Heavy duty presses are subjected to extreme load conditions especially during operations like bending, shearing, drawing etc. It generates very high stresses in the punch and die of the press tool. As a sequel to this, failure of the press tool occurs, sometimes prematurely. Hence estimation of the stresses under severe load conditions is of paramount importance.

1. http://www.iaeme.com/IJMET/index.asp 50 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
Volume 6, Issue 11, Nov 2015, pp. 50-56, Article ID: IJMET_06_11_006
Available online at
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
ELASTO-PLASTIC ANALYSIS OF A HEAVY
DUTY PRESS USING F.E.M AND NEUBER’S
APPROXIMATION METHODS
Mr. J. Jagadesh Kumar
Assistant Professor, Mechanical Engineering Department,
Vidya Jyothi Institute of Technology, Hyderabad, India
Dr. V. V. Satyanarayana
Professor, Mechanical Engineering Department,
Vidya Jyothi Institute of Technology, Hyderabad, India
Mrs. D. Pratibha
Associate Professor, Mechanical Engineering Department,
Anurag Group of Institutions, Hyderabad, India
ABSTRACT:
Heavy duty presses are subjected to extreme load conditions especially
during operations like bending, shearing, drawing etc. It generates very high
stresses in the punch and die of the press tool. As a sequel to this, failure of
the press tool occurs, sometimes prematurely. Hence estimation of the stresses
under severe load conditions is of paramount importance. In the current work
elasto-plastic analysis is carried out employing Finite Element Method for the
evaluation of stresses in the upper tool of an 8000 tonnes heavy duty press.
Neuber’s approximation method is also carried out and the results are found
to be in consonance with the Finite Element Analysis results.
Key words: B.C.s (Boundary Conditions), Elasto-Plastic Analysis, Neuber’s
Approximation Method, SMX (maximum result value on plot), SMXB (result
value, maximum bound estimate).
Cite this Article: Mr. J. Jagadesh Kumar, Dr. V. V. Satyanarayana and Mrs.
D. Pratibha. Elasto-Plastic Analysis of a Heavy Duty Press using F.E.M and
Neuber’s Approximation Methods. International Journal of Mechanical
Engineering and Technology, 6(11), 2015, pp. 50-56.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=11
1. INTRODUCTION
Press tools are commonly used to produce components at high volumes by performing
operations like bending, shearing, deep drawing etc. The metal is pressed between
punch and die set and the article of desired shape is obtained [1].

2. Elasto-Plastic Analysis of a Heavy Duty Press using F.E.M and Neuber’s Approximation
Methods
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Sufficient clearance between punch and die needs to be provided depending on the
type of operation performed, metal used, thickness of sheet metal employed.
Otherwise, failure of punch and die occurs before the estimated design life [1, 2].
Elasto-Plastic analysis accounts for material non-linearity. After exceeding yield
strength, the rigidity of the material is different from that in the elastic range; besides,
after the yield strength is exceeded, unloading can leave deformations from the plastic
state. Note that the assumed material non-linearity does not account for the change in
material rigidity based on external factors, such as temperature. Rheological issues
(change in material properties over time) are also not evaluated [3].
Neuber’s method is used to convert an elastically computed stress or stain into the
real stress or strain when plastic deformation occurs. The Neuber’s method of finding
the elasto-plastic solution is a formula based mathematical approach by which one can
find the elasto-plastic solution without performing the elasto-plastic analysis. This is
an approximation technique that can be used to take into account the redistribution of
stress caused by plastic flow in a zone of stress concentration [4].
1.1. Details of the Press Tool Analyzed
A heavy-duty 8000T press is taken for study which is employed for forming boiler
drums whose thickness ranges from 50 to 150 mm. Failure of this press occurred due
to formation of number of cracks in the upper tool of the press. Cracks were noticed
on the four central limbs, out of the total twelve limbs, of the upper tool of press.
There are two cracks at every arm of the Y section of each limb, totaling to 32 cracks
of 125 mm length in the four limbs. These four limbs of the upper tool are used for
cold pressing operation at the maximum load condition. The cracks were detected and
were found to be propagating with every operation of the press. The upper tool of the
press is made of Nodular Cast Iron. The chemical composition and mechanical
properties of it are given in Table 1.
Table 1 Chemical Composition and Mechanical Properties of Upper Tool Material
C S Mg Si Cr Mn Ni Cu Fe
Yield
strength
Elastic
modulus
3.7% 0.015% 0.055% 2.8% 0.1% 0.2% 0.1% 0.1% Rest 310 MPa
169000
MPa
1.2. Elastic Analysis of the Upper Tool:
The three dimensional solid model of the four limbs of the upper tool of the press is
modeled using the part modeling module of Pro/Engineer (shown in Figure 1). A
quarter portion of one limb of the solid model is selected for the analysis to exploit the
advantage of symmetry in the geometry. It is shown in Figure 2.
The geometry of the upper tool is first imported into Hypermesh from Pro/E and is
then meshed with eight noded brick element by performing mapped meshing. The
geometry with mesh is shown in Figure 3. The three dimensional brick elements are
organized into a new collector and all other collectors containing the geometric
entities and shell elements are deleted. The elements in the new collector are specified
with an element type Solid 45, which is of first order type. Now the elements are
exported to Ansys via data file and is shown in Figure 4.

3. Mr. J. Jagadesh Kumar, Dr. V. V. Satyanarayana and Mrs. D. Pratibha
http://www.iaeme.com/IJMET/index.asp 52 editor@iaeme.com
Figure 1 Solid model of the upper tool Figure 2 Quarter portion of one limb
Figure 3 Meshing in Hypermesh Figure 4 F.E. model imported to Ansys
The required degrees of freedom constraints (boundary conditions) and loads can
be applied to the Finite Element model in Ansys. A pressure of 90.61 MPa is applied
on the bottom face of the tool because it is the equivalent value of the pressure to the
force of 500T acting on the quarter model. When the loads and boundary conditions
are applied, the F.E.model looks as shown in Figure 5. It is solved to obtain the stress
pattern and it is shown in Figure 6.
Performing a single analysis is not be sufficient to present the converged results in
F.E.M. as the percentage difference between the SMX (maximum result value on
plot) and SMXB (result value, maximum bound estimate) in the ‘Von-Misses Stress
plot’ is more than 10%. Hence it is needed to refine the mesh and resolve the problem.
Submodeling is considered to solve for the stresses. The submodel is selected so that
the three critical stress regions of the geometry are present in it and appropriate
boundary conditions with fine mesh are applied on it. After solving, Von-Misses
stress pattern is as shown in Figure 7;

4. Elasto-Plastic Analysis of a Heavy Duty Press using F.E.M and Neuber’s Approximation
Methods
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Figure 5 F.E. Model with loads and B.C.s Figure 6 Von-Misses stress pattern
Figure 7 Von-Misses stress pattern in Submodel with fine mesh
The solution is converged as the percentage difference between SMX & SMXB in
‘Von-Misses Stress’ plot is around 10%. The final results for the elastic solution of
upper tool of the press are given in Table 2.
Table 2 Elastic stresses in upper tool
Stress in Y-direction Von-Misses Stress
- 448.961 MPa 454.519 MPa
1.3. Elasto-Plastic analysis of the Upper Tool
In this analysis too, the Finite Element Model of Ansys with brick elements (Figure 4)
is considered as in Elastic Analysis. However loading is applied in steps and the
pressure applied is varied from 50 MPa to 125 MPa. The load steps are given in Table
3.

5. Mr. J. Jagadesh Kumar, Dr. V. V. Satyanarayana and Mrs. D. Pratibha
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Table 3 Load steps for Elasto-Plastic Analysis
Load Step Number Pressure Applied at Bottom Surface (MPa)
1 50
2 75
3 90.61
4 125
As in the case of Elastic analysis, even here the submodel is considered with fine
mesh and appropriate boundary conditions. The stress pattern after solving the
problem in Ansys is tabulated in Table 4 [7].
Table 4 Elasto-Plastic stress pattern in upper tool at different load steps
Load Step No: Pressure Applied Stress in Y-direction Von-Misses Stress
1 50 -247.743 250.811
2 75 -325.887 318.323
3 90.61 -347.741 319.541
4 125 -378.494 337.558
2. NEUBER’S APPROXIMATION METHOD TO FIND ELASTO-
PLASTIC SOLUTION
The conditions of validity of this method are that the plastic zone must remain
sufficiently contained (surrounded by elastic zone) and that the loading must be
radial. The elastic solution of the problem under the action of the external forces is
assumed to be known. The Elasto-Plastic solution can be found out from the Neuber’s
curve by looking at the point where it cuts the Stress-Strain curve. The Neuber’s
hyperbola must be constructed such that it travels from the elastic solution curve to
the stress-strain (hardening) curve. The stress-strain curve is approximated by the
Ramberg-Osgood equation as follows [8];
%Total Strain = [(σ/E) + (σ/K) (1/n)
] * 100
Here σ = Elastic stress, E = Elastic Modulus, K & n are constants that depend on the
material being considered.
For the chosen material of the tool, the values are tabulated in Table 5.
Table 5 Ramberg-Osgood equation parameters
Elastic Stress Elastic Modulus K n
449 MPa 169000 MPa 575 MPa 0.101
In Ramberg-Osgood equation the values of ‘σ’ is manipulated from 0 to 800 MPa
with steps of 2 MPa to get the corresponding values of the total strain so that the
stress-strain values are available. Thereafter a plot of these values is prepared to get
the stress-strain curve. The stress-strain curve is shown in the Figure 8. The
percentage Minimum Neuber’s strain is calculated as follows [8];
% Minimum Neuber’s strain = {[Elastic Stress] / [Elastic Modulus]}*100
= (σ/ E) * 100
= [449/169000] * 100
= 0.266

6. Elasto-Plastic Analysis of a Heavy Duty Press using F.E.M and Neuber’s Approximation
Methods
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At this stage the Neuber’s stress is calculated as follows;
Neuber’s stress = (σ2
/ (E * % Min Neuber’s Strain)) * 100
In the above equation the %Strain values are manipulated with necessary
increments for the required number of steps. Here, the value is manipulated from
0.266 to 2 with 101 steps and get the corresponding Neuber’s stress values. After
getting the strain and stress values they are plotted with suitable scale on the same
graph on which the Ramberg-Osgood stress-strain curve is plotted. The point where
both the curves meet gives the Elasto-Plastic solution. The solution is tabulated in
Table 6 and the curves are shown in Figure 8.
Table 6 Results from Neuber’s Approximation Method
Property Measured Result from Neuber’s Method
Equivalent Total Strain 0.35 %
Elastic Strain 0.18 %
Plastic Strain 0.17 %
Real (Elasto-Plastic) Stress 320 MPa
Figure 8 Ramberg-Osgood and Neuber’s Curves
3. RESULTS AND DISCUSSION
In the elastic analysis a pressure of 90.61 MPa is applied on the upper tool of the
press. It causes the stress in Y-direction to be in the tune of 448.961 MPa while the
Von-Misses stress is 454.519 MPa [Table 2].
In elasto-plastic analysis, the load is applied in steps on the sub-model ranging
from 50 MPa to 125 MPa. It resulted in a stress range of 247.743 MPa to 378.494
MPa in Y-direction while the Von-Misses stress varied from 250.811 MPa to 337.558
MPa. At a pressure of 90.61 MPa (which is equivalent to 500T load) the stress in Y-
direction is 347.741 MPa, Von-Misses stress is 319.541 MPa. The total strain is
0.002851 (i.e. 0.29 %) [Table 4].
Neuber's Conversion
0
100
200
300
400
500
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
% Strain
Stress
Stress-Strain Curve By Ramberg-
Osgood Method
Neuber's Curve

7. Mr. J. Jagadesh Kumar, Dr. V. V. Satyanarayana and Mrs. D. Pratibha
http://www.iaeme.com/IJMET/index.asp 56 editor@iaeme.com
Neuber’s approximation method is employed and found that the Elasto-Plastic
stress is 320 MPa and the total strain is 0.35% [Table 6]. Neuber’s method does not
take into consideration the geometry and the loading conditions. The method
evaluates the solution based on the value of the elastic stress. Hence there is a minor
variance between F.E.M. results and Neuber’s results.
ACKNOWLEDGEMENTS
The authors express their sense of gratitude to M/S Premier Engineering Industries,
Hyderabad for the support given in the study of their press. The authors also thanks
the Director and Correspondent of Vidya Jyothi Institute of Technology, Aziz Nagar,
Hyderabad, India, for the help and support extended for this work.
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[3] G.R. Nagpal, Tool Engineering and Design, ©2002 Khanna Publishers.
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[5] Cyril Donaldson, George.H.LeCain, V.C.Goold, Tool Design 3rd edition, Tata
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