A notch root radius to attain minimum fracture loads in plates weakened by U-notches under Mode I loading

Abstract

The paper deals with the minimum value of a fracture load, with respect to the notch root radius, in plates weakened by U-notches under Mode I loading. It has been found that the fracture load has a minimum value at a critical value of the notch root radius (ρ), using four criteria, namely, Mean Stress (MS), maximum tangent stress or Point Stress (PS), Critical Strain-Energy (CSE) and Averaged StrainEnergy Density (ASED). Using a characteristic length (l ch ), which is a function of material properties, the results showed that the dimensionless critical notch root radius (ρ/l ch ) cr depended on w/a ratio (the specimen width to the notch depth), Poisson ratio, and loading condition (tensile or bending loading) under Mode I loading. In other words, according to these criteria, a notch root radius different from zero exists, providing a minimum fracture load. Therefore, a crack is not more dangerous rather than a U-notch under Mode I loading. This critical notch root radius is important for a quasi-brittle material, but may not be significant for brittle ones in practical engineering situations. Good agreement was found between theoretical predictions and experimental results on Al356-T6.

Numerical Simulation of the Influence of Width of a Prefabricated Crack on the Dimensionless Stress Intensity Factor of Notched Semi‐Circular Bend Specimens

“…Kolhe et al [35] explored the influence of the crack tip radius on the fracture toughness of CB specimens. Barati and Alizadeh [36] performed research on the ratio of the notch tip curvature to the notch depth and its influence on the plane strain fracture toughness. Cicero et al [37] examined the influence of the three-point bending beam notch radius on the dimensionless stress intensity factor and fracture toughness by the theory of critical distances (TCD) and explicated the influencing mechanism of the notch tip radius by scanning electron microscopy.…”

Study on Micro-Crack Induced Precision Severing of Quartz Glass Chips

“…The critical distances r c * and r c are defined from the coordinate origin O and the microgroove-apex, respectively (see Figure 1 b). The ideal severing force F c * was described as follows [ 15 ]: where σ max and σ nom are the maximum stress and the nominal stress at microgroove-apex, respectively. K t is the stress concentration factor.…”

“…In Equation (13), the K t is achieved in the case of the U-notch with β v = 0 [ 15 ], but it was calculated by the fitting of experimental data in this study. This is because a microgroove with β v > 0 was employed in micro-crack-induced severing.…”

“…Moreover, these criteria were used to predict compressive notch fracture toughness [ 13 , 14 ]. The minimum fracture loading of a U-notches plate was introduced by means of MS and PS criteria [ 15 ]. In the case of low and high loading rates, it was found that the loading rate produced little influence on the maximum load for the V-notch on fracture [ 16 ].…”

Bionic Design of the Bumper Beam Inspired by the Bending and Energy Absorption Characteristics of Bamboo

“…For example, Shao et al [4–6] proposed that bamboo nodes were crucial to improve stiffness and stability of the slender bamboo culm during growth. Barati and Alizadeh [7] claimed that nodes support the culm to prevent failure due to local buckling. Meng et al [8] studied the energy absorption characteristics and material parameters of the bamboo species by drop-weight and dynamic tensile tests.…”