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Numerical Analysis of Crack Initiation Direction in Quasi-brittle Materials: Effect of T-Stress

  • Research Article - Mechanical Engineering
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Abstract

A two-dimensional finite element analysis was adopted to assess the effect of T-stress on predicting crack initiation angle in a quasi-brittle material. Asymmetric semicircular PMMA specimen containing a vertical edge crack subjected to three-point bending was employed. The specimen was assumed as an isotropic and homogeneous material. Relative crack length ratios of 0.3, 0.4, 0.5, 0.6 and 0.7 were examined. Several relative bottom span ratios were included to develop a wide range of mixed-mode I/II loading conditions. The conventional maximum tangential stress (MTS) criterion could not precisely predict the crack initiation angle through the total range of pure mode I to pure mode II. The generalized maximum tangential stress (GMTS) criterion showed a significant effect of T-stress on the numerical prediction of the crack initiation angles in PMMA specimens. In the present study, neglecting the T-stress in the MTS criterion overestimates the crack initiation angle. The numerical predictions using the GMTS criterion showed a good agreement with the relevant experimental data found in the literature. The ability of GMTS in predicting the crack initiation angle is improved by considering the T-stress.

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Abbreviations

ASCB:

Asymmetric semicircular bend specimen

EMTSN:

Extended maximum tangential strain

FE:

Finite element

MTS:

Maximum tangential stress

MTSN:

Maximum tangential strain

GMTS:

Generalized maximum tangential stress

GSED:

Generalized strain energy density

PMMA:

Polymethylmethacrylate

SCB:

Semicircular bend specimen

SED:

Minimum strain energy density

SIF:

Stress intensity factor

a :

Crack length

da :

Smallest element size

a/R :

Ratio of crack length to disk radius

E :

Modulus of elasticity

G :

Maximum energy release rate

K I, K II :

Mode I and mode II SIFs, respectively

K IC :

Mode I fracture toughness

M e :

Mode mixity parameter

P :

Applied vertical load

R :

Semi-disk radius

r, θ :

Polar coordinate components

r c :

Fracture process zone size

S 1 , S 2 :

Left and right bottom span lengths, respectively

S 1 /R, S 2 /R :

Ratio of left span distance to disk radius and right span distance to disk radius, respectively

t :

Semi-disk thickness

T* :

Normalized T-stress

Y I , Y II :

Mode I and mode II geometry factors, respectively

ν :

Poisson’s ratio

θ o :

Crack initiation angle

σ t :

Uniaxial tensile strength

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  1. Materials Engineering Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt

    A. S. Fayed

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Fayed, A.S. Numerical Analysis of Crack Initiation Direction in Quasi-brittle Materials: Effect of T-Stress. Arab J Sci Eng 44, 7667–7676 (2019). https://doi.org/10.1007/s13369-019-03860-4

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