Crack Growth Path Research Articles

A rate-dependent crack bridging model for dynamic fracture of CNT-reinforced polymers

Carbon nanotubes (CNTs) improve the fracture toughness of polymer-based matrix composites by bridging the crack growth path. This research presents a finite element (FE) rate-dependent crack bridging model of Mode-I dynamic crack growth in CNT-reinforced polymers accounting for rate of loading and rapid crack growth. Two distinct CNT bridging and matrix cracking damage mechanisms are taken into account in the fracture process zone (FPZ) accounting for the dissipation of fracture energy. A viscoelastic-viscoplastic material model is adapted for the matrix phase to capture the strain rate effects. The crack in the matrix phase is modeled using cohesive zone elements characterized by experimental data. A rate-dependent traction-separation law obtained from CNT pull-out simulation at relevant crack opening speeds is used to simulate the CNT bridging in the FPZ. Considering the given traction-separation law as a constitutive equation, the CNTs are replaced with non-linear spring elements to facilitate the FE simulation of crack bridging with numerous CNTs in the FPZ. The proposed rate-dependent FE model for crack bridging enables the study of the effect of key CNT factors such as length, orientation, waviness, volume fraction, and agglomeration on fracture energy dissipation at various crack speeds. The developed model can simultaneously consider the interactive effects of all CNT parameters which is useful for considering all processing-induced uncertainties in analyzing the effects of CNTs on the dynamic fracture toughness of nanocomposites.

Study on crack growth path of API-5L X80 welded joints based on inhomogeneous mechanical properties

This study analyses the effect of inhomogeneous mechanical properties on the stress-strain field of crack tips and crack growth path at different locations of API-5L X80 welded joints. First, the inhomogeneous mechanical properties and microstructure of welded joints were analyzed in detail in this paper. Then, the ABAQUS subroutine USDFID was developed to ensure the continuity variation of the mechanical properties of the material in this region. Finally, the cracks in the welded joints were analysed using the extended finite element method (XFEM). The findings demonstrate that the inhomogeneous mechanical properties of welded joints give rise to crack growth path that are deflected towards the weld metal region, exhibiting the greatest rate of growth in this region.

A crystal plasticity phase-field model for microstructure sensitive fatigue crack growth in a superalloy

In this work, a dislocation density-based crystal plasticity phase-field model (CP-PFM) is developed to simulate fatigue crack growth in nickel-based superalloys. Through normalization validation, the plastic dissipation work and crystallographic work are shown to be consistent with the fatigue indicator factors (FIPs), cumulative equivalent plastic strain and cumulative shear strain, and the two energies are computed as the main driving forces of the phase field. Both driving force models are able to obtain fatigue crack growth in close approximation to the experimental rate. However, the model with crystallographic work as the main driving force obtains crack growth paths that are in better agreement with electron backscattering pattern (EBSD) observations, which is attributed to its greater ability to characterize the microstructural susceptibility of fatigue crack growth. Specifically, the model is able to capture the tendency of cracks to crack along the close-packed planes and the hindering effect of grains with large misorientation angles on fatigue crack growth, which together contribute to the curved morphology of fatigue cracks. The combination of large grains or grains with small misorientation angles favors persistent slip band (PSB) formation and leads to softening of the crack tip, which results in lower fatigue crack growth rates.

Physics-based digital twin updating and twin-based explainable crack identification of mechanical lap joint

The mechanical joints, including the lap joint, weld, bolt, and pin, are vulnerable to fatigue failure because of stress concentration and internal flaws. Digital twin (DTw) strategies were proposed to prevent catastrophic system failure by fatigue damage in mechanical joints. In previous studies, the data-driven approach, such as deep learning and machine learning were utilized to estimate severity of the damage. However, it needs to improve its prediction accuracy because of insufficient data and physical interpretability. In this study, the physics-based digital twin model updating and twin-based crack identification of fatigue damage in riveted lap joints were proposed using lamb waves with consideration of uncertain crack growth path. The proposed approach is based on three techniques; (i) Data pre-processing, including filtering and optimization-based signal synchronization, (ii) Lamb-wave propagation analysis with sensor dynamics model and uncertain crack path, and (iii) Optimization based physics-based model updating and inference. In data pre-processing, the excitation frequency magnitude and truncation time are estimated using the observed actuator signal in the Lamb-wave test. The sensor dynamic model and model parameters are updated using the Bayesian optimization method to minimize both the errors in the predicted (y^t) and observed (yt) wave signal and the errors in the inferred (l*) and observed (l) crack length. The crack growth path is sampled based on angular and spline schemes to consider uncertain crack propagation paths. The validity of the proposed method is demonstrated using an open data set (2019 PHM society data challenge). The results conclude that the proposed digital twin approach can improve estimation accuracy considering both the crack growth path and sensor dynamics model.

Creep fatigue interaction at high temperature in C630R ferritic/martensitic heat-resistant steel

The study investigated the creep-fatigue interaction behavior, fracture mechanism, and microstructure evolution of C630R ferritic/martensitic heat-resistant steel at 630 °C and 1% strain amplitude. The results indicate that C630R ferritic/martensitic heat-resistant steel exhibits noticeable cyclic softening behavior, with a decrease in the softening ratio from 0.46 to 0.40 as loading time increases. Microstructure evolution was examined using optical and scanning electron microscopes, revealing the appearance of secondary cracks on the longitudinal section of the sample. These cracks exhibited a curved expansion trend with multiple deformations and highly bifurcated micro-cracks at a low loading time of 30s. However, when the load holding time was increased to 300s, the fatigue cracks tended to expand in a straight line with fewer branches. Furthermore, the observed crack growth path under different loading times showed enrichment in Fe and Cr, with the crack tip containing Cr oxide, which helped prevent fatigue crack propagation. As the loading time increases, the rise in crack closure resulting from oxidation leads to a decrease in crack propagation. Electron backscatter diffraction observation revealed the formation of numerous substructures and recrystallized grains after varying holding times, enhancing the material's resistance to crack propagation. Moreover, the study found that with increasing load dwell time, the deformed grains decreased, and substructural grains became dominant (57.68% and 62.77% under 30s and 300s, respectively). This increased crack resistance resulted in shorter secondary cracks under prolonged load retention, with the secondary crack length decreasing from 146.36 μm at 30s loading time to 109.09 μm at 300s loading time. Additionally, the kernel misorientation angle value decreased significantly after different loading times, leading to a higher likelihood of cracks or holes forming in regions with high KAM values, where low-angle grain boundaries were formed.

A fully recrystallized heterogeneous grain structure with dispersed second phases for enhancing strength-ductility synergy in an Al-Cu-Mn alloy

Introducing heterogeneous grain structures has been demonstrated as an effective strategy to overcome the strength-ductility trade-off in metallic materials. Here, we designed a fully recrystallized heterogeneous microstructure via controlling local recrystallization around the grain boundaries coupled with the second phase. The representative feature of this microstructure is the topology of the nearest grain neighbors, where a fully recovered large grain is surrounded by multiple recrystallized small grains. Meanwhile, the second phase distribution around the grain boundary could be remarkably optimized during the processing. Within a commercial Al-Cu-Mn alloy, a remarkable ultimate tensile strength of 365 MPa with uniform elongation of 30 % was achieved through this heterogeneous structure, corresponding to an 18 % increase in ultimate tensile strength and a 29 % improvement in ductility compared with the uniform-grained counterpart. Characterized by quasi-in-situ EBSD, it was found that the multiple small grain neighbors coordinated local strain incompatibility near the hetero-interface by dislocation slips and local reorientations, which can better sustain the strain hardening. In situ tensile tests unveiled the micro-crack blunting by ductile large grains, endowing superior crack-arrest capability. Moreover, tailored dispersed Al2Cu particles inhibited inter-cluster void coalescence and interface-debonding by eliminating continuous crack growth paths, promoting stable damage evolution. These results give a new insight into the controllable design of heterogeneous-grained alloys with second phases for achieving superior combinations of mechanical properties.

Rate dependent C* fracture parameter using the optimized wedge-split test geometry and vision-based automated crack tip detection

Typical monotonic load-line displacement (LLD) control and crack mouth opening displacement (CMOD) control cracking tests are limited to singular loading rates and testing temperatures. These experimental protocols are not designed to derive a fundamental fracture parameter capable of relating to the viscoelastic property and cracking behavior of asphalt concrete (AC). On the other hand, a multi-rate LLD-control monotonic fracture experiment is capable of capturing the viscoelastic cracking behavior of AC by providing the rate-dependent fundamental C* fracture parameter as an output. Crack length and crack speed parameters are combined with reaction loads to calculate the rate-dependent C* parameter. The current C* experiment protocol implements manual processing of video images and exhibits high variability. The study aims to optimize the wedge-split geometry and improve the C* fracture parameter calculation protocol by applying an automated vision-based crack detection system and recording the crack growth path, considering the horizontal and vertical movement of the crack tip with higher accuracy. The three notch lengths (5, 15, and 30 mm) were evaluated. Plant and laboratory-produced mixes with varying stiffness and fracture characteristics were included in the testing program. An optimized notch length for the test geometry was determined based on the on-specimen strain field observed using the digital image correlation (DIC) technique and crack path analysis. The optimum notch length was found to be 15 mm due to consistent strain localization at the crack tip and less crack deviation in the horizontal direction. The main contribution of this paper is the proposed vision-based crack path detection method, which enables measuring the crack path's true crack length and maximum horizontal deviation. The developed protocol and optimization of the testing geometry led to a significant improvement of the existing C* testing protocol, resulting in higher data quality and consistent results. The proposed protocol was validated using three comparable and distinctively different lab-produced mixtures. The results show that the C* experiment effectively differentiated between the mixes based on crack speed and the C* parameter.

Understanding crack growth within the γ′ Fe4N layer in a nitrided low carbon steel during monotonic and cyclic tensile testing

Nitriding is a cost-effective method to realize simultaneous improvements in tensile and fatigue properties and resistance to abrasion and corrosion. Previous studies reported that nitriding pure Fe enhances tensile strength by ~ 70% and fatigue limit by ~ 200%. It is due to the increase in surface hardness caused by the formation of γ′(Fe4N) and ε(Fe2-3N) nitrogen-containing intermetallic compound phases. However, the intermetallic compound layer is prone to brittle-like cracking. To better design nitrided steels, it is crucial to identify the crack growth mechanisms via analysis of the microstructural crack growth paths within the ~ 4–6 µm thick nitride layer. In the current work, we statistically evaluate the crack propagation behavior in the γ′ Fe4N layer during monotonic and cyclic tensile deformation in nitrided low-carbon steel (0.1 wt% C). Since nitriding typically results in the formation of columnar grains, the effect of morphology needs to be clarified. To this end, the steel was shot-peened and subsequently nitrided to promote equiaxed nitride grains morphology (~ 16% increase). Crack growth paths were comparatively evaluated for multiple cracks, and no significant effect of nitride morphology was observed. {100}γ′ is the predominant transgranular crack path in the monotonic tensile tested specimen, followed by {111}γ′. It is despite the elastic modulus of {111}γ′ < {100}γ′. This contrary behavior is explained by {100}γ′ plane having the lowest surface energy (density functional theory calculations). In the cyclic tensile loaded specimen, experiments revealed that transgranular cracking along {100}γ′ (cracking via symmetric dislocation emission) or {111}γ′ (slip plane cracking) is equally likely.Graphical abstract

Experimental and Meshless Numerical Simulations on the Crack Propagation of Semi-Circular Bending Specimens Containing X-Shaped Fissures Under Three-Point Bending.

Cracks in rock and concrete have a great adverse effect on the stability of engineering structures; however, there are few studies on X-shaped fissures which widely exist in rock and concrete structures. Based on this background, three-point bending fracture tests of SCB specimens containing X-shaped fissures are carried out. The momentum equations in the SPH method are improved, and the crack propagations of SCB specimens under three-point bending are simulated. The results show that cracks grow simply along the vertical direction in the sample with no X-shaped fissures, and the existence of an X-shaped fissure changes the crack growth path and final failure modes of the SCB samples. The crack propagation simulation results are consistent with the experimental results, which verifies the rationality of the improved SPH method. The load-displacement curves mainly present three typical stages: the initial compaction stage, linear elastic deformation stage, and failure stage. The peak load decreases first then increases with an increase in eccentricity. With an increase in X-shaped fissure length and decrease in X-shaped fissure angle, the peak load decreases. The damage counts remain at 0 at the initial loading stage, corresponding to the initial compaction stage and the linear elastic deformation stage, and increase sharply at the later loading stage, corresponding to the failure stage, which is consistent with the experimental results. The influence mechanisms of X-shaped fissures on the crack propagation paths are discussed; the existence of different X-shaped fissure morphologies aggravate the tensile stress concentration at specific positions, leading to different crack propagation modes in the experiments. The research results can provide a certain reference for understanding the failure mechanisms of engineering structures containing X-shaped fissures and promote the applications of the SPH method into the simulations of cross-fissure crack propagations.

A simple, fast, and robust criterion for predicting fracture load and crack growth path in notched elastoplastic plates under mixed-mode loading

This study assesses the combined in-plane tensile/shear failure of aluminum plates containing notches. With this aim, a numerical method, i.e., the so-called equivalent material concept (EMC) in association with the extended finite element method (XFEM), is introduced to simulate the fracture phenomenon. The predicted failure load, initiation angle, and growth path are compared to experimental results reported for aluminum alloys in the literature to evaluate the functionality of the proposed method. Also, the accuracy of the EMC-XFEM model was compared to the conventional Ductile Damage method. The EMC-XFEM combined model is found to be fast and robust with appropriate accuracy in fracture predictions of ductile samples in comparison with the elastoplastic damage model and experimental data.

Thermo-mechanical fatigue crack growth in a nickel-based powder metallurgy superalloy

Fatigue crack growth is studied in a nickel-based powder metallurgy (PM) superalloy (FGH4099) subjected to in-phase (IP) and out-of-phase (OP) thermo-mechanical fatigue (TMF), as well as isothermal fatigue (IF) at peak temperature. The crack growth rate and path are evaluated for both coarse grain (CG) and fine grain (FG) FGH4099, especially the effects of phase angle and polycrystalline microstructure. The results show that the TMF crack propagation is mainly transgranular in OP condition; while in IP condition, fatigue crack propagates intergranularly at low ΔK and transforms to transgranular after passing the transition region. The crack propagation resistance for FG microstructure is lower than that for CG microstructure at elevated temperature, as a result of secondary cracks and grain boundary weakening effect. Crystallographic slip controls the crack propagation process, while the twin boundaries (TB) and special grain boundaries also exert a significant influence on crack deflection. The formation of secondary cracks is closely related to local misorientation and crystallographic deformation during TMF crack propagation. The crack deflection in a single grain reveals a competition mechanism between crystallographic slip and grain boundary effect, which explains the lower crack growth rate for OP when compared to IP or IF.

Small crack growth behavior and correlated microstructure-sensitivity during cyclic deformation of a high-chromium/carbon wrought tool steel

The macro to micro-mechanical mechanisms of cyclic deformation behavior of a carbide-containing ferritic steel was studied, and the exceptional properties obtained in low-cycle regimes were discussed, relying on the sensitivity of the small crack propagation to the microstructural characteristics. In this respect, the evolution of boundaries, sub-boundaries, carbides, and micro-textures in the vicinity of the crack growth path has been characterized in detail. Regarding this matter, the subtle alteration of grain size gradient, resulting in the decrement of incompatibility between mechanical properties of grains, is the main factor that halts the crack growth temporarily. Furthermore, both pre-existed and cyclically developed substructures could tortuous the crack propagation path and induce the crack closure effect, respectively. The advantages and disadvantages introduced by primary carbides, serving as initiators of small cracks, and dispersed high volume fraction of submicron carbides, inducing the formation of an effective strengthening layer (ESL) and acting as deflectors of small cracks, have been investigated, respectively. The {001} <110> oriented grains have been identified as preferred micro-texture contributing to small crack propagation. In total, the small crack sensitivity of the elaborated microstructure has resulted in a prolonged lifetime.

Optimization of cutout characteristics in AISI 1045 steel plates for high-cycle fatigue life extension

Crack growth is a pivotal concern in structural engineering, directly impacting structures’ stability, quality, and overall lifespan. This study addresses this challenge by investigating structural optimization strategies to mitigate fatigue crack growth (FCG) by strategically incorporating stop-drilled cutouts near the crack tip. The research introduces three optimization problems, focusing on determining the optimal cutout position with a fixed radius, the optimal cutout radius with a fixed position, and the optimal cutout shape with a constant position for the cutout’s center. Experimental assessments are conducted on an edge-cracked AISI 1045 steel plate to evaluate the effectiveness of these optimization strategies in enhancing fatigue life. Employing the Extended Finite Element Method (XFEM) for numerical simulations and Particle Swarm Optimization (PSO) for the optimization process, the findings reveal that strategically positioned cutouts substantially reduce the crack growth rate. Optimal cutout placement significantly improves fatigue life, demonstrating an approximate 287% increase. The analysis affirms the accuracy of the numerical model in predicting fatigue life and crack growth paths, validated through comparison with experimental data. In summary, this research underscores the effectiveness of optimization techniques in mitigating fatigue crack growth, providing valuable insights for structural integrity enhancement in structural mechanics.

Phase field simulations on the rate‐ and grain‐size‐dependent crack propagation of polycrystalline NiTi shape memory alloy

AbstractA three‐dimensional non‐isothermal phase field model of polycrystalline NiTi shape memory alloy (SMA) was established based on the Ginzburg–Landau's theory, which considered the interaction between crack growth and martensite transformation (MT). Then, the crack propagation of polycrystalline NiTi SMA and its dependence on the system's grain size and loading rate were studied by the phase field simulations. The results show that the proposed phase field model can characterize the MT behavior, temperature field changes, and stress‐displacement response of NiTi SMA during the crack growth with different grain sizes and loading rates. That is the higher the loading rate, the higher the fracture toughness is; the larger the grain size, the higher the fracture toughness is and the more significant the influence of grain boundary on the crack growth path becomes. Meanwhile, as the grain size increases, the fracture mode gradually changes from the transgranular fracture (for the fine‐grained alloy with a grain size ≈ 15 nm) to the intergranular one (for the coarse‐grained alloy with a grain size ≈ 100 nm).

Compressive residual strength of the pultruded glass-fiber composite after tension-compression fatigue

We experimentally determined the decrease of residual compressive strength of the pultruded glass-fiber laminate after tension-compression cyclic loading. The adapted Arcan rig was used for tension-compression fatigue tests. The cyclic load was applied with the critical stress ratio R=−0.87. The residual compressive strength was determined after applying the predefined number of loading cycles with the stress amplitudes of 242 MPa and 173 MPa. The results indicated that the residual compressive strength was reduced about 20% at 77% of fatigue life under the stress amplitude of 242 MPa and at 83% of fatigue life under the stress amplitude of 173 MPa. The microstructural analysis showed that the crack growth path and failure mode depend on the stress amplitude.

Influences of microstructures and macrozones on the stress corrosion cracking sensitivity of a near alpha titanium alloy

In this study, we investigated stress corrosion cracking (SCC) behaviors in a near alpha titanium alloy (Ti-6Al-3Nb-2Zr-1Mo) with distinct microstructures and microtextures. By analyzing fracture surfaces, crack growth paths, and grain orientations, we found that the SCC crack growth rate increased with an increase in the volume fraction of the primary αp phase, due to elevated crack initiation density and concentrated grain orientations. Additionally, SCC cracks exhibited a preference for propagating along boundaries between neighboring soft macrozones (easy for slip) and hard macrozones (relatively hard for slip), as well as through macrozones favorable for slip.

Rate-dependent augmented finite element method for fast arbitrary crack growth

Experimental observations indicate that fast crack growth often exhibits a rate dependency, which is caused by the viscosity of the material and the dissipation of energy resulting from the branching of microcracks. To address this phenomenon in simulation modeling, this study introduces a rate-dependent augmented finite element method designed for analyzing fast arbitrary crack growth. The method utilizes the maximum principal stress criterion to simulate arbitrary crack growth and predict the path of crack growth. The elements where crack growth is expected are divided into subelements, and they are re-assembled by incorporating rate-dependent cohesive elements between them to construct augmented finite elements. The cohesive elements are based on a rate-dependent trapezoid traction–separation relationship, where the critical traction and fracture toughness are modeled as functions of the separation rate and crack growth speed. The augmented finite elements only contain external nodal degrees of freedom (DoFs), while internal nodal DoFs are condensed. They can be utilized as conventional elements. A numerical algorithm based on the proposed method was developed in this article, and it was implemented in ABAQUS via user element subroutine. The effectiveness of this method and algorithm is validated through an example of dynamic crack growth in a double cantilever beam. The results demonstrate agreement with experimental and computational findings reported in the literature. Additionally, the method was applied to other structures, yielding reasonable outcomes. Analysis of these examples confirms the method’s utility in predicting fast arbitrary crack growth under dynamic load conditions.

Support vector regression-assisted finite element method for mode I-II fatigue crack growth path prediction

Most of failures in mechanical components in engineering are caused by fatigue crack growth (FCG), especially mode I-II cracks. Accurately and fast predict of crack growth paths of mode I-II in structures is important in academic research and engineering applications. Finite element method (FEM) simulation of FCG can be accurately performed for engineering applications. However, the commercial FEM simulation software, e.g., ABAQUS combined with FRANC3D is generally time-consuming. Therefore, an accurately and fast mode I-II crack growth path prediction method is developed by support vector regression (SVR)-assisted FEM analysis. Firstly, the initial location data of FCG path and stress intensity factor (SIFs) are collected by FEM simulations. The SVR model is trained using initial location data and the corresponding FCG path will be predicted for several growth steps. Secondly, the predicted crack results are input into the FEM simulation model to obtain the several other growth steps. Finally, the two procedures are repeat alternately to obtain the full FCG path. The numerical case is given to validate the performance of the present method using the double-hole plates with mode I-II crack growths. Comparisons show that the performance of the present method are superior to those of FEM simulation and SVR alone.

New method for determining the mode I fracture toughness of shotcrete: edge-notched partial disc test

The fracture toughness (mode I) of shotcrete specimens was obtained using edge-notched partial disc (ENPD) specimens. Notched Brazilian discs (NBDs) were also tested to validate the results of the ENPD experiments. Numerical analysis was also conducted on the ENPD results to compare the measured and numerically obtained fracture toughness values. The notch lengths in the ENPD specimens were 15, 30, 45 and 60 mm, while the notch lengths in the NBD specimens were 10, 20, 30, 40, 50 and 60 mm. It was found that the flat joint model accurately predicted the potential crack growth path and crack initiation stress as compared with the experimental results. It was also deduced that the fracture toughness was roughly the same with an increase in the notch length. The tensile strength (σt) and fracture toughness (KIC) of the shotcrete specimens were found to be meaningfully correlated (σt = 7.92KIC). The ENPD tests yielded the lowest fracture toughness values because of the pure tensile stress distribution on the failure surface. It was also found that the derived fracture extension patterns from the laboratory investigations were in acceptable agreement with the outputs of numerical simulations.

Investigating the Influence of Holes as Crack Arrestors in Simulating Crack Growth Behavior Using Finite Element Method

The primary focus of this paper is to investigate the application of ANSYS Workbench 19.2 software’s advanced feature, known as Separating Morphing and Adaptive Remeshing Technology (SMART), in simulating the growth of cracks within structures that incorporate holes. Holes are strategically utilized as crack arrestors in engineering structures to prevent catastrophic failures. This technique redistributes stress concentrations and alters crack propagation paths, enhancing structural integrity and preventing crack propagation. This paper explores the concept of using holes as crack arrestors, highlighting their significance in increasing structural resilience and mitigating the risks associated with crack propagation. The crack growth path is estimated by applying the maximum circumferential stress criterion, while the calculation of the associated stress intensity factors is performed by applying the interaction integral technique. To analyze the impact of holes on the crack growth path and evaluate their effectiveness as crack arrestors, additional specimens with identical external dimensions but without any internal holes were tested. This comparison was conducted to provide a basis for assessing the role of holes in altering crack propagation behavior and their potential as effective crack arrestors. The results of this study demonstrated that the presence of a hole had a significant influence on the crack growth behavior. The crack was observed to be attracted towards the hole, leading to a deviation in its trajectory either towards the hole or deflecting around it. Conversely, in the absence of a hole, the crack propagated without any alteration in its path. To validate these findings, the computed crack growth paths and associated stress intensity factors were compared with experimental and numerical data available in the open literature. The remarkable consistency between the computational study results for crack growth path, stress intensity factors, and von Mises stress distribution, and the corresponding experimental and numerical data, is a testament to the accuracy and reliability of the computational simulations.