Abstract
Analysis of a compact compression specimen used for fracture toughness evaluation of cementitious materials is carried out by the finite element method using isoparametric elements. Both triangular and rectangular elements were used with those surrounding the crack tip being of the quarter point type. Solutions were obtained for different mesh subdivisions and convergenece curves for the stress intensity factor were obtained by several methods based on extrapolation and energy techniques. It is found that monotonic convergence was obtained for all cases considered. Employing uniformly graded rectangular element representations converged solutions for the stress intensity factor (assuming a 1 percent convergence criterion) were obtained by the energy methods using a total of 720 degrees of freedom for solving half the structure.
Tests on modified 100 mm cubes with symmetrical notches were conducted to determine the fracture toughness. The fracture toughness was calculated from the stress intensity factor and the maximum load obtained from the tests which were conducted in a stiff Instron testing machine. The fracture toughness is found to be independent of the size of the notch.
Nomenclature
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a = crack size in tension zone, semi-minor axis of an elliptic surface
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c = crack size in compression zone
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ds = an element of an arc length
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E = elasticity modulus
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G = strain energy release rate
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G c= critical strain energy release rate
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k = stress intensity factor
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k c= fracture toughness
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L = edge length of finite element
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m−n = natural coordinate system
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n 1, n 2 = direction cosines
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P = compressive load
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r, θ = polar coordinate system — origin at crack tip
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T = traction vector
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u = displacement function, displacement vector
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u i = in-plane displacement of node i
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u x, u y= in-plane displacement in x and y directions respectively
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U = strain energy
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W = strain energy density
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x − y = rectangular coordinate system
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σ x , σ y σ xy = direct and shear stresses
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ε x , ε y , ε xy = direct and shear strains
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µ = Poisson's ratio
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Ω = rigidity modulus
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Sabir, B.B. The performance of isoparametric finite elements in stress intensity factor determination. Int J Fract 72, 259–275 (1995). https://doi.org/10.1007/BF00037314
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DOI: https://doi.org/10.1007/BF00037314