A combined DEM–FEM numerical method for Shot Peening parameter optimisation

A numerical modelling approach capable of simulating Shot Peening (SP) processes of industrial interest was developed by combining the Discrete Element Method (DEM) with the Finite Element Method (FEM).In this approach, shot–shot and shot–target interactions as well as the overall shot flow were simulated efficiently using rigid body dynamics. A new algorithm to dynamically adapt the coefficient of restitution (CoR) for repeated impacts of shots on the same spot was implemented in the DEM code to take into account the effect of material hardening. Then, a parametric study was conducted using the Finite Element Method (FEM) to investigate the influence of the SP parameters on the development of residual stresses.Finally, a two-step coupling method is presented to combine the output of DEM simulation with FEM analyses to retrieve the Compressive Residual Stresses (CRS) after multiple impacts with the aim to evaluate the minimum area required to be modelled to realistically capture the field of residual stresses. A series of such coupled analyses were performed to determine the effect of peening angle and the combination of initial velocity and mass flow rate on CRS.     

On the potential applications of a 3D random finite element model for the simulation of shot peening

Shot peening is a cold-working process that is used mainly to improve the fatigue life of metallic components. Experimental investigation of the mechanisms involved in shot peening is very expensive and complicated. Therefore, the Finite Element (FE) method has been recognized as an effective mean for characterizing the shot peening process and several types of FE models have been developed to evaluate the effects of shot peening parameters. However, in most of the existing FE models, the shot peening sequence and impact location were defined a priori. It is therefore the purpose of this study to consider the random property of the shot peening process. A novel 3D FE model with multiple randomly distributed shots was developed combining a Matlab program with the ANSYS preprocessor. The explicit solver LS-DYNA has been used to simulate the dynamic impingement process. Several potential applications of this novel model such as: the quantitative relationship of the peening intensity, coverage and roughness with respect to the number of shots have been presented. Moreover, simulations with multiple oblique impacts have been carried out in order to compare with results from normal impingements. Our work shows that such a computing strategy can help understanding and predicting the shot peening results better than conventional FE simulations.     

Application of ADINA and hole drilling method to residual stress determination in weldments

Residual stress distributions with depth at weld toes in controlled shot-peened, high strength steel weldments were determined through the measurement of relaxed surface strains by the incremental hole drilling method. The stress states were determined from the relaxed surface strains by a novel elasto-plastic interpretation of the strain readings, using the finite element software, ADINA. Residual stress distributions determined from the theory of elasticity, using experimental strain gauge readings from the hole drilling method, gave values much greater than the 0.2% offset yield stress of 613 MPa. The stress states were corrected through elasto-plastic finite element modeling using ADINA. After the corrections, the maximum residual stress was less than 613 MPa. The corrected stress distributions were applied to determine the effect of controlled shot peening on residual stress distributions with depth. The distributions within 0.8 mm below the material surface was used as an indicator of shot-peening depth and the effect of control parameters.     

Modelling of residual stresses in the shot peened material C-1020 by artificial neural network

This study consists of two cases: (i) The experimental analysis: Shot peening is a method to improve the resistance of metal pieces to fatigue by creating regions of residual stress. In this study, the residual stresses induced in steel specimen type C-1020 by applying various strengths of shot peening, are investigated using the electrochemical layer removal method. The best result is obtained using 0.26 mm A peening strength and the stress encountered in the shot peened material is ?276 MPa, while the maximum residual stress obtained is ?363 MPa at a peening strength of 0.43 mm A. (ii) The mathematical modelling analysis: The use of ANN has been proposed to determine the residual stresses based on various strengths of shot peening using results of experimental analysis. The back-propagation learning algorithm with two different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained with four neurons in the hidden layer, which made it possible to predict residual stress with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found the R² values are 0.996112 and 0.99896 for annealed before peening and shot peened only, respectively. Similarly, these values for testing data are 0.995858 and 0.999143, respectively. As seen from the results of mathematical modelling, the calculated residual stresses are obviously within acceptable uncertainties.     

Finite element analysis of residual stress induced by shot peening process

The aircraft industry has only recently begun to explore possible application of welding as an alternative joining method for the design of future large civil airliner wing. One of the main obstacles, encountered in the past years, to welding application within the aircraft industries were due to failure in the weldments, caused by high tensile residual stresses present in the region of the weld, reducing drastically fatigue strength of welded joints. Improvement in the fatigue life of the welded joint can be obtained if compressive residual stresses are introduced at the weld region.Shot peening is a manufacturing process intended to give aircraft structures the final shape and to introduce a compressive residual state of stress inside the material in order to increase fatigue life. This paper presents the modeling and simulation of the residual stress field resulting from the shot peening process. The results achieved show that a significant decrease of welding induced tensile residual stress magnitude can be obtained. Good agreement between experimental and numerical results was achieved.     

Optimal re-design of helical springs using fuzzy design and FEM

The aim of this paper is to present results of using fundamental machine element design principles into re-designing optimally heavy duty springs used in terrain machinery and in industry. Use of standard procedures often results in recurring fatigue fracture failures. This reveals need for correcting also the present standards. Main causes of failures are the local bending due to eccentric highly impact force application at squared and ground ends and wearing away of the shot peening protection. Optimum design of the spring is obtained. Goals are minimisation of wire volume, space restriction, desired spring rate, avoidance of surging frequency and achieving reliably long fatigue life. Conclusions are verified by using full 3D solid FEM analysis with MSC Nastran by which the stresses and also strains, deformations and natural frequencies and modes are obtained.     

Elasto-plastic finite element analysis of orthotropic rotating discs with holes

The elasto-plastic stress analysis of orthotropic rotating discs with holes has been carried out by the finite element method (FEM). An isoparametric rectangular element with nine nodes has been chosen and the Lagrange polynomial has been used as interpolation function. Steel-aluminium composite has been manufactured by upsetting under the pressure and the temperature. Mechanical properties and yield strengths of composite material have been obtained experimentally by using a strain gauge in the tensile testing machine. The expansions of plastic regions have been illustrated for various cases. Residual stresses and tangential stresses have been shown on the elasto-plastic boundaries of the disc. The limit of angular velocities of the orthotropic disc have been increased by using tangential residual stresses and tangential stresses in the disc subjected to the centrifugal force.     

A numerical study of the residual stress pattern from single shot impacting on a metallic component

Shot peening is a process in which a stream of shot is blasted against an engineering component to generate a high compressive residual stress regime at the surface of the component. This paper describes a 3D finite element dynamic analysis of single shot impacting on a metallic component. The model is first validated against a published numerical study. A parametric study is conducted to investigate the effect of shot diameter, impact velocity, incident angle and component material properties on the resulting residual stress profile. Several meaningful conclusions can be drawn regarding the effect of shot diameter, impact velocity, incident angle and initial yield stress. The effect of strain-hardening parameter is more complex as it depends on the relative magnitude of the strain–hardening yield stress to the initial yield stress and the impact energy.     

Elastic–plastic modeling of heat-treated bimorph micro-cantilevers

This paper models the residual stress distributions within micro-fabricated bimorph cantilevers of varying thickness. A contact model is introduced to calculate the influence of contact on the residual stress following a heat treatment process. An analytical modeling approach is adopted to characterize bimorph cantilevers composed of thin Au films deposited on thick poly-silicon or silicon-dioxide beams. A thermal elastic–plastic finite element model (FEM) is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the beam tip deflection following heat treatment. The influences of the beam material and thickness on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a larger beam thickness leads to a greater residual stress difference at the interface between the beam and the film. The residual stress established in the poly-silicon cantilever is greater than that induced in the silicon-dioxide cantilever. The results confirm the ability of the developed thermal elastic–plastic finite element contact model to predict the residual stress distributions within micro-fabricated cantilever structures with high accuracy. As such, the proposed model makes a valuable contribution to the development of micro-cantilevers for sensor and actuator applications.     

An investigation of ultrasonic nanocrystal surface modification machining process by numerical simulation

As a method for surface severe plastic deformation (S²PD), ultrasonic nanocrystal surface modification (UNSM) enhances metal surface properties through striker peening, a metal dimpling process driven by ultrasonic vibration energy. UNSM treatment introduces residual stress, surface hardening, and nano-crystalline structures into metal surfaces which are beneficial for reducing wear, fatigue, and corrosion properties. In this paper, the process of UNSM is described and a simplified physical model created using the equivalent static loading method is presented. Along with the simplified physical model, a finite elements simulation model was developed. Effective plastic strain was considered as a parameter for evaluating the level of work hardening produced in the simulation. The dynamic processes and energy dissipation were also examined, and it was found that different kinds of energy dissipation occur during UNSM treatment. Comparisons between the processing parameters (processing velocity, static load, and feed rate) were performed using a simulated example of UNSM linear processing. The results show that the linear processing produces a uniform region containing identical distributions of residual stress and effective plastic strain. The effects of the parameters on the processing results (residual stress, plastic deformation and work hardening) were likewise studied using UNSM linear processing. Compared to processing velocity, a high static load produced more work hardening and higher compressive residual stress. Surface deformation and residual stress results were also more sensitive to static load than processing velocity. Feed rate was found to be an important parameter as well, greatly influencing both surface deformation and work hardening.     

A knowledge base for finite element mesh design

The finite element method (FEM) is the most successful numerical method, that is used extensively by engineers to analyse stresses and deformations in physical structures. These structures should be represented as a finite element mesh. Defining an appropriate geometric mesh model that ensures low approximation errors and avoids unnecessary computational overheads is a very difficult and time consuming task. It is the major bottleneck in the FEM analysis process. The inductive logic programming system GOLEM has been employed to construct the rules for deciding about the appropriate mesh resolution. Five cylindrical mesh models have been used as a source of training examples. The evaluation of the resulting knowledge base shows that conditions in the domain are well represented by the rules, which specify the required number of the finite elements on the edges of the structures to be analysed using FEM. A comparison between the results obtained by this knowledge base and conventional mesh generation techniques confirms that the application of inductive logic programming is an effective approach to solving the problem of mesh design.     

Elastic–plastic modeling of heat-treated bimorph micro-cantilevers

This paper models the residual stress distributions within micro-fabricated bimorph cantilevers of varying thickness. A contact model is introduced to calculate the influence of contact on the residual stress following a heat treatment process. An analytical modeling approach is adopted to characterize bimorph cantilevers composed of thin Au films deposited on thick poly-silicon or silicon-dioxide beams. A thermal elastic–plastic finite element model (FEM) is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the beam tip deflection following heat treatment. The influences of the beam material and thickness on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a larger beam thickness leads to a greater residual stress difference at the interface between the beam and the film. The residual stress established in the poly-silicon cantilever is greater than that induced in the silicon-dioxide cantilever. The results confirm the ability of the developed thermal elastic–plastic finite element contact model to predict the residual stress distributions within micro-fabricated cantilever structures with high accuracy. As such, the proposed model makes a valuable contribution to the development of micro-cantilevers for sensor and actuator applications.

     

Out-of-plane deformation and pull-in voltage of cantilevers with residual stress gradient: experiment and modelling

The out-of-plane deformation and the pull-in voltage of electrostatically actuated cantilevers with a residual stress gradient, is investigated in the length range 100–300 µm. Measured pull-in voltages are compared with calculations, which are obtained using previously proposed analytical expressions and a finite element method (FEM) modelling. In particular, a simplified model of the residual stress distribution inside cantilevers is formulated that enables FEM simulation of measured out-of-plane deformations and pull-in voltages for all lengths of fabricated cantilevers. The presented experimental results and FEM model are exploitable in the design of cantilever-based microelectromechanical systems, in order to provide a reliable prediction of the influence of residual stress gradient on device shape and pull-in voltage.

     

Scene Detection in Videos Using Shot Clustering and Sequence Alignment

Video indexing requires the efficient segmentation of video into scenes. The video is first segmented into shots and a set of key-frames is extracted for each shot. Typical scene detection algorithms incorporate time distance in a shot similarity metric. In the method we propose, to overcome the difficulty of having prior knowledge of the scene duration, the shots are clustered into groups based only on their visual similarity and a label is assigned to each shot according to the group that it belongs to. Then, a sequence alignment algorithm is applied to detect when the pattern of shot labels changes, providing the final scene segmentation result. In this way shot similarity is computed based only on visual features, while ordering of shots is taken into account during sequence alignment. To cluster the shots into groups we propose an improved spectral clustering method that both estimates the number of clusters and employs the fast global k-means algorithm in the clustering stage after the eigenvector computation of the similarity matrix. The same spectral clustering method is applied to extract the key-frames of each shot and numerical experiments indicate that the content of each shot is efficiently summarized using the method we propose herein. Experiments on TV-series and movies also indicate that the proposed scene detection method accurately detects most of the scene boundaries while preserving a good tradeoff between recall and precision.     

Packing spherical discrete elements for large scale simulations

We introduce a new geometric method to generate sphere packings with restricted overlap values. Sample generation is an important, but time-consuming, step that precedes a calculation performed with the discrete element method (DEM). At present, there does not exist any software dedicated to DEM which would be similar to the mesh software that exists for finite element methods (FEM). A practical objective of the method is to build very large sphere packings (several hundreds of thousands) in a few minutes instead of several days as the current dynamic methods do. The developed algorithm uses a new geometric procedure to position very efficiently the polydisperse spheres in a tetrahedral mesh. The algorithm, implemented into YADE-OPEN DEM (open-source software), consists in filling tetrahedral meshes with spheres. In addition to the features of the tetrahedral mesh, the input parameters are the minimum and maximum radii (or their size ratio), and the magnitude of authorized overlaps. The filling procedure is stopped when a target solid fraction or number of spheres is reached. Based on this method, an efficient tool can be designed for DEMs used by researchers and engineers. The generated packings can be isotropic and the number of contacts per sphere is very high due to its geometric procedure. In this paper, different properties of the generated packings are characterized and examples from real industrial problems are presented to show how this method can be used. The current C++ version of this packing algorithm is part of YADE-OPEN DEM [20] available on the web (https://yade-dem.org).     

Numerical simulation of the stress peen forming process and experimental validation

Stress peening forming is widely used in the aeronautics industry to induce curvatures in wing skins. Most of the investigations of stress peen forming are empirical and experimental. In this paper, a three step numerical model that can simulate this process was developed. First, an implicit Finite Element Analysis (FEA) with ANSYS where a prebending moment along the spanwise direction of the component was performed. Then, an explicit FEA with LS-DYNA simulating shot impacts on the pre-stressed component was executed in order to obtain the resulting stresses inside the component. Finally, an implicit FEA with ANSYS was performed for calculating the arc heights and the curvature radii of the component in chordwise and spanwise directions. Numerical analysis of the process shows that the prebending moments have an influence not only on the residual stress profiles but also on the curvatures of the deformed component in chordwise and spanwise directions. This model was used to establish a relationship between the prebending moment and the resulting arc heights and residual stress profiles. The numerical strategies developed in this paper supply a useful tool for studying and optimizing the stress peening process.     

Quadratic programming method in numerical simulation of metal forming process

In this paper, a quadratic programming (QP) model based on a parametric variational principle is proposed for elastic–plastic (EP) finite element analysis of metal forming processes. The contact problem with friction between blank and tools is treated in the same way as in plastic analysis. The penalty factors, which are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of metal forming, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. The algorithms for contact analysis and plastic analysis are established in one frame and consistent with each other. Compared with the conventional EP FEM, the newly developed method requires no tedious iterative procedures, and has no convergence problems. To apply this method easily to simulation of metal forming, detailed forms of some key matrices or vectors for 2D FEM and 3D FEM are presented, and a parametric loading algorithm for the QP model is developed, which is suitable for QP problem with free variables, and can decrease memory cost by avoiding the introduction of additional slack variables and improve the solution efficiency to some extent. Finally the proposed QP model is validated by two examples, analysis of V-notched tension test and analysis of the drawing of a square box––one of the benchmarks proposed at NUMISHEET93. It can be seen that the accuracy of solution of the new EP FEM based on QP is better than that of the conventional EP FEM based on iteration. To make the new EP FEM more applicable to metal forming industries, It is necessary to develop a more efficient QP algorithm that is suitable for large-scale problems.     

Fracture mechanics J-integral calculations in thermo-elasto-plasticity

A finite element post-processor has been developed to calculate an incremental plasticity-based J-integral for fracture mechanics evaluations. The post-processor accounts for elastic-plastic deformations and thermal strains. The ADINA finite element computer program, with minor modifications by Babcock and Wilcox, was used with the Ramberg-Osgood stress-strain law and provides through its “porthole” files the required results of stresses, strains, displacements, and elastic and plastic strain energies.

The numerical results of the post-processor indicate that the thermal J-integral, which consists of a line integral for the isothermal case and an additional area integral for the thermal effect, can be considered path-independent even in the presence of plastic and thermal strains.     

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.     

Finite element stress formulation for dynamic elastic-plastic analysis

The solution to wave propagation problems in solids with elastic-plastic material properties is obtained by using the finite element method directly in terms of the stresses. A variational principle due to Gurtin is modified by including a plastic strain tensor in the constitutive relationship. The resulting finite element equations, which represent the strain-displacement equations written in terms of the stresses, are simultaneous integral equations in time. With a transformation of variables, a set of simultaneous differential equations is obtained of the form$\text{H}\text{s}\text{?}\text{+ Qs+ Ve}{}_{\mathrm{p}}\text{= q(t)}$, where $\text{H}$ is a symmetric positive-semidefinite matrix, and $\text{Q}$ is a symmetric positive-definite matrix. The stresses and the plastic strains are represented by $\text{s}\text{?}$ and $\text{e}{}_{\mathrm{p}}$, respectively.Finite element equations are developed for an axisymmetric ring element with an arbitrary quadrilateral cross section in which the stresses and the plastic strains vary linearly along the sides of the elements. The equations are numerically integrated with respect to time by Newmark's generalized acceleration method.An iterative procedure is presented, which uses the finite element strain-displacement equations and the plasticity relationships, to determine the state of stress at the end of the time step. Several examples are used to demonstrate the solution technique for elastic and elastic-plastic problems.