Determination Of Stress Intensity Factors Research Articles

Determining Stress Intensity Factors at Varied Inclination Angles through Innovative Discontinuous Digital Image Correlation

An innovative method is proposed for determining stress intensity factors at crack tips with different inclination angles, based on the Adaptive Digital Image Correlation (AD-DIC) method. This method involves fitting a set of nonlinear equations with unknown parameters using displacement field data. The initial values for crack tip coordinates and inclination angles, computed through the AD-DIC method, are employed in this process to obtain stress intensity factors at the crack tips. The results demonstrate that this approach accurately captures the crack tip positions and calculates stress intensity factors for cracks at various inclination angles. This addresses the challenge of computing stress intensity factors during the crack propagation stage, where cracks may deviate, making conventional calculations impractical.

Stress intensity factor and T-stress around hypocycloidal-shaped holes in finite sheets

Hypocycloidal-shaped holes are seen in sheet structures in special designs or because of the crack growth in particular fatigue loadings. The study focused on the determination of stress intensity factor (SIF) and T-stress around these holes’ cusps. Three-cusp and four-cusp hypocycloid holes with various lengths in various plate sizes were simulated in ANSYS. Results showed both SIF and T-stress decrease with the increase in the plate size. The SIF in a finite plate gets close to the infinite plate SIF where the fraction of plate length to hole length is around 10. For the T-stress, a considerable difference was seen between finite and infinite plates. Finally, the numerical results were experimentally validated using the DIC technique.

Determination of notch stress intensity factors for V-notched specimens under mode I loading using the 3D-Digital image correlation and strain energy approach

In this paper, the fracture behaviour of Single Edge Notched Tension Specimen (SENT) is investigated by using the three-dimensional digital image correlation (3D-DIC) method and the mode I notch stress intensity factors (NSIFs) for the SENT specimen is derived. Initially, the concept of NSIFs and different experimental methods are reviewed. This is followed by a review of the theory of the DIC method. Then, the step-by-step process for setting up a 3D-DIC full-field experimental system for the SENT specimens tested is described. In the experiments, the SENT specimens were tested with pinned and clamped boundary conditions (BCs) and different notch initial opening angles. Furthermore, the analytical stress fields around the sharp V-notches are presented. Combining with the strain energy approach (SEA), the experimental strain fields are analysed to calculate the mode I NSIFs. Moreover, the presented numerical mode I NSIF values for the SENT model are validated by the available results in the literature. Finally, the experimental results obtained from the 3D-DIC method are compared with the numerical results from finite element analysis (FEA) to verify the feasibility and accuracy of the 3D-DIC method. The effect of different BCs of pinned and clamped ends is discussed.

Determination of notch stress intensity factors under mode I loading using the 3D-DIC and finite element over-deterministic methods

In this paper, the fracture behaviour of Single Edge Notched Tension Specimens (SENT) is investigated experimentally and numerically using the three-dimensional digital image correlation (3D-DIC) experimental method and the Finite Element Analysis (FEA) technique, respectively. The mode I notch stress intensity factors (NSIFs) for the SENT specimens are derived from the measured and simulated displacement fields using the Finite Element Over-Deterministic (FEOD) method. The step-by-step process of a 3D-DIC experimental system for the SENT specimens is described. The SENT specimens were tested with pinned and clamped boundary conditions (BCs) and different notch initial opening angles. There are three main contributions of the paper: (1) the derivation of the NSIFs under Mode I Loading for thin plates subjected not only to the common pinned BCs, but also to the rare, clamped BCs; (2) the application of the FEOD method to derive the NSIFs from the displacement fields measured using the 3D DIC technique and predicted using FEA; (3) the validation of the NSIFs derived numerically via experimentally-determined NSIFs for notched thin plates subjected to both pinned and clamped BCs. Thus, four sets of NSIF data are provided in the paper and enable confident application of the NSIF values for the conservative (pinned BCs) and light-weight (clamped BCs) design of notched thin plates.

A simple SIF determination method for cracked orthotropic cylindrical shell by means of stress ratio

A convenient and universal calculation method for stress intensity factor (SIF) in cracked orthotropic cylindrical shell under diverse loadings is described. The present expressions are derived from traditional classical numerical method and simplified by extracting and eliminating the complex but regular parameters. A simple relation between SIF and crack tip stress from finite element method (FEM) is constructed by means of reference problem and unknown problem, then a simple SIF formulation can be realized and the impact of material orthotropy is considered. The feasibility and advantages of present study are proved to be analyzed by comparing against published results.

A review of three‐dimensional weight function methods for the analysis of various surface/corner crack problems

AbstractThe stress intensity factor (SIF) is the foundation of fracture mechanics analysis. Accurate determination of SIFs is at the very heart of damage tolerance design and fatigue crack growth life prediction. The weight function method (WFM) is a powerful method for SIF‐determination involving complex load conditions. This article presents a review of the historical development over the past five decades and the current state‐of‐the‐art in three‐dimensional (3D) WFMs. The discussions are focused on the slice synthesis weight function method (SSWFM) and the point weight function method (PWFM). The powerfulness of the 3D WFMs is shown by a variety of examples with complex part‐through crack configurations under uni‐ and bi‐variant loadings. Solution accuracy is verified by comparisons of SIFs with various numerical methods. Use of the substitute geometry concept to expand the capability of 3D WFMs for solving real‐world engineering 3D crack problems is demonstrated. Some remaining challenges are briefly discussed.

Determination of SIFs and application of a SIF-based fracture criterion for concrete-rock interface under sustained loading

This study proposes an effective method to determine the stress intensity factors (SIFs) of the interface crack considering the viscoelasticities of the bilateral materials and verifies the feasibility of the initial fracture toughness-based fracture criterion for the concrete-rock interface under sustained loading. Firstly, low-level sustained loading tests were conducted on the composite concrete-rock specimens with respect to two interface roughness degrees and two sustained load levels less than the initial cracking load. Then, an implicit creep equation was employed to characterise the viscoelasticities of bilateral materials and then calculate the mechanical responses of the concrete-rock interface in the low-level sustained loading test. The SIFs of the interface crack under sustained loading were determined by using the elastic strain energy density ahead of the crack tip. By averaging the SIFs over the radius of the core region of the crack tip, the representative SIFs under sustained loading were obtained. The test results indicated that the SIFs showed decreasing tendencies under sustained loading, and the initial fracture toughness can be considered as a material property of the concrete-rock interface. The initial fracture toughness-based fracture criterion was verified to be feasible to determine the initial cracking status of the concrete-rock interface under sustained loading. In addition, due to the reductions of the SIFs under sustained loading, additional loads were required to compensate the losses of the SIFs, leading to the enhancement of the initial cracking loads after experiencing the sustained loading.

The Multi-Virtual Crack Closure Technique for three-dimensional interface crack problems

The Virtual Crack Closure Technique (VCCT) is a simple method that was found in the past to produce good results for determining stress intensity factors of cracks in homogeneous bodies and poor results for interface cracks. In recent papers, the VCCT was found to produce excellent results for two-dimensional interface cracks where many elements were used in the virtual crack extension (VCE). This approach is called here the Multi-VCCT. A criterion for the optimal number of elements used in the VCE was also found. Here, the M-VCCT is extended to three-dimensional interface crack problems. Results for three-dimensional problems containing a straight through finite length interface crack and a penny-shaped interface crack are presented. The interfaces include that between two homogeneous and isotropic dissimilar materials, as well as two transversely isotropic materials.

Fatigue Crack Growth Studies under Mixed-Mode Loading in AISI 316 Stainless Steel

The objective of this study is to examine the behavior of fatigue crack growth (FCG) in the mixed mode (I/II) of the AISI 316 austenitic stainless steel alloy, considering mode mixity angles of 30°, 45°, and 60°. This particular alloy is widely used in the marine industry and various structural components because of its exceptional properties, such as high corrosion resistance, good formability, weldability, and high-temperature strength. By investigating the crack growth behavior, the study seeks to provide insights into the material’s durability and potential for long-term use in demanding applications. To analyze fatigue crack growth behavior using linear elastic fracture mechanics (LEFM), this study utilizes compact tension shear (CTS) specimens with varying loading angles. The CTS specimens provide an accurate simulation of real-world loading conditions by allowing for the application of various loading configurations, resulting in mixed-mode loading. The ANSYS Mechanical APDL 19.2 software, which includes advanced features such as separating, morphing, and adaptive remeshing technologies (SMART), was utilized in this study to precisely model the path of crack propagation, evaluate the associated fatigue life, and determine stress intensity factors. Through comparison with experimental data, it was confirmed that the loading angle had a significant impact on both the fatigue crack growth paths and the fatigue life cycles. The stress-intensity factor predictions from numerical models were compared to analytical data. Interestingly, it was observed that the maximum shear stress and von Mises stresses occurred when the loading angle was 45 degrees, which is considered a pure shear loading condition. The comparison shows consistent results, indicating that the simulation accurately captures the behavior of the AISI 316 austenitic stainless steel alloy under mixed-mode loading conditions.

Experimental Evaluation of KIEAC of a Carbon Steel Using the Pin-Loaded SENT Geometry

Abstract The experimental determination of the threshold stress intensity factor for environment-assisted cracking (KIEAC) is described by several standards, which allow the use of different specimen geometries and methodologies for crack length estimation. In some cases, the combination of structure, specimen size, or both, main loading direction, and crack orientations of the component that need to be characterized limit the use of standardized geometries. Consequently, alternative geometries must be used. In this study, fatigue pre-cracked pin-loaded single edge notched tension specimens as defined by BS 8571:2018, Method of Test for Determination of Fracture Toughness in Metallic Materials Using Single Edge Notched Tension (SENT) Specimens, were applied for the experimental evaluation of the KIEAC of a carbon steel. The specimens were tested in deaerated substitute ocean water solution saturated with carbon dioxide at 40°C and at 1 and 10 bar (100 and 1,000 kPa) under constant load conditions with incremental (step) loading. The crack length during the tests was monitored by direct current potential drop, which was helpful for defining the applied K corresponding to the onset of subcritical crack growth (KIEAC). Additionally, fractographic analysis of KEAC specimens and results from the fracture toughness evaluation of this material in air at room temperature have also been reported.

Mixed mode brittle fracture of stereolithographic 3D-printed parts

Technical advances in additive manufacturing (AM), also known as three-dimensional (3D) printing, have led to applications of this technology in creation of end-use items. Consequently, performance and the mechanical strength of AMed parts have become of significant importance. In this research, fracture behavior and crack propagation of AMed cracked plates are investigated. To this aim, the stereolithography (SLA) technique is used to fabricate square plate specimens with a hole in the center and radial cracks that started at the perimeter of the central hole. Here, full range of mixed-mode fracture (from pure mode I to pure mode II) are obtained by altering the angle between the crack and the applied load. We used the finite element method to determine stress intensity factors. This study deals with a series of experiments on 3D-printed cracked plates to study mixed-mode fracture and crack propagation in brittle fracture of SLA 3D-printed components. Additionally, the digital image correlation technique was used to determine strain field on the surface of the specimens. As SLA is one of the most commonly used concepts in polymer 3D printing and has garnered significant attention for fabrication of complex structural elements, the outcomes of this study are useful for next developments and innovative designs of 3D-printed polymeric components.

Determination of mixed-mode stress intensity factors for axial crotch corner cracks at cylindrical vessel to nozzle intersections under internal pressure and nozzle loads

In this study, Stress Intensity Factors (SIF) of quarter circle and semi elliptic cracks at the crotch corner of the intersection between a cylindrical pressure vessel and a radial nozzle have been computed for combinations of the actions of internal pressure and external forces on the nozzle. Until now, practitioners have used simplified solutions for SIFs available from the literature, such as the Newman-Raju equations for the mode I SIF produced by an internal longitudinal semi-elliptical crack in a cylinder, to approximate the SIF produced at a crotch corner crack. These equations do not take into account the effect of the opening of the cylinder for the nozzle and the resulting stress distribution along the cylinder. As a result, there is uncertainty about the validity of using these simplified solutions in engineering critical assessments and a more exact determination of the SIFs for crotch corner cracks would be beneficial.The mode I, II and III stress intensity factors have been determined for crotch corner cracks for a single size of vessel and are presented as a function of variables such as location on the crack front, crack size and aspect ratio (a/c), crack angle with respect to the axis of the vessel, and the magnitude of internal pressure and external forces. The results are presented in graphical form. The study concludes with the recommendation that the analysis be extended to a wider range of vessel and nozzle parameters.

Linearized layering method for stress intensity factor determination

AbstractThis paper looks to reduce the complexity of determining stress intensity factors while maintaining high levels of accuracy by the use of a linearized layering approach. Many techniques for stress intensity factor determination exist, but they can be limited by conservative results, requiring too many user parameters, or by being too computationally intensive. Multiple notch geometries with various crack lengths were investigated in this study to better understand the effectiveness of the proposed method. By linearizing the average stresses in radial layers around the crack opening, stress intensity factors were found to have error ranging from −10.03 to 8.94% when compared to analytically exact solutions. This approach proved to be a robust and efficient method of accurately determining stress intensity factors.

Simple crack tip and stress intensity factor determination method for model I crack using digital image correlation

In the past three decades, quantitative characterization of cracks attracted much attention with the development of digital image correlation (DIC), especially for estimation of crack tip position (CTP) and stress intensity factor (SIF). Quantifying CTP and SIF is of great importance in the damage tolerance assessment of fracture-critical components and structures. In previous research, multivariate fitting is performed on the displacement field to determine CTP and SIF. However, high gradient deformation near the crack tip causes inaccurate results and an involving complex estimation process. In this paper, a simple method is proposed to determine the CTP and SIF based on the displacement field calculated by DIC. Instead of the full-field fitting method, two lines symmetrically distributed on both sides of the crack tip are selected to fit the CTP. Vertical displacement differences between two lines are fitted with the theoretical solutions of mode I crack. Compared with the actual position observed by the micrograph, the estimation error is less than 2 pixels (about 6 μm). Additionally, a similar method is proposed to estimate the SIF utilizing the CTP results. To avoid the bias errors caused by the plastic zone, two lines are selected in the elastic zone away from the crack tip. Vertical displacements on two lines are fitted with the theoretical solutions to obtain SIF. The fitting results of the proposed method are close to that of the full-field fitting method. Compared with the previous methods, the computation burden of the proposed method is greatly reduced while the accuracy is not affected.

A novel coupling approach for determination of stress intensity factor for bi-material Reissner plates under bending or twisting

A novel coupling approach is proposed to determine stress intensity factors (SIFs) for interface cracks in bi-material Reissner plates under bending or twisting. The Reissner plate theory is adopted to derive asymptotic solutions around the crack tip and T-spline functions are introduced to establish the model. The approach has two major steps. Firstly, the overall cracked plate is divided into two regions (near and far fields) and is discretized by the T-spline based isogeometric analysis (IGA). Subsequently, the large number of fundamental unknowns of control points in the near field is reduced into a small set of undetermined coefficients of asymptotic solutions obtained by the eigenfunction expansion method. Therefore, explicit expressions of SIFs and singular stress components near the crack tip are obtained simultaneously. A number of numerical examples for various cracks laying at the interface are presented, and are found to be in good agreement with available solutions.

Two-dimensional weight function for the determination of stress intensity factors for semi-elliptical surface cracks in finite-thickness and finite-width plates

In this study, a new two-dimensional (2D) weight function of stress intensity factors (SIFs) for semi-elliptical surface cracks in finite-thickness and finite-width plates subjected to arbitrary stress distributions was proposed. To determine the unknown coefficients in the weight function, parametric three-dimensional finite element (FE) models were developed to obtain the solutions of SIFs. The analysis matrix covers wide ranges of relative crack-length ratios 0.1 ≤ c/W ≤ 0.9, to consider the finite width effect, as well as aspect ratios 0.2 ≤ a/c ≤ 1.0 and relative crack-depth ratios 0.025 ≤ a/T ≤ 0.8. The present weight function was verified against the FE results and the solutions available in the literature. The maximum differences were within 6% for both the surface and deepest points. The proposed 2D weight function can be applied to calculate SIFs and predict the fatigue life of engineering structural components involving surface flaws.

A new path-independent interaction integral for the SIFs of interfacial crack

A new path-independent interaction integral, which is derived from the dynamic Ĵ integral, is developed to compute the stress intensity factors (SIFs) of interfacial crack and the path-independence of the new interaction integral is theoretically proven. In the calculation, the second derivative of the displacement is avoided since the explicit analytical expressions of the auxiliary stress fields near an interfacial crack tip are utilized. In addition, for non-homogenous materials the computation of the derivatives of material properties is not required by introducing the appropriate incompatibility auxiliary fields. This study significantly enhances the application of the interaction integration technique since the determination of SIFs of interfacial crack between two homogeneous or non-homogeneous materials under static or dynamic loadings can be conducted efficiently by the new interaction integral. For more efficient crack modeling, a local refinement technique using the variable-node element (VNE) is implemented into the framework of the extended finite element method (XFEM). The efficiency and accuracy of the proposed new interaction integral are demonstrated by numerical examples.

Evaluating SIFs in finite orthotropic composites from experimentally determined stress coefficients

Unlike with isotropy materials, determining stress intensity factors in orthotropic composites is complicated as they can depend on constitutive properties and principal material directions. Acknowledging the above, this paper develops a novel technique to evaluate stress intensity factors in finite, plane-stressed, orthotropic composites. Upon substantiating the numerical reliability of the approach, KI is determined experimentally in a finite tensile loaded double-edge cracked [013/905/013] graphite-epoxy composite laminate from displacement-evaluated stress coefficients. Only a single DIC-measured displacement field is need. Advantages of the method include applicability beyond a laboratory environment and to other structural shapes, loads and crack configurations, wide acceptable range of stress coefficients and highly arbitrary source locations of the measured input data. Unlike purely numerical or theoretical approaches, the method does not require knowing the external loading. This is significant as loads are often unknown in practice. Results are verified independently.

An accurate method for determining stress intensity factor by caustic

An accurate method for determining stress intensity factor by caustic

Computation of conventional fracture mechanics parameters via molecular dynamics simulations

The Williams series expansion is the fundamental solution of conventional continuum fracture mechanics for characterizing the stress fields around the crack tip in a homogeneous material in the linear elastic regime. Nowadays stress intensity factors, T-stresses and the higher-order coefficients of the Williams series expansion are proved to be important parameters describing the near crack-tip fields in isotropic linear elastic materials. The central aim of this study is to understand if one can obtain these fracture parameters of conventional fracture mechanics from atomistic simulations based on molecular dynamics simulations. The ability to describe fracture processes at atomic scale via stress intensity factors, T-stresses and higher-order coefficients will provide the opportunity to take into account many effects such as material microstructures, crystallographic orientation, chemical compositions and concentrations and others. In this research the values of stress intensity factors, T-stress and coefficients of the Williams series expansion are obtained using atomistic simulations based on molecular dynamics method with a classical molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator. The classical over-deterministic method is used to determine stress intensity factors, T-stresses and coefficients of higher-order terms of the Williams series expansion of the near crack-tip stress field from molecular dynamics modelling of a plate with a central crack. The accuracy of the proposed approach is tested for this rather simple cracked configuration. There is the theoretical analytical solution with all the coefficients of the higher-order terms in the Williams series expansion. The existing theoretical solution allows us to compare the angular distributions of the stress tensor components for a large plane with the central crack. It is shown that results obtained from molecular dynamics simulations and the theoretical analytical solutions are in good agreement.