Report No. ERC/NSM-B-00-20A
Development of Forming Processes for Copper
Components for the Stanford Linear Accelerator
Flow Stress Determination
Phase I Progress Report
By
Dan Hannan, Graduate Research Associate
Gracious Ngaile, Staff Engineer
Dr. Taylan Altan, Professor & Director
August 2000
The Engineering Research Center
For Net Shape Manufacturing
1. Introduction
The flow stress of a material,  , is its resistance to plastic deformation, sometimes
referred to as the “instantaneous yield stress” of the material. For example, in a
compression test without bulging (uniform deformation), the metal will start to flow
when the applied stress reaches the value of the flow stress or yield stress of the
material. The flow stress of a material is represented by a true stress-true strain
curve. Below are the many factors that influence the flow stress of a material.
Factors unrelated to the deformation process

Chemical composition

Metallurgical structure

Phases

Grain size

Segregation

Prior strain history (cold working, hot rolling, etc)
Factors explicitly related to the deformation process

Temperature of deformation, 

Degree of deformation or strain, 


Rate of deformation or strain rate, 
Therefore, the flow stress,  , can be expressed as a function of temperature, ,

strain,  , strain rate,  , and microstructure, S, or:

 = f(  ,  ,, S)
(1)
In general, at room temperature, the flow stress of metals is highly affected by strain
while at hot forming temperatures (above the recrystallization temperature) the strain
rate is far more significant.
There are some exceptions.
For example, lead
recrystallizes at room temperature where its flow stress is significantly affected by
strain rate.
Flow stress data is important because it directly influences the accuracy of FEM
simulations (i.e. the forging load, metal flow, etc.). In finding the flow stress of a
metal, one eliminates the error involved in selecting data of a similar material or the
error involved in using old data at lower strains where extrapolation is necessary.
There are many tests that are used to find the flow stress of materials. These include
the ring test, the tension test, the torsion test, and the compression test.
The ring test is most commonly used for the evaluation of interface friction or finding
the approximate coefficient of friction. Once the friction is known, the test can be
simulated to find the load-stroke curve, which in turn gives the stress-strain curve for
the material. However, this test is not common since the flow stress is not found
experimentally, but through a combination of experiment, simulation, and curve fitting.
The tension test is most often used to find the mechanical properties of metals, but
can also be used to obtain flow stress data. However, the flow stress data obtained
from this test is valid only for relatively small plastic strains. In metal forming, flow
stress data must be valid for a large range of strains since this is what is encountered
in actual metal forming processes.
The torsion test can be used to obtain flow stress data at very high strains (  = 2 to
4) that are encountered in forming processes such as extrusion and radial forging.
With this test a notched tubular specimen is twisted at a given rotational speed to
measure the torque and number of rotations. This information is then used to find the
stress-strain curve of the metal. However, this test is expensive to conduct and,
therefore, not used unless absolutely needed.
The compression test consists of compressing a cylindrical billet between two flat
dies while recording the load and displacement (load-stroke curve).
The
compression test can be used to obtain flow stress data up to strains of about  =
1.0 to 1.5. This test is relatively easy and inexpensive to conduct while giving flow
stress data at strains high enough to be used in analyzing most metal forming
processes. For these reasons, the compression test will be used to find the flow
stress of a copper material that is investigated in this study.
The study is being conducted in several phases as follows:

Phase I – Determination of flow stress for OFE copper

Phase II – Evaluation of lubricant contamination

Phase III – FEM simulation and analysis to evaluate and help in the designing of
the forging process to manufacture the accelerator cell
2. Objectives
The objectives of Phase I of this study are to:

Determine the flow stress of OFE copper to be used in the forging of the
SLAC accelerator cell

Obtain flow stress data for OFE copper that can be input into an FEM
software package so that accurate FEM simulations of the process can be
conducted

Determine the flow stress for OFE copper, processed under the following
conditions:
o
As received, from bar
o
As received, from plate
o
Annealed (1025oC for 15 minutes)
3. Test Preparation
3.1 Manufacture of specimens
To successfully obtain flow stress using a compression test, the deformation of the
cylindrical specimen must be uniform (no barreling can occur – see Figure 2). To
help achieve this condition a special specimen geometry known as a Rastegaev’s
specimen is used (see Figure 1). The “pocket” on the end of the cylindrical specimen
helps keep lubricant between the workpiece and the die, inhibiting metal-to-metal
contact.
The Stanford Linear Accelerator Center (SLAC) was responsible for manufacturing
the specimens to be used for the compression tests.
The specimens were
manufactured in the following numbers (approximate):

10 from bar, as received

10 from plate, as received

10 annealed (1025oC for 15 minutes)
Figure 1. Rastegaev’s Specimen
NO BARRELING
BARRELING
(a)
(b)
Figure 2. a) uniform compression and b) non-uniform
Compression
3.2 Tool and Data Acquisition Set-up
3.2.1 Tool Setup
The existing ERC/NSM compression test tooling was used to conduct the tests for
this project.
The tooling consists of two flat dies with carbide inserts (for wear
resistance and decreasing tool deflection) contained in holders attached to a die set.
Figure 3 shows the basic tool set-up (load cell not shown).
The tests were conducted in a Minster (160-DPA Tranemo) hydraulic press with a
capacity of 160 tons
Die Set
Bottom
Die
Die Holder
Figure 3. Basic tool set-up for the compression tests (load cell not shown)
3.2.2 Data Acquisition
When conducting compression tests to obtain flow stress, the load and displacement
must be recorded.
ERC/NSM has built a data acquisition system to record this
information. The system is run using a PC and the software package Labview.
A displacement transducer was used to record the stroke, while a 50 ton Sensotec
load cell was used to record the load. Both the load and the stroke were recorded in
voltages so a conversion factor was found to obtain the load in lbf and stroke in
inches. The load cell was calibrated using Labview and a 59 k shunt resistor as
outlined by the manufacturer.
3.3 Specimen Preparation
To prepare the specimens for the tests, the diameter and height of each was
measured and recorded. The specimens were each placed in a separate bag and
were labeled by number, type, and dimensions to ensure that specimens were not
mixed. Before the tests, each specimen was coated with industrial grade paraffin
wax. The wax acts as a lubricant and helps keep the specimen from barreling.
4. Testing of Specimens
After all preparations were complete, as outlined in Section 3, the tests were
conducted. Four specimens of each type were tested to check the repeatability of the
results. The procedure consisted of the following steps:

Set the lower slide limit on press (Sets press stroke and establishes
reduction in height of the specimen)

Set press speed (about 10 mm/sec)
After every specimen:

Clean die surfaces with WD-40 (multi-purpose lubricant & cleaner)

Spray dies with Teflon spray

Place Teflon sheets and specimen on center of lower die and bring upper
die down close to top of specimen

Start data acquisition system

Lower upper die and deform specimen

Raise upper die and measure temperature of the specimen surface (to find
what effect temperature has on flow stress)

Check deformed specimen for uniform deformation
5. Results and Discussion
At the conclusion of the tests, the data was analyzed. The load and stroke data was
first converted from voltages to pound force (lbf) and inches, respectively, using a
conversion factor found during calibration of the data acquisition system.
Once
converted the data was placed into an Excel spreadsheet that was developed to
calculate and plot the stress-strain or flow stress curve. The spreadsheet was also
used to find the constant, K, and the strain hardening coefficient, n, that are used in
Equation 2, which is a common exponential flow stress equation for metals at room
temperature.
 = K( ) n
(2)
Often Equation 2 can be used to represent the flow stress of a metal with good
accuracy when compared to the experimental data points.
As mentioned earlier, tests were completed on three types of copper, differing only in
the way they were processed (i.e. the composition is the same). However, data was
only analyzed for the specimens not annealed (as received).
The annealed
specimens showed non-uniform deformation as they were compressed, which makes
the data recorded invalid.
Figure 4 shows the deformation of the annealed
specimens along with the other two types tested.
Figure 4. Shape after deformation of the three specimen types tested
Notice that the specimen machined from plate stock also shows non-uniform
deformation in that the specimen has an elliptical shape rather than a round shape.
Most likely, the elliptical shape is due to anisotropy of the rolled material (i.e. the fact
that the plate stock is rolled in one direction making the material more likely to flow in
that direction). The error from this non-uniform deformation is minor, however, since
the amount of non-uniform deformation is minor.
5.1 Flow Stress Curves
Figures 5 and 6 show the flow stress curves for the copper specimens from bar stock
and the copper specimens form plate stock, respectively. Each figure contains two
curves; one shows the flow stress curve obtained experimentally and the second
shows the flow stress curve found using Equation 2, which was presented earlier.
The copper bar flow stress is slightly higher (2500 psi) than the copper plate flow
stress. Also, the shape of copper bar flow stress curve differs from the copper plate
curve in the beginning of the deformation. It seems like the copper bar material was
work hardened in some way before the compression tests. This would explain the
shape of the copper bar flow stress curve at low strains.
For each copper type, the experimental curve fits well with the curve obtained using
equation 2 (using K & n values), although for copper bar the two curves do differ
somewhat at low strains (<0.3) due to the reason outlined above. This indicates, for
copper bar at low strains (< 0.3), the flow stress curve generated by equation 2 is
incorrect and will produce some error in the FEM simulations. The error would be
small, however, since stains reach values of 0.3 very quickly in most forging
operations. If data at lower strains is necessary, the FEM user should either input the
experimental flow stress curve or use the curve from equation 2, but establish how
the FEM code will extrapolate from the curve to minimize the error. For example, in
the case for copper bar, the user could use Equation 2 for strains of .3 and higher,
but then specify that for strains lower than .3 the flow stress curve would be constant,
thus better mirroring the experimental flow stress curve.
Figure 5. Flow stress curve from experimental and equation for copper bar (as received)
Figure 6. Flow stress curve from experiment and equation for copper plate (as received)
5.2 Load-Stroke Curves
To check the accuracy of the experimental flow stress data, a FEM simulation of the
compression test, using the experimental flow stress data, was conducted. Then the
load-stroke curve was generated and compared to the load-stroke curve found from
experiment (see Figures 7 and 8).
Notice that the load stroke curves from
experiment differ slightly towards the end of the stroke from those found through
simulation. This is seen because friction is considered zero during the entire stroke
in the FEM simulation, but in the actual experiments the friction increases as the
stroke increases. This increase in friction is not high enough to cause barreling, but
is high enough to slightly increase the load giving an error of about 5%.
Figure 7. Load-stroke curves for copper bar (as received)
Figure 8. Load-stroke curves for copper plate (as received)
6. Conclusions
The following conclusions were found during the flow stress tests:

Accurate flow stress data was found for copper from bar (as received, nonannealed) and copper from plate (as received, non-annealed)

Flow stress data could not be generated for the annealed specimens
because of the non-uniform deformation

Good repeatability of the flow stress data was found for specimens of the
same material type

The flow stress data obtained will improve the accuracy of FEM simulations
conducted in future phases of this project
7. Future Work
Phase II of the project will consist of lubricant contamination tests using a single cup
extrusion test and a ring test. The ring test will give an approximate value of the
coefficient of friction, while the single cup backward extrusion test will better simulate
the pressures found in cold forming. Specimens from both tests will be sent to SLAC
for analysis of the contamination.
8. References
1.
2.
Altan, T., Oh, S.I., and Gegel, H. Metal Forming-Fundamentals and Applications,
book published by American Society of Metals (ASM) (1983)
Dahl, C., Vazquez, V. and Altan, T. “Determination of Flow Stress of 1524 Steel
at Room Temperature Using the Compression Test” ERC Report # ERC/NSM99-R-22, May 1999