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Fracture behaviour of V-notched specimens is assessed using two energy based criteria namely the averaged strain energy density (SED) and Finite Fracture Mechanics (FFM). Two different formulations of FFM criterion are considered for fracture analysis. A new formulation for calculation of the control radius Rc under pure Mode II loading is presented and used for prediction of fracture behaviour. The critical Notch Stress Intensity Factor (NSIF) at failure under Mode II loading condition can be expressed as a function of notch opening angle. Different formulations of NSIFs are derived using the three criteria and the results are compared in the case of sharp V-notched brittle components under in-plane shear loading, in order to investigate the ability of each method for the fracture assessment. For this purpose, a bulk of experimental data taken from the literature is employed for the comparison among the mentioned criteria.

Fracture behaviour of V-notched specimens is assessed using two energy based criteria namely the averaged strain energy density (SED) and Finite Fracture Mechanics (FFM). Two different formulations of FFM criterion are considered for fracture analysis. A new formulation for calculation of the control radius Rc under pure Mode II loading is presented and used for prediction of fracture behaviour. The critical Notch Stress Intensity Factor (NSIF) at failure under Mode II loading condition can be expressed as a function of notch opening angle. Different formulations of NSIFs are derived using the three criteria and the results are compared in the case of sharp V-notched brittle components under in-plane shear loading, in order to investigate the ability of each method for the fracture assessment. For this purpose, a bulk of experimental data taken from the literature is employed for the comparison among the mentioned criteria.

In the present work a simple and efficient least squares method is implemented for accurate estimation of notch stress intensity factors (NSIFs) of sharp V-notches. Finite element (FE) stress components near a notch tip is used in the present method for determining the NSIFs. Pure mode I and mixed mode (I/II) examples are considered for numerical investigations. The mixed mode stress components are disintegrated into opening mode and shear mode stress components to separate out the mode I and mode II singularities. Thereafter, least squares method is implemented to calculate mixed mode NSIFs. The present method is easy to incorporate in existing standard finite element codes. The results obtained by the present method are found to be in good agreement with the published data.

A multi-segment sharp-crested V-notch weir (SCVW) was used both theoretically and experimentally in this study to evaluate the length of the hydraulic jump at the downstream of the weir. For this aim, a SCVW with three triangular segments at different tail-water depths (tailgate angles), and ten different discharges at a steady flow condition were investigated. Then, the most effective parameters on the length of the hydraulic jump are defined and several parametric and nonparametric regression models, namely multi-linear regression (MLR), additive non-linear regression (ANLR), multiplicative non-linear regression (MNLR), and generalized regression neural network (GRNN) models are compared with two semi-empirical regression models from the literature. The results indicate that the GRNN model is the best model among the selected models. These results are also linked to the nature of the hydraulic jump and the turbulent behavior of the phenomenon, which masks the experimental results with outliers.

The second term of stress field around a sharp V-notch under mode I loading was investigated. It was found that in the Cartesian coordinate system, unlike the T-stress in cracked bodies, the second term of Williams’ expansion in all three stress components is nonzero and its value depends on the distance from the notch tip. Thus, according to the stress based fracture criteria, in addition to the singular term, the first non-singular term may also play an important role in brittle fracture of sharp V-notched components under mode I loading.

Singular fields near sharp V-notch for power law creep material are examined under plane strain condition. In order to obtain the singular order, stress function is adopted in the control equations under polar coordinate system. C-integral method and iterative scheme are conducted to achieve the singular order in steady state. In transient stage, due to the effect of time parameters, the solution from finite element analysis (FEA) is discussed. The theoretical solution based on the C-integral and iterative method is compared with numerical simulation. Under steady-state condition, the absolute singular order only depends on the creep exponent and the V-notch angle, and becomes large with the decrease of the exponent and the angle. But for the transient, the order corresponds to the time either.

A unified brittle fracture criterion for cracks and V-notches under mixed mode loading is proposed by extending the maximum circumferential stress criterion and Novozhilov’s criterion. The mixed mode fracture toughness and crack orientation of PMMA plates with a sharp V-notch are predicted by the proposed criterion. Tests were also carried out in order to investigate the mixed mode fracture of the PMMA plates. The fracture criterion is validated by comparison to experimental results.

The survey of research on the problems of fracture mechanics of solids with V-shaped notches is discussed. The methods of solution of plane problems of the elasticity theory for domains with angular points on boundary contours are considered. Special attention is paid to the results of the research which authors obtained applying the unified approach to the solution of stress concentration problems in the neighborhood of the vertices of sharp and rounded V-notches. The solutions of elastostatics problems for domains with rounded V-shaped notches were obtained by singular integral equation method. Based on the relation between stress intensity factor at the sharp notch vertex and the stress concentration factor at the vertex of rounded V-notch (notch with straight edges and vertex rounded with circular arc), the stress intensity factors for V-notches in various domains were obtained. The presented examples include notch stress intensity factors for periodically placed notches in the edge of half-plane, diamond and lens-like holes in infinite plane. Through limit transition from the system of periodically placed diamond-shaped ovals to infinite double-sided notch, the stress concentration factors for rounded deep V-notch and the notch stress intensity factors for sharp notch were obtained. The comparison between calculated data and known solutions for the hyperbolic notch documents strong influence of the notch shape in the neighborhood of the rounded vertex on the stress concentration values for small vertex radii. The numerical results are presented not only in graphical form but also the numerous approximation formulas are given. Based on the solution of the nonlinear problem of rounded V-notch with plastic strip at the vertex, the new deformation fracture criterion is proposed. This criterion contains only standard strength parameters and it is intended to determine fracture toughness of the elements with rounded notches made of quasi-brittle materials.

The method of singular integral equations was applied to determine the stress intensity factors for a system of cracks emanating from the vertex of an infinite rounded V-notch subjected to symmetric loading. The numerical values were obtained for two cases—the case of a single crack and the case of a system of two cracks of equal length. The influence of the rounding radius of the vertex of the notch and its opening angle on the stress intensity factors at the crack tips was analyzed. The solution obtained as a result has a general nature—the stress intensity factors at the crack tip are expressed as a function of the V-notch stress intensity factor and, hence, this solution could be treated as an asymptotic relation for finite bodies with deep V-notches subjected to symmetric loads.

The article deals with the determination of the influence of the relative width of an approach channel with a rectangular cross-section on the discharge of clean water flowing over thin-plated weirs with a triangular notch and zero height of the weir above the bottom of the approach channel. To evaluate the influence, the Kindsvater-Shen equation was modified by introducing the basic effective discharge coefficient and the coefficient of the relative width of the approach channel. The coefficient of the relative width of the approach channel was determined based on the evaluation of data from three extensive experimental research investigations. It is valid for the entire possible range of relative widths of the approach channel and for the range of notch angles from 5.25° to 91.17°. The relative error of discharge determination is approximately up to ±2% over the entire range of discharges used in the conducted experimental research. The evaluation made it possible to determine the boundary distinguishing the partially contracted weirs from the fully contracted weirs in terms of impact on discharge.