Notch Stress Intensity Factors Research Articles

On notch fracture mechanics

Different stress distributions for an elastic behavior are presented as analytical expressions for an ideal crack, a sharp notch and a blunt notch. The elastic plastic distribution at a blunt notch tip is analyzed. The concept of the notch stress intensity factor is deduced from the definition of the effective stress and the effective distance. The impacts of the notch radius and constraint on the critical notch stress intensity factor are presented. The paper ends with the presentation of the crack driving forceJρfor a notch in the elastic case and the impact of the notch radius on the notch fracture toughnessJρ,c. The notch fracture toughnessJρ,cis a measure of the fracture resistance which increases linearly with the notch radius due to the plastic work in the notch plastic zone. If this notch plastic zone does not invade totally the ligament, the notch fracture toughnessJρ,cis constant. This occurs when the notch radius is less than a critical one and there is no need to use the cracked specimen to measure a lower bound of the fracture resistance.

Local stress analysis of blunt V-notches using the digital gradient sensing method.

In this study, the digital gradient sensing (DGS) method is extended to determine the local stress fields at the blunt V-notch tip. Completely analytical expressions for angular deflections of light beams in the vicinity of the blunt V-notch tip are deduced based on Filippi's stress equation. Under plane stress conditions, the patterns of angular deflection related to two orthogonal stress gradients are theoretically plotted, and the effects of notch angle and notch radius are synthetically investigated, respectively. New procedures for the evaluation of local stress components and generalized notch stress intensity factor (NSIF) are presented using the experimental patterns of angular deflection contours. The NSIF values at the blunt V-notch tip in polymer materials with different geometric parameters under three-point-bend loading conditions are extracted from the DGS measurements. A good agreement is observed between the experimental data and the finite element simulations, which can verify the effectiveness and accuracy of the proposed DGS method.

Residual Notch Stress Intensity Factors in Welded Joints Evaluated by 3D Numerical Simulations of Arc Welding Processes.

Approaches based on calculating Residual Notch Stress Intensity Factors (R-NSIFs) assume the weld toe to be a sharp V-notch that gives rise to a residual singular stress distribution close to the weld toe. Once R-NSIFs are determined, they might be included in local fatigue criteria for the structural strength assessment of welded joints based on NSIFs due to external cyclic loading. However, the numerical calculation of R-NSIFs through finite element (FE) simulations of the welding process requires extremely refined meshes to properly capture the residual stress singularity. In this context, the Peak Stress Method (PSM) has recently been adopted to estimate R-NSIFs due to residual stresses by means of coarse meshes of 2D 4-node plane or 3D 8-node brick elements. The aim of this work is to investigate the applicability of the PSM to estimate R-NSIFs in a butt-welded joint using coarse meshes of 3D 10-node tetra elements. The R-NSIF distribution at the weld toe line is estimated by applying the PSM to coarse meshes of 3D 10-node tetra elements, and the results are in agreement with those obtained using 3D 8-node brick elements. Accordingly, the PSM based on tetra elements further enhances the rapid estimation of R-NSIFs using coarse meshes and could be effective in analyzing complex 3D joint geometries.

Evaluation of generalized stress intensity factors at blunt V-notch tip in polymer materials using transmitted caustics

The paper deals with the notch stress intensity factors (NSIFs) at a blunt V-notch tip in polymer materials using transmitted caustics. First, the governing equations of transmitted caustics which relate to the experimental measurements and the linear elastic stress fields at blunt V-shaped notches are established. Second, a series of caustic curves at the blunt V-notch tip under mode I loading are simulated. Finally, fracture experiments of polymer materials with a blunt V-shaped notch under three-point-bend loading are performed. The NSIFs obtained from caustic measurements show a good agreement with numerical results.

Local approaches and XFEM used to estimate life of CFRP repaired cracked welded joints under fatigue loading

Three different local approaches, the Theory of Critical Distances (TCD), the Notch Stress Intensity Factor (NSIF) and the Strain Energy Density (SED), and the Extended Finite Element Method (XFEM) were applied to estimate the fatigue life of unrepaired and CFRP patches repaired cracked welded joints. The effects of CFRP modulus and thickness on the fatigue life of welded joints with different initial crack depths were investigated. The fatigue damage evolution equation using the loading frequency as a new damage variable was used to describe the degradation process. Fatigue life assessment results and crack growth paths compared with experimental results using these methods. The results show that the fatigue life and fatigue strength decrease as the increase of the initial crack depth. Three different fatigue failure modes can be observed from experimental results. The TCD, NSIF, and SED can reliably predict the fatigue life of welded joints without CFRP patches, but it needs to further investigate the values of estimation parameters of welded joints with CFRP patches for the NSIF and the SED. Fatigue crack growth paths and lives predicted by the XFEM and actual results are in good agreement, and the accuracy and reliability are validated by test data.

Photoelastic evaluation of stress fields and notch stress intensity factors for blunt V-notches

Fracture loads of engineering components with blunt notches cannot be evaluated by the linear elastic fracture mechanics (LEFM) due to no stress singularity. In this study, an approach to determining stress fields and notch stress intensity factors (NSIFs) at blunt V-notches is developed using the photoelastic technique. To solve the nonlinear governing equations of the NSIFs derived from the Filippi’s stress equation, the overdeterministic least squares method combined with the Newton-Raphson method is applied. The NSIFs for a series of three-point-bending specimens with a blunt V-notch up to fracture are evaluated for different notch angles, tip radii, and notch lengths under mode I loading conditions. It is observed that the NSIFs obtained from photoelastic measurements agree well with the numerical values, and the notch fracture toughness is accordant to the mean stress (MS) criterion. The experimental results will be useful for the fracture characterization and strength evaluation of engineering components with complex notches.

A symplectic analytical singular element for V-notched analyses in elastic and viscoelastic plane problems

The linear elastic and viscoelastic problems with V-shaped notches under in-plane loading are investigated in this paper. We consider two different sets of boundary conditions on the radial edges: Free-Free case and Clamped-Clamped case. A novel singular finite element (SASE) with arbitrary high-order accuracy for the notched problems is proposed. Firstly, via Laplace transform, the original viscoelastic problem is transformed into a corresponding elastic one. Then we construct the SASE by using elastic symplectic eigen solutions with higher order expanding terms. The SASE can depict the characteristics of displacement fields and singular stress fields in the vicinity of the notch vertex having arbitrary opening angle. By taking advantage of the symplectic eigen solutions in the SASE, Mode I and/or Mode II notch stress intensity factors can be determined directly without any post-processing. Fine finite element meshes are not required. Numerical examples are provided to illustrate the validity and accuracy of the present method.

Sharp V‐notches in viscoplastic solids: Strain energy rate density rule and fracture toughness

AbstractDifferent from Neuber's rule or Glinka's energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper, the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G‐NSIF) for sharp V‐notch in viscoplastic solids, the concept of SERD for sharp V‐notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V‐notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V‐notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G‐NSIF have been discussed. Some typical solutions for SERD and SED for sharp V‐notched specimens are investigated.

Limit curves for brittle fracture in key-hole notches under mixed mode I/III loading based on stress-based criteria

In this research, with the aim to estimate the onset of fracture in key-hole notched components, made of brittle materials and subjected to combined tension-tear loading, the fracture limit curves are developed in terms of the notch stress intensity factors (NSIFs) based on the maximum tangential stress (MTS) and mean stress (MS) criteria. In order to verify the curves developed, a series of fracture tests are carried out on key-hole notched specimens made of PMMA using an improved loading configuration. The samples are prepared with three various notch tip radii for the sake of evaluating the influence of the notch tip radius on the fracture toughness of the key-hole notched samples. It is shown that for all notch tip radii, the fracture limit curves for both MTS and MS criteria are in very good consistency with the experimental data. No meaningful difference is found between the curves of MTS and MS criteria, especially under plane-stress conditions. It is also observed that the notch fracture toughness of the PMMA specimens could be well estimated under both plane-stress and plan-strain conditions.

A novel semi-analytical method for notch stress and fatigue strength analysis of tube-flange welded joints

This paper presents a semi-analytic method to rapidly estimate the notch stress and fatigue strength for tube-flange welded joints. Considering the stress singularity effect at the weld toe, the parameters related to geometry and opening angle are simplified as singular intensity factors. The equivalent singular intensity factors can be fitted by the stress distribution rather than the peak stress at the corner. On this basis, the modified notch stress formulas for tube-flange welded joint (TFWJ) under pure bending or torsion load were fitted and verified. Meanwhile, the simple relationships between singular intensity factor, notch stress intensity factor, strain energy density and peak stress were further deduced, separately. The comparison results show that the fatigue assessment parameters calculated by the traditional approaches and the proposed method are in good agreement. Finally, four groups of fatigue data of TFWJs were summarized to verify the simplified assessment formulas.

A simplified method for evaluating singular stress field of V-shaped and U-shaped notches with different opening angle

The existing stress field evaluation formulas for V-shaped and U-shaped notches are complicated and limited to certain specific opening angles. Based on linear elastic fracture mechanics and singular strength theory, the traditional calculation formula of notch stress distribution is simplified by introducing singular intensity factors, and the notch stress formula suitable for different opening angles is further summarized and fitted by comparing the stress distribution laws from 102° to 150° opening angles. After verification, the relative error of stress between the simple formula and finite element results is about 5%. On this basis, the formula of notch stress intensity factor (N-SIF) under different opening angles is further derived. Finally, the notch stress and N-SIF of cruciform welded specimens under different welding angles are separately calculated for fatigue strength evaluation. The evaluation process shows that the simplified formula can be used to quickly and accurately evaluate the notch stress field and fatigue strength of welded structures.

Geometry parameter method to estimate stress intensity in V-notched plate and a small crack ahead from V-notch apex

Abstract An approximate, universal approach called the geometry parameter method is developed to estimate the stress intensity factor (SIF) and notch SIF (NSIF) according to linear elastic fracture mechanics (LEFM). NSIF solutions for sharp V-notches include correction coefficients for edge and central notches. The obtained results agree well with results for a double and central V-notched rectangular plate. Furthermore, explicit closed-form solutions are obtained using the proposed method for small crack ahead from a V-notch, and a reliable finite element model is described to calculate crack SIFs in V-notches under mixed loadings. The proposed method is robust and convenient for engineering applications.

A simplified method to predict the local stress field and N-SIF of V-shaped notch

The V-notch stress formula based on linear elastic theory shows that the notch stress at the corner tends to infinity due to stress singularity effect. In fact, infinite stress will not be obtained by the results of finite element analysis, and the stress results depend on the mesh size. Based on the concept of singular intensity value 'as', this paper presents a simple formula to evaluate the notch stress distribution and notch stress intensity factor (N-SIF). The simple notch stress evaluation formula has higher fitting precision and practicability. Meanwhile, in order to analyze the influence of mesh size on notch stress, a series of stress results of notched specimens with different opening angles and crack depths are systematically analyzed and compared. On this basis, the relationship equation between singular strength value 'as' and mesh size is derived, which provides a basis for accurately obtaining the N-SIF of V-notch under coarse mesh. After a series of verification, it is found that the result of fatigue strength evaluated by the simplified formula has a smaller scatter band.

State-of-the-art review of peak stress method for fatigue strength assessment of welded joints

In the fatigue design framework of welded structures, the peak stress method (PSM) is a rapid engineering, FE-based technique for estimating notch stress intensity factors (NSIFs). This review provides a theoretical background and applies the PSM to assess the fatigue strength of arc-welded joints made of aluminium alloys or structural steels, which are subjected to uniaxial and multiaxial fatigue loads. Because two fatigue design curves are available for each class of materials, a criterion for selecting the appropriate curve depending on the local biaxiality of the stress state is established.

Evaluation of fatigue strength of cruciform welded joints by strain energy density method based on singular strength factor

In order to simplify the fatigue assessment method of the notch stress intensity factors (N-SIFs) and the strain energy density (SED) approach for cruciform welded joints, a simplified notch stress assessment formula was presented based on singular intensity factors asi. It is worth emphasizing that the proposed simple formula is only determined by the distribution of notch stress field and is independent on the peak notch stress. Meanwhile, singular intensity factorsasi are in one-to-one correspondence with N-SIFs and SED parameters, thus avoiding the establishment of a very refined mesh model. On this basis, the evaluation accuracy of SED by the traditional numerical method and the simplified formula method are systematically compared. The comparison results show that the SED calculated by the simplified formula in this paper is in good agreement with the finite element results. Referring to the traditional S-N evaluation curve, the W¯-N evaluation curve is proposed and verified. Through fatigue evaluation of a series of cruciform welding specimens, it is found that the result of fatigue strength evaluated by W¯-N with the simplified formula has a smaller scatter band.

Analysis of Failure Emanating from a Notch

Notch-like defect assessment cannot be done by using classical fracture mechanics (mechanics of cracks). In order to prevent overconservatism, the concepts of notch fracture mechanics, such as notch stress intensity factor or notch energy integral Jρ are generally used for this purpose. A local stress criterion, named volumetric method, defines effective stress. It is used for more advanced assessment when introducing geometry and constraint effects. These effects are taken into account for notch fracture toughness and constraint a modified notch failure-assessment diagram.

An efficient energy-based approach for the numerical assessment of mode I NSIFs in isotropic and orthotropic notched plates

In this work, a computationally efficient and simple approach is presented for the rapid calculation of Notch Stress Intensity Factors due to pointed V-notches in isotropic and orthotropic plates under mode I.Such a method is based on the use of the local strain energy, evaluated numerically over a single finite element close to the notch tip, and on the use of very coarse and non-uniform mesh patterns.The NSIF values can then be back calculated taking advantage of the analytical link, firstly derived in this work, between the local energy on the element and the NSIF.The accuracy of the proposed approach is thoroughly debated on the basis of several examples, considering plates with different notch opening angles and made of different materials.

Universal hybrid method and approximate closed-form solution for V-notched and V-notch-cracked plate under tensile and in-plane bending

This paper investigates finite width un-cracked and cracked notched plates. It extends existing empirical formulae for finite width cracked plates without notches to allow the Notch Stress Intensity Factors (NSIFs) in un-cracked notched plates and Stress Intensity Factors (SIFs) in cracked notched plates to be estimated. This is useful for quickly estimating SIFs or NSIFs, checking more detailed, e.g. finite element, calculation and providing insights that may help the quick estimation of SIF values in more complex locations. Matching results have demonstrated the reliability, and the main advantage of the approximation is its robustness and convenience for engineering applications.

Elastoplastic analysis of cracked Aluminum plates with a hybrid repair technique using the bonded composite patch and drilling hole in opening mode I

The objective of this study is to analyze the performance of composite bonding repair, hole drilling and the combination of the two techniques (hybrid repairs) by tensile tests and to show the interest of a hybrid repair versus to other processes. These repair techniques can apply in different branches of engineering: mechanical, aerospace, civil, naval, etc. The finite element method with the ABAQUS code was used to model the mechanical behavior of the different repair techniques. The Notch Stress Intensity Factor (NSIF) is adopted to model the behavior of the cracked notch based on the volumetric method. The size of the plastic zone, the intensity of the normal σyy stress, the peel stress and CTOD are combined to model the proposed technics repairs. Although the bonded composite is very strong, the application of a drilling hole results in additional energy absorption and reduces the level of the maximum normal stress by about 50% compared to a simple patch only. The use of a hybrid repair has a high resistance compared to other proposed methods, improves the mechanical strength and increases the life of the cracked structure compared to a single composite joint and a repair by drilling hole only.

Rib loading effects on weld root fatigue failure modes at rib‐to‐deck welded joint

AbstractThe service life of orthotropic steel decks is dependent on the fatigue resistance of rib‐to‐deck welded joints, which is often tested using two kinds of experimental models in terms of the rib loading condition. Different weld root fatigue failure modes have been observed in the different models, but the role of rib loading remains unclear. This paper aims to clarify the effect of rib loadings on the weld root fatigue failure modes at rib‐to‐deck welded joints. The loadings are decomposed into the deck loadings and rib loadings according to the principle of superposition. Formulae of the weld root notch stress intensity factors and T‐stress under rib loadings are developed by multiparameter regression analysis and subsequently used for the local stress analysis. The fatigue failure modes determined from the local stress field agree well with the experimental results. The results reveal that the weld root failure modes depend on the rib loadings but are independent of the weld geometries. The averaged strain energy density (SED) that can capture both weld geometry and loading condition effects is used to correlate the fatigue test data of different weld root failure modes. The SED is capable of evaluating the fatigue strength of the rib‐to‐deck welded joint failed by different weld root failure modes with a narrow scatter band.