Propagating Crack Tip Research Articles

Experimental and Numerical Studies on Development of Fracture Process Zone (FPZ) in Rocks under Cyclic and Static Loadings

The development of fracture process zones (FPZ) in the Cracked Chevron Notched Brazilian Disc (CCNBD) monsonite and Brisbane tuff specimens was investigated to evaluate the mechanical behaviour of brittle rocks under static and various cyclic loadings. An FPZ is a region that involves different types of damage around the pre-existing and/or stress-induced crack tips in engineering materials. This highly damaged area includes micro- and meso-cracks, which emerge prior to the main fracture growth or extension and ultimately coalescence to macrofractures, leading to the failure. The experiments and numerical simulations were designed for this study to investigate the following features of FPZ in rocks: (1) ligament connections and (2) microcracking and its coalescence in FPZ. A Computed Tomography (CT) scan technique was also used to investigate the FPZ behaviour in selected rock specimens. The CT scan results showed that the fracturing velocity is entirely dependent on the appropriate amount of fracture energy absorbed in rock specimens due to the change of frequency and amplitudes of the dynamic loading. Extended Finite Element Method (XFEM) was used to compute the displacements, tensile stress distribution and plastic energy dissipation around the propagating crack tip in FPZ. One of the most important observations, the shape of FPZ and its extension around the crack tip, was made using numerical and experimental results, which supported the CT scan results. When the static rupture and the cyclic rupture were compared, the main differences are twofold: (1) the number of fragments produced is much greater under cyclic loading than under static loading, and (2) intergranular cracks are formed due to particle breakage under cyclic loading compared with smooth and bright cracks along cleavage planes under static loading.

Optical Evaluation of In Situ Crack Propagation by Using Mechanoluminescence of SrAl2O4:Eu2+, Dy3+

New theoretical solutions involving conventional crack propagation from static to dynamic fracture in terms of mechanoluminescence (ML) and the experimental techniques to trace the in situ crack and its instantaneous stress intensity factor (SIF) have been suggested in SrAl2O4:Eu2+, Dy3+ (SAO). The direct optical method to determine the moving crack tip on behalf of ML was verified by indirect crack mouth opening displacement (CMOD). The mode I SIF calculated from the instantaneous cumulative ML fringes showed proper agreement with the SIFs and acquired from conventional ASTM E‐399 measurements under quasidynamic condition. The magnitude and shape of the theoretically predicted crack tip stress field was in accordance with the experimental in situ ML evidence while determining the quasidynamic SIF from the cumulative ML intensity. Therefore, the use of ML technology could be one of the possible substitutive and substantial alternatives for structural health monitoring systems due to its simplicity but effectiveness in detecting arrested or propagating crack tips and in assessing the instantaneous structural integrity by means of the ML fracture parameters.

Cleaving the Halqeh-ye-nur diamonds: a dynamic fracture analysis.

The degree of surface roughness and clarity with which a surface in a brittle material can be formed via fracture is known to be related to the speed of the propagating crack. Cracks traversing a brittle material at low speed produce very smooth surfaces, while those propagating faster create less reflective and rough surfaces (Buehler MJ, Gao H. 2006 Nature 439, 307–310 (doi:10.1038/nature04408)). The elastic wave speeds (cl≈18 000 m s−1, cs≈11 750 m s−1) in diamond are fast (Willmott GR, Field JE. 2006 Phil. Mag. 86, 4305–4318 (doi:10.1080/14786430500482336)) and present a particular problem in creating smooth surfaces during the cleaving of diamond—a routine operation in the fashioning of diamonds for gemstone purposes—as the waves are reflected from the boundaries of the material and can add a tensile component to the propagating crack tip causing the well-known cleavage steps observed on diamond surfaces (Field JE. 1971 Contemp. Phys. 12, 1–31 (doi:10.1080/00107517108205103); Field JE. 1979 Properties of diamond, 1st edn, Academic Press; Wilks EM. 1958 Phil. Mag. 3, 1074–1080 (doi:10.1080/14786435808237036)). Here we report an analysis of two diamonds, having large dimensions and high aspect ratio, which from a gemological analysis are shown to have been cleaved from the same 200 carat specimen. A methodology for their manufacture is calculated by an analysis of a model problem. This takes into account the effect of multiple reflections from the sample boundaries. It is suggested that the lapidary had an intuitive guide to how to apply the cleavage force in order to control the crack speed. In particular, it is shown that it is likely that this technique caused the fracture to propagate at a lower speed. The sacrifice of a large diamond with the intention of creating thin plates, rather than a faceted gemstone, demonstrates how symbolism and beliefs associated with gemstones have changed over the centuries (Harlow GE. 1998 The nature of diamonds, Cambridge University Press). The scientific insights gained by studying these gemstones suggest a method of producing macroscale atomically flat and stress-free surfaces on other brittle materials.

Granitic magma emplacement and deformation during early-orogenic syn-convergent transtension: The Staré Sedlo complex, Bohemian Massif

The Late Devonian Staré Sedlo complex, Bohemian Massif, was emplaced as a subhorizontal sheeted sill pluton into a transtension zone. The transtensional setting is documented by strong constrictional fabric, corroborated by the anisotropy of magnetic susceptibility (AMS), with variably developed subhorizontal magmatic to solid-state foliation suggesting vertical shortening. Intrusive contacts of the granitoids with metapelitic screens and tapered sill tips indicate that magma wedging was the dominant process of sill propagation. The sills exhibit two intrusive styles, ranging from thin lit-par-lit injections to widely spaced meter-thick sills. These two styles are interpreted as reflecting variable viscosities of intruding magma where low-viscosity magma percolated along foliation planes whereas high-viscosity magma produced more localized thicker sills. We propose that the magma/host rock system in transtension must have evolved from initial crack tip propagation and vertical expansion due to new magma additions through conduit flow to ductile thinning after the magma input had ceased. The sill emplacement and their subsequent deformation are then interpreted as recording early-orogenic syn-convergent sinistral transtension along the rear side of an upper-crustal wedge, which was extruded both upward and laterally in response to subduction and continental underthrusting.

Effect of Fiber Volume Fraction on the Flexural Properties of Unidirectional Carbon Fiber/Epoxy Composites

In this study, the effect of fiber content on the flexural property of continuous carbon fiber/epoxy composites was investigated. Samples with four different fiber volume fractions, 50, 60, 70, and 80 vol.%, were fabricated. For comparisons, cast epoxy resin was also prepared. It was observed that the flexural strength and modulus of this material are enhanced with increasing fiber volume fractions in the range of 50–70 vol.%. Results show that the carbon fiber/epoxy composites possess the largest fracture force and displacement when the fiber volume fraction is 70 vol.%, which is mainly attributed to the effective stress transfer of fibers. This can restrict crack tip propagation and blunt the crack tip, then consume abundant deformation energy and result in an increase of fracture work. On the other hand, poor flexural property was observed when the sample with high fiber volume fraction (80 vol.%) was tested. Three different types of failure modes were observed according to the fiber content.

Energy release rates in rubber during dynamic crack propagation

The theoretical understanding of the fracture mechanics of rubber is not as well developed as for other engineering materials, such as metals. The present study is intended to further the understanding of the dissipative processes that take place in rubber in the vicinity of a propagating crack tip. This dissipation contributes significantly to the total fracture toughness of the rubber and is therefore of great interest from a fracture mechanics point of view. To study this, a computational framework for analysing high-speed crack growth in a biaxially stretched rubber under plane stress is therefore formulated. The main purpose is to investigate the energy release rates required for crack propagation under different modes of biaxial stretching. The results show, that inertia comes into play when the crack speed exceeds about 50m/s. The total work of fracture by far exceeds the surface energy consumed at the very crack tip, and the difference must be attributed to dissipative damage processes in the vicinity of the crack tip. The size of this damage/dissipation zone is expected to be a few millimetres.

Quantitative Characterization of Mechanical Stress Field and Fracture Strength in Isotropic Brittle Materials During Crack Tip Propagation

A generalized method for characterizing mechanical stresses in brittle materials during crack tip propagation is presented. This approach was derived from classical fracture mechanics and is therefore mechanism independent and applies to any isotropic brittle material, including glasses, fine grained ceramics or metals, and high stiffness polymers. A practical implementation demonstrates the merits of this technique: the fracture strength can be determined by characterizing the angle between the free surface of a flexural overload fracture and stress intensity factor loci. The accuracy of this method was phenomenologically validated using flexural strength tests on glass as a model material system. In addition, such fractographic measurements can also be used to characterize an inhomogeneous internal stress field, and thereby, for example, help discriminate whether the sample failed due to pure bending loads alone, or whether membrane stresses were also present.

Experimental–numerical hybrid stress analysis for a curving crack in a thin glass plate under thermal load

The stress fields around an oscillating crack tip in a thin plate are studied using an experimental–numerical hybrid method. Instantaneous phase-stepping photoelasticity using a CCD camera equipped with a pixelated microretarder array is used for measuring the stress fields around a propagating crack tip. Not only the principal direction but also the principal stress difference around a growing crack is obtained. Then, the stress distributions around a crack are evaluated by the experimental–numerical hybrid method. Results show that the proposed hybrid method is effective for the study of crack growth behavior in the glass plate. The results obtained in this study show that the compressive stresses exist around the tensile stress region at the crack tip. It can be considered that the existence of the compressive stress distribution surrounding the tensile stress field at the crack tip leads to both the high value of the stress intensity factor and the crack oscillation.

Wallner lines, crack velocity and mechanisms of crack nucleation and growth in a brittle bulk metallic glass

Mode I fracture experiments were conducted on brittle bulk metallic glass (BMG) samples and the fracture surface features were analyzed in detail to understand the underlying physical processes. Wallner lines, which result from the interaction between the propagating crack front and shear waves emanating from a secondary source, were observed on the fracture surface and geometric analysis of them indicates that the maximum crack velocity is ∼800ms−1, which corresponds to ∼0.32 times the shear wave speed. Fractography reveals that the sharp crack nucleation at the notch tip occurs at the mid-section of the specimens with the observation of flat and half-penny-shaped cracks. On this basis, we conclude that the crack initiation in brittle BMGs is stress-controlled and occurs through hydrostatic stress-assisted cavity nucleation ahead of the notch tip. High magnification scanning electron and atomic force microscopies of the dynamic crack growth regions reveal highly organized, nanoscale periodic patterns with a spacing of ∼79nm. Juxtaposition of the crack velocity with this spacing suggests that the crack takes ∼10−10s for peak-to-peak propagation. This, and the estimated adiabatic temperature rise ahead of the propagating crack tip that suggests local softening, is utilized to critically discuss possible causes for the nanocorrugation formation. Taylor’s fluid meniscus instability is unequivocally ruled out. Then, two other possible mechanisms, viz. (a) crack tip blunting and resharpening through nanovoid nucleation and growth ahead of the crack tip and eventual coalescence, and (b) dynamic oscillation of the crack in a thin slab of softened zone ahead of the crack-tip, are critically discussed.

On Welding Residual Stresses Near Fatigue Crack Tips

Residual stresses in welded joints are supposed to change during fatigue loading. Residual stresses can be, depending on the loading conditions, relaxed as well as build up and they can be affected by fatigue crack growth. Furthermore residual stresses are supposed to affect the fatigue strength of welded steel structures. However, tensile residual stresses decrease and compressive residual stresses increase the fatigue strength. This residual stress effect on the fatigue strength is mostly explained with different crack propagation rates.The presented work is on welded longitudinal stiffeners, made of unalloyed fine grained carbon steel, with different fatigue crack lengths in which residual stresses have been determined. The residual stress measurement was conducted using Neutron diffraction. The results of the diffraction measurement show that the initial tensile residual stresses near the weld toe are, caused by phase transformation at low temperatures, below the base materials yield strength. Tensile residual stresses in the order of the yield strength can be found below the materials surface. These areas of high residual stresses are moving with the propagating crack tip through the specimen during fatigue loading.

Influence of density variation on the arbitrarily propagating crack tip fields in functionally graded materials

The stress and displacement fields for an arbitrarily propagating crack tip in functionally graded materials (FGMs) with exponential variation of density and shear modulus are obtained. Nonhomogeneous parameters of density and shear modulus are different from each other. The solutions for higher order terms in the dynamic equilibriums are obtained by transforming the general differential equations to the scaled Laplace’s equations. Using the stress fields, the effects of the nonhomogeneous density on stress components is investigated. In addition, the contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of the nonhomogeneous density on the isochromatics are discussed.

The tensile properties and fracture of the Ni/Cr2O3 interface: First principles simulation

The tensile fracture processes of O-terminated Ni(111)/Cr2O3(0001) interface were investigated using first-principles method. The simulation presents the strain–stress relationship, the Ni deformation and the propagation of crack tip. Atomic configuration and charge density indicate the softer Ni layers deform larger than the harder Cr2O3 layers and that fracture occurs along the metal–oxide interface. The process of bond breaking was also elucidated.

Lithiation induced corrosive fracture in defective carbon nanotubes

We perform molecular dynamics simulations to elucidate lithiation induced fracture mechanisms of defective single-walled carbon nanotubes (SWCNTs). Our simulations reveal that variations of defect size and lithium concentration set two distinct fracture modes of the SWCNTs upon uniaxial stretch: abrupt and retarded fracture. Abrupt fracture either involves spontaneous lithium weakening of the propagating crack tip or is absent of lithium participation, while retarded fracture features a “wait-and-go” crack extension process in which the crack tip periodically arrests and waits to be weakened by diffusing lithium before extension resumes. Our study sheds light on the rational design of high-performance CNT-based electrodes.

Historical-Log Recording System for Crack Opening and Growth Based on Mechanoluminescent Flexible Sensor

Recently, there are innovative mechanoluminescent (ML) particles made available, each of which repeatedly emits light in response to small applied stresses even in elastic region. When dispersedly coated onto a structure, each particle acts as a sensitive mechanical sensor, while the two-dimensional emission pattern of the whole assembly reflects the dynamical stress distribution inside the structure and the mechanical information around the crack and defect. To use the remarkable advantage of the ML sensor in flexibility, electricity/lead-free, low-cost, and so forth, and to answer social needs for historical-log of stress/damage accumulation on social infra-structure, we investigate historical-log recording system for crack opening and fatigue crack growth, and finally succeed to record it with responding position and intensity reflecting the trace of propagating crack tip and stress intensity factor around the tip. Furthermore, crack mouse opening displacement accompanied by general traffic of bridge in use is successfully detected.

Balanced Energy Dissipation at Propagating Crack Tip in Quasi-Brittle Materials? - Analysis via Soft-Computing Methods

Analysis on the aspects of the energy dissipation in the case of quasi-brittle fracture is presented. Dissipation both via cohesive forces at the crack faces and the one taking place within the volume of the fracture process zone is considered. Tools from the field of soft computing techniques are employed. The analysis is conducted on results from extensive experimental campaign.

Experimental study of crack propagation in polymethyl methacrylate material with double holes under the directional controlled blasting

ABSTRACTThe crack propagation behaviours of polymethyl methacrylate material with double holes under the directional controlled blasting are studied using dynamic caustic method. A series of dynamic caustic patterns at the propagating crack tip under the explosive loading are recorded using the digital high‐speed camera. Some important dynamic fracture characterizations and parameters about two main cracks are determined including the crack path, the propagating speed and the crack tip stress intensity factors. The fracture mechanisms of the double blasting holes are analysed. The results provide the important experimental basis for evaluating and designing the directional controlled blasting for the rock tunnel and the rock face excavation.

The failure criterion based on hydrogen distribution ahead of the fatigue crack tip

The hydrogen effect on the fracture toughness and fatigue crack growth behaviour in the martensitic high strength steel is investigated. The secondary ion mass spectrometry method has been employed to analyse the distribution of hydrogen concentration in the zone of the crack tip and at its edges. Changes in hydrogen concentration are observed in the vicinity of the propagating crack tip and at a remote site. The hydrogen peak H C is reduced and moves away from the fatigue crack tip with the increase of the maximum stress intensity factor max K . The concept of damage evolution is used to explain fatigue crack propagation in connection with the hydrogen redistribution ahead of the crack tip. The physical failure criterion based on the hydrogen peak in the vicinity of the fatigue crack tip and the maximum stress intensity factor has been proposed. The criterion reflects changes in the hydrogen peak which resulted from the hydrogen redistribution due to the increase of the maximum stress intensity factor as the crack length increases under fatigue loading.

압전재료에서 비정상적으로 전파하는 투과형 모드 III 균열

면외 기계적하중과 면내 전기적하중을 받는 압전재료에서 비정상적으로 전파하는 전기투과형 균열에 대하여 연구하였다. 비정상적으로 전파하는 균열에 대한 평형방정식을 개발하였고 근접해법으로 투과형균열에 대한 응력장 및 변위장을 얻었다. 압전상수, 유전율 그리고 균열선단속도 및 응력확대계수의 시간 변화율이 비정상적으로 전파하는 균열선단부근의 응력 및 변위장에 미치는 영향을 명확히 나타내었다. 이러한 응력장과 변위장을 사용하여 비정상적으로 전파하는 균열선단의 응력장 및 변위장의 특성에 대하여 토론하였다.

Numerical analysis of dynamic crack propagation in rubber

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.

Numerical investigation of dynamic crack branching under biaxial loading

Dynamic crack growth and branching of a running crack under various biaxial loading conditions in homogeneous and heterogeneous brittle or quasi-brittle materials is investigated numerically using RFPA2D (two-dimensional rock failure process analysis)-Dynamic program which is fully parallelized with OpenMP directives on Windows. Six 2D models were set up to examine the effect of biaxial dynamic loading and heterogeneity on crack growth. The numerical simulation vividly depicts the whole evolution of crack and captured the crack path and the angles between branches. The path of crack propagation for homogenous materials is straight trajectory while for heterogeneous materials is curved. Increasing the ratio of the loading stress in x-direction to the stress in y-direction, the macroscopic angles between branches become larger. Some parasitic small cracks are also observed in simulation. For heterogeneous brittle and quasi-brittle materials coalescence of the microcracks is the mechanism of dynamic crack growth and branching. The crack tip propagation velocity is determined by material properties and independent of loading conditions.