Minimum Crack Spacing Research Articles

Curvature-enabled analytical method for bending-induced crack location prediction

Condition assessment of civil infrastructure damaged by naturaldisasters with insufficient structural information has been a challenge for engineers. This paper proposes an analytical method to predict bending-induced crack locations on damaged reinforced concrete (RC) beams merely using curvature characteristics obtained from vision-based technologies. Firstly, critical equations that calculate minimum crack spacing followed by bending curvature information are derived through bond-slip theory and assumed boundary conditions. Secondly, a prediction procedure is proposed using derived critical equations to determine bending-induced crack locations. Two RC beam specimens under four-point bending were investigated to verify the validity and accuracy of the proposed method. Experimental results show that the combination of vision-based technologies and the analytical method proposed in this research has great potential in structural inspection and safety evaluation in field.

A hybrid deterministic-probabilistic approach for the characteristic crack widths and crack spacings in reinforced concrete tension and flexural members

Crack control is an important serviceability design criterion for reinforced concrete members. In this paper a new model is proposed that directly incorporates the deterministic and probabilistic aspects of cracking behaviour. The approach defines the minimum crack spacing and the relationship between crack-spacing and crack-width as a function of the bond between the reinforcement and the concrete using partial-interaction mechanics. This deterministic model is then used as a basis for a probabilistic analysis to identify mean crack-spacing and crack-width allowing for uncertainty in the deterministic model. The fitted variables are estimated using a Bayesian approach drawing upon 463 observations of crack-spacing and 3409 observations of crack-width. Using the hybrid deterministic-probabilistic model the importance of spatial variability of material properties is identified and simulated. The probability distributions for the mean crack spacing and the distribution of cracks are then combined to give parsimonious expressions for the characteristic crack-spacing according to a specified probability of exceedance. The same approach is then applied to determine the characteristic crack-width.

Prediction of tensile response of UHPC with aligned and ZnPh treated steel fibers based on a spatial stochastic process

This paper proposed a new method for predicting tensile response of UHPC based on a spatial stochastic strength distribution model. The steel fibers in UHPC were aligned by a developed device and chemically treated by ZnPh. A direct tension test was conducted to obtain the tensile response of UHPC with treated fibers. Image analysis was used to obtain the frequency of overall fiber orientation distribution. The spatial stochastic distribution model was proposed for cross sectional strength of UHPC based on the Ornstein-Uhlenbeck stochastic process. The model introduced some assumptions such as the correlation coefficient between the cracking strength and fiber bridging strength. Parametric analysis was conducted to obtain the crucial stochastic parameters in the model. Combining with the single fiber pullout model, tensile behavior of a single crack, and minimum crack spacing, the model predicted the strain hardening and multiple cracking behaviors with precise accuracy, as compared to experimental results.

Damage accumulation analysis of cfrp cross-ply laminates under different tensile loading rates

This paper investigates the loading rate effect on both mechanical properties and damage accumulation process of [0°2/90°4]S carbon fiber-polymer laminates under tensile loading. In-situ edge observations, Acoustic Emission and Digital Image Correlation techniques were utilized simultaneously to monitor the state of damage in real time. Results showed that the axial modulus and strength were less sensitive to loading rates than failure strain, which increased with the decrease of the loading rate. In the viewpoint of damage accumulation process, high density and uniform distribution of transverse matrix cracks, and H-shape crack patterns, incorporating inter-laminar cracks, were more likely to occur at low loading rates while variable crack spacing occurred at higher rates. When loading rates were lower than a certain level, maximum transverse matrix crack density decreased slightly due to the restriction of relatively widely generated inter-laminar cracks. Furthermore, the cumulative acoustic emission energy of low-frequency signals was linearly correlated to transverse matrix crack density, providing a promising way to quantify crack accumulation in real time. Finally, spatial consistence was observed between transverse matrix cracks at edges and stress concentrations at the exterior 0° ply, and the peaks of axial strain at local concentration regions locate either near the newest cracks or at the place with minimum crack spacing.

Punchout evaluations and classification of continuously reinforced concrete pavement to improve pavement design

In continuously reinforced concrete pavement (CRCP) research, it has been assumed that transverse crack spacing plays an important role in determining CRCP behaviour and performance. For the longitudinal reinforcement design, the 1993 American Association of State Highway and Transportation Officials (AASHTO) Design Guide recommends a minimum crack spacing of 3.5 ft. The minimum spacing of 3.5 ft is recommended to minimise the occurrence of punchouts. This concept of narrow crack spacing being more prone to punchout has been accepted. Hence, all the available CRCP design algorithms are based on this concept. However, since treated base/non-erodible base is now provided in CRCP, this theory has some discrepancies with the real CRCP performance especially in Texas. In this study, an extensive field evaluation was conducted for the number of punchouts recorded in TxDOT pavement management information system (PMIS). Out of 1472 punchouts, 232 punchouts that developed in major metropolitan Districts in TxDOT were surveyed and evaluated to determine whether punchouts have a relationship with closely spaced transverse cracks and the resulting load transfer efficiency (LTE). Field survey and testing results show that the majority of distresses in CRCP have been caused by quality issues of either materials or construction in the vicinity of transverse construction joint and repair joint.

A directed continuum damage mechanics method for modelling composite matrix cracks

Matrix cracking in continuous fibre reinforced composites follows the fibre orientations, but continuum damage mechanics models are not able to properly capture this. A novel method is presented here to alleviate mesh sensitivity of the damage growth direction and represent discrete matrix cracks. In a ply-by-ply mesoscale model, matrix cracks within a ply usually rely on mesh dependent strain localisation to decide the crack growth direction. The newly proposed algorithm instead uses the ply level fibre orientation as a model input, and maintains crack advancement along this direction, based on a neighbour searching scheme. A further advantage is that it is able to represent individual cracks discretely, with a predefined minimum crack spacing. This overcomes another limitation of continuum damage models, where discrete cracks are only represented in a smeared sense. This procedure has been shown to be able to reproduce complex crack networks in multidirectional laminates, independent of the mesh pattern.

Evaluation of crack width in RC ties through a numerical “range” model

Crack phenomenon in reinforced concrete (RC) ties is studied herein by means of a numerical “range model”, based on bond between steel and concrete. Since a unique definition of the crack pattern evolution is not possible for these elements, through the definition of this “range”, defined by the curves of maximum and minimum crack spacing (and consequently width), all the possible crack patterns of the considered tension member are so included. Comparisons with significant experimental results available in the technical literature prove that the proposed approach can be successfully adopted also for design purposes, since it provides a correct estimate of maximum crack width. The obtained results are compared with Codes provisions (ACI and Model Code 2010) and the effectiveness of different approaches for predicting crack width is analyzed and discussed.

Partial-interaction short term serviceability deflection of RC beams

A widely accepted approach for quantifying the serviceability short term deflection of RC beams is to use some combination of the flexural rigidities of the uncracked (EIfi-uncr) and cracked (EIfi-cr) sections that are obtained from a full-interaction analysis of transformed sections; a full-interaction analysis implies that there is no slip between the reinforcement and concrete. The combination of EIfi-uncr and EIfi-cr, that is the effective flexural rigidity (EIeff) to be used for calculating the deflection, has to be determined purely from testing. In this paper partial-interaction theory, which allows for slip between the reinforcement and concrete and consequently the bond-slip characteristics, is used to determine the partial-interaction flexural rigidity of a cracked section (EIpi-cr). It is shown that: by replacing the cracked section EIfi-cr with EIpi-cr obviates the need to determine EIeff directly from testing; the replacement of EIfi-cr by EIpi-cr allows closed form solutions to be derived for EIeff and also allows for the distinction between the formation of primary and secondary cracks. The partial interaction approach also provides a way of determining, through mechanics, the minimum crack spacing and hence can be used to study the random component of cracking and its influence on member deflection. The partial-interaction flexural rigidity should be a convenient tool for not only refining existing deflection procedures but also for quantifying the deflection of RC beams with new types of reinforcement and new types of bond, in particular those associated with FRP reinforced members.

The effect of temperature and strain rate on the periodic cracking of amorphous AlxOy films on Cu

The high temperature properties of metal/ceramic interfaces play an important role in the operation of microprocessors and coated products. Determination of the interface properties over a range of testing conditions is critical in understanding and improving the performance of such systems. Periodic cracking of ceramic films on metal substrates provides a direct measure of the interface strength. A model AlxOy/Cu system is investigated over temperatures of 25–650°C and at strain rates of 3.5⋅10−2s−1 and 1.7⋅10−5s−1. For this system it is found that temperature does not significantly affect the spacing of film cracks in the steady state, at a given strain rate. However, the high strain rate tests broaden the measured crack spacing distributions compared to the low strain rate tests. This broadening causes an increase in the average crack spacing at high strain rate. The minimum crack spacing was increased 15–20% by both increasing strain rate and increasing temperature.

Cracking of NiTi Thin Films Deposited on Cu Substrate

This study has investigated the cracking of Ti-51.45at.%Ni thin films deposited on Cu substrate. An analysis is presented that relates the crack spacing and the Vickers microhardness values to the strain in the film. Tensile tests are carried out on CSS-44100 electron universal testing machine. The strain rate is 1.1 × 10-4 s-1. The average crack spacing is obtained using scanning electron microscopy (SEM). The Vickers microhardness values are determined by Everone MH-6 microhardness tests. The results have showed that a series of parallel cracks grew in the film and the cracks are equally spaced. The minimum crack spacing is about 87 μm. The mean crack spacing is dependent on the tensile strain in the film. The crack spacing decreases as the film elongation increases. The Vickers microhardness values increase as the film elongation increases.

Crack Propagating and Stress-Promoted the Precipitate of Ni<sub>3</sub>Ti in NiTi Thin Films

This study investigated the stress-induced crack propagation and precipitation in Ti-51.45at.%Ni thin films. Tensile tests were carried out on CSS-44100 electron universal testing machine. The strain rate was 1.1×10-4 s-1. The surface micrographs of the NiTi thin film were obtained using scanning electron microscopy (SEM). The precipitates were determined by X-ray diffraction (XRD) experiments (D8 GADDS). The results showed that a series of parallel cracks grew in the film and the cracks were equally spaced. The fracture toughness of the film was estimated, =0.96MPa∙m1/2. The minimum crack spacing was about . The stress-strain curve can be divided into two stages. The first linear stage corresponded to the elastic deformation of the parent phase. In the following stage, the serrations were considered to be the stress relaxation due to the cracks propagating and the precipitate grain transformation. During tension the (102) peak intensity of Ni3Ti phase increased with elongation increased. The precipitate orientation was same.

Determination of crack spacing and penetration due to shrinkage of a solidifying layer

A method based on energy minimisation is used to determine the spacing and penetration of a regular array of cracks in a layer of material whose thickness is increasing as it solidifies from a liquid. After solidification, the slab shrinks and subsequently cracks due to internal stresses. A simple Stefan solidification model is used to determine the thickness of the slab as time progresses as well as the temperature profile in the slab. The key feature of the results is that a minimum crack spacing occurs early in the solidification process and this minimum defines a basic spacing for the crack array. The minimum spacing occurs for a range of constraints (boundary conditions) and thermal profiles in the material, indicating the robustness of the phenomenon. Cracks propagating with the unique minimum spacing are subject to a period doubling instability that acts to coarsen the crack pattern, which brings the crack spacing close to the minimum energy state for later time. Good numerical comparison between the crack spacings predicted by energy minimisation and those observed in basalt columns is demonstrated.

Crack Spacing and the Flow Stress in NiTi Thin Films Deposited on Cu Substrate

Ti-51.45at.%Ni thin films were deposited onto copper substrates by magnetron sputtering. The copper substrates were pre-punched into dog-bone specimens with 4.5mm×30mm(gauge portion) ×35µm( thickness). The substrate temperature was about 673K. The thin films were about 20µm thick. The as-deposited films were first solution treated at 1073K for 1h, and then aged at 773K for 30min. The grain size was estimated to be 1.5µm from scanning electron microscopy micrographs. Tensile tests were carried out on CSS-44100 electron universal test-machine. The strain rate was 1.1×10-4 s-1. The stress-strain curves of the free-standing film were obtained from the experimental stress-strain curves of copper substrate together with the thin film adherent to the substrate compared with the curves of copper substrate without film. The Hall-Patch coefficient was calculated, k=205Mpa.µm1/2. It seems that the Hall-Patch coefficient decreases with increasing film thickness. The experimental results showed that a series of parallel cracks grew in a concerted fashion across the thin film and the cracks were equally spaced. The cracks were more closely spaced if the film stress was increased. The fracture toughness of the film was estimated, c KΙ =0.96MPa·m1/2. Therefore, the minimum crack spacing is predicted by the film stress given.

Optimal spacing and penetration of cracks in a shrinking slab

A method based on energy minimization is used to determine the spacing and penetration of a regular array of cracks in a slab that is shrinking due to a changing temperature field. The results show a range of different crack propagation behavior dependent on a single dimensionless parameter, being the ratio of the slab thickness and a characteristic length for the material. At low parameter values the minimum energy state can be achieved by continually adding more cracks until a steady state is achieved. At higher values, a minimum crack spacing is reached at finite time, beyond which the cracks are constrained to propagate with the minimum spacing. In the latter case, the uniform propagation is potentially unstable to a spatial period doubling, leading to increasingly complex crack penetration patterns. The energy minimization combined with the period doubling instability provides a means of determining the minimum energy state of cracks for all time. The problem considered here can be seen as a paradigm for cracking phenomena that occur on a large range of scales, from planetary to microscopic.

Film cracking and debonding in a coated fiber

A fracture mechanics based methodology for the determination of interface fracture toughness from crack spacing in a thin coated fiber is presented. The coating (film) may be regarded as the matrix material in typical experiments employing this configuration. Matrix crack spacing is considered to be the result of a competitive process between matrix segmentation and interface debonding which are assumed to be governed by critical energy release rate criteria. Matrix cracks are assumed to form by the process of channeling in the circumferential direction and steady state conditions are assumed at the matrix crack front in the channeling direction. Energy release rates are determined using domain integral procedures in conjunction with the finite element method. The minimum crack spacing is obtained as a function of applied stress for different values of interface fracture toughness. A methodology to relate the saturated crack spacing to interface fracture toughness is developed. Interfaces are classified into three categories: weak, intermediate and strong. It is shown that in experiments of this type, quantitative information about the interface fracture toughness can be obtained for intermediate interfaces while qualitative information may be obtained for weak and strong interfaces.

Failure mechanisms and damage evolutionin crossply ceramic-matrix composites

Failure mechanisms were studied under the microscope in a crossply silicon carbide/glass-ceramiccomposite under axial tensile loading. Failure initiation takes place in the 90° layer. It takes the form of radial matrix cracks around the fibers, followed by interfacial cracks, which in turn coalesce into transverse macrocracks. These transverse macrocracks in the 90° layer reach a characteristic saturation crack density with a minimum crack spacing of the order of the layer thickness. Subsequently, transverse matrix cracks are generated in the 0° layer, increasing in density up to a minimum crack spacing of the order of eight fiber diameters. This stage of failure is accompanied by fiber-matrix debonding and some fiber-failures in the 0° layer. In the third stage of damage development, the macrocracks of the 90dlayer branch off and connect with the 0° layer cracks in a characteristic “delta” pattern. This is finally followed by delamination and additional cracking in the 90° layer prior to ultimate failure. The various failure mechanisms and their interactions were discussed and compared with predictions of prior experimental and analytical studies of unidirectional and crossply composites.

The behavior of ceramic matrix fiber composites under longitudinal loading

Failure mechanisms were studied by reflection light microscopy in a unidirectional silicon carbide/glass-ceramic composite loaded in longitudinal tension. The material behaves linearly up to the point where the first transverse matrix cracks appear. Thereafter, it undergoes a rapid stiffness decrease corresponding to matrix crack multiplication and saturation. These matrix cracks increase in density with applied stress up to a limiting level of 28 cracks/mm or a minimum crack spacing of 36 μm (0·0014 in), which corresponds approximately to two fiber diameters. Fiber breaks and fiber debonding, which start before matrix crack saturation, continue until final failure. In the last stage the material exhibits quasi-linear behavior with small stiffness variation. Experimental results of crack density and stress/strain behavior were compared with predictions based on a modified shear lag analysis.

Crack Spacing in Brittle Films on Elastic Substrates

An approximate, analytical solution is derived for the minimum spacing that can exist between a series of parallel cracks propagating in a thin film. The analysis is pertinent to the specific case of a film and substrate having identical elastic properties. In the absence of plasticity, only three parameters govern the minimum crack spacing. The cracks are predicted to be more closely spaced if the film stress or the film thickness is increased, or if the fracture toughness of the film is decreased.

Spacing of water‐free crevasses

On the basis of the analysis of the stability of an interacting system of straight edge cracks it is shown that when the fracture strength of the ice is taken to be nonzero, there exists a minimum spacing for water‐free crevasses (about 6–8 m). This spacing is, in general, much larger than the minimum crack spacing (about ⅓ m) needed in order to be able to attain the critical value of the stress intensity factor; and therefore, in general, the minimum spacing of the water‐free crevasses is dictated by the stability consideration, rather than by the consideration of the stresses alone. In terms of dimensionless parameters a master chart is developed which separates stable and unstable states. It is shown that the minimum spacing decreases with decreasing fracture strength of the ice, and when the fracture strength of the ice is taken to be zero, the spacing can be very small. At this limit the penetration depth is approximately given by the value found by Nye, which is then independent of the corresponding spacing.

Minimum Spacing of Thermally Induced Cracks in Brittle Solids

When the temperature at the free surface of a linearly elastic brittle half-plane, which is initially uniform throughout the solid, is suddenly reduced by a large amount and then kept constant thereafter, a thermal boundary layer whose thickness increases with time, forms close to the free surface. Because of the consequent thermal contraction, edge cracks may form within the thermal boundary layer. For a system of equally spaced straight-edge cracks, growing collinearly with increasing thickness of the thermal boundary layer, the average minimum crack spacing is estimated on the basis of: (a) energy consideration, (b) stress consideration, and (c) consideration of stability of the growth of interacting cracks. It is shown that for a given temperature profile, one can develop a general stability chart which, in particular, gives a complete growth regime of the interacting cracks (no crack branching is included).