The Critical Damage Evaluation at the Different Condition of Testing.
Authors: Ing. Sonia Benesova, Ph.D. - West Bohemia University in Pilsen
Ing.Jan Krnac, Zelezarny a Dratovny Bohumin, Czech Republic
The software Deform uses for ductile fractures study the modificated formula of the Cockroft
– Latham criterion for monitoring of the fracture behaviour:
 eff
 
*

/  ef d ef  C
0
where σef is the effective stress, εeff is the effective strain in the fracture and (σ*/ σef ) is nondimensional factor of the stress concentration , which represents the highest tensile stress
influence σ* . The achievment of its critical value called the critical damage which is
generally comprehended to be material quantity defines the situation when the plasticity of
material is exhausted which takes effect of the fracture appearance in the concrete forming
condition..
The foregoing papers deal with the quantity of critical damage in the experimental
wiredrawing through two dies with different drawing angle and next in wiredrawing by
standard technological process. It was fond out the values of the critical damage were
different in both processes. In this connecting paper the additional data will be presented that
relate this theme.
Evaluation of Dcr by means of the tensile test.
For critical damage evaluation is routinely utilized the tensile test or upsetting test. The
second test in light of the form of wire and also its practicability can´t be used - the wire
upsetting is with regard to its strenght and wire diameter hardly viable.
During tensile test the fracture starts after the neck is created in the central point of maximal
necking.Therefore the neck radial after fracture was measured and after it the simulation was
implemented.The simulation was analyzed in the step when the diameter of the true neck was
the same as the diameter of the simulated neck.The maximal value of the damage in the neck
central part was think to be the critical Damage (Dcr). The flow stress curve necessary for
simulation was obtained from the digital registration of the functionallity loading – elongation
from which it is possible to express functionallity σef - εeff . The another question is how to
enter the running of the strenghtening after the overdrawing the strenght limit in the zone of
the neck creation and the threedimensional state of stress. If the exactly known part of the
strenghtening curve (i.e. from yield limit to the strenght limit)is used for simulation the
simulation runs after exceeding the tensile limit in such a way the material strenghtening
doesn´t proceed while the deformation continues – but this isn´t in agreement with the reality.
As to the credibility of the simulation it is necessary to enter also the functionallity σef - εeff in
the neck creation zone. It is common knowledge that the effective stress depends on the neck
shape according to the classic Bridgman´s solution [1] so as the knowledge of the final
loading makes us possible to find out the final value of the effective stress by calculation.
The simulation of the tensile test was carried out for the rolled wire producted by technology
Stelmor, diameter 5.5mm, quality C70K (the samples were market T39829) and for
microalloyed wire of the same diameter, quality HDR82V10 ( M58785 – see tab.n.1). The
results from the simulation are summarized at the tab.n.2 – the critical damage for T32064
was sets to be, for the M58785 it was Dcr = 0,45 . In the case of T39829 the flow stress was
entered only to the tensile limit, in the case of M58785 the known part of the flow stress was
completed within the fracture stress, obtained by calculation.
Fig.1: The damage in the tensile test - T32064 Fig.2: The damage in the bend test - T32064
quality
mark
C70K
32064
C70K
C70K
C80D2-CRV
HDR82V10
39829
34001
T48912
M58785
C
[%]
Mn
[%]
Si
[%]
P
[%]
S
[%]
Cr
[%]
Ni
[%]
Cu
[%]
Al
[%]
Mo
[%]
V
[%]
N
[%]
0,72 0,54 0,21 0,011 0,014 0,05 0,02 0,03 0,002
0,73
0,72
0,8
0,83
0,58
0,53
0,66
0,66
0,2
0,19
0,21
0,27
0,012
0,008
0,009
0,006
0,011
0,013
0,013
0,009
0,05
0,03
0,16
0,04
0,02
0,01
0,03
0,06
0,05
0,01
0,07
0,08
0,002
0,003
0,002 0,006 0,067
0,001 0,006 0,083 0,0035
Tab. 1: The chemical composition of the samples
Evaluation of Dcr by means of the bend test.
The bend test was carried out in the laboratory by help of bending device which makes
possible to read the angles after each bend in a way that the spring-back was eliminated. The
devices was fitted with the mandrel of the 5,5mm diameter. The wire was plastically bended
by the angle of 30° and back untill the crack on the surface put in an appearance. The crack
was watched by optics. The bend test was accomplished for hot-rolled wire quality C70K
marked T32064 and T39829. The number of bends until the first crack was observed came to
42 in the case of T32064 and 29 in the case of T39829. Some difficulty occured with the flow
stress determination – the flow stress curves were estimated from the strenghtening course
during wiredrawing so that the material strenghtening in the fracture moment was the same as
after wiredrawing. How can be seen from the tab.2 the critical damage values were higherorder digits and run to Dcr = 10,05 for T39829 and Dcr = 8,93 for T32064.
mark
experiment Dcr.
εef.
notice
T32064 tensile test 0,69 0,65 the flow stress up to the tensile limit
M58785 tensile test 0,46 0,45 the flow stress up to the fracture
T39829 drawing
1,14*) 2,62 without fracture
T34001 drawing
1,12*) 2,91 without fracture
M58785 drawing
1,24 3,22 fracture
T48912 drawing
1,14 2,93 fracture
T39829 bend test
10,05 14,59
T32064 bend test
8,93 12,10
*) the presented value isn´t the critical damage
Tab.2: The damage and effective daformation, fond out by different condition of testing.
Evaluation of Dcr from the standard technology.
The basic findings can be resumed this way: the wiredraving was done by two procedures
when the fracture wasn´t detected and by two procedures when the fracture was detected. The
fracture didn´t appear during wiredrawing of T39829 and T34001(tab.2), both the quality
C70K threated by technology Stelmor. In the case of microalloyed wires (M58785 and
T48912 – tab.1) processed also by Stelmor technology the hot rolled wires were drawn
experimentally to the situation when the formability was exhauset and repeated fractures
occured. The drawing was carried out in the dies with the drawing angle 2α=8°. The final
values of the damage are shown in the tab.n.2 and they move about 1,2 .
The resuls discussion
From the above results it follows the fracture can appear in the quite different values of
deformation and damage. Although it is necessary to take into account the fact of some
inaccuracy especially in the bend test when the exact flow stress curve wasn´t known the
proncipal reason of that behaviour is the different way of the final deformation achievment the significant part featured (?) the factor of deformation history. The cyclic deformation is
typical for the bend test when during the one period the damage increases owing to tensile
stress contemporary accompanied by increasing deformation ( angle from 60° back to the 90°)
during the second period the additional deformation comes on but all principal stresses in the
point of maximal bend are compressive and the damage doesn´t increase ( angle from 90° to
the 60°). By this way we can get a very high values of damage (c.10). These idea implies the
combination of deformation and compressive stress during cycklic straining tends to the
certain “stabilisation” of the damage in each bend and subsequently to it´s high values. In the
other hand the deformation during the tensile test increases continually accompanied by
tensile stress which faces to the fast exhausting of the plasticity and to the subsequent
fracture in relatively small values of effective deformation and damage. In the case of
wiredrawing the deformation and also damage increas in the drawing cone of the each die.
Their increasing is discontinued in the calibration zone. Considerable high values of
deformation and damage are reached with this procedure in comparison of the tensile test.
Odds are the calibration zone can have the similar but inferior “stabilisation” effect to the
damage as the combination of deformation and pressure stresses at the bend test. Therefore
the stress analysis in the calibration zone was performed with a wiev to the maximal principal
stress running (obr.3).
It can bee seen from this figure in the simulation with fracture the presence of the tensile
principal stress in axial part of calibration zone was observed whereas in the cause without
the fracture the principal stress was altogether compressived. The action of calibration zone
probably leads to some damage stabilisation which facilitates the subsequent increasing of the
damage in the next die pass. As far as the the compressive stresses are high enough in the
calibre the stabilisation is effective. In the case the tensile stresses are detected in the
calibration zone the influence of calibre is reduced or restrained ant it leads to the accelerated
exhausting of the plasticity and to the subsequent fracture. During the tensile test the
“stabilisation” doesn´t come therefore the critical damage is low.
Max. princ. stress
M58785-fracture
T48912-fracture
T39829
T34001
400
300
200
stress [MPa]
100
0
-100
-200
-300
-400
-500
-600
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
num ber of pass
Fig. 3: The progression of maximal principal stress in the calibration zone of the die.
Conclusion
The reliable ascertainment of the critical damage after multiple wiredrawing through the dies
isn´t possible to find out from the tensile test or any other similar test. The studium must be
carried out directly in the wiredrawing technology in relation to achieving the final stadium.
The relatively high critical damage values are obtained by action of the calibration zone
which tend to the slow and succesived exhausting of the plasticity. The current results
indicated the presence of the compressive stresses in the axial part of the calibration zone has
positive influence to tle plastic behaviour of the drawing material and in connection with it
also to the critical damage.
References:
1. Bridgman, P.W. : Studies in Large Plastic Flow and Fracture. Harvard University
Press, Cambridge, Massachusetts, 1964
2. Internetová stránka http://www.deform.com
3. Kim, H., Yamanaka, M., Altan, T.: Prediction and Elimination of Ductile Fracture in
Cold Forging using FEM Simulation. Transaction of NAMRI/SME, Vol. XXIII, 1995.