Crack Front Propagation Research Articles

A new approach for fracture process zone evaluation

The study presents a novel method for identifying and monitoring the fracture process zone and its impact on cracking parameters, such as damage rate and fracture energy. Concrete samples subjected to a Wedge Splitting Test were investigated. Digital Image Correlation, a full-field measurement technique, was utilized to measure the experimental displacement fields at various scales. The experimental measurements, optimized through a Newton-Raphson iterative adjustment procedure, revealed the presence of a damaged zone accompanying the cracking process. This analysis also enabled the estimation of the material damage rate and provided a more realistic assessment of cracking parameters by integrating the entire process of damage and macro-cracking into the calculation of fracture energy. The results suggest that the appearance of a fracture process zone correlates with a reduction in the material’s hardness downstream of the crack propagation front.

Mixed mode fracture of geometrically similar FRUHPC notched beams with the localizing gradient damage model

A localizing gradient damage model is proposed in this paper to capture the mechanisms underlying the fracture of fiber reinforced ultra-high performance concrete (FRUHPC): (i) an initially expanding damage process zone due to the formation of numerous fine cracks, each widening up slowly due to the fiber bridging effect; (ii) a gradual formation of a localized macroscopic crack, when at least one of the fine cracks has opened up sufficiently to trigger a fiber pull-out process. Restricting to tensile-shear dominated failures in monotonic loadings, the simplest form of damage model is adopted, where an isotropic damage variable is driven by a strain-like variable. The performance of the proposed localizing gradient damage model is first demonstrated by comparing the damage evolution process against the corresponding intensity of acoustic emission (AE) events obtained experimentally, for a notched FRUHPC beam in three-point bending. It was shown that the model is able to reproduce the slightly widening fracture process zone (FPZ) during strain hardening, as well as the eventual localized damage process zone during strain softening. Specifically, during strain hardening, the proposed localizing gradient damage model predicts an energy dissipation bandwidth that compares well with the AE energy maps, together with a consistent propagation of crack front. With a correct description of the underlying damage mechanisms, the predictive capability of the proposed model is next demonstrated through the mixed mode fracture of a series of geometrically similar FRUHPC notched beams. Since the specimens are of the same casting batch as those in the three-point bending test, the numerical material parameters calibrated earlier are adopted directly for the mixed mode fracture tests. Without any further undue calibrations, the localizing gradient damage model is shown to predict well the structure responses and size effect of the series of geometrically similar FRUHPC notched beams in mixed mode fracture.

Experimental and analytical investigation for fatigue crack growth characteristics of an aero-engine fan disc

Crack growth evaluation should be performed to certify that the fan disc is capable of maintaining adequate integrity in presence of cracks. The spin test was carried out using the pre-flawed fan disc to obtain a more intensive insight of crack growth characteristic in the bore area. The variation of the surface crack length was measured by the replication method, and then the crack surface fractography was observed with scanning electron microscope (SEM). Both 3D numerical simulation and rectangular plate model were utilized to predict growth behavior of this crack. The crack surface fractography revealed a typical striated transgranular fatigue fracture characteristic. The comparison of the spin test result and the predicted crack growth showed that the numerical and theoretical analysis provided a good prediction for crack growth behavior for the fan disc. Taking into account the effect of plasticity-induced crack closure, the crack growth disparity at the disk surface and interior was analyzed and as a result, the shape of crack propagation front can be described more realistically.

Universal Scaling of the Velocity Field in Crack Front Propagation.

The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are, however, difficult to characterize in experiments at a finite drive. Here, we show that the correlation functions of the velocity field along the front allow us to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient, and can be extended to all systems displaying avalanche dynamics.

Assessment of the Impact Resistance of a Composite Material with EN AW-7075 Matrix Reinforced with α-Al2O3 Particles Using a 7.62 × 39 mm Projectile.

The paper presents the results of studies on the effects of shooting composite materials produced by pressure infiltration with the EN AW-7075 alloy as a matrix and reinforcement in the form of preforms made of α-Al2O3 particles. Composite materials were made with two reinforcement contents (i.e., 30% and 40% vol. of α-Al2O3 particles). The composites produced in the form of 12 mm thick plates were subjected to impact loads from a 7.62 × 39 FMJ M43 projectile fired from a Kalashnikov. The samples of composites with different contents of strengthening particles were subjected to detailed microscopic examination to determine the mechanism of destruction. The effect of a projectile impact on the microstructure of the material within the perforation holes was identified. There were radial cracks found around the puncture holes and brittle fragmentation of the front surfaces of the specimens. The change in the volume of the reinforcement significantly affected the inlet, puncture and outlet diameters. The observations confirmed that brittle cracking dominated the destruction mechanism and the crack propagation front ran mainly in the matrix material and along the boundaries of the α-Al2O3 particles. In turn, numerical tests were conducted to describe the physical phenomena occurring due to the erosion of a projectile hitting a composite casing. They were performed with the use of the ABAQUS program. Based on constitutive models, the material constants developed from the identification of material properties were modelled and the finite element was generated from homogenization in the form of a representative volume element (RVE). The results of microscopic investigations of the destruction mechanism and numerical investigations were combined. The conducted tests and analyses shed light on the application possibilities of aluminium composites reinforced with Al2O3 particles in the construction of add-on-armour protective structures.

Critical assessment of the fatigue crack growth rate sensitivity to material microstructure in ferrite-pearlite steels in air and marine environment

This paper presents a critical assessment of the effect of microstructure on the fatigue crack growth rate (FCGR) in ferrite-pearlite (α-P) steels in air and marine environment. This was done by evaluating the resistance of three subgrades of S355 steel, produced by normalized-rolling, NR (S355J2+N) and thermo-mechanical control process, TMCP (S355G8+M and S355G10 + M), to fatigue crack growth (FCG) in air and seawater. The data from the tests were then compared with results of several studies on α-P steels of similar compositions and microconstituents in the literature. It was found that microstructure strongly affected the Paris region of the da/dN vs. ΔK sigmoidal curve in both media. This is contrary to the current belief that microstructure has little or a negligible effect in the linear region of the FCGR curve in air. TMCP and quenched-and-tempered (QT) steels offered better resistance to FCG than NR steel in both media. TMCP steel offered the highest resistance to FCG. The crack path was non-planar with a complex crack front. The tendency for crack deviation, branching, wedging action by metal crumbs and perhaps interlocking majorly explained why the FCGRs of the TMCP and QT steels are lower than that of NR. The result also suggests that ductility and yield stress do not have a strong retarding effect on FCG in α-P steels at low stress intensity factor range (SIFR). This finding has a fundamental implication for analytical and numerical models that wholly depend on the mechanical properties of the steel and assumes plane horizontal crack propagation front in predicting FCGR in steels. Such models are likely to fail in predicting FCGR even in a subgrade of the same grade of steel.

Solitary pulse wave radiated by crack propagation as shock wave

The author proposed the criterion of micro-crack nucleation, which was deduced theoretically from shock wave theory, and derived the micro-crack evolution equation (Kobayashi, 2012). In the previous paper (Kobayashi, 2017a, 2017b), the crack opening criterion was deduced from the proposed micro-crack evolution equation. The dynamics of crack-front propagation in heterogeneous media was theoretically studied and the crack-front stability conditions was discussed based on the fluctuation of crack fronts induced by small heterogeneities (asperities) in fracture energy; the existence of a propagating mode called crack front waves along the crack front with a velocity slightly less than the Rayleigh wave velocity was found (Ramanathan and Fishe, 1997; Morrissey and Rice, 1998, 2000). The crack front waves (CFW) propagating in soda-lime glass and PMMA were experimentally studied and similar in many aspects to the CFW theoretically predicted above (Sharon et al., 2001; Fineberg et al., 2003). In the present paper, the crack front solitary pulse wave radiated from crack propagated as shock wave is theoretically analyzed based on the proposed micro-crack evolution equation and is verified to be soliton. The long-period pulse waves suggested by the solitary pulse wave analyzed in the present paper were observed in the seismograms of the 2016 Kumamoto Earthquake and the 2018 Hokkaido Eastern Iburi Earthquake at the neighborhood of the seismic centers. The crack propagating in the inhomogeneous media, which is characterized by the crack center strain to be largest and the shock wave velocity at the crack center being smaller than the surrounding velocities, is stably propagating such as the guided wave due to self-focusing just like as the brittle fracture progress. It is suggested based on the proposed micro-crack evolution equation considering the effect of the plastic strain that the numerical simulations and discussions in this paper are available under the plastic deformation.

Effect of Micro-Segregation on Impact Toughness of 2.25Cr-1Mo Steel after Post Weld Heat Treatment

2.25Cr-1Mo steel with high strength at high temperatures and superior hydrogen resistance is widely used as power generation boiler material in high-temperature and high-pressure environments. Following the test evaluation of the ASME Boiler and Pressure Vessel Code, specimens from the base metal of a boiler pipe were found to have impact toughness values of 386 and 28J, which are drastically different values. The analysis of the fracture surface of the 28J test specimen revealed MnS inclusions and it was found that cracks were initiated at the inclusions. Observation of the cross-section of the crack propagation front revealed that cracks propagated along the ferrite regions and precipitate voids. Inclusions were also found in the 386J impact specimen. However, the volume fraction of the inclusions was significantly less than that of the 28J specimen. It was also found that the ferrite and carbide content of the 386J specimen was less than the 28J specimen. The reason that the inclusions, ferrite, and carbide content differed in the two adjacent impact test specimens was analyzed. The effects of micro-segregation such as MnS inclusions on ferrite and carbide were compared and analyzed.

Evaluation of crack front shape and propagation under low cycle fatigue

Evaluation of crack front shape and propagation under low cycle fatigue

From telephone cords to branched buckles: A phase diagram

Thin films with low adhesion and large residual stresses may buckle and delaminate from their substrates. This delamination often results in oscillating patterns known as ‘telephone cords’. Other configurations can be observed as well, such as entangled networks of blisters. The present study aims at elucidating how these networks are generated through branching. A model coupling a geometrically non-linear plate model and a cohesive zone with mode dependent interfacial toughness is used. Previous work on the early stage delamination of initially circular blisters during interfacial crack front propagation are revisited and extended to the remote post-critical regime to capture front branching. We also build a partial phase diagram of buckling driven delamination morphologies. An intrinsic critical stress parameter is proposed which can be used to predict delamination morphology and to define ‘safe’ conditions where buckle propagation can be avoided. This critical stress also defines an intrinsic lengthscale which plays the role of a minimum nucleation size.

Approximation of mixed mode propagation for an internally pressurized circular crack

Hydraulic fracturing of rocks has various engineering applications. However, there has been limited research into crack propagation prediction by three dimensional analytical techniques. This paper discusses such a technique for predicting the propagation surface of a pressurized circular crack subjected to various loading conditions. The propagation surfaces predicted from the proposed crack front propagation algorithm align well with published results. The suggested method consumes only a fraction of the time needed for a numerical simulation, and therefore it could be useful in assisting the design of hydraulic fracturing operations.

Cracks in random brittle solids:

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.

Scaling law governing the roughness of the swash edge line.

The paper is devoted to the analysis of the shape of the swash edge line. Formation of the swash boundary is treated as an interfacial phenomenon. The simplest quantitative characteristic of the roughness of interface is its width w, defined as the root-mean-square fluctuation around the average position. For rough interfaces, the scaling with size of the system L is observed in the form w(L)∝Lζ. The concept of scaling supplies a simple framework for classifying interfaces. It is suggested that the fine structure of the swash boundary results from the combined action of the pinning force applied by random defects of the beach and elasticity of distorted swash boundary. The roughness of the swash front was studied at the Mediterranean Sea coast for uprush and backwash flows. Value of exponent ζ for receding swash front line was 0.64 ± 0.02, when in the case of advancing swash the value 0.73 ± 0.03 was calculated. The scaling exponent established for the receding phase of the swash is very close to the values of the exponent established for the roughness of the triple line for water droplets deposited on rough surfaces, crack propagation front in Plexiglas, and for the motion of a magnetic domain walls.

The use of ECT and 6PBP tests to evaluate fracture behavior of adhesively bonded steel/epoxy joints under Mode-III and Mixed Mode III/II

Evaluation of fracture energy of adhesive joints under mode-III and mixed-mode III/II is a key issue when failure analyses have to be performed. It is thus useful to determine fracture toughness under mode-III and characterization of crack front behavior of bonded joints under mixed-mode III/II loading conditions, which were the overall goal of this paper. For this purpose, edge crack torsion (ECT) and six-point bending plate (6PBP) tests were employed using steel/epoxy adhesive joint. The experimental tests were performed under displacement control and three types of configurations were tested to achieve different mixed-mode ratios. Test results showed considerable linearity before the maximum load point both under pure mode III and mixed-mode III/II; also, failure examination indicated that dominate failure under tearing mode was adhesive/adherend interface, which will be discussed in detail. The experimental tests were numerically simulated and virtual crack closure technique (VCCT) was employed to reproduce behavior of crack front propagation. Both experimental compliance method and finite element analysis proved applicable for the fracture mechanism of adhesive assemblies under mode-III and mixed-mode III/II.

Weight function theory and variational formulations for three-dimensional plane elastic cracks advancing

The weight function theory for three-dimensional elastic crack analysis received great attention after the work of Rice (1985, 1989). Several applications have been considered since then, particularly in the context of configurational stability, crack path prediction, stress intensity factor expansions, perturbation approaches. In all cases, a specific hypothesis has been made on the variation of crack shape, in order to formulate the problem in terms of Cauchy principal value. In the present note, such hypothesis is further investigated and consequences discussed. A variational statement given in Salvadori and Fantoni (2013a) is thus rephrased in terms of weight functions. Its discrete formulation shows the potential to accurate approximation of crack front propagation.

Role of the sample thickness in planar crack propagation

We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.

On the mechanism of squat formation on train rails – Part II: Growth

Longitudinal cross-sectioning of squats reveals characteristic features of internal crack front propagation. Leading crack planes propagate over longer lengths and greater depths as compared to more superficial trailing crack planes. A favourite depth of crack propagation occurs in the subsurface (2–3mm), is related to the residual longitudinal stress profile, and may lead to an internal crack ‘terrace’. Especially during deeper crack propagation and branching oxidation processes are found to be metallurgical drivers of crack growth. Contact surface modification during squat growth can be distinguished between phases of transient local stress redistribution and of dynamic wheel–rail contact. If the hypothesized shearing wedge in the failure mechanism loses its load bearing capacity, this gives rise to a redistribution of normal stresses within the actual contact ellipse and the formation of a hardness envelope along the crack pattern. This may partially explain why maturing squats show decoloured and hardened surface areas bordering the surface-breaking cracks. A second effect occurs for contact patches not matching the failure ‘envelope’: due to the Poisson effect the surface overlying the crack planes settles slightly, experiences reduced contact, and corrosive products, ‘pumped’ from inside the cracks, may accumulate on the surface (as confirmed by SEM-EDX analysis). During progressive growth of the defect the harder and decoloured envelope as well as the original wedge is pressed into the deeper elastic material, accompanied by a gradual expansion of the contact band and a bilateral bridging of the defect. This may cause high-frequency impact, resulting into progressive internal crack growth affecting the global stress response and rail fracture.

Analytical Solutions for Corrosion‐Induced Cohesive Concrete Cracking

The paper presents a new analytical model to study the evolution of radial cracking around a corroding steel reinforcement bar embedded in concrete. The concrete cover for the corroding rebar is modelled as a thick‐walled cylinder subject to axisymmetrical displacement constraint at the internal boundary generated by expansive corrosion products. A bilinear softening curve reflecting realistic concrete property, together with the crack band theory for concrete fracture, is applied to model the residual tensile stress in the cracked concrete. A governing equation for directly solving the crack width in cover concrete is established for the proposed analytical model. Closed‐form solutions for crack width are then obtained at various stages during the evolution of cracking in cover concrete. The propagation of crack front with corrosion progress is studied, and the time to cracking on concrete cover surface is predicted. Mechanical parameters of the model including residual tensile strength, reduced tensile stiffness, and radial pressure at the bond interface are investigated during the evolution of cover concrete cracking. Finally, the analytical predictions are examined by comparing with the published experimental data, and mechanical parameters are analysed with the progress of reinforcement corrosion and through the concrete cover.

Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study

We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.

Fracture mechanisms in biopolymer films using coupling of mechanical analysis and high speed visualization technique

The aim of this study was to provide a detailed description of the fracture mechanisms in three different biopolymer thin materials: gelatin, hydroxypropyl cellulose (HPC) and cassava starch films. That was achieved by using a combination of fracture mechanics methodology and in situ visualization with high speed imaging technique. By analyzing the unstable and stable crack propagation that occurs in these materials, the brittle to ductile transition induced by water plasticization was assessed and discussed. Each biopolymer material exhibited a distinctive brittle and ductile fracture mode, which were described in this work. In order to evaluate the occurrence of permanent deformation in the proximity of the crack propagation front, FTIR maps with polarized light microscopy were employed, which enabled the visualization of structural homogeneity and cohesivity. The differences in fracture behaviour were interpreted taking into account the structural organization within these materials during stretching. The coupling of mechanical data and advanced visualization techniques was a particularly effective method to describe and interpret the complex fracture mechanisms in biopolymer materials which is strongly affected by their interaction with water molecules.