PSI - Issue 30

S.V. Suknev et al. / Procedia Structural Integrity 30 (2020) 179–185 S.V. Suknev / Structural Integrity Procedia 00 (2020) 000–000

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make it possible to cover the whole range of stress concentrations and assess the strength of structural members with a blunt notch and a crack from a single point of view. These requirements are met by nonlocal fracture criteria, which are based on the idea of the formation of a prefracture zone around the most stressed point in the material, with local redistribution of elastic stresses occurring in this zone. 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) (Taylor 2007 and 2008). The methods of the TCD are widely applied in order to assess the strength of materials and structural members with notches (Negru et al. 2015, Li et al. 2016, Fuentes et al. 2017, Vargiu et al. 2017, Vedernikova et al. 2019, Justo et al. 2020).

Nomenclature TCD

Theory of critical distances Size of the prefracture zone Intrinsic material length

d

0 d e L

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



Radius of the hole Size of the insert

a B

Stress

 e  c  0 

Equivalent stress

Critical stress

Uniaxial tensile strength

Uniaxial compressive strength

0 C

Pressure

p

Critical pressure

c p

Asymptotic value of the critical pressure

s T 0 T

Asymptotic value of the critical pressure for brittle material

Tensile-to-compressive strength ratio



Loading biaxiality ratio



 , s  Parameters

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 (2019a), 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 prefracture zone, if its size d is not much different from 0 d , i.e., as long as the condition const 0   d d is fulfilled. To expand the scope of application of the criteria for cases of quasi-brittle fracture with a developed prefracture zone, it is proposed by Suknev (2019a) to abandon the hypothesis of the size of the prefracture zone as a material constant associated only with its microstructure. The characteristic length parameter underlying the nonlocal criteria should be considered as a material constant only in one particular case, which is brittle fracture. For quasi-brittle materials, this parameter is represented by the sum of two terms: