Simulation of ductile tearing by the BEM with 2D domain discretization and a local damage model

A numerical procedure based on the Boundary Element Method with internal cells and dedicated to the simulation of the ductile tearing of thin metal sheets is presented. Plasticity is handled with an integral formulation based on the initial strain approach involving a discretization of the planar domain. Time integration is performed in an implicit way for the local strain-stress relationships while the global algorithm relies on an explicit formulation. Damage is represented by the scalar parameter of the uncoupled local damage model of Rice and Tracey. Within the scope of our applications, the cracks propagate along paths a priori known. As damage spreads, boundary elements are gradually released. Elastoplastic problems with large yielding zones are solved and compared to reference solutions. At last, the ductile tearing of a specimen is addressed. The calibration of the critical damage parameter leads to numerical results in good agreement with the experimental ones.     

Dual finite element analysis for plasticity–friction torsion of composite bar

The quasi-static problem of torsion of an elastic–plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic–plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law—it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.     

Study of low‐temperature effect on the fracture locus of a 420‐MPa structural steel with the edge tracing method

Quasi‐static tensile tests with smooth round bar and axisymmetric notched tensile specimens have been performed to study the low‐temperature effect on the fracture locus of a 420‐MPa structural steel. Combined with a digital high‐speed camera and a 2‐plane mirror system, specimen deformation was recorded in 2 orthogonal planes. Pictures taken were then analysed with the edge tracing method to calculate the minimum cross‐section diameter reduction of the necked/notched specimen. Obvious temperature effect was observed on the load‐strain curves for smooth and notched specimens. Both the strength and strain hardening characterized by the strain at maximum load increase with temperature decrease down to ?60°C. Somewhat unexpected, the fracture strains (ductility) of both smooth and notched specimens at temperatures down to ?60°C do not deteriorate, compared with those at room temperature. Combined with numerical analyses, it shows that the effect of low temperatures (down to ?60°C) on fracture locus is insignificant. These findings shed new light on material selection for Arctic operation.     

Dynamic models for low-velocity impact damage of composite sandwich panels – Part B: Damage initiation

Equivalent single and multi degree-of-freedom systems are used to predict low-velocity impact damage of composite sandwich panels by rigid projectiles. The composite sandwich panels are symmetric and consist of orthotropic laminate facesheets and a core with constant crushing resistance. The transient deformation response of the sandwich panels subjected to impact were predicted in a previous paper, and analytical solutions for the impact force and velocity at damage initiation in sandwich panels are presented in this second paper. Several damage initiation modes are considered, including tensile and shear fracture of the top facesheet, core shear failure, and tensile failure of back facesheet. The impact failure modes are similar to static indentation failure modes, but inertial resistance and high strain rate material properties of the facesheets and core influence impact damage loads. Predicted damage initiation loads and impact velocities compare well with experimental results.     

Effect of stress amplitude on uniaxial ratcheting of aluminum alloy 2124‐T851

This paper presents the latest research results of ratcheting behavior of aluminum alloy 2124‐T851 under uniaxial loading. All fatigue tests were carried out at the Technical University of Ostrava mainly under block loading in order to determine the effect of stress amplitude and mean stress on the strain response of the material. Experimental results show that the critical value of the axial deformation is close to the ductility of the material investigated. The aim of this paper also is to draw important conclusions in terms of ratcheting modelling for the material investigated.     

EURAXLES – A global approach for design,production and maintenance of railway axles: WP1 – Advances in fatigue load analysis and reliability assessment of railway axles

The work presented in this paper was led within the collaborative project “Euraxles” of the FP7 program of the European Commission. It aimed at developing processes and methods that contribute to the minimization of the risk of fatigue failure of railway axles in service. This paper focuses on the development of a method to assess the reliability of axles according to fatigue damage. The proposed approach is mainly based on the stress strength interference analysis (SSIA) and the fatigue‐equivalent‐load (FEL) methods. It aims at calculating the axles’ probability of fatigue failure, by characterizing the variability of real in‐service loads and the scatter of the axles fatigue strength, and at evaluating more accurately the actual design margins. First of all, the main lines of the stress strength interference analysis method are recalled. This method aims at evaluating the in‐service reliability of components for their design or their homologation. It is used in many industries for various applications (mechanical components or systems, electronic elements, etc.). In the second part, the fatigue load analysis method that is proposed for railway axles is described. It starts with a post‐processing of an axle load measurement: from a time signal of forces applied to both wheels fitted on the axle, fatigue cycles of bending moment applied to the axle are identified and transformed into a cyclic equivalent load, the M_eq, which is a measurement of the severity of the initial variable load. Then, virtual but realistic load spectra are generated, thanks to a classification operation followed by a random draw of elementary load data that considers the operation and maintenance conditions of the axle. All the spectra are then analysed thanks to the fatigue‐equivalent‐load method in order to build the distribution of in‐service load severities that gives a picture of the stress to which the axles are submitted. In the third and last part of the paper, the methods are applied to real data of “Société nationale des chemins de fer français” (SNCF), the French national railway operator. Sensitivity analyses are performed in order to quantify the effect on the M_eq of variations of parameters and to verify the convergence and robustness of the process. Finally, results obtained for a passenger coach are given. The comparison between the distribution of load severities and the normative load, defined as according to european standards EN13103, shows that, for the studied axle, the normative load is very conservative. Using the axles fatigue limits identified on full‐scale tests, a stress strength interference analysis is performed to calculate the probability of failure of the axle.     

Ductile tearing analyses of cracked TP304 pipes using the multiaxial fracture strain energy model and the Gurson–Tvergaard–Needleman model

Ductile crack growth behaviours of TP304 pipes containing different circumferential defects were investigated in the study. Finite element (FE) damage analysis of the ductile fracture was carried out based on an uncoupled multiaxial fracture strain energy (MFSE) model with only two model parameters, which can be calibrated by data from tensile tests and fracture toughness tests. For the purpose of comparison, the Gurson–Tvergaard–Needleman (GTN) model was also employed in the FE damage analysis. It is observed that the MFSE model can reproduce the ductile tearing experiments as excellently as the GTN model does. Despite its simplicity, the MFSE model can reasonably predict the magnitudes of the crack initiation load and maximum load, the load‐line displacement, the crack mouth opening displacement, the crack extension and the crack profiles in the full‐scale cracked pipe tests.     

Buckling of masonry walls – A new proposal for the Eurocode 6

The buckling of masonry wall depends on the deformation behaviour and can be described with the modulus of elasticity depending on masonry strength. The reduction factor solution considering buckling is described by the Gaussian bell‐shaped curve in Eurocode 6, Part 1‐1 Annex G and was calibrated for masonry with a modulus of elasticity between 700 and 1000 f_k, which describes the masonry currently used in most European countries. In case of historic masonry or where deformability is needed in new construction, the modulus of elasticity can actually be lower. In those cases the approximation procedure according to Annex G of the Eurocode 6 delivers results which do not represent the real behaviour and leads to uneconomical results. The present paper proposes a new empirical method, which can be applied over the whole practical range of the elastic modulus of masonry. The new proposed method has been verified with experimental data and shows a very good fit.     

A fracture framework for Euler–Bernoulli beams based on a full discontinuous Galerkin formulation/extrinsic cohesive law combination

A new full Discontinuous Galerkin discretization of Euler–Bernoulli beam is presented. The main interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model in the formulation. With a classical Continuous Galerkin method, the use of the cohesive zone model is difficult because inserting a cohesive element between bulk elements is not straightforward. On one hand if the cohesive element is inserted at the beginning of the simulation, there is a modification of the structure stiffness and on the other hand inserting the cohesive element during the simulation requires modification of the mesh during computation. These drawbacks are avoided with the presented formulation as the structure is discretized in a stable and consistent way with full discontinuous elements and inserting cohesive elements during the simulation becomes straightforward. A new cohesive law based on the resultant stresses (bending moment and membrane) of the thin structure discretization is also presented. This model allows propagating fracture while avoiding through‐the‐thickness integration of the cohesive law. Tests are performed to show that the proposed model releases, during the fracture process, an energy quantity equal to the fracture energy for any combination of tension‐bending loadings. Copyright © 2010 John Wiley & Sons, Ltd.     

Berechnung der Blitztemperaturen der Mikrokontakte in künstlichen Hüftgelenken unter Benutzung des Kontaktmodells von Greenwood – Williamson

Calculation of Flash Temperatures of Micro‐Contacts in Artificial Hip Joints by Using the Contact Model of Greenwood – Williamson In hip replacement the wear rate is reduced when using femoral heads and acetabular cups made of alumina ceramics. The use of zirconia ceramics (Y‐TZP) is discussed controversy. The process on the articulating surfaces head / cup are not totally understood, especially the temperature rise due to frictional heating. Alumina is a stable material, no problems are expected. When using Y‐TZP, friction temperature can be higher then the coagulate temperature of synovia or the phase transition is induced. The model proposed by Kuhlmann – Wilsdorf was used to calculate the flash temperature under in vivo conditions of micro‐contacts at the different articulating surfaces. The real contact conditions were calculated with the analytical contact model of Greenwood – Williamson. The surface temperature of the wear couple Y‐TZP/Y‐TZP was higher than the one for alumina/alumina.     

The two‐shearfield test – A suitable method for the empirical shear capacity design of masonry / Der Zweifeld‐Schubversuch – Eine praxistaugliche Methode zur versuchsgestützten Bemessung der Schubtragfähigkeit von Bestandsmauerwerk

The investigations [1] demonstrate that the two‐shearfield test is a suitable method for the determination of the shear capacity of masonry. The testing equipment is mounted directly on the wall in order to retain realistic boundary conditions like stiffness, load and prior damage. The behaviour factor q and the capacity curves of certain masonry walls can be directly obtained from the experimental results and realistic material behaviour in earthquake design can be represented. In particular, existing masonry can be assessed realistically with methods like the response spectrum, the push‐over and the capacity spectrum by using the two‐shearfield test.     

Mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard FEM analysis of 3‐D cohesive fractures

A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small‐sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub‐simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton‐Raphson nonlinear iterations at the start of each sub‐simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub‐simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3‐D. Copyright © 2016 John Wiley & Sons, Ltd.     

Structural fire design parameters and procedures – analysis of the potential of Eurocode 3

This paper presents an experimental research carried out for testing the simple calculation models presented in EN 1993‐1‐2 for the determination of the fire resistance of steel structures, as well as the models for calculating the development of temperature in the structure. The analysis was carried out for the simple heat transfer models in protected and unprotected steel elements, for the basic parameters of reduction of mechanical properties of steel at high temperatures, and for simple calculation models for determining fire resistance of elements subjected to vertical force in combination with and without the action of the axial force.     

A combined FIC‐TDG finite element approach for the numerical solution of coupled advection–diffusion–reaction equations with application to a bioregulatory model for bone fracture healing

Numerical schemes for the approximative solution of advection–diffusion–reaction equations are often flawed because of spurious oscillations, caused by steep gradients or dominant advection or reaction. In addition, for strong coupled nonlinear processes, which may be described by a set of hyperbolic PDEs, established time stepping schemes lack either accuracy or stability to provide a reliable solution. In this contribution, an advanced numerical scheme for this class of problems is suggested by combining sophisticated stabilization techniques, namely the finite calculus (FIC‐FEM) scheme introduced by Oñate et al. with time‐discontinuous Galerkin (TDG) methods. Whereas the former one provides a stabilization technique for the numerical treatment of steep gradients for advection‐dominated problems, the latter ensures reliable solutions with regard to the temporal evolution. A brief theoretical outline on the superior behavior of both approaches will be presented and underlined with related computational tests. The performance of the suggested FIC‐TDG finite element approach will be discussed exemplarily on a bioregulatory model for bone fracture healing proposed by Geris et al., which consists of at least 12 coupled hyperbolic evolution equations. Copyright © 2012 John Wiley & Sons, Ltd.     

Shear resistance verification of late 19th century masonry according to EC 6 – State of the art

A large part of buildings in Central European cities like Vienna was built in the Gründerzeit period between about 1840 and 1918 [1]. These buildings were constructed according to traditional rules. Current urban development requires historic buildings to be structurally adapted, which requires retroactive analysis of the masonry walls; in Austria according to ÖNORM EN 1998‐3 [2] and ÖNORM EN 1996‐3 (EC 6) [3]. Here, special focus is on the load transfer of horizontal earthquake loads, i. e. the shear strength of masonry walls. This paper describes the verification of historic masonry in detail and discusses individual components. Initial shear strength, load‐influenced friction and the length of the compressed part of the wall are first determined using results from experimental testing and relevant literature and then compared to the approaches in EC 6. Based on this analysis, recommendations are provided to make theoretical approaches more realistic.     

A multiphase mechanical model for Ti–6Al–4V: Application to the modeling of laser assisted processing

A multiphase model for Ti–6Al–4V is proposed. This material is widely used in industrial applications and so needs accurate behaviour modeling. Tests have been performed in the temperature range from 25 °C to 1020 °C and at strain rates between 10⁻³ s⁻¹ and 1 s⁻¹. This allowed the identification of a multiphase mechanical model coupled with a metallurgical model. The behaviour of each phase is calibrated by solving an inverse problem including a phase transformation model and a mechanical model to simulate tests under thermomechanical loadings. A scale transition rule (β-rule) is proposed in order to represent the redistribution of local stresses linked to the heterogeneity of plastic strain. Finally this model is applied to two laser assisted processes: direct laser fabrication and laser welding.     

The effect of traditional reinforcement – prestressed reinforcement ratio on the behaviour of concrete beams

Firstly, the effect of traditional reinforcement – prestressed reinforcement ratio on the behaviour of concrete beams up to failure was experimentally investigated. The beams were 10 m long and 0.5 m high, with different ratios of traditional and prestressed reinforcement. The total quantity of reinforcement in each beam was selected to provide their equal ultimate bending bearing capacity. Deflections, stresses in concrete, traditional and prestressed reinforcement, as well as concrete cracks, were monitored until the beams failure. Using the previously developed numerical model of authors of this paper for static analysis of spatial frame structures, which can simulate main nonlinear effects of their behaviour, then numerical analysis of tested beams was performed. Good agreement was obtained between the experimental and the numerical results, which confirms the possibility of practical application of the adopted numerical model. Main conclusions and recommendations for practical applications according to results of performed tests are given at the end.     

Deflection limitation of beam‐type reinforced masonry constructions – proposals for future requirements

Deflection limitation of reinforced masonry building elements under bending is undertaken according in DIN EN 1996‐1‐1:2013‐02, Section 5.5.2.6, Table 5.2 [N 4], by limiting the span l _ef or the ratio of l_ef to the effective depth d, for example l_ef/d ≤ 20 for simply supported beams. A further requirement in DIN EN 1996‐1‐1:2013‐02, Section 7.3, states that reinforced masonry elements should not deflect excessively under serviceability loading conditions. For reinforced masonry with dimensions, which are within the limits stated in clause 5.5.2.6 [N 4], acceptable vertical deflection of a beam can normally be assumed. In this scientific paper, the figures stated in [N 4] for the limitation of the bending slenderness l _ef/d of reinforced masonry beams like masonry or prefabricated lintels are checked by calculation with the ”ζ procedure“ from reinforced concrete theory. The suitability of this procedure was first demonstrated by comparing calculated and experimentally obtained values. It was determined that maintenance of the bending slenderness ratio l_ef/d ≤ 20 for the tested calcium silicate masonry lintels does not always lead to deflection values w/l_ef ≤ 1/250. For prefabricated straight (flat arch) calcium silicate lintels and horizontal aerated concrete lintels with limit slendernesses of l_ef/d ≤ 15 and calcium silicate masonry lintels with l_ef/d ≤ 10, w/l_ef ≤ 1/250 was fulfilled. With regard to future requirements for the tested reinforced masonry constructions, a method is proposed for the calculation of the limit slenderness ratio l_ef/d, which leads to maintenance of w/lef ≤ 1/250. Furthermore, the presented ”ζ procedure“ enables reliable calculation of deflection figures at the serviceability limit state considering long‐term effects.