Experimental and Theoretical Assessment of Brittle Fracture in Engineering Components Containing a Sharp V-Notch

A criterion was proposed to predict brittle fracture in engineering components containing sharp V-shaped notches and subjected to mixed mode I/II loading. The criterion, called SV-MTS, was developed based on the maximum tangential stress (MTS) criterion proposed originally for analyzing crack problems. The curves which are obtained from the SV-MTS criterion could be used conveniently to predict the fracture resistance and also the notch bifurcation angle in sharp V-notched components under pure mode II and also mixed mode loading. To evaluate the validity of the proposed criterion, a set of fracture tests were conducted on a new test specimen, called sharp V-notched Brazilian disc (SV-BD), under mixed mode loading conditions. It is shown that the experimental results obtained from PMMA specimens are in very good agreement with the curves of SV-MTS criterion.     

Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen

A brittle fracture criterion is proposed for predicting fracture toughness of U-shaped notches under pure mode II loading. The criterion, called UMTS, is developed based on the maximum tangential stress (MTS) criterion. The UMTS criterion can be generally used for determining the mode II fracture toughness of U-notched components as well as the fracture initiation angle in U-shaped notches under pure mode II loading. To verify the validity of the proposed criterion, a set of experiments were carried out on the U-notched Brazilian disc (UNBD) specimens made of PMMA and also soda-lime glass. It is shown that there is a good agreement between the results of the UMTS criterion and the experimental results both for fracture toughness and for the fracture initiation angle under pure mode II conditions.     

Fracture analysis of V-notched components – Effects of first non-singular stress term

The effect of the first non-singular stress term on the fracture behavior of notched structures was investigated under symmetric geometry and loading conditions. According to the Williams series expansion, for a large domain of notch angles the non-singular stress terms of sharp notches are functions of complex eigenvalues and their corresponding complex coefficients. Hence, a new representation of stress field near the notch tip was developed in which the higher order terms are expressed as several explicit functions of real and imaginary parts of both the complex eigenvalues and their complex coefficients. A critical stress criterion was then applied to the new stress formulations to assess the influence of the first non-singular stress term on the apparent fracture toughness. Several finite element analyses were also performed on two laboratory specimens in order to show the effects of first non-singular term on the near field stress distribution of notched specimens. The results demonstrated that neglecting the first non-singular stress term could lead to significant errors in predicting the apparent fracture toughness of notched components.     

Mixed mode fracture in soda lime glass analyzed by using the generalized MTS criterion

Glasses are known to be vulnerable to tensile stresses particularly in the presence of pre-existing cracks. Since cracks in glass components are very often subjected to mixed mode loading, several researchers have studied mixed mode fracture in soda lime glass using different test specimens. Among these specimens, the cracked Brazilian disc specimen has been used most frequently by investigators. However, it is shown in this paper that the previously reported experimental results obtained from the cracked Brazilian disc specimen for several glasses are always underestimated by fracture theories like the maximum tangential stress criterion. A generalized maximum tangential stress criterion is then employed for predicting the mixed mode fracture test results. It is shown that the experimental results obtained from the cracked Brazilian disc specimen and reported in the literature for soda lime glass can be estimated very well when the generalized criterion is used. It is also shown that the same criterion can be used for predicting the test results available in the literature for brittle fracture in a glass plate containing an angled center-crack.     

Computation of V-notch shape factors in four-point bend specimen for fracture tests on brittle materials

Four-point bend (FPB) specimen is an important test sample in mixed mode fracture study of notched components made from brittle materials like rocks, brittle polymers, ceramics, etc. On the other hand, the notch stress intensity factors (NSIFs) are vital parameters in brittle fracture assessment of V-notched structures. Therefore, computation of NSIFs in FPB specimens is of practical interest to engineers and researchers. Since the available methods for calculating the NSIFs are often cumbersome and need complicated calculations, it is preferred to show them as a set of dimensionless parameters for the FPB specimen. In this research, the finite element method coupled with a recently developed algorithm called FEOD is employed to calculate the NSIFs of a FPB specimen for several V-shape notches and for different combinations of mode I and mode II. The obtained NSIFs are then converted to dimensionless parameters called notch shape factors and are illustrated in a number of figures. It is shown that depending on the notch depth and the location of loading points, full mode mixity from pure mode I to pure mode II can be provided in the FPB specimen. The numerical results obtained in this research are verified by using very limited results reported earlier in literature.     

Analytical representation of the non-square-root singular stress field at a finite angle sharp notch

The stress field near the tip of a finite angle sharp notch is singular. However, unlike a crack, the order of the singularity at the notch tip is less than one-half. Under tensile loading, such a singularity is characterized by a generalized stress intensity factor which is analogous to the mode I stress intensity factor used in fracture mechanics, but which has order less than one-half. By using a cohesive zone model for a notional crack emanating from the notch tip, we relate the critical value of the generalized stress intensity factor to the fracture toughness. The results show that this relation depends not only on the notch angle, but also on the maximum stress of the cohesive zone model. As expected the dependence on that maximum stress vanishes as the notch angle approaches zero. The results of this analysis compare very well with a numerical (finite element) analysis in the literature. For mixed-mode loading the limits of applicability of using a mode I failure criterion are explored.     

A generalized stress intensity factor to be applied to rounded V-shaped notches

In the presence of sharp (zero radius) V-shaped notches the notch stress intensity factors (N-SIFs) quantify the intensities of the asymptotic linear elastic stress distributions. They are proportional to the limit of the mode I or II stress components multiplied by the distance powered 1 − λ_i from the notch tip, λ_i being Williams’ eigenvalues. When the notch tip radius is different from zero, the definition is no longer valid from a theoretical point of view and the characteristic, singular, sharp-notch field diverges from the rounded-notch solution very next to the notch. Nevertheless, N-SIFs continue to be used as parameters governing fracture if the notch root radius is sufficiently small with respect to the notch depth.Taking advantage of a recent analytical formulation able to describe stress distributions ahead of rounded V-notches, the paper gives a generalized form for the notch stress intensity factors, in which not only the opening angle but also the tip radius dimension is explicitly involved. Such parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case.     

The mixed mode brittle fracture criteria in siliding mode fracture

It is well-known that the present mixed mode brittle fracture criteria are all theopening mode fracture criterion.We consider that mixed mode brittle fracture of slidingmode fracture exists too.Hence we propose three criteria of mixed mode brittle fracture ofsliding mode fracture;:the radial shearing stress criterion,the maximum shearing stresscriterion and the distortional strain-energy-density criterion.Thus,we can overall explainthe phenomena of brittle fracture in the structural elements with cracks.     

The effect of notches on the fracture behavior in NiTi shape memory alloys

Tensile fracture experiments have been performed on double-notch plate form specimens with different notch types and sizes. Specimen without notch is also studied. The macro-mechanical responses as well as detail examination of the fracture surface have been carried out. The stress, plastic strain and phase transformation fields are analyzed by finite element (FE) simulations using a pseudoelastic constitutive model which considers the permanent plastic deformation. Experimental results show that different type of notches can influence not only the macro-mechanic pseudoelastic but also plastic behaviors of the specimens. Both notch type and notch size affect the mechanism of crack initiation. Notch size influences the specimen behavior in different way for different type of notches. Most of the experimental observations are interpreted properly by the FE results.     

Inverse notch sensitivity: Cracks can make nonwoven fabrics stronger

The strength of materials is always reduced in the presence of notches and cracks and this phenomenon – known as notch sensitivity – is critical in structural design. Good structural materials (ductile metals, elastomers) tend to be notch insensitive, which was considered to be the optimum behavior. Here, we report that inverse notch insensitivity (where the failure stress of the notched specimen is higher than that of the unnotched counterpart) can be achieved in polypropylene nonwoven fabrics. This behavior is only possible because of the peculiar microstructure of nonwoven fabrics, in which fracture of interfiber bonds provides a source of non-linear deformation and leads to a change in the network topology. The former facilitates crack tip blunting, spreading damage in the ligament, while the re-orientation of the fibers perpendicular to the notch plane strengthens the material and improves the maximum load bearing capability.     

Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading

Fracture phenomenon was investigated both experimentally and theoretically for a type of coarse-grained polycrystalline graphite weakened by a U-shaped notch under mixed mode loading. First, 36 disc-type graphite specimens containing a central U-notch, so called in literature as the U-notched Brazilian disc (UNBD), were prepared for four different notch tip radii and the fracture tests were performed under mode I and mixed mode I/II loading conditions. Then, the experimentally obtained fracture loads and the fracture initiation angles were predicted by using the U-notched maximum tangential stress (UMTS) and the newly formulated U-notched mean stress (UMS) fracture criteria. Both the criteria were developed in the form of the fracture curves and the curves of fracture initiation angle, in terms of the notch stress intensity factors (NSIFs). The results showed that while the criteria could predict successfully the experimental notch fracture toughness values, the UMS criterion provides slightly better predictions than the UMTS criterion, particularly for shear-dominant deformations. Also, found in this research was that the curves of fracture initiation angle were almost identical for the two criteria which both could predict well the experimental results.     

U形切口的有限断裂准则

有限断裂力学准则综合了应力和能量参数,假设裂纹或切口端部有限裂纹长度的增长．特别地,该有限裂纹的长度不是材料的基本常数,而是与构件的结构有关．基于U形切口两种形式：点方式和线方式有限断裂准则,对文献中的铝合金U形切口三点弯曲断裂实验进行了分析验证．一方面基于材料的断裂韧度和抗拉强度,预测切口件断裂载荷;另一方面根据几组不同的切口根部半径及其对应的临界切口应力强度因子,同时估算材料的断裂参数：断裂韧度和抗拉强度．将点方式和线方式两种不同形式有限断裂准则的预测结果,与平均周向应力准则、最大周向应力准则以及文献中相关结果进行了比较得出：无论是预测断裂载荷还是估算材料断裂参数,线方式有限断裂准则,与文献中相关结果比较吻合,尤其是估算的断裂韧度精度较高．     

The dynamic behaviour of sharp V-notches under impact loading

The dynamic behaviour of sharp V-notches which are either symmetric or oblique to the longitudinal boundary of a homogeneous elastic and isotropic strip subjected to an impact plane pulse was studied by the method of caustics. The stress pulse impinging on the flanks of the notch reflects and diffracts in different ways depending on the geometry of the notch relative to the coming pulse. For compressive stress pulses a stress concentration at the bottom of the notch does not create a crack propagation phenomenon, whereas for tensile pulses there is a possibility for an incubation, nucleation and eventual propagation of a crack. A complete experimental study of the incubation nucleation and propagation of cracks from the bottoms of notches in thin strips under tensile stress pulses was undertaken, whereas for compressive stress pulses the stress concentration at the bottom of the notch was evaluated. Interesting results were disclosed concerning the reinforcement of pulses by reflection and caging in, the evolution of stress concentration at the notch and the mode of crack propagation inside the plate. Dynamic stress intensity factors were evaluated all over the paths of crack propagation indicating a close intimacy between crack velocity and values of SIFs.     

Dislocation shielding and flaw tolerance in titanium nitride

Titanium nitride is a very brittle and flaw sensitive ceramic material at temperatures below 750 °C. In this study, we present experimental evidence of room temperature dislocation-based plasticity in the material as well as insensitivity to flaws in form of single edge notches. We performed in-situ fracture experiments inside the transmission electron microscope on 150-300 nm thick, 5 μ wide freestanding films fabricated from titanium nitride/titanium multi-layers with titanium nitride as the notched and titanium as un-notched layers. The calculated stress concentration factor for the 800 nm to 1.5 μ long notches were greater than 8, however, the terminal cracks always nucleated at the un-notched edge of the specimens and not at the notch tip. To explain such remarkable flaw tolerance, we observe motion of dislocations (pre-existing and nucleated away from the notch) towards the notch tip. We suggest that the room temperature dislocation activities are facilitated by the residual stresses in the multi-layer specimens and the thickness dependence of image forces, which reduces the effective shear modulus to promote dislocation motion. The migration of dislocations towards the notch tip shields it from stress concentration to manifest the flaw tolerance in 150 nm specimens, which is observed real time in the microscope.     

Fictitious Notch Rounding approach of pointed V-notch under in-plane shear

The Fictitious Notch Rounding approach (FNR) is applied here for the first time to V-shaped notches under in-plane shear loading. The fictitious radius is evaluated for different opening angles as a function of the Microstructural Characteristic Length (MCL), the actual radius and the failure hypothesis. A multiaxiality factor is introduced and found to be very sensitive to the opening angle. Under mode II loading, the problem is more complex than under mode I and mode III, mainly because the maximum elastic stress is outside the notch bisector line. The main problem is the choice of the expected crack initiation angle, which defines the direction where the relevant stress has to be integrated. This integration carried out over the MCL gives the effective stress value for the pointed V-notch. To this end, two different criteria are used, the Maximum Tangential Stress (MTS) criterion and the Minimum Strain Energy Density criterion (MSED). A large number of finite element analyses have been carried out to determine the multiaxiality factor. This factor has been evaluated by comparing the theoretical stress concentration factor (SCF) obtained from fictitiously rounded notches to the effective stress concentration factor obtained by integrating the relevant stress over the Microstructural Characteristic Length.     

Strain energy approach to compute stress intensity factors for isotropic homogeneous and bi-material V-notches

A strain energy approach (SEA) is developed to compute the general stress intensity factors (SIFs) for isotropic homogeneous and bi-material plates containing cracks and notches subject to mode I, II and III loading conditions. The approach is based on the strain energy of a control volume around the notch tip, which may be computed by using commercial finite element packages. The formulae are simple and easy to implement. Various numerical examples are presented and compared to corresponding published results or results that are computed using different numerical methods to demonstrate the accuracy of the SEA. Many of those results are new, especially for the cases of bi-material notches where the problem is quite complicated.     

Determination of stress intensity factors in three-dimensional problems of fracture mechanics

Dependences of displacements of the surface of a notch on the corresponding stress intensity factors were obtained for axisymmetric bodies with internal and external notches under different deformations (tensile, shear, bending, and torsion). An algorithm is proposed to determine the stress intensity factors of three types (opening mode, longitudinal shear, and transverse shear) from displacements of the notch surface near its tip. The effectiveness of the algorithm is shown, as an example, for numerical analysis of various three-dimensional problems of fracture mechanics.     

Effect of initial flaw shape on crack extension in orthotropic composite materials

An analytical study is presented showing the effects of the notch tip geometry on the location and direction of crack growth from an existing notch in a unidirectional fibrous composite modelled as a homogeneous, anisotropic, elastic material. Anisotropic elasticity and the normal stress ratio theory are used to study crack growth from elliptical notches in unidirectional composites. Sharp cracks, circular holes, and ellipses are studied under far-field tension, and shear loading. Limited comparisons are made showing good correlation with experimental results.     

Elastic stress distributions for hyperbolic and parabolic notches in round shafts under torsion and uniform antiplane shear loadings

Closed-form solutions are developed for the stress fields induced by circumferential hyperbolic and parabolic notches in axisymmetric shafts under torsion and uniform antiplane shear loading. The boundary value problem is formulated by using complex potential functions and two different coordinate systems, providing two classes of solutions. It is also demonstrated that some solutions of linear elastic fracture and notch mechanics reported in the literature can be derived as special cases of the general solutions proposed herein.Finally the analytical frame is used to link the Mode III notch stress intensity factor to the maximum shear stress at the notch tip, as well as to give closed-form expressions for the strain energy averaged over a finite size volume surrounding the notch root.     

Simulating a crack by a notch in the solution of dynamic problems

In the article the method of dynamic photoelasticity is used to investigate the formation of a state of stress at the apexes of cracks and notches under the action of stress waves. Edge and closed cracks in the case of the action of longitudinal and surface waves are discussed. The investigations show that a crack may be simulated by a notch only under definite conditions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 173–178, July–August, 1973.The author thanks Yu. N. Rabotnov for his advice and for his observations during evaluation of the work.