Ying-Qiao Guo

Numerical Modeling of Fatigue Damage and Fissure Propagation under Cyclic Loadings

The purpose of this work is to develop a numerical simulation procedure in order to predict the evolution of the fatigue damage and rupture in mechanical parts (such as rolling bearings and gears) under cyclic loadings. The study of the fatigue damage evolution, from the first defect appearance until the parts failure, is primordial in view of the preventive maintenance. The numerical procedure is based on the continuum damage mechanics and the thermodynamics of irreversible processes. The damage effects are fully coupled with the elasto-plastic constitutive laws on a macroscopic point of view. The Sines fatigue criterion for multiaxial stress states is used to estimate the lifetime of mechanical parts in terms of number of cycles. This numerical model is implemented into Abaqus/Explicit using an users subroutine (Vumat). A cycle jumping algorithm allows to largely reduce the computation time. Some remeshing techniques are used to follow up the damage and rupture evolutions. The birth and the growth of the damage and rupture can be visualized via the element deleting and remeshing. These numerical tools are applied to a 2D specimen under a cyclic stretching.

Damage and Rupture Simulation for Mechanical Parts Under Cyclic Loadings

The purpose of this study is to develop a numerical methodology to simulate the fatigue damage of revolving mechanical parts under cyclic loadings (such as rolling bearings). The methodology is based on the continuum damage mechanics and on a fatigue damage model. The fatigue damage can be caused by numerous loading cycles, even in an elastic state; the damage will then influence the elastoplastic behaviors. The coupling effect of both enfeebles the material strength and leads to the rupture. An important improvement on the Sines fatigue criterion is proposed, which allows the coupling behaviors of damage and plasticity to be described better. This paper deals with the following aspects: (i) the fatigue damage model and the identification of fatigue parameters using S-N curves; (ii) the elastoplastic constitutive behaviors coupled with the fatigue damage; (iii) a cycle jumping algorithm to reduce the computation time; and (iv) an adaptative remeshing to follow the rupture propagation. These mechanical and numerical models are implemented in the framework of ABAQUS software. Two applications are presented in this paper: the fatigue lifetime prediction for a cyclic tension specimen and the fatigue spalling (or chipping) initiation and growth in a thrust roller bearing under a cyclic loading. The present approach is very efficient and helpful for the lifetime prediction of revolving mechanical components.

Efficient pseudo-inverse approach for damage prediction in cold forging process simulation

This article presents an efficient pseudo-inverse approach for the damage prediction in cold forging process simulation. Pseudo-inverse approach combines the advantages of the fast inverse approach and accurate incremental approaches. Some intermediate configurations are created geometrically and corrected mechanically to well describe the deformation path. The formulation of an axi-symmetrical element based on pseudo-inverse approach is presented. A strain-based damage model is introduced in the flow theory of plasticity. A direct scalar integration algorithm of plasticity-damage is developed, leading to a fast and robust algorithm for large strain increments. The cold forging processes of two axi-symmetrical parts are simulated to validate pseudo-inverse approach by the incremental approach ABAQUS/Explicit. Pseudo-inverse approach gives very good results, but uses much less CPU time.

Optimization of Forging Preforms by Using Pseudo Inverse Approach

A simplified method called “Pseudo Inverse Approach” (PIA) has been developed for axi-symmetrical cold forging modelling. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without classical contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, which leads to a very fast and robust plastic integration procedure. Numerical tests have shown that the Pseudo Inverse Approach is very fast compared to the incremental approach. In this paper, the PIA will be used in an optimization loop for the preliminary preform design in multi-stage forging processes. The optimization problem is to minimize the effective strain variation in the final part and the maximum forging force during the forging process. The numerical results of the optimization method using the PIA are compared to those using the classical incremental approaches to show the efficiency and limitations of the PIA.

Simulation of Axi-Symmetrical Forging Process by “Inverse Approach”

The simplified method called Inverse Approach (I.A.) has been developed by Batoz, Guo et al.[1] for the sheet forming modelling. They are less accurate but much faster than classical incremental approaches. The main aim of the present work is to study the feasibility of the I.A. for the axi-symmetric forging process modelling. In contrast to the classical incremental methods, the I.A. exploits the known shape of the final part and executes the calculation from the final part to the initial billet. Two assumptions are used in this study: the assumption of proportional loading for cold forging gives an integrated constitutive law without considering the strain path and the viscoplasticity, the assumption of contact between the part and tools allows to replace the tool actions by nodal forces without contact treatment. The comparison with Abaqus shows that the I.A. can obtain a good strain distribution and it will be a good tool for the preliminary preform design.

Finite Element Simulation of the Strength of Corrugated Board Boxes Under Impact Dynamics

In this study, we propose a model based on the finite element method to study the behavior of corrugated cardboard boxes subjected to shocks. To reduce the preparation of the CAD model and the computational times, we have developed an elastoplastic homogenization model for the corrugated cardboard. The homogenization consists in representing a corrugated cardboard panel by a homogeneous plate. A through-thickness integration on a periodic unit cell containing a flute and two flat linerboards is proposed. Each constituent is considered as an orthotropic elastoplastic material with specific hypotheses for the corrugated medium. The model was implemented in the finite element software ABAQUS. Damage boundary curve (DBC) for corrugated cardboard boxes are defined by experimental testing and finite element simulations using the proposed model. The numerical results obtained are in good agreement with the experimental results.

Parameter Identification by Inverse Analysis Coupled with a Finite Pointset Method for Polyurethane Foam Expansion

This paper deals with the parameter identification for polyurethane foaming process simulation by using an inverse analysis coupled with a Finite Pointset Method. Simultaneous measurements of the foam height rise, the reaction temperature and the viscosity on a cylindrical cardboard test tube are obtained by using the foam measurement system (FOAMAT). The simulation of the foam expansion is obtained by solving unsteady Navier-Stokes equations coupled with the energy equation, the curing reaction (reaction of isocyanate with polyol) and the foaming reaction (reaction of isocyanate with water to emit the CO2 gas) by using a mesh-free method. The inverse identification method consists in determining the parameters by comparing the computed quantities (height rise, reaction temperature and viscosity) computed by the finite pointset method to those measured experimentally.

An analytic homogenisation model for shear–torsion coupling problems of double corrugated core sandwich plates:

The homogenisation of shear–torsion behaviours for orthotropic sandwich plates such as corrugated cardboards is a difficult task, even numerically. We decompose the plate torsion into two beam torsions in order to analytically calculate its torsion rigidity. A simple but fairly accurate model based on Bredt theory is proposed for the torsion rigidity of double corrugated core plates. The in-plane shear rigidity is also analytically determined using beam theory. For non-symmetric plate sections, an analytical formulation is developed for the shear–torsion coupling problem. Very good agreement is obtained between the three-dimensional shell simulations and our fast H-model for a non-linear buckling problem coupling the membrane-shear-bending-torsion effects.

Numerical Simulation of Polyurethane Foaming Process Using Finite Point Method

For the numerical simulation of fluid mechanics problems in complex geometries, the use of the classical grid methods such as the finite element method and the finite volume method can give rise to several problems related to the deformation of the mesh. In this work, a meshfree Lagrangian method is used to avoid these problems. This method called Finite Point Method (FPM) has been developed by Kuhnert. It consists in representing the fluid domain by a set of particles. The efficiency of this method is pointed by studying the problem of polyurethane foaming. To do so, we have adopted a theoretical model describing the contribution of the chemical kinetics and the rheological coupling characterizing such process. This coupling is displayed through the dependency of the fluid viscosity to the evolution of the temperature and the chemical reactions present during the foaming process. The expansion of the mixture is governed by the front velocity which is calculated by solving the Navier-Stokes equations. Compared to the experimental results for polyurethane foaming process in a conical beaker, the numerical results using the FPM code are acceptable.

Optimization of cold forging perform tools using Pseudo Inverse Approach

Abstract A new fast method called “Pseudo Inverse Approach” (PIA) for the multi-stage axi-symmetrical cold forging modelling is presented. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, leading to a very efficient and robust plastic integration procedure. Numerical tests show that the Pseudo Inverse Approach is very fast compared with the incremental approach. The PIA is used in an optimization procedure for the preliminary preform tool design in multi-stage cold forging processes. This optimization problem aims to minimize the equivalent plastic strain and the punch force during the forging process. The preform tool shapes are represented by B-Spline curves. The vertical positions of the control points of B-Spline are taken as design variables. The evolution of the objective functions shows the importance of the tool preform shape optimization for the forging quality and energy saving. The forging results obtained by using the PIA are compared with those obtained by the classical incremental approaches to show the efficiency and accuracy of the PIA.