Individual Cracks Research Articles

Damage mechanisms in the dynamic fracture of nominally brittle polymers

Linear Elastic Fracture Mechanics (LEFM) provides a consistent framework to evaluate quantitatively the energy flux released to the tip of a growing crack. Still, the way in which the crack selects its velocity in response to this energy flux remains far from completely understood. To uncover the underlying mechanisms, we experimentally studied damage and dissipation processes that develop during the dynamic failure of polymethylmethacrylate (PMMA), classically considered as the archetype of brittle amorphous materials. We evidenced a well-defined critical velocity along which failure switches from nominally-brittle to quasi-brittle, where crack propagation goes hand in hand with the nucleation and growth of microcracks. Via post-mortem analysis of the fracture surfaces, we were able to reconstruct the complete spatiotemporal microcracking dynamics with micrometer/nanosecond resolution. We demonstrated that the true local propagation speed of individual crack fronts is limited to a fairly low value, which can be much smaller than the apparent speed measured at the continuum-level scale. By coalescing with the main front, microcracks boost the macroscale velocity through an acceleration factor of geometrical origin. We discuss the key role of damage-related internal variables in the selection of macroscale fracture dynamics.

Discrete rotation deflection of reinforced concrete beams at serviceability

Quantifying the deflection of reinforced concrete flexural members is complex, owing to the formation of discrete cracks which widen through slip between the reinforcement and the adjacent concrete causing increases in deflection. A common method of analysis and design is to use a full-interaction strain-based moment–curvature approach to derive flexural rigidities, which then need to be calibrated by comparison with test results. As this approach is based on full interaction, that is, there is no slip between the reinforcement and the concrete, it cannot cope directly with the discrete rotation at a flexural crack. Consequently, this approach cannot cope directly with the deflection associated with flexural crack widening that requires slip between the reinforcement and the concrete, that is, partial interaction. In this paper, a partial-interaction structural mechanics model is developed for quantifying the deflection owing to the discrete rotation at each individual crack. The results are shown to compare well with the semi-empirical effective flexural rigidity approaches and also with experimental data. Importantly, this is a mechanics-based approach that does not require components of the mechanism, as opposed to the material properties, to be determined experimentally. Hence, this partial-interaction approach should be useful in refining existing deflection design models and in quantifying the deflection of reinforced concrete members with new types of reinforcement.

Imaging stress and strain in the fracture of drying colloidal films

Drying-induced fracture limits the applications of thin films based on colloidal materials. To better understand the mechanics of drying, we directly measure the microscopic distribution of strain and stress of a colloidal silica film during the course of drying and cracking. We observe the build-up and release of internal stresses inside the film before and after the opening of individual cracks, and extract a critical stress for fracture of approximately 1 MPa. We also find an inherent time scale for stress relaxation within the film of 25 minutes, likely due to the competition between elastic deformation of and solvent flow through the porous particle network. By correlating the stress and strain, we estimate the plane strain Young's modulus of our colloidal film of the order of 100 MPa.

Automating the crack map detection process for machine operated crack sealer

Abstract Automated crack-sealing machinery must accurately locate continuous individual crack segments so that they can be processed and treated effectively. In this paper, we illustrate the use of a geodesic minimal path based method for generating the crack map suitable for the path planning process. The user can detect continuous cracks that extend over several miles just by providing the starting point of a crack as an input to the algorithm. The algorithm can also detect transverse cracks by giving a single point on the crack. The continuous crack map generated can be utilized very efficiently to generate the optimal path for the crack sealer. An extensive qualitative and quantitative evaluation on real pavement images was done to show the usefulness of the algorithm. The algorithm is computationally fast and efficient.

Probabilistic leak-before-break analysis with correlated input parameters

The paper presents a probabilistic methodology considering the correlations between the input variables for the analysis of leak-before-break (LBB) behavior of a pressure tube. A computer program based on Monte Carlo (MC) simulation with Nataf transformation has been developed to allow the proposed methodology to calculate both the time from the first leakage to unstable fracture and the time from leakage detection to unstable fracture. The results show that the correlation of the crack growth rates between different cracks has the most significant impact on the LBB behavior of the pressure tube. The impact of the parameters correlation on LBB behavior increases with the crack numbers. If the correlations between different parameters for an individual crack are not considered, the predicted results are nonconservative when the cumulative probability is below 50% and conservative when it is above 50%.

The effect of pitting corrosion on split sleeve cold hole expanded, bare 7075-T651 aluminium alloy

As part of an aircraft fleet fatigue life improvement program, investigation has been carried out into the effect pitting corrosion has on bare 7075-T651 which had undergone split sleeve cold hole expansion. Constant amplitude sinusoidal loading was applied to fatigue test coupons which had pitting corrosion induced upon them by a modified cyclic immersion process using a 3.5% NaCl solution. A pit depth of 39–58μm was found to significantly reduce the increased fatigue life gains achieved by carrying out cold hole expansion. At 137.9MPa fatigue life was reduced from achieving run out of ten million cycles to an average 371×103 cycles, while at 165.5MPa average fatigue life was reduced from 810×103 to 65×103 cycles. The fracture surfaces were analysed under a scanning electron microscope where each displayed an individual crack initiation site located on the material surface within the zone of residual circumferential stress.

Intergranular crack nuclei in polycrystalline alumina

Digital image correlation has been applied to optical images in order to detect crack nuclei in fine-grain size pure and Cr-doped aluminas. Individual intergranular crack nuclei within areas comprising tens of thousands of grains were detectable, and their crack lengths and opening strains obtained as a function of load prior to unstable fracture. Identification of the crack nuclei by this method allowed the grain boundary plane and grain orientations in the vicinity of crack nuclei to be characterised by electron microscopy. Crack nuclei were found to develop at boundaries that are predicted to have higher tensile thermal strains, caused by the orientation of the grain boundary plane relative to the adjacent grains.

Prediction of the propagation probability of individual cracks in brittle single crystal materials

We show that x-ray diffraction imaging (topography) and finite-element modelling can determine accurately the probability of propagation of individual cracks in brittle single crystal materials. The x-ray image of the crack provides a critical parameter for crack propagation which informs a predictive model, enabling us to identify critical defects that lead to catastrophic shattering of silicon wafers during high temperature thermal processing. Wafers fracture on cooling and finite element modelling shows that, during cooling, the tangential stress at the wafer edge is tensile and results in crack propagation. The predicted fracture geometry agrees extremely well with that observed experimentally.

NUMERICAL MODELING OF THE FRACTURE BEHAVIOR OF OPEN CELL FOAMS

The objective of this work is to numerically study the individual and mixed mode fracture behavior of open-cell foams. Three-dimensional tetrakaidecahedron model is adopted and finite element method is employed in analysis. The overall elastic properties of open-cell foams are numerically obtained. Then, modes I, II, III and mixed mode I–II fracture behavior of open-cell foams are numerically predicted respectively, in which both solid/hollow and square/circular strut cross-sections are considered. It is seen that the relationship between the overall critical stress intensity factor and the relative density of foam obeys power law for individual crack problems. Effects of the shape and the topology of strut cross-section are discussed in detail. For mixed mode I–II crack problem, the relationship between KI/KICand KII/KIICis obtained and the effect of the shape of strut cross-section is discussed.

Mechanical and self-healing properties of cementitious composites reinforced with flax and cottonised flax, and compared with polyvinyl alcohol fibres

Flax stems are often considered waste material. However, since flax fibre has superior mechanical properties amongst natural fibres, it can be used as reinforcement in cementitious composites. Durability of flax, however, is endangered in alkaline environments by the deterioration of alkali-sensitive pectin and hemicellulose. Cottonisation of flax not only makes flax suitable for producing textiles; it divides the technical fibre into bundles of elementary fibres and partially removes the alkali-sensitive pectin and hemicellulose. Therefore, the characteristics of cottonised flax (CF) in fibre reinforced cementitious composites were assessed. The fibre and composite properties were compared with technical flax (TF) fibres and synthetic polyvinyl alcohol fibres. Strength/strain curves of the natural fibre reinforced cementitious materials were analysed to evaluate the mechanical performance. Not only were tensile strength and stiffness evaluated, but also first crack strength, peak stress, work of fracture as a measure for multiple cracking (MC), and the visual closure of individual cracks by self-healing. Cottonisation of flax enhanced the modulus of elasticity, the peak stress and the strength at first crack formation of cementitious materials, in comparison to TF fibres. The self-healing of cracks was independent of the fibre type. Cracks narrower than 30 μm healed completely and crack widths between 30 μm and 150 μm only partly healed. ► The ‘green’ flax fibre proves to be a useful construction material. ► Cottonisation of flax reduces the fibre diameter. ► Cottonisation removes partly the alkali-sensitive pectin and hemicellulose. ► Mechanical properties enhance with the cottonisation of flax. ► Self-healing can prevail in specimens containing flax fibres.

Giant strain-sensitivity of acoustic energy dissipation in solids containing dry and saturated cracks with wavy interfaces

Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years, it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismoacoustic loss. In particular, it has been found that strains of order 10-8 produced by lunar and solar tides are capable of causing variations in the seismoacoustic decrement on the order of several percent. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity of assuming the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains.

Amplitude Dependent Damping of Aluminum-Matrix-Nanoparticle-Composites

Aluminum-matrix-nanoparticle-composites were produced by ball milling of micro scale aluminum powder in air atmosphere with subsequent consolidation by hot extrusion and also additional hot swaging. They were investigated in this condition after step by step isochronal annealing with successive increasing annealing temperature and quenching into water to room temperature. The material was investigated by amplitude dependent damping, hardness and density measurements, all at room temperature. For all measured amplitude dependent internal friction (ADIF) curves the damping increases with increasing strain amplitude. After some annealing treatments a knee occurs in the medium strain amplitude region of these curves. Moreover between annealing temperatures from 360°C to 480°C the strain dependent damping becomes a maximum, i.e. a peak in the ADIF curves occurs. Other ADIF curves of quenched and fatigued material show characteristic peaks that can be attributed to individual single cracks. It is shown that all these effects are due to the formation, opening and compression of cracks present in the sample or created by thermally exerted stresses.

Fatigue Behavior of Magnesium Alloy AJ91 Studied by Amplitude Dependent Damping Measurements

The amplitude dependent damping of two bending beam samples of magnesium alloy AJ91 (9 wt.% Al, 1 wt.% Sr) was measured at room temperature in as cast condition, after quenching from high temperatures into water of room temperature and after various bending cycles to fatigue. Some measurements were performed successively with about 33 Hz and 100 Hz resonant frequency. The measurements show typical dislocation damping in as cast condition, after heat treatment at temperatures lower than 420°C, and cycle numbers lower then 50.000. For higher quenching temperatures the damping increases over the whole measured strain range with increasing quenching temperature and number of cycles to fatigue. After quenching from temperatures higher than 478°C the crack damping becomes dominant. The effects of damping seem to increase with increasing frequency. In one sample damping of individual cracks could be identified in the amplitude dependent damping curves by their characteristic course very similar to the ones postulated in an earlier publication by a simple rheological model [4]. The extending of crack length leads to a shift of the damping to lower strains.

A mechanics solution for hinges in RC beams with multiple cracks

The formation of hinges in reinforced concrete beams is important as hinges influence the ability of the beam and, subsequently, the frame to absorb energy and resist extreme loads such as hurricane or seismic loads. A common approach for quantifying the rotational capacity of beams at the ultimate limit is to use a strain based moment–curvature analysis combined with an empirical hinge length to determine the rotation capacity of the member. Being empirically based, this approach is very restrictive as it can only be applied within the bounds of the tests from which they were derived. In this paper, a mechanics displacement based hinge approach is described that can simulate the formation of cracks, the discrete rotation at each individual crack and the formation of wedges. Being mechanics based, this hinge model can be applied to any type of reinforced concrete, such as those with brittle reinforcement and also to all strengths of concrete. This mechanics based model is shown to have good agreement with test results and can be used at all stages of loading from serviceability to failure. Furthermore, it can also used to develop closed form solutions that do not require the moment–curvature assumption of full interaction but specifically allow for partial interaction that is slip between the reinforcement and the concrete.

Simulation of discrete damage in composite Overheight Compact Tension specimens

Damage progression in laminated Overheight Compact Tension specimens was modeled using discrete representations of individual cracks and delaminations. Matrix cracking and delamination initiation, propagation, and interaction, without any prior knowledge and/or meshing of matrix cracking surfaces, is accomplished by combining stress and fracture mechanics-based constitutive modeling within a mesh independent crack-modeling framework. Simulation results including only matrix damage for specimens with [452/902/−452/02]s and [04/904]2s stacking sequences were compared with load–displacement curves and 3D X-ray micro computed tomography results from tested specimens. Excellent correlation was shown between the simulated and experimental load–displacement curves including statistical variations and proper representation of both the curve non-linearity and peak load. Similarly, a high level of correlation between simulated and experimental damage extent was shown. Additionally, a [45/90/−45/0]2s specimen exhibiting significant fiber fracture was modeled and results compared with experiment. Fiber fracture was simulated using a continuum damage mechanics approach in addition to the discrete cracking and delamination damage representations of matrix damage. The simulated load displacement curve and damage extent compared favorably with experimental results.

P2-S5.05 Risk Profiles of Winnipeg Street Populations: A latent class analysis

BackgroundSexually transmitted and bloodborne infection (STBBI) risk is multifaceted and can involve a complex interplay between sexual behaviours, substance abuse and mental health conditions. In Winnipeg, Manitoba Canada we conducted...

Self-sustained fracture waves in a lead oxide-silica glass

Using high-speed framing photography operating at 500000 frames per second, it has been shown that in Prince Rupert’s drops of a lead oxide-silica glass containing 24% by weight of lead oxide, the fracture waves propagate at a stable and self-sustained manner at a speed of (1300 ± 100) m s−1. This fracture wave speed is close to the terminal crack speed in the glass. These results, along with those from Prince Rupert’s drops of soda-lime glass reported by us earlier, confirm that the speed of a self-sustained fracture wave in a glass is controlled by the terminal speed of individual cracks in the glass.

Fatigue extrusions, slip band cracking and a novel hybrid concept for fatigue crack closure close to the crack tip

Small fatigue cracks in the aluminium alloys 2024-T351 and 8090-T8771 have been observed to grow by a heterogeneous process of three-dimensional slip band decohesion. Local, finely-divided crack path excursions at slip bands, the pull-out of small sections of decohered slip band and the formation of fatigue extrusions at slip bands produced micro-roughness on the crack surfaces. The hybrid form of plastic deformation induced surface roughness provides a potential source of crack closure. This may be effective in reducing the nominal crack growth driving force at small cracks and near threshold for long cracks when the crack tip opening displacement is small. A higher magnitude of closure at small mode I crack sizes and a spread in the levels of closure for a given crack size are consistent with the dependence of the slip band related micro-roughness on the individual crack path. Fatigue extrusions imply a dynamic form of crack closure that could develop immediately at the crack tip even for fatigue at high mean load. Complex influences of crack size, grain orientation and crack path on crack closure and crack growth rate indicate that a stochastic approach to determining fatigue life is appropriate for the critical small crack regime in these and similarly behaving materials.

ICONE19-43676 Assessment of Choking Flow Models for Subcooled Flashing Flow through Steam Generator Tube Cracks

The state-of-the-art modeling of leak rates through individual pipe stress corrosion cracks is based on regression analysis of experimentally determined leak rates and defects size. This has relatively large uncertainties. Accurate leak rate predictions require two key parameters, crack area and choking flow rate. The thermalhydraulics models employed in the leak rate calculations are generally based on the Henry-Fauske model of two-phase flow through long channels. For small length to diameter ratio (L/D) channels such as in steam generator tube cracks both mechanical and thermal nonequilibrium must be accounted. Another very important problem in verifying the model of the critical flow through cracks is the limited data on the crack geometry. Recently there is some database available on choking flow through cracks relevant to steam generator (SG) tubes to model the critical flow. These data are used in assessing the key choking flow models. Based on this assessment a mechanistic choking model is developed. The model is used to predict the choking flow rates for various experimental conditions for subcooled flashing flow through narrow slits with L/D varying from small values (〜5) to large values (100). Results are presented on the effects of thermal and mechanical non-equilibrium on the choking flow for small L/D channels.

Self-Sustained Fracture Waves in Soda-Lime Glass

High-speed framing photography in conjunction with circularly polarised light has been employed to monitor qualitatively the state of residual stress in Prince Rupert’s drops of soda-lime glass undergoing disintegration by a self-sustained fracture wave in the glass drops. It is revealed that the fracture wave through a Prince Rupert’s drop is driven by the residual stress in the drop, with the propagation speed of the fracture wave being (1700 ± 100) ms-1, which is close to the terminal speed of individual cracks in the soda-lime glass, but is much smaller than the longitudinal wave speed of 5300 ms-1 in the glass. These observations support our recently reported observations and also give support to our conclusions that the fracture wave speed of a self-sustained fracture wave is equal to the terminal speed of individual cracks in the glass. Some preliminary observations from fracture waves in Prince Rupert’s drops of a lead oxide glass are also described, which show that in Prince Rupert’s drops of the lead oxide glass the fracture wave is also self-sustained and it travels through the drop at a steady and stable speed of (1300 ± 100) ms-1, which is also considerably smaller than the longitudinal wave speed of 4800 ms-1 in the lead glass. A brief comment is also made on the fracture waves observed by other workers in brittle oxide glasses and solids generated by plate impacts and shock waves.