PSI - Issue 17

Michal Vyhlídal et al. / Procedia Structural Integrity 17 (2019) 690–697 Vyhlídal et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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e.g. EN 1992-1-1 (2004), which typically provide concise information on materials and structural behaviour based on experimental and empirical experience (elasticity and plasticity theory). However, structures made of these composites show nonlinear, more precisely, quasi-brittle behaviour – the ability to carry load continues even after the deviation from the linear branch of load-displacement diagram until the peak point and then the decrease of loading force follows until the failure, so called tensile softening Karihaloo (1995). The reason for this behaviour is, except of strong heterogeneity, the existence of internal defects (pores, cracks, transition zones, etc.), which work as obstacles to or promoters of crack propagation and are not taken into consideration by standards. When the structural design of these structures is more difficult (e.g. new materials, difficult geometry), it is suitable to apply the principles of fracture mechanics. Fracture mechanics together with a finite element method (FEM) is a powerful tool for the assessment of concrete structures behaviour which determines the durability within the structure’s lifetime .

Nomenclature a 0

initial crack length

terms of Williams’s expansion thickness of the specimen real thickness of the specimen

A n

B

B 1 B 2

model thickness of the specimen CMOD crack mouth opening displacement d averaging distance E Young’s modulus F loading force F 1 force applied on the real specimen F 2 force applied in the model F app maximum applied force ij (n, θ) shape function g maximum grain size of the aggregate K i

stress intensity factor in loading mode I, II, III fracture toughness (under pure mode I)

K I,c

L specimen’ s length r, θ polar coordinates S span W specimen’s width α relative crack length ν Poisson’s ratio ij ( , ) tangential stress ̅ ( ) average tangential stress ̅ , Airy ’s function stress tensor component

critical value of the average tangential stress

2. Theoretical background Most of the building materials contain internal defects or material discontinuities – cracks, cavities, pores, inclusions, etc. These discontinuities form stress concentrators and serve as potential weak elements which determine the structure’s lifetime. Generalized fracture mechanics deals with the influence of these stress concentrators and derive closed-form solutions for the stress and strain fields in the vicinity of crack tip.