Advances in Fracture and Damage Mechanics VI

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Authors: Michael Wünsche, Chuan Zeng Zhang, Jan Sladek, Vladimir Sladek, Sohichi Hirose
Abstract: In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear elastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The homogeneous and anisotropic layers are modeled by the multi-domain BEM formulation. Time-domain elastodynamic fundamental solutions for linear elastic and anisotropic solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the crack-opening-displacements (CODs). To show the effects of the material anisotropy and the dynamic loading on the dynamic stress intensity factors, numerical examples are presented and discussed.
Authors: Jorge Grasa, José Antonio Bea, Manuel Doblaré
Abstract: The Extended Finite Element Method (XFEM), has become a well-known tool to simulate crack propagation problems using non-structured meshes avoiding the remeshing process usually needed in this type of problems and allowing the inclusion of appropriate shape functions that reflect the asymptotic displacement field, near the crack tip, via a partition of unity fracture approach. However, in this kind of numerical applications, all the variables involved have been considered as deterministic (defined by a single given value), despite the well-known uncertainty associated to many of them (external loads, geometry and material properties, among others). The combination of the XFEM and probabilistic techniques is here proposed and formulated allowing treating fracture mechanics problems from a probabilistic point of view. We present the implementation of this probabilistic extended finite element method and apply it to the prediction of the appearance and propagation of a femur’s neck fracture under probabilistic loads.
Authors: Seung Yong Lee, Cheol Woo Park, Soon Cheol Kwon, Hee Hyun Lee
Abstract: The use of steel plates has been greatly increased in bridge construction, particularly for long-span bridges, and connections between the plates are made usually using high-tension bolts. However, the specifications on the use of large-sized high-tension bolts are not adequately stated in the currently available construction manuals. In order to provide further information on the use of the large-sized high-tension bolts, this study experimentally investigated the relaxation and slip behavior of M30 bolts with varying bolt size and plate thickness. In addition, numerical evaluation using FEM was performed to investigate the compressive stress occurred on the inside of bolt hole. The analyzed results were compared with the stress distribution measured from strain gages attached on the bolts and bolt holes. From the study presented herein, it was found that the relaxation was increased as the size of bolt increased, and that the M30 high-tension bolts developed slip coefficient greater than 0.4. The thickness of plate did not significantly affect the compressive stress distribution around the bolt holes.
Authors: Vijay G. Ukadgaonker, Sunil Bhat
Abstract: When a Mode I crack in soft steel body grows and reaches near the perpendicular interface of ultra strong steel body, its cohesive zone penetrates into the interface body which influences the crack tip parameter. The paper presents finite element analysis of the cohesive zone across the interface of such elastically matched but strength mismatched bodies in linear elastic regime. Parent alloy steel (ASTM 4340) body and interface maraging steel (MDN 250) body are considered for analysis. The cohesive zone is modeled in accordance with the Dugdale criterion. J integral is evaluated over the path around the interface to examine the effect of cohesive stresses on the crack tip. The results are compared vis-à-vis those obtained from the theoretical model. The two are in very good agreement with each other.
Authors: Tore Lucht, Ferri M.H.Aliabadi
Abstract: In an incremental crack extension analysis each crack increment is in general modelled with a straight extension. In order to avoid introduction of an error when the local crack growth criterion is used with an incremental formulation, each straight crack extension would have to be infinitesimal as the crack growth direction changes when the crack grows. A correction procedure to correct the extension direction of the increment can however be applied to ensure that a unique crack path is achieved with different analyses of the same problem performed with different size of the crack-extension increments. A proposed correction procedure and an reference correction procedure are demonstrated by solving a computational crack growth example. The demonstration shows that analyses of the crack path performed with big crack extensions and the proposed crack correction procedure are in excellent agreement with analyses of the crack path performed with very small crack extensions. Furthermore it is shown that the reference correction procedure has a tendency to overcorrect the crack growth direction if the stop criterion for the iterative correction procedure is not specified for each new crack growth analysis.
Authors: Christian Carloni, Lucio Nobile
Abstract: Carbon fiber reinforced polymer (CFRP) sheets have been extensively used for strengthening deteriorated concrete structures. The effectiveness of such strengthening depends upon the load transfer from concrete to the FRP composite. Shear debonding is usually caused by a crack that forms and then propagates at the interface between the adherents. The influence of the geometric parameters of the adherents on the fracture propagation is still a subject of research. This paper presents an experimental investigation performed on direct shear specimens to study the influence of the relative width of FRP and concrete on the load carrying capacity of the bond and the stress transfer between the adherents.
Authors: Cristina Gentilini, Lucio Nobile
Abstract: This paper deals with a simple and reliable method for the probabilistic characterization of the linear elastic response of frame structures with edge cracks of uncertain depth and location in the three-dimensional setting. A numerical test evidences the performance of the approach.
Authors: Martin Petrenec, Karel Obrtlík, Jaroslav Polák
Abstract: Cylindrical specimens of cast polycrystalline nickel base superalloy Inconel 713 LC and Inconel 792-5A were cyclically strained under total strain control at 23 and 700 °C. Morphology and volume fraction of γ´ precipitates are different in both materials. Cyclic hardening/softening curves, cyclic stress-strain curves, and fatigue life curves were obtained at both temperatures. The cyclic hardening/softening curves depend both on temperature and plastic strain amplitude. The cyclic stressstrain curves can be fitted by power law. Experimental data of fatigue life curves can be approximated by the Manson-Coffin and Basquin laws. Dislocation structure was studied in transmission electron microscope. Planar dislocation arrangements in the form of bands parallel to {111} planes were identified in both superalloys at both temperatures. Stress-strain response and fatigue life characteristics are compared at both temperatures and discussed in relation to dislocation arrangement and structural parameters of the materials studied.
Authors: Sylvie Pommier
Abstract: Cyclic plasticity in the crack tip region is at the origin of various history effects in fatigue. For instance, fatigue crack growth in mode I is delayed after the application of an overload because of the existence of compressive residual stresses in the overload’s plastic zone. Moreover, if the overload’s ratio is large enough, the crack may grow under mixed mode condition until it has gone round the overload’s plastic zone. Thus, crack tip plasticity modifies both the kinetics and the crack’s plane. Therefore modeling the growth of a fatigue crack under complex loading conditions requires considering the effects of crack tip plasticity. Finite element analyses are useful for analyzing crack tip plasticity under various loading conditions. However, the simulation of mixed mode fatigue crack growth by elastic-plastic finite element computations leads to huge computation costs, in particular if the crack doesn’t remain planer. Therefore, in this paper, the finite element method is employed only to build a global constitutive model for crack tip plasticity under mixed mode loading conditions. Then this model can be employed, independently of any FE computation, in a mixed mode fatigue crack growth criterion including memory effects inherited from crack tip plasticity. This model is developed within the framework of the thermodynamics of dissipative processes and includes internal variables that allow modeling the effect of internal stresses and to account for memory effects. The model was developed initially for pure mode I conditions. It was identified and validated for a 0.48%C carbon steel. It was shown that the model allows modeling fatigue crack growth under various variable amplitude loading conditions [1]. The present paper aims at showing that a similar approach can be applied for mixed mode loading conditions so as to model, finally, mixed mode fatigue crack growth.
Authors: Yi Sun, Fan Lin Zeng
Abstract: The deformation and damage process of POSS nanocomposite is investigated by molecule mechanics (MM) simulation. Firstly, the nano-scale models of two kinds of homopolymers, pure polystyrene (PS) and polystyrene attached with 5 mol% propyl-POSS (P-POSS-PS) were built. Then the mechanical behaviors of these two kinds of hybrid materials under focused uniaxial tensile loading and the remote uniaxial tensile loading are examined by MM simulations. It is found that a small quantity of POSS can observably increase the tensile modulus of the normal polymers. During tensile loadings, micro voids appear in the polymer matrix. With the increase of deformation, the micro voids become bigger and then connect to form the damage in bigger area. The POSS monomers prevent these micro voids from coalescence and thus retarding the formation of the damage. This would be helpful in understanding the reinforcement mechanism of POSS and provide important referential message for the applications of POSS.

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