Involving Crack Initiation Research Articles

Crack phase‐field enhanced finite cover method for dynamic fracture at finite strain

SummaryThis study presents an enhancement of the diffusive‐discrete crack transition scheme (10.1002/nme.7169) to describe dynamic fracture at finite strain. In the enhanced scheme, the crack initiation, propagation, and bifurcation processes are determined from an energy minimization problem based on crack phase‐field theory, and the predicted diffusive crack is replaced by the discrete representation using the finite cover method. In the meantime, numerical damping is introduced to maintain computational stability and avoid distortion of the physical mesh in the finite cover context. By taking advantage of the features of the diffusive‐discrete crack transition scheme, the proposed approach enables us to stably simulate a series of dynamic fracture events involving crack initiation at an arbitrary location, propagation, and bifurcation in arbitrary directions, arbitrary divisions of an original object into multiple portions, and independent motions of divided portions. After spatial and temporal discretizations by the finite cover method and the Newmark method are described, as well as the simulation algorithm of the enhanced finite cover‐based staggered iterative procedure for dynamic fracture, several representative numerical examples are presented to demonstrate the performance and capabilities of the developed approach.

An enhanced adaptive coupling strategy of peridynamics and finite element method via variable horizon approach for simulating quasi-static fracture problems

An enhanced adaptive coupling method of peridynamic (PD) theory and the finite element method (FEM) is performed that combines the advantages of both approaches and can be used to simulate quasi-static fracture problems. In the proposed model, PD is used to simulate crack initiation and propagation, whereas the FEM is used to simulate domains without damage to improve efficiency. The influence of ghost forces is reduced by introducing a transition subregion with a variable horizon, thereby significantly improving the accuracy of the model, which is verified by application to a plane stress problem. The conventional coupling model requires pre-partitioning of the solution domain, which is difficult to achieve when modeling certain problems, such as the initiation of cracks at unknown locations. Hence, the adaptive conversion criterion is introduced to ensure that subregions automatically evolve as cracks grow, thereby obviating the need for prior knowledge of crack propagation paths. The proposed model is applied to three standard laboratory tests of quasi-static fracture and its performance is validated by the good agreement of its results with reference solutions or experimental observations. The model accurately simulates complex fracture problems involving crack initiation, irregular crack propagation, and crack coalescence.

Ductile fracture simulation using phase field method with various damage models based on different degradation and geometric crack functions

For simulation of ductile fracture, plasticity and damage are two essential aspects. The phase field method emerged as an efficient mathematical tool to address the fracture processes involving crack initiation, merging, and branching. From the wide literature, it has been observed that the information on the suitability of the existing phase field models for simulation of ductile fracture is scanty. This paper proposes a phase field methodologies for simulation of ductile fracture considering the aspects like different degradation and crack geometric functions. The proposed formulation couples the damage model, constitutive behaviour of elasto-plastic solid and J2 plasticity. Numerical simulations are carried out using ABAQUS with user-defined element (UEL) subroutine codes, defining the displacement field and phase field variable. Several benchmark problems were analysed to investigate the (i) behaviour of the specimen (ii) the performance of various phase field damage models (PFDM) and (iii) the effect of non-dimensional parameters considered in the damage models. The maximum percentage difference between the numerically predicted maximum load and its corresponding displacement is in good agreement w.r.t experimental value under PFDM4 (±10% range). The output of the study provides an insight on the use of various damage models and other parameters for the simulation of ductile crack propagation. This proposed model can be further extended to the prediction of remaining life or residual strength of the structural component.

Overview of Stage 1b Stress Corrosion Crack Initiation and Growth of Pipeline Steels

Stress corrosion cracking (SCC) can cause catastrophic failure of buried pipelines for oil and gas transmission. The life cycle of pipeline steels experiencing SCC consists of five stages: incubation stage, stage 1a (crack initiation), stage 1b (early-stage crack growth), stage 2 (sustainable crack growth caused by mechanical driving force), and stage 3 (rapid crack propagation to rupture). Stage 1b encompasses a large portion of the pipeline’s lifespan, which is of great significance to pipeline integrity management aimed at service life extension. However, this stage is less studied so far. This invited paper provides a brief review of the recent progress on stage 1b stress corrosion crack initiation and growth for buried pipeline steels. Emphasis is placed on the effects of loading conditions and their interactions on stage 1b growth of high pH SCC, while some progress of near-neutral pH SCC is included for the purpose of comparison. It first introduces SCC in pipeline steels which is followed by a definition of stage 1b and its significance in terms of the service life of pipeline steels. Then the most recent advancements in understanding early-stage crack growth in stage 1b are reviewed and discussed. In summary, stage 1b growth can be self-induced by existing cracks (the so-called mother-daughter analogy), involving crack initiation in the plastic zone ahead of the surface tip of a surface crack, which is quite different from the stochastic process of coalescence of randomly formed individual cracks. Stage 1b growth extends crack length and increases the stress intensity factor at the depth tip without a physical increase in crack depth, serving as a bridge to stage 2. Further, the need for future research on stage 1b SCC initiation and growth of pipeline steels is discussed.

Effect of track curvature on the microstructure evolution and cracking in the longitudinal section of lower gauge corner flow lips formed in rails

The microstructure of the flow lips formed at the lower corner of gauge face in the longitudinal section of worn high rails serving in curved tracks has been investigated. The radii of the curved tracks are 1500 m (S1, sharper curve) and 4000 m (S2, milder curve). Sharper curves result in a higher angle of attack (AOA) between rail-wheel thus leading to higher lateral contact forces as well as tangential frictional forces thus facilitating plastic flow. Such conditions favour formation of flow lips where rail material flows from the rail upper gauge face to the lower corner of the gauge face. A combination of optical microscopy (OM), scanning electron microscopy (SEM), electron backscattered diffraction (EBSD) and nano-indentation hardness measurements have been used for the characterization of the flow lip. It is observed that the outermost region of the flow lip consists of a uniformly present white etching layer (WEL) followed by an intermittently present brown etching layer (BEL) where the WEL and BEL thickness is less for milder curves. The WEL has the highest hardness and consists of fine grains of ferrite and particles/fine fragments of cementite. The BEL is relatively softer than WEL and has a similar appearance to WEL, but patches of lamellar structure appear with increasing depth from the outer edge. Beyond the BEL region, layers of deformed pearlitic structure are observed, and a more intact pearlitic structure is observed at a much lower depth for the milder curve than the sharper curve. For both the curvatures at a given depth, the hardness of pearlite bears a Hall-Petch type of relationship to the pearlitic interlamellar spacing. However, the alignment of the deformed microstructure is heavily dependent on the curvature. It has been found to align almost parallel (4°–10°) to the rail longitudinal axis for the milder curvature and at around 21°–35° for the sharper curvature. Cracks originate from the brittle WEL region due to contact fatigue whereas crack propagation is driven by bending stresses. Cracks have been found to move parallel to the alignment of the deformed pearlite along longitudinal direction for the milder curvature. Alignment of pearlite also motivates the crack propagation trajectory for the sharper curvature and hence the crack moves at an angle between 21° and 35° with the longitudinal direction but becomes almost perpendicular after a distance. Shallow cracks travelling parallel to the rail outer edge in S2 can result in spalling of the rail material leading to wear, whereas for sharper curves, cracks run deeper into the railhead. Thus, the tendency for rail failure through 'Reverse Transverse Fracture' – which involves crack initiation at the lower gauge corner and propagation into the railhead – increases with the sharpness of the rail curvature.

Fatigue life estimation of continuous girder bridges based on the sequence of loading

A need exists to determine the fatigue life of multi-span continuous bridges in the design stage. It is difficult to conduct a full-scale fatigue test of a bridge, hence the simulation of bridge-vehicle interaction dynamics is important to estimate the fatigue life of bridges. The vehicles entering the bridge are random in nature. In the present study, the arrival time of the vehicles is considered a random variable following Poisson process to simulate the actual traffic. The bridge-vehicle coupled system equations have been derived wherein the vehicle arrival rate appears as random variable casting difficulty in obtaining a direct solution. The solution approach has been devised using Orthogonal Polynomial Expansion method. Response statistics so obtained for a multi-span continuous bridge has been used in fatigue life estimation involving crack initiation phase and crack propagation phase modifying conventional linear damage rule. The sequence of loading is also considered in the modified fatigue formulation. The effect of the vehicle speed, road surface irregularity and the arrival rate of the vehicle on fatigue life estimation of the bridge have been studied.

Fatigue behaviour of laser spot welds in dual phase 780 steel

High cycle fatigue performance was evaluated on circular shaped laser spot welds (LSW) of dual phase DP 780 steels. Fibre laser with two different parameter sets were applied to produce the spot welds. The weld size growth is concomitant to laser power. The failure mechanism under fatigue loading, involving crack initiation and propagation till failure, is explained using analytical stress models and experimental data. Interrupted fatigue tests were done and the crack path was captured by observing under scanning electron microscope. Stress models show that during tensile shear loading of overlapping sheets having spot weld, there is a countering effect of shear stress and bending stress; the latter acts perpendicular to the shear stress and arises from the bending moment along the plane of contact during load transfer. The dominant stress depends on the contact area, i.e. the weld size, which largely controls the crack path route and concurrent fatigue life. Incidentally smaller welds show marginally longer life wherein the stronger axial stress component propels the crack through a longer route consuming more number of cycles. Again, with lowering of fatigue load there is a shift in the mode of failure with transition from interfacial to partial to pull-out failure. However, large welds fail in pull-out mode only irrespective of the fatigue load levels. As compared to the size effect, the weld microstructure has less influence on fatigue crack propagation.

A Comparative Study of Dynamic Fracture of Soda-Lime Glass Using Photoelasticity, Digital Image Correlation and Digital Gradient Sensing Techniques

The dynamic fracture of high-stiffness and low-toughness materials such as soda-lime glass (SLG) typically involves crack initiation and growth prior to branching, underlying mechanics of which is not yet fully understood. Investigation of this issue using full-field optical techniques face numerous spatio-temporal challenges since crack speeds in these materials reach 1500 m/s or more and are accompanied by highly localized deformations. However, often it is tacitly assumed that most optical methods are equally capable of studying this challenging problem and it turns out not to be true. To this end, three prevalent optical techniques - transmission photoelasticity, 2D Digital Image Correlation (DIC) and transmission Digital Gradient Sensing (DGS) - are implemented concurrently to visualize crack-tip fields and quantify fracture characteristics associated with crack initiation, crack growth and macroscopic crack bifurcation in SLG plates subjected to nominally identical loading in three separate experiments. Each method is implemented in conjunction with ultrahigh-speed (1 Mfps) photography, flash/pulse illumination, and a modified-Hopkinson pressure bar for impact loading of specimens. The feasibility of measuring fracture parameters and imposed force histories along with the pros and cons of each approach for this material system are examined.

Topology optimization for maximizing the fracture resistance of quasi-brittle composites

In this paper, we propose a numerical framework for optimizing the fracture resistance of quasi-brittle composites through a modification of the topology of the inclusion phase. The phase field method to fracturing is adopted within a regularized description of discontinuities, allowing to take into account cracking in regular meshes, which is highly advantageous for topology optimization purpose. Extended bi-directional evolutionary structural optimization (BESO) method is employed and formulated to find the optimal distribution of inclusion phase, given a target volume fraction of inclusion and seeking a maximal fracture resistance. A computationally efficient adjoint sensitivity formulation is derived to account for the whole fracturing process, involving crack initiation, propagation and complete failure of the specimen. The effectiveness of developed framework is illustrated through a series of 2D and 3D benchmark tests.

Very High Cycle Fatigue Failure Analysis and Life Prediction of Cr-Ni-W Gear Steel Based on Crack Initiation and Growth Behaviors.

The unexpected failures of structural materials in very high cycle fatigue (VHCF) regime have been a critical issue in modern engineering design. In this study, the VHCF property of a Cr-Ni-W gear steel was experimentally investigated under axial loading with the stress ratio of R = −1, and a life prediction model associated with crack initiation and growth behaviors was proposed. Results show that the Cr-Ni-W gear steel exhibits the constantly decreasing S-N property without traditional fatigue limit, and the fatigue strength corresponding to 109 cycles is around 485 MPa. The inclusion-fine granular area (FGA)-fisheye induced failure becomes the main failure mechanism in the VHCF regime, and the local stress around the inclusion play a key role. By using the finite element analysis of representative volume element, the local stress tends to increase with the increase of elastic modulus difference between inclusion and matrix. The predicted crack initiation life occupies the majority of total fatigue life, while the predicted crack growth life is only accounts for a tiny fraction. In view of the good agreement between the predicted and experimental results, the proposed VHCF life prediction model involving crack initiation and growth can be acceptable for inclusion-FGA-fisheye induced failure.

Degradation of nanostructured bainitic steel under rolling contact fatigue

Abstract The consequences of rolling contact fatigue on a carbide-free nanostructured bainitic steel intended for bearing applications are presented for the first time. Tests performed at various intervals followed by mechanical, microscopical, and crystallographic characterization lead to the conclusion that the degradation mechanism is ductile void formation at interfaces, followed by growth and coalescence into larger voids that lead to fracture along the direction of the softer phase. This is different from the conventional damage mechanism that involves crack initiation at inclusions and propagation, for example in typical bearings steels such as 52100. The huge density of interfaces in the nanostructure allows the formation of a large dispersion of voids, and ultimately cracks, at depths consistent with the maximum orthogonal shear stress below the contact surface. This study should prove useful for the eventual usage of nanostructured bainitic steels in rolling bearings.

On the interfacial fracture of porcelain/zirconia and graded zirconia dental structures

Porcelain fused to zirconia (PFZ) restorations are widely used in prosthetic dentistry. However, their susceptibility to fracture remains a practical problem. The failure of PFZ prostheses often involves crack initiation and growth in the porcelain, which may be followed by fracture along the porcelain/zirconia (P/Z) interface. In this work, we characterized the process of fracture in two PFZ systems, as well as a newly developed graded glass-zirconia structure with emphases placed on resistance to interfacial cracking. Thin porcelain layers were fused onto Y-TZP plates with or without the presence of a glass binder. The specimens were loaded in a four-point-bending fixture with the thin porcelain veneer in tension, simulating the lower portion of the connectors and marginal areas of a fixed dental prosthesis (FDP) during occlusal loading. The evolution of damage was observed by a video camera. The fracture was characterized by unstable growth of cracks perpendicular to the P/Z interface (channel cracks) in the porcelain layer, which was followed by stable cracking along the P/Z interface. The interfacial fracture energy GC was determined by a finite-element analysis taking into account stress-shielding effects due to the presence of adjacent channel cracks. The resulting GC was considerably less than commonly reported values for similar systems. Fracture in the graded Y-TZP samples occurred via a single channel crack at a much greater stress than for PFZ. No delamination between the residual glass layer and graded zirconia occurred in any of the tests. Combined with its enhanced resistance to edge chipping and good esthetic quality, graded Y-TZP emerges as a viable material concept for dental restorations.

Electro-Mechanical Impedance (EMI)-Based Incipient Crack Monitoring and Critical Crack Identification of Beam Structures

Fatigue-induced damage is often progressive and gradual in nature. Fatigue is often deteriorated by corrosion in ageing structures, creating maintenance problems, and even causing catastrophic failure. This ushers the development of structural health monitoring (SHM) and nondestructive evaluation (NDE) systems. Recent advent of smart materials applicable in SHM alleviates the shortcomings of the conventional techniques. Autonomous, real-time, remote monitoring becomes possible with the use of smart piezoelectric transducers. For instance, the electro-mechanical impedance (EMI) technique, employing piezoelectric transducers as collocated actuators and sensors, is known for its ability in damage detection and characterization. This article presents a series of lab-scale experimental tests and analysis to investigate the feasibility of fatigue crack detection and characterization employing the EMI technique. This study extends the work by Lim and Soh [1] to incorporate the phases involving crack initiation and critical crack. It is suggested that the EMI technique is effective in characterizing fatigue induced cracking, even in its incipient stage. Micro-crack invisible to the naked eyes can be detected by the technique especially when employing the higher frequency range of 100–200 kHz. A quick and handy qualitative-based critical crack identification method is also suggested by visually inspecting the admittance frequency spectrum.

Coupled Fatigue Crack Initiation and Propagation Model Utilizing a Single Blunt Notch Compact Tension Specimen

Many power generation facilities equipped with turbomachinery are designed to provide electric energy on an as-needed basis and, as a consequence, impart a mixture of fatigue and creep damage to high-value components at elevated temperatures. Cracks are often initiated on free surfaces of these parts near stress-raising features and propagate under thermal-mechanical cycling until the component is removed from service. Whether the emphasis is on creep or fatigue failure, most conventional structural life prediction approaches decouple crack initiation from crack propagation. Turbine designers are in need of approaches that span the full life cycle of components in which both initiation and propagation are the consequences of a variety of mechanical failure modes. Although recent fracture mechanics methods have been developed to account for fatigue- and creep-crack growth, a tacit assumption is that a precrack exists. Another main limitation of these approaches is the small scale yielding assumption, associated with linear elastic fracture mechanics, in which extensive plasticity invalidates such analyses. In this study, utilizing a blunt notch compact tensile specimen, experimental routines involving crack initiation and propagation within a single specimen at elevated temperatures with plastic-inducing loads and hold periods were conducted. Founded on existing elastic and elastic-plastic fracture mechanics (EPFM), a coupled crack initiation and propagation model is presented. Through the use of the EPFM parameter J, the proposed models are observed to accurately predict crack initiation and replicate crack propagation rates based on the imposed experimental conditions. The model is demonstrated on an austenitic stainless steel, type 304, subjected to moderate temperatures in air. Mechanical testing, metallurgical analysis, and analytical modeling allow for a simplified phenomenological life prediction model capable of predicting crack initiation and propagation at elevated temperatures. Consequently, structural analysis of critical locations of components can span the gamut of crack initiation, crack growth, and instability (i.e., total life assessment).

Determination of atomistic J-integral of graphene sheet using the molecular dynamics method

Over the past decade, mechanical characterization data for nanoparticle-reinforced polymer matrix composites have shown significant improvements in compressive strength and interlaminar shear strength, in comparison with baseline properties. While the synergistic reinforcing influence of nanoparticle reinforcement is obvious, a simple rule-of-mixtures approach fails to quantify the dramatic increase in mechanical properties. Consequently, there is an immediate need to investigate and understand the mechanisms at the nanoscale that are responsible for such unprecedented strength enhancements. A multi-scale and multi-physics simulation approach is considered computationally more viable since relying on a single time or length scale may require huge amounts of computational resources and can potentially lead to inaccurate results. A proof-of-concept case study involving crack initiation in a graphene nanoplatelet is presented, together with a methodology for computing the atomistic J-integral based on Hardy estimates of continuum fields. The same methodology will be used to gain a better understanding of the influence of nanoscale phenomena on continuum-scale mechanical properties of a polymer nanocomposite. It is envisioned that the current research will contribute towards the understanding of advanced nanostructured composite materials within the context of integrated computational materials engineering.

Three-dimensional numerical simulation and cracking analysis of fiber-reinforced cement-based composites

Three-dimensional graphic objects created by MATLAB are exported to the AUTOCAD program through the MATLAB handle functions. The imported SAT format files are used to produce the finite element mesh for MSC.PATRAN. Based on the Monte-Carlo random sample principle, the material heterogeneity of cement composites with randomly distributed fibers is described by the WEIBULL distribution function. In this paper, a concept called "soft region" including micro-defects, micro-voids, etc. is put forward for the simulation of crack propagation in fiber-reinforced cement composites. The performance of the numerical model is demonstrated by several examples involving crack initiation and growth in the composites under three-dimensional stress conditions: tensile loading; compressive loading and crack growth along a bimaterial interface.

Roles of microstructure in fatigue crack initiation

Fatigue failure in the high-cycle and ultrahigh-cycle regimes is often dominated by the crack initiation processes, which are strongly influenced by the salient features and defects in the microstructure. Competing fatigue mechanisms involving crack initiation at persistent slipbands, grain boundaries, pores, and non-metallic inclusions or particles, have been reported to occur at surface sites in the high-cycle fatigue regime (10 6–10 7 cycles), but shift to interior sites in the ultrahigh-cycle fatigue regime (10 9–10 10 cycles). The changes in fatigue mechanism and crack initiation site result in large variations in fatigue life. This overview article examines the roles of microstructural features such as grain size, texture, porosity, non-metallic inclusion in the fatigue crack initiation process and the manners by which these microstructural effects affect the shape of the stress–life curves.

Abrasive wear of Al 2O 3–SiC and Al 2O 3–(SiC)–C composites with micrometer- and submicrometer-sized alumina matrix grains

The response of Al 2O 3, Al 2O 3–SiC–(C) and Al 2O 3–C nanocomposites to grinding was investigated in terms of changes of quality of ground surfaces and of the weight losses with time. The study used monolithic polycrystalline aluminas as references, and alumina-based composites with nanosized SiC and C inclusions and with alumina matrix grain size varying from submicrometer to approximately 4 μm. The studied materials can be roughly divided into two groups. Materials with submicrometer alumina matrix grains (Group 1) wear predominantly by plastic deformation and grooving. Coarse-grained materials (Group 2) wear by mixed wear mechanism involving crack initiation and interlinking accompanied by grain pull-out, plastic deformation and grooving. The wear rate of composites increases with increasing volume fraction of SiC. The Group 2 materials wear much faster then those with submicron microstructure. In all cases (with one exception) the wear resistance of composites was higher than that of pure aluminas of comparable grain sizes used as reference materials.

Fracture initiation revealed by variations in the fatigue fracture morphologies of PA 66 and PET fibers

The tensile and fatigue fracture morphologies of polyamide 66 (PA 66) and polystyrene (PET) fibers are well known [1]. Tensile, and also creep, failure in both fibers is similar and generally involves crack initiation at or near the fiber surface, followed by slow crack propagation, as shown in Fig. 1 [2]. Tensile failure occurs when the remaining cross section can no longer support the induced stress and rapid failure occurs, giving the type of failure morphology shown in Fig. 2. Crack propagation under conditions which induce fatigue in these fibers is markedly different from tensile failure. In both fibers, crack initiation is, usually, as in monotonic tension, at or near the surface. However, under fatigue conditions the crack propagation is deviated so as to run at a slight angle to the fiber axis, gradually reducing the load bearing cross section [3]. Complementary broken ends of a PA 66 fiber broken in fatigue are shown in Fig. 3. It can be seen from Fig. 3 that the one broken end consists of a long tongue of material, the free end of which is the point of crack initiation. It can be noted that the tongue is always curved inwards towards the fiber axis, suggesting a residual compressive stress in the surface of the formally intact fiber. A closer inspection of the tongue shows that the fatigue fracture surface is concave, with respect to the fiber surface and not convex as would be expected if a pealing mechanism was driving crack propagation [4]. The complimentary end reveals the reduction of the load bearing section and both areas of final failure show that the final stage of fracture is by the tensile process shown above. Fatigue failure in PET fibers occurs under similar cyclic conditions to those which produce fatigue failure in PA 66, but the angle of crack penetration is smaller so that longer tongues are generally seen and final failure occurs often behind the fatigue crack tip by a creep process. In both tensile and fatigue failure the process of crack initiation is poorly understood, though some fracture morphologies seem to indicate the role of a thin surface layer on some fibers or the presence of an irregularity at the point of initiation. The present study has identified several unusual fracture morphologies, which have been induced under conditions which were known to provoke fatigue failure. The slower crack propagation which occurs during the fatigue process has allowed the causes of the initiation of some cracks to be determined. It is thought that these observations may be of relevance in the understanding of crack initiation in both tensile and fatigue failure. Figure 1 Slow crack growth from the surface of a PA 66 fiber under monotonic tensile loading.

Effect of Fe-content on fatigue crack initiation and propagation in a cast aluminum–silicon alloy (A356–T6)

The effect of Fe-content on the fatigue damage evolution in a cast A356–T6 alloy was investigated both experimentally and through microscale finite element simulations. High cycle fatigue tests indicated that iron content has little influence on the fatigue life in the short lifetime regime (<10 5 cycles) but it significantly reduces the fatigue life in the long lifetime regime (>10 6 cycles). At high applied stress levels in the short lifetime regime, fatigue life is dominated by the crack propagation stage. The large plate-like Fe-rich intermetallic particles in high Fe-content castings were observed metallographically to retard the growth of small cracks through crack branching and meandering. For the long lifetime regime, the crack initiation stage is important. Fracture surface examination and finite element analysis revealed that in the absence of other defects such as porosity or oxide films, the large plate-like Fe-rich intermetallic particles in high Fe-content castings promote crack initiation by raising the stress-strain concentration in the eutectic region. Based on experimental observations and finite element analysis, a microstructure-based model was developed involving crack initiation and propagation, which allows quantitative assessment of the influence of Fe-content on the fatigue life. Good agreement was obtained between the model and experimental results.