Crack Surface Contact Research Articles

Plasticity-induced crack closure identification during fatigue crack growth in AA2024-T3 by using high-resolution digital image correlation

Fatigue crack growth in ductile materials is primarily driven by the interaction between damaging and shielding mechanisms. In the Paris regime, the predominant mechanism for retardation is plasticity-induced crack closure (PICC). However, some of the mechanisms behind this phenomenon are still unclear. Identifying and separating the three-dimensional aspect from other shielding aspects during experiments is extremely complex. In this paper, we analyze the crack opening kinematics based on local crack opening displacement measurements in both 2D high-resolution digital image correlation data and 3D finite element simulations. The results confirm that the crack opening stress intensity factor Kop differs along the crack path. we present a new method to determine Kop at the crack front allowing to identify PICC as the predominant shielding mechanism in fatigue crack growth experiments. Furthermore, this work contributes to the discussion on the damage-reducing effect of PICC, since we find that the influence on fatigue damage in the plastic zone remains negligible when the crack is closed and crack surface contact is directed towards the surface.

A numerical study on the relationship between local defect resonance and sub-harmonic resonance for closed cracks

Abstract The sub-harmonic resonance in closed cracks is caused by resonant properties of the system and the contact of crack surfaces. Local defect resonance is considered a potential resonant phenomenon near cracks. This study compares local resonance and sub-harmonic resonance in a surface-breaking crack using numerical simulations. The authors previously simulated nonlinear sub-harmonic resonance using the harmonic balance-boundary element method. The investigation of local defect resonance utilizes both the boundary element method and the Sakurai-Sugiura method. The numerical results indicate a strong relation between the vibration fields of sub-harmonic frequency components and local defect resonance.

Experimental and Numerical Investigations on Crack Intersection and Propagation of Concrete Structures

This study presents experimental and numerical methods to reveal concrete structures’ crack propagation and intersection laws under static and dynamic loads. Firstly, a numerical simulation method was established using the user-defined material subroutines to solve the free crack surface contact problem of concrete structures. Secondly, three-point bending tests of concrete beams containing double cracks of different approaching angles were carried out based on the digital image correlation (DIC) technology to study the intersection and propagation of cracks. Finally, the fracture processes of double-crack concrete beams and concrete gravity dams with and without a longitudinal crack were simulated and analyzed under static and dynamic loads. The numerical results were compared with the test results to verify the effectiveness and accuracy of the proposed method in simulating crack intersection and propagation in concrete structures. Results indicate that the crack intersection affects the fracture path of concrete structures, weakens their bearing capacity, and accelerates the failure of the structures. The proposed simulation method provides an effective technical approach for crack propagation prediction and safety evaluation of engineering structures.

Towards three dimensional aspects of plasticity-induced crack closure: A finite element simulation

The mutual interactions between intrinsic (damage) and extrinsic (shielding) mechanisms are essential for understanding fatigue crack growth in ductile materials. In the latter case, plasticity-induced crack closure is the dominating retardation mechanism in the Paris regime. The transition between plane strain and plane stress states leads to a locally different fracture surface contact, which is difficult to access during experiments. In this work, plasticity-induced crack closure under constant amplitude loading of an AlCu4Mg (AA2024) aluminium sheet material is studied from a three-dimensional perspective. An elastic–plastic 3D finite element model of an M(T)160 specimen with a bilinear isotropic hardening model is used to study the evolution of plasticity during fatigue crack growth. Cyclic crack propagation is simulated with the releasing-constraint method.In the results, plasticity-induced crack closure is present up to a load ratio R = 0.3. Detailed investigations of the contact pressure distributions indicate a strong dependence on the stress intensity factors and the sheet thicknesses. The contact pressure distributions on the fracture surface can be divided into three characteristic regions. Near the plastic zone, plastic energy is still induced during the unloading process after the crack is already closed. However, the crack surface contact does not affect the shape of the plastic zone. Additionally, further plastic energy accumulates in the plastic wake region during crack closure within subsequent load cycles, described here as cyclic plastic wake. In summary, the finite element model can reproduce the major features of fatigue crack closure like Kop or Kcl and the three-dimensional and load-dependent evolution of plasticity-induced crack closure.

Analysis of closed branched and intersecting cracks by the boundary element method

The boundary element method (BEM) and a computer code for the analysis of plates with closed branched and intersecting cracks are developed. The BEM enables simple and accurate modelling of cracked plates by using boundary elements. Contact tractions between crack surfaces are computed using an iterative procedure. Stress intensity factors (SIFs) are determined using the path-independent integral. Three numerical examples are studied: a star-shaped crack in a square plate, multiple interacting cracks in an infinite plate and randomly distributed and intersecting cracks in a square plate. The examples demonstrate the simplicity of numerical modelling, the accuracy of the method and the possible applications. The influences of load directions, distances between cracks and the contact of the crack surfaces on SIF are investigated. For the plate with randomly distributed cracks, the effective elastic properties are additionally computed by considering or neglecting contact of crack surfaces. The results show that the importance of the contact procedure depends on how the cracked material is loaded.

Continuous-discontinuous cellular automaton method for intersecting and branching crack problems

In this work, a continuous-discontinuous cellular automaton method is developed to simulate crack propagating for multiple intersecting and branching cracks, which can deal with both shear-compression and tensile loading problems. Firstly, the local cell cutting relation and cellular neighbor information are proposed to track multiple discontinuities. Besides, mathematical descriptions of strong discontinuities for intersecting and branching cracks are developed; furthermore, in order to deal with the frictional contact of crack surfaces for intersecting and branching cracks, complex strong discontinuity frictional contact theory for intersecting and branching cracks is also proposed, in which additional enrichment functions for branching cracks are developed. Then, a fast adaptive cellular automaton updating scheme is developed for cells with and without intersecting and branching cracks. Additionally, stress intensity factors for intersecting and branching cracks are studied, and crack propagating processes for multiple intersecting and branching cracks are also discussed. Finally, numerical examples for stress intensity factor and propagation of multiple intersecting and branching cracks are given to examine the accuracy and efficiency of the proposed method.

A stretchable elastomer with recyclability and shape memory assisted self-healing capabilities based on dynamic disulfide bonds

Shape memory assisted self-healing (SMASH) material is a kind of smart materials that can automatically close local microscopic cracks and heal those cracks by bonding the damaged surfaces. Here, we designed a SMASH elastomer via introducing polylactide (PLA) and disulfide bonds into the epoxidized natural rubber (ENR). PLA chains interspersed in ENR network as control switch to fix or release the temporary shape, providing ENR with enhanced mechanical strength and shape memory properties. After achieving the physical contact of crack surfaces by intrinsic shape memory, the exchange reaction of disulfide bonds healed the damaged area at elevated temperature. Meanwhile, the dynamic feature of disulfide bonds endowed ENR with recyclability, which could be further promoted by the thermoplasticity of PLA phase. Additionally, we also verified the feasibility of this strategy in designing PLA/ENR thermoplastic vulcanizate with SMASH behavior via dynamic vulcanization, expanding the research scope of self-healing elastomers and dynamic vulcanization.

Polyhedral oligomeric silsesquioxane (POSS)-based epoxy nanocomposite involving a reversible Diels–Alder-type network as a self-healing material

Epoxy-polyhedral oligomeric silsesquioxane (POSS) nanocomposites were prepared by incorporating POSS nanofiller into the epoxy-amine network. The monofunctional epoxy-POSS monomer or nonfunctional octaphenyl POSS unit were applied to reinforce the epoxy network by producing the nanocomposite with chemically bound pendant POSS or physically admixed POSS. The combination of reactive and unreactive POSS, leads to a synergistic effect and to the most efficient reinforcement of the epoxy network. Both polymer-POSS and POSS–POSS interactions are present in the system and lead to a strong physical crosslinking through the path polymer-bound POSS-unbound POSS domain. The nanocomposite was modified by incorporation of the thermoreversible Diels–Alder (DA) type network. The produced interpenetrating network composed of the irreversible reinforced epoxy and the reversible DA networks exhibits an efficient self-healing capability. This strong nanocomposite, showing a modulus of 800 MPa at room temperature, was healed with an efficiency of 61%. The developed stiff nanocomposite is shown to be a promising material because self-healing of strong thermosets is still a big challenge. With the increasing content of POSS nanofiller and heterogeneity of the nanocomposite, however, the healing efficiency diminishes. The insufficient contact of crack surfaces due to involved inhomogeneities results in a worse sealing of the material crack.

Crack Tip Stress Field Analysis of Crack Surface Contact and Opening during <i>In Situ</i> Wedge Loading of Human Enamel

Shallow cracks are often observed in dental enamel, however do not normally lead to deep fractures. Previous work has highlighted the toughening mechanisms that operate in enamel during crack propagation, but very little is known about the deformation and stress fields arising around the propagating cracks during realistic loading conditions. This work aims to elucidate how the stresses are distributed within human dental enamel when a pre-existing crack is subjected to opening and surface contact with in situ indentation. We present a synchrotron-based insitu analysis coupled with a linear elastic finite element method simulation. The experimental reconstructed stress fields identified a prominent residual stress within the enamel, accompanied by a visible pattern that appeared clearly associated with its underlying microstructure. The numerical modelling of the stress field and discerning of surface contact and crack opening caused by the indentation was subsequently possible, even if in this study the influence of the anisotropy induced by the presence of features at a smaller scale was neglected. The implications of these findings and directions for future research are discussed.

Effect of crack surface contact forces on vibration fatigue characteristics of beam structure

The vibration fatigue characteristics of a beam structure with breathing cracked links are studied, with the consideration of the contact forces at the breathing crack surfaces. First, a dynamic model of the breathing cracked beam element was formulated using the finite element method (FEM) and the theory of fracture mechanics. Subsequently, the coupled dynamic equation of a beam structure with breathing cracked links was established by FEM based on the dynamic model of the breathing cracked beam element. Then, the law of opening and closing of the breathing crack in the beam element was analyzed and the expressions for contact forces at the crack surfaces were derived using FEM. The sensitivity of the breathing crack surfaces to structural parameters and crack parameters was analyzed, by which the influence of contact forces on the structural parameters and crack parameters was revealed. Finally, the dynamic stress characteristics of the beam structure with breathing cracked links were analyzed. The vibration fatigue characteristics were described by the Paris fatigue crack growth curve model, by which the effect of the contact forces at the breathing crack surfaces on the vibration fatigue life of a beam structure with breathing cracked links was studied. Some concluding remarks based on an example have also been given.

Strain visualization of growing short fatigue cracks in the heat-affected zone of a Ni–Cr–Mo–V steel welded joint: Intergranular cracking and crack closure

Physically short fatigue crack growth behavior in the heat-affected zone of a Ni–Cr–Mo–V steel welded joint was investigated in-situ in SEM to reveal effects of crack closure and tortuous crack growth path on crack-tip straining behavior with the help of high resolution digital image correlation technique. The crack growth path and associated fatigue damage at microstructural scale was characterized by electron backscatter diffraction and electron channeling contrast imaging techniques. Results showed that the short crack growth was influenced by both local microstructure and global strength gradient. The short crack could deflect intergranularly when meeting with one large grain due to misfit deformation and strain localization. The crack closure, which was accompanied during loading and unloading in terms of crack surface contact, shielded the real crack-tip and manifested itself well in both compressive strain at crack wake and strain development at crack-tip. It is indicated that strain localization at lathy boundaries and formation of sub-grains was responsible for the fatigue of short cracks.

About Compression Fracture

The paper discusses fracture processes occurring under compressive loads. The processes are considered from two points of view: (i) compression fracture mechanisms and their effect on the strength and fracture resistance of the material, and (ii) the effect of geometric constraints on the stress-strain state and fracture conditions of bodies (natural objects) with cracks and crack-like defects. These are particularly the effects associated with crack surface contact, friction, and loading history. Fracture structures are described which form in the conditions of high-rate compression under extreme loads typical of tectonic processes and deep hydrocarbon production. The structures include crack-like compaction regions in highly porous brittle materials (rocks) formed under compression, which present a new form of quasi-brittle mode I fracture (a compression crack). A method is proposed for estimating the effective strength of compressed bodies with one dimension (thickness) being much smaller than the other two and that have through-thickness variable properties and/or composition. As an example, the ice cover strength with respect to longitudinal compression is considered taking into account a partial loss of the ice bearing capacity. The influence of geometric constraints on the fracture mechanisms in fractured thin bodies is discussed. It is shown that the compression fracture of bodies with elongated through holes (or crack-like defects), whose length is much larger than the body thickness, occurs by a mechanism induced by the overlapping of crack surfaces.

Subsurface crack nucleation and growth behavior and energy-based life prediction of a titanium alloy in high-cycle and very-high-cycle regimes

Fully reversed and pulsating tension fatigue tests were performed to clarify the subsurface failure behavior of TC11 titanium alloy in high-cycle and very-high-cycle regimes. The deflection of crack surfaces induces the premature contact of crack surfaces and slow crack growth. The whole failure processes mainly include: (i) nucleation of microcracks, (ii) coalescence and growth of microcracks, (iii) formation of facet cluster area, (iv) early macrocrack growth, (v) formation of fisheye, (vi) unstable macrocrack growth and (vii) momentary fracture. Based on the modeling of crack nucleation and growth, an energy-based approach is well proposed to predict the total fatigue life.

Crack-face frictional contact modelling in cracked piezoelectric materials

Actuators, sensors, micro- and nano-electromechanical systems and other piezoelectirc components are generally constructed in block form or as a thin laminated composites. The study of the integrity of such materials in their various forms and small sizes is still a challenge nowadays. To gain a better understanding of these systems, this work presents a crack surface contact formulation that includes friction and thus makes it possible to study the integrity of these advanced materials under more realistic crack surface multifield operational conditions. The dual boundary element method (BEM) is used for modeling frictional crack surface contact on piezoelectric solids in the presence of electric fields, further taking into account the electrical semipermeable boundary conditions on the crack. The formulation uses contact operators over the augmented Lagrangian to enforce contact constraints on the crack surfaces. The BEM reveals to be a very suitable methodology for these interface interaction problems because it considers only the boundary degrees of freedom, what makes it possible to reduce the number of unknowns and to obtain accurate results with a much lower number of elements than formulations based on the standard finite element method or the eXtended finite element method. The capabilities of this methodology are illustrated by solving some benchmark problems.

Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method

Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we introduce a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), to explicitly simulate the crack induced nonlinear elasticity in solids with both horizontal and inclined cracks. In the FDEM model, the solid is discretized into finite elements to capture the wave propagation in the bulk material, and the finite elements along the two sides of the crack also behave as discrete elements to track the normal and tangential interactions between crack surfaces. The simulation results show that for cracked models, nonlinear elasticity is generated only when the excitation amplitude is large enough to trigger the contact between crack surfaces, and the nonlinear behavior is very sensitive to the crack surface contact. The simulations reveal the influence of normal and tangential contact on the nonlinear elasticity generation. Moreover, the results demonstrate the capabilities of FDEM for decoding the causality of nonlinear elasticity in cracked solid and its potential to assist in Non-Destructive Testing (NDT).

Fatigue crack behaviors under asynchronous biaxial loading

Crack behavior of aluminum alloy 2A12-T4 is investigated experimentally and numerically using cruciform specimens subjected to in-plane biaxial loadings applied in horizontal (x axis) and vertical (y axis) directions. Different cruciform configuration plans, with variant sizes of slots in loading arms and different transitional fillet radius between adjacent arms, are analyzed by means of FEM to confirm a final specimen geometry with relative uniform stress distribution in its central area. The tests for fatigue crack growth behavior under cyclic biaxial sinusoidal loadings with phase differences of 0° or −60° between two orthogonal fatigue loads are conducted by using a biaxial fatigue test system. The biaxial load ratio, Pmaxx/Pmaxy, varies from −0.5 to 1.0. Initial central cracks are inclining in angles of 0°, 45° and 60° to x-axis. Crack growth path and lives are obtained. It is observed that the crack growth behavior under biaxial loading differs from that with only uniaxial loading. A widely accepted fatigue crack growth model, which combines Paris equation, maximum tangential stress (MTS) criterion and an equivalent stress intensity factor (SIF) proposed by Tanaka, is used for mixed mode-I/II crack subjected biaxial loading. The combined model is evaluated by the SIFs analysis based on analytical and numerical solution. The mixed mode SIFs are calculated based on finite element analysis with mesh updating. The simulated crack growth path and growth lives correlate well with the experiments in most cases. Both the experiments and the simulations demonstrate that the tensile load parallel to crack path behaves as the retarder to the crack growth, and the compressive load parallel to crack path behaves as the promoter to the crack growth. It is found that equivalent SIF used in the model overestimates the effect of mode II SIF on the fatigue crack growth rate by Paris equation. It is questionable to use the combined model for the cases with asynchronous biaxial loadings or those leading to crack surface contact.

Crack Surface Frictional Contact Modelling in Piezoelectric Materials

Piezoelectric materials exhibit an electromechanical coupling which allows for their use assensors or energy harvesting devices (direct piezoelectric effect) or actuators and shape control de-vices (inverse piezoelectric effect). They are applied in many technological sectors of current interestsuch as the aerospace and automotive industries, and they are generally constructed in block form orin a thin laminated composite. The study of the integrity of such materials in their various forms andsmall sizes is still a challenge nowadays. To gain a better understanding of these systems, this workpresents a crack surface contact formulation which makes it possible to study the integrity of theseadvanced materials under more realistic crack surface multifield operational conditions. The formu-lation uses the BEM for computing the elastic influence coefficients and contact operators over theaugmented Lagrangian to enforce contact constraints on the crack surface, in the presence of electricfields. The capabilities of this methodology are illustrated solving a benchmark problem.

Effect of initial contact surface condition on the friction and wear properties of bearing steel in cyclic reciprocating sliding contact

Delamination failure is one of the most important engineering problems. This failure can frequently be detrimental to rolling contact machine elements such as bearings, gear wheels, etc. This phenomenon, called rolling contact fatigue, has a close relationship not only with opening-mode but also with shear-mode fatigue crack growth. The crack face interference is known to significantly affect the shear-mode fatigue crack propagation and its threshold behavior. Quantitative investigation on friction and wear at fatigue crack faces in the material is essentially impossible. Previously, thus, a novel ring-on-ring test by making use of fatigue testing machine was proposed to simulate a cyclic reciprocating sliding contact of crack surfaces. However, this test procedure had some problems. For instance, in order to achieve the uniform contact at the start of test, the rubbing of specimens must be conducted in advance. By this treatment, the specimen surfaces were already damaged before the test. In this study, an improvement of experimental method was made to perform the test using the damage-free specimens. The friction and wear properties for heat-treated high carbon-chromium bearing steel were investigated with this new method and the results were compared to the results obtained by using the initially damaged specimens.

Atomic scale investigation of nanocrack evolution in single-crystal and bicrystal metals under compression and shear deformation

The objective of this work is to investigate the plastic deformation induced nanocrack evolution in single-crystal and bicrystal copper using molecular dynamics simulations, focusing on the effect of loading condition on crack closure. The results show that the compressive stress induced by defects such as dislocation, 9R phases and deformation twinning drives the crack closure. The microstructural evolution of nanocrack closure zone can be divided into four stages which include crack surface contact, local closure with discontinuously, closure zone expanding, and global closure. In addition, the crack in a bicrystal heals more easily than that in a single-crystal, due to the formation of a 9R phase. After one cyclic shear loading in both single-crystal and bicrystal copper, there is no crack nucleation in the crack-closure zone. The MD results from this work may provide useful guidance for designing the optimal nanomaterial with high damage tolerance and long service life.

Crack closure effects in thermal fracture of functionally graded/homogeneous bimaterials with systems of cracks

In the presented model the microstructure of a functionally graded material (FGM) is accounted in two ways: via FGM properties and by distributed small cracks which could be on grain boundaries of the material. The contribution to the solution of material gradation of FGM and of material structure reflected via geometry of distributed cracks is investigated. Besides, some additional effects arising due to possible crack closure and contact of crack surfaces are taken into account in the model and its contribution is also assessed. The goal of this investigation is to show these affects and to estimate the contribution on the SIFs of each of these, if they are strong or can be neglected.