Estimation Of Stress Intensity Factors Research Articles

Particle- and crack-size dependency of lithium-ion battery materials LiFePO<sub>4</sub>

Lithium-ion batteries have become a widely-used commodity for satisfying the world’s mobile power needs. However, the mechanical degradation of lithium-ion batteries initiated by micro cracks is considered to be a bottleneck for advancing the current technology. This study utilizes a finite element method-based virtual crack closure technique to obtain particle- and crack-size-dependent estimates of mixed-mode energy release rates and stress intensity factors. Interfacial cracks in orthotropic bi-materials are considered in the current study, whereas the crack extension along the interface is assumed. The results show that energy release rate, stress intensity factor, and the propensity of crack extension are particle- and crack-size- dependent. In particular, our results show that for smaller plate-like LiFePO4 particles (100 nm × 45 nm), a crack has lesser tendency to extend if crack-to-particle size is less than 0.2, and for 200 nm × 90 nm particles, similar results are obtained for crack-to-particle sizes of less than 0.15. However, for larger particles (500 nm × 225 nm), it requires an almost flawless particle to have no crack extension. Therefore, the current study provides insight into the fracture mechanics of LiFePO4 and the associated crack-to-particle size dependency to prevent crack extensions.

Stress Intensity Factor Solution for a Naturally Emanating Crack Out of a V-Notched Round Bar

During the estimation of Stress Intensity Factor (SIF) of a notched round bar, standard crack geometries such as elliptical, semi-circular, and straight crack fronts are commonly considered at the notch root region. In the present work, the SIF solution for a naturally initiating crack out of a V-notched round bar has been estimated experimentally and the results are compared with data obtained from 3D finite element analysis. The fractographic investigation of the fractured surface suggested a non-symmetric crack propagation and the strong influence of stress concentration factor on SIF, especially in the early stages of crack growth (up to a/d ratio of 0.15, where “a’” is crack length and “d” is notch root diameter). Four aspect ratios (a/c = 0.4, 0.5, 0.75, and 0.85, where “c” is semi-major axis of elliptical crack) and seven crack depth (a/d) ratios in the radial directions were considered with and without offset of surface crack origin to match experimental observations. It was noted that a naturally formed crack had an elliptic shape with aspect ratio of 0.75, with its center offset by 0.5 mm in an upward direction from the notch root region.

A linear least squares approach for evaluation of crack tip stress field parameters using DIC

In the present work, an experimental study is carried out to estimate the mixed-mode stress intensity factors (SIF) for different cracked specimen configurations using digital image correlation (DIC) technique. For the estimation of mixed-mode SIF׳s using DIC, a new algorithm is proposed for the extraction of crack tip location and coefficients in the multi-parameter displacement field equations. From those estimated coefficients, SIF could be extracted. The required displacement data surrounding the crack tip has been obtained using 2D-DIC technique. An open source 2D DIC software Ncorr is used for the displacement field extraction. The presented methodology has been used to extract mixed-mode SIF׳s for specimen configurations like single edge notch (SEN) specimen and centre slant crack (CSC) specimens made out of Al 2014-T6 alloy. The experimental results have been compared with the analytical values and they are found to be in good agreement, thereby confirming the accuracy of the algorithm being proposed.

Experimental assessment of toughness in ceramic matrix composites using the J-integral with digital image correlation part II: application to ceramic matrix composites

This paper is the second of a two-part series assessing the feasibility of using the J-integral with full-field deformation data from digital image correlation (DIC) to characterize toughness in continuous fiber, SiCf/SiCc ceramic matrix composites (CMCs). In part I, line and area integral adaptations of the J-integral were validated with analytical and experimental deformation fields. It was found that variability in experimental data and contour truncation at the crack wake introduced error and path-dependency, but this could be mitigated through data filtering. In this paper, the line and area integral methods were evaluated for cross-ply and longitudinal CMC tensile specimens. It is demonstrated that these approaches cannot be used for quantitative characterization, but can be successfully used to examine qualitative trends. For both architectures, area integral measurements of the potential energy release rate, J, were larger (and arguably more accurate) than line integral measurements. Resistance curves were characteristic of tough materials, but the stress intensity magnitudes were larger in the longitudinal laminates than the cross-ply (for equivalent crack extension). Experimentally derived bridging laws showed that fiber bridging tractions were largest in the cross-ply laminates, which was attributed to a lower volume fraction of longitudinal fibers. Quantitative, single-value measurements of fracture toughness could not be established since (1) noise in the DIC data masked strain signals indicative of first matrix cracking, and (2) widespread matrix cracking rendered the J-integral invalid (regardless of size and position, the boundaries of the line and area contours inevitably intercepted microcracks). Rather, gross estimates of toughness and stress intensity factors were made under the assumption that the limitations in the spatial resolution of the DIC data essentially transforms regions with fine microcracking along the contour into continuous regions of elastic deformation. When evaluated with the J-integral, the smoothed deformation fields manifest as resistance curves indicative of a tough material. Thus, the J-integral was valuable for qualitative assessments of toughening mechanisms in the CMCs.

Radiation response of the overlay cladding from the decommissioned WWER-440 Greifswald Unit 4 reactor pressure vessel

The Results of tensile and crack extension testing conducted on irradiated austenitic overlay cladding material are presented. The specimens were machined from three trepans sampled from the decommissioned WWER-440/V-230 reactor pressure vessel of the nuclear power plant Greifswald Unit 4. Crack extension curves were measured with Charpy size SE(B) specimens using the unloading compliance technique according to ASTM E1820-11 at different temperatures. Provisional crack initiation fracture toughness values JQ and KJQ are determined. The highest KJQ values were found in the temperature range from 20 to 80°C. A significant scatter was observed in the initiation values. This is due to the inhomogeneous structure of the welded overlay cladding. During the loading the crack moves through regions with different tearing strength, thus the J–Δa values show discontinuities caused by fast crack propagation or crack jumps. The comparison of the measured KJQ values and conservatively estimated stress intensity factors at an assumed surface crack shows that the cladding would remain intact during pressurized thermal shock transient.

DIC identification and X-FEM simulation of fatigue crack growth based on the Williams’ series

A unified Digital Image Correlation (DIC)/eXtended Finite Element Method (X-FEM) framework based on the Williams’ series for fatigue crack growth identification and simulation is proposed. Williams’ series are used for post-processing the displacement measured by digital image correlation. It gives access to the change of stress intensity factors and crack length with the number of cycles. A Paris’ crack propagation law is subsequently identified and further validated by simulating the experiment. The simulation uses measured displacements as Dirichlet boundary conditions and a direct estimation of stress intensity factors based on a coupling between a finite element model and the analytical Williams’ solutions. It is shown that the use of actual boundary conditions is crucial. The use of the Williams’ formalism is further investigated on an elasto-plastic simulation to validate the extraction of nonlinear features in the crack tip vicinity.

Three‐dimensional simulation of crack with curved front with direct estimation of stress intensity factors

SummaryThis paper consists of an extension of simulation with direct estimation of stress intensity factors to the three‐dimensional case. Here, it combines X‐FEM with localized multigrids and direct estimation of quantities of interest along the crack front (SIF, T‐stress, etc.) based on crack tip asymptotic series expansion. In practice, a three‐dimensional patch is introduced locally with a truncated basis of Williams series expansion and is linked in a weak sense with the X‐FEM localized multigrids. Some examples (with available analytical solutions) illustrate the efficiency and the robustness of the method. These examples consider planar cracks with curved front, but the proposed method aims to apply to any continuously curved crack. Copyright © 2014 John Wiley & Sons, Ltd.

Stress intensity factor estimation for unbalanced rotating cracked shafts by artificial neural networks

ABSTRACTThe knowledge of the stress intensity factor (SIF) values along a crack front is essential to calculate the crack growth rate and the remaining life of a mechanical component. In the case of a rotating shaft, usually it presents disalignments, which modify the SIF data with regard to a balanced one. This paper presents the use of an artificial neural network (ANN) for estimating the SIF at the crack front in an unbalanced shaft under rotating bending, previously, a quasi‐static numerical (finite element) model, which simulates a rotating shaft, has been developed to create the training cases for the ANN. The obtained results allow to study the influence of the unbalance of rotating shafts in the crack breathing mechanism and will allow to predict the influence of this behaviour on the values of the SIF and in the propagation of cracks.

Effect of subset parameters selection on the estimation of mode-I stress intensity factor in a cracked PMMA specimen using digital image correlation

Polymethyl methacrylate (PMMA) tension specimens with double edge cracks are considered in this study. Surface displacements of the samples are obtained using digital image correlation technique using different values of subset size and subset distance. Results of displacement components from various regions in front of the crack are utilized in a least squares fitting procedure to obtain the first stress intensity factor. This is accomplished using series representation of displacement components of a cracked structure in plane loading conditions. Effects of two adjustable parameters of digital image correlation analysis, including subset size and subset spacing, on the obtained values of stress intensity factor are investigated, while the number of terms truncated from the series representation and the radius of data extraction zone are varied. Results indicate that small subsets may not properly converge to accurate results, irrespective of the value of subset spacing. Moderate subset sizes will usually yield acceptable results while large subset sizes and subset spacing may not include sufficient data to reproduce the desirable value of stress intensity factor. It is also shown that at least three or more terms in conjunction with a sufficiently large radius of data extraction region should be considered in least squares fitting to acquire a reasonable estimate of stress intensity factor in cracked specimens.

Development of design charts for stress intensity factors at tips of multi-site cracks in unstiffened curved panels

Multi-site damage need to be addressed and evaluated in order to assess the integrity of aging aircraft structures. One of the problems recognized in the recent times is the effect of interaction between two or more cracks in the close neighborhood in such structures. The present paper deals with such a problem and presents numerical estimates of stress intensity factors at a crack tip in an un-stiffened curved panel with a secondary crack in the vicinity of a primary crack. The results are presented in the form of design charts. These results should be useful in evaluation in the damage tolerance evaluation of aircraft structures with multi-site damage.

Fatigue Crack Growth on Heterogeneous Stress Fields: Best Analytical Approach

ABSTRACTA way of estimating Stress Intensity Factors is proposed by extending available solutions (solid and crack configurations) to stress fields not considered in available formulations. The accuracy of the proposed estimation is considered with respect to fatigue life assessment and crack shape tracing. It is aimed as very fast initial estimation, in comparison with the use of Finite Elements, in those cases were a high stress gradient is observed: stress concentrations (holes, notches, grooves) or due to surface residual stresses produced by machining techniques or induced –on purpose- to improve fatigue life (for example, by shot-peening), where no SIF solutions are available.

Influence of Residual Stress on Stress Intensity Factor Estimation of Multiple Cracks in a Dissimilar Welded Joint

Influence of residual stresses on mixed mode Stress Intensity Factor (SIF) of dissimilar (steel and aluminium) butt welded joint is investigated numerically. Opposite cracks with various crack depth ratio, crack aspect ratio and heat fluxes were considered. The geometry correction factor was calculated by considering the effect of mode-II and mode-III fracture. For short cracks [(a/d) = 0.1] as the residual stress increases, SIF for steel decreases and increases for aluminium at crack surface region [(P/P0) = ±1]. When the crack depth ratio increases, SIF for both materials decreases along the crack front due to relieving of stresses at higher depths [(a/d) = 0.4]. Non uniform crack opening was observed along the crack front and in between the front side and back side cracks.

Numerical and experimental study of crack behaviour at the zinc/TRIP steel 800 interface

In the present study, the behaviour of a crack with different orientations at the zinc/steel bi-material interface was investigated. ABAQUS finite element simulation was used for the estimation of stress intensity factor and energy release rate. It was found that the normalised stress intensity factor in the coating decreases and rapidly increases once the crack crosses the interface. The computation of the ratio between the energy release rate for deflection and penetration showed a value much lower than 1 whatever the crack orientation is. This result means that a crack is much more likely to deflect than to penetrate into the interface. In addition, analytical and numerical results were confirmed by microscopic examinations obtained from SEM observations.

Two-dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis

When the loading or the geometry of a structure is not symmetrical about the crack axis, rupture occurs in mixed mode loading and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation. The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method in a FE code and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors. In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we presented the examples of crack propagation in structures containing inclusions and cavities.

Numerical Lifetime Prediction of Polymer Pipes Taking into Account Residual Stress

In this paper a methodology for assessment of residual stress effects on crack behaviour in the polymer pipe is developed. For simplicitys sake, a linear distribution of residual stresses across the pipe wall is assumed. Linear elastic fracture mechanics is used for the fracture mechanics analysis of the cracked pipe. An approximate relation for the stress intensity factor estimation for a crack in a polymer pipe, with residual stress taken into account is suggested and discussed. The methodology presented can be helpful for a rapid lifetime estimation of polyolefin pipelines.

Strengthening of Misaligned Welded Pipes with Outer Circumferentially Crack Using FRP Bandage Finite Element Analysis

Finite element analysis is used to investigate the effectiveness of Fiber Reinforced Polymers (FRP) bandage in rehabilitating misaligned welded pipes with outer circumferential surface crack. It is assumed that the pipes are subjected to an axial tensile stress. Linear Elastic Fracture Mechanics (LEFM) regime is adopted to estimate the stress intensity factor (SIF). ANSYS software is used in the study through 3D-axisymmetric finite element analysis. The results demonstrated that stiffening with FRP bandage has a great influence on the reduction of the stress intensity factor at the crack tip improving the fracture integrity of the misaligned welded pipes. The most common solution of the rehabilitation process for damaged pipes fabricated from metals is very important mater. The rehabilitation technique for pipes is needed because of external erosion and corrosion for pipes or due to external damages .Usually such process requires using heavy machines and skilled workers in addition to the time needed. By using Fiber Reinforced Polymers (FRP) techniques to increase the strength for existing pipes, it is very important for the corroded and damaged pipes to increase the resistance to the surrounding environment. The conventional techniques for repairing damaged pipes need operation of cutting, welding and inspecting in addition. This may also require stopping the system during the repair period. Furthermore, for many cases the repair process is undesirable because of the residual stress induced in the pipe during the welding process which tends to decrease the fatigue performance of the pipe material in addition to the weakness of the pipe wall due to any of corrosion types such as pitting. Therefore, the final rehabilitation cost using FRP is low compared with the traditionally usual trends using welding techniques. Pipeline welding contractors are very often used in mechanized and semi-automatic welding processes. It is generally accepted that the most welded structures enter service containing tiny cracks or flaws (1). Moreover, these flaws may extend to a size where the safety of the structure becomes dangerous. It is therefore essential that engineers and designers have methods of assessing the significance of flaws detected during manufacture or after the structure has entered its service life, especially the structures that are connected with the human safety, such as pipes. Generally, cracks in piping system often occur at welding joint and around it (2). Most of these cracks are located in circumferential direction. For this reason circumferential cracks play an important role in the safety analysis of pipes (3). Strengthening techniques have drawn attention by many researchers to investigate the effectiveness of the stiffeners in the rehabilitation processes through using experimental as well as finite element methods. Ahmed et al. (4-6) investigated the effect of using FRP strengthening techniques to rehabilitate structural members under numerous loading conditions through FEA. Mourad et al. (7-18) have studied the effect of stiffening on crack growth through three-point bending TPB, compact tension CT and compact shear CS specimens. Chang-Young Oh et al. (19) investigated existence methods to estimate stress intensity factors due to welding residual stresses and compared with finite element (FE) solution for welding residual stress profiles, generated by simulating repair welds and compared with analytical solution. On the other hand, finite element analysis (FEA) was carried out to obtain the elastic stress distribution at cylinder to cylinder junction in pressurized shell structures that have applications in space vehicle design (20). The peak stress value is found to reduce due to filleted butt joint as expected and also confirmed through test results. Pipes with a flawed girth weld for two common girth weld tension tests: the curved wide plate test and the full scale pressurized pipe tension test, and subjected to global plastic deformation were studied by finite element models (21). Xiaohui Chen et. al. (22) presented an overview of recent progresses in experimental investigation and finite element analysis (FEA) of ratcheting behaviour of pressurized piping. The stress-intensity factor for the circumferential semi-elliptical surface cracks in a hollow cylinder's cross

Finite Element Investigation of Stress Intensity Factors of Multiple Semi-Elliptical Surface Cracks in Solid Shaft

Fatigue cracks nucleate at the surface of the shaft operating under cyclic load. These cracks then grow into semi-elliptical shapes while extending into the shaft. The paper presents numerical estimation of stress intensity factor (SIF) of such cracks in circular solid shaft when subjected to bending and twisting loads in elastic conditions. The finite element model is first validated with the help of results reported elsewhere for a single surface crack. Later on, multiple coplanar surface cracks are modeled and the effect of the number of cracks and the distance between them on SIF of the main crack is investigated. The results are in line with the expectations.Nomenclature

Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

A Local/global non-intrusive coupling algorithm is proposed for the analysis of mixed-mode crack propagation. It is based on a three scale multigrid and extended finite element method, that was proposed recently for the direct estimation of stress intensity factors of static cracks. The algorithm couples a linear elastic global model (possibly performed by a industrial software) with an enhanced local model capable of modeling a crack and accurately estimating SIFs (performed by a separate research code). It is said non-intrusive since it does not modify the global mesh, its connectivity and solver. For the global model, the contribution of the local patch consists in additional nodal efforts near the crack, which makes it compatible with most softwares. Further the shape of the domain over which the local model is applied is automatically adapted during propagation.

Fatigue crack growth of arbitrary planar cracks in welded components

Engineering components that are subjected to cyclic loads frequently contain imperfections which can rationally be assessed using linear elastic fracture mechanics. Fatigue crack growth models make use of the stress intensity factor (SIF) range and the maximum SIF or R-ratio to describe the driving force for crack propagation. Determining the stress intensity factor in welded components is difficult because the stress field is complex due to the structural geometry of the component, the local geometry of the weld and the residual stresses caused by the welding process. In many cases, the crack geometry will also be complex. Weight function (WF) solutions for numerous crack geometries have been published, e.g. for through cracks, edge cracks, surface cracks and corner cracks. However, the use of the WF for cracks of arbitrary shape is less developed. The point-load WF method for arbitrary planar cracks gives sufficiently accurate estimates of stress intensity factors for embedded cracks, but the results for the surface and edge cracks are less accurate. A new form of the general point-load WF more suitable for surface breaking cracks is proposed and is combined with a crack tip plasticity-based crack growth model. During numerical simulations, cracks are normally modelled using a discrete number of linear segments. A new method for shifting these segments as a crack advances is also proposed. The method is verified based on comparison with published experimental results for welded rectangular hollow section joint subjected to bending and torsion.

Effect of Helix Angle on the Stress Intensity Factor of a Cracked Threaded Bolt

The fracture behavior of a crack in a threaded bolt depends on the stress intensity factor (SIF). Available SIF solutions have approximated the threaded bolt as a circular groove, thus, the SIF predominantly corresponds to the opening mode, mode-I. As a thread in a bolt has a helix angle, the crack propagates under mixed mode conditions (opening, sliding and tearing), esp. when the crack sizes are small. This paper presents the results of SIF solutions for a part-through crack emanating from a Metric threaded bolt. A 3D finite element model with preexisting flaws was generated to calculate the SIF values along the crack front. Crack aspect ratios in the range of (0.2 < (a/c) < 1) and crack depth ratios in the range of (0.1 < (a/d) < 0.5) (where “a” is crack length, “c” is semi major axis of ellipse and “d” is minor diameter of the bolt) were considered along the crack plane for the SIF estimation. The SIF values at the midregion decreases with an increase in aspect ratio (a/c), and SIF increases when the crack depth ratio (a/d) increases in the midregion. Close to the free edges, higher SIF values was observed for crack depth and aspect ratios ranging between 0.2 and 0.6 compared to midregion. In the crack surface region, up to a crack depth ratio of 0.25, significant influence of mode-II and mode-III fracture was noted for shallow cracks (a/c < 0.2). Significant influence of mode-II and mode-III fracture was observed for semicircular cracks (a/c = 1) beyond the crack depth ratio of 0.3.