Fracture Mechanical Properties Research Articles

Coconut coir fiber reinforced polypropylene composites: Investigation on fracture toughness and mechanical properties

Nowadays, research and development is focused on environmentally benign, sustainable materials to replace and reduce the dependence on existing petroleum-based products. In this framework, the growth of natural and man-made fiber reinforced composite materials is rising at a faster rate in the field of engineering and technology due to its promising characteristics. The current research work is focused on the development of coir fiber reinforced polypropylene composites (PPC) that is having widespread variety of applications and their characteristics are equivalent to present synthetic composites.The work is focused on the study of fracture toughness behavior of these composites and further characterization of mechanical properties. The fabrication of the specimen was carried out using Injection molding technique. Fracture toughness (Compact Tension) tests were done as per ASTM D-5045 standards. The Tensile, Impact, Flexural Strength, and Hardness tests were done to evaluate the mechanical characteristics. It is found that natural coconut coir fiber reinforced composites showed higher fracture toughness values and improved mechanical properties when compared to neat polypropylene.

Research on Anisotropic Fracture Mechanical Behavior of Cortical Bone with Combined Method of Fractal and Gray Level Co-Occurrence Matrix

The irregular fracture surface of cortical bone, which is caused by complex multilevel micro-nanostructure, reflects the mechanical properties and fracture mechanisms. It is of great significance to characterize some characteristic parameters from the fracture surfaces of bone. In this research, anisotropic fracture mechanical properties of bovine femoral cortical bone along transverse, longitudinal and radial direction are firstly obtained by three-point bend experiment. Then the fracture routes and fracture surfaces are observed by scanning electron microscope. The observation shows that the formed fracture surfaces, which are caused by different crack routes, are extremely rough and have complex textures. Lastly, the combined method of fractal and gray level co-occurrence matrix are adopted to describe the morphology of fracture surface of cortical bone objectively and quantitatively. It is shown that the fracture surface of cortical bone has obvious fractal characteristics and four statistical texture feature parameters (contrast,angular second moment, correlation and entropy) of GLCM of fracture surfaces can describe a certain fracture texture character. The relationship between the characteristic parameters and macroscopic mechanical properties are established. The quantitative analysis and automatic class identification for the fracture surfaces of cortical bone can be achieved.

Ex-vivo biomechanical testing of pig femur diaphysis B type fracture fixed by novel biodegradable bone glue

AimsThe aim of this study was to answer the question whether our newly developed injectable biodegradable “self-setting” polymer-composite as a bone adhesive is a good “bone-glue” candidate to efficiently fix comminuted fractures of pig femoral bones used as an ex-vivo experimental model. MethodsMechanical properties of adhesive prepared from α-tricalcium phosphate (TCP) powder and thermogelling copolymer were optimized by selecting the appropriate composition with adhesion enhancers based on dopamine and sodium iodinate. Setting time and injectability were controlled by rheology. Ex-vivo experiments of fixed pig bones were provided in terms of either the three-point bending test of bending wedge type fractured pig femurs (with LCP) or the axial compression test of 45° oblique fractured femurs (without LCP) in physiological saline solution at 37 °C. Fractured bones treated with optimized adhesive before and after bending tests were imaged by X-ray microtomography (μCT). ResultsBased on the rheological measurement, the adhesive modified with both dopamine and sodium iodinate exhibited optimal thixotropic properties required for injection via thin 22 G needle. This optimal adhesive composition showed an 8 min lag phase (processing time) followed by fast increase in storage modulus at 37 °C up to 1 GPa within 110 min. Self-setting of dopamine/iodinate modified adhesive was completed in 48 h exhibiting the maximum strength at compression of 7.98 MPa ± 1.39 MPa. Whereas unmodified adhesive failed in glue-to-bone adhesion, dopamine and dopamine/iodinate modified adhesive used for 45° oblique fracture fixation showed good and similar strength at compression (3.05 and 2.79 MPa, respectively). However, significantly higher elasticity of about 250% exhibited adhesive with iodinate enhancer. Moreover, mechanical properties of B2 fractures fixed with both LCP and dopamine/iodinate adhesive were approaching closely to the properties of original bone. Excellent adhesion between the adhesive and the bone fragments was proved by μCT. ConclusionThe polymer-composite bone adhesive modified with dopamine/iodinate exhibited very good fixation ability of femoral artificial comminuted fractures in an experimental model.

Interface behavior and tensile properties of Mg-14Li-3Al-2Gd sheets prepared by four-layer accumulative roll bonding

Mg-14Li-3Al-2Gd sheets were prepared by four-layer accumulative roll bonding (ARB) with two-step rolling in one cycle. The interface behavior of Mg-14Li-3Al-2Gd sheets was investigated, and the fracture morphology and mechanical properties of the alloy sheets were analyzed. Results show that, the number of grains in the direction of normal direction of the single-layer decreases rapidly and the grain size decreases gradually in the ARB process. With the increase of the ARB cycle, the microstructure evolution transits from single-layer evolution to multi-layer evolution gradually. Meanwhile, the strength, interfacial bond strength increases and plasticity decreases constantly.

Comprehensive fracture tests of concrete for the determination of mechanical fracture parameters

AbstractAdvanced experimental evaluation of the mechanical fracture properties of quasi‐brittle materials is an important part of the design, assessment, and computational modeling of structures made of these materials. The aim is to determine parameters independent of the test configuration or the size of the test specimens. This paper presents the results of an extensive experimental program which is part of the development of a comprehensive multilevel approach for experimental–computational determination of the mechanical fracture parameters of concrete. Three‐point bending and wedge‐splitting tests were performed simultaneously using three different geometrically similar specimen sizes and two well‐separated depths of initial notches. Before the start of the main testing program, the pilot tests that were performed were aimed at the design of the most appropriate concrete mixture. Special attention was paid to the selection of a maximum aggregate grain size. In order to study the process of concrete aging and the development of its mechanical properties, the accompanying destructive and non‐destructive tests were carried out at different ages of hardening. Fracture parameters were evaluated using the effective crack‐length formulation and work‐of‐fracture method. Finally, the size‐independent specific fracture energy was back‐calculated from the measured specific fracture energy.

Strength and fracture properties of roller compacted concrete (RCC) prepared by an in-situ compaction procedure

The use of roller compacted concrete (RCC) technology in pavement applications has been steadily increasing owing to its economical as well as practical advantages. Past literature studies on RCC mixtures, focused mainly on the effects of RCC mixtures on their strength and durability properties, and there is a lack in the fracture properties. In this experimental study, a total of seven different RCC mixtures were designed with four different binder ratios ranging from 200 kg/m3 to 600 kg/m3, and two different aggregate gradations with maximum aggregate sizes of 12 mm and 19 mm to investigate the effect of mixture design on RCC mechanical performance and fracture properties. All RCC mixtures were compacted in a plate mold with dimensions of 15x85x200 cm3 by applying first a vibratory plate compactor, then a double drum vibratory hand roller to simulate the actual field compaction procedures. Cores and prismatic beam specimens were taken from the plates to determine the strength and fracture properties of RCC mixtures. Single-point bending test was applied on the notched beams to determine the fracture parameters by using RILEM procedure based on the non-linear two parameter fracture model. According to the statistical analysis results, it was found that the strength and the fracture properties of RCC mixtures were affected not only by the mixture proportions but also by the compaction amount. Moreover, it was shown that the critical stress intensity factor (KIc) was enhanced with the increase of maximum aggregate size, compaction ratio, then binder dosage. On the other hand, critical crack tip opening displacement, CTODc seems to be affected only by the fine to total aggregate ratio or the maximum aggregate size.

Mechanical and fracture properties of alkali activated concrete containing different pozzolanic materials

Environmental considerations have caused the alkali-activated slag (AAS) cements to emerge as a promising sustainable substitute for the ordinary Portland cement (OPC). This study is aimed to the results of some comprehensive experimental researches performed on the AAS concrete with different types of partial replacement of binder including fly ash, silica fume, and red mud in terms of mechanical and different-mode fracture properties. According to the results, all AAS concrete mixes made with mineral admixtures (except 70% fly ash) exhibited mechanical strength comparable to that of the OPC concrete, and results of the fracture toughness in pure mode I (tensile opening), mode II (shear in-plane), and results of the fracture toughness in pure mode I (tensile opening), mode II (shear in-plane) and mode III (shear out-plane) showed that the trend of tensile and shear performance of concrete mixes are nearly similar. Based on the results of pull-off adhesion test and image processing, the high paste strength in different AAS concrete mixes caused a better aggregates-paste bonding strength.

Environmental influence on cracking and debonding of electrically conductive adhesives

Electrically conductive adhesives (ECAs) are starting to replace metallic solders in recent designs of photovoltaic (PV) modules. This transition represents a significant material change, and a proper understanding of the durability and reliability of the new interconnect needs to be established. This paper presents our continued work on developing a degradation model for ECA interconnects in PV modules. Here, we characterize the fracture mechanics properties of an epoxy-based ECA, for both critical and subcritical, mode I and mode II loading conditions. Emphasis is on the influence of different environmental conditions such as temperature and humidity. We use the Finite Element Method to account for residual stresses, induced by temperature changes and moisture absorption, and correct the apparent fracture toughness. We found that high moisture levels not only can weaken the fracture resistance of the ECA interconnect, but can also promote subcritical debonding at significantly lower driving forces than in dry environments.

Visualization and quantification of aggregate and fiber in self-compacting concrete using computed tomography for wedge splitting test

Wedge splitting test gained popularity as a stable and simple method to predict the fracture mechanism properties of concrete specimens. The present research focuses on understanding the behavior of self-compacting concrete specimens made with and without steel fibers tested using wedge splitting test, later scanned under high resolution computed tomography. The contribution of hooked end steel fiber and coarse aggregates in fiber reinforced specimens was compared without steel fiber reinforced concrete specimens using high resolution computed tomography. As fracture takes place across the plane perpendicular to the splitting force, i.e. along the depth of specimens. High resolution computed tomography technique was adopted in visualizing the changes taking place across the matrix, coarse aggregate and steel fibers, along with the specimen’s depth. Datasets of the images, obtained from computed tomography, after images analysis and volume reconstruction, revealed a higher coarse aggregate and steel fiber participation in the failure region of without and with fibers specimens. Computed tomography investigation indicated a total of 23 coarse aggregate and 64 steel fibers participated in resisting the failure, during wedge splitting test of without and with fibers specimens. Therefore, high resolution computed tomography can be used in understanding, quantifying the participation of coarse aggregate and steel fiber in the failure plane, under fracture loads.

Fracture behavior of Longmaxi shale with implications for subsurface applications

Fracture mechanical properties of shales have gained continued interest recently due to their critical role in many shale-related applications such as unconventional petroleum systems and subsurface carbon and waste disposal. However, due to their strong reactive nature to fluids, fracture mechanical properties of shales have not been extensively studied like other rock types. A more comprehensive understanding of fracture system development in shales under reactive fluids is needed for subsurface applications. We have measured fracture mechanical properties of Longmaxi shale outcrop samples in the Sichuan Basin, China, under different environments of ambient air, deionized water, saline fluids of NaCl and KCl at 0.5 M concentration, and acidic HCl fluid at pH of 5. All aqueous fluids tested show strong weakening effects on fracture propagation compared to the air environment, with the fracture toughness reduced by 75% and the subcritical fracture growth index reduced by 50%. Microstructural analysis reveals the predominantly grain boundary opening cracking mode for all tests, but the fracture traces branch more in reactive aqueous fluids. Natural fractures are comparable with artificial fractures in morphology. Bedding-perpendicular opening mode fractures with multiple-stage fracture fillings of calcite, quartz, and organic matters develop well in natural fractures. Our results suggest that clay mineral hydration and expansion are the main cause for the fluid weakening effect in Longmaxi shale, which has substantial implications for subsurface shale failure processes.

Properties of paving epoxy asphalt with epoxy-terminated hyperbranched polyester

ABSTRACT Epoxy asphalt is a high performance pavement material, but the poor toughness of epoxy asphalt at low temperature has limited its utilisation. Hyperbranched polyester (HBP) is a spherical polymer with highly branched structures, which can effectively improve the toughness of epoxy asphalt. However, hydroxyl-terminated HBP would accelerate the reaction rate of epoxy asphalt because of the rapid reaction between hydroxyl groups of HBP and epoxy groups of resin. We modified the hydroxyl end groups of HBP as epoxy end groups to avoid its curing reaction with epoxy resin and further reduce the viscosity of epoxy asphalt. Epoxy-terminated HBP also has good compatibility with epoxy resin to improve phase structure uniformity of epoxy asphalt. Moreover, with the help of hyperbranched structure, epoxy-terminated HBP still can improve the toughness of epoxy asphalt, which can be proved by the fracture surface morphology, mechanical properties, and dynamic thermomechanical properties.

Simplified approach for ductile fracture mechanics SSTT and its application to Eurofer97

Abstract The determination of fracture-mechanical properties is often very challenging, because the available standards like ASTM E1820 need specific size-requirements for the specimen dimensions to obtain valid fracture toughness. Especially in the ductile regime, where the presence of plasticity around the crack tip is affected by the multiaxial stress state and its triaxiality, the size-requirements are frequently not met. The fulfilment of the size-requirements needs the testing of big specimens, which is often not possible. If we now think of specimens, which are irradiated in test modules for future fusion reactors, their size cannot be as big as required, because the available volume for irradiation is restricted. This fact highlights the need of Small Specimens Test Techniques (SSTT) for the determination of fracture-mechanical properties in the ductile regime. The presented work focuses on an approach for the determination of fracture-mechanical properties in the ductile regime including stable crack growth and crack-resistance behavior. The authors have developed the initial approach some years ago and within this work the approach was simplified as much as possible. The basic idea of the approach is, that the crack growth can be simulated using Finite Element Method combined with a cohesive zone model. The cohesive zone model is a two parametric model, namely the cohesive stress σ c and the cohesive energy Γ c , which are identified on small specimens only. The new simplified approach was now validated on ferritic-martensitic steel Eurofer97 at room temperature. In the past, the approach used complicated features like a CCD camera system and has now been simplified in a way that no CCD camera system is required. The main part of the approach is the identification of cohesive zone parameters (cohesive stress σ c and energy Γ c ) on small specimens. The cohesive stress σ c can be determined on notched round tensile specimens with different notch root radius to account for different stress states or stress triaxialities in the specimen. With dedicated Finite Element modelling a local fracture stress dependent on stress triaxiality can be identified. The cohesive energy Γ c can be carried out by simulating the small fracture-mechanical specimen using the Finite Element Method combined with the cohesive zone model and parameter fitting to experimental results. The cohesive energy Γ c is treated to be identified, if the simulated crack-resistance curve describes the experimental behavior. After identification of these parameters, a big fracture-mechanical specimen can be simulated using the cohesive zone parameters already determined on small specimens. Finally, the crack-resistance curve of a big specimen can be predicted and a valid fracture toughness can be identified if the size-requirements of the big specimens are met. In case the requirements are not fulfilled, a bigger specimen geometry can be simulated until all size criteria are met. With this method, the testing of big specimens can be avoided. For the future there is a Round Robin exercise planned including defined test matrices to demonstrate the general applicability of the approach.

Experimental Study on the Mechanical Properties of Rock Fracture after Grouting Reinforcement

Grouting reinforcement plays an important role in repairing fractures and improving the strength of the surrounding rock. To address practical engineering challenges such as caving and chip off-falling of surrounding rock in deep roadways, normal splitting was adopted to prefabricate fractures on rock samples gathered from underground coal mines. This was done to better match the rock fracture specimen with actual conditions. Based on the elementary unit of a fracture surface, systematic experiments were conducted on the tensile properties of rock fractures after grouting reinforcement, and the shear properties were studied after considering the presence of gas. As per the results, the tensile strength of rock fractures increased with the increase in viscosity of grout, but the overall tensile strength was relatively low. The overall tensile effect of surrounding rock was improved less by grouting approach. When the presence of fracture gas in grouting was considered, the peak shear strength of fractures after grouting was 8.34–29.9% less than that without considering the fracture gas. The cemented pore surface produced by unsaturated cementation in the grouting reinforcement was the main cause of reduction in cohesion and frictional angle of rock fractures. The conclusions of this study have great significance for guiding engineering grouting and evaluating the grouting effect.

Fracture patterns and mechanical properties of GFRP bars as internal reinforcement in concrete structures

Glass Fiber Reinforced Plastic (GFRP) composites as rolled bars can be used as steel rebar to prevent oxidation or rust which is one of the main reasons concrete structures deteriorate when exposed to chlorides and other harmful chemicals. GFRP is successful alternative for reinforcement with high tensile strength- low strain, corrosion resistance and congenital electromagnetic neutrality in terms of longer service life. The main goal of the study is to investigate the mechanical and bonding properties of GFRP bars and equivalent steel reinforcing bars then compare them. GFRP and steel rebar are embedded in concrete block with three different levels. Mechanical properties of GFRP and steel bars in terms of strength and strains are determined. On the other hand; modulus of elasticity of GFRP and steel bars, modulus of toughness and modulus of resilience were calculated using stress-strain curves, as a result of the experiments. Pull-out tests are conducted on each GFRP and rebar samples which are embedded in concrete for each embedment level and ultimate adherence strengths are determined in terms of bar diameter–development length ratio. Yield strength, strain and modulus of elasticities of GFRP samples are compared to steel rebar. According to the test results reported in this study, GFRP bars are used safely instead of steel bars in terms of mechanical properties.

Whey protein gel — mechanical cleaning capability through modelling and experimental testing including compression and wire cutting investigation

Abstract Whey protein has been used extensively to investigate the efficiency of procedures for cleaning dairy production equipment owing to the chemical reaction it undergoes at high temperature, similar to the formation of fouling deposits during heat treatment. In addition to the chemical and thermal aspects, a detailed understanding of the fundamental mechanical and fracture mechanisms that significantly influence the success of the cleaning procedure is indispensable. Consequently, to determine the basis for the mechanical detachment of whey protein isolate, in the present study, the mechanical characteristics and fracture properties of whey protein gels (WPGs) with a protein content of 15% and a treatment temperature of 80 °C were determined. For purely mechanical characterisation, axial compression and compression relaxation experiments were performed. The results suggest a non-linear stress–stretch behaviour combined with time-dependent mechanical characteristics. To characterise the fracture properties of WPGs, wire cutting experiments were performed. Based on a viscoelastic numerical model and the corresponding parameters identified from the experimental investigations, the cutting procedure of WPGs was simulated by assigning a fracture criterion, and the critical stress was determined based on the measured cutting forces.

Research into the mechanical properties of wet-sprayed polypropylene fibre-reinforced concrete

As the depth of mines increases, the in situ stress increases gradually, resulting in increasingly demanding requirements for the support strength of coal-mine roadways and making it more difficult to provide this support. For this reason, more effective forms of support are needed. Concrete is a typical support form, but ordinary concrete has low support strength, cracks easily and is prone to brittle failure, whereas polypropylene fibre-reinforced concrete has a good inhibition effect on crack propagation and can remarkably improve the post-cracking performance and toughness of concrete. This paper studies the mechanical properties and application effects of wet-sprayed polypropylene fibre concrete in the mining context. A final mix proportion is obtained, a flexural toughness test on the round slabs of the concrete is conducted, and the corresponding initial cracking strength, peak strength, fracture energy and toughness are studied. This wet-sprayed polypropylene fibre concrete was applied and its application effect investigated. The results show that wet-sprayed polypropylene fibre concrete has advantages such as enhanced integrity and more uniform stress distribution. The initial cracking strength, peak load and energy absorbed of wet-sprayed polypropylene fibre concrete specimens are higher than those of dry-sprayed reinforcing mesh concrete specimens. An engineering practice application indicates that the resilience rate and dust concentration were significantly reduced during wet-sprayed polypropylene fibre concrete construction, and construction efficiency and economic benefits clearly increased. The research achievements are of great theoretical and practical significance in developing a further understanding of the fracture instability mechanism and mechanical properties of wet-sprayed polypropylene fibre concrete. This method may be applied widely in sinking and driving engineering to improve the support effect and ensure mine safety.

Density functional theory calculation of fracture surfaces of siderite and hematite

The relationship between the fracture surface and mechanical properties of siderite and hematite was studied by density functional theory (DFT). The mechanical properties of crystals with an O-vacancy defect were also investigated to take into account the ubiquitous defects present in both minerals. Colored contour surfaces were generated to illustrate the elastic anisotropy of siderite and hematite with or without a defect. The calculated elastic-constant matrixes showed that shear deformation is the most likely deformation type in the crystals with or without a defect. The O-vacancy defect in both mineral types alters their crystal. Specifically, for siderite, the B/G ratio decreased to 1.66 in the presence of this defect, indicating a significant change in the brittle/ductile behavior of the crystal. The contour surfaces indicated that the symmetry of the distribution of mechanical properties was unaffected by the defects. For both siderite and hematite, the diagonal surfaces were weakest, so the (110), (101), and (011) planes were predicted to be the most commonly fractured surfaces. This was consistent with the surface fracture behavior of trigonal systems according to previous literature. This study provides a novel understanding of the link between the fracture surface and the mechanical properties of crystals.

Fracture toughness and crack propagation behavior of nanoscale beryllium oxide graphene-like structures: A molecular dynamics simulation analysis

Defects present in the structure of nanostructures strongly affect and determine their performance, especially at high loadings and temperatures. Herein, molecular dynamics simulation (MD) was employed to theoretically pattern the fracture toughness, mechanical properties and crack propagation behavior of the defective monolayers of beryllium oxide graphene-like nanostructures (BeOGLNSs) subjected to some shape defects. The significance of this work lies in the ability to analyzing the mechanical behavior of BeOGLNSs as a key semiconductive structure with high bandgap, possessing great potential for the usage in electronics industry. Using Tersoff potential and periodic boundary conditions, samples of various kinds of defects were modeled to examine their mechanical properties as well as toughness varying the temperature. The results revealed that the mechanical properties of both pristine and defective BeOGLNSs were decreased by increasing the temperature as well as the dimensions of the defects. The Young’s modulus of the nanosheets with the crack length of 150 Å, circular and square notches of diameters 150 Å decreased at room temperature by about 66%, 77%, and 64%, respectively. A similar behavior was observed for the failure stress and failure strain. Moreover, higher stress concentration in the corners was the reason why the samples with square defects revealed the weakest properties. Furthermore, stress intensity factor of BeGLONSs was increased by enlargement of the crack dimension. Eventually, the defects were propagated along a direction perpendicular to the stress loading, while the detrimental effect of temperature on the failure stress was lowered once the dimension of the defect increased.

Identification of Fracture Mechanic Properties of Concrete and Analysis of Shear Capacity of Reinforced Concrete Beams without Transverse Reinforcement.

The study of new and innovative quasi-brittle materials offers new possibilities for use in construction, but detailed knowledge of their behavior and mechanical properties is required. The use of new materials in the design solution of a structure is usually associated with numerical methods, which has a number of both advantages and disadvantages. Sophisticated numerical methods, without a sufficiently detailed input knowledge, can provide highly variable results with little informative value. The main goal of this article is to present the procedure for the identification of fracture mechanical parameters for a specific concrete with the use of developed inverse analysis combining multi-criteria decision analysis, stochastic modelling and nonlinear analysis. Subsequently, the identified mechanical parameters of concrete are used for the parametric study of shear resistance of structural beams without shear reinforcement, as an alternative or generalized approach to the study of damage to concrete and concrete structures. This research includes an experimental program using 24 reinforced concrete beams and a detailed determination of basic and specific mechanical properties during laboratory tests. The process of inverse analysis is illustrated in detail for the solved task. The use of nonlinear analysis for detailed failure modelling is based on a 3D computational model and a fracture plastic material model for concrete. Finally, the results of the experimental program and numerical modelling are discussed, leading to a number of conclusions.

Improved fracture resistance of the Ag/SnO2 contact materials using Cu nanoparticles as additive

For improving fracture resistance, metal Cu nanoparticles were used as additive in Ag/SnO2 contact materials. The fracture behaviors and mechanical properties of the Ag-8wt%SnO2 contact materials adding nano Cu additive were investigated by tensile tests. The fracture morphologies and strain distributions of the tensile samples were characterized using a scanning electron microscope (SEM) equipped with an EBSD system. The test results showed that the uniform elongation and yield stress of the Ag/SnO2 materials were significantly increased with the addition of nano Cu additive. Many dimples with different sizes were generated around SnO2 particles, indicating an obvious improvement of plastic deformation ability. The results of EBSD analysis revealed that the highest misorientation value occurred in the interfaces between SnO2 and Ag matrix. And, the plastic deformation region was mainly distributed near the larger SnO2-rich phase during tension. Due to the existence of fine Cu phase at the interfaces of SnO2 and Ag, the initiation and propagation of the intergranular cracks were effectively suppressed. More importantly, the Ag/SnO2 contact materials with nano Cu additive exhibited an excellent creep resistance because of the increased interfacial strength and plastic strain.