Non-linear finite element analysis of light gage steel shear diaphragms
Finite Element Analysis of Shear Punch Testing ppt
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Transcript of Finite Element Analysis of Shear Punch Testing ppt
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Finite element analysis of shear
punch testing and experimental
validation
Nishant gaurav
Division :B
Roll no : 60
Guided by :Mr. V. D. Padalkar
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Index
Introduction to shear punch test
Introduction of finite element analysis
Ideology
literature review
Recent developments
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Why shear punch test ????
It requires very small volume of material as comparedto conventional tensile tests. So its an efficient testtechnique for evaluating mechanical properties whenthe material availability is limited.
The advantage of using the SPT technique for materialswith limited availability has attracted the nuclearindustry for assessing the properties of irradiatedmaterials.
This technique is used where conventional machinetests are practically not used like in weld joints .
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What is Finite Element Analysis???
FEM: Method for numerical solution of fieldproblems.
Description:
-FEM cuts a structure into several elements(pieces of the structure).
-Then reconnects elements at nodes as if nodeswere pins or drops of glue that hold elements
together. -This process results in a set of simultaneous
algebraic equations.
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Ideology
Many engineering phenomena can be expressed bygoverning equations and boundary conditions
Governing Equation (Differential equation)
L() + f=0
Boundary ConditionsB() + g=0
These equation lead us to a set of simultaneous
algebraic equations .
[K]{U}={F}In mechanics problem , K is the stiffness , U is the
displacement and F is the force .
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Literature review
In previous research involving the use of the shearpunch test, it was assumed that the displacementof the punch tip was only slightly different than thecrosshead displacement.
The shear punch test done by Toloczko(1) suggestedthat punch tip displacement is much less thanpreviously assumed, and that for the test frames whichhave been used, crosshead displacement is over anorder of magnitude greater than punch tip
displacement and It altered the slope of the loadingcurve masking the true yield point . These suggestionswere made based on the analysis done using FEA.
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Figure 1. a) Shear stress versus crosshead
displacement trace for a real shear punch test
of a cold-worked steel, and b) shear stress
versus punch tip displacement trace for an
FEA simulated shear punch test on the same
steel.
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The FEA of ShP testing by Guduru et al.[2] showed
that the elastic loading lines of FEA generated LDC
was found to be much steeper than theexperimental curve.
Its important to note that both Toloczko et
al.[1]and Guduru et al.[2]had measured the punch
displacement by a displacement sensor coupled tothe moving punch.
Fig 2:
Displacementsensor
coupled to
the moving
punch.
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In one of our recent work [3], a modified
shear punch experimental setup in which
displacement was measured at specimenbottom directly using a Linear Variable
Differential Transformer (LVDT) has been
demonstrated.
Fig : LVDT is
coupled to thespecimen
bottom.
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The intent of current work is to
simulate the shear punch test using FEA
and compare the initial loading curveswith the experimentally generated
curves.
We will see that the elastic portion ofthe FEA generated loaddisplacement
curve overlaps with the corresponding
experimental curve only when the
fixture compliances are eliminated in
experiments.
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Shear punch test :experimental
procedure The shear punch test is a small specimen test
technique for extracting yield strength,
ultimate strength.
A punch of 3 mm diameter and die of 3.04 mm diameter
was used for the present study. Small disc specimens were cut by Electric Discharge
Machining (EDM) from the various materials and theirsurfaces were gently ground .
Ideally, the load on the punch is measured as a function of
punch tip displacement, but due to the difficulty in actuallymeasuring the punch tip displacement, it has beenpreviously assumed that crosshead displacement isapproximately equal to punch tip displacement, and thus,the load on the punch has been measured as a
function of crosshead displacement.
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Fig:
Sketch of the shear punch
fixture.
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Shear punch load versus crosshead displacement
traces are similar in appearance to uniaxial tensile test
traces.
Yield is measured from these traces at deviationfrom linear elastic loading, and ultimate is measured at
the peak load.
The loaddisplacement data is converted to stress-
normalized displacement data using the following
expressions.
where P is the applied load, t is the specimen
thickness, r is the average of punch and lower die radius
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Experimental: The Finite Element
Analysis Simulation
The MARC finite element analysis software was used tosimulate the shear punch test. To reduce computingtime and costs, an axisymmetric mesh was utilized andis shown in Fig.
There are three main components to the mesh: thespecimen, the punch, and the receiving die.
The specimen was modeled as elastic-plastic. In aneffort to make the simulation as realistic as possible,the punch and the receiving die were modeled as
elastic. This allows for a small amount of elasticdeformation in these components which alters thestress distribution in the specimen mesh.
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Fig :
Sketch of the mesh used in the
present study.
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As with any finite element analysis, material
properties must be inserted into the model. For
this simulation, the punch and the receivingdie were assigned the elastic properties of BCC
steel (E = 200 GPa, = 0.28). The specimen was
assigned the uniaxial deformation behavior of
several different materials of interest .
The FEA boundary conditions were as
follows:
1) Translations in the radial direction
were prevented because the
model is axisymmetric.
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2) The bottom of the receiving die was held
stationary in the axial direction.
3) An immovable boundary was placed in contactwith a portion of the top of the specimen to
simulate the presence of the upper-half of the shear
punch fixture. No clamping force was applied to
the specimen with this boundary condition.
4) Friction between the components was set
equal to zero. The previous FEA based study has
shown the effect of friction between components tobe minimal.
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Under the assumption that real shear punch tests
are performed in the strain rate independent realm,
the FEA simulations were run in static mode.
Due to the difficulty in simulating the cutting and
failure behavior which occur in a real shear punch
test, the FEA simulations were run to only a small
amount beyond yield.
Simulated shear punch tests were performed on
several different materials. Different materials
were tested by assigning true stress versus trueplastic strain data and elastic deformation properties
from different materials to the specimen elements.
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During a simulation, the MARC program keeps
track of the load on the punch and the
displacement of the top of the punch.
To obtain the punch tip displacement, it was
necessary to run simulations using a rigid punch and
receiving die.
By comparing the elastic loading obtained from arigid component test to an elastic component test, it
was possible to measure the compliance of the
punch and receiving die.
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This compliance value was then
used to estimate the punch tip displacement as a
function of the displacement at the top of
the punch using the following formula:
where x is the punch tip displacement, x is thedisplacement at the top of the punch, P is the load
on the punch, and C is the measured compliance of
the punch and receiving die.
Using the calculated punch tip displacement data,
load versus punch tip displacement traces
were created.
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Figure 1. a) Shear stress versus crosshead
displacement trace for a real shear punch test
of a cold-worked steel, and b) shear stress
versus punch tip displacement trace for an
FEA simulated shear punch test on the same
steel.
C li
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Compliance :
The key aspect of this comparison is that the elastic
loading slope for the FEA simulation is 2 orders of
magnitude steeper than the elastic loading slope of the
real shear punch test (look at the x-axis scales in figures).
Since the main difference between an FEA simulationand a real shear punch test is the location at which
displacement is measured, it is reasonable to assume
that this is leading to the dissimilar traces. This could be
determined by measuring the compliance of the testmachine, but performing such a compliance
measurement is not a simple task because of the
geometry of the shear punch test.
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Following the idea that the differences in the traces
for the FEA simulations and the real shear punch
tests is due to test machine compliance, a
compliance was added to the FEA punch tip
displacement data. By adding a compliance, the
punch tip displacement was converted to a
hypothetical crosshead displacement. The
equation which describes this hypothetical
crosshead displacement is
where is the hypothetical crosshead displacement, x
is the displacement of the punch tip, P is the load on the
specimen, and C is the estimated test machine compliance
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C was found by comparing the elastic loading slope
in shear punch test traces obtained from real tests
and from FEA simulations.
The resulting shear stress versus hypothetical
crosshead displacement trace is compared to the
real test trace in Fig. The FEA generated trace has
been transformed into a trace that looks nearlyidentical to the real trace.
This further confirms the idea that crosshead
displacement measured in real tests is much larger
than the actual punch tip displacement.
It also shows that a large amount of compliance can
strongly alter the appearance of a load versus
displacement trace.
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Fig: Comparison of a real trace and an FEAsimulated trace where the FEA punch tip
displacement data has been converted to a
hypothetical crosshead displacement.
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Yield stress management
Initiallyyielding takes place at the punch and die
corners and interior is
still elastically deformed. The transition from elastic to plastic deformation
in the specimen occurswithin a few microns of
punch displacement. As the punch penetrates the specimen, the
plastic deformation extends throughoutthe
specimen. Yielding in the specimen was assumedwhen theplastic deformation takes place
through the thickness.
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It is seenfromFig. that at a stress corresponding
to 0.15% offset of normalized displacement, fully
developed plastic deformation spreadsthrough the
thickness of the sample. We conclude that the stressevaluated at 0.15% offset truly represents the shear
yield stressbased on through section plasticity.
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Using the experimental data, shear yield strength is
computed at offsets of 0.15% and 1%. It has been
found that the
experimentally obtained shear yieldstrength at 0.15% offset compares well with that
obtained from FEA curves for all the materials
studied.
h l h ld l b d f
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The tensileshear yield correlation obtained from
the experimental data using 0.15% offset definition
is seen to have high correlation coefficient for a
linear fit Fig. as compared to that obtained using1% offset values .
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It also obeys the von Mises yield relation.
A material is said to start yielding when its von Mises
stress reaches a critical value known as the yield
strength . The von Mises stress is used to predict yielding of
materials under any loading condition from results of
simple uniaxial tensile tests.
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Conclusion: FEA of the shear punch testing indicated a large influence
of the punch compliance on the elastic portion of load
displacement plot. The elastic loading lines of experimental curve obtained
with displacement measured at specimen bottom matcheswell with the FEA generated curve.
The yield strength based on through thickness plasticity
corresponded to an offset of 0.15% of normalizeddisplacement. The experimental shear yield strengthevaluated at 0.15% offset compares well with the FEAgenerated value.
The tensile-shear yield correlation obtained using 0.15%
offset definition was found to obey the von Mises yieldrelation.
The results of FEA are thus verified and validated withexperimental data.
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References
[1] Hamilton ML, Toloczko MB, Lucas GE.Recent progress in shear punch testing.In:
Hans Ullmaier, Peter Jung, editors.miniaturized specimens for testing ofirradiated materials. IEA international
symposium; 1995. p. 4651
Guduru RK, Nagasekhar AV, Scattergood RO,
Koch CC, Murty KL. Finite element analysis of ashear punch test. Metall Trans A
2006;37:147783
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Thank you