Search results for: transversely isotropic

Authors: Evy Van Puymbroeck, Wim Nagy, Ken Schotte, Heng Fang, Hans De Backer

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The knowledge of residual stresses for welded bridge components is essential to determine the effect of the residual stresses on the fatigue life behavior. The residual stresses of an orthotropic bridge deck are determined by simulating the welding process with finite element modelling. The stiffener is placed on top of the deck plate before welding. A chained thermal-mechanical analysis is set up to determine the distribution of residual stresses for the bridge deck. First, a thermal analysis is used to determine the temperatures of the orthotropic deck for different time steps during the welding process. Twin wire submerged arc welding is used to construct the orthotropic plate. A double ellipsoidal volume heat source model is used to describe the heat flow through a material for a moving heat source. The heat input is used to determine the heat flux which is applied as a thermal load during the thermal analysis. The heat flux for each element is calculated for different time steps to simulate the passage of the welding torch with the considered welding speed. This results in a time dependent heat flux that is applied as a thermal loading. Thermal material behavior is specified by assigning the properties of the material in function of the high temperatures during welding. Isotropic hardening behavior is included in the model. The thermal analysis simulates the heat introduced in the two plates of the orthotropic deck and calculates the temperatures during the welding process. After the calculation of the temperatures introduced during the welding process in the thermal analysis, a subsequent mechanical analysis is performed. For the boundary conditions of the mechanical analysis, the actual welding conditions are considered. Before welding, the stiffener is connected to the deck plate by using tack welds. These tack welds are implemented in the model. The deck plate is allowed to expand freely in an upwards direction while it rests on a firm and flat surface. This behavior is modelled by using grounded springs. Furthermore, symmetry points and lines are used to prevent the model to move freely in other directions. In the thermal analysis, a mechanical material model is used. The calculated temperatures during the thermal analysis are introduced during the mechanical analysis as a time dependent load. The connection of the elements of the two plates in the fusion zone is realized with a glued connection which is activated when the welding temperature is reached. The mechanical analysis results in a distribution of the residual stresses. The distribution of the residual stresses of the orthotropic bridge deck is compared with results from literature. Literature proposes uniform tensile yield stresses in the weld while the finite element modelling showed tensile yield stresses at a short distance from the weld root or the weld toe. The chained thermal-mechanical analysis results in a distribution of residual weld stresses for an orthotropic bridge deck. In future research, the effect of these residual stresses on the fatigue life behavior of welded bridge components can be studied.

Keywords: finite element modelling, residual stresses, thermal-mechanical analysis, welding simulation

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Authors: M. N. Nwodo, Y. P. Cheng, N. H. Minh

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In the process of recovering oil in weak sandstone formations, the strength of sandstones around the wellbore is weakened due to the increase of effective stress/load from the completion activities around the cavity. The weakened and de-bonded sandstone may be eroded away by the produced fluid, which is termed sand production. It is one of the major trending subjects in the petroleum industry because of its significant negative impacts, as well as some observed positive impacts. For efficient sand management therefore, there has been need for a reliable study tool to understand the mechanism of sanding. One method of studying sand production is the use of the widely recognized Discrete Element Method (DEM), Particle Flow Code (PFC3D) which represents sands as granular individual elements bonded together at contact points. However, there is limited knowledge of the particle-scale behavior of the weak sandstone, and the parameters that affect sanding. This paper aims to investigate the reliability of using PFC3D and a simple Darcy flow in understanding the sand production behavior of a weak sandstone. An isotropic tri-axial test on a weak oil sandstone sample was first simulated at a confining stress of 1MPa to calibrate and validate the parallel bond models of PFC3D using a 10m height and 10m diameter solid cylindrical model. The effect of the confining stress on the number of bonds failure was studied using this cylindrical model. With the calibrated data and sample material properties obtained from the tri-axial test, simulations without and with fluid flow were carried out to check on the effect of Darcy flow on bonds failure using the same model geometry. The fluid flow network comprised of every four particles connected with tetrahedral flow pipes with a central pore or flow domain. Parametric studies included the effects of confining stress, and fluid pressure; as well as validating flow rate – permeability relationship to verify Darcy’s fluid flow law. The effect of model size scaling on sanding was also investigated using 4m height, 2m diameter model. The parallel bond model successfully calibrated the sample’s strength of 4.4MPa, showing a sharp peak strength before strain-softening, similar to the behavior of real cemented sandstones. There seems to be an exponential increasing relationship for the bigger model, but a curvilinear shape for the smaller model. The presence of the Darcy flow induced tensile forces and increased the number of broken bonds. For the parametric studies, flow rate has a linear relationship with permeability at constant pressure head. The higher the fluid flow pressure, the higher the number of broken bonds/sanding. The DEM PFC3D is a promising tool to studying the micromechanical behavior of cemented sandstones.

Keywords: discrete element method, fluid flow, parametric study, sand production/bonds failure

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Authors: Carla M. Machado, André A. Silva, Armando Bastos, Telmo G. Santos, J. Pamies Teixeira

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Advanced high-strength steels (AHSS) are increasingly being used in automotive components. The use of AHSS sheets plays an important role in reducing weight, as well as increasing the resistance to impact in vehicle components. However, the large-scale use of these sheets becomes more difficult due to the limitations during the forming process. Such limitations are due to the elastically driven change of shape of a metal sheet during unloading and following forming, known as the springback effect. As the magnitude of the springback tends to increase with the strength of the material, it is among the most worrisome problems in the use of AHSS steels. The prediction of strain hardening, especially under non-proportional loading conditions, is very limited due to the lack of constitutive models and mainly due to very limited experimental tests. It is very clear from the literature that in experimental terms there is not much work to evaluate deformation behavior under real conditions, which implies a very limited and scarce development of mathematical models for these conditions. The Bauschinger effect is also fundamental to the difference between kinematic and isotropic hardening models used to predict springback in sheet metal forming. It is of major importance to deepen the phenomenological knowledge of the mechanical and microstructural behavior of the materials, in order to be able to reproduce with high fidelity the behavior of extension of the materials by means of computational simulation. For this, a multi phenomenological analysis and characterization are necessary to understand the various aspects involved in plastic deformation, namely the stress-strain relations and also the variations of electrical conductivity and magnetic permeability associated with the metallurgical changes due to plastic deformation. Aiming a complete mechanical-microstructural characterization, uniaxial tensile tests involving successive cycles of loading and unloading were performed, as well as biaxial tests such as the Erichsen test. Also, nondestructive evaluation comprising eddy currents to verify microstructural changes due to plastic deformation and ultrasonic tests to evaluate the local variations of thickness were made. The material parameters for the stable yield function and the monotonic strain hardening were obtained using uniaxial tension tests in different material directions and balanced biaxial tests. Both the decrease of the modulus of elasticity and Bauschinger effect were determined through the load-unload tensile tests. By means of the eddy currents tests, it was possible to verify changes in the magnetic permeability of the material according to the different plastically deformed areas. The ultrasonic tests were an important aid to quantify the local plastic extension. With these data, it is possible to parameterize the different models of kinematic hardening to better approximate the results obtained by simulation with the experimental results, which are fundamental for the springback prediction of the stamped parts.

Keywords: advanced high strength steel, Bauschinger effect, sheet metal forming, springback

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Authors: Adil Murtaza, Muhammad Tahir Khan, Awais Ghani, Chao Zhou, Sen Yang, Xiaoping Song

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The morphotropic phase boundary (MPB); a boundary between two different crystallographic symmetries in the composition–temperature phase diagram has been widely studied in ferroelectrics and recently has drawn interest in ferromagnets for obtaining enhanced large field-induced strain. At MPB, the system gets a compressed free energy state, which allows the polarization to freely rotate and hence results in a high magnetoelastic response (e.g., high magnetization, low coercivity, and large magnetostriction). Based on the same mechanism, we designed MPB in a ferromagnetic Tb₁₋ₓNdₓCo₂ system. The temperature-dependent magnetization curves showed spin reorientation (SR); which can be explained by a two-sublattice model. Contrary to previously reported MPB involved ferromagnetic systems, the MPB composition of Tb₀.₃₅Nd₀.₆₅Co₂ exhibits a low saturation magnetization (MS), indicating a compensation of the Tb and Nd magnetic moments at MPB. The coercive field (HC) under a low magnetic field and first anisotropy constant (K₁) shows a minimum value at MPB composition of x=0.65. A detailed spin configuration diagram is provided for the Tb₁₋ₓNdₓCo₂ around the composition for the anisotropy compensation; this can guide the development of novel magnetostrictive materials. The anisotropic magnetostriction (λS) first decreased until x=0.8 and then continuously increased in the negative direction with further increase of Nd concentration. In addition, the large ratio between magnetostriction and the absolute values of the first anisotropy constant (λS/K₁) appears at MPB, indicating that Tb₀.₃₅Nd₀.₆₅Co₂ has good magnetostrictive properties. Present work shows an anomalous type of MPB in ferromagnetic materials, revealing that MPB can also lead to a weakening of magnetoelastic behavior as shown in the ferromagnetic Tb₁₋ₓNdₓCo₂ system. Our work shows the universal presence of MPB in ferromagnetic materials and suggests the differences between different ferromagnetic MPB systems that are important for substantial improvement of magnetic and magnetostrictive properties. Based on the results of this study, similar MPB effects might be achieved in other ferroic systems that can be used for technological applications. The finding of magnetic MPB in the ferromagnetic system leads to some important significances. First, it provides a better understanding of the fundamental concept of spin reorientation transitions (SRT) like ferro-ferro transitions are not only reorientation of magnetization but also crystal symmetry change upon magnetic ordering. Second, the flattened free energy corresponding to a low energy barrier for magnetization rotation and enhanced magnetoelastic response near MPB. Third, to attain large magnetostriction with MPB approach two terminal compounds have different easy magnetization directions below Curie temperature Tc in order to accomplish the weakening of magnetization anisotropy at MPB (as in ferroelectrics), thus easing the magnetic domain switching and the lattice distortion difference between two terminal compounds should be large enough, e.g., lattice distortion of R symmetry ˃˃ lattice distortion of T symmetry). So that the MPB composition agrees to a nearly isotropic state along with large ‘net’ lattice distortion, which is revealed in a higher value of magnetostriction.

Keywords: magnetization, magnetostriction, morphotropic phase boundary (MPB), phase transition

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Authors: Lijuan Li

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Nitric oxide (NO) has become a fascinating entity in biological chemistry over the past few years. It is a gaseous lipophilic radical molecule that plays important roles in several physiological and pathophysiological processes in mammals, including activating the immune response, serving as a neurotransmitter, regulating the cardiovascular system, and acting as an endothelium-derived relaxing factor. NO functions in eukaryotes both as a signal molecule at nanomolar concentrations and as a cytotoxic agent at micromolar concentrations. The latter arises from the ability of NO to react readily with a variety of cellular targets leading to thiol S-nitrosation, amino acid N-nitrosation, and nitrosative DNA damage. Nitric oxide can readily bind to metals to give metal-nitrosyl (M-NO) complexes. Some of these species are known to play roles in biological NO storage and transport. These complexes have different biological, photochemical, or spectroscopic properties due to distinctive structural features. These recent discoveries have spawned a great interest in the development of transition metal complexes containing NO, particularly its iron complexes that are central to the role of nitric oxide in the body. Spectroscopic evidence would appear to implicate species of “Fe(NO)2+” type in a variety of processes ranging from polymerization, carcinogenesis, to nitric oxide stores. Our research focuses on isolation and structural studies of non-heme iron nitrosyls that mimic biologically active compounds and can potentially be used for anticancer drug therapy. We have shown that reactions between Fe(NO)2(CO)2 and a series of imidazoles generated new non-heme iron nitrosyls of the form Fe(NO)2(L)2 [L = imidazole, 1-methylimidazole, 4-methylimidazole, benzimidazole, 5,6-dimethylbenzimidazole, and L-histidine] and a tetrameric cluster of [Fe(NO)2(L)]4 (L=Im, 4-MeIm, BzIm, and Me2BzIm), resulted from the interactions of Fe(NO)2 with a series of substituted imidazoles was prepared. Recently, a series of sulfur bridged iron di nitrosyl complexes with the general formula of [Fe(µ-RS)(NO)2]2 (R = n-Pr, t-Bu, 6-methyl-2-pyridyl, and 4,6-dimethyl-2-pyrimidyl), were synthesized by the reaction of Fe(NO)2(CO)2 with thiols or thiolates. Their structures and properties were studied by IR, UV-vis, 1H-NMR, EPR, electrochemistry, X-ray diffraction analysis and DFT calculations. IR spectra of these complexes display one weak and two strong NO stretching frequencies (νNO) in solution, but only two strong νNO in solid. DFT calculations suggest that two spatial isomers of these complexes bear 3 Kcal energy difference in solution. The paramagnetic complexes [Fe2(µ-RS)2(NO)4]-, have also been investigated by EPR spectroscopy. Interestingly, the EPR spectra of complexes exhibit an isotropic signal of g = 1.998 - 2.004 without hyperfine splitting. The observations are consistent with the results of calculations, which reveal that the unpaired electron dominantly delocalize over the two sulfur and two iron atoms. The difference of the g values between the reduced form of iron-sulfur clusters and the typical monomeric di nitrosyl iron complexes is explained, for the first time, by of the difference in unpaired electron distributions between the two types of complexes, which provides the theoretical basis for the use of g value as a spectroscopic tool to differentiate these biologically active complexes.

Keywords: di nitrosyl iron complex, metal nitrosyl, non-heme iron, nitric oxide

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Authors: Gyu-Dong Kim, Wuk-Jae Yoo, Sang-Youl Lee

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Composite structures offer numerous advantages over conventional structural systems in the form of higher specific stiffness and strength, lower life-cycle costs, and benefits such as easy installation and improved safety. Recently, there has been a considerable increase in the use of composites in engineering applications and as wraps for seismic upgrading and repairs. However, these composites deteriorate with time because of outdated materials, excessive use, repetitive loading, climatic conditions, manufacturing errors, and deficiencies in inspection methods. In particular, damaged fibers in a composite result in significant degradation of structural performance. In order to reduce the failure probability of composites in service, techniques to assess the condition of the composites to prevent continual growth of fiber damage are required. Condition assessment technology and nondestructive evaluation (NDE) techniques have provided various solutions for the safety of structures by means of detecting damage or defects from static or dynamic responses induced by external loading. A variety of techniques based on detecting the changes in static or dynamic behavior of isotropic structures has been developed in the last two decades. These methods, based on analytical approaches, are limited in their capabilities in dealing with complex systems, primarily because of their limitations in handling different loading and boundary conditions. Recently, investigators have introduced direct search methods based on metaheuristics techniques and artificial intelligence, such as genetic algorithms (GA), simulated annealing (SA) methods, and neural networks (NN), and have promisingly applied these methods to the field of structural identification. Among them, GAs attract our attention because they do not require a considerable amount of data in advance in dealing with complex problems and can make a global solution search possible as opposed to classical gradient-based optimization techniques. In this study, we propose an alternative damage-detection technique that can determine the degraded stiffness distribution of vibrating laminated composites made of Glass Fiber-reinforced Polymer (GFRP). The proposed method uses a modified form of the bivariate Gaussian distribution function to detect degraded stiffness characteristics. In addition, this study presents a method to detect the fiber property variation of laminated composite plates from the micromechanical point of view. The finite element model is used to study free vibrations of laminated composite plates for fiber stiffness degradation. In order to solve the inverse problem using the combined method, this study uses only first mode shapes in a structure for the measured frequency data. In particular, this study focuses on the effect of the interaction among various parameters, such as fiber angles, layup sequences, and damage distributions, on fiber-stiffness damage detection.

Keywords: stiffness detection, fiber damage, genetic algorithm, layup sequences

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Authors: Andres Nieto-Leal, Victor N. Kaliakin, Tania P. Molina

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The nature of most engineering materials is quite complex. It is, therefore, difficult to devise a general mathematical model that will cover all possible ranges and types of excitation and behavior of a given material. As a result, the development of mathematical models is based upon simplifying assumptions regarding material behavior. Such simplifications result in some material idealization; for example, one of the simplest material idealization is to assume that the material behavior obeys the elasticity. However, soils are nonhomogeneous, anisotropic, path-dependent materials that exhibit nonlinear stress-strain relationships, changes in volume under shear, dilatancy, as well as time-, rate- and temperature-dependent behavior. Over the years, many constitutive models, possessing different levels of sophistication, have been developed to simulate the behavior geomaterials, particularly cohesive soils. Early in the development of constitutive models, it became evident that elastic or standard elastoplastic formulations, employing purely isotropic hardening and predicated in the existence of a yield surface surrounding a purely elastic domain, were incapable of realistically simulating the behavior of geomaterials. Accordingly, more sophisticated constitutive models have been developed; for example, the bounding surface elastoplasticity. The essence of the bounding surface concept is the hypothesis that plastic deformations can occur for stress states either within or on the bounding surface. Thus, unlike classical yield surface elastoplasticity, the plastic states are not restricted only to those lying on a surface. Elastoplastic bounding surface models have been improved; however, there is still need to improve their capabilities in simulating the response of anisotropically consolidated cohesive soils, especially the response in extension tests. Thus, in this work an improved constitutive model that can more accurately predict diverse stress-strain phenomena exhibited by cohesive soils was developed. Particularly, an improved rotational hardening rule that better simulate the response of cohesive soils in extension. The generalized definition of the bounding surface model provides a convenient and elegant framework for unifying various previous versions of the model for anisotropically consolidated cohesive soils. The Generalized Bounding Surface Model for cohesive soils is a fully three-dimensional, time-dependent model that accounts for both inherent and stress induced anisotropy employing a non-associative flow rule. The model numerical implementation in a computer code followed an adaptive multistep integration scheme in conjunction with local iteration and radial return. The one-step trapezoidal rule was used to get the stiffness matrix that defines the relationship between the stress increment and the strain increment. After testing the model in simulating the response of cohesive soils through extensive comparisons of model simulations to experimental data, it has been shown to give quite good simulations. The new model successfully simulates the response of different cohesive soils; for example, Cardiff Kaolin, Spestone Kaolin, and Lower Cromer Till. The simulated undrained stress paths, stress-strain response, and excess pore pressures are in very good agreement with the experimental values, especially in extension.

Keywords: bounding surface elastoplasticity, cohesive soils, constitutive model, modeling of geomaterials

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Authors: Jenifer Alam, Rima Chatterjee

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Upper Assam sedimentary basin is one of the oldest commercially producing basins of India. Being in a tectonically active zone, estimation of tectonic strain and stress magnitudes has vast application in hydrocarbon exploration and exploitation. This East North East –West South West trending shelf-slope basin encompasses the Bramhaputra valley extending from Mikir Hills in the southwest to the Naga foothills in the northeast. Assam Shelf lying between the Main Boundary Thrust (MBT) and Naga Thrust area is comparatively free from thrust tectonics and depicts normal faulting mechanism. The study area is bounded by the MBT and Main Central Thrust in the northwest. The Belt of Schuppen in the southeast, is bordered by Naga and Disang thrust marking the lower limit of the study area. The entire Assam basin shows low-level seismicity compared to other regions of northeast India. Pore pressure (PP), vertical stress magnitude (SV) and horizontal stress magnitudes have been estimated from two wells - N1 and T1 located in Upper Assam. N1 is located in the Assam gap below the Bramhaputra river while T1, lies in the Belt of Schuppen. N1 penetrates geological formations from top Alluvial through Dhekiajuli, Girujan, Tipam, Barail, Kopili, Sylhet and Langpur to the granitic basement while T1 in trusted zone crosses through Girujan Suprathrust, Tipam Suprathrust, Barail Suprathrust to reach Naga Thrust. Normal compaction trend is drawn through shale points through both wells for estimation of PP using the conventional Eaton sonic equation with an exponent of 1.0 which is validated with Modular Dynamic Tester and mud weight. Observed pore pressure gradient ranges from 10.3 MPa/km to 11.1 MPa/km. The SV has a gradient from 22.20 to 23.80 MPa/km. Minimum and maximum horizontal principal stress (Sh and SH) magnitudes under isotropic conditions are determined using poroelastic model. This approach determines biaxial tectonic strain utilizing static Young’s Modulus, Poisson’s Ratio, SV, PP, leak off test (LOT) and SH derived from breakouts using prior information on unconfined compressive strength. Breakout derived SH information is used for obtaining tectonic strain due to lack of measured SH data from minifrac or hydrofracturing. Tectonic strain varies from 0.00055 to 0.00096 along x direction and from -0.0010 to 0.00042 along y direction. After obtaining tectonic strains at each well, the principal horizontal stress magnitudes are calculated from linear poroelastic model. The magnitude of Sh and SH gradient in normal faulting region are 12.5 and 16.0 MPa/km while in thrust faulted region the gradients are 17.4 and 20.2 MPa/km respectively. Model predicted Sh and SH matches well with the LOT data and breakout derived SH data in both wells. It is observed from this study that the stresses SV>SH>Sh prevailing in the shelf region while near the Naga foothills the regime changes to SH≈SV>Sh area corresponds to normal faulting regime. Hence this model is a reliable tool for predicting stress magnitudes from well logs under active tectonic regime in Upper Assam Basin.

Keywords: Eaton, strain, stress, poroelastic model

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Authors: Sonam Behl, Raju, Ginu Rajan, Paul Farrar, B. Gangadhara Prusty

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Reinforcing dental composites with micro-sized fibres can significantly improve the physio-mechanical properties of dental composites. The short fibres can be oriented randomly within dental composites, thus providing quasi-isotropic reinforcing efficiency unlike unidirectional/bidirectional fibre reinforced composites enhancing anisotropic properties. Thus, short fibres reinforced dental composites are getting popular among practitioners. However, despite their popularity, resin-based dental composites are prone to failure on account of shrinkage during photo polymerisation. The shrinkage in the structure may lead to marginal gap formation, causing secondary caries, thus ultimately inducing failure of the restoration. The traditional methods to evaluate polymerisation shrinkage using strain gauges, density-based measurements, dilatometer, or bonded-disk focuses on average value of volumetric shrinkage. Moreover, the results obtained from traditional methods are sensitive to the specimen geometry. The present research aims to evaluate the real-time shrinkage strain at selected locations in the material with the help of optical fibre Bragg grating (FBG) sensors. Due to the miniature size (diameter 250 µm) of FBG sensors, they can be easily embedded into small samples of dental composites. Furthermore, an FBG array into the system can map the real-time shrinkage strain at different regions of the composite. The evaluation of real-time monitoring of shrinkage values may help to optimise the physio-mechanical properties of composites. Previously, FBG sensors have been able to rightfully measure polymerisation strains of anisotropic (unidirectional or bidirectional) reinforced dental composites. However, very limited study exists to establish the validity of FBG based sensors to evaluate volumetric shrinkage for randomly oriented fibres reinforced composites. The present study aims to fill this research gap and is focussed on establishing the usage of FBG based sensors for evaluating the shrinkage of dental composites reinforced with randomly oriented fibres. Three groups of specimens were prepared by mixing the resin (80% UDMA/20% TEGDMA) with 55% of silane treated BaAlSiO₂ particulate fillers or by adding 5% of micro-sized fibres of diameter 5 µm, and length 250/350 µm along with 50% of silane treated BaAlSiO₂ particulate fillers into the resin. For measurement of polymerisation shrinkage strain, an array of three fibre Bragg grating sensors was embedded at a depth of 1 mm into a circular Teflon mould of diameter 15 mm and depth 2 mm. The results obtained are compared with the traditional method for evaluation of the volumetric shrinkage using density-based measurements. Degree of conversion was measured using FTIR spectroscopy (Spotlight 400 FT-IR from PerkinElmer). It is expected that the average polymerisation shrinkage strain values for dental composites reinforced with micro-sized fibres can directly correlate with the measured degree of conversion values, implying that more C=C double bond conversion to C-C single bond values also leads to higher shrinkage strain within the composite. Moreover, it could be established the photonics approach could help assess the shrinkage at any point of interest in the material, suggesting that fibre-Bragg grating sensors are a suitable means for measuring real-time polymerisation shrinkage strain for randomly fibre reinforced dental composites as well.

Keywords: dental composite, glass fibre, polymerisation shrinkage strain, fibre-Bragg grating sensors

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Authors: Jatziri Y. Moreno-Martínez, Arturo Galván, Israel Enrique Herrera Díaz, José Ramón Gasca Tirado

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In recent years, for the elevated viaducts in Mexico City, a construction system based on precast/pre-stressed concrete elements has been used, in which the bridge girders are divided in two parts by imposing a hinged support in sections where the bending moments that are originated by the gravity loads in a continuous beam are minimal. Precast concrete girders with dapped ends are a representative sample of a behavior that has complex configurations of stresses that make them more vulnerable to cracking due to flexure–shear interaction. The design procedures for ends of the dapped girders are well established and are based primarily on experimental tests performed for different configurations of reinforcement. The critical failure modes that can govern the design have been identified, and for each of them, the methods for computing the reinforcing steel that is needed to achieve adequate safety against failure have been proposed. Nevertheless, the design recommendations do not include procedures for controlling diagonal cracking at the entrant corner under service loading. These cracks could cause water penetration and degradation because of the corrosion of the steel reinforcement. The lack of visual access to the area makes it difficult to detect this damage and take timely corrective actions. Three-dimensional non-linear numerical models based on Finite Element Method to study the cracking at the entrant corner of dapped-end beams were performed using the software package ANSYS v. 11.0. The cracking was numerically simulated by using the smeared crack approach. The concrete structure was modeled using three-dimensional solid elements SOLID65 capable of cracking in tension and crushing in compression. Drucker-Prager yield surface was used to include the plastic deformations. The longitudinal post-tension was modeled using LINK8 elements with multilinear isotropic hardening behavior using von Misses plasticity. The reinforcement was introduced with smeared approach. The numerical models were calibrated using experimental tests carried out in “Instituto de Ingeniería, Universidad Nacional Autónoma de México”. In these numerical models the characteristics of the specimens were considered: typical solution based on vertical stirrups (hangers) and on vertical and horizontal hoops with a post-tensioned steel which contributed to a 74% of the flexural resistance. The post-tension is given by four steel wires with a 5/8’’ (16 mm) diameter. Each wire was tensioned to 147 kN and induced an average compressive stress of 4.90 MPa on the concrete section of the dapped end. The loading protocol consisted on applying symmetrical loading to reach the service load (180 kN). Due to the good correlation between experimental and numerical models some additional numerical models were proposed by considering different percentages of post-tension in order to find out how much it influences in the appearance of the cracking in the reentrant corner of the dapped-end beams. It was concluded that the increasing of percentage of post-tension decreases the displacements and the cracking in the reentrant corner takes longer to appear. The authors acknowledge at “Universidad de Guanajuato, Campus Celaya-Salvatierra” and the financial support of PRODEP-SEP (UGTO-PTC-460) of the Mexican government. The first author acknowledges at “Instituto de Ingeniería, Universidad Nacional Autónoma de México”.

Keywords: concrete dapped-end beams, cracking control, finite element analysis, postension

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Authors: M. M. Hassani, S. Ammann, F. K. Wittel, P. Niemz, H. J. Herrmann

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Application of engineered wood, especially in the form of glued-laminated timbers has increased significantly. Recent progress in plywood made of high strength and high stiffness hardwoods, like European beech, gives designers in general more freedom by increased dimensional stability and load-bearing capacity. However, the strong hygric dependence of basically all mechanical properties renders many innovative ideas futile. The tendency of hardwood for higher moisture sorption and swelling coefficients lead to significant residual stresses in glued-laminated configurations, cross-laminated patterns in particular. These stress fields cause initiation and evolution of cracks in the bond-lines resulting in: interfacial de-bonding, loss of structural integrity, and reduction of load-carrying capacity. Subsequently, delamination of glued-laminated timbers made of hardwood elements can be considered as the dominant failure mechanism in such composite elements. In addition, long-term creep and mechano-sorption under changing environmental conditions lead to loss of stiffness and can amplify delamination growth over the lifetime of a structure even after decades. In this study we investigate the delamination process of adhesively bonded hardwood (European beech) elements subjected to changing climatic conditions. To gain further insight into the long-term performance of adhesively bonded elements during the design phase of new products, the development and verification of an authentic moisture-dependent constitutive model for various species is of great significance. Since up to now, a comprehensive moisture-dependent rheological model comprising all possibly emerging deformation mechanisms was missing, a 3D orthotropic elasto-plastic, visco-elastic, mechano-sorptive material model for wood, with all material constants being defined as a function of moisture content, was developed. Apart from the solid wood adherends, adhesive layer also plays a crucial role in the generation and distribution of the interfacial stresses. Adhesive substance can be treated as a continuum layer constructed from finite elements, represented as a homogeneous and isotropic material. To obtain a realistic assessment on the mechanical performance of the adhesive layer and a detailed look at the interfacial stress distributions, a generic constitutive model including all potentially activated deformation modes, namely elastic, plastic, and visco-elastic creep was developed. We focused our studies on the three most common adhesive systems for structural timber engineering: one-component polyurethane adhesive (PUR), melamine-urea-formaldehyde (MUF), and phenol-resorcinol-formaldehyde (PRF). The corresponding numerical integration approaches, with additive decomposition of the total strain are implemented within the ABAQUS FEM environment by means of user subroutine UMAT. To predict the true stress state, we perform a history dependent sequential moisture-stress analysis using the developed material models for both wood substrate and adhesive layer. Prediction of the delamination process is founded on the fracture mechanical properties of the adhesive bond-line, measured under different levels of moisture content and application of the cohesive interface elements. Finally, we compare the numerical predictions with the experimental observations of de-bonding in glued-laminated samples under changing environmental conditions.

Keywords: engineered wood, adhesive, material model, FEM analysis, fracture mechanics, delamination

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