Crack Front Research Articles

Observing the crack tip behavior at the nanoscale during fracture of ceramics

Ultimately, brittle fracture involves breaking atomic bonds. However, we still lack a clear picture of what happens in the highly deformed region around a moving crack tip. Consequently, we still cannot link nanoscale phenomena with the macroscopic toughness of materials. The unsolved challenge is to observe the movement of the crack front at the nanoscale while extracting quantitative information. Here, we address this challenge by monitoring stable crack growth inside a transmission electron microscope. Our analysis demonstrates how phase transformation toughening, previously thought to be effective at the microscale and above, promotes crack deflection at the nanolevel and increases the fracture resistance. The work is a first step to help connecting the atomistic and continuous view of fracture in a way that can guide the design of the next generation of strong and tough materials demanded by technologies as diverse as healthcare, energy generation, or transport.

Effect of fiber orientation of adjacent plies on the mode I delamination fracture of carbon fiber reinforced polymer multidirectional laminates

AbstractThe extensive use of multidirectional composite laminates requires to understand the delamination behavior at interfaces between plies with different fiber orientations. In this study, double cantilever beam testing was performed to investigate the mode I interlaminar fracture of carbon fiber reinforced polymer laminates with different central interfaces (0//0, 0//+45 and +45//−45). X‐ray microtomography revealed the curved crack front shape that was incorporated to calculate fracture toughness. The fracture toughness varies with the crack length in a typical delamination resistance curve, which can be quantified by an empirical equation. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate, compared to constant toughness. It was found that the delamination mechanism is independent of central interfaces. However, compared to unidirectional laminates, multidirectional laminates are less resistant to crack initiation, but more resistant to propagation with higher toughness and shorter fiber bridging zone.Highlights Mode I interlaminar fracture of CFRP laminates with different central interfaces was investigated experimentally and numerically. Curved crack front shape was incorporated to calculate fracture toughness. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate. Multidirectional laminates are less resistant to crack initiation but more resistant to propagation with higher toughness and shorter fiber bridging zone.

Size Selection of Crack Front Defects: Multiple Fracture-Plane Interactions and Intrinsic Length Scales.

Material failure is mediated by the propagation of cracks which, in realistic 3D materials, typically involves multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures, such as step defects on tensile fracture surfaces. Steps form once a slowly moving, distorted crack front segments into disconnected overlapping fracture planes separated by a stabilizing distance h_{max}. Our experiments on numerous brittle hydrogels reveal that h_{max} varies linearly with both a nonlinear elastic length Γ(v)/μ and a dissipation length ξ. Here, Γ(v) is the measured crack velocity v-dependent fracture energy, and μ is the shear modulus. These intrinsic length scales point the way to a fundamental understanding of multiple-crack interactions in 3D that lead to the formation of stable out-of-plane fracture structures.

Three-dimensional fracture modes decoupling by means of invariant integrals in wood under mixed mode loading

This paper addresses the determination of the energy release rate in an orthotropic elastic material such as wood with a three-dimensional view of the problem. The mixed mode loading associated with the anisotropy of the material required mode decoupling by isolating the energy release rates in mode I, mode II and in mode III. These energy release rates are calculated using the invariant integral M of Linear Elastic Fracture Mechanics (LEFM). This decoupling has necessitated the introduction of kinetically and statically admissible three-dimensional virtual displacement and stress fields in the vicinity of the crack front. The fracture mode decoupling strategy is presented and implemented through finite element modelling of a Mixed Mode Crack Growth (MMCG) specimen. Different thicknesses are investigated to highlight the 3D effects. The modelling highlighted the effect of Mode II at the edges of free surfaces for mixed loadings including mode III (mode III, mode (II+III) and mode (I+II+III)), while mode III was the predominant at the middle of the specimen. In cases of mixed mode (I+II), the energy release rate GI was highest at the middle of the specimen and lowest at the edges of the free surfaces, regardless of the degree of mixing for a given thickness. The correlation between the results obtained using the proposed approach and the non-dependence of the integration domain, as well as with the usual approaches employed in the literature, is demonstrated.

Deformation, fracture, and fatigue crack growth behavior in TiB-reinforced near-α Ti matrix composites fabricated using powder metallurgy technique

Titanium matrix composites with TA15 alloy as the matrix and TiB (ranging from 0 to 4 vol%) as reinforcement were produced via powder metallurgy-based hot press sintering, employing AlB2 precursor. The addition of TiB to TA15 led to a substantial reduction in the colony and prior β grain sizes, and an increase in the lath thickness in the composites. Plastic deformation due to planar slip, which traverses across the α/β-ligament phase boundaries within each colony, may cause TiB particles located on colony boundaries to break, potentially more so than those within the colony. The composite containing 1 vol% TiB exhibited simultaneous improvements in strength, ductility, and strain hardening rate, attributed to colony refinement and possibly a sizable amount of intra-boundary TiB. Further increase in the TiB content led to significant drops in ductility, which was further exacerbated by the precipitation of α2-Ti3Al phase. A substantial decrease in the mode I fracture toughness, attributed to reduced colony size and diminished crack deflection, was noted in the composite with 1 vol% TiB. The colony size refinement also contributed to a reduction in the threshold stress intensity factor range, ΔK0, for the fatigue crack growth, owing to the decreased tortuosity of the fatigue crack front. This study elucidates the intricate relationship between TiB location, microstructure, and mechanical properties, providing insights for the design of TiB-reinforced titanium alloys with both α and β phases.

Fatigue life prediction for Q420qFNH weathering steel welded joints considering the effect of multiple cracks

Multiple semi-elliptical cracks frequently develop at the weld toes of welded joints. These interfering multiple cracks significantly accelerate crack growth rates and reduce the fatigue life of a welded joint compared to a single crack. This study proposes a method for predicting the fatigue life of a welded joint with multiple cracks, considering weld toe amplification effect, multiple crack interference amplification effect, and crack closure effect. The method is validated through fatigue tests on Q420qFNH weathering steel welded joints. The main factors influencing the interference amplification effect are investigated, and theoretical formulas for the interference amplification factor of the stress intensity factor are derived using the finite element method and the superposition principle. The initiation, aggregation, and morphological evolution during the propagation process of multiple cracks is accurately simulated, and the fatigue life of both cruciform-welded and butt-welded joints is predicted. Additionally, a quantitative analysis is conducted to assess the impact of the number of fatigue cracks on fatigue strength. The results indicate that the interference amplification effect of cracks depends on their distance and mainly affects the surface point where the crack front is closest. The proposed fatigue life prediction method can accurately estimate the fatigue life of Q420qFNH steel welded joints considering the effect of multi-cracks. The interference and coalescence of multiple cracks significantly reduce the fatigue life of welded joints. An increase in the number of fatigue cracks notably decreases the fatigue strength.

Fracture Mechanisms and Toughness in Polymer Nanocomposites: A Brief Review

This article underlines the observation that, unlike the underperformance of nanocomposites in as far as their static mechanical properties of modulus and strength are concerned, fracture toughness exhibits exceptional behavior. This is attributed to the fact that fracture toughness expresses a measure of the energy absorbed in crack propagation, namely, the energy involved in creating new surface area, which, in turn, is controlled by a specific type of energy-dissipating interaction of the crack front with nanoparticles. This concise review focuses on two micromechanisms that are considered representative of energy dissipation due to their frequent presence in nanocomposites of both nanoparticles and nanofibers. Examples taken from recent relevant articles are presented to showcase fracture toughness improvements by nanoparticles.

Investigation of individual lack-of-fusion defects in the fatigue performance of laser-powder bed fusion Ti6Al4V alloys: A finite element analysis

Laser-Powder Bed Fusion (L-PBF) techniques have revolutionized the production of Ti6Al4V alloys across various industries. However, the widespread adoption of L-PBF Ti6Al4V alloys is impeded by their inadequate fatigue performance, particularly in high cycle regimes. A significant contributing factor to this limitation is the presence of internal defects inherent to the L-PBF process, act as sites for fatigue crack initiation. Previous investigations have focused on the fatigue performance of L-PBF Ti6Al4V alloys with gas porosities, while research on lack-of-fusions (LOFs) which are recognized as the most detrimental defects, remains limited. In order to deepen our understanding of the factors influencing the reduced fatigue performance observed in L-PBF Ti6Al4V alloys associated with inherent LOFs, this study employed three-dimensional (3D) finite element analysis approaches. Such approaches allow to assess fatigue indicator parameters to evaluate fatigue life and predict fatigue crack propagation. A 3D average Smith-Watson-Topper method has been proposed, which is able to rationally estimate the fatigue life of L-PBF Ti6Al4V. In addition, a novel finite element method has been developed to accurately calculate stress intensity factors along irregular shaped crack front of a notch-like feature embedded on a LOF. Additionally, parametric studies were conducted to gain further insights into the influence of LOFs on fatigue performance. The results shown the presence of embedded humps and notch-like features, and their topologies play key roles in the fatigue performance of LOF predominated L-PBF Ti6Al4V alloys.

Simulation of fatigue crack growth in aluminium alloy 7075-T7351 under spike overload and aircraft spectrum loading

The trend towards virtual testing and digital-twin assisted management means that the accurate and reliable simulation of fatigue crack propagation behaviour is more important than ever. Reliable but conservative approaches to support this are in widespread use in the aerospace industry. Nevertheless, the conservatism comes at a significant cost in terms of reduced structural life and an increased ongoing inspection requirement and, as such leads to questions about the economic burden of these approaches. Recent comparisons between blind predictions and test results revealed the extent of the issue for cracking in aluminium alloy 7075-T7351 coupons with configuration and loading representative of military transport aircraft wing skins. The current models were generally conservative by a factor of two or more in terms of crack propagation life. This suggested that there was significant scope to improve the modelling to better reflect all the complex contributing factors. The current work has investigated the issue of changes in the crack front constraint as the crack progresses from a state of high constraint (close to plane strain) to a lower constraint (approaching plane stress). This issue was investigated both experimentally and with the development of an improved analytical model. A test program was conducted on several specimens, loaded under constant-amplitude, constant-amplitude with spike-overloads and a variable amplitude spectrum. Crack-opening stress levels were measured at key points in the tests and the results were used to develop and evaluate improved modelling approaches. The improved model was generally able to predict crack growth within about ± 30 % of that demonstrated along with the correct form of the crack growth, which is a significant advance and will lead to reduced costs and increased safety.

Determination of the plastic J integral of ductile material using the XFEM with only Heaviside function and variable-node elements

In this paper, the extended finite element method (XFEM) with only Heaviside function is proposed for the elastic–plastic fracture mechanics (EPFM) modeling. The proposed method removes tip enrichment functions depending on the polar coordinates at the crack front, and a step function only determined by the level set function is utilized to track the crack front. To alleviate the volumetric locking phenomena caused by the plastic incompressibility, the B-bar method is incorporated into the three dimensional (3D) XFEM program. Therefore, the fully integration scheme can be chosen to ensure the accuracy when addressing large plastic deformation in EPFM analysis. Additionally, the material tangent stiffness matrix of Ramberg-Osgood constitutive is given, and the local refinement technique using variable-node elements is adopted to reduce the number of elements and nodes for efficient analysis. A Newton-Raphson iterative algorithm is developed to solve the nonlinear algebraic equations caused by material nonlinearity. Several numerical examples including the determination of crack opening displacement, and the fully plastic J integral in the ductile materials are presented to test the performance of the proposed method. Comparisons with the results from the existing methodologies show that the new enrichment scheme can save computational cost and obtain sufficient accuracy even in the case of 3D curved crack.

Crack Growth Patterns of Aluminum Tubular Specimens Subjected to Cyclic Tensile Loads

This study presents a detailed analysis of a fatigue test campaign in order to identify different crack patterns. It was conducted on 6061-T6 aluminum tubular specimens featuring an internal diameter of 10 mm and different thicknesses (2, 3 and 4 mm). These specimens were subjected to cyclic tensile loads with a load ratio of R = 0.1, utilizing a sinusoidal load function at a frequency of 3 Hz. The investigation examines the crack growth rates, the stress intensity factor, and the final and intermediate fracture zones by applying overloads in some cases. The differences with two-dimensional specimens and the importance of this study for the interpretation of results with biaxial loading states are highlighted. The different states of crack growth detected are analyzed using artificial vision techniques. The differences between the exterior and interior faces of the specimen are revealed, and a series of states prior to the formation of the radial crack front expected in these specimens are identified.

DoE-based modeling of cracked 3D orthotropic panels with stiffeners

This study uses the Design of Experiments (DoE) technique to develop analytical formulations for the stress intensity factor and other non-singular variables near the crack front of a stiffener-reinforced three-dimensional orthotropic panel. The method employs a 52 fractional factorial design, effectively reducing the number of finite element simulations required. The input variables consist of four parameters, each with five levels, which directly affect the process responses. The statistical analysis is performed using the Ellistat software, which offers powerful tools for Design of Experiments (DoE) and incorporates specialized algebraic-statistical approaches. These techniques are utilized for analysing the outcomes and formulating a mathematical model of the cracking characteristics for panels that are strengthened with five stiffeners. The findings of the analysis of variance (ANOVA) indicate strong statistical significance for all tested models, hence verifying their validity based on statistical evaluation criteria. In addition, the residual analysis demonstrates a normal distribution, which strengthens the reliability of the underlying models and fulfils a vital requirement for numerous statistical analyses. The analytical formulations that come from this study have enormous potential for practical use in the field of engineering, specifically for structures that are orthotropic and feature cracks. This study signifies a notable progress in integrating numerical simulation, statistical analysis, and mathematical modelling to develop pragmatic and dependable analytical instruments for the examination of intricate systems.

A closed form expression of stress intensity factor for an arbitrarily shaped planar crack in 3-D under tensile loading

A closed-form equation was developed in this work to quantify the stress intensity factor (SIF) along an arbitrarily shaped planar crack under mode-I loading by substituting the ellipse-related parameters in Irwin’s solution with geometry-related parameters fi of the crack. This allowed incorporation of the local crack curvature effect on SIF at each discrete point along the crack front and its relative weighted contribution to SIF of the neighboring crack point i, where either stress concentration or shielding took place, into computation of the SIF distribution along the crack front. Good agreement was obtained between the KI values derived in the current work and previous numerical simulation-based studies. The current method could capture the KI distributions for surface and embedded cracks having the same shape, with their maximum values being consistent with Murakami’s area method. This solution of KI allows for highly efficient calculation of ΔKI for quantification of the 3D growth behaviors of a fatigue crack with a complex shape, paving the way for studying the statistical nature of short fatigue crack growth.

Finite element analyses of rail head cracks: Predicting direction and rate of rolling contact fatigue crack growth

A numerical framework in 3D for predicting crack growth direction and rate in a rail head is presented. An inclined semi-circular surface-breaking gauge corner crack with frictionless crack faces is incorporated into a 60E1 rail model. The investigated load scenarios are wheel–rail contact, rail bending, thermal loading, and combinations of these. The crack growth direction is predicted using an accumulative vector crack tip displacement criterion, and Paris-type equations are employed to estimate crack growth rates. Results are evaluated along the crack front for varying crack radii and crack plane inclinations. Under the combined load cases and in the presence of tractive forces, the crack is generally predicted to go deeper into the rail than under pure contact. Crack growth rates for the combined load cases are higher than (but still close to) that for pure contact. A tractive force will increase growth rates for smaller cracks, whereas a steeper (45°) inclination will decrease the growth rate under the studied conditions as compared to a shallower (25°) inclination. Results should be of use for rail maintenance planning where deeper cracks require more machining efforts.

A strain-based J-integral formulation for an internal circumferential surface crack of pipeline under inner pressure and large axial deformation

The presence of cracks on pipelines poses a potential threat to their operational status, and it is critical to assess the permissibility of pipelines containing cracks. The dimensional analysis combined with the finite element method is applied to investigate the fracture behavior of circumferential crack on the internal surface of pipe under internal pressure and large axial deformation. Dimensionless parameters are determined to represent the effects of crack size, pipe geometry, pipe material, and external load on the crack front driving force, and a strain-based J-integral formulation is obtained by a stepwise coefficient fitting approach rather than a polynomial fitting method. This J-integral formula can be used to quickly assess the crack front driving force of a pipe in service condition and subjected to axial displacement. The diameter-to-thickness ratio of the pipe and the dimensionless pressure of the pipe are found to act together in a combined form on the crack front driving force. Increases in dimensionless crack depth, dimensionless crack length, the ratio of circumferential stress to yield strength of the pipe, and strain hardening exponent cause an increase in the crack front driving force. The effect of dimensionless crack depth on crack front driving force is more significant than other dimensionless parameters. Changes in the other dimensionless parameters do not significantly change the crack front driving force when the dimensionless crack depth is small. Other dimensionless parameters have a progressively greater influence on the crack front driving force as the crack dimensionless crack depth increases. Large deformations in the ligament zone and increasing axial stress are the main reasons for the high crack front driving force. The J-integral formula has a similar form to that of the J-integral in the Electric Power Research Institute (EPRI) method when the effect of internal pressure is not considered. It can be reduced to predict the crack front driving force of a surface cracked plate subjected to uniaxial tensile loading. For the interaction between an internal surface crack and an embedded crack, re-characterizing the crack size using BS 7910 will overestimate the equivalent crack depth, and a more accurate equivalent crack size can be obtained using the J-integral formula proposed.

Effects of Surface Crack Shape on Fracture Behavior of Oil Pipelines Based on the MMC Criterion.

This study employs a hybrid numerical-experimental calibration method based on phenomena to determine the fracture parameters of the Modified Mohr-Coulomb (MMC) model. Using a self-developed VUMAT subroutine and the element deletion technique, the fracture process of a wide plate pipeline is thoroughly analyzed. This study investigates the impact of various crack shapes on the fracture response under tensile loading and the influence of surface crack size on the initiation location of a wide plate. These results demonstrate the calibrated MMC fracture model's accurate prediction of the toughness fracture behavior of X80 pipeline steel. Under equal area conditions of the dangerous section, circular cracks exhibit lower bearing capacity compared to elliptical cracks. Elliptical cracks predominantly propagate in the thickness direction, whereas circular cracks show nearly uniform growth in all directions. Furthermore, when the crack depth is less than half of the wall thickness, the damage accumulation value at the midpoint of the crack front is maximized; conversely, when the crack front is closer to the internal measurement point of the wide plate, the damage accumulation value is maximized.

Colloidal droplet desiccation on a electrowetting-on-dielectric (EWOD) platform

The physics of the effects of electric field on the desiccation of colloidal droplets, comprising of dispersed negatively charged nanoparticles [2 μl, 1(w/w. %)], are studied in a standard electrowetting-on-a-dielectric configuration. The extent of contact line pinning during evaporation is found to be a function of the magnitude of the applied voltage and quantified in terms of the dimensionless electrowetting number (η). The pinned contact line led to higher particle compaction as evidenced by the characterization of dried colloidal film thicknesses. Crack formation and their dynamics have been analyzed in detail to elicit the interplay of forces near the contact line region and on the compaction front. These aspects of crack formation are elucidated in the light of magnitude and polarity of the applied electric field. It is found to influence the crack front initiation velocity, the geometry, the number of cracks, and an attempt is made to explain the same via first principle-based approaches. Therefore, this study indicates the possibility of using electrowetting as a technique to fine-tune the crack formation behavior in thin colloidal films.

Research on the propagation characteristics of multiple cracks in steel bridge joints

This study explores the morphological changes and interaction mechanisms of multiple crack propagations in steel bridge joints. Fatigue testing was conducted to determine the locations at which multiple cracks initiated and to obtain fatigue fracture surfaces with easily discernible crack propagation traces. Based on the theory of fracture mechanics, the propagation behavior of coplanar and out-of-plane cracks in joints was simulated using ABAQUS and FRANC3D joint simulation technology. The characteristics of the morphological changes were analyzed, and the interaction mechanism between different crack spacings was investigated to quantitatively characterize the relative positions at which cracks were enhanced or suppressed. The results showed that coplanar cracks exhibited different morphological trends and propagation rates in different stages of propagation. The shape of the crack front continuously changed, and the merging point that appeared during fusion rapidly expanded and evolved into a semi-elliptical crack. The fatigue life was more sensitive to the relative position of multiple cracks. In particular, the fusion of coplanar cracks significantly reduced the fatigue life, and the mutual suppression effect between heterogeneous cracks increased the fatigue life. When the ratio of coplanar crack spacing to crack length (s/2c) was less than 0.2, the crack fusion process significantly accelerated. In addition, when the a2/a1 ratio of the crack propagation depth dropped below 0.5, the suppression effect was significant. Finally, by determining the spacing between multiple cracks, the method established this study can provide a reference for the design of fatigue resistance and joint optimization.

Low constraint fracture toughness testing for master curve reference temperature determination using 10 mm-thick SE(B) and SE(T) specimens

The constraint correction methodology for defect assessment is not widely applied in fitness-for-service codes in the nuclear industry and there are a limited number of testing standards to account for low-constraint testing. In this work, fracture toughness testing was performed with two different types of alloy steels. SE(B), C(T), and SE(T) specimen configurations were used, along with varying a/W ratios and specimen sizes, allowing for varying levels of constraint. New quality assurance measures related to selection of testing temperature, crack front straightness, and compliance for low constraint specimens are suggested. The results show that the SE(B) specimens are sensitive to CMOD measurement point location. Future work should be focused on improving and validating the instrumentation and analysis practices for low constraint specimens. Yet, the obtained SE(T) T0 values follow models predicting the effect of constraint loss developed using larger specimens. The work impacts the development of quality criteria for future low constraint testing standards.

3D analysis of crack propagation in nuclear graphite using DVC coupled with finite element analysis

The initiation and propagation of cracks within nuclear graphite components compromise the lifespan of advanced gas-cooled reactors and even lead to safety incidents. A thorough understanding of fracture properties in nuclear graphite is crucial for the effective management and design of graphite structural components. In this work, an in-situ test of a double cleavage drilled compression (DCDC) specimen was conducted using X-ray tomographic imaging to fully analyze the 3D crack propagation behavior in IG-11 nuclear graphite. “Subvolume Splitting” digital volume correlation (SS-DVC) was employed to accurately quantify the displacement fields surrounding the crack. The entire 3D crack propagation and crack surface around the crack front were precisely captured through 3D imaging processing of the gray level residual (GLR) field. Additionally, crack opening displacements (CODs) and stress intensity factors (SIFs) were determined using finite element (FE) analysis with extended finite element method (XFEM). Experimental results indicate that although mode I crack remains predominant throughout the whole process, complex crack propagation exists around the crack front. The utilization of irregular crack surfaces in FE analysis helps to obtain refined displacement fields and accurate SIFs of the crack front. This work provides comprehensive insights into crack propagation and reveals the influence of complex crack morphology on SIF calculations, facilitating accurate prediction of structural integrity and rational design of graphite components.