Stress Intensity Factor History Research Articles

The effect of material defect orientation on rolling contact fatigue of a ball bearing

In this study, finite element method (FEM) is applied to investigate the effect of material defect orientation on subsurface crack initiation in rolling bearings. First, the history of stress intensity factors (SIFs) of a subsurface cubic material defect is calculated. SIFs calculation is conducted when it is parallel to the rolling surface of a bearing ring (varphi = 0^circ) under a ball rolling on the ring. Then, the effect of defect orientation, varying from varphi = 0^circ to varphi ; = ;30,; 45; {text{and}} ;60^circ, on the history of SIFs is investigated. It is deduced that changing the defect orientation results in a threefold increase in the equivalent SIF range compared to parallel orientation.

Mixed-mode dynamic fracture parameters for soda-lime glass

Dynamic mixed-mode fracture of soda-lime glass (SLG) was experimentally investigated using a full-field optical method - Digital Gradient Sensing (DGS) - in conjunction with ultrahigh-speed photography. Single edge-notched specimens were subjected to reverse impact loading using a modified Hopkinson pressure bar. The specimens were eccentrically loaded at different offset distances relative to the initial notch to achieve a wide range of mode-mixities, from mode-I to nearly mode-II condition, at initiation. Two time-resolved orthogonal angular deflection fields of light rays proportional to the respective full-field stress gradients were optically measured during experiments on different geometries. Mode-I and -II stress intensity factor histories spanning pre- and post-initiation behaviors were evaluated via over-deterministic least-squares error minimization of optically measured full-field data. By considering the critical stress intensity factors at different crack initiation modes, a fracture envelope for SLG encompassing various mode-mixities was developed for the first time for SLG and compared with predictions from prevailing approaches. An empirical fit of data seems to capture the overall trend whereas the prevailing methods do not. Measured crack kink angles are compared with the popular MTS and SED fracture criteria; both predict the kink angles reasonably well. Unlike brittle polymers, the critical effective stress intensity factors for SLG are independent of mode-mixity over a large range of values but show a decreasing trend as mode-II conditions become dominant and an extrapolated critical mode-II stress intensity factor of 0.37 MPa√m, approx. one-half of its mode-I counterpart, is seen.

Crack initiation and slow growth in soda-lime glass from a self-healed crack

Soda-lime glass (SLG) is a widely used structural material with many advantages in terms of thermal, physical and mechanical properties besides esthetics, sustainability and environmental impact. As a highly brittle, low-toughness and high-stiffness material, understanding its failure behavior in general and fracture mechanics in particular is critical for structural applications. The propensity for hairline crack formation at stress concentration sites during service is particularly a critical issue. Hairline cracks in SLG can occasionally heal when the structure is unloaded, become optically invisible and go undetected, causing unexpected and catastrophic failure upon reloading. In this work, crack initiation and quasi-static crack growth from a self-healed crack in SLG plate is recreated and investigated under laboratory conditions. A wedge-splitting test (WST) geometry is adopted to carry out the study. A pre-cut notch is loaded using a wedge to generate a hairline crack and let to heal without any external stimulus. An opto-mechanical study of crack (re)initiation and growth is carried out while mapping the crack-tip stress gradients in the whole field using the transmission-mode Digital Gradient Sensing (DGS) method. An abrupt re-initiation and extension of the self-healed crack, subsequent initiation of the natural crack-tip followed by a slow crack growth are all captured by the far-field load–displacement response as well as the local crack-tip fields. The stress intensity factor (SIF) history for the entire event is extracted subsequently. The results indicate approx. 50% lower value of critical SIF at re-initiation of the self-healed crack relative to the natural/virgin crack. The crack growth resistance behavior shows a nominally constant energy release rate of 6.5 ± 0.5 J/m2 during slow crack growth. A companion finite element (FE) model that mimics optical measurements is also included. The simulations suggest that the contact stiffness of the self-healed crack is about 60% of the virgin material.

Dynamic propagation behaviors of pure mode I crack under stress wave loading by caustics

Abstract It is always a difficult task to study the dynamic fracture of prefabricated cracks under stress wave loading. To investigate loadings of stress waves on dynamic cracks, a crack propagation testing configuration consisting of a one-point bend specimen loaded in split Hopkinson pressure bar (SHPB) was used, which loaded an unconstrained polymethyl methacrylate (PMMA) plate (120 mm × 60 mm × 5 mm) on the edge opposite to the cracked edge. A modified simple pre-cracked specimen geometry under impact stress wave loading to generate pure mode I crack at crack initiation was demonstrated, which can avoid the superposition and interference of various waves to facilitate the research. The numerical simulation was performed firstly by ABAQUS to prove the existence of the mode I field at the crack tip leading to crack propagation and indicate the stress distribution and evolution in the specimen caused by the propagation of the impact stress wave, analyze the propagation characteristics of the wave. Then dynamic caustics method in conjunction with high-speed photography was utilized in SHPB impact experiment. The propagation of shock stress wave in the specimen and its interaction with the prefabricated crack and the stress concentration at the tip of the prefabricated crack were analyzed. The corresponding stress intensity factor history is precisely determined. Finally, it is concluded that the observed distortion phenomenon at the impact point belongs to a caustic behavior under compression load, which reflects the stress concentration at the impact point. And the mode I failure occurs along the pre-crack direction. Specifically, the pre-crack shows obvious pure mode I crack propagation characteristics under symmetrical reflected tensile wave, the stress at the crack tip changes from compressive stress to tensile stress. And crack propagates under tensile stress wave reflected from its two free boundaries without crack, while the compressive stress wave can not make crack initiate and has little influence on crack propagation. Which agree with the numerical prediction.

Nonplanar Crack Growth Simulation of Multiple Cracks Using Finite Element Method

This work deals with a 2D finite element simulation of nonplanar multiple cracks using fracture and crack propagation analysis. This analysis was performed by using the developed source code software written by Visual Fortran Language. This source code includes the adaptive mesh generation utilizing the advanced front method and also the mesh refinement process. In order to correctly represent the field singularity, the quarter-point singular elements are constructed around the tip of the crack. The crack growth criteria are used to predict the crack growth direction by utilizing the circumferential stress factor in calculating the yielding stress in elastic fracture assumptions. The stress intensity factor determination is one of the most critical procedures as it determines the crack initiation and propagation mechanism. Moreover, the stress intensity factor histories during the crack growth are measured with the use of equivalent domain integral methods. The crack path simulation and stress intensity factor calculations are compared with the literature and revealed that the results are in agreement with research carried in this domain.

Evaluation of SIFs for cracks under thermal impact based on Green-Naghdi theory

This paper presents a study on the crack behavior under a thermal shock in a wide range of applications. The Stress Intensity Factors (SIFs) for a stationary crack under a non-Fourier thermal shock according to the Green-Naghdi (GN) theory is computed. The crack is considered as an adiabatic line in the framework of the eXtended Finite Element Method. The interaction integral is employed to extract the SIFs for three types of the Green-Naghdi theory. The differences in the time history of SIFs due to the thermal shock based on all types of the GN theory is studied. Also, the effect of damping coefficient on the SIFs and the temperature field is investigated. Finally, the role of inclined cracks, which disturb the time history of SIFs, displacement and temperature distributions for type II and III of the GN theory are discussed.

Effect of aspect ratio on dynamic fracture toughness of particulate polymer composite using artificial neural network

The present study discusses about the effect of the aspect ratio of the fillers on the fracture toughness of the glass-filled epoxy composites under impact loading. Three different kinds of fillers (spheres, flakes and rods) were used with different volume fractions (5%, 10% and 15%). Experimental results for Stress Intensity Factor (SIF) were obtained using a gas gun setup and a high speed camera. Further experimental investigation was done using fractographs obtained from Scanning Electron Microscope (SEM). Then the potential of using Artificial Neural Network (ANN) in predicting the effect of filler shape on the fracture behavior is studied. The framework of Multi-Layer Perceptron (MLP) feed forward network was used to predict the SIF history using four input parameters viz. time, dynamic elastic modulus, aspect ratio and volume fraction of the glass fillers. Experimental results of fracture test under impact loading were fed to train the ANN network and later the predicted results were compared with the experimental ones. Owing to the fact that predicted values had an accuracy of 91%, crack initiation toughness was predicted corresponding to the intermediate values of aspect ratio for which the experiments were not performed. Among the four input parameters, aspect ratio (largest/shortest dimension) was found to be the most important parameter in the prediction of SIF after time, followed by the dynamic modulus and volume fraction. The significance of aspect ratio lies in increasing the surface area to volume ratio which is responsible for the interfacial strength between the matrix and the filler and hence affects the fracture toughness of the overall composite material.

Method using XFEM and SVR to predict the fatigue life of plate-like structures

The hybrid method using the extended finite element method (XFEM) and the forward Euler approach is widely employed to predict the fatigue life of plate structures. Due to the accuracy of the forward Euler approach is determined by a small step size, the performance of fatigue life prediction of the hybrid method is not agreeable. Instead the forward Euler approach, a prediction method using midpoint method and support vector regression (SVR) is presented to evaluate the stress intensity factors (SIFs) and the fatigue life. Firstly, the XFEM is employed to calculate the SIFs with given crack sizes. Then use the history of SIFs as a function of either number of fatigue life cycles or crack sizes within the current cycle to build a prediction model. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Three numerical cases composed by a homogeneous plate with edge crack, a composite plate with edge crack and center crack are introduced to verify the performance of the proposed method. The results show that the proposed method enables large step sizes without sacrificing accuracy. The method is expected to predict the fatigue life of complex structures.

Analytical Solution of Cracked Functionally Graded Magneto-Electro-Elastic Half-Plane Under Impact Loading

The distributed dislocation technique is developed for the transient analysis of functionally graded magneto-electro-elastic half-plane where cracks are parallel/perpendicular with respect to the half-plane boundary. Laplace and Fourier transforms are employed to solve the governing equations leading to a system of Cauchy singular integral equations on the Laplace transform domain. The dynamic stress intensity factor history can be calculated by numerical Laplace transform inversion of the solution of the integral equations. Numerical results are provided to show the effect of the length and position of the cracks, geometry of interacting between the cracks, the magnitude and direction of magnetoelectrical loads and functionally graded constant on the resulting DSIFs. Also, the obtained solutions can be used as a Green’s function to solve dynamic problems involving multiple parallel finite cracks.

Dynamic analysis of cracks under thermal shock considering thermoelasticity without energy dissipation

This article reports a study of a cracked finite isotropic medium under nonclassic thermal shock based on thermoelasticity without energy dissipation. The time history of stress intensity factors as well as the temperature distribution around the crack tip is analyzed thoroughly. The fully coupled governing equations are discretized in the space by employing the extended finite-element method. The Newmark method is used as the time integration scheme to solve discretized equations. The stress intensity factors, which are extracted using the interaction integral method, are compared with other theories of thermoelasticity. The results of a cracked plate under temperature shock demonstrate that the stress intensity factors based on thermoelasticity without energy dissipation are significantly greater than those based on classic and Lord–Shulman models, whereas the peaks of stress intensity factors under heat flux shock are nearly equal for various theories of thermoelasticity. Furthermore, a mobile cold region is created along slanted crack in the temperature distribution, in which the temperature is less than the applied thermal boundary condition.

Fracture behavior of carbon fiber reinforced polymer composites: An optical study of loading rate effects

Crack initiation and growth in single-edge notched unidirectional T800s/3900-2 CFRP laminates are studied under stress wave and quasi-static loading conditions. An optical technique called reflection-mode Digital Gradient Sensing is also extended to study fracture mechanics of CFRP by using it in conjunction with ultrahigh-speed photography to perform full-field measurement of crack-tip deformations in the pre- and post-crack initiation regimes. DGS is capable of measuring two orthogonal surface slopes in the crack-tip vicinity as angular deflection of light rays. A method for extracting crack-tip parameters – the instantaneous crack speed and stress intensity factor (SIF) histories – associated with the stationary and propagating cracks using measured surface slopes is presented. The effect of fiber orientation in the range 0°–60° relative to the initial notch and two loading rates are investigated. Nominally mode-I fracture occurs when the fiber orientation is 0° whereas mixed-mode fractures ensue in others. Besides crack initiation occurrence at higher loads as fiber orientation increases, the SIF histories imply strong fiber bridging at low fiber orientations under quasi-static conditions. Furthermore, this CFRP shows significant loading rate dependence during crack growth. Unlike stress wave loading conditions, an increasing crack growth resistance immediately after crack initiation is seen under quasi-static conditions.

Dynamic fracture of soda-lime glass: A full-field optical investigation of crack initiation, propagation and branching

Dynamic crack initiation, growth and branching phenomena are comprehensively investigated in soda-lime glass using a vision-based method, Digital Gradient Sensing (DGS), in conjunction with digital ultrahigh-speed photography. Being a high-stiffness and low-toughness structural material, soda-lime glass poses enormous temporal and spatial challenges to opto-mechanical measurements using legacy techniques. Unlike the past works on indirect evaluation of instantaneous stress intensity factors in glass via crack speed, DGS is capable of direct quantification of both crack-tip fields and crack speeds. This is useful for examining the dynamic fracture characteristics such as pre- and post-crack initiation histories, crack initiation toughness, energy release rate (Gd)-apparent velocity (V) variation, and to shed light on crack bifurcation phenomenon. Accordingly, directly measured mixed-mode stress intensity factor histories and crack-tip velocity histories at branching and subsequent growth are reported. These are supplemented with Gd–V plots which show certain unique signatures at branching. From the measured fracture parameters, a material length characteristic based on microcracking due to normal stress in the crack growth direction ahead of the propagating crack that triggers branching is advanced.

Dynamic mixed-mode fracture behaviors of PMMA and polycarbonate

Mixed-mode dynamic crack initiation and growth in polymethymethacrylate (PMMA) and polycarbonate (PC) are studied experimentally. A simple specimen geometry in conjunction with a dynamic loading configuration to generate different mode-mixities at crack initiation is demonstrated. A Hopkinson pressure bar is used to rapidly load free-standing edge cracked samples in a reverse impact configuration. By eccentrically loading the specimen relative to the crack line, various mode-mixities at crack initiation are achieved by increasing the initial crack length while keeping all other experimental parameters the same. A relatively new full-field optical technique, Digital Gradient Sensing (DGS), along with high-speed photography is used to perform full-field measurements. DGS measures instantaneous angular deflections of light rays representing two orthogonal stress gradients under plane stress conditions. The mode-I and -II stress intensity factor histories are evaluated via over-deterministic least-squares analysis of optically measured data. By quantifying the critical stress intensity factors evaluated at crack initiation, dynamic fracture envelopes are developed for both the polymers. The results are studied comparatively and relative to the brittle fracture criteria. From measured stress intensity factors and crack speeds in the post-initiation regime, energy release rate vs. velocity plots for different mixed-mode configurations are produced for both the polymers.

Experimental investigation of dynamic crack propagation in PMMA plates

In this paper we present experimental data on dynamic crack propagation in square PMMA plates of two types – 3.5 and 20 mm thick. Samples were loaded dynamically (mode I loading type) and crack tip position was registered using high speed camera. Explosion of a copper wire due to high electrical current was used to load faces of the initially prepared cracks. In order to investigate stress intensity factor (KI) history, method of caustics was applied. Thick samples demonstrated considerably higher values of final crack travel distance and higher crack velocity values. Additionally, dependence of stress intensity factor on crack velocity was observed.

Investigation of dynamic multi-cracking behavior in PVB laminated glass plates

Radial multi-cracking phenomenon can be observed in Polyvinyl Butyral (PVB) laminated glass subject to the dynamic loading which may contain abundant impact information along with the material properties of the plate. Firstly, the cracking problem is investigated experimentally based on the high-speed photography in terms of crack propagation speed and morphology. In the meantime, a numerical simulation 3D model describing the same setup is suggested and the extended finite element method (XFEM) is introduced to study the multi-crack problem after the validation from the experiment results. The length history of brittle dynamic stress intensity factors (DSIFs) of various failure modes and the crack propagation mechanism based on the displacement field of crack tip and the K criterion of brittle solid is unraveled. A parametric study is then carried out to investigate the influence of four impact and material variables on the DSIFs. It is shown that the PVB interlayer is proven to play a very important role in glass cracking DSIFs and thus governs the crack propagation behavior. Results may provide fundamental explanation to the basic crack propagation mechanism on radial multi-crack in PVB laminated glass, thus to offer guidance for impact information extraction and cracking-resistant structure design and material selection.

Determination of Dynamic Crack Initiation and Propagation Toughness of a Rock Using a Hybrid Experimental-Numerical Approach

AbstractIn order to determine the mode-I (opening mode) dynamic fracture toughness of a rock, cracked-straight-through Brazilian disc (CSTBD) specimens with strain gauges glued on the specimen’s surface were diametrically impacted by a split Hopkinson pressure bar. A hybrid experimental-numerical approach was used to determine the dynamic initiation toughness, and it was also used in conjunction with a universal function to obtain the dynamic propagation toughness. Precautions were taken for getting the time history of dynamic stress intensity factors. Numerical accuracy, stability, and convergence to the solution were guaranteed by analyzing beforehand a widely-recognized benchmark dynamic crack problem. Using the numerical technique the result of the conducted trial analysis corresponded almost exactly with the classical result. The dynamic initiation toughness and dynamic propagation toughness of the rock increase with increasing dynamic loading rate and crack propagation speed, respectively, demonstra...

Dynamics of crack penetration vs. branching at a weak interface: An experimental study

In this paper, the dynamic crack-interface interactions and the related mechanics of crack penetration vs. branching at a weak interface are studied experimentally. The interface is oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. The focus of this investigation is on the effect of interface location and the associated crack-tip parameters within the bilayer on the mechanics of the ensuing fracture behavior based on the optical methodologies laid down in Ref. Sundaram and Tippur (2016). Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories in different bilayer configurations is performed using Digital Gradient Sensing (DGS) technique in conjunction with high-speed photography. The results show that the crack path selection at the interface and subsequently the second layer are greatly affected by the location of the interface within the geometry. Using optically measured fracture parameters, the mechanics of crack penetration and branching are explained. Counter to the intuition, a dynamically growing mode-I approaching a weak interface at a lower velocity and stress intensity factor penetrates the interface whereas a higher velocity and stress intensity factor counterpart gets trapped by the interface producing branched daughter cracks until they kink out into the next layer. An interesting empirical observation based on measured crack-tip parameters for crack penetration and branching is also made.

Dynamic Fracture of Layered Plates Subjected to In-Plane Bending

Layered structures typically used in applications such as windshields, thermal protection systems, heavy armor, etc., have property jumps at the layer interfaces. Present study focuses on understanding crack initiation and propagation in such systems under dynamic loading particularly when the property jumps are across the crack front. Layered plates were fabricated by joining polymethylmethacrylate (PMMA) and epoxy sheets using an epoxy-based adhesive (Araldite). Single-edge notched (SEN) specimens were subjected to dynamic loading using a modified Hopkinson bar setup. High-speed imaging coupled with dynamic photoelasticity was used to record the crack-tip isochromatic fringes from which the stress intensity factor (SIF) history was obtained. In selected experiments, a pair of strain gages installed on surfaces of specimen was used to record the strain history in the layers, from which the SIF in each layer was obtained. The results indicated that, prior to crack extension, the strain in both layers was identical. The crack tips in the layers start extending at different time instants with the one in the relatively brittle epoxy layer extending first followed by the one in the PMMA layer. At low impact velocity, the delay obtained was significantly higher than that at high impact velocity. The speed of epoxy crack was lower initially due to the bridging of the crack by the uncracked portion of the PMMA layer till initiation of the crack in the PMMA layer. This effect reduced at higher impact velocity for which the delay was much lower and the cracks propagated at a higher-speed.

Measurement of fatigue crack deformation on the macro- and micro-scale: Uniform and non-uniform loading

This paper describes the experimental measurement of near-tip displacement fields for a fatigue crack growing in a small compact-tension specimen. The specimen is pre-cracked conventionally, but then loaded in-situ in a scanning electron microscope. Digital image correlation is applied to the images collected and is analysed using an elastic model to produce stress intensity factor histories. A simple elastic/plastic model due to Pommier and Hamam is also applied, and the resulting behaviour is discussed. A single overload is applied to the specimen, and the effect of this on the elastic and elastic–plastic results is examined. The results are also compared to earlier work of a similar nature using a long-distance microscope, which gives an understanding of crack behaviour at a macroscopic length scale.

Fatigue evaluation of a composite railway bridge based on fracture mechanics through global–local dynamic analysis

An enhanced fatigue assessment of critical welded details in a steel–concrete composite railway bridge was carried out by fatigue crack propagation analysis based on linear elastic fracture mechanics (LEFM). The most fatigue critical connections concerned in this study were identified by the preliminary fatigue assessment based on the S-N method in the previous research of the authors Zhou et al. (2013) . Three-dimensional crack models of the critical connections were incorporated into the global–local finite element model of the bridge. The stress intensity factor (SIF) histories of the cracks were calculated through dynamic analysis of the bridge due to the high-speed train passages, which validated the applicability and the accuracy of the empirical SIF formulas for the concerned bridge details. The fatigue crack growth curve, represented by crack size versus number of train passages, was obtained through crack propagation analysis based on the Paris law and LEFM, and fatigue propagation life was predicted for each critical connection. The proposed crack propagation analysis method provides a general and alternative approach to evaluate the fatigue life of welded details in steel bridges.