PSI - Issue 20

S.V. Suknev / Procedia Structural Integrity 20 (2019) 30–36

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S.V. Suknev / Structural Integrity Procedia 00 (2019) 000 – 000

Nomenclature TCD

Theory of critical distances Fracture process zone

FPZ

Size of the FPZ

d

Intrinsic material length

d 0 L e

Size of the stress concentration zone Parameter of plasticity of the material



ASC PSC

Average stress criterion Point stress criterion

Stress

  y  e  c

Normal stress Equivalent stress Critical stress Maximum stress

 max

Uniaxial tensile strength

 0

Pressure

p

Critical pressure Radius of the hole Diameter of the hole

p c

a

l

Critical diameter of the hole

l c x

Coordinate

Coordinate of the point of maximum stress Uniaxial compressive strength Tensile-to-compressive strength ratio

x 0 C 0



Typical representatives of such quasi-brittle materials are geomaterials (concrete, gypsum, and rock), composites, high-strength metal alloys, cast iron, graphite, etc. The foundations of nonlocal fracture criteria were laid down in the works by Wieghardt (1907), Neuber (1937), Peterson (1959), Novozhilov (1969). Currently, nonlocal criteria are developed within the framework of the theory of critical distances (TCD) proposed by Taylor (2007). The methods of the TCD are widely applied in order to assess the strength of materials and structural components with notches in the works by Negru et al. (2015), Li et al. (2016), Fuentes et al. (2017), Justo et al. (2017), Vargiu et al. (2017). The common property of nonlocal criteria is a new introduced constant – an intrinsic material length 0 d , which characterizes its microstructure, thereby allowing one to describe the size effect in the case of stress concentration and thus expand the scope of application as compared to traditional fracture criteria. As it is noted in the work by Suknev (2018), stress redistribution within the size of 0 d is related to the fact that the structure of the material is discrete, having nothing to do with its plastic properties. Therefore, the scope of application of nonlocal criteria is a predominantly brittle fracture of materials with notches. Nonlocal criteria can be applied to the case of quasi-brittle fracture, accompanied by the formation of a small-scale yielding zone d , if its size is not much different from 0 d , i.e., as long as the condition const 0   d d is fulfilled. This paper considers the possibility of expanding the scope of application of these criteria for the cases of quasi-brittle fracture with a developed FPZ. 2. Size of the Fracture Process Zone There were some attempts made by Pipes et al. (1979) and Tan (1987) to modify nonlocal criteria by correcting 0 d . That modification was strictly phenomenological and aimed at describing the results of separate experiments more accurately. Another approach was proposed by Suknev (2018), based on analyzing brittle, quasi-brittle, and ductile fracture diagrams that show the effect of notch size on the residual strength of notched specimens.