AKADEMIA GÓRNICZO - HUTNICZA
im. Stanisława Staszica w
Krakowie
Wydział Inżynierii Mechanicznej i Robotyki
Katedra Systemów Wytwarzania
PRACA DOKTORSKA
mgr inż. Paweł Bałon
Analiza zjawiska powrotnego odkształcenia
w procesach tłoczenia
An analysis of springback phenomenon in
forming processes
Promotor pracy:
Prof. dr hab. inż. Andrzej Świątoniowski
I thank my doctoral advisor, prof. Andrzej Świątoniowski, PhD eng., my wife, my both mothers and my brother-in-law for immeasurable kindness, understanding, devoted time and invaluable discussions which helped me in realizing the work. What is more, I want to thank the board manager of SZEL-TECH – Grzegorz Szeliga and the board manager of Kirchhoff Polska – Mr. Janusz Soboń.
3
AKADEMIA GÓRNICZO - HUTNICZA 1
KRAKÓW 2016 1
LIST OF SYMBOLS: 5
1. THE GENESIS OF THE WORK 7
2. ANALYSIS OF THE STATE OF KNOWLEDGE IN THE RANGE OF
MANUFACTURING TECHNOLOGY FOR CAR BODIES 12
2.1.1. Formability and Blank Sheet Metal Forming 21 2.1.2. Evolution of Computer-Aided Engineering for Blank Sheet Metal
Forming 22
2.1.3. Simplistic Approaches 24
2.2. Material 26
2.2.1. Advanced High Strength Steel 30
2.2.2. DP - CP steels 31
2.2.3. Low-alloyed TRIP steels 32
2.2.4. High-manganese TWIP and TRIP steels 34
2.3. Material parameters for analysis 36
2.3.1. Anisotropy 38
2.3.2. Stress and strain curve 40
2.3.3. Forming Limit Diagram 43
2.4. Springback 46
2.4.1. Springback definition 54
2.4.2. Pure Bending – Classical Results of Springback 56 2.4.3. Rigid, Perfectly Plastic Result of Springback 59
2.4.4. Elastic, Perfectly Plastic Result 60
2.4.5. Rigid, Strain-Hardening Results of Springback 61
2.4.6. Elastic-Plastic Result of Springback 62
2.4.7. Residual stress and springback 63
2.4.8. Springback Prediction 64
2.4.9. Springback reduction methods: 65
3. AIM OF THE WORK 68
4. MODELING OF THE STATE OF STRESS AND STRAIN IN THE
STAMPED ELEMENT USING MES 70
4.1. Methods and tools in solving the problem 80
4.1.1 Defining the calculating model 84
4.1.2 Description of the model 85
4.2. Results and conclusions of the simulation 89
5. SPRINGBACK COMPENSATION 95
5.1. Trimming tool compensation 102
5.2. Realistic Shape Compensation 104
5.3. The surface compensation with scanner 107
6. TWISTING SPRINGBACK 110
6.1. Forming method in case twisting springback 112
6.2. Application of various calculation models 113
6.3. The influence of a stamping conception on dimension of a springback
4
6.4. The experimental verification of FEM results 121
6.5. The part formability 122
6.6. Forming conceptions 124
7. VERIFICATION OF THE RESULT 128
7.1. Description of the equipment with technical characteristics 131
7.2. Tolerances and clients requirements 138
7.3. Description of research and work-place 139
8. SUMMARY AND CONCLUSION 140
8.1. Scientific aim of the work 140
8.2. The aim considering an industry 143
9. DIRECTION OF FUTURE RESEARCH 146
9.1. Development view 147
9.1.1. Current automotive trend hot forming production 149 9.1.2. Development of technologies for an aluminum alloy 155
REFERENCES 157
SUMMARY 162
STRESZCZENIE 164
5
List of symbols:
– ultimate strength [N/mm2] - proof stress [N/mm2] A – elongation [%] – intercrystalline phases F – ferrite M – martensite δ - controlled displacement [mm] - cross-sectional initial area [mm2]A – current area [mm2] – initial length [mm]
σeng – engineering stress [N/mm2] σtrue – true stress [N/mm2]
eng – engineering strain [-]
F, P – forces [N] ΔL – elongation [mm]
- initial volume [mm3] - volume [mm3]
OP-20, OP-30 etc. – operation number 20, operation number 30 etc. R, r – bend radiuses [mm]
YS – field stress [N/mm2]
UTS – ultimate strength [N] E – elastic module [N/m2] σ – yield stress [N/mm2] M – bending moment [Nm] x - circumferential strain [-] σx - circumferential stress [N/mm2] t- sheet thickness [mm] w – sheet width [mm]
E` - Young's modulus (plane-stress case) [N/m2] – Poisson ratio [-]
I – inertia moment for the cross section [Nm] σ(0) - yield stress [N/mm2]
6
K - parameter [-]
K` - effective strength parameter [-] n – strain-hardening index [-]
- radius of curvature [mm] - radius of curvature [mm]
- coefficient of anisotropy in 0 deg rolling direction [-] - coefficient of anisotropy in 45 deg rolling direction [-] - coefficient of anisotropy in 90 deg rolling direction [-]
- coefficient of anisotropy in the sample direction [-] b - width of the sample [mm]
t - thickness of the sample [mm]
- strains in main coordinate directions [-] G,H,F,N - Lankford coefficients [-]
- maximum fiber strain at the outer radii [-] - maximum fiber strain at the inner radii [-] - Coulomb's coefficient [-]
- springback value [-]
f - real compensation value [-] t - analysed compensation value [-] - precision of compensation [-]
- force [N]
p – pressure [N/mm2]
, - areas of blank holder [mm2]
7
1. The genesis of the work
Process of metal forming in automotive parts construction becomes more and more demanding due to tightened up tolerance and trials to realize very complex and in many cases unworkable design in mass production. Moreover, it is required to cut and limit costs of die production and simultaneously keep high quality. Furthermore, construction elements are more often produced from materials which belong to High Strength Steel or Ultra High Strength Steel (Fig. 1.2). Nevertheless, it results in appearance of springback effect. Springback value depends mainly the material as well as part geometry, and in extreme cases, the deviation value from the target part might reach a high level in some areas. Reduction of implementation time, development of metal components, and greater restrictions about designing and producing stamping tools generate extra costs. The process of designing dies requires the use of appropriate Finite Element Method software to make them more economic and less time-consuming. Therefore, analysis of the forming process alone is not enough to take into account. During the design process it is necessary to include the die compensation to achieve an optimized blank sheet. The prediction of springback effect by trial and error method followed by correction of deviation is difficult, arduous, and painstaking. Virtual compensation methods make it possible to achieve precise results in a short time. This way provides a huge economic advantage, eliminating excessive milling and allows for just-in-time production.
8
The optimization process can refer to individual operations, as well as take into consideration intermediate stages in the final result, at the same time increasing the accuracy. Die compensation using software application was experimentally verified by prototype die. Quality requirements for products made by the sheet stamping process are very high due to the technologies surrounding automatic assembly of formed components. Springback, as the main source of drawpieces inaccuracy, is the function of material data, shape of tools, and process parameters. Therefore, springback deformation becomes a critical problem - especially for AHSS steel - when the geometry is complex. Hence, it is necessary not only to find the springback effect value but also to include and consider it during the design stages by tooling designers.
Fig. 1.2. Implemented materials in body structure (with SSAB cooperation). Elements of car construction are commonly produced from materials which belong to Ultra High Strength Steel (UHSS) or High Strength Steel (HSS) (Fig. 1.3). Application of these kinds of materials considerably reduces construction mass. Prediction of springback effect by trial and error and subsequent adjustment of deviation is burdensome. Numerical compensation methods make it possible to achieve a precise result in a short time. This method results in a huge economic advantage, eliminating wasteful milling during die production and allows for just-in-time production according to customers’ expectations and forecasts of vehicle demand.
9
An innovative compensation method of both forming and trimming die for the construction parts of vehicle parts manufactured on a transfer press (Fig. 1.4). This method allows for correction in the accuracy of compensation, consequently reducing springback in a more exact way than current methods. The previous methods took into account only the influence of trimming on springback but without generating compensated surfaces for the trimming die or the next forming operation. Moreover, there is the possibility to include positioning effect during multi operation forming because of the huge impact of springback results on separate operations. If positioning between operations is not taken into consideration there are problems with proper fitting, even if the final part has correct shape. These problems generate additional costs during die production which could be avoided by using multi compensation.
Fig. 1.3. Designed elements of vehicle body structure (brown color – DP600, purple color – HC380, light blue color – DP1000, green color – HX340, yellow color – DC04).
More and more stringent ecological requirements, economic competition on the global market, as well as growing safety and comfort standards continue to impose permanent technological changes in the productio modern cars. The rigorous norms aimed at protecting the Earth’s atmosphere influence the construction of engines and power
10
transmission systems in order to improve fuel consumption and the minimization of forming resistances. It also has an impact on the refinement of self-supporting car bodies in terms of reducing their weight and improving their aerodynamics (Fig. 1.1). A 100 kilograms lighter car emits an average of 4,7 grams of CO2 less every kilometer travelled.
The issue of vehicle passengers’ safety is also a highly important factor. It requires the durability of passenger compartment to be as high as possible. This high durability is related to high crush and torsion resistances and also to accurately defined strain characteristic curve of body framework.
Fig. 1.4. Transfer press with servo movement and a maximum force of 1600.000 kg.
The state of technical progress in car body structures is the proper development of material engineering, which involves providing materials to car producers. The materials need to be characterized by required mechanical strength, operating life, simple forming, market availability, relatively low costs, and potential for subsequent recycling or utilization. Despite common expectations, steel still remains the main material used for building car bodies. However, more and more often, new sorts and technologies of steel treatment are
11
being used. In the material structure of standard a car body, the portion derived from deep drawn steel sheets (the name derives from its high plasticity) decreased to barely 30%, whereas they were dominant on the market at the start of the 21st century. In present maximally stiff and light constructions, steels are absolutely more useful.
Parts made by this method have a high application in the car industry. Using elements made by hot-forming allows reduction of car mass up to 12- % and ensures higher collision safety due to its strength.
The author established wide scientific cooperation with the steel forming processing department at the SSAB company. It resulted in common benefits through the development of further research of AHSS steel springback (Dogal 600, Dogal 800, Dogal 1000).
The SSAB company is a world-class producer of the best AHSS and UHSS steels having its own R&D laboratory. This allowed for the performance of numerous experiments that checked the relationships between dual-phase steels in an analytical way. What is more, the springback issue was investigated with the cooperation of the SSAB steel producer who has many specialists in the areas of materials, steel manufacturing, and defect-free-technology. This work has been conducted over 4 years mainly through research and processing the research in the best possible way. A lot of material tests, designs, and numerical analyses have been done. Furthermore, many design tests and prototype experiments of forming tools have been conducted.
12
2. Analysis of the state of knowledge in the range of manufacturing
technology for car bodies
Forming processes are widely used in the manufacturing of vehicle construction parts. Their main attribute is high efficiency, repeatability, and most of all economy, simultaneously maintaining their proper surface condition in mass production. Efforts are being made to replace construction elements with aluminium alloy, magnesium alloy and composites. In 2017 constructions contained about 0.5% magnesium and 8% aluminium but were respectively, 2% and 12% inn 2020 (Fig. 2.1) (Vogt, 2011). There are some mass production trials of construction elements as integral composite parts. Moreover, their durability is similar to the high mechanical parameters of Advanced High Strength Steel (AHSS). Their main advantage is low mass, being even 30% less than in the same elements made from conventional HSS steel. However, the composite is not able to provide all properties in constructions that have stamped parts. This is caused by a lack of repeatability with a divergence up to 30%.
Fig. 2.1. Comparison of implemented materials in body structure in 2016 and 2020. Technologies of composite materials are said to be transferred from construction of high-performance vehicles to standard automotive applications. However, a problem occurs concerning the practical possibility of servicing cars after a collision. In fact, composite material structures are typically beyond standard repair methods after being damaged, especially compared to steel elements.
13
Fig. 2.2. Comparison of formability for steel [with SSAB cooperation].
Main qualitative expectations of customers are: exterior appearance, safety, comfort, high engine performance and low fuel consumption. Higher standards of comfort and safety have caused a continuous rise in average vehicle weight (Ford, 2011;Seki, 2011). Therefore, new solutions are still being sought in order to ensure an optimal mass supporting structure and positive crash test results. Creating some brand new steel grades with strong mechanical properties made a ground-breaking contribution to steel research (Fig. 2.2) (Thyssen Krupp, 2009).
Fig. 2.3. Overview Current Bumper Front (% of analyzed designs).
AHSS materials are the result of much research done by joint international projects over the last decade. They facilitate the attainment of high endurance structures, while, at the
17% 12% 3% 10% 2% 51% 5% Hotforming steel cold forming rollforming alu sheet alu extrusion hybrid 60 0 DP 8 0 0 D P 12 00 M 1000 DP 1400 M D C 0 6
14
same time, preserving desired plasticity. Although these two parameters do not appear simultaneously, and an increase in one of them is often at the expense of the other, some material groups do posses the beneficial values of both.
These competitive properties and economic considerations are the main reasons that steel is the dominant material in the automotive industry. According to the near-term forecast, for the next few years, the portion of HSS and AHSS materials in car bodies is expected to be about 90%. These trends are about to coincide with requirements regarding a decrease in overall construction mass, as well as simultaneous enhancement of safety and reduction in fuel consumption (Ford, 2011).
Traditional design and production methods were mainly based on designers’ experience. However, an effective method of stamping processes design must use CAD/CAM (Fig. 2.4) capabilities as well as join the abilities of numerical analysis and one based on optimization methods. Currently, for the analysis of the forming process, as well as the design of the forming tool, Finite Element Method (FEM) software is widely used.
Fig. 2.4. Die process design.
In the automotive, the numerical analysis is used to explore and predict forming possibilities in practice, in order to avoid some drawpiece mistakes. The potential problems in the stamping process during the design of the tool can be eliminated by virtual software rather than byprocess of trial and error (Fig. 2.5). The advanced and complex software enables fast and certain verification if the assumed method is correct, which imparts an advantage over traditional trial methods.
15
Fig. 2.5. Crack in FEM model and in real forming process.
The most up-to-date methods of designing, manufacturing, and production planning must be used to meet market demands. Planning is one of the most important stages of designing the tooling technology to shorten the time of manufacturing process start. For the process of sheet stamping this stage is not only extremely crucial but also difficult. It is not easy to predict the number and type of forming stages, the accuracy of springback effect and to take into account inhibit factors, such as wrinkling and cracking (Fig. 2.5) (Kang et al., 2002; Choil et al., 2000).
Since the second half of the 1990s intense research was carried out regarding the linking of designing surfaces and die stampings in parametric way (Smith, 1990; Suchy, 1997). The first objective was development of the parametric models using extra surface which strictly corresponds with the surfaces involved in the process. The next step was the creation of a general solution for various designs by linking known features. Die softwares such as: METHOPLAN (iCapp, Zurich), Viking (Inpro, Berlin), DIEDESIGNER (Autoform, Zurich) were being developed which tended to design complex and parametric assemblies of bodywork construction. Designing in a parametric way ensures the linking of software supporting die stampings construction and FEA method in order to design a proper surface (Fig. 2.6) (Danzberg et al., 2004).
Generally, it is required to use parametric methods of car design which enable fast modification and implementation of essential constructional changes.
16
Fig. 2.6. Describing forming part creation.
The optimization of the geometry of all parts is found through the application. The parts are produced in many forming processes, creating the assembly which is built by components manufactured in different ways. One example of such is the combination of parts whereby one is made by cold forming and the other made by hot forming. The entire assembly, joined by a binder must fulfil the assumptions made at the beginning of the design process. Therefore, the optimization corresponds with a complex chain of forming stages rather than a single operation.
The manufactured parts are very often made of AHSS steel, which are less deformable and show a greater tendency to springback effect than mild steel. Springback compensation by means of tooling geometry change is necessary for the part to be situated in narrower tolerance intervals. The quality of stamped parts has greater and greater importance. It influences the assembly stage and the final product quality. One of the factors affecting the quality of drawpiece is the shape-dimensional accuracy connected with material springback (Fig. 2.7). Research done during recent years caused the narrowing constraint of the tolerance range in constituent components, as well as in assemblies. Increasingly, some elements are designed in order to obtain high geometry stiffness. Their production reaches limiting values for possible for mass production. In the computer age, tool compensating is evaluated via the application of an analysis based on FEM methods.
17
2.7. Part design process.
The accuracy problem in springback modelling is treated in literature as highly complex. The main reason for this view has been computers’ limited design power, forcing the application of a lower amount of nodes and number of elements at high time intervals, as well as a lower refinement level that leads to a large computer springback error. Limits on computer hardware possibilities vastly reduced the application of the full capabilities of numerical analysis software before 2001 (Fig. 2.8). This resulted in low accuracy of elements with complex geometry in relation to thickness of parts and a long calculating time. The progress of the 64-bit software version was a huge breakthrough that led to higher output from the Central Processing Unit (CPU) and simultaneously reduced computing time. Numerical calculations of forming are reduced to describe a surface with elements that are based on nodes. The number of nodes is given to ensure high calculation precision. A good way to determine the size of elements is the functional dependence between the smallest radius and the thickness of a sheet. Computation of springback requires extreme accuracy. Therefore, elements with small dimensions, little time increments, and accurate material data are used in zones where some contact with a tool appears (Fig. 2.9). A very important factor is the use of proper elements during an analysis of the forming process. Usually, FEM programmes dedicated for stamping use surface elements that have more developed counting algorithms and, most significantly, they reduce their time. Volume elements take into account 3D plasticity due to double contact.
18
Application of TTS (Through Thickness Stress) elements is well-founded for flanging on account of process specification. Use of computer supported design and an analysis of stamping process tools helps to achieve a target in the recommended way and most of all, in attainable time. The analysis itself is not enough because of the necessity to take tool compensation. into account.
Fig. 2.8. Comparison of a stamped blank with a reference part.
Nowadays, compensation calculations are carried out automatically, or at least semi-automatically, with the use of FEM software (e.g. Pam Stamp, Autoform, Ls-Dyna, Outifo, Mashal). Development of the compensation method for Pam-Stamp 2G software took place in 2002-2004. The accuracy and correctness of this method was affirmed for parts design in the years 2004-2005 for: Arcelor B-pillar and Renault bodywork elements (similar part (Fig. 2.8).
The Pam-Stamp 2G software module is based on a method from 2005. In 2011, research that was done on the progress of compensation methods led to enlargement of the basic optimization process tool. Cooperation between the ESI Group and the Atlas Tool company led to verification of the experimental method. Trials were conducted on a few parts, for example, on a deep stamped A-pillar made from UHSS steel. In result, it was found that using the complex process optimization allows for compensation to be achieved with at least 80% compatibility with the part (Atlas Tool, 2011).
At present, it is possible to compensate the whole operation chain, which enables the springback effect to be considered at every process stage. It also gives an advantage in
19
solving some problems by finding an accurate surface for the cutting operation and matching the sheet to the tool during every individual operation. Skipping of the multi-operational compensation tool requires taking into account unstressed surfaces at particular trimming stations, which can change the state of stress in the part causing larger deformation.
2.1. Metal Forming Processes
The steel forming process in the automotive industry is one of the significant processes. Conventional stamping is a very common method because of its rapidity and low per-piece cost. CAE technologies need an analysis of simulations for each forming method. In order to reduce considerations, the electromagnetic and explosive forming methods are assumed as separate forming processes that are not taken into account. The initial condition ensuring proper results of the CAE simulation is precise mapping of physical processes taking place during forming. The numeric analysis needs to contain details of the physical process in order to conform to reality in a proper way. In the conventional forming process the metal part is created by the result of a few operations such as:
Stage 10: (drawing) forming Stage 20: trimming
Stage 30: flanging
Stage 40: final trimming and flanging (Fig. 2.9)
20
The first operation is usually the most important because one is mapping the main geometric shape. The first tool usually consists of a die, a punch and a blankholder. However, there may occur a tool with two blankholders or any at all. Other stages depend
21
on the geometry and the degree of tool making. For example, flanging can replace the restriking operation. The main deformation appears in the first stage of drawing on the first tool. Generally, two types of forming may be classified: blankholder forming and forming from the air (without the blankholder). Both methods are the opposite of each other due to the deformation caused by the contact between die and the punch. There are two separate forming concepts that give two different parts as a result. Each method has some pros and cons which are used alternatively, depending on the type of forming structure. Blankholder forming requires adouble-action press or using nitrogen cylinders where the punch and the blankholder can be controlled independently. The bottom tool section is stable but the top section moves towards the bottom, holding the blank in proper position. Pad force increases with the growth of press feed. Changing the value of the radius is highly important to reduce the thinning phenomenon (Fig. 2.10).
2.1.1. Formability and Blank Sheet Metal Forming
Before using CAE methods, the forming analysis aim, which is solving formability, problems have to be known. Formability (Tab. 2.1.) is defined as the capability to form the blank for designed shape geometry without any faults for particular process conditions. It can be divided into the most important groups:
- Product design (shape of the part) - Die-face development
- Blank shape and location - Boundary conditions - Material properties - Process development
The most disappointing part is the one having the greatest interaction at one of the factors above, for example boundary conditions and blank shape that may be more critical factors than changing steel for aluminium alloy. In the last decade, stamping simulations have been refined and effectively implemented. More precise and more detailed models highly improved the capabilities of forming analysis as methods of approving, leading and controlling the solutions.
22 Formability
atribute Test method
Formability parameteres characterized
Factors influencing formability
Forming limits Full dome test Forming-limit diagram n-value, thickness
Sheared-edge
stretching limits Hole extrusion test % hole expansion
Ultimate tensile strength (UTS), r-bar value
Bending under tension limits
Angular stretch-bend test
Height at failure,
stretch-bendability index (UTS), r-bar value Springback and
curl Channel draw test
Springback opening angle, radius of sidewall curl
Yield strength, tool radii, draw bead restraining force, tool gap
Stretch formability
Pan forming (fully
locked conditions) Height at failure n-value, thickness Stretch
drawability Square draw test
1. Height at failure 2. Binder control 3. Strain measurement
Uniform elongation, r-bar, blank size, coating, lubrication
Tab. 2.1. Formability attribute.
However, during recent years, new requirements have suggested the benefit of getting information like: parts quality, springback, dimensional tolerance, effectiveness of production and assembly, fatigue and crashworthiness. These demands have become more permanent in order to implement materials such as: aluminium alloys, ultra high strength steels or dual phase steels into mass production with current access to stamping analyses that are supported by formability testing reaching intended limits. New generation software is an indisposable and required tool for industrial use. As a result, a solver considering the algorithm elements, contact and parametric modeling of the material is compatible with stress and deformation.
2.1.2. Evolution of Computer-Aided Engineering for Blank Sheet Metal Forming
Using finite element method in blank sheet forming processes made scientists and industrial users concerned, giving new approach view. At the turn of the 1970s and 1980s most of the research was strongly limited because of the three-dimensional (3D) strain problems concerning simple geometries. Unfortunately, the research provided overall information for variable problems for the formed material without the possibility of using
23
it in industrial way. This technology was being continued and developed for 10 years focusing on its industrial use. Dominant material models like Barlat’s 1989 and Hill’s 1990 yield were used for numeric analysis in practical usage. A lot of automotive applications such as: hoods, mudguards, and bumpers were analysed in terms of using them in the FEM analysis relying on systems and professional knowledge. In the next period of time, there were two shifts at the beginning of 1999.
Fig. 2.11. Simulation time in Pam-Stamp versions.
The first one concerned improving springback predictions as a result of a few international institutes and universities. The most important aspect in predicting the springback effect were designs innovated by National Institute of Standards and Technology Advanced Technology Program (NIST-ATP). Thanks to their theses, the industry received the code provided for predicting the springback of a particular part. Another main development was creating a more friendly and integrated system of calculating material forming with all computer design supporting functions. The simulation time was reduced a lot from the 1990s when the front panel analysis was limited from 50 days in 1990 to 10 days in 2002. Overall time reduction for all analyses of forming possibilities containing prediction of springback was cut to one week in 2004. Extreme reduction of overall simulation time approached in 2010 with the implementation of 64 bit operating systems. Besides, time reduction influenced on standardization and high experience of CAE analysis in producing demanded parts very fast. Proper simulation of forming process may effectively reduce physical testing and solve some problems during
0 10 20 30 40 50 60 70 80 OPTRIS/PAM-STAMP 2000 PAM-STAMP 2G V2002 PAM-STAMP 2G/DMP V2004 Si m u lation tim e Springback Forming Holding Gravity Mesh
24
the early stage of design. Over the years, the simulation analysis helped reduce costs and time in the automotive industry, partly via technological growth. In recent years, using the simulating blank forming in industry resulted in eliminating cracking and wrinkling problems at the design stage. The last decade has clearly changed cost reduction by optimization of the process and implementing present possibilities of CAE programs.
2.1.3. Simplistic Approaches
Length-of-line analysis is one of the spectrums of 3D FEA analyses for current standards. This method simply calculates the ratio between the final length and the section of original length. Before popularising this analysis, 2D analyses were developed.
There are two main reasons for using the 2D way. The first one concerns the impractical using of 3D in the mid-1990s considering rapidity and better consistency of solutions having weak computing stations. The earliest form of FEM calculations started in 1940 was calculating the parts stiffness. However, Wang and Budiansky’s work was one of the initial completed ones for the 3D model. Despite the fact that most of the initial theses were developed by the academy and the code was implemented in commercial software of companies as worldwide applications, currently the market is dominated by producers such as: AutoForm of AutoForm Engineering, LSDYNA of Livermore Software Technology Corporation and PAM-STAMP of ESI Group (Fig. 2.11). Their well prepared codes are based on the academy’s code. Over the years, the industry has been using all three codes. One of the most important technologies in the 3D FEM code is the schedule of time integration. Overally, it was divided into two main codes: explicit time integration code and implicit time integration code. Both algorithms can be used for static and dynamic governing equations. Moreover, there are four fundamental possibilities of forming the FEM code:
Static Implicit (SI) Static Explicit (SE) Dynamic Implicit (DI) Dynamic Explicit (DE)
Widely used implicit method is dedicated to static or quasi-static problems. Dynamic explicit is widely used to analyse crash simulations. Main static implicit reaserches of were initially more rigorous and adjusted for precise results of the blank forming analysis. There
25
is not a perfect method for all forming types. Everything depends on a proper choice of calculation and for critical problems it depends on using application form for a particular case. The implicit simulation method for a small scaling static implicit element causes an increase of elements amount in the third power. There is also another problem in reducing the application of static implicit codes in the production. The forming blank sheet is not a “pseudostatic” problem indeed. In the standard stamping operation, total displacement of the press is 150 mm in 2 seconds, with the speed peak close to 500 mm/s, There occurs large displacement, metal rotation and large deformation. Another challenge is the highly nonlinear contact between metal and the tool (Fig. 2.12).
Fig. 2.12. Simulation of linear and non-linear loadcases. Investigation of stress, strain and deflection. Creation of stressmap.
The fundamental application of static implicit algorithm is inversing stiffness matrix. Different codes may use different formulations, but the concept of the momentum equation is the same. In the dynamic explicit equilibrium code there is a dynamic balance. The static explicit code is presented as the one having benefits of both static implicit and dynamic explicit codes. Autoform Engineering has its own unique code that is often classified as implicit code. However, a lot of specialists claim that the Autoform code generates good results.
26
Defining and choosing the finite elements is always very important for the FEM simulation. However, it is not practical to use precise mesh for an initially unknown analysed element. Usually, accurate calculations are related to the high CPU loading of computing stations and also a long calculation time. The users cannot always properly define the deformation gradient at the beginning of the forming process analysis. This problem particularly affects the drawing operation, where large displacements appear. Adaption was mainly common in mid-1990s because of the limits of the used algorithms. Soon afterwards, the development of intelligent algorithms for blank forming took place. The algorithms solved the problems of the contact and refine mesh. The used algorithms worked very well for each forming process. However, various parameters and needs require particulars for special applications (Chung-Yeh, 2006).
2.2. Material
In spite of much information about elaborating and implementing cars made of aluminium alloys, magnesium alloys, composites and plastic into the production, steels are the dominant material in the automotive industry. This is caused not only by economic considerations but mainly by competitive properties and simple recycling. Realising a few international programs in the last 15 years in Europe, Japan and the USA caused appearing attractive novelties of the used materials. They meet the requirements concerning the reduction of body mass, which causes reduction in fuel consumption and also ensure greater passive safety of passengers. Currently, thin sheets with small sections made by ultra-high strength steels or aluminum/magnesium alloys are used for structural elements.
27
Fig. 2.13. Comparison of material mechanical parameters (with SSAB cooperation). In terms of the automotive industry, the following parameters should be taken into consideration:
a) mechanical properties, especially high strength (the ratio of immediate strength of the material to its density), which allows to reduce weight of vehicle (Fig. 2.13.); b) high capability to absorb energy in case of collision;
c) properties that minimize technological problems during production and which ensure high productivity, especially: vulnerability to plastic forming (stamping of panels, bending, hydroforming and others), simplicity of using coverages (Zn and Al coatings, lacquers) and also good weldability;
d) good behaviour during exploitation (fatigue strength of the material and welds, corrosion resistant, simple exchange of the elements);
e) economic considerations; f) recycling.
Presently, mostly conventional hot-rolled and cold-rolled low carbon steels are used in car body building. However, new generation steels require special processing, which causes the output of more complex structures. The dominant method of assembling car bodies remains resistant spot welding, in spite of the spread welding and laser soldering, gluing, riveting and clamping (Gould et al., 1998; Chuko et al., 2002).
Generally, there is not an accepted ordination of construction steels for the automotive industry so far. According to the actual body of knowledge, they can be classified in the three basic groups (Fig. 2.14):
28
Fig. 2.14. Yield strength and formability (in terms of tensile ducitility) of conventional high-strength steels and advanced high-strength steels (Arcelor Mittal).
I. mild, plastic low-carbon steels (DQSK, IF steel) with immediate tensile strength Rm - below 300 MPa and total extension A - 30÷60%;
II. conventional High Strength Steels (Bake Hardenable, Carbon Manganese, IF with micro additions, HSLA) with 300< Rm<700 MPa and lowered A comparing to the previous group;
III. Advanced High Strength Steel (Rm above 700 MPa reaching even 2000 MPa) and extension included in quite wide limits - 5÷30%, but strength increase accompanies with lowered plasticity.
29 Forming temperature Minimum bend radius -sheet
thickness Springback, degrees
Metal or alloy °C °F
Test
data Preferred
C-103, C-129Y Room <1r 1r 2-6
Tantalum alloys (annealed)
Tantalum Room <1r 1r …
Ta-10W Room <1r 2r 1-5
Molybdenum alloys (stress relieved) Mo-0.5 Ti, TZM
titanium-zirconium-molybdenum 150 300 2r-5r 5r 3-8
Tungsten (stress relieved)
Tungsten 315 600 2r-5r 5r 2-8
Tab. 2.2. Formed to a 120° bend angle in a 60° V-die at a ram speed of 254 to 3050 mm/min.
The two first groups can be considered classic. These materials are widely used in building self-supporting car bodies on a massive scale. The steels of group III are progressively being implemented into production and their contribution is systematically rising. However, there have been recently elaborated high-manganese TRIP/TWIP steels that are not included in the classification. They are undoubtedly a new generation of materials having very high plasticity and strength of 1200 MPa (Lehman et al., 1996).
Drawing Quality Special Killed and IF are ultra-low carbon steels. They have ferrite structure and high vulnerability to forming, whereas IF steels do not contain roots forming interstitial solutions including also carbon (C<0,005%, N<0,005%, S<0,005%).
Test t Rp0,2 Rm A50mm A80mm r n
direction mm N/mm2 N/mm2 % % 10% 5-10%
0° 1.22 433 634 29 24 0.73 0.16
45° 1.24 446 626 31 25 1.09 0.16
90° 1.23 454 636 29 24 0.83 0.16
30
The High Strength Steels from the second group (IF-HS and BH) contain micro additions (Ti, Nb, V) bonding leavings of interstitial roots, forming carbides, carbon nitrides and also compounds of carbon and sulfur in ferritic matrix. BH steels are hardened in the process of lacquer firing on the finished body. High Strength Low Alloy steels also belong to the group of carbon content below 0,1%. They are hardened by Mn and various microscopic additive such as: Cr, Nb, Al, Si in hundredths of % (Tab. 2.3).
CMn steels owe their properties to the ferritic structure hardened by solutions. All these steels have low carbon equivalents and very good welding as a result (Radakovic et al., 2008; AWS, 2002; Tumuluru, 2006).
2.2.1. Advanced High Strength Steel
AHSS group contains steels hardened by phase transformation, not by hardening by solution or hardening by dispersion as it took place in the two previous groups. However, Complex Phase, Dual Phase and Martensitic steels hardening is done at the stage of preparing the material, whereas TRIP hardening takes place during vehicle collision (Fig. 2.15). The part presented in the Fig. 2.15 is a cross car beam element and it illustrates stress pattern for knees pressure during collision.
Fig. 2.15. Crash simulation knee-impact (blue color – area of high stresses, yellow color – neutral area, brown color – area of increased stresses, green color – area of low
31
Common technological operation for CP, DP and TRIP steels is treatment in intercritical temperature (the area of coexisting of α and γ phases) after cold-rolling followed by low-temperature austenite change. The appropriate choice of annealing low-temperature is formed by the relation between austenite and ferrite. The final structure depends on controlling the temperature course during cooling and might be a combination of ferrite, bainite, martensite and retained austenite. MS steels are made during fast cooling in the field of existing of the γ phase to obtain the 100% martensite structure. Their immediate strength gains even 2000 MPa. In order to improve ductility, a controlled tempering has to be done.
2.2.2. DP - CP steels
The structure of DP steels is made of a mix of fine-grained polygonal ferrite or non-carbide acicular ferrite with martensite islands in an amount of 5÷40% or even more. What is more, there may occur small amounts of retained austenite. As was mentioned, these steels are made by appropriate cooling after annealing in the temperature field of coexisting of α and γ phases (Fig. 2.16). The sample presented in the picture below was made by microsection. Then, it was examined through the scanning microscope.
Fig. 2.16. UHSS material micro structure (ferrite – light color, martensite – dark color). During fast cooling, the austenite transforms into the martensite (the ferrite does not transform, obviously) and the diphase F+M structure is made. Another method is thermo-mechanical treatment that is based on heat treatment and plastic forming (hot-rolling) with subsequent cooling (Fig. 2.17). It is possible to obtain a bit more fine-grained structure and therefore, better mechanical properties in the second method. Essentially, the variety of the DP steels are CP steels. Their cooling is proceeded in the way enabling to obtain the third
32
micro-constituent – bainite. Impurities in DP-CP steels are contained in order to control austenite content in annealing temperature. The carbon content may vary widely between 0,05 and 0,2% (Dogal, 2010; Rathbun et al., 2003).
Fig. 2.17. High rolling milling (with SSAB cooperation).
The properties of DP steel (that is a sort of specific composite) are resultant of fractions of hard and tough martensite and ductile ferrite. They depend mainly on both phases ratio and ferrite grains size. The immediate tensile strength gains 1000 MPa with the elongation of over a dozen %. The DP steels have also large initial difference of ultimate strength and yield stress that rapidly decreases during cold working. Consequently, it causes less springback effect than in low-alloyed steels (e.g. HSLA) with the same strength, which is highly beneficial in stamping of panels (Tab. 2.2) (Dogal, 2010). Other advantageous properties are: lack of Lüders effect during deformation, crack resistance in low temperature and low anisotropy of plastic properties (Dogal, 2010; Rathbun et al., 2003).
2.2.3. Low-alloyed TRIP steels
During a properly processed (slower than for DP steel) cooling cycle with a stop, there is created a mixed structure composed of ferrite, bainite and much amount of retained austenite in low-alloyed TRIP steels (earlier processed by annealing in the field of coexisting of α and γ phases). Similarly, as for composite materials, the properties of
low-33
alloyed TRIP steels are the resultant of particular phase properties, their fraction and morphology.
Fig. 2.18. Car simulation testing (deformation model).
The bainite is the toughest phase and the ductile ferrite and austenite simplify the plastic forming. Therefore, this kind of steel is beneficial because of strength and from a technological point of view. However, its impressive properties are most saliently revealed during violent deformation (e.g., in the case of a car crash (Fig. 2.18)). Then, the retained austenite transforms into martensite absorbing energy and additionally hardening the material. This last feature makes it very attractive for the automotive industry. Moreover, during the A → M transition, there appears a particular plasticity called the transition plasticity. Current low-alloyed TRIP steels have a diversified chemical composition with the total fraction of alloying components equaled several percentages by weight. Carbon content is crucial and usually oscillates in the field of 0,10÷0,25%. Higher contents, to 0,6% C, despite beneficial impact on the structure (bainite and austenite are created and strength reaches over 1200 MPa with good plasticity) have not come out of experimental phase because of impairing weldability (DeCooman, 2004). Another alloying components are Mn (0,4÷2,5%), Si (0,4÷1,8%), Al (about 1%). There are also used little additions of P to harden the ferrite by solution
34
(unfortunately, it impaires weldability) and microadditions of Nb, Ti and V to refine the structure and create carbon nitrides and dispersion carbides (DeCooman, 2004).
Fig. 2.19. Low speed bumper test.
2.2.4. High-manganese TWIP and TRIP steels
TWIP steels appeared on the market in 2004. They have a unusually wide grade of deformation retaining high strength at the same time. It is a unique feature, especially important in the event of a vehicle collision. Under these conditions, the material should exhibit two opposed properties:
– high ductility, in order to absorb the maximal amount of striking energy during plastic deformation;
– maximal stability of the element that protects the passenger cabin.
The already used steels were either very tough (e.g. for car frame) and of low ductilily, which caused cracking during dynamic overloading or inversely: they were plastic and low strength. The TWIP steels may revolutionise this segment. A number of such unique materials have been obtained so far inter alia: in Germany (Frommeyer et al., 2003), in Korea (Kim et al., 2006) and in Japan (Ueji et al., 2008). The steel researched at the Max Planck Institute for Iron Research shows 1100 MPa with 90% elongation (Frommeyer et al., 2003; Mehta, 2007).
35
Fig. 2.20. Automotive part production
The chemical composition of the TWIP steel contains a high concentration of Mn (15÷35%), which stabilizes the austenite to room temperature. The other alloy additions are 2÷4% Al and/or Si. The 100% austenite structure, without martensite and other phases (potential cracking nuclei) is characterised by high ductility and plastic forming treatability. At high deformation speeds, there occurs a twinning. The steel deforms locally, hardens (Re increases with the deformation speed) and transfers the remaining energy to another region. That way, the deformation by twinning moves as a characteristic wave, splitting and effectively absorbing the striking energy (Ueji et al., 2008; Mehta, 2007). The deformation by twinning occurs for alloys having a low stacking fault energy, which characterises the TWIP steels (Kim et al., 2006; Ueji et al., 2008; Mehta et al., 2007; Kliber et al., 2008).
Decreasing Mn content to 15÷20% in the presence of the other alloy additions causes appearing the TRIP effect in the discussed steel (Frommeyer et al., 2003). The stacking fault energy is changing and the mixed TWIP/TRIP steels are also possible. As a result of the A → M transformation for the high-manganese TRIP steel, the energy absorption is more effective because it runs in two steps. Initially, the hexagonal martensite is created that transforms into hexagonal body-centred martensite afterwards. HSS and AHSS steel have found their stable place in automotive industry (Fig. 2.20). The decreasing
36
contribution of mild low carbon steels is observed. Currently, they have lost their primacy in favour of the HSS steel and especially Interstitial Free-HS and HSLA. The contribution of the AHSS steels is increasing and they are predicted to become a dominant alternative in building safe constructions in 2016. It is worth mentioning that in the USA, the DP-CP steels from the AHSS group are preffered, whereas in Europe, the low-alloyed steels with the Transformation Induced Plasticity effect are more desired by producers (DeCooman, 2004). Presently, the high-manganese TWIP/TRIP steels enters the commercial market and it is probable that they will get some significant part in it in the future. Comparing these steels with the other steels makes them quite expensive because of more difficult technology of melting, casting and plastic forming (tendency to form hard oxides during hot-rolling and necessity of using high pressures for cold-rolling process Fig. 2.21).
Fig. 2.21. Rolling AHSS steel process.
In the car body construction, ultra high strength steels (MS, DP, TRIP) will dominate the strengthenings of passenger cabins, whereas Twinning Induced Plasticity steels will create the outer zone absorbing the energy during collision, both in the vehicle axis and especially during side impacts. The development activities concerning increasing mechanical properties are being continued. Both for TRIP steels and for high-manganese TWIP/TRIP steels, it appears that the most promising is commercial implementing of alloy micro-additions (especially B, N, Ti, V, V and Zr) (DeCooman, 2004; Frommeyer et al. , 2003; Kim et al., 2006; Ueji et al., 2008).
2.3. Material parameters for analysis
DP-1000 material is steel that belongs to the UHSS group, diphase, cold rolled (Tab.2.4). Steel structure is formed by the compound in die form of martensite precipitates on fine-grained ferrite warp. There also may appear small amounts of retained austenite.
37
These steels are received by suitably leaded cooling after annealing from temperature range conforming coexisting of α and γ phases.
Tab. 2.4. Mechanical property of DP-1000 (SSAB, 2009).
Fig. 2.22. Hardening curve extrapolation for material DC04 and St14 for the roof hardening part. 0 0,1 0,2 0,3 0,4 0,5 0,6 0 0,2 0,4 0,6 0,8 1 1,2 σ(ε) [ G Pa] ES_DC04_P-S DC04_1-5 St14_P-S
38
Fig. 2.23. Hardening curve extrapolation for material DP-34, SSAB Dogal 600, Krupkowsky extrapolation, Kirchhoff testing for the B-pillar part.
The properties of this steel which are a kind of specific composite, are the result of a portion of hard and resistant martensite and ductile ferrite. There is also high initial yield point and ultimate strength which quickly decline during the plastic working. Hill 48 material using isotropic hardening curve was approved despite of the fact that the software uses the criterion of isotropic-kinematic consolidation hypothesis (Fig. 2.22 and Fig. 2.23 show hardening curves for various materials). Chosen material requires following basic parameters describing material.
Young Modulus E, Poisson coefficient υ; density ρ, rolling direction along edge of blank sheet and blank thickness g0.
2.3.1. Anisotropy
Reference parameters functions (G,H,F,N) are expressed by anisotropy coefficients for characteristic rolling directions 0°, 45°, 90° (called also as Lankford coefficients- see Eq. 5.2.1) , , : 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 σ(ε) [ G Pa] DP-34 SSAB_Dogal600DP_1mm SSAB_Dogal600DP_1,2mm Kirchhoff_testing Krupowsky_extr
39 (2.1) The coefficient describing normal anisotropy r (Eq. 2.2) is treated as the average value which can be determined from the formula:
r = 0.25(r0+2 r45+ r90)= 0.25(0.86+2*0.89+0.91)= 0.89 (2.2)
A low r- value gives higher thinning effect in opposite way a high r- value gives higher strain levels in width direction.
Normal anisotropy can be expressed by in direction:
(2.3)
Where: ⍺ - the direction of the sample; b – the width of the sample; t – the thickness of the sample; - accordingly initial values.
Fig. 2.24. Anisotropy properties in all directions (with SSAB cooperation). Coefficient describing normal anisotropy r is regarded as the average value which can be determined from the formula:
40
Definitions describing material properties in all directions (Fig. 2.24): Isotropy: Equal properties in all directions
Anisotropy: Not equal properties in all directions
Planar anisotropy: Different properties within the plane of the sheet
Normal anisotropy: The properties in the thickness direction differs from the properties in the plane (Lundh et al., 1998; Bergstrom et al., 1996).
2.3.2. Stress and strain curve
Stress-strain curves are an extremely important graphical measure of a material's mechanical properties (Fig. 2.25, Fig. 2.27). Perhaps the most important test of a material's mechanical response is the tensile test, in which one end of a rod or wire specimen is clamped to a loading frame and the other subjected to a controlled displacement δ.
The engineering measures of stress and strain are determined from the measured load and deflection using the original specimen cross-sectional area A0 and length L0.
In the early (low strain) portion of the curve, many materials obey Hooke's law to a reasonable approximation, so that stress is proportional to strain with the constant of proportionality being the modulus of elasticity or Young's modulus.
Engineering stress = force / initial area:
σeng = F/A0 (2.5)
True stress = force / current area:
σtrue = F/A (2.6)
Engineering strain = elongation / initial length
σeng = ΔL/L0 (2.7)
True strain = In (current length / initial length)
dε = dL / L → σtrue = ∫1/L dL = ln (L/L0) (2.8) eng true eng eng eng true L L L A PL A A A P A P (1 ) 0 0 0 0 0 (2.9) 0 0 0 0 0 L L A A L A L A V V Const Volume (2.10)
41
As strain is increased, many materials eventually deviate from this linear proportionality, the point of departure being termed the proportional limit. This nonlinearity is usually associated with stress-induced “plastic” flow in the specimen.
Fig. 2.25. Hardening curve by formulas for the Docol 800 DP steel for the B-pillar part.
Elasticity is the property of complete and immediate recovery from an imposed displacement up on release of the load, and the elastic limit is the value of stress at which the material experiences a permanent residual strain that is not lost up on unloading. This is done because the material unloads elastically, there being no force driving the molecular structure back to its original position. Since it is often difficult to pinpoint the exact stress at which plastic deformation begins, the yield stress is often taken to be the stress needed to induce a specified amount of permanent strain, typically 0.2%. The stress at the point of intersection with the σeng curve is the offset yield stress.
eng true eng true L L L L L
ln ln ln(1 ) 0 0 0 (2.11) 400 600 800 1000 1200 1400 0 0,2 0,4 0,6 0,8 1 T rue st ress [ MPa] True strain [-] Docol 800 DP Ludwig Swift Hockett-Sherby Combined S-H42 900 950 1000 1050 1100 1150 1200 1250 1300 0 0,2 0,4 0,6 0,8 1 1,2 T rue st res s [MPa] True strain [-]
Here it appears that the rate of strain hardening diminishes up to a point labeled UTS, for Ultimate Tensile Strength. Beyond that point, the material appears to soften to strain, so that each increment of additional strain requires a smaller stress.
The apparent change from strain hardening to strain softening is an artifact of the plotting procedure, however, as is the maximum observed in the curve at the UTS (Roylance, 2011).
Fig. 2.27. Material parameters testing.
43
Hardening curve determined by static test of bumping for 0° direction after calculating stress value and actual strain (Fig. 2.25). Next, the curve was extrapolated in order to increase the range of actual strain (Firat et al., 2008). To reach that, the Krupowsky formula was used (Fig. 2.26):
σw=K( 0) n
(2.12)
Work hardening could be also determinate by Ludwik - Hollomons equation:
m n p
K
(2.13)
where: n determines the ability for the material to distribute the strain n = 1; a straight line, n = 0; ideally plastic.
2.3.3. Forming Limit Diagram
During most stamping operations, the sheet metal is strained in a total of three different modes. In the stretch mode, biaxial strain occurs on a positive basis along both the major and minor axes. In the draw mode, strain is positive along the major axis and negative along the minor axis. While in the plane strain mode, strain is positive along the major axis, but at or near zero along the minor axis.
The hardening curve obtained from the forming analysis is not enough. Forming Limit Diagram (FLD) must be used additionally, in order to precisely verify the nodes which are critical in terms of maximal stress (Fig. 2.28). It is a diagram of steel drawability shown with the use of main straining (Wagoner et al., 2011). The curve can be determined by the Nakajima Test or by other experimental method. (Lundh et al., 1998; Leppin et al., 2008). A Forming Limit Diagram, such as the one shown in (Fig. 2.31), can subsequently be used to match up the strain modes present in a stamped part with a sheet metal that can be relied up on to form the part without failure (Fig. 2.29 and Fig. 2.30 show comparing of FLD charts for various materials).
44
Fig. 2.28. FLD diagram by different type of steel (with SSAB cooperation). A forming failure is typically defined for automotive applications as a split in the part, a reduction in part thickness below acceptable limits or an unacceptable surface wrinkle. To determine the limit of formability of a sheet metal, the Forming Limit Curve (FLC) is a generally accepted tool.
45
The FLC is determined by proportionally straining the material, in other words upon increasing the strain during testing, the ratio between strain components should be maintained. Experimentally, FLCs are obtained via either Nakazima or Marciniak methods, of which the Nakazima is probably the most widely used since the Marciniak method is more complex in operation. The initial strain is always bi-axial. (Eisso, 2002; Leppin et al., 2008).
Fig. 2.31. FLD diagram for t=1.2 mm.
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 -0,2 -0,1 0 0,1 0,2 0,3 Major stra in Minor strain
46
2.4. Springback
Requirements regarding reduction of cars’ fuel consumption play a key role in the automotive as they make cars lighter by application of more and more resistant materials. Usage of steel of increased endurance results in a higher tendency to springback. A problem occurs not only during control of elements but mostly during process of joining of formed parts into subassemblies. Maintenance of a narrow tolerance range taking into consideration deviation of springback effect for Ultra High Strength Steel (UHSS) and Advanced High Strength Steel (AHSS) is not easy, especially that newer materials tend to release the residual stress as a result of deformation during the trimming process (Fig. 2.33) shows or punch unloading (Vogt, 2011). Application of these kinds of materials considerably reduces construction mass thanks to high durability. However, after removal of forming loads, results include springback effect (Fig. 2.32).
Fig. 2.32. Springback effect for different type steel bending (with SSAB cooperation).
Springback value depends mainly on used material as well as part’s geometry and in extreme cases deviation value may reach high level in some areas. Springback is a process of elastic recovery (Fig. 2.36) with a local plastic deformation appearing at the end (Fig. 2.34, Fig. 2.35) show the springback value depending on various operations.
47
Fig. 2.33. The springback value for tailage part after the trimming operation.
48
Moreover, by currently available approaches it is not still exactly predicted. Standard springback is expected as an angle or distance deviation to the reference model but in some cases it would be more complicated due to the torsion. It is required to eliminate this type of springback in the initial design phase because of problematic die compensation. Additionally, the influence of geometric shape, springback pattern and magnitude is determined mainly by stress level and its distribution in a stamped part. The main influences on springback effect are:
Coefficients: friction coefficient, anisotropy coefficient, mechanical properties of material;
Tool geometry: radius of a die and blank sheet geometry;
Process parameters: mesh quality, punch displacement velocity, blank holder strength.
49
Fig. 2.36. Elastic recovery occurs when stress is removed from a specimen that has already undergone plastic deformation.
The accuracy of compensation effectiveness prediction is one of the main challenges in design of a tool construction with the aim to minimize its trials. Designing of dies demands the use of appropriate Finite Element Method software to make them more economic and less time-consuming. Therefore, it is not enough to take into account only analysis of forming process. That method results in a considerable economic benefit eliminating useless milling and allowing production of a die just in time. Geometric compensation of a tooling surface is a direct way to eliminate springback effect of a tool in an iterative way by system of solving nonlinear equations. Currently, the springback analysis is becoming the routine process to form steel in CAE engineering analysis in automotive (Fig. 2.40). However, for a big springback deviation and twisting springback the conventional methods of compensation fail (Ford, 2011; Seki, 2011). The necessity to find another way of forming arises for that which ensures stability of the process with the simultaneous reduction of twisting springback to the standard case with a deviation towards the height of part. Even though it is mostly feasible, it is time consuming and costly.
50
There is shown what is necessary to do to find the best resolution. In some cases changing of forming conception is the only way to get a good result with controlled springback. However, in the next step compensation is needed to reduce standard deviation in direction towards material thickness (Fig. 2.37, Fig. 2.38).
Fig. 2.38. The springback compared to the part thickness.
Springback effect is a deviation occurring after the stamping process. Its size depends on used materials and their properties, such as: elastic modulus, yield stress, strength. Springback of designed parts may be compensated by overforming. Material overbending mostly appears at the final surface of whole compensation process (That surface can be analytically estimated for some simple geometry of the part. For constitutive models, the σ(z,t) stresses are predicted in specified point and section (Fig. 2.39).
51
Fig. 2.39. Section of overbending process.
Mostly, the springback effect occurs during low-carbon steel bending for 0,5-1,5 degree values. It can be reduced by overbending or restriking. Coefficients affecting the springback are: ratio of bending angle to blank thickness stock; bending angle (bending degree, flatness); bending method U-bending, V-bending (Fig. 2.41). For the bend radius that is several times higher than blank thickness, the stress is much larger. Therefore, press power will have to be higher than for two times lower radius. Overbending size which is necessary to compensate the springback for low angle will be different than for high
