On a numerical simulation for stable crack extension process and a nonlinear fracture criterion

In this note a numerical simulation for a stable crack extension process has been worked out by an incremental finite element method. Utlizing the critical opening angle at the crack tip and accounting for the effect of stress history, we have visualized the stable crack extension process from initiation to instability. Several field variables including $\text{J-}\text{integrals}$, stresses and strains, have been computed for every incremental load step. It appears that the critical opening angle at the crack tip may serve as an important parameter in these fracture phenomena including the stable crack extension process. Based on the numerical results an idea for a nonlinear fracture criterion is proposed.     

翼子板零件拉延成形的有限元分析

针对某轿车前翼子板的拉延成形工艺,用有限元的数值模拟分析定性地判断了成形件的危险区域,并通过调整拉延筋的布置、压边力以及坯料的形状等,定量的给出了拉延成形过程中的工艺参数,实现了拉延成形工艺的优化,为实际生产提供了指导,并最终得到了符合质量要求的拉延件产品.     

Analysis of temperature and speed effects on the drawing stress for improving the wire drawing process

This paper deals with experimental investigations in order to study the influence of drawing conditions on temperature rise and drawing stress in cold drawn copper wires. In the multipass drawing machine, the temperature rise and drawing stress are measured with thermocouples and load cell systems, respectively, for different drawing speeds. The results obtained show that the drawing stress and temperature rise vary during the drawing process. This certainly comes from the variation of the friction coefficient and the flow stress of the material depending on the drawing speed. From the experimental results, a relationship between temperature rise, drawing stress and friction coefficient is built. Based on this, a modification of Avitzur’s model is presented. This new model can help to select the process parameters which satisfy the conditions of minimum drawing stress for copper material.     

Numerical simulation and experimental validation of a multi-step deep drawing process

This paper presents the numerical simulation of an industrial multi-step deep drawing process. A large strain finite element formulation including a hyperelastic elastoplastic constitutive model and a contact-friction law is used to this end where the steel sheet material parameters considered in the analysis are previously derived through a characterization procedure of its mechanical response. The numerical predictions of the final shape and thickness distribution of the blank are compared and discussed with available experimental values measured at the end of three successive drawing steps. In addition, a plastic work-based damage index is used to assess failure occurrence during the process. The damage values computed at the end of the drawing process are found to be lower than that corresponding to rupture in the tensile test, considered here as the threshold of failure, confirming, as observed experimentally, that neither fracture nor necking is developed in the blank during the whole drawing process. Finally, the possibility to carry out a reduced two-step drawing process, obtained by merging the second and third steps of the three-step process, is precluded since the damage criterion predicts in this case excessively large values that indicate that failure may occur in specific zones of the sheet.     

平底筒形件主动径向加压充液拉深的数值模拟

针对低塑性、大高径比航天铝合金板材零件成形需要,提出了带主动径向加压的充液拉深新技术.通过数值模拟方法,采用动力显式分析软件ETA/Dynaform5.5对5A06铝合金平底筒形零件主动径向加压充液拉深成形过程进行了研究.以零件成形最终壁厚分布为评定标准,分析了不同主动径向压力加载路径对成形质量的影响.通过数值模拟证明了在主动径向加压充液拉深过程中,法兰变形区存在一个应力分界线,随着主动径向液压力的增加,分界线的位置内移.研究表明,采用40 MPa的液室压力加载曲线,并配合45 MPa的主动径向压力加载路径,获得的铝合金平底筒形件的拉深比为3.1,零件质量好.     

固定短芯棒拔管残余应力分布规律研究

为了研究固定短芯棒拔管残余应力的产生机理和分布规律,采用弹塑性有限元法模拟拉拔过程,讨论模具形状参数、拉拔变形参数、摩擦条件对残余应力的影响.结果表明,当模具半锥角α较小时,随着α的增加,残余应力增大;在减径率εs一定的条件下,随着减壁量ΔS的增加,钢管内外表面的残余应力逐渐减小,在ΔS一定而εs增加时,内外表面上残余应力呈先增大后减小变化趋势;同时,轴向残余应力随着拉拔速度v和摩擦系数μ的增加而增大.     

Fracture criterion for the axisymmetric disking process

Disking is a process designed to cut brittle plates and rods. In axisymmetric disking, a pre-cracked cylindrical rod is placed in an elastic, annular sheath and the composite is subjected to biaxial fluid pressure. At a critical pressure the crack runs across the circular section of the rod producing a clean cut. A linear elastic fracture mechanics analysis is used to develop a fracture criterion for the process. A concentric circular cylinders model is assumed with perfect bonding at the interface. The flaw that initiates fracture in the rod is modeled as an annular crack perpendicular to the interface with one crack tip at the interface. The problem is formulated as a singular integral equation of the first kind with a Cauchy type kernel. The stress intensity factors are determined as a function of crack size and shear moduli.     

Numerical simulation of damage evolution in multi-pass wire drawing process and its applications

This paper presents a numerical simulation of damage evolution in multi-pass wire drawing process and its potential relevance to manufacturing design. The Gurson–Tvergaard–Needleman model (GTN model) is introduced to describe damage evolution in the drawn wire. Based on a three-dimensional model of the drawn wire generated through ABAQUS, the numerical analyses on damage behavior in multi-pass wire drawing are undertaken for the purpose of investigating the damage evolution during all phases of the process. Convergence problems in the process of simulation are discussed. The results illustrate the damage evolution of the drawn wire in each of the eight passes and the damage distribution along axial and circular directions. It turns out that the damage values continuously rise up with the increase of drawing passes and the damage evolution in the drawing process shows obvious nonlinear characteristic. The damage distribution along axial and circular directions agrees well with actual drawing situation. Wire breakage is expected to occur in those areas of the drawn wire where fractures most possibly initiate. Furthermore, the numerical analyses contribute a new approach for the optimization of the drawing parameters. Based on the principle of least damage accumulation in the drawing process, the optimal area reduction is chosen and selection of material processes is proposed. The currently standard 8-pass wire drawing process can be potentially optimized by a proposed 7-pass wire drawing process.     

On numerical simulation of the continuous casting process

In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.     

Optimal control of a non-isothermal tube drawing process

We consider an optimal control problem for a non-isothermal tube drawing process. The goal is to control the circular cross-sectional area of the tube using the drawing speed as the control variable. To achieve this goal, a cost functional of tracking-type is defined, the first-order optimality condition is derived and the Hessian of the reduced cost functional is derived. Numerical simulations based on a steepest descent and a Newton-Conjugate-Gradient algorithm are presented.     

The critical tensile stress criterion for cleavage

An elastic-plastic analysis was used to accurately measure the microscopic cleavage strength _inff ^sup* of notched bars of high nitrogen steel in bending. It was found that _inff ^sup* increases as the root radius of the notch decreases. For > 0.010, the variation of _inff ^sup* with , and the difference between _ingff ^sup* and the cleavage fracture strength of a plane tensile specimen, _f, may result from a statistical effect, due to differences in the volume of highly stressed material in the plastic zone. For < .010, the primary reason for the apparent increase in _inff ^sup* with decreasing , is the steep stress gradient at the notch tip, which forces the critical plastic zone size to extend further to insure that unstable microcraek propagation can occur. Both the statistical and stress gradient effects have been quantitatively evaluated and found to be in good agreement with the experimental data.

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Zusammenfassung Man benutzte eine elastisch-plastische Analyse, um die miktoskopische Spaltungssärke _inff ^sup* von eingekerbten Stahlbarren mit hohem Stickstoffgehalt im Krümmen sorgfältig zu messen. Man stellte fest, dass _inff ^sup* sich vergrösserte während der Wurzelradius der Kerbe sick verringerte. Da > 0.010 ist, ist die Variation von _inff ^sup* mit der Spaitungsfrakturstärke einer planaren Spannungsprobe, _f durch einen statistischen Effekt und durch Unterschiede in dem Volumen von stark angespanntem Material in der plastischen Zone verursacht. Da > 0.010 ist, ist der ursprüngliche Grund für die augenscheinliche Zunahme in _f mit verringertem , der tiefe Anspannungsgradiente an der Kerbenspitze, durch welche sich die kritische, plastische Zonengrösse weiter ausdehnen muss, um die labile Mikrorissausbreitung zu sichern. Die statistischen und Anspannungsgradienteffekte wurden quantitative ausgewertet und man fand gute Übereinstimmung mit den experimentellen werten.

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Résumé Une analyse élastoplastique a été utilisée pour la mesure précise de la résistance microscopique du clivage _inff ^sup* de barreaux entaillées d'acier à haute teneur en azote et soumis à flexion.On a trouvé que _inff ^sup* s'accroit lorsque diminue le rayon d'arrondi à la racine de fentaille. Lorsque est supérieur à 0,25 mm, la variation de _inff ^sup* en fonction de est due à un effet statistique du aux différences de volume de matière soumis, dans la zone de déformation plastique, à des contraintes; élevées. Il en est également de même l'écart entre _inff ^sup* et la contrainte de rupture par clivage dune éprouvette de traction sans entaille.Lorsque est inférieur à 0,25 mm, la raison principale de l'accroissement de _inff ^sup* avec des valeurs de décroissantes réside dans l'existence d'un gradient aigu des contraintes à la pointe de la fissure. Un tel gradient force à s'accrcître lesdimensions de la zone critique de deformation plastique, pour que puisse se produire une propagation instable dune microfissure.On a pu évaluer quantitativement ces effets statistiques d'une part et de gradients de contraintes d'autre part, et l'on s'est trouvé en accord satisfaisant avec les données expérimenetales.

     

On the numerical simulation of sheet metal blanking process

The use of the blanking process has been widely spread in mass production industries. In this technique, the quality of the final product is directly related to the setting parameters of the process and the material response of the sheet. In the present work, a general framework based on the finite element method for the simulation of the sheet metal blanking process is presented. The proposed approach properly addresses all the numerical challenges related to blanking. First, an extension of elasto-viscoplastic constitutive equations for the large strain regime is used to take into account the material strain-rate sensitivity. Then, the inertial effects coming from high velocity operations are considered by means of an implicit time integration scheme. Moreover, the frictional contact interactions are simulated with the classical Coulomb law and an energetically consistent formulation of area regularization. Finally, ductile fracture is modeled thanks to the element deletion method coupled with a fracture criterion. The blanking process is then simulated for different setting parameters. The accuracy of this approach is evaluated by comparing the numerical predictions to experimental results for both quasi-static and dynamic conditions. Good agreement is found between experimental and numerical results for all cases.     

Verification of a non-local stress criterion for mixed mode fracture in wood

An extension of a non-local stress fracture criterion to orthotropic materials based on the damage model of an elastic solid containing growing microcracks was presented in this paper. By taking this approach, a new fracture condition expressed in terms of the mixed mode stress intensity factors for orthotropic materials was proposed and its applicability to predict of a crack initiation and propagation in wood was validated. Predicted values of the stress intensity factors at failure were compared to experimental observations carried out on wood specimens for cracks arbitrarily oriented with respect to the orthotropy axes. Special considerations were applied to the comparison of the non-local stress fracture criterion with some classical fracture criteria for orthotropic materials.     

Experimental validation of numerical sensitivities in a deep drawing simulation

Deep drawing of a benchmark B-pillar is numerically modelled and experimentally performed with varying blankholder force and several blank shape parameters. The most influential parameters are selected for optimisation. Direct application of Autoform sigma software was used to determine sensitivities, as well as indirect application using response surfaces. Interesting nonlinear sensitivities were found that will be missed with simple linear screening techniques.     

Design of stationary plane strain drawing based on the ideal flow theory and a fracture criterion

Summary The ideal flow theory provides a tool for designing metal forming processes. However, quite often the design based on this theory is not unique. The purpose of the present work is to investigate a possibility of using an additional design criterion driven by fracture. The fracture criterion adopted is based on the concept of workability diagram for rate-independent materials and its generalization for rate-dependent materials. It is shown that for stationary forming processes of rate-independent materials this criterion does not lead to a design criterion, whereas for stationary forming processes of rate-dependent materials it does. In the latter case, a numerical example for plane-strain drawing is given.     

The influence of the fiber drawing process on intrinsic stress and the resulting birefringence optimization of PM fibers

The propagation properties of optical fibers can be significantly influenced by intrinsic stress. These effects are often undesired but in some cases essential for certain applications, e.g. in polarization maintaining (PM) fibers. In this paper, we present systematic studies on the influence of the fiber drawing process on the generated stress and demonstrate an approach to significantly increase the stress induced birefringence of PM-fibers. It is shown that the thermal stress caused by the material composition is superimposed with the mechanical stress caused by the fiber fabrication process. This intrinsic stress has a strong effect on the optical and mechanical properties of the glass and thus influences the fiber stability and modal behavior. By applying a thermal annealing step, the mechanical stress due to the fiber drawing process can be canceled. It is shown that this annealing step compensates the stress reducing influence of the drawing process on the birefringence of PM-fibers with panda structure. The comparison of the intrinsic stress states after fabrication with the state after the additional high temperature annealing step clearly shows that it is possible to improve the overall birefringence of panda fibers using appropriate preparation steps.