EFFECT OF QUASI-STATIC PRESTRAIN ON SUBSEQUENT DYNAMIC
TENSILE CURVES
L. Durrenberger1, A. Rusinek1, A. Molinari1, D. Cornette2
1 Laboratory of Physics and Mechanics of Materials, UMR CNRS 75-54, University of Metz, Ile du
Saulcy, 57045 Metz cedex, France
2 Arcelor Research, Voie Romaine, BP 30320, F-57283 Maizières les Metz, France
[email protected]
ABSTRACT
The effects of a quasi-static prestrain on subsequent dynamic tensile curves have been investigated by using interrupted tests
where the specimen was completely unloaded before reloading at high strain rate. The reloading flow curve was compared
with results obtained at constant loading rate (same strain rate as during the previous reloading). The behaviour of three cold
rolled steels produced by ARCELOR was analyzed in this study.
Introduction
Ecological and safety preoccupations require the development of Ultra High Strength Steels in the automotive industry. Thanks
to the very high mechanical characteristics of these steels, the safety performance is improved without increasing car weight. It
has been shown in [1] that a prestrain process improves the crash behaviour of a crash-box structure. For an efficient
numerical simulation of industrial applications, a good knowledge of material behaviour is needed. During the quasi-static
manufacturing of crash structure, a microstructure evolution is observed which leads to a modification of the material response
at high strain rate. In this study, the effects of strain rate history have been investigated using an interrupted test in which the
specimen is loaded at quasi-static strain rate, unloaded, and then reloaded at high strain rate. A convincing demonstration of
history effects by means of a rapid change in strain rate frequently requires a change of more than three orders of magnitude
in the value of strain rate [2]. Bake hardening steels, dual phase steels and TRansformation Induced by Plasticity (TRIP) steels
are frequently used in automotive industries. A grade of each of these families (BH260, DP600 and TRIP800) is analyzed in
this paper.
Experimental procedure
The thicknesses of the sheet steels are respectively 1.643mm, 1.585mm and 1.335mm for BH260, DP600 and TRIP800
-1
steels. The material characterization was performed applying two experimental methods: the quasi-static behavior (0.008 s )
-1
was determined using a screw controlled machine whereas the high strain rates (~1000 s ) was obtained by a tension split
Hopkinson bar. The chemical compositions of the investigated steels are listed in Table 1.
Material
[%]
Mn
[%]
Si
[%]
Al
[%]
P
[%]
BH260
0.002
0.632
0.101
0.051
0.071
DP600
0.107
1.460
0.136
0.035
0.025
TRIP800
0.204
1.649
1.694
0.037
0.011
C
Table 1. Chemical compositions of the investigated steels
Micrograph observations of non-prestrained materials have been performed with an optical microscope. The analysis of the
BH260 micrograph, after a Dino etching, reveals an average grain size of about 15 µm, Figure 1.a. For the case of DP600 and
TRIP800 steels, Lepera and Klemm etchings have been respectively performed. In Figure 1.b, the different phases of the
DP600 can be observed. The ferrite appears in clear brown, the martensite in white and carbureted phases (cementite+perlite)
in dark brown. The volume fractions of the above phases are respectively 85%, 5% and 10%. In Figure 1.c, the ferrite phase of
the TRIP steel appears in brown, whereas the residual austenite and the bainite phases appear in white. The initial volume
fraction of austenite is 19%.
a)
b)
c)
Figure 1. Micrograph of the investigated steels a) BH260 b) DP600 c) TRIP800
The prestrain process has been performed using sheet steels with dimensions of 350*460mm. The tensile specimens were
then machined using the previous sheet steel only in the homogenous strain zone [1]. All the tests were performed
perpendicularly to the rolling direction. At the end of the quasi-static process, the strain tensor is the following,
⎛1
⎜
0
⎜0
⎝
0
ε = ε ⎜ 0 - 0.435
⎞
⎟
0 ⎟
- 0.565 ⎟⎠
0
(1)
Schmitt et al [3] have proposed a parameter α =(D1:D2)/(||D1||.||D2||) to characterize a two-stage strain path. In this expression,
D1 and D2 represent the strain rate tensor during the prestrain and the subsequent deformation, respectively, and ||D|| is the
0.5
norm of D defined by ||D||=(DijDij) . The so-called quasi-monotonic, quasi-Bauschinger, and orthogonal strain-path changes
are defined by α = 1, -1 and 0 respectively. In our case the subsequent loading corresponds to a quasi-monotonic loading
because α = 0.997.
Results
Klepaczko et al [2,4] have already shown that the effects of strain rate history on the flow stress depend of the microstructure
of the material. For the case of BCC metals, a dynamic tensile loading after an initial quasi-static deformation leads to an
increase of the flow stress compared to the dynamic loading curve without quasi-static prestraining. Conversely, for FCC
metals, a dynamic tensile loading after an initial quasi-static deformation leads to a decrease of the flow stress compared to
the dynamic loading curve.
Von-Mises equivalent plastic strains ε eq = 2 / 3 × ε ijp ε ijp are used to compare the behaviour before and after the prestrain process.
The bake hardening steels, which are mild steels with solid solutions, show a typical behavior of BCC metal, Figure 3.a.
-1
Uenishi [5] had performed TEM observations on specimens of solution-hardened steels deformed at high (1000 s ) and low
-1
(0.001 s ) strain rates. It has been shown that an increase of strain rates leads to an increase of the dislocation density,
especially at low strains, and delays the onset of dislocation organization (Figure 2). During a jump of strain rate, the
dislocation density increases inside an organized structure (Figure 2.c), leading to a high macroscopic work-hardening rate
θ = ∂σ ∂ε just after the jump.
a)
b)
c)
Figure 2. Microstructure observed in a hot-rolled IF steel [5] a) after 17% at low strain rate b) after 15% at high strain rate c)
after 4% in high strain rate following a quasi-static prestrain of 17%
In Dual Phase steels, the dislocation distribution is initially non uniform. Dislocation cells are arranged around the martensitic
islets because the ferrite phase has to accommodate the volume variation of the martensite during the cooling phase of the
manufacturing of the steel [6]. This accommodation is performed by plastic deformation of the ferrite phase, which explains
that the dislocations cells are created at the interface. The plastic deformation process depends on the dimensions of the
martensitic islands [7,8], which are very hard metallurgical elements (mean ~ 60 HRC) [9]. All phases are first deformed
elastically. Then, the martensitic phase continue to be elastically deformed whereas the ferrite phase is deformed plastically;
the dislocation cells are propagating from the interface to the grain interior of the ferrite. If martensitic islands are smalls, they
undergo no plastic deformation and can be described as rigid particules dispersed in a ferritic matrix, whereas if their
dimensions are bigger a plastic deformation can occur after excessive elongation of the ferrite phase [10]. It appears that the
presence of the martensite plates explains the high stress level of these steels but the hardening is mainly controlled by the
evolution of the ferrite phase. As a result, the effect of strain rate history on DP steels, Figure 3.b, is typical of the behaviour of
BCC metal.
900
BH260
916 s
600
DP600
-1
938 s
800
1057 s -1
819 s
940 s -1
970 s
500
-1
-1
-1
700
600
0.008 s
400
-1
0.008 s -1
500
300
400
200
300
0
0.05
0.1
0.15
Von-Mises equivalent plastic strain ε
0.2
eq
[-]
0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16
Von-Mises equivalent plastic strain ε
a)
eq
[-]
b)
Figure 3. Strain rate history effect a) BH260 b) DP600
For the case of the TRIP800 steel considered in this study, dynamic tensile loading following initial quasi-static deformation
leads to a decrease of the flow stress compared to the pure dynamic loading curve, Figure 4.a.
1400
20
TRIP800
dε/dt = 0.008 s -1
1040 s
-1
1200
1067 s
-1
15
1000
1066 s
-1
10
800
0.008 s
-1
5
600
400
0
0
0.05
0.1
0.15
Von-Mises equivalent plastic strain ε
0.2
eq
0
0.05
0.1
0.15
Von-Mises equivalent plastic strain ε
[-]
a)
0.2
eq
[-]
b)
Figure 4. TRIP800 steel a) Strain rate history effect b) Evolution of the residual austenite volume fraction as a function of the
plastic strain (dots are experimental data)
TRIP steel’s microstructure is composed of soft ferrite grains with bainite (or martensite) and retained austenite. The retained
austenite (mean ~ 30 HRC [9]) transforms into martensite during deformation. The evolution of the ferrite microstructure and
the growth of the martensite volume fraction fM are mainly responsible of the increasing stress during deformation. The Figure
4.b provides the evolution of the volume fraction of austenite fA in terms of the plastic strain for a tensile quasi-static loading.
No experimental data are available at high strain rate because all specimens were fractured during the test with tension split
0
0
0
0
Hopkinson bars. The evolution of the volume fraction of martensite is given by: fM = fA + fM - fA where fA and fM are
respectively the initial volume fractions of austenite and martensite. It has been shown in early studies that the volume fraction
of martensite depends on strain, strain rate and temperature [12] and also on the strain path [13]. In fact, for a given value of
the plastic strain, the volume fraction increases with strain rate and stress triaxiality. Tomita et al [12] have proposed a
formulation to model the strain-induced martensitic transformation kinetics. In the proposed expression, the volume fraction of
martensite fM is considered to be dependent upon plastic strain, strain rate and temperature. Using this formalism, a schematic
evolution of the volume fraction of martensite in terms of the plastic strain is shown in Figure 5.
Quasi-static loading
Dynamic loading
Jump of strain rate
Plastic strain [-]
Figure 5. Schematic illustration of the evolution of the martensite volume fraction with the plastic strain
If the evolution of the volume fractions of austenite and martensite are considered as frozen, the overall plastic response of the
TRIP steel is solely governed by the deformation of the (BCC) ferrite phase. Indeed, the martensite phase is very hard and
does not contribute to the total deformation. Therefore, under the hypothesis of fixed volume fractions, the macroscopic
response of the TRIP steel to a strain rate jump would be typical of a material with a BCC structure as in Figure 3. To have a
full understanding of flow stress evolution, the additional effect due to the growth of the martensitic phase must be analysed.
The evolution of fM for different strain rate histories, as illustrated in Figure 5, shows that the growth of the martensitic phase
leads to a flow stress evolution similar to that of a FCC structure. The global response of a TRIP steel being the result of the
interplay of the deformation of the BCC ferrite and of the growth of the martensitic phase, strain rate history effects can be
viewed as a “combination” of BCC and FCC responses.
It is worth noting that the TRIP800 steel considered in this study shows a typical behaviour of FCC metals, while
experiments made by Bleck et col [11] on a TRIP700 with 11% of initial volume fraction of austenite show that the strain rate
history effects are identical to those of BCC metals. These different responses can be attributed to the initial volume fraction of
austenite which is larger for TRIP800 than for TRIP700. Thus the potential of martensitic transformation is larger for TRIP800,
which favors “FCC like effects”.
Conclusion
It has been shown in earlier studies that the effect of strain rate history on the flow curve depends on the material
microstructure. The evolution of the ferrite microstructure, which depends on strain, temperature and strain rate, governs the
evolution of the flow stress in BCC steels. It has been shown in this study that DP steels exhibit the same behaviour as BCC
metals. Since TRIP steels are composed of different phases, strain rate history effects are the result of the competition
between the microstructure evolution of the ferrite phase and the austenito-martensitic transformation.
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