Search results for: orthotropic fracture criterion

Authors: Mahdi Fakoor, Hannaneh Manafi Farid

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In order to predict the fracture behavior of cracked orthotropic materials under mixed-mode loading, well-known minimum strain energy density (SED) criterion is extended. The crack is subjected along the fibers at plane strain conditions. Despite the complicities to solve the nonlinear equations which are requirements of SED criterion, SED criterion for anisotropic materials is derived. In the present research, fracture limit curve of SED criterion is depicted by a numerical solution, hence the direction of crack growth is figured out by derived criterion, MSED. The validated MSED demonstrates the improvement in prediction of fracture behavior of the materials. Also, damaged factor that plays a crucial role in the fracture behavior of quasi-brittle materials is derived from this criterion and proved its dependency on mechanical properties and direction of crack growth.

Keywords: mixed-mode fracture, minimum strain energy density criterion, orthotropic materials, fracture limit curve, mode II critical stress intensity factor

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Authors: Mahdi Fakoor, Seyed Mohammad Navid Ghoreishi

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Investigation of fracture of wood components can prevent from catastrophic failures. Created fracture process zone (FPZ) in crack tip vicinity has important effect on failure of cracked composite materials. In this paper, a failure criterion for fracture investigation of cracked wood specimens under mixed mode I/II loading is presented. This criterion is based on maximum strain energy release rate and material nonlinearity in the vicinity of crack tip due to presence of microcracks. Verification of results with available experimental data proves the coincidence of the proposed criterion with the nature of fracture of wood. To simplify the estimation of nonlinear properties of FPZ, a damage factor is also introduced for engineering and application purposes.

Keywords: fracture criterion, mixed mode loading, damage zone, micro cracks

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Authors: S. Houcine Habib, B. Elkhalil Hachi, Mohamed Guesmi, Mohamed Haboussi

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In this paper, dynamic fracture behaviors of cracked orthotropic structure are modeled using extended finite element method (X-FEM). In this approach, the finite element method model is first created and then enriched by special orthotropic crack tip enrichments and Heaviside functions in the framework of partition of unity. The mixed mode stress intensity factor (SIF) is computed using the interaction integral technique based on J-integral in order to predict cracking behavior of the structure. The developments of these procedures are programmed and introduced in a self-software platform code. To assess the accuracy of the developed code, results obtained by the proposed method are compared with those of literature.

Keywords: X-FEM, composites, stress intensity factor, crack, dynamic orthotropic behavior

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Authors: A. Falsafi, M. Dadkhah, S. Shahidi

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The destruction and defeat of drill pipes and drill rigs in oil wells often combined with a combination of shear modulus II and III. In such a situation, the strength and load bearing capacity of the drill are evaluated based on the principles of fracture mechanics and crack growth criteria. In this paper, using the three-dimensional stress equations around the Turkish frontier, the relations of the tense-tense criterion (MTS) are extracted for the loading of the combined II and III modulus. It is shown that in crisp deflection under loading of combination II and III, the level of fracture is characterized by two different angles: the longitudinal angle of deflection θ and the angle of the deflection of the alpha. Based on the relationships obtained from the MTS criterion, the failure criteria, the longitudinal angle of the theta failure and the lateral angle of the failure of the alpha are presented. Also, the role of Poisson's coefficient on these parameters is investigated in these graphs.

Keywords: most tangential tension criterion, longitudinal angle of failure, side angle of fracture, drills crack

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Authors: Yang Zhong, Meijie Xu

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The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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Authors: R. Bensaada, M. Almansba, M. Ould Ouali, R. Ferhoum, N. E. Hannachi

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The aim of this work is to simulate the ductile fracture of SEN specimens in aluminium alloy. The assessment of fracture toughness is performed with the calculation of Jc (the critical value of J-Integral) through the resistance curves. The study is done using finite element code calculation ABAQUSTM including an elastic plastic with damage model of material’s behaviour. The procedure involves specimens of four different thicknesses and four ligament sizes for every thickness. The material of study is an aluminium alloy 6061-T6 for which the necessary parameters to complete the study are given. We found the same results for the same specimen’s thickness and for different ligament sizes when the fracture criterion is evaluated.

Keywords: j-integral, critical-j, damage, fracture toughness

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Authors: Xi Yang, Bulent Chavdar, Alan Vonseggern, Taylan Altan

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Fracture in hot precision forging of engine valves was investigated in this paper. The entire valve forging procedure was described and the possible cause of the fracture was proposed. Finite Element simulation was conducted for the forging process, with commercial Finite Element code DEFORMTM. The effects of material properties, the effect of strain rate and temperature were considered in the FE simulation. Two fracture criteria were discussed and compared, based on the accuracy and reliability of the FE simulation results. The selected criterion predicted the fracture location and shows the trend of damage increasing with good accuracy, which matches the experimental observation. Additional modification of the punch shapes was proposed to further reduce the tendency of fracture in forging. Finite Element comparison shows a great potential of such application in the mass production.

Keywords: hotforging, engine valve, fracture, tooling

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Authors: Sang-Woo Kim, Young-Seon Lee

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An important concern in metal forming, even at elevated temperatures, is whether a desired deformation can be accomplished without any failure of the material. A detailed understanding of the critical condition for crack initiation provides not only the workability limit of a material but also a guide-line for process design. This paper describes the utilization of ductile fracture criteria in conjunction with the finite element method (FEM) for predicting the onset of fracture in warm metal working processes of magnesium alloy sheets. Critical damage values for various ductile fracture criteria were determined from uniaxial tensile tests and were expressed as the function of strain rate and temperature. In order to find the best criterion for failure prediction, Erichsen cupping tests under isothermal conditions and FE simulations combined with ductile fracture criteria were carried out. Based on the plastic deformation histories obtained from the FE analyses of the Erichsen cupping tests and the critical damage value curves, the initiation time and location of fracture were predicted under a bi-axial tensile condition. The results were compared with experimental results and the best criterion was recommended. In addition, the proposed methodology was used to predict the onset of fracture in non-isothermal deep drawing processes using an irregular shaped blank, and the results were verified experimentally.

Keywords: magnesium, AZ31 alloy, ductile fracture, FEM, sheet forming, Erichsen cupping test

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Authors: Daniel O'Shea, Mario M. Attard, David C. Kellermann

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In this paper, we propose a hyperelastic strain energy function that maps isotopic hyperelastic constitutive laws for the use of orthotropic materials without the use of structural tensors or any kind of fiber vector, or the use of standard invariants. In particular, we focus on neo-Hookean class of models and represent them using an invariant-free formulation. To achieve this, we revise the invariant-free formulation of isotropic hyperelasticity. The formulation uses quadruple contractions between fourth-order tensors, rather than scalar products of scalar invariants. We also propose a new decomposition of the orthotropic Hookean stiffness tensor into two fourth-order Lamé tensors that collapse down to the classic Lamé parameters for isotropic continua. The resulting orthotropic hyperelastic model naturally maintains all of the advanced properties of the isotropic counterparts, and similarly collapse back down to their isotropic form by nothing more than equality of parameters in all directions (isotropy). Comparisons are made with large strain experimental results for transversely isotropic rubber type materials under tension.

Keywords: finite strain, hyperelastic, invariants, orthotropic

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Authors: Eliska Smidova, Petr Kabele

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This paper describes non-linear finite element simulation of laminated veneer lumber (LVL) under tensile and shear loads that induce cracking along fibers. For this purpose, we use 2D homogeneous orthotropic constitutive model of tensile and shear fracture in timber that has been recently developed and implemented into ATENA® finite element software by the authors. The model captures (i) material orthotropy for small deformations in both linear and non-linear range, (ii) elastic behavior until anisotropic failure criterion is fulfilled, (iii) inelastic behavior after failure criterion is satisfied, (iv) different post-failure response for cracks along and across the grain, (v) unloading/reloading behavior. The post-cracking response is treated by fixed smeared crack model where Reinhardt-Hordijk function is used. The model requires in total 14 input parameters that can be obtained from standard tests, off-axis test results and iterative numerical simulation of compact tension (CT) or compact tension-shear (CTS) test. New engineered timber composites, such as laminated veneer lumber (LVL), offer improved structural parameters compared to sawn timber. LVL is manufactured by laminating 3 mm thick wood veneers aligned in one direction using water-resistant adhesives (e.g. polyurethane). Thus, 3 main grain directions, namely longitudinal (L), tangential (T), and radial (R), are observed within the layered LVL product. The core of this work consists in 3 numerical simulations of experiments where Radiata Pine LVL and Yellow Poplar LVL were involved. The first analysis deals with calibration and validation of the proposed model through off-axis tensile test (at a load-grain angle of 0°, 10°, 45°, and 90°) and CTS test (at a load-grain angle of 30°, 60°, and 90°), both of which were conducted for Radiata Pine LVL. The second finite element simulation reproduces load-CMOD curve of compact tension (CT) test of Yellow Poplar with the aim of obtaining cohesive law parameters to be used as an input in the third finite element analysis. That is four point bending test of small-size arch of 780 mm span that is made of Yellow Poplar LVL. The arch is designed with a through crack between two middle layers in the crown. Curved laminated beams are exposed to high radial tensile stress compared to timber strength in radial tension in the crown area. Let us note that in this case the latter parameter stands for tensile strength in perpendicular direction with respect to the grain. Standard tests deliver most of the relevant input data whereas traction-separation law for crack along the grain can be obtained partly by inverse analysis of compact tension (CT) test or compact tension-shear test (CTS). The initial crack was modeled as a narrow gap separating two layers in the middle the arch crown. Calculated load-deflection curve is in good agreement with the experimental ones. Furthermore, crack pattern given by numerical simulation coincides with the most important observed crack paths.

Keywords: compact tension (CT) test, compact tension shear (CTS) test, fixed smeared crack model, four point bending test, laminated arch, laminated veneer lumber LVL, off-axis test, orthotropic elasticity, orthotropic fracture criterion, Radiata Pine LVL, traction-separation law, yellow poplar LVL, 2D constitutive model

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Authors: Ashkan Golgoon, Arash Yavari

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In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with line and point defects distributions. In particular, we determine the induced stress fields of a parallel cylindrically-symmetric distribution of screw dislocations in infinite orthotropic and monoclinic media as well as a cylindrically-symmetric distribution of parallel wedge disclinations in an infinite orthotropic medium. For a given distribution of edge dislocations, the material manifold is constructed using Cartan's moving frames and the stress field is obtained assuming that the medium is orthotropic. Also, we consider a spherically-symmetric distribution of point defects in a transversely isotropic spherical ball. We show that for an arbitrary incompressible transversely isotropic ball with the radial material preferred direction, a uniform point defect distribution results in a uniform hydrostatic stress field inside the spherical region the distribution is supported in. Finally, we find the stresses induced by a discombination in an orthotropic medium.

Keywords: defects, disclinations, dislocations, monoclinic solids, nonlinear elasticity, orthotropic solids, transversely isotropic solids

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Authors: Faraj Ahmed E. Alhegagi, Anagia M. Khamkam Mohamed, Bassam F. Alhajaji

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Duplex stainless steels (DSS) are widely employed in industry for apparatus working with sea water in petroleum, refineries and in chemical plants. Fracture of DSS takes place by cleavage of the ferrite phase and the austenite phase ductile tear off. Pop-in is an important feature takes place during fracture of DSS. The procedure of Pop-ins assessment plays an important role in fracture toughness studies. In present work, Zeron100 DSS specimens were heat treated at different temperatures, cooled and pulled to failure to assess the pop-ins criterion in crack initiation prediction. The outcome results were compared to the British Standard (BS 7448) and the ASTEM standard (E1290) for Crack-Tip Opening Displacement (CTOD) fracture toughness measurement. Pop-in took place during specimens loading specially for those specimens heat treated at higher temperatures. The standard BS7448 was followed to check specimen validity for fractured toughness assessment by direct determination of KIC. In most cases, specimens were invalid for KIC measurement. The two procedures were equivalent only when single pop-ins were assessed. A considerable contrast in fracture toughness value between was observed where multiple pop-ins were assessed.

Keywords: fracture toughness, stainless steels, pop ins, crack assessment

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Authors: Mahdi Fakoor, Nabi Mehri Khansari, Ahmadreza Farokhi

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Evaluation of mode II fracture toughness (KIIC) in composite materials is very hard problem to be solved, since it can be affected by many mechanisms of dissipation. Furthermore, non-linearity in its behavior can offer an extra difficulty to obtain accuracy in the results. Different reported values for KIIC in various references can prove the mentioned assertion. In this research, some solutions proposed based on the form of necessary corrections that should be executed on the common test fixtures. Due to the fact that the common test fixtures are not able to active toughening mechanisms in pure Mode II correctly, we have employed some structural modifications on common fixtures. Particularly, the Iosipescu test is used as start point. The tests are applied on graphite/epoxy; PMMA and Western White Pine Wood. Also, mixed mode I/II fracture limit curves are used to indicate the scattering in test results are really relevant to the creation of Fracture Process Zone (FPZ). In the present paper, shear load consideration applied at the predicted shear zone by considering some significant structural amendments that can active mode II toughening mechanisms. Indeed, the employed empirical method causes significant developing in repeatability and reproducibility as well. Moreover, a 3D Finite Element (FE) is performed for verification of the obtained results. Eventually, it is figured out that, a remarkable precision can be obtained in common test fixture in comparison with the previous one.

Keywords: FPZ, shear test fixture, mode II fracture toughness, composite material, FEM

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Authors: Srikanta Tagore Sarkar, Prasanta Kumar Mandal, Dibakar Roy

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The association of a capitate fracture with a scaphoid fracture has been termed as the naviculocapitate syndrome. The existence of some nondisplaced fractures of scaphoid and capitate with or without the fracture of lunate or radius suggests that there is a spectrum of these injuries, and this confuses the terminology. With our case; we report an unusual variety of this naviculocapitate syndrome with distal radial Colles fracture in addition to the nondisplaced fractures of the scaphoid, capitate and the dorsal lip of radial fracture. When we looked at the literature there is no another Colles fracture reported together with undisplaced scapho-capitate syndrome. The coronal and sagittal images that obtained from the MDCT (Multidetector computed tomography) is useful and effective imaging modality to diagnose complex wrist fractures with more details that are not detected in X-rays.

Keywords: scaphoid, capitate, Colles’ fracture, syndrome, MDCT, unusual

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Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

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A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

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Authors: P. Ravinder Reddy, Chaitanya Vishal Nalli, B. Tulja Lal, Anusha Kankanala

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The chassis frame of an automobile with different sections have been considered for different loads. The orthotropic materials are selected to get the stability by varying fiber angle, fiber thickness, laminates, fiber properties, matrix properties and elastic ratios. The geometric model of chassis frame is carried out with parametric modelling approach. The analysis of chassis frame is carried out with ANSYS FEA software. The static and dynamic analysis of chassis frame is carried out by varying geometric parameters, orthotropic properties, materials and various sections. The static and dynamic response is discussed in detail in different sections.

Keywords: chassis frame, dynamic response, geometric model, orthotropic materials

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Authors: Farid Saeidi, Serkan Dag

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In this study, fracture analysis of a fibrous composite laminate with variable fiber spacing is carried out using Jk-integral method. The laminate is assumed to be under thermal loading. Jk-integral is formulated by using the constitutive relations of plane orthotropic thermoelasticity. Developed domain independent form of the Jk-integral is then integrated into the general purpose finite element analysis software ANSYS. Numerical results are generated so as to assess the influence of variable fiber spacing on mode I and II stress intensity factors, energy release rate, and T-stress. For verification, some of the results are compared to those obtained using displacement correlation technique (DCT).

Keywords: Jk-integral, Variable Fiber Spacing, Thermoelasticity, T-stress, Finite Element Method, Fibrous Composite.

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Authors: Ahmad N. Shuid, Azri Jalil, Sabarul A. Mokhtar, Mohd F. Khamis, Norliza Muhammad

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Micro-CT provides a 3-D image of fracture callus, which can be used to calculate quantitative parameters. In this study, micro-CT was used to assess the fracture healing of orchidectomised rats, an androgen-deficient osteoporosis model. The effect of testosterone (hormone replacement) on fracture healing was also assessed with micro-CT. The rats were grouped into orchidectomised-control (ORX), sham-operated (SHAM), and orchidectomised; and injected with testosterone intramuscularly once weekly (TEN). Treatment duration was six weeks. The fracture was induced and fixed with plates and screws in the right tibia of all the rats. An in vitro micro-CT was used to scan the fracture callus area which consisted of 100 axial slices above and below fracture line. The analysis has shown that micro-CT was able to detect a significant difference in the fracture healing rate of ORX and TEN groups. In conclusion, micro-CT can be used to assess fracture healing in androgen-deficient osteoporosis. This imaging tool can be used to test agents that influence fracture healing in the androgen-deficient model.

Keywords: androgen, fracture, orchidectomy, osteoporosis

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Authors: Suleyman Karabal, Timothy L. Burnett, Egemen Avcu, Andrew H. Sherry, Philip J. Withers

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SA508 Grade 3 steel is widely used in the construction of nuclear pressure vessels, where its fracture toughness plays a critical role in ensuring operational safety and reliability. Understanding the ductile failure mechanisms in this steel grade is crucial for designing robust pressure vessels that can withstand severe nuclear environment conditions. In the present study, round bar specimens of SA508 Grade 3 steel with four distinct notch geometries were subjected to tensile loading while capturing continuous 2D images at 5-second intervals in order to monitor any alterations in their geometries to construct true stress-strain curves of the specimens. 3D reconstructions of X-ray computed tomography (CT) images at high-resolution (a spatial resolution of 0.82 μm) allowed for a comprehensive assessment of the influences of second-phase particles (i.e., manganese sulfide inclusions and cementite particles) on ductile failure initiation as a function of applied plastic strain. Additionally, based on 2D and 3D images, plasticity modeling was executed, and the results were compared to experimental data. A specific ‘two-parameter criterion’ was established and calibrated based on the correlation between stress triaxiality and equivalent plastic strain at failure initiation. The proposed criterion demonstrated substantial agreement with the experimental results, thus enhancing our knowledge of ductile fracture behavior in this steel grade. The implementation of X-ray CT and fractography analysis provided new insights into the diverse roles played by different populations of second-phase particles in fracture initiation under varying stress triaxiality conditions.

Keywords: ductile fracture, two-parameter criterion, x-ray computed tomography, stress triaxiality

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Authors: Amar Sabih, James Nemes

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The occurrence of internal ductile failure within the Adiabatic Shear Band (ASB) in cold-headed products presents a significant barrier in the fast-expanding cold-heading (CH) industry. The presence of internal ductile failure in cold-headed products may lead to catastrophic fracture under tensile loads despite the ductile nature of the material causing expensive industrial recalls. Therefore, this paper presents a new workability criterion that uses stress instability as an indicator to accurately reveal the locus of initiation of internal ductile failures. The concept of the instability criterion is to use the stress ratio at failure as a weighting function to indicate the initiation of ductile failure inside the ASBs. This paper presents a comprehensive experimental, metallurgical, and finite element simulation study to calculate the material constants used in this criterion.

Keywords: adiabatic sher band, ductile failure, stress instability, workability criterion

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Authors: Amar Sabih, James Nemes

Abstract:

The occurrence of internal ductile failure within the Adiabatic Shear Band (ASB) in cold-headed products presents a significant barrier in the fast-expanding cold-heading (CH) industry. The presence of internal ductile failure in cold-headed products may lead to catastrophic fracture under tensile loads despite the ductile nature of the material causing expensive industrial recalls. Therefore, this paper presents a workability criterion that uses stress instability as an indicator to accurately reveal the locus of initiation of internal ductile failures. The concept of the instability criterion is to use the stress ratio at failure as a weighting function to indicate the initiation of ductile failure inside the ASBs. This paper presents a comprehensive experimental, metallurgical, and finite element simulation study to calculate the material constants used in this criterion.

Keywords: adiabatic shear band, workability criterion, ductile failure, stress instability

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Authors: Ying Zhang

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In ASME Boiler and Pressure Vessel Code, the plastic load is defined by applying the twice elastic slope (TES) criterion of plastic collapse to a characteristic load-deformation curve for the vessel. Several other plastic criterion such as tangent intersection (TI) criterion, plastic work (PW) criterion have been proposed in the literature, but all exhibit a practical limitation: difficult to define the load parameter for vessels subject to several combined loads. An alternative criterion: plastic work-tangent (PWT) criterion for evaluating plastic load in pressure vessel design by analysis is presented in this paper. According to the plastic work-load curve, when the tangent variation is less than a given value in the plastic phase, the corresponding load is the plastic load. Application of the proposed criterion is illustrated by considering the elastic-plastic response of the lower head of reactor pressure vessel (RPV) and nozzle intersection of (RPV). It is proposed that this is because the PWT criterion more fully represents the constraining effect of material strain hardening on the spread of plastic deformation and more efficiently ton evaluating the plastic load.

Keywords: plastic load, plastic work, strain hardening, plastic work-tangent criterion

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Authors: S. Alireza Mirghasemi, Narges Rahimi Gabaran

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Although sacral fractures in children are rare due to the fact that the occurrence of pelvic fracture is not common in childhood. Sacral fractures present a high risk of neurological damage. This kind of fracture is often missed because the routine pelvic X-rays imaging scarcely show this fracture. Also, the treatment is controversial, and it ranges from fine reduction to conservative treatments without any try to reduce the dislocation. In this article, a case of fracture dislocation of S1 and S2 along with a suggested diagnostic test and treatment based on similar cases are presented. The case investigates a 14-year-old boy who entered the hospital one week after a car accident that knocked him to the ground in crawling position and a rack fell down on his body. Pain and tenderness in the sacral region and a fracture in the left leg were notable--we detected incomplete bilateral palsy of L5, S1 and S2 roots. In radiographs of the spine fracture dislocation of S1, the sacral fracture was seen. The treatment included a skeletal traction with a halo over the patient’s head and two femoral pins. After one week, another surgery was performed in order to stabilize and reduce the fracture, and we employed a posterior approach with CD and a pedicular screw. After two years of follow-up, the fracture is completely cured without any loss of reduction.

Keywords: adolescent, fracture in adolescent, fracture dislocation, sacrum

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Authors: Rajesh Bansal, Amit Raj Sharma, Vakil Singh

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The success and predictability of titanium implants for long durations are well established and there has been a tremendous increase in the popularity of implants among patients as well as clinicians over the last four decades. However, sometimes complications arise, which lead to the loss of the implant as well as the prosthesis. Fracture of dental implants is rare; however, at times, implants or abutment screws fracture and lead to many problems for the clinician and the patient. Possible causes of implant fracture include improper design, overload, fatigue and corrosion. Six retrieved fractured dental implants, with varying diameters and designs, were collected from time to time to examine by scanning electron microscope (SEM) to characterize fracture behavior and assess the mechanism of fracture. In this investigation, it was observed that fracture of the five dental implants occurred due to fatigue crack initiation and propagation from the thread roots.

Keywords: titanium, dental, implant, fracture, failure

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Guoyang Fu, Wei Yang, Chun-Qing Li

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The most common type of cracks that appear on metal pipes is longitudinal cracks. For ductile metal pipes, the existence of plasticity eases the stress intensity at the crack front and consequently increases the fracture resistance. It should be noted that linear elastic fracture mechanics (LEFM) has been widely accepted by engineers. In order to make the LEFM applicable to ductile metal materials, the increase of fracture toughness due to plasticity should be excluded from the total fracture toughness of the ductile metal. This paper aims to develop a model of elastic fracture toughness for ductile metal pipes with external longitudinal cracks. The derived elastic fracture toughness is a function of crack geometry and material properties of the cracked pipe. The significance of the derived model is that the well-established LEFM can be used for ductile metal material in predicting the fracture failure.

Keywords: Ductile metal pipes, elastic fracture toughness, longitudinal crack, plasticity

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Authors: Rajendra Kumar Kanojia

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Treatment of fracture both bones of leg following trauma is done intially at nearby primary health care center.primary management for shock,pain,control of bleeding,plaster application. These are treated for primay fixation of fracture, debridment of wound. Then, they were refered to tertiary care where they were again and planned for further treatment. This leads to loss of lot of time, money, job, etc.

Keywords: fracture both bones leg, non-union, ilizarov, cost

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Authors: Mojtaba Hakimi-Moghaddam

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Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Dibu Dave Mbako, Bin Cheng

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This paper study the stress variation of the welded joints in the rib-to-deck connection structure, the influence stress of the deck plate and u-rib thickness at different positions. A Finite-element model of orthotropic steel deck structure using solid element and shell element was established in ABAQUS. Under a single wheel load, the static response was analyzed to understand the structural behaviors and examine stress distribution. A parametric study showed that the geometric parameters have a significant effect on the hot spot stress at the weld toe, but has little impact on the stress concentration factor. The increase of the thickness of the deck plate will lead to the decrease of the hot spot stress at the weld toe and the maximum deflection of the deck plate. The surface stresses of the deck plate are significantly larger than those of the rib near the joint in the 80% weld penetration into the u-rib.

Keywords: orthotropic steel bridge deck, rib-to-deck connection, hot spot stress, finite element method, stress distribution

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Authors: D. Bäcker, H. Chaves

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The key to improve surface cleaning of the fouling is understanding of the mechanism of separation process of the deposit from the surface. The authors give basic principles of characterization of separation process and introduce a corresponding criterion. The developed criterion is a measure for the moment of separation of the deposit from the surface. For this purpose a new measurement technique is described.

Keywords: cleaning, fouling, separation, criterion

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