Crack Nucleation Research Articles

The origin of the energy split in phase‐field fracture and eigenfracture

AbstractThe energy splits, which are used in phase‐field fracture and eigenfracture, are frequently motivated by the statement that crack nucleation and crack growth have to be prevented at compression loads. The intention of the article at hand is to show that the energy decomposition is an essential part of such fracture models, and to investigate the underlying problem and its physical interpretation. Finally, a general framework for the derivation of physically motivated energy splits is presented, which is not limited to certain bulk material models.

Micro-deformation behavior of laser melting deposited multi-gradient TC4/TC11 alloy under tension–tension cyclic loading

The microstructure of additive manufacturing titanium alloy is closely related to its mechanical properties. In this study, a TC4/TC11 titanium alloy with 20 layers was prepared by laser melting deposition (LMD) technology. Microstructure analysis revealed a transformation of the columnar grains into equiaxed grains along the build direction (BD), accompanied by the presence of heat affected zone (HAZ) bands and pore defects. The defect families of specimens in different directions were characterized by X-ray micro-computed tomography (micro-CT). The porosity of BD specimens was 0.0021%, and the porosity of the transverse direction (TD) specimens was 0.0001%, indicating that the material was dense. Specimens with different directions were subjected to tension–tension cyclic loading, and their deformation was analyzed by digital image correlation (DIC). The results show that the presence of noticeable pore defects leads to crack initiation around these regions due to local strain concentration. Moreover, the dispersion and anisotropy of mechanical properties are attributed to the influence of porosity and microstructure deformation, the latter being the dominant factor. In addition, the deformation mechanism and failure mode of the microstructure in LMD TC4/TC11 are proposed in this paper. The deformation of the α laths of TD specimen is hindered by the columnar grain boundary, resulting in improved resistance against crack nucleation and propagation compared to the BD specimen.

Experimental observations of nucleation and crack growth paths of hydrogen-induced cracking in pipeline steel

The microstructural features that favor hydrogen-induced cracking (HIC) in internal, middle, and external layers of pipeline steels were investigated. The electrochemical cathodic charging was used to induce HIC, and straight beam ultrasonic inspection was identified in which steel layers HIC nucleate and grow. The cracked plates were examined by optical microscope and scanning electron microscope (SEM). The hydrogen microprint technique (HMT) was used to visualize the site of high hydrogen concentrations. Electron backscatter diffraction (EBSD) was used to analyze the role of crystallographic texture in HIC pathways. The results revealed that HIC nucleation and growth are influenced by the segregation degree and inclusion contents, which are higher in the internal surface layer of our studied steels but not consistently so in the middle thickness layer. Further, HIC nucleated in cuboidal and spinal inclusions and propagated along ferrite/pearlite bands with high misorientations. The HMT results showed that hydrogen is present in pearlite colonies, grain boundaries, and non-metallic inclusions. The results indicated that HIC is not solely controlled by the crack geometry.

From stress concentrations between inclusions to probability of breakage: A two-dimensional peridynamic study of particle-embedded materials.

Particle-embedded materials consist of a dispersed phase of particles in a sticking matrix. We used a bond-based peridynamics method to investigate their elastic properties, rupture, and probability of failure. We performed an extensive two-dimensional parametric study where particles are disk-shaped inclusions diluted into a pore-filling matrix. Both particle and matrix are considered to be brittle elastic with a perfectly bonded interface. The inclusion volume fraction φ and the inclusion matrix toughness ratio β (β≥1) were varied from 0.254-0.754 (jamming point) and 1.5-100.0, respectively. A total of 5000 uniaxial tensile tests up to failure were performed. We showed that the Halpin-Tsai model fits well all Young elastic moduli even for nearly in-contact particles. The stress distribution strongly depends on φ and β. As the highest stresses (at the origin of crack nucleation) occur between neighboring particles, we analyzed the average stress in gaps. We found that, regardless of the particle volume fraction, the yield stress is a power law of a grain-scaled stress concentration factor. We also investigated the probability of failure of the samples. We found that whatever φ and β, this probability follows a classical Weibull law. Finally, we showed that Weibull modulus, normalized by its value for infinitely rigid particles, is inversely proportional to a function of the stress concentration factor.

Failure mechanisms of equipment hatch area in prestressed concrete containment vessel

The failure mechanisms of the equipment hatch area under two load cases (LCs), i.e. in-plane shear/tension and tension/tension to consider the combined action of ground motion and internal pressure and the action of internal pressure only, respectively, were experimentally studied with three specimens for each LC.The results show that the failure of the LC1 specimens is due to the eccentric tension in the vertical direction. The shear force in the lateral direction changes the stress distribution in the specimensand thus influence the crack nucleation and propagation. The failure modes of the LC2 specimens depend on the magnitude of the lateral tension. With the increase of the maximum lateral tension, the failure modes vary in the sequence of the horizontal cracking of concrete at the bottom of the specimen, the critical diagonal cracks on the top of the specimen and the failure of the narrowest part of the specimen.

Continuum damage mechanics based computational framework for prediction of the lifetime and degradation of wind turbine coatings with defects

The repeated raindrop impact significantly decreases the life of wind turbine blades (WTB) coating. Several computational frameworks have been developed in the literature to understand the damage behaviour and to predict the safe life of WTB's coating under such conditions. Experimental findings show that coatings may contain voids which adversely affect the coating's life. However, the computational models of coating often ignore this effect. This paper develops a new framework based on Continuum Damage Mechanics (CDM) to predict the life of WTB’s coating with voids due to rain. To determine the fatigue life of WTB’s coating, (i) a stochastic rain field simulation model has been employed, which provides data on the raindrop size distribution and impact locations. (ii) The stresses due to the impact of these raindrops are computed using smoothed particle hydrodynamics. (iii) Thereafter, CDM is implemented to predict fatigue damage life. Since damage can be visualized as nucleation and propagation of pits, voids, and cracks, hence, the complete life of the wind turbine blade's coating can be predicted by CDM. The computational result of the proposed CDM framework has been verified with fatigue damage results available in the literature. This study establishes that the proposed CDM-based computational framework is a reliable tool to predict the rain-induced fatigue life of the blade's coating in the presence of flaws.

Microstructural characterisation of brittle fracture initiation sites in reactor pressure vessel steels

Neutron embrittlement of reactor pressure vessel (RPV) steels potentially limits the safe operational time of nuclear reactors. In tested RPV steel samples microcracks are known to originate from cleaved precipitates, inclusions or grain boundaries, which eventually lead to brittle fracture. In most cases, these precipitates are reported as carbides. Latest research indicates the critical fracture event to be the crossing of grain boundary instead of the particle–matrix interface by the microcrack. Very few works have performed detailed fractography, which revealed the size and type of the feature found in the crack nucleation centre, together with metallographic bulk investigations. Additionally, the effect of subsequent neutron irradiation on microcrack nucleation is unknown. In the present work, detailed fractography and metallography is performed on a RPV steel in both its unirradiated as well as neutron irradiated state. A particle in the centre of the initiation site has been identified in a majority of the cases, while no specific type of particles were involved in more than 1/3 of all samples. Those particles are either Mo-rich carbides or Al-rich inclusions. In comparison, the metallographic analysis of the bulk steel reveals Mo-rich and Mn-rich carbides. Mn-rich carbides constitute the majority of all carbides in the steel but are never found to be responsible for brittle fracture initiation. Only a small fraction of observable carbides is Mo-rich which are responsible for fracture. Thus, the present work demonstrates a discrepancy between particles found in brittle fracture initiation sites and particles that are directly observable in bulk steel. Some of the initiating particles are extremely rare in the bulk. Furthermore, it is revealed that the local fracture stress does not depend on the type or size of particle or grain involved at the initiation site. In conclusion, the fracture stress strongly depends on the type of the grain boundary, rather than on a stress based upon a Griffith criterion, which considers particle or grain size alone. The brittle fracture mechanism was found to be unaffected by neutron irradiation. These findings could help refine modelling of the critical brittle fracture stress and fracture toughness using microstructural parameters as input.

A dimensional analysis based multi-scale thermal damage framework of brittle materials at elevated temperatures

Research on macro-scale damage prediction and micro-scale damage mechanisms of brittle materials at elevated temperatures is extremelyimportantto the design and application of practical engineering structures. In this study, a multi-scale thermal damage framework is proposed for both describing macro-scale damage evolution and collective micro-scale cracks behavior of brittle materials atelevatedtemperatures. In the framework, the evolution equation of ideal micro-crack system is deduced to establish the relationship between the macro-scale damage and the micro-scale crack nucleation and growth based on dimensional analysis method. To support the multi-scale thermal damage framework, the multi-scale damage of the benchmark fracture test of the Brazilian disk at elevated temperatures is predicted and compared with the experimental results. The results support the effectiveness and ability of the multi-scale thermal damage framework, which can achieve thermal damage prediction of brittle materials in macro-scale as well as physical mechanisms description in micro-scale.

A robust interface finite element formulation for modeling brittle material failure problems

AbstractFailure of many brittle materials and structures can be modeled using interface‐oriented finite elements combined with intrinsic cohesive zone models. The discontinuous Galerkin (DG) finite element method provides an innovative framework for modeling brittle crack propagation with zero‐thickness interface elements, which can accommodate extrinsic cohesive laws to avoid the artificial compliance required in intrinsic cohesive models. However, robust formulations and implementations of DG methods are critical in alleviating the well‐known convergence issues for both crack nucleation and propagation with reduced instability. This paper presents a robust interface element formulation by modifying the incomplete interior penalty Galerkin (IIPG) method, which successfully avoids the initial element interface penetration across elements that occurs prior to crack nucleation, and thereby greatly reduces the instability issue as cracks open. We further verified and validated our implementation by using a bar tension test and a beam fracturing benchmark. The robustness of our proposed interface element method was demonstrated by a micromechanics fiber/matrix debonding problem with 64 fibers embedded in a bulk matrix.

High and low cycle fatigue properties of selective laser melted AISI 316L and AlSi10Mg

In the last years, additive manufacturing has widely adopted to enable lightweight design based on the topological optimization. In fact, this technology allows generation of lattice structures with complex geometries and small thicknesses. In this work, both the low-cycle-fatigue and high-cycle-fatigue behaviors of selective laser melted AISI 316L and AlSi10Mg were investigated. Fatigue samples were designed to characterize small parts and tested in the as-built condition since reticular structures are usually adopted without any finishing operation. Microstructural features were studied by light-optical microscopy and scanning-electron microscopy. Finally, fatigue failures were studied considering the fracture mechanics principles with the Kitagawa-Takahashi diagram. The analysis of fracture surfaces revealed that crack nucleation mainly occurs close to the surface because of both poor surface quality and presence of near-surface defects. As expected, because of the face-centered cubic lattice, the final rupture of all the investigated alloys was characterized by micro-dimples confirming the presence of a ductile behavior.

Micro-mechanisms underlying enhanced fatigue life of additively manufactured 316L stainless steel with a gradient heterogeneous microstructure

The fatigue life of additively manufactured 316L stainless steel (SS) in an aqueous corrosive medium is shown to improve markedly when the surfaces were processed by surface mechanical attrition treatment (SMAT). SMAT induced surface nano-crystallization owing to severe plastic deformation and yielded a gradient microstructure beneath the surface of additively manufactured SS 316L, which increases the resistance to fatigue crack initiation and propagation. During cyclic deformation, dislocations are generated and accumulated in the cell boundary, resulting in the evolution of persistent slip bands (PSBs) at the surface of the as-manufactured specimen. Continuous intrusions and extrusions of PSBs provide crack initiation sites due to strain localization at the surface of the as-manufactured specimen, whereas the crack initiation region moved from the surface to the sub-surface layer after SMAT. Mainly, the mutual crossing of shear bands or twin boundaries accommodates most of the plastic deformation and provides crack nucleation sites at subsurface regions in this case. To elucidate the fatigue failure mechanism associated with fatigue loading (interactions of stacking faults, slip bands, and deformation twins), electron back-scattered diffraction and transmission electron microscopy analysis of the fatigue-failed alloy after SMAT was performed at different distances adjacent to the fatigue-failed tip. The interfaces between dislocation forest and twin-twin boundaries hinder dislocation motion and disrupt stress concentration. In addition, amorphous bands were formed at the interfaces between twin and shear bands which co-deform with the matrix during dynamic loading and act as a natural sink for dislocations, delaying decohesion and commencement of fracture. The changes in the crack initiation site and fatigue micro-mechanism cause considerable changes in fatigue life. This work provides insight into the failure mechanisms of additively manufactured SS for designing surface modification techniques to enhance the fatigue life of the parts post-printing.

Crack‐like effectiveness of some discontinuities in AA2024

AbstractMaintaining aircraft airworthiness to ensure the fleet's safe operation and maintain its readiness is critically dependent on accurate modelling and reliable predictions of fatigue crack growth. In this process, a knowledge of the representative initial discontinuity sizes that cause fatigue crack nucleation and early growth in aircraft is essential. Here the effective pre‐crack size of aluminum alloy 2024, from samples of aircraft production material and tested under aircraft spectra, are considered.

Evolution of Fretting-Induced Cracks and Delamination Wear on Alloy 690 Steam Generator Tubes During Mixed Fretting Regime in Air at Room Temperature

The occurrence of fretting-induced cracks and delamination wear processes in a mixed fretting regime on Alloy 690 steam generator tubes against 304L stainless steel pads was analyzed. Fretting tests in 90° cross-cylinder configuration were performed in air at room temperature. Changes in the contact conditions were evaluated using the energy ratio and the sliding ratio criteria. Damage was characterized using light microscopy, scanning electron microscopy, and optical profilometry. Vickers microindentation was applied to characterize the initial plastic deformation process. It was found that during the initial 1 × 103 cycles, plastic deformation constitutes the main damage mechanism. Thereafter, between 1 × 103 and 1 × 104 cycles, cracks nucleation and propagation accompanied by negligible wear were detected. Beyond 1 × 104 cycles, the dominant main damage mechanism consists of delamination wear assisted by cracks coalescence, and a change from a U-shaped to a W-shaped scar profile was observed in correspondence with the appearance of the delamination wear process.

Mechanical behaviors and microstructure evolution of Ni[sbnd]W medium heavy alloy at various strain rates under uniaxial tension

In this study, a novel medium-heavy alloy (MHA) of 56Ni-38 W-5Co-1Ta was prepared using conventional casting and forging methods. This novel NiW alloy exhibits a unique combination of medium density, high strength and ductility under quasi-static loading conditions. In this study, the dynamic mechanical behaviors and deformation mechanisms of this novel NiW alloy were systematically investigated. The NiW alloy exhibited that yield strength increase form ∼1.6 GPa (1 × 10−3 s−1) to ∼2.0 GPa (3 × 103 s−1) owing to the formation and accumulation of nano-sized deformation twinning at dynamic loading condition. Although twin boundaries are attributed to their higher strength owing to the Hall-Petch effect, nano-sized cracks also prefer to nucleate at twin boundaries because of the strong interaction between dislocations and twins. This strong interaction introduces local stress concentration and crack nucleation at deformed zone and finally lead to the decreasing of uniform elongation form ∼0.31 (1 × 10−3 s−1) to ∼0.18 (1–3 × 103 s−1). The major deformation mechanism exhibited a clear transition from dislocation slip to deformation twinning in the NiW alloys under dynamic loading. Our results provide a comprehensive picture of how the deformation modes govern the mechanical behavior and failure of NiW MHA at high strain rates.

Four-dimensional microstructurally small fatigue crack growth in cyclically loaded nickel superalloy specimen

We nondestructively image a low-solvus high refractory (LSHR) nickel base specimen microstructure during cyclic loading to characterize crack propagation during the microstructurally small crack (MSC) growth regime. Micro-computed tomography (μCT) is used to characterize the material density and identify crack interfaces, while high-energy diffraction microscopy (HEDM) provides snapshots of the microstructural orientation field changes. From these measurements, data are computationally reconstructed and coregistered to describe the specimen’s configuration before load, before crack nucleation, and throughout the crack propagation/loading process. An MSC forms at a FIB-cut notch, which was previously placed to concentrate stress at the center of the specimen gauge, and propagates along a facet parallel to the local {111} crystallographic plane. Analysis of available crystallographic slip directions and measured point-to-point disorientation axes indicate probable single and coplanar slip activity along FCC octahedral planes within this region. Similar analyses of other crack propagation facets reveal generally slower growth along directions favoring zig-zag cross and codirectional cross slip, which are often disfavored at room temperature.

A phase field approach to model crack-interface interaction in ceramic matrix composites

Ceramic matrix composites are widely applied in coatings, engines, and space vehicles because of their superior thermo-mechanical properties. Various failure modes can be possible in ceramic matrix composites, notable ones are fiber breakage, matrix cracking and fiber matrix debonding. In order to predict the failure mechanisms at microstructural level (matrix-fiber system) of such composites, understanding crack nucleation and propagation across different phases, namely, fiber, and matrix is significant. To assess structural integrity, the material parameters that govern the crack growth should be determined. Nonlocal approaches consider the interactions between infinitesimal material volumes by considering a material length scale parameter. Phase field method is one of the popular nonlocal approach to model failure in cracked solids. In the present work, phase field approach is adopted to model the crack propagation through different phases of a ceramic matrix composite at microstructural level. The performance of the proposed formulation is illustrated through representative numerical examples. The model proposed is implemented in the framework of the finite element method. Crack propagations are studied by considering two ceramic matrix composites, namely, carbon fibers in carbon matrix (C/C) composite, and carbon fibers in silicon carbide (C/SiC) composite. For the case of C/SiC composite, parametric study is conducted by varying the fiber volume fraction.

In-Situ Study on the Tensile Deformation and Fracture Mechanism of a Bimodal-Structured Mg-Gd-Y Alloy.

The as-extruded (EX) Mg-Gd-Y alloy studied here exhibited a bimodal structure, composed of fine dynamic recrystallized (DRXed) grains with random orientations and longitudinal coarse hot-worked grains. The slip analysis showed the DRXed grains exhibited mainly basal slips, while the hot-worked grains exhibited mainly prismatic slips during the tensile deformation. The distribution of geometrically necessary dislocations (GNDs) showed that there was strain partitioning between the fine and coarse grain regions. The hetero-deformation induced (HDI) hardening occurred between the two domains. It improves the strength and strain hardening capability of the alloy, leading to good strength-ductility synergy. Microcracks tended to nucleate at the DRXed grain boundaries, as well as at the interface between the two domains. The calculation of geometric compatibility parameter (m') indicated that strain incompatibility between the adjacent grains induced the crack nucleation. The toughening effect of the fine DRXed grains hindered the crack propagation. However, the major crack formed at the interface between the two domains propagated unstably, due to the high stress concentration and the large crack size, causing the final failure.

The cohesive zone crack analogue for incomplete contacts under mild wear conditions

Fretting fatigue may appear in mechanical components that are in contact under vibrational loading, inducing oscillatory frictional stresses, often combined with alternating bulk stresses. Fretting fatigue cracking is important, with its initiation being difficult to estimate. This work extends a well-known fretting fatigue model, the crack analogue model that examines fretting fatigue induced by incomplete contacts of metallic surfaces. This is done by inserting a mode II type cohesive zone at the contact edges. In our previous work on fretting fatigue of complete contacts, we proposed mixed mode I and II cohesive zones because of the nature of the stress fields around the contact edges. The proposed cohesive zones address several issues related to the mechanics of friction and wear, by combining them in the case of mild wear where asperity plastic shakedown is the dominant inelastic mechanism. Thus, the micromechanical behaviour of the surface topology and its evolution are naturally introduced into the analysis. The surface roughness becomes an internal variable that evolves with the cyclic loading, establishing a steady state friction coefficient. Alternatively, friction evolution can be established pointwise by monitoring the accumulated micro-slip. The work of friction dissipates the mechanical work and at the same time becomes the precursor of large scale wear. A predictive methodology for fretting crack nucleation is proposed through the fatigue threshold stress intensity factor used in ordinary fatigue.

Hydrogen embrittlement in a metastable high Mn TWIP-assisted steel: Correlation between grain size and hydrogen-enhanced ε-martensite

The correlation between hydrogen-enhanced deformation-induced ε-martensite and hydrogen embrittlement at two different grain sizes has been investigated in a metastable high Mn steel. The variation in the fraction of ε-martensite was detected to be 34% for coarse grain (CG) and 10% in (FG) after hydrogen charging. The significant difference in ε-martensite fraction between CG and FG was attributed to a higher concentration of hydrogen per unit area (CHgb) of high-angle boundaries (θ > 15°) in CG compared with FG one, which caused a local decrease of stacking fault energy (SFE) at the vicinity of these boundaries in favor of martensitic transformation. Intergranular cracks were identified as the primary form of hydrogen damages, occurring more frequently than transgranular features in both alloys. The drastic hydrogen embrittlement in CG was attributed firstly to higher hydrogen concentration per grain boundary unit area and secondly to the more severe hydrogen cracking in CG than FG resulting from explosive hydrogen-enhanced martensite formation. In the FG , deformation twins and single-variant ε-martensite were the primary mechanisms triggering intergranular crack nucleation. However, they played a dual role in crack propagation, either arresting or facilitating crack growth. They were capable of arresting the crack if suitably aligned with the direction of crack propagation and the tensile axis. Conversely, in CG structure, the intense impingement of multiple-variant ε-martensite grains with each other and with grain boundaries can create severe microstructural stress concentration zones, promoting severe hydrogen-induced cracking.

Intrinsic Fatigue Limit and the Minimum Fatigue Crack Growth Threshold.

In the field of long-life fatigue, predicting fatigue lives and limits for mechanical components is crucial for ensuring reliability and safety. Fracture mechanics tools have enabled the estimation of fatigue lives for components with small cracks or defects. However, when dealing with defects larger than the microstructural characteristic size, estimating the fatigue resistance of a material requires determining the cyclic resistance curve for the defect-free matrix, which depends on knowledge of the material's intrinsic fatigue limit. This study focuses on the experimental evidence regarding the intrinsic fatigue limit and its correlation with naturally nucleated non-propagating cracks. Fracture mechanics models for small crack propagation are introduced, and their disparities and limitations are analyzed. The concept of intrinsic fatigue limit is then introduced and applied to reanalyze a recent publication. Methods for estimating the intrinsic fatigue limit are explored and applied to experimental results reported in the literature. The need to clarify and accurately predict the intrinsic fatigue limit is highlighted in alloys where the processing generates defects larger than the microstructural size of the matrix, as often observed in materials and components produced using additive manufacturing.