PSI - Issue 16

Jaroslaw Galkiewicz / Procedia Structural Integrity 16 (2019) 35–42 Jaroslaw Galkiewicz / Structural Integrity Procedia 00 (2019) 000 – 000

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2

Nomenclature G TC

the critical strain energy release rate the critical energy release rate for mode I the critical energy release rate for mode II

G IC G IIC

T U δ n δ s

the amplitude of the second term in the Williams’ asymptotic solution

the nodal dispalcement

the normal displacement jumps across the cohesive surfaces the tangential displacement jumps across the cohesive surfaces

σ n max the maximum stress for mode I σ 0 the yield strength τ s max the maximum stress for mode II

Fig. 1 presents only the neighborhood surrounding each selected inclusion. An attempt to investigate the phenomenon of the inclusion degradation (on a microscale) using a full geometry model of the element (on a macro scale) is a difficult but feasible task (Huber et al. (2005 ), Hütter et al. (2014)). It seems considerably more effective to investigate the behavior of a representative material volume, a so-called elementary cell with dimensions that are determined based on fractographic studies, while the load is based on the stress analysis inside the element on a macro scale. In this case, it is possible to maintain an appropriate level of accuracy for the obtained results at low costs of computation.

a

b

c

Fig. 1. Examples of manganese sulfide damage by: (a) debonding, (b) breaking, (c) breaking and debonding

The behavior of the inclusion and surrounding matrix under the influence of the load is of fundamental importance for the process of nucleation of voids and, consequently, for the whole process of element failure. At the initial stage of material damage, one of two phenomena may occur: fracture of the inclusion or its debonding from the matrix. The way in which nucleation will occur is determined by numerous factors. In the study Babout et al. (2004) , it was demonstrated that the matrix of a material with a low Young’s modulus hinders the stress increase below the critical level , favoring inclusion debonding, while the matrix of a material with a high Young’s modulus favors fracture of the inclusion. In the papers Lewandowski et al. (1989), Dighe et al. (2002), the influence of the inclusion size on the fracture of the inclusion was analyzed. Additionally, the shape of the inclusions (Neimitz and Janus (2016)) and their distribution (Kwon and Asaro (1990)) are important factors for the void nucleation process. With so many variables that are difficult to quantify, attempts were made to investigate the nucleation process using different criteria. Originally, it seemed that the amount of elastic energy locally concentrated in the vicinity of the inclusion would be sufficient to assess the critical moment. However, this criterion was not practical for large inclusions with dimensions on the order of micrometers because it was always met. The stress criterion in the form of   p c m eq       , wherein σ c is the critical value of normal stress to the surface of the inclusion acting between the inclusion and the matrix, σ m is the hydrostatic stress and σ eq is the average effective stress corresponding to the average effective plastic strains ε p at the moment of nucleation of the void, turned out to be much more practical (Argon (1976), Argon et al. (1975), Argon and Im (1975)). Despite the simplicity of the formula, determination of the critical value σ c is a problem because of difficulty in the determination of its components. In this case, a highly