Elastoviscoplasticity with plastic strain memory 425
Table I. Different experimental conditions used in the test sequence.
T
◦
C 20
200 300
500 600
˙ε s
−1
Cyclical tests
in different
strain ranges 1ε 1
1.2 1.4
1.6 1.8
1 1.2
1.4 1.6
1.8
1 1.2
1.4 1.6
1.8
1 1.2
1.4 1.6
1.8
0.9 1
1.2 1.4
1.6 1.8
10
−3
Relaxation tests for differ- ent ε
4 1
4 1
1 Timehours
3 3
2 2
2
Table II. Material parameters for 28CrMo V5-8 steel at 300
◦
C. k
∗
a
∗ 1
c
∗ 1
a
∗ 2
c
∗ 2
b
∗
bst
∗
Qst
∗
η
∗
m
∗
Q
∗ M
n
∗
K
∗
201 272
2378 276
221 1.8
20 −40
0.2 338
−131 17
528
Table III. Material parameters for 28CrMo V5-8 steel at 500
◦
C. k
∗
a
∗ 1
c
∗ 1
a
∗ 2
c
∗ 2
b
∗
bst
∗
Qst
∗
η
∗
m
∗
Q
∗ M
n
∗
K
∗
162 162
2457 207
300 1.8
20 −40
0.2 399
−135 14
600
4. Introduction of the obtained constitutive equations into a Finite Element model
This section presents simulations of cyclic behaviour of 28CrMo V5-8 steel in different strain ranges. These parameters were introduced into a finite elements program Castem 2000. Figure 2 shows an axisymmetric
version of this sample. Only one finite element was used for the simulation. This element in the middle of the sample was submitted to an imposed strain figure 2. If 1σ = σ
maxi
− σ
mini
, figures 3 and 4 give a comparison between experimental data and the finite element modelling for the strain range 1ε = 1.4 and 1ε = 1.8
when the temperature is at 20
◦
C. Figure 5 gives the simulation curve for the relaxation test at the same temperature. Figure 6 shows the
stabilized curve σ − ε for 1ε = 1.4 at 20
◦
C. In all cases, we have good agreement between the experimental data and the finite element modelling deduced from the proposed constitutive model.
5. Metallurgical analysis
a About the hypothesis of microstructural stability The material in the railway brake discs is a resistant steel which has been submitted to thermal processing
before its use. The austenising temperature of 975
◦
C was imposed over 5 hours. After this stage, the discs were submitted to a water quench. After quenched, the structure consists of martensite and residual austenite.
Because of the high level of hardness of this structure, the brake discs were tempered in a furnace at 635
◦
C for 9 hours before being air cooled. The final structure obtained is a tempered martensite which offers a better
resistance to shattering. Table IV gives the chemical composition of 28CrMo V5-8 steel. The samples used in these tests were extracted radially from the brake discs.
426 R. El Abdi et al.
Figure 2. Axisymmetric view of the sample.
Figure 3. Comparison between experimental curve and finite element simulation for strain range 1ε = 1.4 at 20
◦
C.
Elastoviscoplasticity with plastic strain memory 427
Figure 4. Comparison between experimental curve and finite element simulation for strain range 1ε = 1.8 at 20
◦
C.
Figure 5. Comparison between experimental data and numerical curve of the relaxation test at 20
◦
C ε = 4.
Figure 6. Stabilized loop σ − ε at 20
◦
C 1ε = 1.4.
428 R. El Abdi et al.
– Preparation of the specimens Etching polished metal surfaces with a chemical reagent is a means of differentiating the metal’s structural
constituents when as is most often the case, they are not readily distinguishable. The usual practice for etching a polished surface is to immerse it in a cold etchant Nital for a required period time. The etching is then
stopped by washing the specimen with water and drying it rapidly with hot air. This method gives clean metal surfaces which are generally free from all etching debris.
– Measuring the hardness The Vickers hardness of the specimens was determined with a load of 30 daN. Various points of the measure
taken on every specimen were distributed over the surface in order to obtain representative results. We note a hardness stability for the relaxation tests in the temperature field figure 7. For the cyclic tests, the hardness
stays stable until 300
◦
C whatever the imposed strain figure 7. Above 500
◦
C we have declining hardness which grows in speed when the strain increases. The reduction of this mechanical characteristic becomes more
pronounced as we approach the tempering temperature.
b Analysis under an optical microscope The object of the micrography is to reveal the internal structure of the alloy, which depends on its
crystallography and its constitution. This is why an analysis under a light microscope is necessary for a polished and etched surface. We have observed inclusions in the material. Their locations are visible in the
Table IV. Chemical composition of 28CrMo V5-8 steel.
Carbon Chromium
Molybdenum Vanadium
Concentration 0,28
1,25 0,8
0, 2 x 0, 4
Figure 7. Evolution of the sample hardness.
Elastoviscoplasticity with plastic strain memory 429
Photo 1. Microstructure after relaxation test under 20
◦
C.
Photo 2. Microstructure after cyclical test at 1ε = 1.8 under 600
◦
C.
adjoining photos where a phenomenon has turned the surrounding structure black. The microstructure shows no appreciable change, even the one which was submitted to 1ε = 1.8 see photos 1 and 2.
The observation of the microstructure shows the presence of martensite needles called acicular martensite. Although the martensite needles directions seem to be aleatory, we can observe a particular orientation inside
every initial grain of the austenite see De Ferry, 1966. All the observations lead to a microstructural stability until 600
◦
C. In fact, we observe the same tempering martensite whatever the temperature or the mechanical loading.
430 R. El Abdi et al.
The decreasing hardness can be explained by a new coalescence of the precipitations in the matrix. As opposed to the microstructure, the decreasing hardness is the result of the influence of the temperature and
the imposed strain during the cyclic tests as shown in figure 7. Therefore, during the cyclic loading, the hardness slowly decreases as the test temperature increases up to 500
◦
C as does the mechanical toughness. This decreasing tendency becomes considerably more pronounced above 500
◦
C. However, the hypothesis of microstructural stability of the material stays valid as far as 600
◦
C.
6. Conclusion
