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• An asymptotic solution was proposed for the elastic stress and displacement fields in the vicinity of blunt V-notches. • Although the solution is approximate and simple, it provides reasonable accuracy. • The proposed solution is able to describe the stress field around some other types of notches with reasonable accuracy. • For the case of sharp V-notches, the solution is exactly the same as what was proposed previously. • Eigenvalues and some of the relations are equal to those of sharp V-notches. This paper provides a simple approximate solution for the stress and displacement fields around the blunt notches in bimaterial media under in-plane loading. The Kolosov-Muskhelishvili's method is used to determine the stress and displacement components according to the complex potential functions. Then, by imposing the boundary conditions of bimaterial blunt V-notches, the asymptotic solutions of the stress and displacement fields are obtained. Due to the convenient selection of the boundary conditions, the solution is shown to be the same as the one proposed by Williams' for sharp V-notches, in case the notch tip radius becomes zero. Finally, finite element method is employed to benchmark the precision of the suggested asymptotic solution. Some sample examples are selected, and the results obtained by the proposed analytical solution are compared with the numerical results of the finite element method. It is demonstrated that the proposed stress field is not only applicable to obtain the stress distribution around the blunt V-notches but also is suitable for stress field calculation around some other types of bimaterial notches. [ABSTRACT FROM AUTHOR]

Stress distribution is analyzed around the tip of V-notches in a disk-type test sample, called V-notched Brazilian disk (V-BD), under in-plane mixed mode loading conditions. The notch stress intensity factors (NSIFs) which are basic parameters in brittle fracture assessment of V-notched components are computed for the V-BD specimen by using the finite element (FE) method for different notch geometries and a wide range of mode mixities from pure positive mode I to pure mode II loading and from pure mode II to pure negative mode I loading conditions. Then, in order to make use of the NSIFs more conveniently in practical applications, the NSIFs are converted to the dimensionless parameters, called the notch shape factors (NSFs). These parameters are useful to compute more rapidly and conveniently the NSIFs in the V-BD specimen for various notch angles and different notch tip radii. The obtained results are partially validated by means of some results reported in the open literature and also by numerical analysis of stress distribution around the V-notch. Very good agreements are shown to exist between the stress distributions obtained from the computed NSIFs and those directly resulted from the FE analysis. [ABSTRACT FROM AUTHOR]

In this study, an easy procedure is proposed to improve the strength of Single Lap Joints (SLJs) by introducing a notch in the adherends right after the overlap length. At first, the effect of different notch parameters on the peel, shear and von Mises stress distributions of the adhesive mid-plane layer is investigated by using the Finite Element (FE) method. The considered parameters are the notch angle, the notch width, the notch depth, and the notch distance from the overlap length. Afterwards, a simple 90-degree notch angle which can be easily manufactured is selected for adherend notching based on the numerical results. In addition, in order to experimentally investigate the effects of different notch parameters on the failure load of adhesive joints, five various notch depths with two different adhesive curing methods are considered. Finally, the experimentally obtained fracture loads are compared with the theoretical ones which are based on the predictions of von Mises stress and peel. The results show that using the adherend notching can significantly improve the load bearing capacity of SLJs. For instance, a simple notch with 20% notch depth ratio can improve the load bearing capacity of the SLJ about 60%. [ABSTRACT FROM AUTHOR]

• An analytical stress field solution is developed for sharp and blunt notches. • The over-deterministic approach is used for deriving the coefficients of stress field. • Finite element method is employed to validate the results of the analytical solution. • Significant contribution of higher order terms is shown for blunt and sharp notches. The complex potential method is used to derive the asymptotic stress field around the V-notches with end holes (VO-notches). Although the classical methods take into account only the singular stress terms, herein the stress distribution is presented in the asymptotic form considering both singular and non-singular terms. In order to calculate the coefficients of the singular and non-singular terms of the stress distribution, an over-deterministic method is employed. Based on the over-deterministic method, the nodal displacement values for a large number of points around the VO-notch are obtained from finite element analysis and fitted to the asymptotic displacement field. The method is then applied to two laboratory test specimens containing VO-notches with three different notch angles and four notch tip radii under mode I loading condition. Moreover, by comparing the results obtained from the truncated stress series with the output stress results of the finite element analysis, the accuracy of the calculated coefficients is evaluated. Finally, by using some numerical examples, it is shown that the proposed asymptotic stress distribution can appropriately describe the stress field around sharp V-, key-hole and U-notches. The results obtained for all mentioned notch types show that neglecting the higher order terms can result in significant errors while considering the first two non-singular stress terms presents very good results. [ABSTRACT FROM AUTHOR]

• Elastic stress and displacement solutions around blunt V-notches were revisited. • Asymptotic solutions taking account of higher order terms were derived. • Coefficients of asymptotic series were calculated using least square method. • Classical singular term solution can be of significant errors even along notch border. This paper presents the in-plane asymptotic displacement and stress fields for blunt V-notched components based on Kolosov–Muskhelishvili's approach. In the first part, the displacement and stress components in the polar coordinate system are determined by choosing appropriate complex potential functions. In order to construct the notch geometry, the Neuber's mapping relation is utilized. Then, the notch boundary conditions are imposed to calculate the free parameters of the stress distribution. Eventually, the stress and displacement components are calculated in the Cartesian and polar coordinates in the forms of series expansion. In the second part, the coefficients of series expansions are computed by using the least square method (LSM). The blunt V-notched Brazilian disk (BV-BD) specimen under mixed mode loading is used as an example to verify the proposed procedure. The stress components in arbitrary distances and directions are determined for different blunt V-notches in order to evaluate the accuracy of the calculated stress series solutions and their associated coefficients. The numerical results indicate that a single-term solution can lead to considerable errors, and to achieve good accuracy in the stress field calculation, one should take account of at least three terms in the stress series solution. [ABSTRACT FROM AUTHOR]

In the present study, the asymptotic stress and displacement solutions related to mixed mode I/II loading are calculated in the vicinity of the V-notches with end holes (VO-notches). After deriving the asymptotic stress and displacement fields, in order to calculate the coefficients of the series, a numerical technique called the over-deterministic method is utilized. According to the over-deterministic method, the unknown coefficients are calculated by fitting the asymptotic displacement field to the nodal displacement values. To show the accuracy of the derived asymptotic stress series and the effectiveness of higher order terms, the Brazilian disk specimen is modeled using finite element analysis. Different examples under pure mode I, pure mode II and mixed mode I/II loading for three different notch opening angles and four notch tip radii are considered and the coefficients of stress series are computed for each example. Finally, the obtained coefficients are used to compare the stress distribution of the truncated stress series with its relevant finite element values. The results show that considering the singular terms alone will generate large amounts of errors while very good accuracy could be achieved by considering the higher order terms. [ABSTRACT FROM AUTHOR]

In the present study, the failure load improvement obtained from adherend notching for adhesive single lap joints (SLJs) is studied. In the first step, a finite element (FE) analysis is employed to investigate the influence of different adherend notch parameters including the notch width and the notch depth on the adhesive behavior. Then, the peel, shear, longitudinal and von Mises stress distributions in the adhesive mid-plane layer are compared for different adherend notch parameters. In the next step and based on the numerical results, four values of notch depth are selected to perform experiments. For each notch configuration, one ductile and one brittle adhesive are considered. The results demonstrated that the failure load improvement due to the adherend notching is dependent on both the notch depth and the mechanical properties of the adhesive material. For instance, the average value of the failure loads in SLJs containing a brittle adhesive and a notch depth ratio of 20% was improved about 100% while the improvement in SLJs with a ductile adhesive with the same notch depth was about 25%. • Adherend notching is used to improve failure load in single lap adhesive joints (SLJs). • Tensile tests are performed to obtain failure loads with and without adherend notching. • Both brittle and ductile type adhesive materials are used for preparing adhesive joints. • Finite element results show reduced stresses when adherend is notched. • Improvement in failure load was more significant when brittle adhesive was used. [ABSTRACT FROM AUTHOR]

• A new analytical solution was developed for stress field around blunt V-notches. • The proposed asymptotic solution has higher accuracy than previous solutions. • No conformal mapping was used for describing the notch geometry. • The solution is capable of specifying stress distribution around some other types of notches with proper accuracy. • Effect of higher order terms in the proposed stress field is less than that of previous solutions. This paper presents a new relation for the stress field around blunt and sharp notches in a linear elastic body. The stress components are determined by using Kolosov-Muskhelishvili's approach and considering proper complex potential functions. Then, to reduce the number of free parameters in the stress components, the boundary conditions of blunt V-notches are satisfied without applying a conformal mapping method. After replacing the free parameters, the stress components are calculated in the form of two series expansions related to mode I and mode II loading. In the case of sharp V-notches, it is demonstrated that the eigenvalues of the problem are the same as those of the well-known Williams' solution. Afterwards, the stress intensity factors of blunt V-notches are presented by utilizing two different approaches. In order to evaluate the accuracy of the proposed relation, finite element analysis is conducted on a number of different types of notches and the results are compared with those of the presented and classical solutions. It is shown that the proposed relation is more accurate than the best available solutions for blunt V-notches. Furthermore, the proposed stress field solution is capable of specifying the stress distribution around some other types of notches with proper accuracy. Finally, some advantages of the proposed stress relations in comparison with other stress field solutions are presented and discussed. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• DIC method is utilized to determine the stress field around blunt notches. • A variety of notch geometries including U, VO, and Keyhole is included. • Different spectrums of mixed-mode loading using the BD test are investigated. • The effect of HOTs on the stress field of blunt notched components is investigated. An appropriate evaluation of the stress field for designing new or optimizing existing engineering structures is required. The primary goal of this paper is to use the digital image correlation (DIC) approach to ascertain the stress field around the root of various blunt notches. At first, extensive tests were performed using the Brazilian Disc (BD) specimen containing three distinct notches (U, VO, and Keyhole) under diverse loading conditions, including pure mode I, pure mode II, and mixed-mode I/II. The displacement fields output from the DIC experiments were employed as the input data for a computer program, and the coefficients of the stress and displacement fields were then determined utilizing the over-deterministic technique. Afterward, the computed coefficients were used to calculate the analytical stress field around the notch root by considering singular and higher-order terms for each notch type. Subsequently, the finite element (FE) method was employed to verify the accuracy of the stress field obtained from the DIC experiments. In addition, the influence of some major parameters such as notch opening angle, notch tip radius, and geometry on the stress distribution was investigated. This study validated the efficiency of the DIC approach in determining the unknown stress coefficients of rounded notches, especially the first non-singular term of the stress expansion, which is revealed to have a considerable impact on appraising the exact stress field around the notch curvature. [ABSTRACT FROM AUTHOR]