镁合金变形的晶体塑性有限元分析

晶体塑性理论已被广泛应用于现有的有限元分析中,从微观角度来模拟和预测晶体材料的宏观各向异性力学行为及塑性变形过程中织构的演化与发展。现有的晶体塑性理论框架核心主要基于由滑移引起的塑性变形机制,在预测由滑移和孪晶引起塑性变形的材料力学响应方面还不够完善。本文以具有密排六方(HCP)结构的变形镁合金塑性变形过程为例,综述了以滑移和孪晶为核心的晶体塑性理论的理论研究和应用现状,重点评述了现有孪晶的数值实现方法,并预测了相应理论的发展方向。     

Rapid Finite Element Analysis of Bulk Metal Forming Process Based on Deformation Theory

 The one-step finite element method (FEM), based on plastic deformation theory, has been widely used to simulate sheet metal forming processes, but its application in bulk metal forming simulation has been seldom investigated, because of the complexity involved. In this paper, a bulk metal forming process is analyzed by using a rapid finite element simulation method based on deformation theory. The material is assumed to be rigid-plastic, strain hardening. The constitutive relationship between stress and total strain is adopted, whereas the incompressible condition is enforced by penalty function. The geometrical non-linearity in large plastic deformation is taken into consideration. Furthermore, the force boundary condition is treated by a simplified equivalent approach, considering the contact history. Based on constraint variational principle, the deformation finite element method is proposed. The one-step forward simulation of axisymmetric upsetting process is performed by this method. The results are compared with those obtained by the traditional incremental FEM to verify the feasibility of the proposed method.     

3D‐FE Modelling and Simulation of Multi‐way Loading Process for Multi‐ported Valves

Multi‐ported valves are widely used in the marine, sanitary, petrochemical and power industry. Multi‐way loading forming technology provides an efficient approach for integral forming of high strength multi‐ported valves, such as tee pipe coupling, high‐pressure cross valves, large‐scale complex valves, and so on. Since the multi‐way loading process is a very complicated plastic forming process due to the complexity of loading path, finite element numerical simulation is adopted to investigate the multi‐way loading process in order to predict and control the multi‐ported valve forming process. A reasonable model of the process is developed under DFEORM‐3D environment based on the coupled thermo‐mechanical finite element method. Then the reliability of the model is validated with respect to geometry development and forming defects. Numerical simulations of multi‐way loading forming for a tee valve and a cross valve have been carried out via using the developed model. Further, the forming processes of tee valve and cross valve have been compared. Moreover, the modelling method is also suitable for multi‐way loading processes of other complex components.     

A Coupled Crystal Plasticity and Anisotropic Yield Function Model to Identify the Anisotropic Plastic Properties and Friction Behavior of an AA 3003 Alloy

A multi-scale simulation of the tip test, developed to determine the tribological characteristics of the back-extrusion process, was conducted on an AA 3003 alloy. A microstructure-level simulation, coupled with crystal plasticity finite element (CPFE) analysis, was utilized to characterize the macro-mechanical properties of the AA 3003. Owing to the limited size of the material provided, we performed CPFE analyses rather than multiple mechanical tests to determine the plastic anisotropy characteristics of the AA 3003 alloy. A three-dimensional finite element (FE) model of the tip test was developed using two different yield functions, namely the generalized von Mises yield function and Hill’s (1948) yield function, with material parameters identified from the CPFE analyses. The results revealed the following: 1. The directionality observed during the tip test is governed by the plastic anisotropy, rather than the frictional conditions. 2. The plastic anisotropy results in different Coulomb friction values. Therefore, the anisotropy should be carefully addressed in the tip test.

     

Modelling of Incremental Bulk and Sheet Metal Forming

In incremental forming operations, forming is accomplished by a number of single, local forming steps with simple, generic tools, and in some cases even by laser or plasma beams. This makes incremental forming processes very flexible. However, complex tool kinematics with a large number of degrees of freedom can cause severe problems for process planning and optimization. In addition, new questions regarding the material behaviour under cyclic plastic deformation arise. This article gives an overview of current problems in the finite element modelling of incremental forming processes, focusing on two examples, hammer forging and incremental CNC sheet metal forming. Based on this, insight is given into current research at the Metal Forming Institute (IBF) regarding adapted simulation methods for incremental forming processes.     

Characterisation of the Forming Behaviour of Patchwork Blanks

In order to satisfy the increasing demand for environmental sustainability and passengers’ safety, automotive manufacturers are more and more obliged to develop improved body concepts for lighter but also safer vehicles. At the same time, production costs have to be minimised in order to cope with the international market. Besides the application of new materials and innovative production processes mainly the use of tailor‐made semi‐finished products such as tailored welded blanks, tailored rolled blanks or tailored tubes can contribute substantially to this objective. Furthermore, for the production of sheet metal components with a load adapted material distribution, the patchwork blank technique represents a potential alternative to the widely‐used concept of tailored blanks. But even if patchwork blanks offer some additional advantages, this innovative technique has hardly found its way into series production due to a number of unsolved challenges regarding their formability and numerical modelling of corresponding forming processes. In this contribution the forming behaviour of welded patchwork blanks is investigated by means of experimental trials and finite element analyses. In order to simulate the forming processes of patchwork blanks accurately, knowledge about the characteristics of the weld metal, including the weld bead and the heat affected zone, is essential. For this purpose, Martens hardness measurements, which allow the analysis of the weld seam and the determination of the lateral extension of the heat affected zone, have been carried out. Subsequently, uniaxial tensile tests with longitudinally welded samples have been applied to characterise the constitutive behaviour of the weld metal. The results obtained from these experimental investigations have been implemented to different finite element models for patchwork blank forming processes. A comparison of the numerical results with experimental data obtained from a series of Nakajima tests allows a validation of the presented modelling techniques. It can be stated that the accuracy of the finite element analysis may be improved if the modified material properties along the weld seam are considered in the numerical model.     

Computer Aided Product Optimization of High‐Pressure Sheet Metal Formed Tailor Rolled Blanks

In view of today's increasing economic pressure the industry has to rationalize in order to remain internationally competitive. Achieving higher product quality using less material and machine‐man‐hours is one possibility to reach this goal. The high‐pressure sheet metal forming of tailor rolled blanks (TRB) allows to produce optimized components specially developed for their future function and which cannot be made from conventionally rolled sheet metal. This paper aims at showing that the two processes, i. e. flexible rolling and high‐pressure sheet metal forming (HPSMF), can be well represented in finite element simulations. By linking the finite element models with a combinatory optimizing tool, it is possible to simulate and optimize the entire process chain. Two example components were used to illustrate the principle of the optimization.     

Stampability parameters of automotive steel

The methods of estimating the plasticity of sheet metals subjected to standard and nonstandard tests of their mechanical and technological properties have been analyzed and compared. A strain-hardening exponent and a coefficient of normal plastic anisotropy are found to adequately characterize the stampability of metals. It is demonstrated that a plastic stability criterion can be used to estimate the energy required for metal forming at the stage of uniform deformation.     

Biaxial Deformation of the Magnesium Alloy AZ80

The multiaxial deformation of magnesium alloys is important for developing reliable, robust models for both the forming of components and also analysis of in-service performance of structures, for example, in the case of crash worthiness. The current study presents a combination of unique biaxial experimental tests and biaxial crystal plasticity simulations using a visco-plastic self-consistent (VPSC) formulation conducted on a relatively weak AZ80 cast texture. The experiments were conducted on tubular samples which are loaded in axial tension or compression along the tube and with internal pressure to generate hoop stresses orthogonal to the axial direction. The results were analyzed in stress and strain space and also in terms of the evolution of crystallographic texture. In general, it was found that the VPSC simulations matched well with the experiments. However, some differences were observed for cases where basal 〈a〉 slip and $ \left\{ {10\bar{1}2} \right\} $ extension twinning were in close competition such as in the biaxial tension quadrant of the plastic potential. The evolution of texture measured experimentally and predicted from the VPSC simulations was qualitatively in good agreement. Finally, experiments and VPSC simulations were conducted on a second AZ80 material which had a stronger initial texture and a higher level of mechanical anisotropy. In the previous case, the agreement between experiments and simulations was good, but a larger difference was observed in the biaxial tension quadrant of the plastic potential.     

The Impact of Microstructure on Yield Strength Anisotropy in Linepipe Steels

We describe here the effect of microstructure on the yield strength anisotropy in high-strength microalloyed linepipe steels. The anisotropy in steel with ferrite-bainite microstructure was lower compared to the steel with ferrite-pearlite microstructure and is attributed to the significant difference in their transformation texture components, {112}〈110〉 and {332}〈113〉. The yield strength anisotropy is discussed in terms of crystal plasticity concept involving estimation of average orientation factor and its relation to yield strength.     

Macromodelling of Transformation Induced Plasticity combined with Viscoplasticity for Low‐Alloy Steels

Metal forming processes are important technologies for production of engineering metal components. In order to optimize the resulting material properties, it becomes necessary to simulate the entire forming process by taking into account physical effects such as phase transformations. In this work we concentrate on the phase change from austenite to martensite and present a macroscopic material model, which combines the effects of viscoplasticity with the effect of transformation induced plasticity (TRIP). An extensive experimental data basis for a low‐alloy steel is used for parameter identification, thus taking into account the effects of uniaxial compressive and tensile stress on the kinetics of phase transformation at different temperatures. In a finite element simulation the austenite to martensite phase transformation within a shaft subjected to thermal loading is investigated.     

Hybrid Monte Carlo Simulation of Stress-Induced Texture Evolution with Inelastic Effects

A hybrid Monte Carlo (HMC) approach is employed to quantify the influence of inelastic deformation on the microstructural evolution of polycrystalline materials. This approach couples a time explicit material point method (MPM) for deformation with a calibrated Monte Carlo model for grain boundary motion. A rate-independent crystal plasticity model is implemented to account for localized plastic deformations in polycrystals. The dislocation energy difference between grains provides an additional driving force for texture evolution. This plastic driving force is then brought into a MC paradigm via parametric links between MC and sharp-interface (SI) kinetic models. The MC algorithm is implemented in a parallelized setting using a checkerboard updating scheme. As expected, plastic loading favors texture evolution for grains that have a bigger Schmid factor with respect to the loading direction, and these are the grains most easily removed by grain boundary motion. A macroscopic equation is developed to predict such texture evolution.     

Determination of volume fractions of texture components with standard distributions in Euler space

The intensities of texture components are modeled by Gaussian distribution functions in Euler space. The multiplicities depend on the relation between the texture component and the crystal and sample symmetry elements. Higher multiplicities are associated with higher maximum values in the orientation distribution function (ODF). The ODF generated by Gaussian function shows that the S component has a multiplicity of 1, the brass and copper components, 2, and the Goss and cube components, 4 in the cubic crystal and orthorhombic sample symmetry. Typical texture components were modeled using standard distributions in Euler space to calculate a discrete ODF, and their volume fractions were collected and verified against the volume used to generate the ODF. The volume fraction of a texture component that has a standard spherical distribution can be collected using the misorientation approach. The misorientation approach means integrating the volume-weighted intensity that is located within a specified cut-off misorientation angle from the ideal orientation. The volume fraction of a sharply peaked texture component can be collected exactly with a small cut-off value, but textures with broad distributions (large full-width at half-maximum (FWHM)) need a larger cut-off value. Larger cut-off values require Euler space to be partitioned between texture components in order to avoid overlapping regions. The misorientation approach can be used for texture's volume in Euler space in a general manner. Fiber texture is also modeled with Gaussian distribution, and it is produced by rotation of a crystal located at g ₀, around a sample axis. The volume of fiber texture in wire drawing or extrusion also can be calculated easily in the unit triangle with the angle distance approach.     

Plastic anisotropy of textured steel sheet

The plastic anisotropy ratio of the main texture components of low-carbon deep-drawing steel is calculated, using Taylor’s theory for the bcc pencil glide case in its original form. By mixing certain sharp texture components the plastic anisotropy of steel sheet can be reproduced fairly well.     

An exponential hardening model for anisotropic sheet metals

A new exponential hardening rule is brought forward to apply for planar anisotropy strain‐hardening sheet metals. Three exponential hardening relations measured along the rolling direction, 45°‐angle and 90°‐angle direction against rolling direction are just the special cases of this model. Based on this model to solve some plastic deformation problems for anisotropic strain‐hardening materials, some functions and calculating results, such as constitutive relations, forming limit characteristic, springback and other parameters associated with these types of materials, should be more likely to approach real states. So this anisotropic strain‐hardening model is very important for applying sheet metal forming simulation.     

Material Characterisation for Reliable and Efficient Springback Prediction in Sheet Metal Forming

In this paper, a novel experimental‐numerical methodology for an accurate prediction of springback after sheet forming is presented. An advanced phenomenological material model is implemented in the FE‐code ABAQUS. It includes the Bauschinger effect, the apparent reduction of the elasticity modulus at load reversal after plastic deformation, the strain rate dependence and the elastic‐plastic anisotropy and its evolution during the forming process. The required material parameters are determined from stress‐strain curves measured in tension‐compression tests. These tests are carried out with a special test rig designed to avoid buckling of the specimens during compression. The benefits of this procedure for springback prediction are demonstrated. Additionally, parameters for the phenomenological models are determined from texture simulations.     

Formability of Fe-Mn-C Twinning Induced Plasticity Steel

A comparative analysis of formability was investigated between Fe-Mn-C twinning induced plasticity steel with different Mn contents and interstitial-free steel. Tensile test combing with the morphology of fracture reveals that element Mn is helpful for the forming of inclusion or particles with film or rod shapes inducing the crack initiation and propagation. During stamping process, twinning induced plasticity steel without earing shows better anisotropy than interstitial-free steel because a typical <111> fiber texture forms accompanied by a weaker <100> fiber texture. The difference between the two steels is not evident during Erichsen cone cupping test, but the result of cone cupping test indicates that the twinning induced plasticity steel has superior drawing ability compared with interstitial-free steel. The different performances can be attributed to the different deformation mechanism during cupping test. FLD (forming limit diagram) of tested steels further suggests twinning induced plasticity steel has slightly superior deep drawability but low stretchability than that of IF steel, whose FLD₀ value can reach 30%.     

Determination of volume fractions of texture components with standard distributions in euler space

The intensities of texture components are modeled by Gaussian distribution functions in Euler space. The multiplicities depend on the relation between the texture component and the crystal and sample symmetry elements. Higher multiplicities are associated with higher maximum values in the orientation distribution function (ODF). The ODF generated by Gaussian function shows that the S component has a multiplicity of 1, the brass and copper components, 2, and the Goss and cube components, 4 in the cubic crystal and orthorhombic sample symmetry. Typical texture components were modeled using standard distributions in Euler space to calculate a discrete ODF, and their volume fractions were collected and verified against the volume used to generate the ODF. The volume fraction of a texture component that has a standard spherical distribution can be collected using the misorientation approach. The misorientation approach means integrating the volume-weighted intensity that is located within a specified cut-off misorientation angle from the ideal orientation. The volume fraction of a sharply peaked texture component can be collected exactly with a small cut-off value, but textures with broad distributions (large full-width at half-maximum (FWHM) need a larger cut-off value. Larger cut-off values require Euler space to be partitioned between texture components in order to avoid overlapping regions. The misorientation approach can be used for texture’s volume in Euler space in a general manner. Fiber texture is also modeled with Gaussian distribution, and it is produced by rotation of a crystal located at g ₀, around a sample axis. The volume of fiber texture in wire drawing or extrusion also can be calculated easily in the unit triangle with the angle distance approach.     

Effects of Anisotropy in Drawing and Extrusion Processes of Bulk Metal Forming

The effects of anisotropy of axisymmetric materials (round bars, tubes) on metal forming processes are discussed. These effects are strongest for thin‐walled hollow materials in metal forming processes when the wall thickness is not predetermined by the die (tube drawing without mandrel, free extrusion of hollow components). Similarly to the normal anisotropy of sheet metal, a high radial anisotropy increases the resistance against a variation of wall thickness in tube drawing. There are also effects in forming solid materials such as forward extrusion of bars whereby the buckling of cross sections is influenced through the variation of radial anisotropy with the distance from the axis. The favourable anisotropy properties depend on the actual priorities. If, for example, for a metal forming process the material anisotropy results in high compressive stresses this may be favourable for increasing the ductility of the material whereas the increase of the load acting on the tool reduces tool life.     

Effect of Lubrication during Hot Rolling on the Evolution of Through‐Thickness Textures in 18%Cr Ferritic Stainless Steel Sheet

Samples of a ferritic stainless steel sheet were hot‐rolled with and without application of lubrication. The effect of the different hot rolling processes on the evolution of texture and microstructure after hot rolling, cold rolling and subsequent recrystallization annealing was studied by means of macro and micro‐texture analysis and microstructure observations. After hot rolling, the sample rolled with lubrication displayed uniform rolling textures through the sheet thickness, while the sample rolled without lubrication showed shear textures in the outer layers of the sheet. The finite element method was employed to reveal the strain states during hot rolling with and without lubrication. The texture of the hot rolled sheet strongly influenced the formation of texture after cold rolling and final recrystallization and, therewith, planar anisotropy as well as the severity of ridging of the final gauge sheet. Hot rolling with lubrication was beneficial to the formation of strong recrystallization textures through the whole thickness layers leading to an enhanced planar anisotropy of the sheet. The recrystallized sheet hot‐rolled without lubrication displayed less severe ridging, however, which was attributed to a less frequent formation of orientation colonies in the outer thickness layers of the sheet.