten off.

Standards for tearing resistance curves include BS 7448 Part 4 and ASTM E1820 (see FAQ: Are there any differences between fracture toughness tests carried out to BS 7448 and those using ASTM E1820?). Data that can be generated from a tearing resistance curve include:

  • the equation for the entire resistance curve (typically in the form of an offset power law, e.g. J = m + l (Δa)x,
  • the value of J or CTOD at initiation of stable ductile tearing (δ0.2BL, J0.2BL)
  • the value of J or CTOD at maximum load (δm, Jm)

There are three main standards which describe the fracture toughness testing of ductile alloys by generating tearing resistance curves: BS 7448-4 (1997), ISO 12135 (2016) and ASTM E1820 (2018). Each of these standards differs in significant details relating to the generation and analysis of the test data. Find out more about the techniques and methods given in these standards for the determination of tearing resistance curves (R-curves) in single-edge notched bend (SENB) fracture toughness test specimens.

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