SPRINGBACK EFFECT CONCEPTS IN SHEET METAL

INTRODUCTION
The springback in sheet metal forming is described as the change of sheet metal shape compared with the shape of the tools after forming process operations. Sheet metals with high strength-to-modulus ratio such as high strength steels and aluminum alloys are particularly prone to springback, and these materials are becoming more important in automotive industry to reduce the car weight and increase fuel efficiency. Springback makes die design difficult because the final part shape does not conform to the tool geometry. In order to compensate springback, die tryout is required in current automotive die development and construction process. Die designs and construction is one of the most time-consuming steps in new car type developing process. Therefore, finding an effective and reliable method for springback prediction is very important. [1]
Currently, finite element method (FEM) is used for calculating the springback of sheet metal in forming process, but due to inherent errors it can’t be directly used for die design. In the automotive industry, engineering guidelines and finite element software are used in the design process for new sheet metal parts.
Metal forming has historically played a distinctive role in the process of industrialization, and remains one of the most important industries. Metal forming processes can be categorized into two major groups: one is bulk forming, which contains various traditional forming methods, such as: forging, rolling, extrusion etc. and the other is sheet metal forming which primarily refers to stamping processes. Metal forming has been a traditional research field in mechanical engineering. Most of the time, its content has been exclusively related to the mechanical behavior of metal forming processes. The theoretical development in this field has been closely connected to the developments of the theory of plasticity and computer methods. Although most of the mathematical fundamentals on plasticity have been established for nearly one hundred years, metal forming processes still represent a major challenge to modern engineering analysis methods. In terms of mechanics, almost all metal forming processes involve large deformation with nonlinear material behavior and contact boundaries. The analysis of such a process extremely nonlinear and finite element method (FEA) has brought a new tool the analysis of metal forming processes. With FEM, metal forming processes could be solved with minimum mathematical simplifications, which made it possible to simulate the whole deformation process with the history of material yielding, hardening, loading and unloading, etc. Finite element simulation of sheet metal forming is a powerful tool, which allows testing any modifications of the deep drawing process parameters, prior to the actual tools manufacturing.
In sheet metal forming the quality of the final product depends on the proper tools’ design, choice of the blank material, blank holder force, lubrication and some other process parameters. As there is always a discrepancy between the level of springback obtained in simulations and reality, especially for the products with complicated geometry, the aim of this study is to understand the springback phenomenon and to ascertain the reasons of its inaccurate numerical prediction. Based on this prediction, the tools geometry and process parameters are modified to obtain the required product shape.
There is a need to start an extensive experimental trial and error process to determine the necessary tools’ geometry and other variables, which will enable production of the required product shape.

1.1. SPRINGBACK EFFECT CONCEPTS IN SHEET METAL
Springback is the amount of elastic distortion a material has to go through before it becomes permanently deformed, or formed. It is the amount of elastic tolerance, which is to some extent present in every material, be it a ductile, annealed metal or hard-strength merging steel. In ductile materials, the springback is much lower than in hard metals, with dependence on the modulus of elasticity (also called Young Modulus) of a particular material. The amount of springback increases with greater yield strength or with the material’s strain-hardening tendency. Comparably, the springback of low-strength steel material will be smaller than that of high-strength steel and springback of aluminum will be two or three times higher yet.[4]

Fig.1.1 Springback Terminology.

Fig.1.2 Stress ‘Strain Curve.
Springback occurs in all formed or bent-up parts on release of forming pressure and withdrawal of the punch. The material, previously held in a predetermined arrangement by the influence of these two elements, is suddenly free from outside restrictions and immediately makes an attempt to return to its original shape and form. This is a common phenomenon in forming of sheet. So, springback can either positive or it can be in some cases in case of some metals, it can be negative also. So, it depends that under what conditions we are trying to bend. So, depending upon the conditions and the requirements it will be seen that either the plastic recovery sorry the elastic recovery will be positive or the elastic recovery will be negative. Thereby, we can say that springback, either it will be positive or the springback can be even be negative. So, now we have to device some ways in which we can avoid this phenomenon of springback. So, how we can avoid springback, we will see in this project. [12]

LITERATURE REVIEW
Following literature have been studied for analysis of springback effect of sheet metal in forming process:
Slota Jan et al [1] described springback in air bending process. Using three different categories of steel first part deals with experiment of air bending process, different bending depths and different die geometry. Implicit and explicit commercial codes were used performed in MATLAB system. In experimental same yield criterion and hardening curve were used.
Fahd Fathi Ahmed Abd El AU[2] stated springback resulting from unloading following stretch forming. This is concerned with the development of a finite element mode1 of the stretch forming process accounting for material and geometric nonlinearities, and interface conditions using ANSYS software.
Wan Cheng et al[3] described modem nonlinear mechanics in forming i.e. large deformation, boundary contact and material nonlinearity. In this difficulties arise are stated like element distortion, volume locking and shear locking.
Ander Jerberg [4] talked about amount of springback which occurs during the bending procedure so that an anticipated part profile. Parametric study conducted in order to reduce the time spent on manual corrections of the die showed how the inclusion of a step in the die can reduce the springback. Besides affecting the bending tools, springback largely affects the dimensional accuracy of the bent sheets.
G.M. Sayyed Ahmed et al[5] experimentally studied of spring back in mild steel and the results are validated with finite element analysis software LS-DYNA with factors like different thickness of sheet metal and at different die angles.
Prabhakar.A et al[6] described process includes larger deformation of the structure either with temperature or without temperature application. But in the every mechanical process certain defects exists due to the inherent resistance property of the material for forming it to the required shape. In this work, sheet metal thickness and depth of forming effect on spring back is analyzed using Finite element methods.
Esther T. Akinlabi[7] stated about the bending operation and springback based geometrical inaccuracies of bent parts. To curb springback, various factors such as bending parameters and material properties need to be considered. Experimental work using circular bending was conducted to analyze the effect of springback on the formed steel sheets. It was found that the 2 mm formed sheets exhibited an average springback of 4.24%.
Mohamed Faraj Alfaidi[8] described instantaneous unloading method and which found not applicable for predicting springback of buckling dominated problems. In this slight variations of a yield stress, R-values, hardening parameters and a sheet thickness comparable with scatter of material properties due to production process influence the springback behavior.
Maciej Nowosielski et al [9] described stamping process simulations using the eta/Dynaform for non-deformed samples and achieved compatibility at the level of 90%.
H K Yi et al[10] studied the springback of sheet metal during unloading causing deviation from a desired shape in sheet stamping operations. The analysis of the springback of sheet metal during bending to a radius with applied tensile strain requires the use of six different deformation patterns. These patterns are elastic’elastic, plastic’ elastic, and plastic’plastic for the outer and inner surfaces and plastic’plastic with an elastic core, elastic’plastic, and plastic’plastic for the inner and outer. Two different analytical models for springback have been derived.
A-M. Yan and I. Klappka [11] stated the springback behaviors of panel forming productions using multi-point stretch forming technique. Various possible influencing factors on the springback effect were analyzed. Numerical simulations indicated that the springback effect is loading-path dependent and may be linearly related to material properties in the case of simple geometry. The effect of sheet thickness and curvature found to be less significant due to strain distribution through the sheet thickness.
Hariharasudhan Palaniswamy et al [12] studied springback of the part during unloading. Finite element analysis has been used to simulate a flex forming operation and to predict the springback in the manufacturing of a cone shaped part. Sensitivity analysis on the influence of interface friction and blank dimensions on springback were carried out. Based on the results of the sensitivity analysis, an optimization problem was formulated to find the optimum blank dimensions that minimize the springback.
2.1 FINDINGS FROM LITERATURE REVIEW
In literature review most of the researcher used Numerical method (FEA) to find amount of springback effect occurs in sheet component using variable: Thickness and bend angle of sheet. FEA method used to know where and how the stresses occur in the component surface. Using software’s like LS-DYNA, ANSYS, MATLAB etc. FEA analysis carried out of sheet metal part to find various stresses like Von-Mises, yield stress occurs in it. Some researchers find out causes of springback effect using experimental method changing with process parameters. Most of papers comprise process parameter: Thickness, bend angle and punch radius. Various materials also studied to see springback.

PROBLEM STATEMENT

After studying findings from literature review, and live problem of Wiper motor bracket, following problem statement is defined:
To make Analysis of Springback Effect of Sheet Metal in Forming Process of Wiper motor bracket by considering various influencing parameters for spring back and so using various methods to minimize the Springback occurs during sheet metal operation.
3.1 OBJECTIVES
1. The main purpose of this work is to investigate causes of sheet metal spring back effect, such as process parameter, geometry of tools etc.
2. Using theoretical Method and assuming different bend radius and sheet thickness get the variations in springback value.
3. After analytical method experiments on press machine get the variations in springback values, take different height of punch using different thicknesses of sheet component.
4. To know stresses in part in forming process, analysis on ANSYS software of its design.
5. After theoretical, experimental and FEA analysis then again springback is produce, and then it is required to changes in die design parameters where springback occur in forming area of sheet metal part.
METHODOLOGY
4.1 SHEET METAL FORMING PROCESS
Following processes included in forming of sheet metal to form a shape as per design.

Fig.4.1 Method Plan of Forming Process.
The prediction of Springback has proven challenging for a variety of reasons, including numerical and physical sensitivity. The material poorly characterized behavior under loading and unloading conditions. Springback of sheet metal parts after forming causes deviation from the designed target shape and produce quality problems as well as assembly difficulties in vehicle where wiper motor bracket. In this project first sheet metal part FEA Non-linear analysis with applying boundary conditions. Experimental analysis performing on press machine takes different height of punch and thicknesses.
4.2 FORMING OPERATION ON PRESS MACHINE

Fig. 4.2 Press Machine.
and reliability. Maintenance and components of hydraulic power equipment technicians required who know how to service hydraulic in manufacturing. New fast acting valves, electrical components, and more efficient hydraulic circuits have enhanced the performance capability of hydraulic presses.
Sheet metal forming operations consists of simple bending, press forming, stretch forming, roll forming, rubber-pad forming, stamping, flanging, spinning, embossing, bulging, hyper plastic forming, peen forming, explosive forming, magnetic-pulse forming and deep drawing of complex parts. The sheet metal products have become current also due to low price, accuracy of dimensions, durability and favorable physical properties. In today’s industry, where the costs play a very important role the sheet metal products have replaced many products made by forming process. In every industry, quality and productivity are major issues for being competitive. For example, a car frame needs to be designed to achieve strength requirements and aesthetic aspects; on the other hand, cost of production and repeatability is crucial to the business.

Fig.4.3 Wiper Motor Bracket.
A forming process has been used in practice to achieve these goals in the sheet metal fabrication business. However, Springback, a shape discrepancy between the fully loaded and unloaded configurations, undermines the stamping benefits, since a major effort on the tooling design is needed to reduce Springback. In many industries, e.g. automotive industries, Springback plays an important role in tooling, process designs and forming operations. To effectively predict Springback for a potential applicant determining optimal tooling shapes and process parameters, understanding the mechanics of Springback, a mainly elastic recovery process, is essential. In the forming technology it is difficult to achieve accurate and repeatable angle of a bend. This problem is caused by elastic Springback, which is considerable in processes of sheet metal forming. Springback in processes of sheet metal forming causes troubles in assembling processes, because Springback entails anomaly of required shape of the part.

After experimental analysis theoretical method to assuming different bend angle and thickness to get variations springback values then with the help of Ansys changing parameters like thickness, bend angle to know springback decrease or not.

Fig.4.4 Flow Chart Method Approach.
It has been shown that many process variables such as friction, temperature, variations in the thickness and mechanical properties of the incoming sheet metals along with numerical parameters such as material model, element type and size, integration algorithms, contact definition and convergence criteria, etc. affect the accuracy and validity of the solution. Moreover, complex strain histories and highly nonlinear deformation of the material during the forming process add to the difficulty of predicting springback. Therefore, it is important to critically review related studies before selecting the appropriate solution method for the problem.

4.3 SHEET MATERIAL
As discussed, many purely hardening laws have been proposed in the literature with the purpose of describing the cyclic behavior of metal sheets. The complexity of these models can vary considerably with respect to the number of material parameters and strain history variables. Sheet material used in this study D513 SS4010 Grade Steel having malleability property; it is formed shape to hammering and pressing.

Table 4.1 Chemical Composition of the sheet material.
Sr. No. Chemical Composition %
1. Carbon 0.16 Max
2. Manganese 0.30 Min
3. Phosphorus 0.03 Max
4. Silicon 0.25 Max
5. Sulphur 0.03 Max
6. Aluminum 0.02Min

Table 4.2 Sheet Material Properties.
Sr. No. Material Properties Value
1. Density 7850(Kg/m3)
2. Young Modulus 2×105(N/mm2)
3. Tensile Strength 350(Kgf/mm2)
4. Yield Strength 250(Kg/mm2)

THEORETICAL METHOD
The forming of sheet metal requires an understanding of a wide range of technical knowledge, the geometric difference between the loaded and unloaded configurations, is affected by many factors, such as material properties, sheet thickness, lubrication conditions, tooling geometry and process parameters. It is extremely difficult to develop an analytical model for springback effect control including all of these factors. The major difficulty with the analytical solution is due to the lack of understanding of the stress distribution throughout the sheet, which limits the analytical approach to simple geometries and simple deformation. In the manufacturing industry, it is still a practical problem to predict them final geometry of the wiper motor bracket part after springback and to design the appropriate tooling in order to compensate for springback. One is to predict springback for dies design and compensation in order to obtain high dimension accuracy of sheet forming parts. Different methods such as analytical method, semi-analytical method and finite element method have been applied to analyze the forming process. Analytical method is a time-saving method and has been widely used for predicting springback of bending parts.

Fig.5.1 Sheet Bending [5].
Elastic recovery of the sheet after the bend load is removed is called springback. Even after plastic deformation, small elastic recovery may happen in ductile materials, after removal of load. In bending springback reduces the bend angle. Similarly, the bend radius after springback is larger. Springback will be larger for materials having lower elastic modulus and higher yield strength. Springback increases for a sheet with higher width to thickness ratio as the stress state is biaxial or plane stress. After releasing the punch load during forming bent radius changes. However, the bend allowance does not change. Therefore, we have:
Consider a sheet metal thickness-‘t’ subjected to bending so that it is bent to a radius of curvature ‘r’
Fig.5.2 Sheet Bending Terminology [6]

Bend Radius (Ri) = 7mm
Profile Angle (”1) = 700
Bend Angle (”i)= 1800-”1
= 180-70
”i = 1100
Sheet Thickness (t) = 1mm

5.1 BEND ALLOWANCE

Lb = ”i (Ri + t/2) = (Rf + t/2) ”f (1)

From equation (1),
Lb = ”i (Ri + t/2)
= 110 x ”/180 (7 +1/2)
Lb = 14.39mm

5.2 R/T RATIO
There are two ways to understand and evaluate for spring back. One is to develop a predictive model of the amount of springback and the other way is to define a quantity to describe the amount of springback. Positive springback is a situation in which the bend angle becomes smaller after removal of load. The material bends inward after the load removal due to large strains. Another expression for springback in terms of bend radius is:

Ri/Rf=1-3(”yRi/Et)+4(”yRi/Et)3 (2)
Where:
t = Thickness of the sheet =8mm.
E = Modulus of elasticity =2×105 N/mm”.
Ri = Initial radius curvature (before spring back) (mm)
= 7 mm
Rf = Final radius curvature (after spring back) (mm)
”y = Yield stress = 250 Mpa
= 2.5 x 108 N/m”
= 250 N/mm”.

From equation (2),
Ri/Rf=1-3((7x 250)/(‘2×10’^5 x1) )+4((7x 250)/(‘2×10’^5 x1))3

= 1- 3 (8.75x 10-3) + 4 (8.75x 10-3)3

= 1- 0.0262 + 2.6796 x 10-6

Ri/Rf = 0.9738
7/Rf = 0.9738
Rf = 7.21mm

From equation (1),
For Final Bend Angle (”f),
Lb = ”i (Ri + t/2) = (Rf + t/2) ”f
= 14.39 = (7.21+1/2) ”f
”f = 1.866 x 180/”
”f = 106.930
The above equation is derived from forming a full plasticity and flexibility beam, and by calculating final bend angle and in order to know to the modulus of elasticity and the yield stress. The amount of the value Ri/Rf depends on the mechanical properties of the metal which will vary depending on the value of (”yRi / ET) , if Ri/Rf= 0, so the metal is with full spring back but if Ri/Rf =1 there is no spring back in the metal. In the first step the forming process itself is optimized with the help of accurate parameters, the spring back after forming is calculated with the required accuracy. Spring back is analyzed by variation in some input parameters, e.g. material properties and lubrication. This can be done by different problem solving method, based on springback behavior; final shape of the formed part is seriously affected by spring back phenomenon and tries to prove the important role of the metal sheet thickness and bend angle in the spring back effect.
5.3 RESULT: THEORETICAL APPROACH
Table 5.1 Results of theoretical method.

Sr. No
Thickness
(mm)
Bend Radius Before Springback (Ri)
Bend Radius After Springback (Rf)
Initial Bend Angle(”i)
Final Bend Angle(”f)
Springback
(mm)

1
1
7
7.21
110
106.93
3.06

2
1.5
6.5
6.60
120
117.99
2.01

3
2
6
6.06
130
128.87
1.12

4
2.5
5.5
5.54
140
139.14
1.05

Fig.5.3 Variations of Springback when Sheet Thickness changes.

From the table it is observed that the springback effect changes with change the parameters like bend radius and bend angle. Stretch bending, in which the sheet is subjected to tensile stress at the time of bending can also reduce springback.

Fig.5.4 Variations of Springback when bend angle changes.

Above theoretical results graph shows that the springback decreases from 3.06mm to 1.05mm.This is because excess tensile stress applied during stretching reduces the bending moment for bending.in theoretical studies we change parameters like bend radius, bend angle thickness and get the springback respectively.

6. EXPERIMENTAL METHOD
6.1 EXPERIMENTAL SETUP
In recent years, various experimental techniques have been developed to study and characterize springback in sheet metals. Reduce the Sensitivity of springback to basic parameters, such as the tool radius to sheet thickness (R/t) ratio, mechanical properties of sheet material and contact parameters is usually studied.
In experimental setup first take different entry height of punch to minimize springback effect in sheet metal using different thicknesses. After taking different height of punch observed that springback decrease or not, then decide continue next procedure of experiment. To minimize some more amount the springback get an alignment of forming die and do same procedure. In second experiment, some amount of springback is reduce in the first experiment then again get glue test of forming die and same procedure as early used on press machine. The major drawback of the stretch bending test is the lack of control or direct measurement of sheet tension, which makes this experimental procedure less suitable for verifying the results of simulations.

Fig.6.1 Mechanical Press Machine.[9]
The amount of springback during unloading depends on the Young’s modulus and yield strength of the material. In analysis of sheet metal forming it is common practice to assume that the elastic modulus remains constant. However, experimental investigations revealed that elastic constants of a material may change during the plastic deformation.

Fig.6.2 Second Forming Die.
Simulation of springback comprises of two major steps: loading (actual forming) and unloading. In most springback analysis the instantaneous release method is employed, According to this method the change of shape of the drawn sheet due to the release of the tools is calculated in one increment. Sometimes this increment is subdivided into a number of sub increments to avoid numerical instabilities in forming. This method is used since it is more computationally costly; it is more realistic because the contact forces are present during the unloading step. Additional difficulties may arise unloading during springback step in buckling dominated problems.. The gradual unloading method is commonly used to stabilize the computation stabilization techniques or numerical damping. The main disadvantage of the gradual unloading method comparing to the instantaneous unloading is the computation time.
In gradual unloading requires a lot of time and is very often accompanied with bad convergence behavior of the simulation due to the presence of tools sliding with low normal forces. There are two main solution procedures for the simulation of sheet metal forming: the dynamic explicit and the static implicit. There is no need to generate the stiffness matrix and there are no unbalance forces, since the difference between the external and internal forces determines the values of nodal accelerations at the start of every time increment. Absence of unbalance forces means that the explicit method does not suffer from the convergence problems within the time increment. The major disadvantage of the explicit integration scheme is its conditional stability and prohibitively small maximum allowable time increment. Usually to solve this problem and to decrease the total computation time mass scaling is employed. In this way the critical time increment is enlarged by artificially increasing the mass of the material. The implicit time integration method is unconditionally stable. The sensitivity of springback decrease solution procedures was studied by various researchers.
6.2 CO-ORDINATE MEASURING MACHINE: CMM
With the advent of numerically controlled machine tools, the demand has grown for some means to support this equipment. There has been growing need to have an apparatus that can do faster first piece inspection and many times, dimensional inspection. The Coordinate Measuring Machine (CMM) plays a important role in the mechanization of the inspection process. Some of the CMMs can even be used as layout machines before machining and for checking feature locations after machining.
Coordinate measuring machines are relatively recent developments in measurement technology. Basically, they consist of a platform on which the work piece being measured is placed and moved linearly or rotated. A probe attached to a head capable of lateral and vertical movements records all measurements. Coordinate measuring machines are also called measuring machines. They are versatile in their capability to record measurement of complex profiles with high sensitivity (0.25 ”m) and speed. In this unit, we will discuss the principle and the working of a Coordinate Measuring Machine (CMM).

Fig.6.3 Co-ordinate Measuring Machine.
6.2.1 Advantages of CMM
CMM has got a number of advantages. The precision and accuracy given by a CMM is very high. It is because of the inherent characteristics of the measuring techniques used in CMM. Following are the main advantages that CMM can offer:
Flexibility
CMMs are essentially universal measuring machines and need not be dedicated to any particular task. They can measure almost any dimensional characteristic of a part configuration, including cams, gears and warped surfaces. No special fixtures or gages are required. Because probe contact is light, most parts can be inspected without being clamped to the table.
Reduced Setup Time
Part alignment and establishing appropriate reference points are very time consuming with conventional surface plate inspection techniques. Software allows the operator to define the orientation of the part on the CMM, and all subsequent data are corrected for misalignment between the parts-reference system and the machine coordinates.

Single Setup
Most parts can be inspected in a single setup, thus eliminating the need to reorient the parts for access to all features.
Improved Accuracy
All measurements in a CMM are taken from a common geometrically fixed measuring system, eliminating the introduction and the accumulation of errors that can result with hand-gage inspection methods and transfer techniques.
Improved Productivity
The above-mentioned advantages help make CMMs more productive than conventional inspection techniques. Furthermore, productivity is realized through the computational and analytical capabilities of associated data-handling systems, including calculators and all levels of computers.
6.3 EXPERIMENTAL RESULTS
Table 6.1 Experimental Results (CMM).

Sr No.
Sheet Thickness
(mm)
Entry Height of Punch
(mm)
Surface
Co-Ordinates
Spring-
Back Effect
(mm)
A N D
1.

1

450 X/R
2814.9858
2811.5447
3.4411
3.44
Y/A
138.8938
138.0193
0.8745
Z/H
767.6458
767.1210
0.5248
2.

1.5

300 X/R
2814.9468
2811.5447
3.4021

3.40
Y/A
138.8828
138.0193
0.8635
Z/H
767.6302
767.1210
0.5092
3.

2

Glue Test of Die

450 X/R
2814.088
2811.5447
2.5433

2.54
Y/A
138.8743
138.0193
0.8550
Z/H
767.6211
767.1210
0.5001

300 X/R
2813.8459
2811.5447
2.3012

2.30
Y/A
138.8616
138.0193
0.8423
Z/H
767.611
767.1210
0.4900

4.
2.5
Alignment of Die

450 X/R
2812.5807
2811.5447
1.7036

1.70
Y/A
138.8504
138.0193
0.8311
Z/H
767.5901
767.1210
0.4691

300 X/R
2812.937
2811.5447
1.3923

1.39
Y/A
138.8427
138.0193
0.8234
Z/H
767.5812
767.1210
0.4602

It is observed that the metal outside the bend radius is stretched and the metal on the inside of the bend radius is compressed. This means that the metal near the neutral axis may be stressed to values below the elastic limit and the metal far away from the neutral axis may be stresses beyond the yield stress. The stress distribution changes until plastic and elastic zone inside the deformed sheet comes to equilibrium. This final configuration change is known as Springback. In other words, springback is mainly due to elastic recovery of the bending process. Experiments have been carried out of the work piece after forming operation and measuring springback on CMM with difference (D) between nominal value (N) to actual value (A) as shown in table 6.2

Fig.6.4 Forming Parts With Different Thicknesses.
When Part is formed, the base metal must be transformed from flat blank into a complicated, undesirable shape dimensional part. This requires permanent deformation of the base metal. However, most connector materials are chosen due to their resistance to permanent deformation. Naturally, this tends to complicate the fabrication process. This conflict between manufacturability and required performance can best be seen in elastic springback.
Fig.6.5 Variations of Springback in Experimental Analysis when Sheet Thickness.
When a component is formed, the stamping tool bends the metal into a certain angle with a given bend radius. Once the tool is removed, the metal will spring back, widening the angle and increasing the radius. The springback ratio is defined as the final angle after springback divided by the initial stamping angle. In order to understand springback, it is necessary to look at a material’s stress-strain curve. When a bend is being formed, the material is deliberately over-stressed beyond the yield strength in order to induce a permanent deformation. When the load is removed, the stress will return to zero along a path parallel to the elastic modulus. Therefore, with some exceptions, the permanent deformation will usually be less than the designer-intended deformation of the sheet blank. The springback will be equal to the amount of elastic strain recovered when the die is removed. From the graph it was observed that springback decreases 3.44mm to 1.39mm and thickness 1mm, 1.5mm, 2mm, and 2.5mm respectively.

FINITE ELEMENT METHOD
7.1 FINITE ELEMENT ANALYSIS
The finite element method is a numerical method, which can be implemented to solve many problems. An assembly process, duly considering the loading and constraints, results in a set of equations, solution of these equations gives us the approximate behavior of the continuum. The analysis which uses FEM is known as FEA. A general purpose FEA program consists of three modules; a pre-processor, a solver, and a post processor. Commercial FEA programs can handle very large number of nodes and nodal degrees of freedom provided a powerful hardware is made available. User’s manual, theoretical manual, and verification problems manual, document a commercial FEA program.

Fig.7.1 Part Drawing.
7.2 A TYPICAL ANSYS STEPS:
7.2.1 Material Specifications
Material: D513 SS4010 Young’s modulus=200Gpa, Density =7800kg/m3
Fig.7.2 Material Specifications.

The material is considered as elasto-plastic with strain hardening behavior. Up-to yield point tangent modulus will be defined and later plastic or tangent modulus will be defined for the problem. Generally plastic modulus value is small compared to the Young’s modulus value specified. The material will follow linear relation up to yield point and later follows tangent modulus for strain calculation. This is region is the source of residual stresses in the structure. Also this region influences the spring back phenomenon.
7.2.2 Building a Model
Building a finite element model requires more time than any other part of the analysis. First, the user specifies a job name and analysis title. Then using the pre-processor, the element types are defined, element real constants, material properties, and the model geometry.

Fig.7.3 Sheet Metal Part.

Loading
The main goal of a finite element analysis is to examine how a structure or component responds to certain loading conditions. Specifying the proper loading conditions is, therefore, a key step in the analysis. Loads can be applied on the model in a variety of ways in the ANSYS program. The word Loads in ANSYS terminology includes boundary conditions and externally or internally applied forcing functions.
In this work, for sheet metal forming load 100 tonne will be applied.
Post Processing
The postprocessors in the ANSYS program can help the user to obtaining the solution and others. Post processing means reviewing the results of an analysis. It is probably the most important step in the analysis.
Contact Stress Analysis
Contact problems are highly nonlinear and require significant computer resources to solve. Contact problems present two significant difficulties. First, the exact area of contact will not be known until the problem is executed. Depending on the loads, materials, boundary conditions, and other factors, surfaces can come into and go out of contact with each other in a largely unpredictable and abrupt manner. Second, most contact problems need to account for friction.
Performing
We can use the surface-to-surface contact elements to model either rigid-flexible or flexible-flexible contact between surfaces. The Contact Manager, accessible through the Main Menu>Preprocessor>Modeling> Create> Contact Pair menu item, provides an easy-to-use interface to help to construct and manage contact definitions.
Fig.7.4 Nodes Model.

The dimensional details are given in the problem. The primary objective is to analyze the effect of thickness on spring back of the problem. ANSYS mixed approach is used to build the geometry. Different colors are used to represent the problem. Thickness of the sheet metal is considered as 1 mm. The mixed up approach considers point, line and area approach for complicated object (Punch and die) and direct rectangle creation for the sheet metal.

Mesh Generation

Fig.7.5 Mesh Model.
The members are map mesh with the appropriate material properties. Steel properties are given for sheet metal and rigid material properties are given for die and punch members. Since the sheet metal is the point of interest, the body is meshed with deformable material properties.Solid185 element with plane strain option is used for meshing. Plane182 element has the properties of large deformation effects which is the essential requirement of the forming materials. A finer mesh is considered at the corner regions for better convergence. 41454 elements and 14364 nodes are used for meshing half symmetric geometry.
SOLID185 is used for 3-D modeling of solid structures. It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element has plasticity, hyper elasticity, stress stiffening, creep, large deflection, and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and fully incompressible hyperplastic materials.

7.3 FEA RESULTS
Analysis has been carried out after giving displacement to the punch elements. Here the area mesh of both punch and die are cleared to increase the speed of computation. This is possible after the contact pairs are created. So the punch target elements are given the required displacement load for bending process. The die target nodes are fixed in the position. Incremental procedure based on Newton Raphson method applied to solve the problem in the nonlinear material and geometrical domain.
Fig.7.6 Time vs Deformation Graph.

Spring back phenomenon in the metal forming process has been analyzed using Finite element Analysis. Spring back phenomenon is a undesirable process in the manufacturing industry. Many parameters influence spring back phenomenon. In the present work, sheet metal thickness and depth of forming effect on spring back is analyzed using Finite element methods.
As see in ANSYS results shows the large deformation takes place in part

Total Deformations
If a structure experiences large deformations, its changing geometric configuration can cause the structure to respond nonlinearly. Following figures shows deformations in sheet metal.

Fig.7.7 Total deformation 1.

Fig.7.8 Total deformation 2.

Fig.7.9 Total Deformation 3.
Equivalent(Von-Mises) Stress
The figure shows final equivalent (von mises )stress in the structure. Maximum stress is around 268.9 Mpa at the bottom bent corner of the sheet metal. This can be attributed to higher deformation at the bent region. The strain is directly proportional to stress. Here strain is maximum due to plastic yielding of the sheet metal. Minimum stresses are developed at the end portions of sheet metal which are not displaced from the original configuration.

Fig.7.10 Equivalent (Von Mises) Stress 1.
The status bar at side shows the stress variation in the geometry along the sheet metal. Von-mises stress is considered for plastic condition as the von-mises theory of failure is the most used theory in the failure of ductile materials. Von-mises stress is the stress corresponding to the stored energy and also it is called as equivalent stress. Generally the structures are called yielded after it is crossing the yielding stress of the material.

Fig.7.11 Equivalent (Von Mises) Stress 2.

During design, compensation for the spring back has to be incorporated such that the bend part attains the desired shape and schematic optimization inputs as shown in figure. Springback becomes more severe with increase in yield strength of sheet metals (as the same implies greater possibility of elastic deformation and recovery) and section thickness.
7.4 CHANGE PARAMETERS
Experiments have been carried out to measure springback angle of the work piece after forming operation with steel material under different bend angles and thickness is constant. The materials used in this study are grade: D513 SS4010 steel Young’s modulus=200Gpa, Density =7800kg/m3, steel part of length 276.5mm,thicknesses is 1mm,1.5mm,2mm,2.5mm and bending at angle 60o,50o,40o,30o Respectively.

Fig.7.12 Software Inputs.

Bending is the simplest sheet forming operation. The greatest formability in bending is obtained when the bend is made across the metal grain or in the direction of rolling The largest possible bend radius should be used and it should not usually be lesser than the sheet thickness ‘t’. The cost in sheet metal forming operation can be reduced by using thinner sheets if the strength and rigidity are increased by bending and forming into ribs configuration.

Fig.7.13 Schematic Optimization.

Table.7.1 Variation of springback Thickness and bend Angle of sheet metal Using FEA.
Sr No
Thickness
(mm)

Part bend Angle
(degree)
Springback
(mm))

1.
1
60
3.25

2.
1.5
50
3.02

3.
2
40
2.21

4.
2.5
30
1.78

It is observed that the metal outside the bend radius is stretched and the metal on the inside of the bend radius is compressed. This means that the metal near the neutral axis may be stressed to values below the elastic limit and the metal far away from the neutral axis may be stresses beyond the yield stress. When the bending moment is removed, the elastic deformation tends to return to the original configuration but is restricted by the plastic deformation. The stress distribution changes until plastic and elastic zone inside the deformed sheet comes to equilibrium. From above table it was observed that springback decreases from 3.25mm to 1.78mm.

7.5 ANALYSIS OF MODIFIED DESIGN COMPONENT
Spring back is one of the key factors which influence the quality of forming sheet metal parts. Modified Design Component shows the dimples on surface because of this reinforcement of part is strong than the first part.
Fig. 7.14 Modified Part Design.

In this design model we embossing the dimples on sheet metal where the formed shape. The diameter of a dimple should be no more than 6 times the material thickness. The inside depth of a dimple should be no more than the inside radius. A hole should be at least three times material thickness away from the edge of the dimple, or the inside radius of the dimple plus three times material thickness. From the parts edge, dimples should be at least four times material thickness plus the radius of the dimple. Dimples should be at least two times material thickness from a bend from another dimple dimples should be four times material thickness plus the inside radius of each dimple.

Fig.7.15 Force Reaction of Modified Design Part.

Metal forming has been a major challenge to modem nonlinear mechanics, because almost every such process involves all three major nonlinearities, i.e. large deformation, boundary contact and material nonlinearity. In applications, difficulties arise also numerically, such as, element distortion, volume locking, shear locking and etc. Therefore, the success of the numerical simulation of metal forming processes demands a systematic effort to attack various aspects of such a procedure. In this work, efforts are focused on three major areas.

Source: Essay UK - http://www.essay.uk.com/essays/engineering/springback-effect-concepts-sheet-metal/


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