Growing Crack Tip Research Articles

Experimental and numerical insights into fatigue crack propagation of railway component with gradient residual stress

As a representative structure with an acute radial gradient in terms of residual stress (RS) and grains, the induction-hardened railway S38C axle exhibits excellent mechanical properties and fatigue resistance. To investigate the effect of gradient features on fatigue crack growth (FCG) behaviors, we designed three-point bending (TPB) tests with different gradient features, including the negative-gradient, positive-gradient, and matrix specimens. Finite element modeling was introduced to simulate the FCG of the TPB specimens in terms of the cyclic J-integral (ΔJ) and equivalent plastic strain at the growing crack tip. The results reveal that the FCG rates in both negative- and positive-gradient structures decrease and a more pronounced tendency of decline is achieved in the positive-gradient ones. The substantial compressive residual stress (CRS) within the negative-gradient structure directly influences the crack tip area, while the CRS in the positive-gradient structure indirectly mitigates the crack driving force by impeding the overall structural deformation. Coarser grains aid in enhancing energy absorption along the zigzag crack path, thereby diminishing the crack driving force. ΔJ and the equivalent plastic zone surrounding the crack tip indicate significant reductions in the presence of CRS.

Determination of Ductile Tearing Resistance parameter of Interstitial-Free Steel Sheet

The present work deals with the characterization of ductile tearing resistance of 1 mm thick interstitial free steel sheet using crack tip opening angle (φ), and δ5 concepts with some experimental modification. CTOA (φ) measurements on the specimen surface at the growing crack tip have been performed using light microscope on both pre-cracked DENT and SENT specimens at three ramp rates following the essence of ASTM E 2472. In order to determine the effect of pre-cracking, CTOA of the notched (ρ:0.1 mm) SENT specimen has also been measured at 10-4 s-1. The transferability of φ−Δα and δ5−Δα between two geometries has been verified. It is concluded that for a specified thickness both φ−Δα and δ5−Δα plots can be used for crack growth characterisation of sheet metals even without using pre-cracked specimens. However, the angle φ(δ5) determined from δ5−Δα curve is not the true measure of optical CTOA,φ as the δ5 gauge position does not follow the tip position of the growing crack.

A Review of the Factors That Can Increase the Risk of Sulfide Stress Cracking in Thermomechanical Controlled Processed Pipeline Steels

This review aims to improve our understanding of the important factors which influence the susceptibility of thermomechanical controlled processed (TMCP) steels to sulfide stress cracking (SSC). Mechanisms involved in hydrogen embrittlement (HE) from three perspectives are focused on: the microstructure constituents of TMCP steels; environmental factors; and fracture mechanism of SSC. Microstructures are reviewed as they affect the diffusion and trapping of hydrogen that can reduce the resistance to fracture. Environmental factors discussed highlight that when exposed to an aqueous H2S environment, a sulfide layer can form and influence the ingress of hydrogen, and this is affected by pH, temperature, and H2S partial pressure. Fracture is influenced by the nature of the crack tip and the crack tip plastic zone during crack propagation, and hydrogen can significantly affect crack tip growth. This review provides a critical assessment of the interplay between these three factors and aims to provide understanding to enhance our engineering approaches to manage and mitigate against fracture of TMCP steels.

Geometry independent J-Tz domination of three-dimensional steady growing crack-tip fields in ductile materials

The crack-tip in-plane (Q and A2) and out-of-plane constraint (Tz) parameters have been extensively studied for ductile fracture problems on the basis of the pioneering HRR and J-Tz solutions. However, these analytic solutions rarely focus on the steady growing cracks, which play a vital role in J-R curve and integrity assessments of complicated structures. In this work, three-dimensional finite element method and GTN damage model are adopted to simulate quasi-static ductile crack growth under different plastic exponents, geometries and load levels. With the follow-up coordinate system, the J-Tz solution is extended to describe the crack-tip stress distributions of the quasi-static elastic–plastic growing cracks. It is found that in front of steady growth cracks, Tz strongly depends on specimen geometry. In the range of small-scale yielding, tensile stress and Tz gradually increase with increasing load J/JC. When the large-scale yielding stage is approaching, tensile stress and Tz tend towards a stable state. The maximum relative errors between the J-Tz solution and three-dimensional finite element results are 4.16% and 9.28% with J/JC smaller than 1 and 2, respectively. Such dominance and geometry independence of the leading order J-Tz solution make it more simply and effectively to assess the ductile fracture problems.

Dynamic fracture analysis in quasi-brittle materials via a finite element approach based on the combination of the ALE formulation and M−integral method

This work proposes an efficient FE-based approach for reproducing dynamic crack propagation phenomena in quasi-brittle materials. The proposed model uses a Moving Mesh technique based on the Arbitrary Lagrangian-Eulerian formulation (ALE) to adapt the computational mesh consistently to the geometry variations caused by dynamically growing cracks. Specifically, the motion of mesh nodes occurs according to Fracture Mechanics criteria, which provide suitable conditions regarding the direction and velocity of a growing crack tip. These conditions usually depend on the Dynamic Stress Intensity Factors (DSIFs) at the crack front. For extracting the DIFSs at a moving crack tip, this work introduces the ALE formulation of the dynamic M−integral as a key novelty. This strategy offers the key advantage of performing numerical integration procedures on deforming finite elements without losing accuracy. The validity of the proposed method has been assessed through comparisons with experimental and numerical data reported in the literature.

The physical meanings of two incremental-J-integral-based fracture criteria for crack growth in elastic-plastic materials

According to a previous paper (Lu LK, Liu ZL, Zhuang Z. Eng Frac Mech. 2021, 254: 107907), the Rice J-integral can be generalized into two incremental J-integrals for crack growth in elastic-plastic materials: one is based on free energy density, and the other is based on internal energy density. This paper aims at providing the physical meanings of these two criteria. The fracture criterion of incremental-J-integral based on free energy corresponds to a direct generalization of the classic Griffith equilibrium condition. This fracture criterion means no net change in total energy during the quasi-static crack growth in an elastic-plastic solid. For a small crack extension, the body’s potential energy is reduced by a value, which can be balanced by the increment of plastic dissipation work plus an extra energy term. The crack growth could happen if this extra energy term equals the energy required for forming these new crack surfaces. For the incremental-J-integral based on the internal energy density, its fracture criterion is a direct result of the first law of thermodynamics of a cracked body containing two independent thermodynamic systems: the volumetric and surface systems. In addition, the cases that a part of crack surfaces has tractions are discussed. If the loaded part of crack surfaces is stationary during crack growth, the results are identical to cases that crack surfaces are traction-free. If the loaded-part of crack surfaces moves with the growing crack tip, the derived fracture criteria become the incremental J-integral criteria in which the integral contour is a boundary of this loaded-part of crack surfaces.

A systematic study on the synergistic effects of MWCNTs and core\u2013shell particles on the physicomechanical properties of epoxy resin

Here, core–shell impact modifier particles (CSIMPs) and multiwalled carbon nanotubes (MWCNs) were used as reinforcing agents for improving the toughness and tensile properties of epoxy resin. For this purpose, emulsion polymerization technique was exploited to fabricate poly(butyl acrylate-allyl methacrylate) core-poly(methyl methacrylate-glycidyl methacrylate) shell impact modifier particles with an average particle size of 407 nm. It was revealed that using a combination of the prepared CSIMPs and MWCNTs could significantly enhance the toughness and tensile properties of the epoxy resin. Also, it was observed that the dominant factors for improving the fracture toughness of the ternary composites are crack deflection/arresting as well as enlarged plastic deformation around the growing crack tip induced by the combination of rigid and soft particles. The Response Surface Methodology (RSM) with central composite design (CCD) was utilized to study the effects of the amounts of CSIMPs and MWCNTs on the physicomechanical properties of the epoxy resin. The proposed quadratic models were in accordance with the experimental results with correlation coefficient more than 98%. The optimum condition for maximum toughness, elastic modulus, and tensile strength was 3 wt% MWCNT and 1.03 wt% CSIMPs. The sample fabricated in the optimal condition indicated toughness, elastic modulus, and tensile strength equal to 2.2 MPa m1/2, 3014.5 MPa, and 40.6 MPa, respectively.

Differential time-dependent fracturing and deformation characteristics of Jinping marble under true triaxial stress

The conventional (σ1 > σ2 = σ3) multi-step creep test and true triaxial (σ1 > σ2 > σ3) multi-step creep test of Jinping marble with rectangular shape were conducted. In this way, the effects of σ1, σ2, σ3 and time on creep behaviour were compared and analysed. Unlike conventional creep tests, Jinping marble showed differential creep deformation and failure characteristics in σ2 and σ3-directions under true triaxial stress. The crack time-dependent evolution was-directional, and the crack tip growth was nearly parallel to the σ1-direction with high stress and opened along the σ2 and σ3-directions with low stress. Moreover, when σ2 > σ3, the crack growth in the σ2-direction was inhibited, and the crack evolution mainly occurred along the σ3-direction. This difference eventually led to the macroscopic failure plane of Jinping marble generally acting parallel to the σ2-direction and along the σ3-direction. The larger the value of σ2, the steeper the macroscopic failure surface, and the failure mode of the rock samples changed from shear to near-splitting failure: however, increasing σ2 can only cause closure of initial cracks opening along the σ2-direction, but did not change the number of initial cracks opening along the σ3-direction. The experimental data also showed that the differential creep deformation in the σ2 and σ3-directions caused by true triaxial stress did not change with time and σ1, but was only affected by σ2 and σ3. The differential creep deformation in σ2 and σ3-directions can be described by the formula DI = a(1-exp(b((σ2-σ3)/σ3))).

Thermodynamic Approach for the Identification of Instability in the Wood Using Acoustic Emission Technology

In order to monitor the crack growth of the wood material better and reduce failure risks, this paper studied the attenuation characteristics of acoustic emission signals in wood through pencil lead breaking (PLB) tests, in the aim of estimating the true amplitude value of the acoustic emission source signal. The tensile test of the double cantilever beam (DCB) specimens was used to simulate the crack tip growth within wood material, monitoring acoustic activity and location of crack tips within wood material using acoustic emission technology and digital image correlation (DIC). Results showed that the attenuation degree of acoustic emission signals increased exponentially as the propagation distance increased, and the relationship between relative amplitude attenuation rate and the propagation distance of the acoustic emission signal was established by the regression method, which provides the input parameters for the establishment of the crack instability prediction model in the next step. Based on a thermodynamic approach, a theoretical model for predicting crack instability was established, and the model was verified by DCB tests. The model uses acoustic emission parameters as the basis for judging whether the crack is instable. It provides theoretical support for the application of acoustic emission technology in wood health monitoring.

Quasi-statically growing crack tip fields in plastically compressible hardening-softening-hardening solid

PurposeAs the normality concept for frictional dilatant material has a serious drawback, the key feature in this numerical study is that the material here is characterized by elastic-viscoplastic constitutive relation with plastic non-normality effect for two different hardness functions. The paper aims to discuss this issue.Design/methodology/approachQuasi-static, mode I plane strain crack tip fields have been investigated for a plastically compressible isotropic hardening–softening–hardening material under small-scale yielding conditions. Finite deformation, finite element calculations are carried out in front of the crack with a blunt notch. For comparison purpose a few results of a hardening material are also provided.FindingsThe present numerical calculations show that crack tip deformation and the field quantities near the tip significantly depend on the combination of plastic compressibility and slope of the hardness function. Furthermore, the consideration of plastic non-normality flow rule makes the crack tip deformation as well as the field quantities significantly different as compared to those results when the constitutive equation exhibits plastic normality.Originality/valueTo the best of the authors’ knowledge, analyses, related to the constitutive relation exhibiting plastic non-normality in the context of plastic compressibility and softening (or softening hardening) on the near tip fields, are not explored in the literature.

Analysis of the fatigue crack growth behavior of a low N Austenitic stainless steel

Austenitic stainless steels are known to undergo stress/strain induced localized transformation toughening at a growing crack tip, contributing to load-ratio (R) effects. Presence of Nitrogen (N) can stabilize the austenite thus inhibiting this transformation. It has been shown earlier that crack closure does not seem to account the R-effects. We examine the behavior of such an alloy using the unified approach involving ΔK and Kmax, and show that the localized transformation can influence fatigue crack growth predominately via the Kmax - parameter. Crack growth trajectory map is extracted to show the role of the superimposed Kmax-dependent process.

An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems

By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications.

On the crack tip propagation monitoring within wood material: Cluster analysis of acoustic emission data compared with numerical modelling

In this study, crack length evolutions evaluated from both experimental analysis (cluster analysis of acoustic emission activity) and numerical modelling are compared. The highlight of the work presented herein is to show the good ability of acoustic emission technique (AET) combined with statistical tools to monitor the crack tip growth within wood material. At the current state of this work, findings put in evidence a good correlation between AE results and numerical predictions. Results also show a good correlation between energy release rate values evaluated from both compliance method and numerical modelling through integral invariant method and equivalent crack length approach.

Cluster analysis of acoustic emission activity within wood material: Towards a real-time monitoring of crack tip propagation

Non-destructive monitoring of crack growth within material becomes an essential tool to better understand cracking mechanisms of materials, and therefore to reduce failure risks. This paper presents results from laboratory static tests that were conducted to investigate the monitoring of crack tip growth within wood material. Double Cantilever Beam specimens with variable inertia were tested in opening mode configuration. Acoustic emission (AE) technique was used to monitor the acoustic activity within wood material. In a first step, the reliability of the crack tip monitoring is evaluated in terms of Probability of Detection (PoD). Results show that for all specimens the PoD is larger than 70% for a detection threshold of 1mm. In a second step, a K-means++ algorithm was used to perform a cluster analysis of AE data, and to allow the AE events that were generated by the crack tip growth to be identified. Evolutions of both strain energy and AE energy are compared, and the experimental results show that the first AE events appear when the wood material reaches its limit to store strain energy, so at the vicinity of the end of its linear elastic behaviour.

Energy & crack tip stress interactions in mixed mode I/III fracture of DX51 steel sheets

DX51D sheet is subjected to mixed mode I/III loading in a purposely designed fixture apparatus. The resulting stable crack-tip growth, direction, slant angle and typical factory-roof crack were observed and discussed as the loading mixity was varied. The total essential work of fracture or fracture toughness, for each mixity loading, was evaluated adopting energy methods during experimentation, whilst theory details how the total may be separated into its individual mode components. The fracture type and direction of crack path were based on the von Mises failure theory and the fracture criteria of maximum shear stress, maximum hoop stress and maximum normal stress along with the application of Hill’s theory. The findings described clearly establish the link between the applications of the energy based equations governing crack initiation and propagation and the equations describing the stress field surrounding the crack tip in the mixed mode I/III field.

Overload effect revisited − Investigation by use of configurational forces

The configurational force concept enables the derivation of the incremental plasticity J-integral Jep, which is, in contrast to the conventional J-integral, physically appropriate to characterize the crack driving force in cyclically loaded elastic–plastic materials with growing cracks. In this paper we apply Jep, combined with an analysis of the configurational force distribution, for the investigation of fatigue crack growth retardation after a single tensile overload. The motivation for this investigation is that the main reason for the overload effect, i.e. crack flank contact behind or residual stresses around the growing crack tip, is today still an open question in fatigue. Numerical case studies are performed for two-dimensional Compact Tension specimens with long cracks that grow under cyclic Mode I loading and plane strain conditions. Variables of the numerical case studies are the overload ratio and the load ratio during constant cyclic loading. The influence of crack flank contact is examined by a comparison of two different simulations: The first simulation assumes frictionless contact between the upper and lower crack flank; in the second, fictive case, it is assumed that crack flank overlap is possible. The results show that all features of the overload effect even occur, if crack flank contact is not possible. Finally, the ability of the effective stress intensity range ΔKeff to characterize the overload effect is also discussed.

In Situ Experimental Study of Near-Tip Strain Evolution of Fatigue Cracks

Near crack tip strain fields in a stationary and a growing fatigue crack have been studied in situ using the Digital Image Correlation (DIC) technique in a compact tension specimen of stainless steel 316 L under tension-tension cyclic loading. The evolution of near-tip strains normal to the crack plane was monitored at selected locations ahead of the crack tip in consecutive cycles during fatigue crack growth experiments. A stationary crack was examined first to provide a baseline reference whilst the evolution of the strain field ahead of a growing crack was monitored in situ at peak loads during fatigue cycling. The results show that strain accumulation with loading cycle occurred at all tracked locations in both cases, and it is particularly evident close to the crack tip. Moreover, a higher strain accumulation rate was found near the growing crack tip than that near the stationary crack tip. The results on near-tip strain evolution were collected for the first time in situ during the fatigue crack growth experiments, which may hopefully inform a physical-based modelling strategy of fatigue crack growth.

Effect of Crack Statically Growing on Stress and Strain at Crack Tip for Power Hardening Materials

Crack statically growing would induce the re-distribution of the stress and strain at the crack tip for power hardening materials, and the process of crack statically growing would be affected by the change of the stress and strain at the crack tip. To understand the effect of crack statically growing on the stress and strain at the crack tip, a simulation and analysis of the stress and strain at the stable growing crack tip is performed by using elastic-plastic finite element software for the power hardening materials in this paper, which establishes a foundation for improving the capability of predicting environmentally assisted cracking growth rate in key structural materials of nuclear power plants.

Inelastic deformation and microcracking process in human dentin

Dentin is a mineralized collagen tissue with robust mechanical performance. Understanding the mechanical behavior of dentin and its relations to the dentinal structure can provides insight into the design strategies to achieve tooth functions. This study focuses on the inelastic deformation of human dentin and its underlying mechanisms. By combining four-point bending tests with fluorescent staining and laser scanning confocal microscopy, it was found that human dentin, especially root dentin, exhibited significant inelastic deformation and developed extensive microdamage in the form of microcracks prior to fracture. Dense and wavy microcracks spread uniformly across the tensile surface of root dentin, while compressive microcracks formed cross-hatched patterns. The presence of peritubular dentin in coronal dentin dramatically decreased the extent of microcracking, reducing inelasticity. Dentinal tubules were found to be initiation sites of both tensile and compressive microcracks. A unique crack propagation process was observed in root dentin under tension: numerous ring-shaped cracks formed at each dentinal tubule ahead of a growing crack tip. The advance of the tensile microcracks occurred by the merging of those ring-shaped cracks. The current findings on the microcracking process associated with inelastic deformation helps to understand the nature of strength and toughness in dentin, as well as the mechanical significance for structural variations across the whole tooth.

A fracture-ALE formulation to predict dynamic debonding in FRP strengthened concrete beams

A dynamic modeling technique able to reproduce interfacial debonding phenomena in FRP reinforced concrete beams is proposed to investigate the unstable behavior of concrete beams produced by interlaminar debonding mechanisms. The structural formulation adopts plane stress modeling and beam theory to predict the behavior of the RC beam and the FRP external reinforcement, respectively. The proposed methodology is consistent with a numerical methodology, which couples the Arbitrary Lagrangian–Eulerian (ALE) formulation with the Fracture Mechanics approach. The moving mesh strategy is used to reproduce the crack tip growth at the interfacial scale level by means of a geometry variation of the computational mesh points. Moreover, fracture variables, evaluated by means of the J-integral decomposition technique, define the crack growth motion during the debonding phenomena on the basis of an explicit crack tip speed criterion. Comparisons between static and dynamic behaviors are proposed to quantify, numerically, the dynamic amplification effects on the debonding variables produced by external and inertial loads. Moreover, a parametric study in terms of the structural characteristics of the beam constituents is developed to investigate the effects produced by the dynamic nature of the debonding phenomena on the crack evolution.