Sub-modelling Approach Research Articles

Probabilistic notch fatigue assessment under size effect using micromechanics-based critical distance theory

Geometrical discontinuities are inevitable in engineering structures due to various functional requirements, which often yield complex stress–strain state and thereby significantly impact their fatigue performances. In this study, crystal plasticity theory is coupled with traditional critical distance theory for notch effect modelling considering microstructural heterogeneity. Specifically, microstructural and geometrical size effects on critical distance and fatigue performance are studied based on Sub-modelling approach. In addition, critical distance theory is coupled with Weibull distribution for probabilistic fatigue life evaluation of notched components. The developed method is verified and compared by using experimental data of GH4169 alloy. The findings demonstrate that the evaluated P-S-N curves exhibit strong agreement with tested data and geometrical size effect poses larger influence than the grain size effect on critical distance and fatigue life.

Microstructural size effect on the notch fatigue behavior of a Ni-based superalloy using crystal plasticity modelling approach

Fatigue performances of critical structures are strongly affected by the microstructural (e.g. grain, defect, inclusion, etc.) size effect, and it is thus important to quantify their detrimental effect. In this work, a numerical procedure is constructed to quantify the influence of microstructure on the mechanical and fatigue behaviors of Ni-based superalloy GH4169. Specifically, by combining sub-modelling approach with crystal plasticity constitutive model, a dual-scale modelling approach is developed for studying grain-level mechanical behavior of Ni-based superalloy GH4169 notched components. In addition, the dislocation-based Tanaka-Mura-Wu model is applied for fatigue crack initiation life prediction. The Paris law is then utilized for fatigue crack propagation analysis based on the simulated short crack. To study the microstructural size effect on fatigue crack initiation and propagation behaviors, sub-models containing various grain orientation, grain size, defect size/shape are built and analysed. Finally, a series of fatigue tests on notched specimens of Ni-based superalloy GH4169 were carried out for method validation. Results indicate that the established dual-scale modelling approach and fatigue life prediction framework yields good agreement with experimental results.

Laser-Welded Corrugated-Core Sandwich Composition—Numerical Modelling Strategy for Structural Analysis

Laser-welding technology has recently enabled the production of corrugated-core steel sandwich panels (CCSSPs) as an innovative large-scale, lightweight structural solution in maritime and infrastructure applications. Detailed numerical analyses, specifically weld-region stress prediction in the presence of transverse patch loading and supports, are computationally challenging and time-consuming for their optimal design. This paper introduces an efficient, simplified combined sub-modelling approach for accurately predicting the detailed structural response of welded corrugated-core steel panels. The approach rests on the homogenisation of the three-dimensional (3D) panel into a two-dimensional equivalent orthotropic single layer (EOSL), where the effect of transverse compressive loads and local support conditions are captured separately via different 2D and 3D sub-modelling techniques, together with a model introduced for calculation of the weld region’s equivalent spring stiffnesses. A laser-welded corrugated-core steel sandwich panel (CCSSP), as a future generation of the steel bridge deck, was examined using different modelling approaches. It was shown that the proposed combined sub-modelling approach can accurately predict stresses and displacements in all the constituent members of the cross-section, including the welds, in a reasonable calculation time when compared with a 3D reference model, unlike the conventional homogenisation approaches.

A numerical estimation of leak-tightness in rolled joint under thermal creep

In the present work, a numerical framework is developed to estimate the leak-tightness of tube to end-fitting rolled joint used in various industries under thermal creep. The leak-tightness of the rolled joint depends on the contact pressure (at the contact surfaces of the tube and end-fitting) and residual stresses (on inner and outer tube surfaces) generated during manufacturing through the rolling process. An axisymmetric finite element model is developed and validated (with literature) to accurately determine the contact pressure and residual stresses at the end of the rolling process. The relaxation in contact pressure and residual stress due to thermal creep during the service life of rolled joint (after manufacturing rolling process) is also accounted in the model. Further, to estimate the leak-tightness (leak rate), a radial plane strain model is chosen that yields the same results as the axisymmetric model. The submodelling approach in the plane strain model handles the modelling of micro-sized leakage paths efficiently. From the FE modelling, it is observed that the contact pressure and residual stresses reduce significantly due to thermal creep. The effect of different leak geometries is examined on the leak-tightness of the rolled joint. It is found that an elliptical leak with major axis in radial direction has a more rate of increase in leakage as compared to other geometries.

Investigation of creep-fatigue crack initiation by using an optimal dual-scale modelling approach

In this work, three dual-scale modelling approaches containing sub-modelling approach, coupled modelling approach and full-field crystal plasticity finite element (CPFE) approach are implemented for notched structures under creep-fatigue loading conditions. Based on the comprehensive comparisons, the sub-modelling approach is determined to be an optimal simulation strategy among them. Furthermore, the combined effects of grain orientation and stress concentration on crack initiation are investigated by adopting the sub-modelling approach. Under low stress concentration factor, the most potential positions of crack initiation randomly locate at the root of geometric discontinuities owing to the influence of grain orientation distribution. With the increase in stress concentration factor and decrease in the number of grains at hotspots, the cooperative relation between grain orientation and stress concentration factor for creep-fatigue crack initiation is revealed through a sequence of simulation results, followed by the competitive relation. On this basis, a feature region map is constructed to distinguish the factor-dominated crack initiation. Finally, a case study of turbine disk is provided to illustrate the engineering meanings of the dual-scale modelling approach. The link from scientific problem to engineering application for the crack initiation prediction is bridged by the damage mechanics approach, which is also expected to be promoted in many high-temperature components.

Advantages of the extended finite element method for the analysis of crack propagation in power modules

• XFEM and Level set methods with submodelling has been implemented in this study. • Method easily allows inclusion of crack growth in IGBT wire bond reliability analysis • Bond wire diameter and loop height significantly affect IGBT wire bond reliability. • Wire bond degradation parameter values decrease with increasing crack length. • For similar load density, smaller wire diameter produces longer wire bond lifetime. The techniques of extended finite element method, level set method and the submodelling approach are implemented in this study to model crack and crack growth in ultrasonically bonded thick aluminium wire for the IGBT power electronics modules under different loading conditions for the purpose of lifetime prediction and reliability assessment during design and manufacturing stages. The crack growth and lifetime prediction were performed under cyclic fatigue passive thermal cycling and active power cycling for the bond wire lift-off failure mechanism while the J-integral for different heel crack lengths are predicted under mechanical loads. The analyses showed that the techniques implemented in this paper are effective for modelling such complex geometries and loading conditions and can easily be integrated in a virtual design platform for power electronics. The accuracy of the technique is evaluated by comparing with trends in the published experimental tests and simulation results as well as the standard finite element method which are all in a good agreement. The wire bond crack growth rate under cyclic loading is strongly influenced by the bond thickness and loading conditions.

Structural assessment of the EU-DEMO water-cooled lead lithium central outboard blanket segment adopting the sub-modelling technique

The development of a sound conceptual design of the Water-Cooled Lead Lithium Breeding Blanket (WCLL BB) is pivotal to make a breakthrough towards the selection of the driver blanket concept for the EU-DEMO. To achieve this goal, an intense research campaign has been performed at the University of Palermo, in cooperation with ENEA Brasimone, under the umbrella of EUROfusion. In this paper, structural analyses of different poloidal regions of the WCLL BB Central Outboard Blanket (COB) segment are reported. In particular, starting from the results of the thermo-mechanical analysis of the whole WCLL BB COB segment, the sub-modelling technique has been applied to the most significant poloidal regions, located at the top, middle and bottom of the segment. The aim is to focus on the stress field locally arising under purposely selected steady-state nominal and accidental loading scenarios. The nominal BB operating conditions, as well as steady-state scenarios derived from both the in-box LOCA and Vertical Plasma Disruption accidents have been considered. Thanks to the sub-modelling approach, the deformative action of the entire segment can be imposed at the boundaries of each local model to realistically assess its structural performances. Moreover, each local model reproduces structural details not included in the global one, such as the Segment Box (SB) cooling channels. Then, the structural behaviour of the selected regions has been assessed in compliance with the RCC-MRx code. The obtained results highlighted that the structural behaviour predicted by the whole segment analysis is similar to that predicted by sub-modelling calculations within the Stiffening Plates, whereas the application of the sub-modelling is a must to investigate in detail the SB structural performances. In addition, results indicate that the BB attachments should be revised, as they contribute to produce the WCLL COB large deformation originating excessive stresses, mainly within the equatorial region.

Submodelling approach to screw-to-bone interaction in additively manufactured subperiosteal implant structures.

Thanks to new digital technologies, complex cases of severe maxillary atrophy may now be treated with additively manufactured subperiosteal implant structures (AMSISs). However, there are few studies addressing this topic and most of them focus on the mechanical behaviour of the AMSIS itself without considering its interaction with the maxilla bone. The aim of this study is to provide a methodology based on finite element analysis (FEA) to evaluate the effect of interaction between the maxilla bone and the screws fixing the AMSIS. The mechanical performance of an AMSIS was examined via a FEA based on submodelling. Significant differences were encountered in displacements and reaction forces when bone-screw interaction was considered. Stress in the cortical layer was found to be close to the maximum strength while the trabecular layer seems to have no effect on the results; stresses in the AMSIS are lower than the fatigue stress limit. Finally, the comparison of stresses between models with and without osseointegration shows how stresses drop once osseointegration is complete. The proposed submodelling approach considerably reduces the computational effort and enables both a detailed model of the interaction between the thread of the screws and the bone and an accurate evaluation of displacement and stress fields on the interface. The results have shown that stresses in the cortical bone are highly affected by the initial geometry of the thread inside the bone, which demonstrates the importance of modelling the effect of the thread.

An FSRW numerical simplification approach for vehicle frontal crashworthiness analysis

Vehicle frontal crashworthiness analysis is an important topic in the field automotive community, as it relates to legislative requirements. Frontal crash models contain a large number of elements and therefore present a high computational cost, especially when performing crashworthiness structural performance optimisations. A new numerical methodology is proposed in this paper with the aim to increase computation speed by implementing a sub-modelling approach on the frontal structure-rear wheels (FSRW) method. In this new method, the vehicle body structure behind the rear seats is replaced by a point mass, with an equivalent mass to the rear structure removed, and attached to the rear frame of the front structure and its wheels. This new method was rigorously tested against validated full size vehicle computer models of different classes provided by NHTSA, and included MPV, SUV, van, and sedan, against fixed rigid barrier (FRB), small overlap and a mobile progressive deformable barrier (MPDB) tests. The research has demonstrated that this new sub-modelling approach correlated against all the full size NHTSA computer models in deformations, intrusions, velocities, and accelerations, as well as providing a runtime average reduction between 7% and 23%. This new simplified method, which can be easily implemented, is innovative and will have an important impact vehicle design, as it will allow an easier use of optimisation techniques, which will lead to safer vehicles.

Double diaphragm forming simulation using a global-to-local modelling strategy for detailed defect detection in large structures

A global-to-local modelling strategy is presented based on a sub-modelling approach to predict the formation of macroscale defects in bi-axial non-crimp fabric (NCF) during double diaphragm forming (DDF). A full-scale global simulation is initially performed using a coarse membrane element mesh (5 mm edge length) to locate areas containing potential defects. Refined local simulations are subsequently performed using high a fidelity shell-element mesh (1 mm edge length) to explicitly predict the shape of forming induced defects in these areas, using boundary conditions derived from the global simulation. The methodology is validated by forming a fabric blank over a generic geometry comprising local changes in cross-sectional shape, in order to invoke forming induced defects in a controlled manner. The defective areas predicted by the simulation agree well with the locations observed from the forming experiments, including the shape and length of surface visible defects such as fabric wrinkling and bridging. The CPU time for this two-stage approach is shown to be approximately 13% compared to the CPU time required for the high fidelity full-scale model for the same geometry.

Submodelling method for modelling and simulation of high-density electronic assemblies

In order to enable the computation of fatigue life prediction of high-density electronic assemblies (solder joints > 4000), a modified submodelling approach was developed to integrate the detailed interconnections into equivalent layers with consistent mechanical parameters and thus reduce the complexity of modeling and simulation. The approach incorporates the uniform equivalent interconnect layers into the global model and simulate the general system response to thermo-mechanical loads. Displacements calculated from this first simulation are fed into a local model with more details of worst-case solder joints, in order to obtain local indicator of fatigue life. In this paper, referred to mechanical experimental methodology, a FEA process was used to extract the mechanical parameters of the equivalent layer. The validity of the modified submodelling approach was verified on fatigue life prediction of a high-density flip-chip package under thermal cycling.

Multi-scale optimisation of thin-walled structures by considering a global/local modelling approach

In this work, a design strategy for optimising thin-walled structures based on a global-local finite element (FE) modelling approach is presented. The preliminary design of thin-walled structures can be stated in the form of a constrained non-linear programming problem (CNLPP) involving requirements of different nature intervening at the different scales of the structure. The proposed multi-scale optimisation (MSO) strategy is characterised by two main features. Firstly, the CNLPP is formulated in the most general sense by including all design variables involved at each pertinent scale of the problem. Secondly, two scales (with the related design requirements) are considered: (a) the structure macroscopic scale, where low-fidelity FE models are used and (b) the structure mesoscopic scale (or component level), where more accurate FE models are involved. In particular, the mechanical responses of the structure are evaluated at both global and local scales, avoiding the use of approximated analytical methods. The MSO is here applied to the least-weight design of an aluminium fuselage barrel of a wide-body aircraft. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one, thanks to the implementation of a sub-modelling approach. The whole process is completely automated, and once set, it does not need any further user intervention.

Multi-scale Least-Weight Design of a Wing-Box Through a Global/Local Modelling Approach

In this work, a multi-scale optimization strategy for lightweight structures, based on a global-local modelling approach is presented. The approach is applied to a realistic wing structure of a civil aircraft. The preliminary design of the wing can be formulated as a constrained optimization problem, involving several requirements at the different scales of the structure. The proposed strategy is characterized by two main features. Firstly, the problem is formulated in the most general sense, by including all design variables involved at each problem scale. Secondly, two scales are considered: (i) the structure macroscopic scale, where low-fidelity numerical models are used; (ii) the structure mesoscopic scale (or component-level), where enhanced models are involved. In particular, the structural responses are evaluated at both global and local scales, avoiding the use of approximated analytical methods. To this end, fully parametric global and local finite element models are interfaced with an in-house genetic algorithm. Refined models are created only for the most critical regions of the structure, and linked to the global one by means of a dedicated sub-modelling approach.

A multi-scale two-level optimisation strategy integrating a global/local modelling approach for composite structures

In this work, a multi-scale optimisation strategy for the preliminary design of composite structures involving design requirements at different scales, is presented. Such a strategy, denoted as GL-MS2LOS, has been formulated by integrating a dedicated global-local (GL) modelling approach into the multi-scale two-level optimisation strategy (MS2LOS).The GL-MS2LOS aims at proposing a very general formulation of the design problem, without introducing simplifying hypotheses and by considering, as design variables, the full set of geometric and mechanical parameters defining the behaviour of the composite structure at each pertinent scale. By employing a GL modelling approach, most of the limitations of well-established design strategies based on analytical or semi-empirical models are overcome.The effectiveness of the presented GL-MS2LOS is proven on a meaningful study case: the least-weight design of a composite fuselage barrel of a wide-body aircraft undergoing various loading conditions and subject to requirements of different nature. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm to perform the optimisation. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one thanks to the implementation of a sub-modelling approach. The general nature of the GL-MS2LOS allows finding an optimised configuration characterised by a weight saving of 40% when compared to an optimised aluminium solution obtained through a similar GL optimisation strategy.

Surface roughness influences on localization and damage during forming of DP1000 sheet steel

Abstract Surface roughness strongly influences the occurrence of edge cracks in metal forming processes. Recently, a sub-modelling approach has therefore been presented that is capable of predicting whether an edge forming process could be performed without failure events, but the macroscopic load-deformation behavior could not be predicted. This approach is extended to consider roughness induced micro damage even on the macroscopic scale. The concept is based on the idea to define an individual set of material parameters for those elements that are located at the sample´s surface. In order to calibrate the required set of parameters for these surface elements, sub-models are created which geometrically represent the roughness profiles that were determined experimentally before the bending tests were conducted. The procedure is demonstrated for the example of bending tests performed on samples made of steel DP1000 that have undergone two different surface treatments to adjust roughness conditions - fine grinding and polishing in the one extreme case and grinding with 80-grit sand paper in the other one. Experimental results reveal significant differences between the two sample configurations: while the samples with smooth surfaces remain free from cracks during the entire duration of the experiment, the samples with rough surfaces show fracture events. For both cases, the new simulation framework allows to reproduce both the macroscopic load-deflection curves and the individual damage and fracture behaviours.

A methodology for a global-local fatigue analysis of ancient riveted metallic bridges

PurposeRecent studies have proposed the application of local fatigue approaches based on fracture mechanics or on strain-life material relations for the fatigue analysis of metallic structures. However, only few studies in the literature apply local approaches in the riveted bridges analysis; although these approaches can be applied to any type of connections, requiring a detailed stress analysis of joints and, consequently, considerable computational resources costs. The approach based on S-N curves, formulated in nominal or net stresses, is more usual in the fatigue analysis of riveted bridges. Due to economic factors, riveted bridges have had their operating life extended, while changes in the transport system over the years have subjected such structures to overloads different from those originally planned. These bridges, most of them centenary, were not originally designed accounting for fatigue damage; they represent an important group of structures that are very likely subjected to significant fatigue damage indexes. These factors make necessary detailed residual fatigue life studies to substantiate the decisions of extend (or not) the operational period of these bridges. The paper aims to discuss these issues.Design/methodology/approachThe present paper presents a methodology aiming at applying the local approaches in the fatigue analysis of riveted joints of metallic bridges, through the use of sub-modeling techniques and procedures automation. The use of such techniques made such an application viable by keeping the computational costs involved at a moderate level. The proposed procedures were demonstrated using the Trezói Railway Bridge, located on the Beira Alta line, Portugal, built shortly after the Second World War. The proposed set of procedures allowed, through finite elements analysis, to obtain the relevant stresses to perform local fatigue damage analysis. A global structural model was constructed, using beam elements, and local models of a critical node were built with solid finite elements. The structure is analyzed under the passage of regulatory trains. The details of the modeling performed and the computation of the principal stresses in the vicinity of a node and the tangential/circumferential stresses at the holes of two critical riveted connections of that node are analyzed and a fatigue damage analysis is carried out.FindingsIn the proposed submodelling approach, disassembling the complex riveted nodes into riveted subassemblies allowed the evaluation of the local stresses at riveted holes at an affordable computational cost.Originality/valueA methodology is proposed to allow the application of local fatigue analysis in real complex riveted joints, mitigating the computational costs that would result from a full model of the node with all rivets.

Fatigue crack growth in a compressor stage of a turbofan engine by FEM-DBEM approach

In this work, the fatigue crack-growth process in a rotating disk of an aircraft gas turbine engine has been simulated. The considered crack nucleated in the attachment between a blade and the disk of a compressor stage, both made of a two-phase titanium alloy.The fatigue crack-growth process of such crack has been simulated by means of two codes, ABAQUS and BEASY, based on Finite Element Method (FEM) and Dual Boundary Element Method (DBEM) respectively. In particular, a variant of the submodelling technique, based on the superposition principle, has been used for coupling the two codes in order to exploit simultaneously their peculiar strength points. The FEM code has been used to compute the global stress field whereas the DBEM code has been used to calculate the fracture parameters, useful to predict the crack-growth evolution. The J-integral method and the Minimum Strain Energy Density Criterion (MSED) have been used for calculating K values and predicting crack kinking respectively.In this work, the FEM-DBEM crack path is compared with both the path obtained by a full-scale experimental test and the path predicted via a full FEM approach: having in an initial stage considered the only centrifugal load, with no allowance e.g. for the fluid pressure on the blades and for the blade dynamic behaviour, some discrepancies are found between numerical and experimental results.The computational advantages of the proposed submodelling approach are highlighted, in addition to a preliminary fatigue assessment provided for the considered compressor disk (further analyses are under development).

FEM-DBEM approach to simulate crack propagation in a turbine vane segment undergoing a fatigue load spectrum

In this work a thermo-mechanical fatigue application, related to a crack propagation in an aircraft turbine vane undergoing a complex load spectrum, is simulated. A computationally efficient FEM-DBEM submodelling approach, whose implementation leverages on the principle of linear superposition, is adopted.When tackling a crack propagation problem with a FEM-DBEM combined approach, the global analysis is generally worked out by FEM whereas the fracture problem is solved in a DBEM environment. In particular, a DBEM submodel is extracted from the global uncracked FEM model and, generally, is loaded on the boundaries with temperatures and either displacements or tractions; then the crack propagation is simulated by repeated thermal-stress DBEM analyses. Differently from that, the proposed equivalent approach solves the crack propagation problem by adopting a simpler pure stress DBEM analyses in which the boundary conditions, in terms of tractions, are just needed on the DBEM crack faces. Such tractions are evaluated by the FEM global analysis along a virtual surface traced by the advancing crack (the FEM model is uncracked). Such an approach provides accuracy enhancement and computational advantages.

Fatigue life assessment in lateral support element of a magnet for nuclear fusion experiment “Wendelstein 7-X”

Wendelstein 7-X (W7X), a nuclear fusion experiment of modular stellarator type, started operation in 2015 and will be upgraded with a water cooled first wall for steady state operation in 2020. A hot hydrogen plasma of ultra-low density is confined in a plasma vessel by an electromagnetic field generated by specially shaped superconducting coils. Such coils, embedded in a cryostat working at 4K, are kept by a central support ring and joined together by welded lateral support elements (LSEs). In this paper, a coupled FEM-DBEM (Dual BEM) submodelling approach is adopted for crack-growth simulations of the cracks detected in LSEs and driven by a fatigue load spectra.A global analysis on one fifth of the fivefold symmetric magnet system is performed by FEM, whereas the submodelling approach is adopted to solve the crack propagation by DBEM. In particular, the adopted approach is based on the application of the superposition principle to solve a LEFM problem: the only boundary conditions for the DBEM submodel consist of tractions, calculated by the FEM global analysis and applied to the crack faces in the local submodel. The obtained speed of crack advance and crack kinking are compared with literature results to highlight the accuracy of the proposed approach together with inherent computational advantages.

Failure Analysis for a Low Pressure Aeroengine Turbine Vane

Background & ObjectiveIn this work, a thermo-mechanical fatigue application related to a fracture process simulation in a turbine vane is implemented, using a submodelling approach based on the principle of linear superposition.MethodThe proposed crack propagation approach leverages on a combined use of FEM and DBEM methodologies: the global analysis is solved by using FEM whereas the fracture problem is demanded to DBEM. In particular, a DBEM submodel is extracted from a global uncracked FE model and, in the new proposed formulation, boundary conditions are applied just on crack faces rather than loading subdomain boundaries with displacements/tractions and temperatures, as in the classical approach.Results & ConclusionThe adopted approach solves the fracture problem by using simpler pure stress analyses rather than by thermal-stress analyses, as requested by the classical approach. Boundary conditions applied on the submodel crack faces come from the solution of a FE uncracked global model. The computational advantages of such alternative approach are highlighted and, in addition, a fatigue assessment is provided for a turbine vane, considering as initial crack the maximum design defect dictated by GE-Avio regulations for such kind of components.