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Fracture properties of graphite materials and analysis of crack growth under bending conditions

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Abstract

The elastic and strength properties of different grades of graphite materials as well as their fracture toughness properties are studied. The method for the determination of crack length and the values of fracture toughness characteristics of materials during stable equilibrium crack growth under bending conditions is considered. The unstable or non-equilibrium crack growth from short initial crack is observed in experiments, and corresponding theoretical explanation is given. The process of unstable crack growth is analyzed for different loading conditions. It has been shown that in the cases of short cracks, some part of stored energy transforms into kinetic energy, which can be described by the equation of energy balance during unstable crack growth.

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Notes

  1. State Research Institute of Graphite-Based Structural Materials, Moscow.

Abbreviations

α :

Cross-head speed

β :

Rate of load decrease

β 1 :

Non-dimensional rate of load decrease

B :

Specimen thickness

A i :

Coefficients of the polynomial Y(ω)

b :

Height of the specimen

C :

Compliance of notched specimen

C 0 :

Initial compliance of notched specimen

E :

Young’s modulus

F(ω):

Integral of ωY 2(ω)

G :

Elastic strain energy release rate

\({\text{K}}\) :

Kinetic energy

\({\bar{\text{K}}}\) :

Non-dimensional kinetic energy

K I :

Stress intensity factor

\(K_{{I_{C} }}\) :

Critical stress intensity factor

a :

Crack length

a 0 :

Initial crack length

L :

Length of the specimen

M :

Resulting moment at the central section of the specimen

P с :

Critical load applied to the specimen

\(\bar{P}_{c}\) :

Non-dimensional critical load

P 0 c :

Critical load for initial crack length

S :

Distance between supports of the specimen

\({\text{U}}\) :

Elastic energy

υ :

Load line displacement

υ c :

Critical displacement

\(\bar{\upsilon }_{c}\) :

Non-dimensional critical displacement

Y(ω):

4-th order polynomial

ν :

Poisson’s ratio

Π:

Energy spent on new crack surface formation

ω :

Relative crack length

ω 0 :

Initial relative crack length

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Acknowledgments

This work was carried out in the Perm National Research Polytechnic University with the support of the Government of the Russian Federation (The Decree No 220 on April 9, 2010) under Contract 14.B25.310006 on June 24, 2013.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, 1 Leninskiye Gory, Moscow, Russia, 119991

    E. V. Lomakin

  2. Center of Experimental Mechanics, Perm National Research Polytechnic University, Perm, Russia, 614990

    M. P. Tretyakov

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  1. E. V. Lomakin
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Correspondence to E. V. Lomakin.

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Lomakin, E.V., Tretyakov, M.P. Fracture properties of graphite materials and analysis of crack growth under bending conditions. Meccanica 51, 2353–2364 (2016). https://doi.org/10.1007/s11012-016-0370-x

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