Crack Tip Region Research Articles

Deformation behavior of plastic zone at crack tip of 304 stainless steel

AbstractIn this paper, the deformation behavior of plastic zone at crack tip during crack propagation of 304 stainless steel was studied. Firstly, the fatigue crack propagation tests of 304 stainless steel material were carried out. Combined with digital image correlation (DIC) technology, the strain field data of plastic zone at crack tip, the size of plastic zone, and the strain evolution law of crack tip region at different positions were obtained. Then, combined with the theoretical model and the numerical model, the theoretical, numerical, and experimental results were compared to verify the accuracy of the model. Finally, the effects of cyclic loading, specimen thickness, and weld position on plastic zone at crack tip were analyzed. The research results provide a reference for accurately predicting the fatigue crack growth of 304 stainless steel.

Modeling thermo-mechanical fatigue for rolling die under continuous casting process

In the continuous casting process, the rolling die is exposed to non-steady stress conditions that can initiate thermo-mechanical fatigue damage. Understanding the rolling die failure mechanism is essential in metal-forming industries. Thermo-mechanical fatigue damage mechanism (crack growth) is governed by highly localized stresses in the crack tip region. This paper presents analytical models to determine thermo-mechanical fatigue failure mechanism based on the elastoplastic fracture mechanics and continuum damage mechanics. The model includes new proposed analytical equations for low-cyclic fatigue crack propagation. To verify the analytical models, experimental data and finite element simulation are considered. Results show good agreement with experimental data and finite element simulation.

In-Situ Near Crack Tip pH Measurements to Confirm Alkaline Crack Conditions Causing Crack Arrest in Cathodically Polarized AA5456-H116

ABSTRACT In-situ crack tip pH measurements for corrosion fatigue (CF) cracks in sensitized AA5456-H116 loaded under low loading frequencies show that cathodic polarization has the ability to arrest actively growing stress corrosion (SCC) and CF cracks and produce a local alkaline crack tip pH. A method for measuring crack tip pH in-situ was developed. For AA5456-H116 under a single level of high sensitization, CF experiments while loading in the Paris regime at a loading frequency of 0.1 Hz were conducted under freely corroding conditions and a cathodic polarization of −1.3 VSCE. Results show that under freely corroding conditions the crack actively grows, and the crack tip pH is slightly acidic, while at −1.3 VSCE an alkaline crack tip develops with a pH of 10-12. The findings of this study support the earlier published hypothesis that crack arrest of SCC and low loading frequency CF cracks is due to corrosion-induced blunting after the development of highly alkaline conditions that causes corrosion of the crack tip region blunting and halting the crack.

Isothermal and thermomechanical fatigue crack growth behavior of 316LN stainless steel under load‐ and strain‐controlled modes

AbstractCrack growth tests of 316LN stainless steel under load‐controlled and strain‐controlled thermo‐mechanical fatigue (TMF) loadings at the temperature range of 350°C ~ 550°C were conducted. Moreover, the isothermal fatigue (IF) crack growth tests at the maximum temperature of 550°C were performed for comparison. The differences in IF and TMF crack propagation behavior under different loading conditions were thoroughly discussed, and the underlying mechanisms were revealed by a comprehensive characterization of the deformation state of the crack tip region using digital image correlation (DIC) and electron backscatter diffraction (EBSD) methods. Furthermore, it was found that the EBSD characterization was simply based on a single plane made it difficult to evaluate the complex crack growth behavior. In addition, the limitations of the classical parameter of stress intensity factor under TMF loading were presented.

Investigating the influence of various three-point bending specimen configurations on rock fracture parameters testing: an experimental study

The fracture parameters of rocks, including fracture toughness and fracture energy, represent their resistance to crack propagation under external stress. These parameters play a critical role in engineering design, construction safety, geological mechanics research, and rock material assessment. This study determined the fracture parameters of granite under Mode I loading conditions using notched semicircular bend (NSCB) and single-edge notched beam (SENB) specimens. Although there was little difference between the initial and unstable fracture toughness values of the two specimen configurations, significant differences were observed in the fracture process and other fracture parameters. For example, the NSCB specimen exhibits a higher elastic modulus, and it witnessed rapid failure after reaching the peak load, whereas the SENB specimen displayed a more gradual failure process with a distinct post-peak stage. This may be one of the reasons for the higher fracture energy in the NSCB specimen than in the SENB specimen. Based on finite element analysis and the extraction of the tangential stress at the crack tip region, the application of the maximum tangential stress fracture criterion provided a robust explanation for the coherence observed in the unstable fracture toughness test results between the two specimen configurations.

Automating the determination of low-temperature fracture resistance curves of normal and rubberized asphalt concrete in single-edge notched beam tests using convolutional neural networks

As materials undergo large-scale yielding or exhibit large sizes of fracture process zone in the crack tip region, multi-parameter fracture concepts should be employed to describe the complex crack-tip stress-strain fields. Fracture resistance curves (R-curves) are an established tool in characterizing the entire fracture process of such materials. However, for complex materials such as bituminous mixtures, the development of these curves is subject to experimental and computational intricacies. In this research, a framework is developed to automate the construction of R-curves for normal and rubberized asphalt concrete (AC) mixtures. AC mixtures are produced using PG58–22 and PG58–28 binders. Limestone and siliceous aggregates are used, and three binder contents are considered for the mixtures. Single-edge notched beam (SE(B)) fracture testing is conducted on AC beams with two different notch patterns. A convolutional neural network (CNN) model is developed and trained over 1260 test images with varying temperatures, notch geometries, and setups. The CNN model was used to detect the growing crack on the beam surface and each crack-detected image was sent to an image processing framework to measure the crack length. Crack extension increments were calculated and synchronized with test time and magnitude of load, load-line displacement, and cumulative fracture energy, and the R-curve could be constructed. A training accuracy of 0.91 was obtained for the model and a loss of below 0.10 as a result of a hyperparameter tuning indicating reliable classifications by the CNN architecture. The R-curves showed desirable agreement for control mixtures at temperatures of 0 °C and −15 °C. As the mixtures are rubberized, the R-curves showed favorable agreement in the crack blunting phase, transition zone, as well as the unstable propagation phase at −20 °C. Cohesive energy magnitudes were compared for the two methods with a Pearson coefficient of 0.81 while fracture rate and fracture energy magnitudes showed favorably close magnitudes with coefficients of 0.89 and 0.98 respectively.

Interface crack analysis in 2D bounded dissimilar materials using an enriched physics-informed neural networks

This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples.

A material energy–momentum flux-driven phase field fracture mechanics model

This work introduces a novel phase-field solution for simulating and predicting fractures in elastic solids. In this phase-field fracture model, the crack growth is driven by the material energy–momentum flux, or the configurational force, inspired by a null divergence conservation law and its variational theory, as opposed to employing the commonly-used strain energy degradation-based crack-driving force. By doing so, the crack growth or material configuration change is solely determined by the physics-based Eshelby energy–momentum tensor density or the Rice J-integral flux, which aligns with the energy release criterion of the celebrated Griffith–Eshelby–Rice (GER) theory. The proposed method not only preserves the integrity of the balance of linear momentum principle at the crack tip region but also provides a correct stress asymptotic field in front of the crack tip, while accurately capturing the crack growth.The key idea of this approach is to use the monotonically increasing and irreversible phase field as the marker of the configurational change and form a phase field variational principle that couples the strain energy density with the configurational strain energy density. By doing so, we only damage the displacement field as a form of diffused crack, as opposed to damaging the stress field in the existing phase-field method. Moreover, from numerical simulations, we discovered two different forms of energy release rates: one drives crack growth by enforcing the crack-tip traction loading condition, and one drives crack growth by enforcing the crack-tip deformation condition, demonstrating the ability of the proposed method to naturally capture two distinct modes of fractures due to two different near-crack tip loading conditions. These advancements and contributions reveal previously unknown insights into fracture mechanics.

A modified model for calculating crack tip opening displacement (CTOD) considering fracture process zone (FPZ) in rock

A new CTOD calculation method is investigated in this study, considering the FPZ and the effective Young’s modulus. The calculated CTOD values from four theoretical models are compared with the measured CTOD values from the three-point beam experiments, and the differences between them are analyzed. The measured CTOD consists of two parts: (1) the displacement generated by the elastic–plastic deformation in the crack tip region, and (2) the displacement generated by micro-damage in the FPZ. CTOD value caused by micro-damage in the FPZ accounts for 81–92% of the overall CTOD. Thus, the FPZ and the effective Young’s modulus are introduced to modify the models for calculating CTOD. The result indicates that the modified plastic zone model is better than the strip-yield model, the plastic zone model and the modified strip-yield model in calculating CTOD, and CTOD error is reduced from 81 to 90% between the plastic zone model and the experiment to 4–34% between the modified plastic zone model and the experiment, with nearly half of the specimens having an error of less than 10%.

Structural and nonlinear J-integral fracture toughness for nanoclay toughened ternary HDPE/LDPE-g-MA/ABS blend nanocomposites

High-density polyethylene (HDPE) has a higher strength-to-density ratio and stiffness but a low branching degree for the packed linear chains that restrict the ability to bond and resist cracking. This study conducts the role of inserting rigid nanoclay (NC) and soft acrylonitrile butadiene styrene (ABS) on the structural, nonlinear fracture toughness and crack resistance of a ternary HDPE/low-density polyethylene-grafted maleic anhydrite (LDPE-g-MA)/ABS blend. Varying additions of 1, 3, 5, and 7 % NC and 5, 10, 15 wt. % ABS were inserted into neat HDPE and HDPE90/LDPE-g-MA10. All materials were hand-mixed before feeding into a single screw extruder and directly melt-blended twice to achieve a good dispersion of nanofiller in the matrix. The structural characteristics and the fracture surfaces of NC/HDPE/LDPE-g-MA and NC/HDPE/LDPE-g-MA/ABS were investigated by TEM, XRD, SEM, and FTIR spectra. Tensile strength and the critical dissipated energy (JIc) determined by quasi-static J-integral fracture mechanic revealed a higher absorbing fracture energy of 75 KJ/m2 for the binary and 85 KJ/m2 for the ternary nanocomposites. The synergistic percolated role of the NC particles and ABS copolymer in front of the crack tip region hinders crack growth for the presence of micro-void coalescence and massive shear-yielding toughening mechanisms.

Crack tip mechanics of multiscale change

Singularity representation at the crack tip and/or smaller region will be considered using six scale transitional physical parameters: three assigned for the nano/micro range (*na/mi, *na/mi, d*na/mi) and three assigned for the micro/macro range (*mi/ma, *mi/ma, d* mi/ma). The subscripts nano, micro, and macro are self-evident. Only the ratio of two successive scale sensitive parameters are needed. Although time dependent physical parameters at the lower scale can be found analytical, they regarded as fictitious, mainly because they are not conducible to measurements. The transitional character of multiscale changes according to nano→micro→ macro with the respective singularity strength of  are given by 1.00/0.75/0.50. Since =0.5 corresponds to the inverse square root r-0.5, where r is the distance from the macro singular point. The micro and nano singular point possess the singularities r-0.75 and r-1.00, respectively. For example, a critical device component may be designed to operate at the nano/micro/macro scale with a life distribution of 2.5+ /3.5+ /5.5+ and total life of 11.5 + years. Progressive changes are assumed to occur in the direction of nano→micro→macro.

Study on fatigue temperature evolution and failure behavior of Q460 steel

In order to address the complexity of fracture damage behavior in metallic materials during service, the thermography technique was used to analyze the temperature evolution behavior of Q460 steel during cyclic deformation. The microscopic organization and microstructural mechanical properties of the crack tip (CT) region of the specimen were also examined to study the fatigue damage mechanism and crack propagation mechanism of Q460 steel from the perspectives of microstructure and energy evolution. The results showed that under the action of fatigue load, dislocation formation and motion occurred in the specimen, accompanied by energy release, which led to a change in surface temperature. The temperature of the fatigue failure area rapidly increased, leading to the formation of a large number of low-angle grain boundaries (LAGB). The nano-indentation results effectively studied the mechanical properties of the stress field area at the CT and revealed that the fatigue crack propagation process of Q460 steel is a result of the synergistic effect between the variation of grain orientation the crack region and the aggregation of a large number of micro-defects in the work-hardened zone. Based on the fatigue heat generation mechanism and entropy evolution mechanism, the study comprehensively analyzed consistency and differences in the damage mechanisms of Q460 steel under tensile load and fatigue load, employing temperature as a bridge. The research results ensure the safety and reliability of Q460 steel during its operation and provide new insights into the study of fatigue fracture behavior in metallic materials.

Multiscale Analysis of the Mechanical Properties of the Crack Tip Region

Multiscale Analysis of the Mechanical Properties of the Crack Tip Region

Time-dependent subcritical crack growth and its mechanism in Ni-based single crystal superalloys at 500 °C

The subcritical crack growth behavior under sustained loading and its microscopic mechanism in <100> oriented single crystal (SC) Ni-based superalloys subjected to a relatively low temperature condition (500 °C) are critically investigated. An evident time-dependent crack growth (TDCG) phenomenon is observed even at such a temperature condition, but its rate (da/dt) is significantly small and weakly dependent on the crack length, i.e. the stress intensity (K) value. The cross-sectional observation of a crack tip region by electron microscopy (SEM/TEM), together with the conventional fractography, reveals the following points: the macroscopic crack path shows pronounced branching influenced by the {100} planes; most dislocations in the γ’ phase near the crack tip are rectilinearly aligned and locked on the {100} planes; the crack tip dislocations provide the microscopically preferable oxidation paths. These points strongly suggest that the dislocation-mediated micro-oxidation process plays a major role in the observed anisotropic TDCG mechanism that eventually leads to the anomalous da/dt - K property.

Towards the understanding of fracture resistance of an ultrahigh-strength martensitic press-hardened steel

Identifying the fracture resistance capabilities and gaining a deeper understanding of the controlling damage mechanisms are important to the development of press-hardened steels (PHS) for automotive applications. In this study, the fracture properties of a novel PHS alloyed with Cr and Si (CrSi-PHS) were assessed by using uniaxial tensile and double-edge notched tensile (DENT) tests. Under uniaxial tension, the fracture resistance is characterized by the fracture strain and work of fracture, and the CrSi-PHS presents a desirable compromise with strength when comparing with other grades of advance high-strength steels (AHSS). The large fracture strain is attributed to the high resistance to damage nucleation even with a high density of grain boundaries. Fracture toughness is characterized by the DENT tests. The fracture toughness parameters of CrSi-PHS are lower than that of the commercial PHS 22MnB5 but comparable to the multiphase AHSSs with lower strength levels. The stress triaxiality near the fatigue pre-crack in DENT tests leads to a change of damage mechanism in CrSi-PHS. The crack propagates discontinuously by joining the micro-cracks and subsequently by the ductile fracture of micro-ligaments. The local plasticity at the crack tip region is suggested to contribute significantly to the energy dissipation. The observations demonstrate a strong dependence of the fracture mode and fracture resistance on the loading condition in the ultrahigh-strength martensitic steels.

Effect of microstructure heterogeneity on the cryogenic fracture toughness of the dissimilar joint between SA645 and 304L made by laser welding

The cryogenic fracture toughness of the SA645/304L dissimilar weld, produced using continuous wave IPG fiber laser welding with a 0.3 mm beam offset towards the 304L side, and the microstructural effects on the fracture behavior were systematically investigated. The weld metal consists of ∼89% columnar dendritic martensite and ∼11% retained austenite (RA), where the ununiform distribution of constituent phases as well as the distinctions between martensite and RA in terms of morphology and mechanical properties lead to the microstructure heterogeneity of weld metal. Pop-in phenomenon appears on the Force-Displacement (F-V) curve during the crack tip opening displacement (CTOD) test for the weld. The CTOD value for the weld is ∼0.057 mm, about 8 times less than that when pop-in effect is ignored (∼0.563 mm). Rapid propagation of the pre-fatigue crack tip along the center of the weld leads to the pop-in phenomenon. Fracture surface in pre-fatigue crack tip (PCT) region shows quasi-cleavage features, while fracture surface in stable crack propagation (SCP) region presents a ductile-fractured surface with dimples. The crack propagation path in SCP region is frequently deflected. Inhibition effect of grain boundaries on crack propagation and TRIP effect of retained austenite (RA) result in the improvement in fracture toughness of the SCP region.

Snap-through Crack Propagation in Architected Bonded Interfaces Analyzed Using a Mechanoluminescent SAO/E Coating.

We investigate the mechanics of crack propagation in architected adhesive joints whose adherends are inspired to the base plate of the barnacle Amphibalanus (=Balanus) amphitrite, and feature an array of buried hollow cylindrical channels located perpendicularly to the direction of crack growth. Selective laser sintering is used to obtain the adherends that are subsequently bonded in the double cantilever beam configuration to ascertain the mechanics of crack growth. Finite element (FE) simulations are deployed to determine the strain energy release rate (ERR) and to elucidate the salient features of the fracture process. It is shown that the channels induce a modulation of the ERR and enable a crack tip shielding mechanism. Besides, FE simulations based on a cohesive zone approach indicate the occurrence of crack pinning/depinning cycles that are validated via experiments. A highlight of the present study is the use of a mechanoluminescent (ML) coating to unravel the evolution of the transient stress field in the crack tip region. The coating comprises an optical epoxy resin loaded with doped strontium aluminate phosphors (SrAl2O4/Eu2+) and converts mechanical energy into light emission with intensity proportional to the magnitude of mechanical stress. By combining the ML emission patterns with the stress distribution obtained from FEA, we unveil interesting details of snap-through cracking in architected bio-inspired adhesive joints.

Effect of Inhomogeneous Mechanical Properties on the Stress-Strain Field at the Crack Tip and Crack Growth Direction in Dissimilar Metal Welded Joints

In the failure analysis and safety assessment of dissimilar metal welded joints, the mechanical heterogeneity of local regions is usually ignored and limited sampling locations are selected. The mechanical behavior of the crack tip region is the main variables affecting the environmentally assisted cracking behavior, and it is crucial for understanding the impact of mechanical heterogeneity on the local stress-strain state at the crack tip in welded joints. In this study, the effect of mechanical heterogeneity on the local mechanical behavior at the crack tip and on the stress-strain condition at the crack tip front for different crack sizes was investigated through finite-element simulations based on user-defined material subroutines. The local mechanical behavior of an interface region and crack propagation direction with mechanical heterogeneity and a series of initial crack locations were analyzed. The results show that mechanical heterogeneity has a significant effect on the mechanical condition and growth path of cracks at different sampling locations. The interaction between the mechanical heterogeneity around the crack and the crack depth determines the stress and plastic strain in front of the crack tip, which causes a substantial change in the crack growth path. The interface cracks have high stress and plastic strain; thus, the interface is often the weak position where damage occurs. To guarantee a reliable integrity assessment of cracks in mechanically heterogeneous interface regions, local mechanical properties related to crack locations should be determined and utilized.

Free flexural vibration of cracked composite laminated plate using higher-order XFEM

In this work, a higher-order XFEM approach is presented and implemented to analyze free flexural vibration in cracked composite laminated plate using higher-order shear deformation theory. The composite laminated plate experiences flexural vibration during its service life due to transverse shear loading. Out-of-plane modulus of the plate is much lesser than the in-plane modulus, so the free vibration study of the plate has become a crucial parameter for a safe service environment. The proposed methodology introduce higher-order tip enrichment functions (r2 terms) for crack simulation in laminated plate. These enrichment functions efficiently capture all conceivable displacements and rotations near the crack tip region. A comparative analysis between higher-order XFEM and conventional XFEM approach is presented in terms of computational accuracy. Several numerical examples are presented to demonstrate the accuracy of these higher-order enrichment functions, which contain variations in natural frequency with respect to crack sizes for different symmetric ply composite laminate plates under varied boundary conditions. The numerical results demonstrate that the proposed higher-order XFEM approach is significantly enhancing computational accuracy than the classical XFEM approach.

Enriched physics-informed neural networks for 2D in-plane crack analysis: Theory and MATLAB code

In this paper, a method based on the physics-informed neural networks (PINNs) is presented to analyze 2D in-plane crack problems in the linear elastic fracture mechanics. Instead of using a discretizing mesh, the PINNs-based method is meshless and can be trained on batches of discretely sampled collocation points. In order to capture the asymptotic behavior of the near-tip displacement and stress fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the local behavior in the crack-tip region can be modeled accurately without a nodal refinement. The trainable parameters of the enriched PINNs are learned to satisfy the governing partial differential equations of the cracked elastic solid and the corresponding boundary conditions. It is found that the incorporation of the crack-tip enrichment functions in the PINNs is substantially simpler and more feasible than in the conventional finite element method (FEM) or boundary element method (BEM). The present PINNs-based algorithm is tested and verified by several representative benchmark examples for different loading and crack-mode types. Numerical results show that the present PINNs-based method can provide highly accurate stress intensity factors (SIFs) with only few degrees of freedom. For interested readers, a self-contained MATLAB code and data-sets supplementing this paper are also provided in the Supplementary material.