Crack Interaction Research Articles

The linear steady state analysis of multiple moving cracks in a piezoelectric half-plane under in-plane electro-elastic loading

In this work, the steady state problem of multiple Yoffe-type cracks propagating in a piezoelectric half-plane within the framework of linear electroelasticity under in-plane electro-elastic loading is studied. At first, the closed-form solution of the moving electric and Volterra type climb and glide edge dislocations are derived using the complex Fourier transforms to achieve the integral equations of a piezoelectric half-plane with several moving cracks. Then, the integral equations with Cauchy-kind singularity are solved numerically to determine the mixed mode stress intensity factors and the electric displacement intensity factors in a piezoelectric medium. Finally, the effects of the loading conditions, crack moving speed, cracks lengths, cracks interactions and geometrical parameters on the field intensity factors are considered.

Simulation of the thermal shock behavior of ultra-high temperature ceramics with the consideration of temperature-dependent crack propagation criterion and interaction between thermal shock cracks evolution and thermal conduction

The constitutive relation of micro-cracked ultra-high temperature ceramics deduced by energy method and the temperature-dependent critical energy release rate of ceramics were demonstrated in this paper. Taking advantage of the constitutive relation and temperature-dependent critical energy release rate, the thermal shock behavior of Al2O3 had been simulated firstly with finite element method. Results showed that the crack patterns of simulation approximated in the experiments. That confirmed the accuracy of our model. The ZrB2-based ceramic was then used as an example to study the effects of the temperature dependence of crack propagation criterion on the evaluation of thermal shock resistance of ultra-high temperature ceramics. In addition, given that the cracks forming during thermal shock lead to discontinuities in the ceramic material and influence thermal conduction. The interaction between thermal shock cracks evolution and thermal conduction, and the corresponding effects on the thermal shock behavior of ultra-high temperature ceramics were studied for the first time. Results indicated that the thermal shock crack patterns and temperature fields were significantly different while the thermal conductivities at the cracks were different for identical thermal shock conditions. Therefore, in order to improve the accuracy of simulation and the evaluation of thermal shock resistance of ultra-high temperature ceramics, the temperature dependence of the crack propagation criterion and the interaction between the cracks evolution and thermal conduction must be taken into consideration.

Using a Beta (β) Correction to Improve the Life Predictions of Cold-Expanded Holes in 2024-T3 & 7075-T6 Aluminum Alloys

Fastener holes represent the most common fatigue details found in airframe structures. In order to minimize the impact fastener holes have on the fatigue behavior of critical aircraft components, many are processed by cold expansion (Cx). Cx imposes a residual compressive stress field around a hole that retards fatigue crack growth (FCG) and increases the fatigue life of the component. In order to take analytical advantage of the Cx process, a “one size fits all” method of reducing the initial flaw size to a minimum of a 0.005 in. (0.127 mm) symmetric corner crack is often employed. This approach leads to predictions that do not represent the physics of crack growth behavior within materials that have been processed using Cx. A physics-based approach was investigated to take analytical advantage of the Cx process. The authors developed an empirical-based factor (β) to characterize the effect of Cx on the FCG behavior within 2024-T351 and 7075-T651 aluminum alloys. This method takes into account the interaction of the fatigue crack and the residual stress field. This β can be used in FCG analysis to provide an accurate model of the crack growth behavior at Cx holes. In order to develop accurate da/dN versus ΔK plots for the Cx configuration, finite element modeling was used to calculate stress intensities along the crack front. By using the fracture-mechanics-based similitude principle, the nonCx and Cx da/dN versus ΔK data were compared and β corrections representing the residual stress field in the body were calculated.

An interaction factor to estimate the over-constraining effect in plates with co-planar cracks

This paper reports an over-constraining effect on the near-tip stress field caused by the presence of a nearby coplanar crack, through detailed numerical investigations. The crack driving force, measured by the leading term in the near-tip stress solution, underestimates the stresses near the coplanar crack fronts. This study thus proposes a crack interaction factor based on the average Q-stress over a finite distance from the crack tip. The proposed interaction factor provides a close estimate of the near-tip stress for the coplanar cracks, and predicts successfully the interaction among coplanar elliptical crack-front locations, using an equivalent through-thickness coplanar crack model.

The effect of thickness on the creep properties of a single-crystal nickel-based superalloy

Creep rupture tests were conducted at 980 °C/250 MPa on specimens with different wall thickness values obtained from a single-crystal nickel-based superalloy. Experimental results showed that the thin specimens had an inferior creep life compared with the thick ones. All specimens were oxidised during the creep tests. Electron probe microanalysis and scanning electron microscopy combined with energy-dispersive X-ray spectroscopy revealed that internal nitrides developed in the γ′-free zone and even in the matrix. The presence of internal nitrides induced the nucleation of creep voids and initiation of cracks during creep rupture, thereby increasing the growth rate of cracks and facilitating the failure of the creep specimens. The morphology of the fracture sections indicated that the interaction of cracks and creep damage also contributed to this phenomenon. Cracks played an important role in the creep behaviour of the thin specimens, and creep damage effectively influenced that of the thick specimens.

Topology optimization of particle‐matrix composites for optimal fracture resistance taking into account interfacial damage

SummaryThis paper presents a topology optimization framework for optimizing the fracture resistance of two‐phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bidirectional evolutionary structural optimization method. The sensitivity formulation accounts for the whole fracturing process involving crack nucleation, propagation, and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended bidirectional evolutionary structural optimization method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.

Analysis of a main fatigue crack interaction with multiple micro-cracks/voids in a compact tension specimen repaired by stop-hole technique

Fatigue is a process in engineering materials in which damage accumulates due to the fluctuating loading. One solution for a component under the fatigue process is to arrest the crack propagation before the final failure using different available retardation methods, such as drilling/stop-hole technique. In addition, structural components may also suffer from the existence of micro-cracks or voids due to their forming process or service lives. These micro-cracks/voids are very critical to study, since they can effectively play an important role in the behavior of the existing main crack in a component. This article aims to investigate the effect of the stop-hole retardation technique and multiple micro-cracks/voids with different characteristic lengths and geometries on the fatigue crack propagation in a compact tension specimen. A modified Forman equation, the so-called NASGRO equation is used to define the transition between crack initiation and crack growth period. Also, the extended finite element method is adapted in the crack propagation phase in order to model crack path in the geometry eliminating the need for remeshing procedure. The whole analyses are conducted in a commercial package through a user-written code that handles all fatigue crack growth analysis. The reference solutions from the literature are used to compare and to validate results obtained from current work.

Interaction of a conductive crack and of an electrode at a piezoelectric bimaterial interface

The interaction of a conductive crack and an electrode at a piezoelectric bi-material interface is studied. The bimaterial is subjected to an in-plane electrical field parallel to the interface and an anti-plane mechanical loading. The problem is formulated and reduced, via the application of sectionally analytic vector functions, to a combined Dirichlet–Riemann boundary value problem. Simple analytical expressions for the stress, the electric field, and their intensity factors as well as for the crack faces' displacement jump are derived. Our numerical results illustrate the proposed approach and permit to draw some conclusions on the crack–electrode interaction.

Theoretical analysis of fatigue failure in mechanically fastened Fibre Metal Laminate joints containing multiple cracks

Mechanically fastened joints are susceptible to the presence of multiple-site damage (MSD) cracks in the critical fastener row. Different from the MSD growth in joints consisting of metallic substrates, the two coupled metal crack growth and interfacial delamination propagation failure mechanisms in Fibre Metal Laminates (FMLs) make the prediction of fatigue behaviour in FML joints with MSD scenario burdensome and impractical when considering all factors influencing the fatigue performance. This paper presents a theoretical study on the MSD crack growth behaviour in mechanically fastened FML joints with a focus of modelling the effects of bearing and bypass loads. The proposed model in this paper is built upon analytical models dealing with MSD growth in flat FML panels and single crack growth in FML panels subjected to a combined tension-pin loading case. This model would be particularly useful for symmetric FML joints where no secondary bending effects present. A deliberately designed symmetric FML joint was tested to validate the proposed model. The model captures the rapid crack growth in the vicinity of fastener holes due to bearing stresses and crack acceleration due to the interaction of cracks. It is identified that the load redistribution between intact fastener rows and the cracked fastener row accelerates crack growth with crack length. The effects of secondary bending stresses in FML joints on the crack growth behaviour is extensively discussed. The performance of the proposed model for single lap FML joints is also examined using test data from open literature. It is found that the proposed model provides a conservative prediction for the tested single shear lap FML joint from open literature.

Flexural fatigue behavior of LSI based plain weave carbon fabrics reinforced ceramic composites

An experimental investigation was performed to study the fatigue behavior of plain-weave fiber fabrics reinforced C/C-SiC composites (2D C/C-SiC composites) prepared by liquid silicon infiltration (LSI) under dynamic flexural stresses at room temperature. The results indicate that the fatigue limit (105 cycles) of 2D C/C-SiC composites subjected to flexural fatigue stresses is 95 MPa, corresponding to approximately 78% of flexural strength of virgin specimens. Moreover, as the fatigue loading/unloading proceeds, both strength enhancement and strength degradation are successively observed in the post-fatigue specimens under quasi-static flexural tests. Maximum residual flexural strength (RFS) of post-fatigue specimens increases to 135.7 MPa when the 2D C/C-SiC specimens are exposed to maximum fatigue stress of 95 MPa for 5000 cycles. The microstructures and fractured surfaces indicate that evolution of RFS is determined by the interaction of matrix cracking and interfacial degradation. The interfacial debonding and relief of residual thermal stresses induced by matrix cracking are mainly responsible for the enhanced strength in the post-fatigue specimens.

4D Structural Characterization of Mechanical Degradation in Reinforced Fuel Cell Membranes Using in Situ Visualization

Perfluorosulfonic acid (PFSA) ionomer membranes in fuel cells are susceptible to operational mechanical stresses resulting in fatigue and/or creep failures that compromises their durability and lifetime. The fatigue based mechanical degradation is typically a result of repeated wet/dry humidity cycles that cause micro crack initiation and /propagation within the membrane [1]. Fatigue induced membrane failure in the form of cracks/tears/pinholes leads to a gradual increase in gas crossover and ultimately to fuel cell failure. Membranes with less conductive mechanical reinforcements have been developed to alleviate mechanical degradation yielding demonstrated improvements in lifetime and durability. Nevertheless, development of membrane damage remains a critical failure mode and the fundamental understanding of membrane mechanical degradation is a subject of ongoing research. Scanning electron microscopy (SEM) based studies have been used to characterize the degradation-induced structural changes in fuel cell membranes; however, SEM imaging is inherently destructive and inhibits any tracking of structural changes at a particular location over time. Hence, membrane degradation evolution studies are limited to ex situ analysis at various stages of degradation and with different samples. Recently, laboratory-based X-ray computed tomography (XCT) was introduced as an alternative imaging technique, which has enabled three-dimensional (3D) failure analysis of fuel cell membranes revealing novel insights on membrane failure [2,3]. In the present work, the XCT-based 3D failure analysis approach is extended to an in situ investigation of pure mechanical membrane degradation by utilizing a custom designed fixture. This X-ray transparent fixture houses a gas diffusion electrode (GDE) based MEA with a reinforced membrane, which is subjected to wet/dry cycling of N2 gas flowing through both anode and cathode sides, thereby producing a pure mechanical fatigue type degradation within the membrane. XCT-based 3D identical location tracking of membrane morphology as a function of degradation time facilitates a novel four-dimensional (4D) in situ workflow [4], which enables the characterization of the damage growth or evolution. Preliminary results show that no through- thickness membrane cracks developed until 3000 wet/dry cycles. However, minor crazes initiated on the cathode side membrane surface (Fig. 1) between 2000 and 2500 cycles. Crack initiation and growth within the reinforced membrane are comprehensively examined from various perspectives by simultaneously studying the two-dimensional (2D) planar and cross-sectional views. A clear interaction of membrane cracks with defect features, such as delamination and catalyst layer cracks is observed. Furthermore, the centrally located reinforcement layer is found to restrict the through-thickness growth of membrane cracks at several locations in the early stages of damage initiation. Overall, the size and density of membrane crack formation at a given number of cycles is found to be considerably reduced with the use of a reinforced membrane when compared to a non-reinforced membrane. A detailed study to understand the variation in degradation mechanisms between reinforced and non-reinforced membranes is carried out. Overall, the work summarized here is a unique study on the evolution of reinforced membrane degradation with a 4D perspective. The new findings from this work demonstrate the distinct advantage of XCT technology in gaining an improved fundamental understanding of membrane degradation by capturing critical failure modes and mechanisms at their different developmental stages. Acknowledgement This research was funded by the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, British Columbia Knowledge Development Fund, and Ballard Power Systems through an Automotive Partnership Canada (APC) grant. This research was undertaken, in part, thanks to funding from the Canada Research Chairs program. The authors thank Kevin Dahl and Alex Boswell for technical support.

In Situ Scanning Electron Microscope (SEM) Observations of Damage and Crack Growth of Shale.

To better understand the formation and evolution of hierarchical crack networks in shales, observations of microscopic damage, and crack growth were conducted using an in situ tensile apparatus inside a scanning electron microscope. An arched specimen with an artificial notch incised into the curved edge was shown to afford effective observation of the damage and crack growth process that occurs during the brittle fracturing of shale. Because this arched specimen design can induce a squeezing effect, reducing the tensile stress concentration at the crack tip, and preventing the brittle shale from unstable fracturing to some extent. Both induced and natural pores and cracks were observed at different scales around the main crack path or on fractured surfaces. Observations indicate that the crack initiation zone develops around the crack tip where tensile stresses are concentrated and micro/nanoscale cracks nucleate. Crack advancement generally occurs by the continuous generation and coalescence of damage zones having intermittent en echelon microscopic cracks located ahead of the crack tips. Mineral anisotropy and pressure build-up around crack tips causes crack kinking, deflection, and branching. Crack growth is often accompanied by the cessation or closure of former branch cracks due to elastic recovery and induced compressive stress. The branching and interactions of cracks form a three-dimensional hierarchical network that includes induced branch cracks having similar paths, as well as natural structures such as nanopores, bedding planes, and microscopic cracks.

Interaction of periodic arrays of wing cracks

A method for evaluating the interaction of wing cracks in 2-D and 3-D is presented. The method utilizes the assumption that the wing crack can be represented by its extensions and the interaction is solved using a superposition method presented by Kachanov. The method is applied to arrays of parallel initial cracks to determine the critical crack array orientations and assess whether the coalescence of closely-spaced small cracks causing a shear-like failure observed in 2-D is possible in 3-D. The results show that the shear failure can be achieved also in 3-D, but not with such an instability as in 2-D.

Predicting the 3D fatigue crack growth rate of small cracks using multimodal data via Bayesian networks: In-situ experiments and crystal plasticity simulations

Small crack propagation accounts for most of the fatigue life of engineering structures subject to high cycle fatigue loading conditions. Determining the fatigue crack growth rate of small cracks propagating into polycrystalline engineering alloys is critical to improving fatigue life predictions, thus lowering cost and increasing safety. In this work, cycle-by-cycle data of a small crack propagating in a beta metastable titanium alloy is available via phase and diffraction contrast tomography. Crystal plasticity simulations are used to supplement experimental data regarding the micromechanical fields ahead of the crack tip. Experimental and numerical results are combined into a multimodal dataset and sampled utilizing a non-local data mining procedure. Furthermore, to capture the propensity of body-centered cubic metals to deform according to the pencil-glide model, a non-local driving force is postulated. The proposed driving force serves as the basis to construct a data-driven probabilistic crack propagation framework using Bayesian networks as building blocks. The spatial correlation between the postulated driving force and experimental observations is obtained by analyzing the results of the proposed framework. Results show that the above correlation increases proportionally to the distance from the crack front until the edge of the plastic zone. Moreover, the predictions of the propagation framework show good agreement with experimental observations. Finally, we studied the interaction of a small crack with grain boundaries (GBs) utilizing various slip transmission criteria, revealing the tendency of a crack to cross a GB by propagating along the slip directions minimizing the residual Burgers vector within the GB.

Fatigue crack growth under large scale yielding condition in a cast automotive aluminum alloy

Low Cycle Fatigue crack growth tests have been performed at 250 °C in order to study fatigue crack growth under large scale yielding conditions in a material widely used at high temperature by the automotive industry for cylinder head applications. The studied material was a cast aluminum alloy AlSi7Cu3Mg (close to A319) produced by Lost Foam Casting. Two different microstructures were investigated: one containing large natural pores and another where pores have been removed by Hot Isostatic Pressing (HIP). Fatigue Crack Growth Rates (FCGR) have been measured by in situ surface optical microscopy for different loading conditions all inducing generalized plasticity and compared to assess the influence of pores on the FCGR. In situ observations coupled to post mortem analysis revealed strong crack interactions with both pores and large hard particles on specimen surfaces and in the bulk. FCGR ranging between 10−6 and 10−4 m/cycle appear to be mainly sensitive to applied strain amplitudes. Although pores promoted secondary crack initiations and crack coalescences, they seemed to have a limited effect on steady-state FCGR which has been analytically modeled using energy densities.

Characterization of the creep interaction effect for twin semi-elliptical surface cracks under combined tension and bending loading

The interaction of twin semi-elliptical surface cracks subjected to combined tension and bending in the creep regime is studied. Moreover, the crack growth behavior in the presence of multiple cracks is simulated to reveal the effect of creep interaction factor. The tension load produces a larger creep interaction factor than those for pure bending and combined tension and bending. For the combination of cracks, a greater value of the creep interaction factor is permitted compared with the linear-elastic condition. The enhancement of creep crack growth rate in multiple cracks is diminished as the improvement of creep interaction factor is lower than 30%.

Direct in situ observation of toughening mechanisms in nanocomposites of silicon nitride and reduced graphene-oxide

In situ observations are performed, for the first time, of stable crack propagation in nanocomposites of silicon nitride (Si3N4) and reduced graphene-oxide (rGO) inside a scanning-electron microscope. Two different specimen geometries (wedge-splitting and double-cantilever beam) are used to observe crack interactions with rGO stacks in two different orientations (cross-section and in-plane). These observations provide new insights into the unique, effective pull-out of crack-bridging rGO stacks, which appears to be responsible for the extraordinary toughness in the Si3N4/rGO nanocomposites. These insights could be used to design and create future ceramic/rGO nanocomposites with superior mechanical properties.

Influence of specimen thickness on the creep behavior of a directional solidification nickel-based superalloy

The effects of thickness and surface signature on the creep life of a directionally solidified nickel based superalloy were investigated. The creep tests of ground specimens in the thickness of 0.61 mm and 0.89 mm, as well as polished ones with 0.66 mm and 0.87 mm in thickness were performed at 980 °C/160 MPa. Based on the experimental results, the thin ones had inferior creep life compared with thick specimens. XRD exhibited that all the specimens were oxidized during the creep tests, however, the non-loading bear zones which caused by oxidation was insufficient to explain the creep life of specimens under different wall thicknesses. On the other hand, the morphology of fracture sections indicated that the interaction of cracks and creep damage could reveal this phenomena. It worth noting that the cracks played a more important role in the creeping of thin specimens, but creep damage influenced the thick specimens more effectly. In addition, the polished specimens had a better behavior during creep tests than the ground ones.

Definition and validation of an interaction rule for two cracks submitted to a complex loading

The article deals with the question of flaws interaction when two cracks are too close to each other to apply a conventional Fracture Mechanics justification approach based on isolated crack consideration.Within that frame, a bibliography and FE modeling were performed in order to define precisely interaction limits and cracks analysis in the case of two isolated cracks submitted to various modes of loading. Those limits, firstly defined through an exhaustive 2D FE modeling, were modified and completed through 3D FE modeling in order to take into account cracks with a finite length, plasticity and/or a complex stress states.From that important work, a simple limit for cracks interaction is proposed and then validated through the application to an industrial case.

Study on the Interaction of Collinear Cracks and Wing Cracks and Cracking Behavior of Rock under Uniaxial Compression

This paper investigates the crack interaction, initiation, and propagation rules of rock‐like materials containing two collinear cracks. Based on the Kachanov method, the formulations for stress intensity factors (SIFs) of two collinear cracks and two winged cracks are derived, respectively. The influences of bridge ligament and crack length on the crack interaction are analyzed theoretically. The results show that the propagation of a long crack is independent of crack interaction when d ≥ a2 and the same rule applies for a short crack when d ≥ a1. With the growth of wing cracks, the SIF of wings first remarkably decreases and then it tends toward a steady value. Subsequently, the propagation of collinear cracks and cracking processes under uniaxial compression are analyzed experimentally and numerically. Both the experimental results and simulation results demonstrate that shear cracks tend to initiate and propagate at higher inclination angle. The crack coalescence is affected by the inclination angle of bridge ligament. For increasing the inclination angle, the crack coalescence varies from wing crack failure to shear crack coalescence. As bridge ligament increases, the crack coalescence varies from shear crack coalescence to shear‐wing crack coalescence and then to wing crack failure.