Middle EastTechnical University

Metallurgical and MaterialEngineering Department

METE 304

Fundamentals ofMechanical Shaping Assignment 2

Effect of Frictionin Compression Test

Student: Fatih Sıkan (1739275)

Submission Date: 27.05.2013

A. Description of the ModelFor this simulation, a compression test is introduced and the effectof the friction coefficient on deformation is revealed. There are 3cases with 3 different friction coefficients under same loading foran elastic-plastic material in axisymmetric loading conditions. Forcomputational efficiency a semi-cylindrical sample is introduced.The sample has dimensions of 4 mm for length and 11 mm for diameter.Loading applied is 45000 N of compressive load which is appliedgradually within 13 seconds.

Figure 1 Sketch to describe the model and the asymmetric loadingcondition

The sample is loaded in x-direction as shown in figure 1 andsymmetry axis of the cylinder is x-axis. For boundary conditions acontrol node is constructed, separately. Loading conditions areintroduced and applied on the control node in x-direction. Note thatthe control node is fixed in y-direction and the sample is elastic-plastic.

Apart from sample model, material properties are as below;Elastic modulus (E) = 200GPaPoisson’s ratio (v) = 0.31.

Symmetry Axis

Base

(Wa

ll)

Push

er

LOAD SAMPLE

4 mm5.5

mm

Meshing is 10x10 and there is no bias factor. Contact bodies, flowcurve and loading vs. time plots can be seen in the figure sequencesbelow.

Figure 2 Contact bodies for the model

Figure 3 Flow curve diagram for the model

Figure 4 Loading versus time diagram for the model

The data for the flow curve diagram in the figure 3 can be seen intable 1;

Table 1. Total Equivalent Plastic Strain and Stresses Strain 0 2 6Stress 370 380 385

This part so far is same for all 3 different simulations; however,the main focus of the simulation is introducing effect of thefriction coefficient on deformation. Thus, 3 different frictioncoefficient values between sample and wall are used from now on.These values are respectively; 0, 0.35 and 0.7.

B. Results of the AnalysisDisplacements in x and y directions, equivalent Von Mises and totalequivalent plastic strain are shown by contour bands with 3

different friction coefficients. Note that for better representationpurposes, each of these four one initial stage and one final stageframe is captured for the first case where friction coefficient is0. In certain regions there is very little or no plastic deformationis occurred. Such regions can be seen as blue regions in thesecontour bands in figures for total equivalent plastic strain andknown as dead metal zone.

Figure 5 (a) displacements in x-direction initial stage as frictioncoefficient 0

Figure 5 (b) displacements in x-direction final stage as frictioncoefficient 0

Figure 6 (a) displacements in y-direction initial stage as frictioncoefficient 0

Figure 6 (b) displacements in y-direction final stage as frictioncoefficient 0

Figure 7 (a) displacements in equivalent Von Mises initial stage asfriction coefficient 0

Figure 7 (b) displacements in equivalent Von Mises final stage asfriction coefficient 0

Figure 8 (a) displacements in total equivalent plastic straininitial stage as friction coefficient 0

Figure 8 (b) displacements in total equivalent plastic strain finalstage as friction coefficient 0Since there is no friction in sample/pusher and sample/wallinterfaces, there is no bulging effect as seen in all the figures 5to 8. Displacement in x-direction is 0.7710 mm and that of y-direction is 0.6320 mm. There is no dead metal zone since there isno friction.

Figure 9 displacements in x-direction as friction coefficient is0.35

Figure 10 displacements in y-direction as friction coefficient is0.35

Figure 11 displacements in equivalent Von Mises as frictioncoefficient is 0.35

Figure 12 displacements in total equivalent plastic strain asfriction coefficient is 0.35As seen in figures 9, 10, 11 and 12, there occurs bulging byintroducing friction coefficient of 0.35. Displacement in x-direction is 0.7610 mm and that of y-direction is 0.6252 mm. Deadmetal zone can be observed in figure 12.

Figure 13 displacements in x-direction as friction coefficient is0.7

Figure 14 displacements in y-direction as friction coefficient is0.7

Figure 15 displacements in equivalent Von Mises as frictioncoefficient is 0.7

Figure 16 displacements in total equivalent plastic strain asfriction coefficient is 0.7As seen in figures 13, 14, 15 and 16 bulging effect increases withincreasing friction coefficient. Bulging effect for the figures with0.7 friction coefficients is more than the figures with 0.35friction coefficients. Displacement in x-direction is 0.7314 mm andthat of y-direction is 0.5991 mm. Dead metal zone can be observed infigure 16 too.

To sum up the findings of these 3 simulations, the frictioncoefficient and displacement is inversely related to one another.Increase in the friction coefficient causes a decrease indisplacement both in x- and y- directions. This relationship can beseen in the table 2 clearly.

Table 2 Displacements in x- and y- directions for different frictioncoefficientsDisplacements µ=0 µ=0.35 µ=0.7

X 0.7710 0.7610 0.7314Y 0.6320 0.6252 0.5991

Critical engineering (ex, ey) and true strains (εx, εy) are calculatedusing the equations below:

ex=dx

x0(1)

ey=yy0

(2)

εx=ln (1+ex) (3)εy=ln (1+ey) (4)

ex = engineering strain in x directioney = engineering strain in y directiondx = displacement in x-direction dy =displacement in y-direction x0 (length) = 4 mm y0

(radius) = 5.5 mm

Calculation for first case friction coefficient (µ=0)

ex=dx

x0=0.7710

4=0.19275

ey=yy0

=0.63205.5

=0.1149

εx=ln(1+ex )=ln (1.19275 )=0.176εy=ln(1+ey )=ln (1.1149 )=0.1088

Calculation for second case friction coefficient (µ=0.35)

ex=dx

x0=0.7610

4=0.19025

ey=yy0

=0.62525.5

=0.1136

εx=ln(1+ex )=ln (1.19025 )=0.174εy=ln(1+ey )=ln (1.1136 )=0.1075

Calculation for third case friction coefficient (µ=0.7)

ex=dx

x0=0.7314

4=0.1828

ey=yy0

=0.59915.5

=0.1089

εx=ln(1+ex )=ln (1.1828 )=0.1678

εy=ln(1+ey )=ln (1.089 )=0.0852By the calculations for strains table 3 is constructed.

Table 3 Engineering and true strains in x- and y- directions fordifferent friction coefficientsµ ex ey εx εy0 0,19275 0,1149 0,176 0,10880,35 0,19025 0,1136 0,174 0,10750,7 0,1828 0,1089 0,1678 0,0852

By the data obtained from the table 3, graph 1 is drawn.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.05

0.1

0.15

0.2

0.25

exeyεxεy

Friction Coefficient

Stra

in

Friction Coefficient

Stra

in

Graph 1 Strain versus friction coefficient diagram

All calculated strain values are plotted against frictioncoefficient as seen in graph 1. True and engineering strains in bothx- and y-directions are shown in the diagram. Conclusion that isdone in the table 2 is supported. Graph 1 reveals with increasingfriction coefficient at contact interfaces of deformable body,strain in x- and y- directions decreases.

References[1] (Academic Center for Computing and Media Studies, Kyoto University)[2] (William D. Callister, 2007)