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Computation of V-notch shape factors in four-point bend specimen for fracture tests on brittle materials

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Abstract

Four-point bend (FPB) specimen is an important test sample in mixed mode fracture study of notched components made from brittle materials like rocks, brittle polymers, ceramics, etc. On the other hand, the notch stress intensity factors (NSIFs) are vital parameters in brittle fracture assessment of V-notched structures. Therefore, computation of NSIFs in FPB specimens is of practical interest to engineers and researchers. Since the available methods for calculating the NSIFs are often cumbersome and need complicated calculations, it is preferred to show them as a set of dimensionless parameters for the FPB specimen. In this research, the finite element method coupled with a recently developed algorithm called FEOD is employed to calculate the NSIFs of a FPB specimen for several V-shape notches and for different combinations of mode I and mode II. The obtained NSIFs are then converted to dimensionless parameters called notch shape factors and are illustrated in a number of figures. It is shown that depending on the notch depth and the location of loading points, full mode mixity from pure mode I to pure mode II can be provided in the FPB specimen. The numerical results obtained in this research are verified by using very limited results reported earlier in literature.

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Abbreviations

a:

Notch length (m)

A n  (n = 1, 2, . . .):

Mode I coefficients of the notch tip asymptotic field \({\left({N\,{\rm m}}_{n}^{-(1+\lambda)}\right)}\)

B n  (n = 1, 2, . . .):

Mode II coefficients of the notch tip asymptotic field \({\left({N\,{\rm m}}_{n}^{-(1+\lambda)}\right)}\)

E :

Young’s modulus (N m−2)

\({K_{\rm I}^{\rm V}}\) :

Mode I notch stress intensity factor \({\left({N\,{\rm m}}_{1}^{-(1+\lambda)}\right)}\)

K I :

Mode I stress intensity factor (N m−1.5)

\({K_{\rm II}^{\rm V}}\) :

Mode II notch stress intensity factor \({\left({N\,{\rm m}}_{2}^{-(1+\lambda)}\right)}\)

K II :

Mode II stress intensity factor (N m−1.5)

L, L 1, L 2, L 3, L 4, W :

Geometrical parameters of FPB notched specimens (m)

\({M_{V}^{e}}\) :

Notch mode mixity

P:

Applied load (N)

r :

Radial coordinate (m)

t :

Specimen thickness (m)

\({Y_{\rm I}^{\rm V}}\) :

Mode I notch shape factor

\({Y_{\rm II}^{\rm V}}\) :

Mode II notch shape factor

θ :

Angular coordinate

α :

Parameter related to the notch angle

γ :

Notch opening angle

\({\lambda_{n}^{\rm I}}\) :

Mode I eigenvalues

\({\lambda_{n}^{\rm II}}\) :

Mode II eigenvalues

ν :

Poisson’s ratio

σ x , σ y , τ xy :

Notch tip stresses in Cartesian coordinate (N/m2)

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Authors and Affiliations

  1. Fatigue and Fracture Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, 16846, Tehran, Iran

    M. R. Ayatollahi, M. Dehghany & Z. Kaveh

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  1. M. R. Ayatollahi
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  2. M. Dehghany
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  3. Z. Kaveh
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Correspondence to M. R. Ayatollahi.

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Ayatollahi, M.R., Dehghany, M. & Kaveh, Z. Computation of V-notch shape factors in four-point bend specimen for fracture tests on brittle materials. Arch Appl Mech 83, 345–356 (2013). https://doi.org/10.1007/s00419-012-0654-0

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