Strain evolution in the single point incremental forming process: digital image correlation measurement and finite element prediction

Incremental Sheet Forming (ISF) is a relatively new class of sheet forming processes that allow the manufacture of complex geometries based on computer-controlled forming tools in replacement (at least partially) of dedicated tooling. This paper studies the straining behaviour in the Single Point Incremental Forming (SPIF) variant (in which no dedicated tooling at all is required), both on experimental basis using Digital Image Correlation (DIC) and on numerical basis by the Finite Element (FE) method. The aim of the paper is to increase understanding of the deformation mechanisms inherent to SPIF, which is an important issue for the understanding of the high formability observed in this process and also for future strategies to improve the geometrical accuracy. Two distinct large-strain FE formulations, based on shell and first-order reduced integration brick elements, are used to model the sheet during the SPIF processing into the form of a truncated cone. The prediction of the surface strains on the outer surface of the cone is compared to experimentally obtained strains using the DIC technique. It is emphasised that the strain history as calculated from the DIC displacement field depends on the scale of the strain definition. On the modelling side, it is shown that the mesh density in the FE models plays a similar role on the surface strain predictions. A good qualitative agreement has been obtained for the surface strain components. One significant exception has however been found, which concerns the circumferential strain evolution directly under the forming tool. The qualitative discrepancy is explained through a mechanism of through-thickness shear in the experiment, which is not fully captured by the present FE modelling since it shows a bending-dominant accommodation mechanism. The effect of different material constitutive behaviours on strain prediction has also been investigated, the parameters of which were determined by inverse modelling using a specially designed sheet forming test. Isotropic and anisotropic yield criteria are considered, combined with either isotropic or kinematic hardening. The adopted constitutive law has only a limited influence on the surface strains. Finally, the experimental surface strain evolution is compared between two cones with different forming parameters. It is concluded that the way the plastic zone under the forming tool accommodates the moving tool (i.e. by through-thickness shear or rather by bending) depends on the process parameters. The identification of the most determining forming parameter that controls the relative importance of either mechanism is an interesting topic for future research.     

Simulation of Multiple Cold Rolls Progressive Forming for Non-symmetrical Channel Section

In cold roll forming process, the sheet is progressively formed into a very complex three dimensional surface. The design procedure for the roll formed products, forming rolls, and roll pass sequences was considered more an art than a science. Good roll pass design was the Key to successful roll forming. In order to reduce forming defects and trial production cost, computer     

Modelling of cold roll forming of steel strip

Abstract

Good roll pass design is the key to successful roll forming. To reduce forming defects and trial production costs, computer aided simulation of cold roll forming is employed. In this paper, a theoretical model, based on the updated Lagrange method of deformation mechanics and using the elastic–plastic large deformation B-spline finite strip method, is presented. The model is applied to analyse progressive roll forming of a channel section: the three-dimensional displacement field, strain field, and stress field between two stands during multiple cold roll forming are calculated. The results indicate that deformation is greatest in the leg and corner regions of the channel section. The principal deformation is in the transverse direction, the longitudinal deformation being small. The program, written in C language, can also be used to analyse other simple cross-sectional profiles.     

Effect of roll pass schedule on through thickness texture development in Al–Mn alloy

Abstract

During hot rolling a texture gradient is developed through the thickness of the slab. This is directly related to the different strain paths experienced by the material between the surface and the centre plane. The difference in strain path not only affects the texture, but can also give differences in stored energy though the thickness, which in turn affects the recrystallisation kinetics and ultimately the recrystallisation texture. The strain path is further complicated when a number of roll passes are involved, since the material is subjected to more complex strain paths. In the current investigation the effects of roll pass schedule (rolling direction, i.e. reverse rolling or continuous rolling) on the texture development during deformation and subsequent annealing have been characterised for an Al-1%Mn alloy. The study has shown that the texture of the surface region of the slabs is dependent on the roll pass schedule. This effect is at a maximum in the near surface region, although the effect of roll pass schedule on the recrystallisation kinetics is at a maximum 20% of the half thickness below the surface of the slabs.     

Further observations on the plastic deformation of a normalized low carbon steel

The plastic deformation of a commercial grade low carbon steel has been investigated using microhardness and grain strain measurement techniques. Two distinct modes of deformation during plastic flow in low carbon ferritic steel have been identified. The initial stage involves the propagation of the Luder's band along the gauge length of the sample by slip strain in the surface and near surface grains only, the strain accommodation in the interior of the material being attained by a predominantly grain translation mode. The second stage involves the propagation of a strain hardening front through the cross-section of the material as the macro-strain is increased through the flow stress region.     

Evolution of elastic modulus in roll forming

Roll forming is a continuous process in which a flat strip is incrementally bent to a desired profile. This process is increasingly used in automotive industry to form High Strength Steel (HSS) and Advanced High Strength Steel (AHSS) for structural components. Because of the large variety of applications of roll forming in the industry, Finite Element Analysis (FEA) is increasingly employed for roll forming process design. Formability and springback are two major concerns in the roll forming AHSS materials. Previous studies have shown that the elastic modulus (Young’s modulus) of AHSS materials can change when the material undergoes plastic deformation and the main goal of this study is to investigate the effect of a change in elastic modulus during forming on springback in roll forming. FEA has been applied for the roll forming simulation of a V-section using material data determined by experimental loading-unloading tests performed on mild, XF400, and DP780 steel. The results show that the reduction of the elastic modulus with pre-strain significantly influences springback in the roll forming of high strength steel while its effect is less when a softer steel is formed.     

Analytical modeling of deformed plain woven thermoplastic composites

This research addressed the deformation predictability of post-manufactured, plain weave architecture composite panels. Often times during the production of deep drawn composite parts, a fabric preform experiences various defects ranging from local buckling, interply slip, intraply shear, delamination, overheating and thickness variations. Minimizing these defects is of utmost importance for mass produceability in a practical manufacturing process. Considering intraply shear as the enabler for panel alteration, characterization of the local trellis angles can lead to better understanding of defects. The approach is analogous to forming limit diagrams used as a design tool in the sheet metal industry when developing new products to predict draw depth based upon the strain characteristics of the material. There were two broad objectives of this research. The first objective was to adapt a grid strain analysis technique to characterize surface deformations. These deformations were related to the extent of local trellis shearing and were used as a validation tool. The second objective was to generate a predictive model with the use of a bilinearly blended Coons patch to predict formability for the top surface of a composite panel. This model was generated independently of the results obtained from the grid strain analysis. By implementing this analytical, predictive model, it was possible to characterize formability of a composite part using nothing more than geometry of tooling, material thickness and imposed boundary conditions.     

基于弯曲实验的DP980力学性能研究

目的 针对仅通过单向拉伸实验无法准确表征金属板材在弯曲成形过程中的力学性能变化的问题,研究通过弯曲实验获取材料力学性能参数.方法 对高强钢DP980展开力学性能测试研究,主要通过弯曲实验对材料弯曲变形过程中形成的弯矩曲率进行测试,将得到的弯矩曲率转化为应力-应变.分别将弯曲和拉伸得到的应力-应变数据导入到三点弯和辊弯成...     

Modelling studies of sheet metal formability of friction stir processed Mg AZ31B alloy under stretch forming

Magnesium alloys have poor formability at room temperature. The formability can be improved through hot forming at the cost of deterioration in strength and other mechanical properties. Improvements in texture and grain refinement are the alternate ways for formability improvement. The economically viable process for such applications is alloying or grain refinement technologies like equal channel angular pressing (ECAP), friction stir processing (FSP), and accumulative roll bonding (ARB), etc. Friction stir processing is an emerging solid state microstructure modification technique that can produce homogeneous microstructure with fine-grains in a single pass. The desirable characteristics for sheet formability are the maximum limiting dome height under plane and biaxial strain deformation conditions and the major fracture strain limits through forming limit diagrams (FLDs). Equiaxed homogeneous microstructure with fine grains through FSP results in the enhancement of formability of the material. The objective of the present work is to establish the methodology for viable sheet metal forming practices by altering the process conditions. This needs a clear understanding of the friction stir processed Mg alloy under different strain conditions to get optimized process parameters.     

A first step towards a simple in-line shape compensation routine for the roll forming of high strength steel

The roll forming process is increasingly used in the automotive industry for the manufacture of structural and crash components from Ultra High Strength Steel (UHSS). Due to the high strength of UHSS (<1GPa) even small and commonly observed material property variations from coil to coil can result in significant changes in material yield and through that affect the final shape of the roll formed component. This requires the re-adjustment of tooling to compensate for shape defects and maintain part geometry resulting in costly downtimes of equipment. This paper presents a first step towards an in-line shape compensation method that based on the monitoring of roll load and torque allows for the estimation of shape defects and the subsequent re-adjustment of tooling for compensation. For this the effect of material property variation on common shape defects observed in the roll forming process as well as measurable process parameters such as roll load and torque needs to be understood. The effect of yield strength and material hardening on roll load and torque as well as longitudinal bow is investigated via experimental trials and numerical analysis. A regression analysis combined with Analysis of Variance (ANOVA) techniques is employed to establish the relationships between the process and material parameters and to determine their percentage influence on longitudinal bow, roll load and torque. The study will show that the level of longitudinal bow, one of the major shape defects observed in roll forming, can be estimated by variations in roll load and torque.     

Strain behaviour of aluminum 99.5 in micro-forming conditions of the coining process

The coining process can be identified as a shallow die forging. By using this process, it is possible to produce very fine surface geometries. This leads to dimension scaling into micro dimensions and causes the specific material behavior. In the micro area, continuum laws are not strictly followed anymore. The leading role in determining the deformation and strain level is taken by the fine surface geometry dimension and the size of the crystalline grain of the workpiece material. This is known as the size effect and defines all micro-forming processes. In order to provide monitoring of the filling of the smallest die dimensions, additional supporting procedures should be used. In this case, radiography testing procedures for observing the specific points of the workpiece geometry are applied, characterized with very small dimensions (less than 0.5 mm). Testing aluminum samples are formed using two techniques – open and closed die coining, with identical surface geometry. Their crystalline structures are in two-grain sizes of 34 μm and 80 μm. Scanning results show different material behaviour and different surface deformation for the same level of forming force in all four testing cases.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

Superplastic behaviour of Inconel 718 sheet

Abstract

Inconel 718 is a nickel based alloy used extensively in the aerospace industry, having good service capabilities, in terms of strength and fatigue resistance, at high temperatures. Inconel 718, in the form of sheet, has the capability of being shaped using gas pressure forming techniques similar to those used for a number of aluminium and titanium based alloys. An extensive research programme has been carried out to investigate the high temperature formability of this alloy. This has involved both uniaxial tensile testing to determine such parameters as flow stress and strain rate sensitivity, and microstructural examination to investigate grain stability under both static heating and following deformation. The forming characteristics of the material have been correlated with the δ phase solvus temperature determined using SEM techniques. Optimum forming temperatures and strain rates are discussed.     

THE DEVELOPMENT OF A MATHEMATICAL MODEL FOR PREDICTING THE DEPTH OF PLASTIC DEFORMATION IN A MACHINED SURFACE

The development and verification of a mathematical model for the prediction of plastic deformation in a machined surface are presented. The main assumption for developing this model is that there is a linear relation between plastic strain and the depth to which it extends. The model relates the work required to shear the workpiece material to the work needed to compress the workpiece material ahead of the cutting tool. The resulting depth of plastic deformation in the machined surface is a function of the true stress-strain characteristics of the workpiece material, the shear stress and shear strain on the shear plane, and the distribution of plastic strain. Results of the model agree well with data found in the literature. An improvement of the model is suggested through application of actual distribution data of plastic strain and calculation of frictional behavior on the rake face of the tool.     

Application of the two-dimensional Hermitian finite difference method to linear shear deformation theory of plates and arbitrarily curved shells

Summary Starting from the linear, partial differential equations of thin shell theory including the effect of transverse shear deformation a matrix formulation is presented in which all kinematic and dynamic variables appear as differential quotients of first order.The transformation of the local field equations into an algebraic form by appropriate two-dimensional finite-difference operators leads to an unsymmetrical banded algebraic equation system from which all variables requested are directly evaluated.The constitutive equations take into consideration a symmetrically layered cross section consisting of tangentially isotropic and transversally orthotropic material. Because of the kinematic assumptions of a first approximation shell theory the deformation of the cross section can be seized in an integral sense only.Since the basic equations are formulated in tensor notation with the procedure presented shells of arbitrary curvature may be analyzed, of which surface is given as an analytic continuously differentiable function. The algorithm pointed out shows good convergence attributes. Its efficiency is demonstrated by two examples of which analytical solutions are known.     

2D adaptive mesh methodology for the simulation of metal forming processes with damage

In this work, a fully adaptive 2D numerical methodology is proposed in order to simulate with accuracy various metal forming processes. The methodology is based on fully coupled advanced finite strain constitutive equations accounting for the main physical phenomena such as large plastic deformation, non-linear isotropic and kinematic hardening, ductile isotropic damage and contact with friction. The adaptivity concerns the space discretization using FEM as well as the applied loading sequences. Mesh size distribution is based on various error indicators making use of the hessian of the plastic strain rate combined with a specific damage error function and a specific local curvature error function evaluated at contact boundaries. 2D mesh size can be refined or coarsened when necessary according to these error indicators. Particularely, the smallest size is found to be inside the zones where the damage is highly active. The applied loading paths are also adaptively decomposed into various sequences depending on both number and size of the fully damaged elements. The adaptive procedure is validated through various sheet and bulk metal forming examples. In this paper, a plane stress tensile test, an axisymmetric blanking process of two materials with different ductilities and a cold extrusion process are presented.     

Study of size effect in micro-extrusion process of pure copper

The size effect on material deformation behaviors are characterized by grain size, part feature size, forming material size and interfacial condition. These factors have a close relationship with material flow behavior, which in turn affects the geometry accuracy of micro-formed parts. In this study, a general-purpose tooling set for realization of micro-forward, backward, combined forward rod-backward can and double cup extrusions is developed and the micro-extrusions of pure copper with different grain sizes are conducted. The size effect phenomena are analyzed based on the deformation load, interfacial friction behavior and microstructure evolution. It is found that the interfacial friction is high in micro-extrusion processes and the grain size effect on deformation load is sensitive to the friction force at the tooling–workpiece interface. The microstructures of the extruded parts show the occurrence of inhomogenous deformation and a large number of slip bands passing through the grain boundaries to accomplish the strain continuity in the cases with coarse grains. In addition, the flow stress curves obtained from micro-compression are used to model the micro-extrusion processes using finite element (FE) simulation based on the conventional material model. It is found that the conventional material model is not applicable in simulation of the material deformation behavior and evaluation of the interfacial friction in micro-extrusion processes due to the size effect. This research therefore provides an in-depth understanding of size effect in micro-extrusion processes, which is critical to further formulate design rules to facilitate the development of micro-parts.     

Experimental investigation of the deformation of Hopkinson bar specimens

Split Hopkinson bar (SHB) experiments are often used to study the strain rate dependent mechanical properties of materials. During a SHB experiment a small sample of the material under study is subjected to a high strain rate, uni-axial, tensile, compressive or torsion load. From the classical measurements the time history of the mean stress, strain rate and strain in the specimen can be derived. For some applications, more detailed information concerning the variation of the deformation in the specimen is necessary. In this contribution a technique is presented which makes it possible to obtain the deformation along the length of the specimen. The deformation of a line grid attached to the specimen is recorded during an experiment by means of a streak camera. An advanced and innovative numerical technique, based on a combination of geometric moiré and phase shifting, is developed to extract the time history of the deformation along the axis of the specimen from the picture of the deforming grid automatically. Large specimen deformations are allowed, and the technique proved to give highly accurate results. In this contribution results are presented of a SHB experiment on a steel sheet specimen. Some remarks are formulated concerning the generally assumed homogeneity of the deformation in the specimen, and the deformation obtained with the classical measurement techniques.