Local Stress Intensity Factor Research Articles

Study of the mechanical behavior and multiscale simulation of the crack propagation in a bilinga wooden beam

The mechanical behavior of local wood species (Bilinga) in the south west region in Cameroon during rainy and dry seasons and the mechanical behavior of wooden beam under bend loading are studied. The three points flexural tests were used to determine the mechanical properties of the wood under study. ANSYS 2020 R1 finite element (FE) software is used for numerical simulations at a macroscopic level using one of the newer technologies called Smart crack growth, which was introduced in the 2019 version. The geometry was modeled in SolidWorks with an initial crack length of 4 and 8 mm introduced in each sample and then imported to ANSYS workbench for further analysis with ANSYS which has all the tools to perform linear fracture. The stress intensity factor (SIF) determines the fracture toughness of a material which is subjected to linear-elastic fracture mechanics (LEFM) where a variable of the critical stress intensify is denoted as KIc. The fatigue crack growth was modeled using Paris’ law. The crack growth was simulated based on Mode I crack specimen with an initial crack length of 4 and 8 mm, respectively. The stochastic multiscale modeling of crack growth on meso- and microscale is used to compare the crack growth rate in the approach of a heterogeneous material and taking into account the microstructure and fracture mechanism of the Bilinga wood. The results of stochastic modeling of the crack growth in the array of cracks and pores of a characteristic size shows that the simulation is close to FE-modeling results. Therefore, the stochastic simulation of the crack growth in wood at meso- and microscale shows the lower local stress intensity factors and slower crack growth due to the existence of the scale-time hierarchy. The crack growth rate vcr at a macroscale ranges within 0.845 – 0.9 × 10–3 m/sec which corresponds to the macroscopic value of the fracture toughness KIc.

Singular integral based closed-form solutions for modified EMPS models in semipermeable magneto-electro-elastic materials

The singular integral equation method is applied to present analytical solutions for modified electric-magnetic-polarization saturation (EMPS) models subjected to semipermeable center cracked magneto-electro-elastic (MEE) materials. A generalized methodology is presented to explicitly solve the EMPS model under any arbitrary saturated electric and magnetic conditions using the distributed dislocation method (DDM) and finding the analytical solutions for developed singular integral equations. The explicit expressions are derived for distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), saturated zone lengths, and local stress intensity factor (LSIF) for particular cases of the generalized EMPS model such as constant, linear, quadratic and cubic polynomial varying saturated electric and magnetic conditions. Using an iterative scheme and the explicit solutions of COD, COP, and COI, the exact semipermeable crack-face conditions are evaluated at the center of the crack, and the same applies throughout the crack-surface for the study of semipermeable modified EMPS models. A comparative analysis of the fracture parameters has also been carried out between the results of exact semipermeable crack-face conditions and the results of semipermeable crack-face conditions of the center crack problem to analyze the impact of polynomial varying saturated conditions on the crack-face conditions. Numerical studies performed under different electromagnetic-mechanical loadings, volume fractions, and crack-face conditions demonstrate the increasing effects in the fracture parameters' values with the degree of the polynomial varying saturated conditions.

3D characterization of closure of surface and internal fatigue cracks in nodular cast iron using Digital Volume Correlation of laboratory X-ray tomography images

Digital volume correlation (DVC) of laboratory X-ray tomography images has been used to characterize the closure of artificial internal fatigue cracks in nodular graphite cast iron. DVC allows to produce crack opening displacement (COD) map from 3D tomography images at the sub-voxel scale thanks to the graphite nodules which can be used as internal natural markers. Fatigue samples containing controlled internal defects have been produced in a nodular cast iron by diffusion bonding plates containing laser-machined sharp notches. Specimens with internal cracks and surface cracks were respectively characterized by laboratory tomography at different loads during fatigue crack propagation tests. The local stress intensity factors (SIFs) have been extracted from the measured displacement fields by using Williams series, based on those results the closure levels of internal cracks and surface cracks were comparatively analyzed and discussed. Crack closure levels were found to be linearly related to the location of the surface crack front, and the level of internal crack closure was comparable to that of the surface crack in bulk.

High-cycle and low-cycle fatigue life prediction under random multiaxial loadings without cycle counting

A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers.

A multiscale fracture model to reveal the toughening mechanism in bioinspired Bouligand structures

The Bouligand structure has been observed in a variety of biological materials, such as lamellar bone and exoskeleton of lobsters. It is a hierarchical and non-homogeneous architecture that exhibits excellent damage-resistant performance. This paper presents a multiscale fracture model considering the material inhomogeneity, the multiscale property, and the anisotropy to reveal the toughening mechanisms in the Bouligand structure. Firstly, the macro and micro constitutive properties of this composite are derived. Then, a multiscale fracture model is developed to characterize the local stress intensity factors and the energy release rates at the crack front of twisted cracks. Our results demonstrate that the decrease in the local energy release rate can be attributed to two-step mechanisms. The first mechanism is that the multiscale structure and the material inhomogeneity cause a release of stress near the initial crack tip. The second mechanism is that the twisted crack leads to the transformation from single-mode loading to mixed-mode loading, which enhances the fracture toughness. These results can not only reveal the toughening mechanism of the Bouligand structure but also provide guidelines for the design of high-performance composites. Statement of significanceBiological materials in nature often possess excellent mechanical properties that have not been achieved by synthetic materials. Bioinspired Bouligand structures provide prototypes for designing high-performance materials. In this study, we propose a multiscale theoretical fracture model to investigate the fracture properties of Bouligand structures with twisted cracks. We systematically consider the roles of material inhomogeneity, anisotropy, and multiscale properties. Our analysis demonstrates that the remarkable toughness of Bouligand structures results from the combined effects of material inhomogeneity and twisted cracks. This research contributes to unveiling the secret behind the outstanding toughness of Bouligand structures and provides inspiration for the development of novel designs for man-made composites.

Singular integral method based closed form solution for moving EMPS model in semipermeable two‐equal‐collinear cracked MEE material

AbstractThis paper presents the analytical closed‐form solutions of moving two equal collinear semipermeable cracks in magneto‐electro‐elastic material considering the strip electric‐magnetic polarization saturation (EMPS) model. To simulate the dynamic/moving cracks problem, two equal collinear Yoffe type cracks moving with a constant subsonic velocity along the plane of the cracks is considered. The problem is solved by considering semipermeable crack face conditions and under the in‐plane electro‐magnetic‐mechanical loading. Applying distributed dislocation technique and symmetry of the collinear cracks, the problem is reduced into simultaneous singular integral equations which have been solved in closed form expressions using finite Hilbert approach. The explicit expressions for dynamic distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), and local stress intensity factors (LSIFs) are evaluated for both the cases of the EMPS model (magnetic zone is smaller or greater than electric zone). For evaluation of inner and outer electric and magnetic zone lengths (MZLs), an iterative approach is applied to solve the developed two non‐linear equations. Also, to implement the semipermeable crack‐face conditions, a bisection iterative method has been applied. Based on the developed closed form solutions, numerical studies are presented for standard fracture parameters with respect to crack propagation velocity, electrical loading and inter‐crack space distance. This study shows that electric displacement and magnetic induction defined over the crack‐surface for semipermeable conditions decrease whereas the numerical values of saturated zone lengths, COD, COP, COI, and LSIFs increase with increasing crack propagation velocity. Moreover, for both static and dynamic cracks problems, the significant crack‐interaction effects have been observed on all the studied fracture parameters except the crack‐face conditions.

Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique

AbstractIn this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.

Fatigue analyses and life predictions of copper laser-welded lap-shear samples

This study experimentally and numerically investigated the fatigue response of laser-welded (LW) lap-shear samples in copper (Cu) sheets of dissimilar thicknesses. Fatigue tests were first conducted, and the resulting fatigue data and failure modes were recorded. To investigate the failure processes and mechanisms, microscopic examinations, including microhardness tests for Cu LWs, were conducted before and after the failure. The experimental results showed the interfacial failure under high-load-range and low-load-range conditions and the top sheet separation under median-load-range conditions. Next, finite element analyses for LW lap-shear samples were conducted to calculate the global stress intensity factors (GSIFs) and local stress intensity factors (LSIFs) for interfacial and kinked cracks, respectively. The GSIFs, LSIFs, and Paris law were further used to derive the two fatigue models to analyze the evolution of interfacial and kinked cracks, respectively. Finally, two fatigue models estimated a series of fatigue lives that matched the general trends of experimental data.

A microstructure-sensitive analytical solution for short fatigue crack growth rate in metallic materials

Short fatigue crack growth in engineering alloys is among the most prominent challenges in mechanics of materials. Owing to its microstructural sensitivity, advanced and computationally expensive numerical methods are required to solve for crack growth rate. A novel mechanistic analytical model is presented, which adopts a stored energy density fracture criterion. Full-field implementation of the model in polycrystalline materials is achieved using a crystallographic crack-path prediction method based on a local stress intensity factor term. The model is applied to a range of Zircaloy-4 microstructures and demonstrates strong agreement with experimental rates and crack paths. Growth rate fluctuations across individual grains and substantial texture sensitivity are captured using the model. More broadly, this work demonstrates the benefits of mechanistic analytical modelling over conventional fracture mechanics and recent numerical approaches for accurate material performance predictions and design. Additionally, it offers a significant computer processing time reduction compared with state-of-the-art numerical methods.

Defect-based characterization of the fatigue behavior of additively manufactured titanium aluminides

The additively manufactured titanium aluminide alloy TNM-B1 was characterized microstructurally and mechanically in the as-built and hot isostatically pressed (HIP) condition. Tensile and constant amplitude tests were performed at room temperature and 800 °C. Using fractographic SEM images, the fracture-inducing defect was identified. With the HIP, defect number and size could be reduced, increasing fatigue strength by 43% to 500 MPa. Using the model approaches of Murakami and Shiozawa, the fatigue life was correlated with the local stress intensity factor and could be described as function of the stress amplitude as well as the size and location of fracture-inducing defects.

Dynamic effects and an oscillator model of a spatio-temporal representative volume describing fracture process at the crack

An analytical investigation of a fundamental dynamic fracture effect observed in samples with a crack under shock-wave pulse load is provided. Particular attention is paid to the phenomenon of delayed fracture. The effect can be described in the following way: the fracture in the crack tip vicinity can possibly take place after the local stresses reached their maximum value. A number of important features of dynamic fracture under the threshold and beyond threshold loads, observed in various experiments, are discussed. It was found that the experimentally registered fracture delay can be clearly explained within the framework of the structural-temporal approach based on the concept of the incubation time of fracture. The conditions for the delay are found and the corresponding analytical formulas are given. Additionally, a simple analogy based on a mass-spring model is discussed. Analytical formulas available for the oscillator model help to find some non-obvious similarities between the crack behaviour under short pulse loads and the oscillator failure due to analogous loads. It is concluded that it is essential to study threshold cases in which the most important time effects appear that do not fit into the classical concepts of strength and crack resistance – the concepts that rely on local ultimate stress and/or critical intensity factor parameters.

Crack propagation modelling for service life prediction of large slewing bearings

Slewing bearings in wind turbines are meant to last 20 years or longer. But wind turbine accidents (structural failure) occur nevertheless in some cases earlier. Minimizing the risk and with this enhancing the public acceptance of wind turbines is of great importance for the increase of alternative energy production. For a more accurate prediction of the service life of slewing bearings XFEM calculations with crack initiation and crack propagation are developed using Abaqus XFEM. The material parameters such as Paris coefficients for crack propagation and fracture toughness values (KIC) were measured in advance on samples of different heat treatment conditions. With a linear elastic fracture mechanics approach the local stress intensity factor range ΔK for a given starting crack front is calculated. Coupling this information with the Paris-law and a maximum crack propagation interval of 0.1-0.3 mm, the number of cycles to failure during crack propagation is determined. The crack is extended stepwise until ΔK reaches the limiting fracture toughness of the material. The crack propagation model was first validated on different test specimen geometries. Correlating these first simulated test results with experimental data the crack initiation phase can be estimated. The simulation of real components, such as bearings, will be developed subsequently, using calculated stress distributions provided by other partners in the project as input parameters (sub-structure approach). Fatigue tests are also done on pre-corroded specimens since bearing failure may also be promoted by an unfavorable combination of overloads and corrosion damage.

Kinked and forked crack arrays in anisotropic elastic bimaterials

The fracture problem of multiple branched crack arrays in anisotropic bimaterials is formulated by use of the Stroh formalism to the linear elasticity theory of dislocations. The general full-field solutions are obtained from the standard technique of continuously distributed dislocations along finite-sized cracks of arbitrary shapes, which are embedded in dissimilar anisotropic half-spaces under far-field stress loading conditions. The bimaterial boundary-value problem leads to a set of coupled integral equations of Cauchy-type that is numerically solved by using the Gauss–Chebyshev quadrature scheme with appropriate boundary conditions for kinked and forked crack arrays. The path-independent Jk-integrals as crack propagation criterion are therefore evaluated for equally-spaced cracks, while the limiting configuration of individual cracks is theoretically described by means of explicit expressions of the local stress intensity factors K for validation and comparison purposes on several crack geometries. The short-range interactions resulting from the idealized configurations of infinitely periodic cracks are investigated as well as various size- and heterogeneity-effects on the mixed-mode cracks in complex stress-state environments. The influences of anisotropic elasticity, elastic mismatch, applied stress direction, inter-crack spacings and crack length ratios on the predictions from the Jk- and K-based fracture criteria are examined in the light of different configurations from the single kinked crack case in homogeneous media to the network of closely-spaced forked cracks in presence of bimaterial interfaces.

Analysis of prospective SIF and shielding effect for cylindrical rough surfaces obtained by L-PBF

Fatigue properties of parts built by Additive Manufacturing (AM) are strictly related to process-induced defects and complex surface morphology. Several studies have proved that surface valleys act as crack initiation sites, similarly to surface micro-notches. However, different roughness parameters have been considered in literature for the depth of the surface notches, together with the adoption of a shielding factor. The aim of this study is to understand how the surface complexity of L-PBF (Laser-Powder Bed Fusion) AlSi10Mg cylindrical specimens in as-built condition can affect the fatigue behaviour. In detail, CT (Computer Tomography) scans were adopted to characterize the surface quality and 2D FE (Finite Element) analyses were used to calculate the local stress intensity factor at the most critical valleys in the surface. The results of the FE analyses were compared with a shielding factor determined for regularly spaced notches. In spite of the significant scatter, the average geometric factor value for surface notches in L-PBF surfaces is correctly predicted by the traditional shielding factor.

3D predictions of the local effective stress intensity factor as the fatigue crack propagation driving force

The objective of this study is to develop a numerical tool using the commercial software, Abaqus and Python, to predict the fatigue crack front shape while taking into account the influence of plasticity induced crack closure on crack propagation in three Dimensional (3D) structures. In this aim, a 3D model of a compact tension specimen made out of stainless steel 304L, and subjected to a constant loading scheme, is proposed. The crack propagation is considered to be driven by the stress fields developed in the vicinity of the crack tip and thus by the stress intensity factor K. Two parallel simulations are used: an elastic simulation intends to calculate the local maximum stress intensity factor while the other, an elasto-plastic one, aims at obtaining the plastic wake and the resulting crack closure load. The results of both simulations are combined in order to constitute the effective stress intensity factor range, which is in turn used, along with Paris law, to calculate the crack propagation along the thickness. The local crack advancements obtained allow to construct the new crack front. Finally, a node release technique is used with geometry remeshing to issue new iterations with new boundary conditions that respond to the changes in the crack front. The procedure is repeated until the stabilization of the effective stress intensity factor values all along the specimen thickness is reached. The results obtained are compared with previously issued experimental results, showing very good results in small scale yielding and beyond that a large dependency on the plastic zone size developed in the neighborhood of the crack front.

Closed-form solutions for modified polarization saturated models in two unequal collinear cracked piezoelectric media considering coalesced interior zones

In this paper, we present polynomial varying modified polarization saturation models for semipermeable two unequal collinear cracks with coalesced interior zones in piezoelectric media. Under the influence of far-field electromechanical loadings, the cracks situated in an infinite arbitrary polarized piezoelectric media are opened in self-similar manner, forming a strip saturated zone in front of the cracks-tips. Here, we modify the polarization saturation (PS) model in a way by arresting these zones with linear, quadratic and cubic polynomials types variable saturated conditions in place of constant saturated condition. Such modified PS models are, by using complex variable and Stroh formalism techniques, firstly reduced into simultaneous non-homogeneous Riemann–Hilbert problems in complex variable field functions, and the corresponding solutions are then obtained. The closed-form solutions for standard fracture parameters such as saturated zone lengths, local stress intensity factors(LSIFs), crack opening displacements and crack opening potentials are derived. Numerical studies are illustrated for all the modified PS models by analyzing the effects on saturated zone lengths and LSIFs with respect to the variations in electrical loadings, poling direction and crack lengths. Moreover, the obtained results are compared with the results of PS model. The study concludes that the saturated zone lengths and LSIFs increase significantly with the increase in degree of polynomial varying saturation condition.

Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.

Analysis and verification of a biomimetic design model based on fish skin

Many biological architectures are Bouligand structures, which comprise uniaxial fiber layers stacked in a periodic helical arrangement and are characterized by high damage resistance. As an effective flexible protective structure, fish skin is a Bouligand structure that protects the body while ensure flexibility during swimming and predation. In this paper, an analytical model inspired by fish skin is established based on previous studies, and the parameters for describing crack growth are determined. Then, mathematical expressions for the local stress intensity factors and plastic zone are used to predict how the helical stacking angle α influences the crack propagation. The results show that crack deflection and twisting improve the fracture toughness of the composite structure greatly, with the optimal fracture toughness being that for α = 60° – 70°. Moreover, biomimetic flexible composite structures inspired by fish skin are produced using silicone and Kevlar fibers. Scanning electron microscopy is used to observe the cross-sectional morphology of the composite structures, showing that the interfaces between the silicone and Kevlar fibers are highly compact. Results from experimental impact tests agree well with the predicted results.

Complex variable solution for mode-III quadratically varying PS model in piezoelectric media

Complex variable technique and extended Stroh formalism approach are applied to develop the closed-form solutions for mode-III quadratically varying polarization saturation (PS) model in an infinite piezoelectric media. A semipermeable centre crack problem is considered for study under the influence of out of plane far-field mechanical loading and in-plane electrical displacement loading. Similar to PS model, the electrical yielding zones or saturated zones are considered just infront of the crack-tips in the form of a strip. But in place of constant PS condition imposed on yielding zones, the quadratically varying PS condition is considered for study. Mathematically, this problem reduces into simultaneous non-homogeneous Riemann-Hilbert problems which are solved by finding the solutions of involved singular integrals. Hence, some standard fracture parameters are derived in explicit forms such as saturated zone lengths, crack sliding displacement, crack potential drop and local stress intensity factor. Also, the comparative studies for quadratically varying PS model and PS model are presented graphically.

Effect of cyclic heating on subcritical crack growth of rock beams under four-point bending test

This study considers the effects of cyclic differential heating on the velocity of the subcritical crack growth (SCG) from a central notch in rock beams under four-point bending test. Beams of both Carrara marble and Fujian granite are subjected to non-uniform heating, with heating from the top surface containing the notch (at about 60° Celsius) and with cooling to the bottom side with no notch (at about 25° Celsius). Beams are heated for 7–188 days before they are subject to constant load creeping test under four-point bending configuration, and the compliance method is used to interpret crack growth from the crack mouth opening displacement (CMOD). The compliance method is verified by using acoustic emissions from cracking events together with simultaneous microscopic observations. It was discovered that a microcrack processing zone (PZ) was observed in the form of white patches ahead of the notch tip during the creeping test, followed by sudden jumps of macrocrack growth. Linear elastic fracture mechanics (LEFM) is used to calculate the local stress intensity factor, which is then further related to crack growth velocity, through the commonly adopted power law. After the application of non-uniform cyclic heating, the P-wave velocity of Fujian granite increases (due to microcrack closure) whilst that of Carrara marble decreases (due to parallel crack formation). The SCG parameters in the power law (power index n and threshold velocity v0) are obtained. There is no clear trend in the variation of the SCG parameters with the number of heating cycles. However, these parameters are used to simulate subcritical crack growth velocity for both heated and unheated specimens. In the light of fracture mechanics analysis, we conclude that Fujian granite is clearly preferable to Carrara marble in making rock panels on cladding of buildings.