Opening-mode Fractures Research Articles

Residual Stress and Opening-Mode Fracture Analysis of Multilayered Structures Subjected to Thermal Loading

AbstractTemperature change after formation commonly results in thermal residual stress in multilayered structures due to the different thermal and mechanical properties of each layer. In this paper...

Structural evolution and deformation near a tertiary salt weld, Willouran Ranges, south Australia

Abstract We combine insights from subsurface studies and published numerical models to propose a three-phase conceptual model that considers the potential deformation patterns that form during the emplacement, evacuation and welding, and post-welding phases of tertiary weld formation. The proposed model aims to: 1) help establish the timing of deformation adjacent to a tertiary weld based on the geometry of deformation patterns, and 2) serve as a guide for future work that examines deformation adjacent to tertiary welds and beneath allochthonous salt. We apply the model, along with new, 1:10,000 scale geological mapping and mesostructural analysis of deformation patterns along the Kingston tertiary salt weld and contiguous Witchelina-Breaden Hill salt canopy in the Willouran Ranges of South Australia to constrain the evolution of the allochthonous salt system and the style, extent, and timing of adjacent deformation. Deformation near the weld is dominated by opening mode fractures that exhibit spatial heterogeneity in their orientation both along the strike of allochthonous salt and in suprasalt versus subsalt strata. A halokinetic drape fold, decimeter to decameter scale folding, and localized debris flow deposits are present in subsalt strata, whereas no evidence of thrust imbricates, or laterally continuous shear and/or rubble zones was observed anywhere below the canopy-weld complex. We hypothesize that remnant evaporite distribution and the juxtaposition of units exert the primary, largest-scale control on the hydrological behavior of tertiary welds. The influence of deformation occurs at a much smaller scale and is more heterogeneous and difficult to predict. Higher resolution models and additional field studies are required to identify and rank the many variables that control this deformation.

Comparison of carbonate reservoir fractures from core and modern electrical borehole images

Abstract Several methods exist for collecting data about opening-mode fractures (hereinafter fractures) in subsurface reservoir rocks. The datasets, with the exception of core data, are indirect and subject to limited resolutions. This paper includes new results on the detection of fractures in carbonate reservoirs by modern electrical borehole imagers. Barren fractures and calcite-filled fractures (calcite veins) were described and compared from whole core and borehole images. These datasets were obtained from directional drilling into the Arab petroleum reservoirs in a low-relief dome structure in Eastern Arabia. The comparison of fracture abundance resulted in a significant mismatch, because many reservoir fractures in the core could not be detected from corresponding borehole images. Most calcite veins were undetected because of their small widths, below 2 mm. Exceptions include a few calcite veins of 0.5 mm that were detected because of the strong contrast between resistive veins and conductive host rock beds. The barren fractures that are aligned sub-parallel to the maximum horizontal principal stress (SHmax) were detected more abundantly than other non-aligned barren fractures. The present-day SHmax is roughly trending between 60° and 100° azimuth in Eastern Arabia. The aligned fractures have larger apertures in the borehole images than the non-aligned fractures. The apertures diminish in size as the fractures gradually deviate in orientation from the SHmax. Most of the non-aligned barren fractures were undetected, except the fractures with rough and mismatching walls. This indicates that the walls of the non-aligned fractures are mechanically closed by the normal SHmax, and that the remaining apertures were dependent on the availability of roughness mismatches between the closed fracture walls. Electrical borehole images are biased in measuring fracture abundance, but indispensable to detect and measure the orientations and apertures of fractures, especially the large (i.e., more conductive) fractures in reservoir rocks.

Tectonic Control on the Formation of Cleats in the Coal Beds of the Sajau Formation, Berau Basin, Northeast Kalimantan

DOI: 10.17014/ijog.5.3.235-250Coal seams of lignite- to subbituminous rank of Pliocene-age from the Sajau Formation of the Berau Basin are characterized by the presence of a natural fracture system, including cleats. Often, these opening-mode fractures consist of two orthogonal sets (face and butt cleats), both almost perpendicular to the bedding. This paper describes the distribution of orientation, spacing, and aperture of cleats formed in the seams of the Sajau Formation. All observations and measurements were conducted at macroscopic, mesoscopic, and microscopic scales. The butt cleat mean orientations are NE-SW and NW-SE, whereas the face cleat mean orientations are NNE-SSW and NE-SE, and the cleat dip is at a high angle of 75° to the north. The angles between the orientations of these cleat sets are nearly 90°; that is, they are orthogonal. The spacing of the macroface cleats is between 9.52 and 14.46 cm (averaging 11.61 cm), while the spacing of the butt cleats is between 2.3 and 11.3 cm (averaging 5.35 cm). The mean aperture is 0.54 mm. In contrast, the mean spacing of the mesoface cleats is 3.09 mm, and the aperture measurements of these cleats range from 0.0478 to 0.0741 mm (averaging 0.0549 mm). The results obtained from outcrops and X-ray CT (computed tomography) scan clearly indicate that the NNE-SSW face cleat orientations are strictly parallel to the elongation of the main tectonic structures in the studied area. Their origin may be explained by their relationship with local tectonic stress (the maximum principal stress, σ1, was horizontal). Partial least square analysis of data collected from cleats and faults in the area indicates that a power law distribution exists between the cleat characteristics (spacing, density, and aperture), and the distance of the faults (R2 = 0.56). Cleat formation in the Sajau Formation was mainly controlled by the mechanical response to tectonic stresses, which generated a unique cleat network in the coal. Based on the SEM photography, it is concluded that the development of microcleats in the Sajau Formation resulted from both endogenic processes and tectonic activities as indicated by the change in the shape of the cleats, from straight line to curved shape and branching (intersection of multiple cleats that form a conical network at the end).

Fluid pressure drops during stimulation of segmented faults in deep geothermal reservoirs

Hydraulic stimulation treatments required to produce deep geothermal reservoirs present the risk of generating induced seismicity. Understanding the processes that operate during the stimulation phase is critical for minimising and preventing the uncertainties associated with the exploitation of these reservoirs. It is especially important to understand how the phenomenon of induced seismicity is related to the pressurisation of networks of discrete fractures. In this study, we use the numerical simulator CFRAC to analyse pressure drops commonly observed during stimulation of deep geothermal wells. We develop a conceptual model of a fractured geothermal reservoir to analyse the conditions required to produce pressure drops and their consequences on the evolution of seismicity, fluid pressure, and fracture permeability throughout the system. For this, we combine two fracture sets, one able to be stimulated by shear-mode fracturing and another one able to be stimulated by opening-mode fracturing. With this combination, the pressure drop can be triggered by a seismic event in the shear-stimulated fracture that is hydraulically connected with an opening-mode fracture. Our results indicate that pressure drops are not produced by the new volume created by shear dilatancy, but by the opening of the conjugated tensile fractures. Finally, our results reveal that natural fracture/splay fracture interaction can potentially explain the observed pressure drops at the Rittershoffen geothermal site.

Quantifying vein attributes in massive mudstones (Triassic, SW England): Implications for progressive evolution of opening-mode fracture networks

Abstract Attributes of gypsum vein arrays in the Triassic massive mudstones of SW England were analyzed to infer the process of vein network evolution. Field data demonstrate that there is no clear correlation between vein orientation and thickness; however, sub-horizontal veins have a higher average thickness than the inclined veins. Vein thickness distribution is best characterized by a log-normal distribution. The fractal dimensions ‘D’ of vein networks analyzed range from 1.44 to 1.71. Vein networks, which contain abundant bridging veins between neighbouring sub-horizontal veins to form an anastomosing pattern, exhibit a higher D value. The fraction of vein volume derived from image analysis ranges from 6.75 to 17.94%. A positive correlation is revealed by plotting the fractal dimensions of the vein networks versus the number of vein-intersection points, suggesting that an anti-clustering distribution of veins could contribute to more interactions and also intersections of the gypsum veins. The vein attribute data presented indicate that mineralization in the massive mudstones is mainly localized to some of the largest veins as a result of mechanical interaction of neighbouring veins during vein propagation, hindering the nucleation of new veins as a consequence. Accommodation of the bulk rock strain could be facilitated mainly by expansion of the large, backbone veins, which follow a positive feedback mechanism of growth. This study reveals a strong link between the geometric parameters of opening-mode fractures with the history of their formation, propagation and intersection.

Effect of CO2–brine–rock interaction on fracture mechanical properties of CO2 reservoirs and seals

The effect of CO2–water–rock interactions on fracture mechanical properties of reservoir and seal rocks due to injection of CO2 in the subsurface may impact long-term (102–104 yr) storage security. At the Crystal Geyser and Salt Wash field sites near Green River, Utah, sandstone of the Salt Wash Member of the Morrison Formation and Mancos Shale have undergone chemical alteration associated with flow of CO2-bearing water under natural conditions over geologic time scales of 103–105 yrs. To quantify the effects of these diagenetic changes on rock fracture mechanical properties we conducted opening-mode fracture mechanics tests using the double torsion method on a suite of CO2-altered and unaltered siliciclastic samples. We show that dissolution of hematite and carbonate cement in Entrada Sandstone by CO2-rich brine lowers fracture toughness by nearly 40% relative to adjacent, unaltered samples from the same unit. In contrast, precipitation of calcite pore cement in a sandstone of the Salt Wash Member of the Morrison Formation, attributed to CO2 degassing during upward fluid flow along the Little Grand Wash Fault, results in a 100–700% increase in fracture toughness. Similarly, precipitation of carbonate mineral cements and replacement of matrix measurably strengthens Mancos Shale, considered a regional top seal. Subcritical fracture growth index (SCI) which quantifies reaction-assisted subcritical fracture propagation is also affected by CO2-related alteration. Based on previous numerical simulations of fracture network growth with varying fracture mechanical parameters, we find that the measured variations in fracture mechanical properties qualitatively match observed differences in opening-mode fracture distributions along the fault, with short, non-connected fractures in CO2-bleached rock, long, throughgoing fractures in calcite-cemented shale, and short, closely spaced, interconnected fracture networks in highly altered rock directly adjacent to fault conduits. Our fracture mechanics tests demonstrate that fracture mechanical properties of reservoir and seal rock can change as a result of chemical CO2–brine–rock interaction. These chemical interactions may favor or inhibit subcritical fracture growth processes and thus reservoir and seal flow properties. In regions of CO2-related mineral dissolution, subcritical fracture growth may reduce seal integrity over time scales beyond those of active injection and reservoir monitoring, thus negatively affecting seal integrity over the expected design lifetime of a CO2 reservoir.

Fractures in mudrocks: Advances in constraining timing and understanding mechanisms

Recent advances in fracture-timing techniques have led to new insights about sequences and mechanisms of fracture formation in mudrocks. Methods to constrain fracture timing in mudrocks include: (i) field evidence, including crosscutting relationships and evidence of compaction; (ii) petrographic evidence, including signs of soft-sediment deformation and diagnostic mineral assemblages or textures; (iii) stable-isotopic evidence; (iv) thermometric dating using burial history modelling; and (v) radiometric age-dating. In this contribution, we briefly review each method with salient examples from the literature. Many documented examples of mudrock-hosted fractures formed during early burial, a non-intuitive finding that demands a re-assessment of our assumptions about what types of materials can develop opening-mode fractures. In general, the style and distribution of fractures varies dramatically based on fracture timing, highlighting the importance of constraining timing for predicting fracture patterns and interpreting their mechanisms, including the role of fluid flow.

Reappraising columnar joints in different rock types and settings

Columnar joints comprise a network of opening-mode fractures that divide material into prismatic columns. They are known in several materials and rock types, including basalt, mud, sandstone, and starch. In all types, the resultant prismatic columns have a similar geometry, facilitating a comparison of columnar joints in different materials and processes such as cooling and drying. In this study, we provide a unique example of columnar joints in low-grade meta-chalks that are the product of spontaneous combustion metamorphism of organic-rich chalks in the “Mottled Zone Complex”, Israel. Although the geometry of the prismatic columns observed in these rocks resembles those seen in basalts, our approximate calculations, based on thermal expansion and temperature difference, show that contraction due to cooling is two orders of magnitude less than the measured contraction. Moreover, the cooling effect should be much more significant in high-grade (ca. 550–900 °C) rather than in low-grade (ca. 200 °C) rocks, but only the latter contain prismatic columns. The prismatic columns are restricted to a discrete stratigraphic level between 1 and 10 meters above a chert and phosphorite unit. We suggest that burning of organic matter in the protolith results in mass and volume losses, and is the principal process that leads to contraction. Changes in texture and pore-structure (recrystallization) accompany the contraction resulting in the rearrangement of the protolith into columnar meta-chalk. This intriguing example of columnar joints in meta-chalk indicates that the geometric similarity of prismatic columns should not serve as the sole argument for their formation during cooling.

Influence of microfluidic flow rates on the propagation of nano/microcracks in liquid core and hollow fibers

Melt-spinning is a conventional method for the production of synthetic fibers. The development of melt-spun liquid core or liquid filled fibers in which the liquid component is already incorporated during fiber spinning has been reported as a viable alternative to traditional hollow fibers. The elucidation of the mechanical behavior of this new type of bicomponent fiber is of interest, with particular emphasis on its fracture mechanics. In this paper we describe a microfluidics method used to induce liquid flows through these fibers (internal diameter 15–30 μm), aiming at analyzing the influence of flow rate on crack formation and/or propagation. Although only a very small number of fibers show the presence of cracks (1–4% of the tested specimens), it is possible to establish a clear correlation between flow rate and the appearance of cracks. The main fracture mechanism found to be operating in these melt-spun fibers is the type I (opening mode) fracture, evidenced as the internal pressure exerted by the liquid being injected through the fibers increases during microfluidic testing. As fiber spinning and drawing force the polymer chains that compose the sheath to be preferentially oriented in the fiber direction, the formation of axial cracks over transverse cracks is favored due to a lack of strong intermolecular interactions between polymer chains in the transverse direction of the fiber.

Interaction analysis of propagating opening mode fractures with veins using the Discrete Element Method

Cemented natural fractures (veins) in shale formations generate mechanical heterogeneities which contribute to complex hydraulic fracture network development. Lee et al. (JGR, 2015) experimentally investigated the interaction of propagating tensile fractures with calcite-filled veins in Marcellus shale using Semi-Circular Bend (SCB) tests. In this study, we investigate those experimental results with three-dimensional Discrete Element Method (DEM) modeling to gain further insight in the fracture interaction processes that generate hydraulic fracture complexity. In addition, we quantified the length of fracture diversion distance to show the effect of vein properties, including approach angle, thickness, strength, stiffness, penetration length, on fracture diversion results.The numerical results compared well with the laboratory fracture diversion results. There is a tendency towards fracture diversion as the approach angle becomes smaller and more oblique to the propagating fracture plane. As the stiffness of the vein increased, the microcrack-related damage increased and the bond breakages extended longer to either side of the main fracture path. Samples with thicker veins and increasing penetration length showed a weaker vein response; the induced fracture propagated for a longer distance in veins before kinking back into the rock matrix. In addition, the numerical model confirmed that the opening mode fracture initiated from the notch tip and the intergranular bond failure created microcracks within the vein before the approaching fracture intersected the vein. The failure mode of the bonds between discrete elements in the vein was predominantly tensile mode rather than shear.

Numerical methods for coupled fracture problems

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

Manufacturing and mechanical characterization of Al2O3/β-TCP/TiO2 biocomposite as a potential bone substitute

This paper focuses on the mechanical characterization of a bioceramic based on commercial alumina (Al2O3) mixed with synthesized tricalcium phosphate (β-TCP) and commercial titania powder (TiO2). The effect of β-TCP and TiO2 addition on the mechanical performance was investigated. After a sintering process at 1600 °C for 1 h, various mechanical properties of the samples have been studied, such as compressive strength, flexural strength, tensile strength, elastic modulus, and fracture toughness. The measurements of the elastic modulus (E) and the tensile strength (σ t ) were conducted using the modified Brazilian test while the compressive strength (σ c ) was determined through a compression test. Also, semi-circular bending (SCB) specimens were used to evaluate the flexural strength (σ f ) and the opening mode fracture toughness (K IC). From the main results, it was found that the best mechanical performance is obtained with the addition of 10 wt.% TCP and 5 wt.% TiO2. Alumina/10 wt.% tricalcium phosphate/5 wt.% titania composites displayed the highest values of mechanical properties and a good combination of compressive strength (σ c ≈ 352 MPa), flexural strength (σ f ≈ 98 MPa), tensile strength (σ t ≈ 86.65 MPa), and fracture toughness (K IC ≈ 13 MPa m1/2).

Analyzing of Wedge Splitting Test on Asphalt Pavement Using Optical Measurements

Abstract This paper dealt with the characterization of opening mode fracture using Digital Image Correlation, coupled with a kinematic approach. Tests were carried out using a Wedge Splitting sample made in asphalt concrete AC12. The asphalt concrete was provided in the RILEM-SIB. The samples were a bi-layered asphalt concrete with or without a carbon fiber grid at interface. During experimentation, the sample deformation was recorded by using Digital Image Correlation. Based on the optical measurements coupled with the analytical approach, the energy release rate was performed by means the crack relative displacement and stress intensity factors. Using an adjustment procedure, based on an iterative Newton–Raphson algorithm, the crack relative displacement factor was calculated from optical measurements. the stress intensity factor was estimated from an analytical approach. Furthermore, the crack opening displacement was measured from the mark tracking method. This approach allowed the assessment of fracture parameters for the real structures to be considered.

Spatial arrangement of faults and opening-mode fractures

Spatial arrangement is a fundamental characteristic of fracture arrays. The pattern of fault and opening-mode fracture positions in space defines structural heterogeneity and anisotropy in a rock volume, governs how faults and fractures affect fluid flow, and impacts our understanding of the initiation, propagation and interactions during the formation of fracture patterns. This special issue highlights recent progress with respect to characterizing and understanding the spatial arrangements of fault and fracture patterns, providing examples over a wide range of scales and structural settings. Five papers describe new methods and improvements of existing techniques to quantify spatial arrangement. One study unravels the time evolution of opening-mode fracture spatial arrangement, which are data needed to compare natural patterns with progressive fracture growth in kinematic and mechanical models. Three papers investigate the role of evolving diagenesis in localizing fractures by mechanical stratigraphy and nine discuss opening-mode fracture spatial arrangement. Two papers show the relevance of complex cluster patterns to unconventional reservoirs through examples of fractures in tight gas sandstone horizontal wells, and a study of fracture arrangement in shale. Four papers demonstrate the roles of folds in fracture localization and the development spatial patterns. One paper models along-fault friction and fluid pressure and their effects on fault-related fracture arrangement. Contributions address deformation band patterns in carbonate rocks and fault size and arrangement above a detachment fault. Three papers describe fault and fracture arrangements in basement terrains, and three document fracture patterns in shale. This collection of papers points toward improvement in field methods, continuing improvements in computer-based data analysis and creation of synthetic fracture patterns, and opportunities for further understanding fault and fracture attributes in the subsurface through coupled spatial, size, and pattern analysis.

Quantifying opening-mode fracture spatial organization in horizontal wellbore image logs, core and outcrop: Application to Upper Cretaceous Frontier Formation tight gas sandstones, USA

The Upper Cretaceous Frontier Formation is a naturally fractured gas-producing sandstone in Wyoming. Regionally, random and statistically more clustered than random patterns exist in the same upper to lower shoreface depositional facies. East-west- and north-south-striking regional fractures sampled using image logs and cores from three horizontal wells exhibit clustered patterns, whereas data collected from east-west-striking fractures in outcrop have patterns that are indistinguishable from random. Image log data analyzed with the correlation count method shows clusters ∼35 m wide and spaced ∼50 to 90 m apart as well as clusters up to 12 m wide with periodic inter-cluster spacings. A hierarchy of cluster sizes exists; organization within clusters is likely fractal. These rocks have markedly different structural and burial histories, so regional differences in degree of clustering are unsurprising. Clustered patterns correspond to fractures having core quartz deposition contemporaneous with fracture opening, circumstances that some models suggest might affect spacing patterns by interfering with fracture growth. Our results show that quantifying and identifying patterns as statistically more or less clustered than random delineates differences in fracture patterns that are not otherwise apparent but that may influence gas and water production, and therefore may be economically important.

Correlation analysis of fracture arrangement in space

We present new techniques that overcome limitations of standard approaches to documenting spatial arrangement. The new techniques directly quantify spatial arrangement by normalizing to expected values for randomly arranged fractures. The techniques differ in terms of computational intensity, robustness of results, ability to detect anti-correlation, and use of fracture size data. Variation of spatial arrangement across a broad range of length scales facilitates distinguishing clustered and periodic arrangements—opposite forms of organization—from random arrangements. Moreover, self-organized arrangements can be distinguished from arrangements due to extrinsic organization. Traditional techniques for analysis of fracture spacing are hamstrung because they account neither for the sequence of fracture spacings nor for possible coordination between fracture size and position, attributes accounted for by our methods.All of the new techniques reveal fractal clustering in a test case of veins, or cement-filled opening-mode fractures, in Pennsylvanian Marble Falls Limestone. The observed arrangement is readily distinguishable from random and periodic arrangements. Comparison of results that account for fracture size with results that ignore fracture size demonstrates that spatial arrangement is dominated by the sequence of fracture spacings, rather than coordination of fracture size with position. Fracture size and position are not completely independent in this example, however, because large fractures are more clustered than small fractures. Both spatial and size organization of veins here probably emerged from fracture interaction during growth. The new approaches described here, along with freely available software to implement the techniques, can be applied with effect to a wide range of structures, or indeed many other phenomena such as drilling response, where spatial heterogeneity is an issue.

What controls diffuse fractures in platform carbonates? Insights from Provence (France) and Apulia (Italy)

Fractures are widespread in rocks and regional opening-mode arrays are commonly ascribed to major tectonic events. However, fractures occur in otherwise undeformed rocks. Some of these are early-developed features independent of tectonics and forming a background network at regional scale.To overcome this lack of understanding, two hydrocarbon reservoir analogues from platform carbonates have been targeted: the Provence (SE France), and the Apulian platform (SE Italy). In both areas, an early fracturing stage has been observed, made of high-angle-to-bedding opening-mode fractures, and bed-parallel stylolites. These features developed synchronously during the first burial stages and prior to major tectonic events. The fracture sets are not genetically related to the present-day layering. Contrarily, fractures developed in a brittle media where facies transitions were not sharp and did not act as mechanical discontinuities.Carbonate facies distribution and early diagenetic imprint constrained the mechanical stratigraphy when fractures occurred. In addition, we observed that fractures related to late tectonic inversion were partly inhibited. Indeed, rock mechanical properties change through time. Characterizing the temporal evolution of carbonate rocks has revealed that diagenesis and sedimentary facies are the prime actors for brittleness and mechanical layering in carbonates.

Strengthening mechanism of channel steel plate for notched concrete beams against fracture: Test and numerical study

Concrete structures are intentionally built with notches or incomplete joints in many engineering practices to deal with complex loading conditions. It is of great significance to improve the crack resistance and the installation of a channel steel plate ahead of the purpose-built notch (or joint) tip may serve such a purpose. This paper presents an investigation into the strengthening mechanism of installing a channel steel plate at the head of a notch for concrete beams against opening mode fracture failure. Both test and numerical studies have been undertaken and particular attention is given to the effects of key factors on the load carrying capacity and the failure pattern. Two types of three-point bending tests were conducted on concrete beams with or without channel steel plate reinforcement for a comparison study. The test results demonstrated the capability of channel steel plate measure for increasing the beam load capacity, and the interface debonding and matrix cracking were responsible for the eventual failure of reinforced concrete beams. Correspondingly, finite element based numerical models were established to investigate the progressive cracking in test beams and the strengthening mechanism by the installation of a steel plate. A damage-plasticity material model was used for simulating the cracking development in concrete, whilst two different approaches were adopted for the steel-concrete interface modelling: one assumed a perfect bond while the other incorporated a discrete thin layer of interface to allow for potential debonding and slippage. A comparison between the numerical and test results was given, and the effects of key factors on the performance of beams with steel plate measure were investigated through parametric numerical studies. The paper ends with some discussions on the strengthening mechanism and conclusions.

An elasto-plastic solution for channel cracking of brittle coating on polymer substrate

In this article, an elasto-plastic channel-cracking model is presented to study the open-mode fracture of a thin layer brittle coating grown on a polymer substrate. A linear elastic shear interlayer is introduced to describe the stress transfer from the elasto-plastic substrate to the brittle coating, on basis of the shear-lag principle. The channel cracking behavior involves three stages: elastic, elasto-plastic and plastic stages, which are solved in a continuous manner based on the deformation status of the substrate. Explicit solutions are derived for the mutli-stage cracking process. Corresponding experimental tests for a titanium oxide (TiO2) coating on a poly (ethylene terephthalate) substrate are conducted. The fracture toughness of the coating layer is estimated based on the crack spacing versus layer thickness relationship at certain strain levels. This method is found to be more reliable than the traditional methods using crack onset strain. Parametric studies of the fracture energy release rate for the coating and interfacial compliance of the thin film system are conducted, through which the effect of plastic deformation on the channel cracking behavior is studied extensively. The results indicate that the tangent modulus of the substrate controls the evolution curvature of crack spacing where a smaller tangent modulus corresponds to a slower saturation of crack spacing. The energy release rate also varies significantly with the properties of the interlayer. The study highlights the necessity of an elasto-plastic model for the thin film systems of brittle coating on a plastic substrate.