TEMPERING EFFECT ON CYCLIC BEHAVIOUR
OF A MARTENSITIC TOOL STEEL

Z. Zhang

Institute of Metal and Technology

Dalian Maritime University

Dalian 116026

China

D. Delagnes, G. Bernhart

Research Center on Tools, Materials and Processes (CROMeP)

Ecole des Mines d’Albi-Carmaux

81013 Albi, CT Cedex 09

France

Abstract

A tempered martensitic steel is investigated in order to define a microstructural
parameter which may be used in combination with a cyclic constitutive model
for numerical simulation of forging dies. A tempering kinetic law was defined
in the form of a Johnson-Mehl-Avrami law, by using a "tempering ratio"
concept. The tempering ratio takes into account the actual, the as-quenched
and the annealed hardness. Mechanical parameters are discussed with respect
to tempering ratio and testing temperature and special attention was paid to
the cyclic softening behaviour.

INTRODUCTION

Hot work tool steels are generally used at various tempering states, i.e.

with different mechanical properties, depending on requirements of the in-
dustrial application (die dimension, workpiece temperature, forging equip-
ment). Moreover, numerous investigations have shown that the die-workpiece
interface may reach temperature levels higher than the tempering tempera-

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6TH INTERNATIONAL TOOLING CONFERENCE

ture. As a consequence, steel may be subjected to a continuous evolution of
the microstructure and related properties during his life.

Considering the tool lifetime increase, there is an interest in having a good

understanding of the steel "ageing" effect on the cyclic fatigue behaviour,
which corresponds to there classical loading condition. With the help of
simulation, it may then be possible to try to optimise the tool design, if cyclic
constitutive models are available. Such models have been investigated over
the last years [1, 2, 3, 4] but assume microstructural stability of the steel. As
a consequence, model parameters have to be identified for each tempering
state and cannot take into account the over ageing during industrial life. In
order to overcome these limitations, a new parameter has to be added in the
model. This paper reports part of the work [5] performed to introduce a
microstructural parameter in a cyclic constitutive model. It describes, in a
first part, the tempering test program and the kinetic law defined to follow
steel ageing. Then, it shows the effect of steel hardness and test temperature
on the cyclic behaviour. Results are discussed in the last part in relation
to a more industrial interest: i.e. relation between mechanical properties,
hardness, ageing, testing temperature and strain rate.

MICROSTRUCTURE AND TEMPERING KINETIC LAW

TEMPERING TEST PROGRAM

Material investigated in this work is a 55NiCrMoV7 (AISI L6/6F3) hot

work tool steel widely used in forging industry for die manufacturing. The
classical heat treatment consists in annealing, austenitising, quenching and
one tempering. In order to establish a tempering kinetic law, a tempering
test program including temperatures between 100

◦

Cand 700

◦

Cand times

up to 660 hours was performed (Table 1). Initial state is the as vacuum-
quenched condition leading to a Rockwell Hardness of 60 HRC. Samples are
introduced in a hot furnace and temperature are controlled by a thermocouple
welded on the samples. At the end samples are taken out of the hot furnace
and slowly cooled.

As shown in Table 1, tempering test program consists in two parts: in the

first part, time and temperature were chosen in order to permit the verification
of the Hollomon and Jaffe [6] relation, as well as the Lifshitz and Wagner
[7, 8] equation (r

3

t

−r

3

0

= Kt) defining the increase of carbide size (diameter)

during tempering. In the second part, times and temperatures are completed

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

689

Table 1.

Tempering test program

Tempering

Tempering duration (hours)

temperature(

◦

C)

Part 1

Part 2

350

0,25

2

665

0,025

0,083

0,5

1

75

189

460

0,25

2

25,63

0,025

0,083

0,5

1

75

100

500

0,25

2

75,3

0,025

0,083

0,5

1

25

100

560

0,25

2

18,87

0,025

0,083

0,5

1

25

75

600

0,25

2

16

0,025

0,083

0,5

1

25

75

100

0,25

2

0,025

0,083

0,5

1

4

200

0,25

2

0,025

0,083

0,5

1

4

300

0,25

2

0,025

0,083

0,5

1

4

650

0,25

2

0,025

0,083

0,5

1

4

700

0,25

2

0,025

0,083

0,5

1

4

in order to get enough results for kinetic law definition. All samples were
polished, and Vickers hardness (HV

0,2

) was measured under a load of 200 g;

thirty indentations were performed for each sample, general scatter was
10 HV.

MICROSTRUCTURAL EVOLUTION DURING TEMPER-

ING

Part of the samples were subjected to further analysis in order to inves-

tigate evolution of microstructural features during tempering: this concerns
grain sizes, martensitic laths width, length and aspect ratio, carbide volume
fractions, compositions and sizes. Those observations were performed us-
ing, optical microscopy, Scanning Electron Microscopy, Transmission Elec-
tron Microscopy, Electron Dispersive Analysis, X-Ray Analysis and Image
Analysis. More details can be found in reference [5]. Major results are
summarised in the following:

grain sizes and martensitic laths are not modified by tempering as
shown in Fig. 1, 2

carbide volume fraction is constant and close to 8.2%, for every tem-
pering temperature

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6TH INTERNATIONAL TOOLING CONFERENCE

inter-laths carbides are M

3

C cementites (Fig. 3) whereas intra-laths

carbides (Fig. 4) are M

3

C or V

8

C

7

vanadium carbides

mean size of intra-laths carbides (which strongly contribute to the
strengthening) does not follow the Lifshizt and Wagner equation, but
increases rapidly with time and linearly with temperature as shown in
Fig. 5a, 5b

A linear relation between carbide mean size and Vickers hardness
(Fig. 6) was established. This is an indication that among the two
mechanisms which may explain the softening during tempering, i.e.
dislocation structure evolution and carbide coalescence, the second
one has been clearly demonstrated. Dislocation evolution analysis
was not performed during this work, but is in progress in an other
work [9]

TEMPERING RATIO AND KINETIC LAW

To establish the tempering kinetic law, it was assumed that tempering cor-

responds to a phase transformation promoted by a diffusion process between
a martensite state towards a ferrite + globular carbide. Such solid phase trans-
formations may be described by the general Johnson, Mehl, Avrami (JMA)
[10, 11] relationship as follow:

f

v

= 1 − exp(−(bt)

m

)

(1)

where f

v

corresponds to the volume fraction of the new solid phase, m is a

material constant and, if we assume that tempering is a thermally activated
process, b may be expressed with an Arrhenius equation,

b

= b

0

exp



−Q

RT



(2)

with b

0

constant, Q activation energy, R perfect gaz constant and T tempera-

ture in Kelvin. As it was found a direct relation between carbide coalescence
and hardness, Vickers hardness was chosen to define the tempering ratio, con-
sidering that the tempered state, with a hardness HV is an intermediate state
between the as quenched (hardness HV

0

) and the annealed state (hardness

HV

∞

). As a consequence, tempering ratio τ

v

is defined by the equation

τ

v

=

H

v

− H

0

H

∞

− H

0

(3)

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

691

Figure 1.

Tempering effect and mean grain size.

Figure 2.

Tempering effect and martensitic laths width.

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6TH INTERNATIONAL TOOLING CONFERENCE

Figure 3.

Interlath carbides (SEM).

Figure 4.

Intralaths carbides (TEM).

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

693

Figure 5a.

Relation between mean car-

bide size and tempering time at 600

◦

C.

Figure 5b.

Relation between mean car-

bide size and tempering temperature after
2 hours.

Figure 6.

Relation between mean carbide size and Vickers hardness.

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6TH INTERNATIONAL TOOLING CONFERENCE

With such a definition, tempering ratio is between 0 (as quenched state)
and 1 (annealed state). For the steel investigated, HV

0

=776 and HV

∞

=210.

Combining equations (1) and (3), the current hardness can be written as

H

v

= H

0

− (H

∞

− H

0

)(1 − exp(−(bt)

m

))

(4)

The parameters identifications b

0

, Q and m are performed using the SidoLo

software [12]. The values obtained are b

0

= 2.7 × 10

8

(s

−

1

), m

= 0.0518

and Q

= 230957 (J · K

−

1

· mol

−

1

). The latter value is close to the values

reported in literature for low or medium alloyed steels and also close to the
activation energy of the diffusion of classical alloying elements (Cr, Mn, Ni,
V) in ferrite [5]. Figures 7 and 8 show respectively hardness evolution and
tempering ratio evolution for short times (less than 4 hours). On Fig. 8 are
also drawn the curves coming from the model, showing the validation of
the choice of a JMA kinetic law to describe tempering.

When complex

Figure 7.

Vickers hardness and tempering temperature and time.

time-temperature routes are followed, differential equation of kinetic law
has to be used

˙τ

v

= (1 − τ

v

)mb



ln

1

1 − τ

v



m

−1

m

(5)

This equation was validated by multiple level tempering experiments [5]. If
we consider equation (4), various routes can be followed to reach a given

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

695

Figure 8.

Tempering ratio with respect to time for various temperature (experimental and

simulation).

hardness H

v

; those routes are defined by the relation

t

exp



−

Q

RT



= const

(6)

which gives the well known Hollomon and Jaffe relation

T

(k + log t) = const

(7)

TEMPERING EFFECT ON CYCLIC FATIGUE BEHAVIOUR

FATIGUE TEST PROGRAM

In order to investigate the effect of tempering on the cyclic fatigue be-

haviour, samples have been manufactured with four different hardneses.
Tempering conditions, Rockwell and Vickers hardness and corresponding
tempering ratio’s are reported in Table 2. For each hardness, samples have
been subjected to cyclic loads at different temperatures (20

◦

C, 300

◦

C,

400

◦

C, 500

◦

C, 600

◦

C). Tests were carried out with a closed-loop 810

MTS servo-hydraulic testing machine. The round specimen was mounted
in water-cooled grips and heating was achieved with a 6 kW induction gen-
erator. Temperature was controlled by thermocouples mechanically applied
on the middle of the sample. Strain is recorded with a 12 mm gauge length
contact extensometer with alumina rods. The test itself consists in a total

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6TH INTERNATIONAL TOOLING CONFERENCE

strain amplitude reversed (+0.8/-0.8 %) fatigue test under triangular wave
form divided in two stages:

during the first stage, strain rate is fixed on a level of

1 · 10

−

2

s

−

1

,

and number of cycles were selected in order to reach a near constant
cumulated plastic strain close to 4 mm/mm whatever the test temper-
ature and hardness. As an example, Fig. 9 shows the evolution of the
semi-stress amplitude with the cumulated plastic strain for the 50 HRc
samples at all temperatures.

during the second stage, strain rate is varied form

1 · 10

−

2

s

−

1

to

1 · 10

−

3

s

−

1

and

1 · 10

−

4

s

−

1

, but only three cycles were performed at

each strain rate. This allows to get information on the steel strain rate
sensitivity that may modify considerably the mechanical properties,
especially at high temperatures. Fig. 10 shows the change of stress-
strain loops for a 42 HRc specimen at 600

◦

C. The three levels of strain

rates have been selected to cover the industrial strain rate conditions,
between mechanical and hydraulic forging.

Figure 9.

Semi-stress amplitude with respect to cumulated plastic strain for the 50 HRC

hardness.

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

697

Table 2.

Calculated and experimental hardness of fatigue equivalent sample

Fatigue test

Initial

tempering

temperature

(

◦

C)

temperature

(

◦

C)

duration (s)

Hardness

before test

(HV

0,2

)

Hardness after

test (HV

0,2

)

350

300

5474

581

517

350

400

4799

580

491

350

500

4122

584

442

350

600

3458

584

359

600

500

3647

374

338

600

600

3570

378

329

Equivalent temperature ageing

Initial

tempering

temperature

(

◦

C)

Temperature of

equivalent

ageing (

◦

C)

duration (s)

Hardness after

ageing (HV

0,2

)

Hardness

calculated with

kinetic law

(HV

0,2

)

350

300

5520

567

581

350

400

4800

541

546

350

500

4140

494

498

350

600

3480

446

456

600

500

3660

373

374

600

600

3600

374

378

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6TH INTERNATIONAL TOOLING CONFERENCE

Figure 10.

Stress-total strain for 3 strain rates at 600

◦

Cfor a 42 HRC sample.

CYCLIC BEHAVIOUR IN RELATION WITH HARDNESS

As shown in Fig. 9, tempered martensitic steels undergo cyclic softening

during fatigue testing. This softening is divided in two parts which are
generally explained by the rapid (exponential) modification of the dislocation
density and structure for the first one, and the modification of dislocation
sub-structure and carbide morphology for the second linear one.

Figures 11 and 12 show the semi-stress amplitude evolution at 20

◦

Cand

600

◦

Cfor the four different hardneses. At 20

◦

C, curves are clearly sepa-

rated: stress amplitudes are increasing with the hardness level. Softening is
very important and may reach level as high as 250 MPa. At 600

◦

C, three

of the curves are very close, and only the 35 HRC sample is lower. This
surprising result can easily be explained considering the tempering ratio af-
ter testing which are respectively 0.79, 0.67, 0.68 and 0.72 for the initial
35 HRC, 42 HRC, 45.5 HRC and 50 HRC samples. It becomes obvious
that samples with similar tempering ratio show same cyclic softening be-
haviour. The origin is related to the fatigue testing procedure which requires
a heating time and a temperature stabilisation time of at least 75 seconds.
When using the tempering kinetic law, tempering ratio may be calculated
after heating and after fatigue testing. Results show that when testing tem-
perature is greater than the tempering temperature, samples undergo a rapid

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

699

Figure 11.

Semi-stress amplitude evolution at room temperature for the 50, 45.5, 42 and

35 HRC samples.

Figure 12.

Semi-stress amplitude evolution at 600

◦

Cfor the 50, 45.5, 42 and 35 HRC

samples.

microstructural evolution to reach a similar state. Moreover, this modifica-
tion continues during fatigue testing whereas this is not the case for samples
tested at temperatures lower than the tempering temperature.

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6TH INTERNATIONAL TOOLING CONFERENCE

As a consequence, mechanical properties may change drastically when

the steel is subjected to temperatures higher than tempering temperatures,
even for short times, and the tempering kinetic law seems to be a good
tool to get a reliable estimation of the hardness variation associated to the
microstructural evolution.

DISCUSSION

TEMPERING AND TEST TEMPERATURE EFFECT ON

MECHANICAL PROPERTIES

Previous results have been obtained in order to define a cyclic consti-

tutive model able to describe the fatigue behaviour and the effect of time-
temperature ageing on this cyclic behaviour. More information can be found
in references 1 to 5. It allows to reproduce all experimental features of the fa-
tigue behaviour of tempered martensitic steels: fatigue loops using two kine-
matic variables (back stress), two phase cyclic softening using two isotropic
variables (drag stress), strain memory accounting for the increase of soften-
ing when strain range is increased, and at least time-temperature ageing with
the tempering ratio variable (equation (5)). After parameter identification,
it is possible to predict with simulation all mechanical properties, whatever
tempering and testing history.

Figure 13.

Yield stress with respect to temperature for different initial hardness.

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

701

Figure 14.

Strain rate effect on yield stress for the 50 and 35 HRC material.

In the first example, model results are presented to discuss the evolution of

the classical yield stress (R

0.2

). In Figures 13 and 14, yield stress is drawn

with respect to testing temperature for the different tempering conditions
and for three different strain rates (

10

−

2

s

−

1

,

10

−

3

s

−

1

,

10

−

4

s

−

1

) that cor-

respond to typical strain rates seen by the various forging equipments. The
more the testing temperature is high, the closer are the yield stresses, and the
more the yield stress differs between low and high strain rates (this difference
reaches values as high as 150 MPa at 600

◦

C). As a consequence, the useful

yield stress for die design is equipment dependent and not a material con-
stant. Moreover, this yield stress decreases when subjected to cyclic fatigue
due to the material softening, as reported in Fig. 12 at 600

◦

C. Combined

influences of temperature, strain rate and cyclic softening may decrease the
conventional yield stress by a factor of two in the worst case (at highest
temperatures).

The relation between yield stress and tempering ratio is plotted in Fig. 15

for different temperatures. It can be seen that there is a linear relationship,
but the higher the testing temperature is, the lower is the slope. That means
that the important effect of the tempering ratio level at low temperatures
vanishes at high temperature, where the heating up to testing temperature
has a major effect.

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6TH INTERNATIONAL TOOLING CONFERENCE

Figure 15.

Yield stress in relation with tempering ratio for different test temperatures.

Figure 16.

Simulated forging cycle.

In the second example the evolution of an initial 45.5 HRC material ex-

posed to a forging cycle of 20s between 400

◦

Cand 600

◦

C(Fig. 16) is simu-

lated. It can be seen in Fig. 17, that tempering ratio increases with the num-
ber of cycles, as a result of the in-service temperature which is higher than
the tempering temperature (460

◦

C). Room temperature and 600

◦

Cyield

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

703

Figure 17.

Material evolution with respect to the number of forging cycles.

stresses predicted by the model are also reported in Fig. 17, in order to show
the capacity of the model to take into account the material ageing.

HARDNESS EVOLUTION AFTER CYCLIC FATIGUE

TEST

After fatigue testing, up to a cumulated plastic strain close to 4mm/mm

(i.e. without rupture), Vickers hardness was measured in the middle of each
fatigue specimen. The amount of hardness decrease is reported in Fig. 18
with respect to the difference between the testing and tempering tempera-
ture. If testing temperature is lower than tempering temperature, hardness
decrease is low and no evolution occurs at room temperature. A maximum
decrease of 50 HV at tempering temperature is measured. Conversely, when
fatigue testing is performed at temperatures more than 50

◦

Chigher than tem-

pering temperature, hardness decrease is much higher and can reach 50% of
the initial hardness as for example for the 50 HRC sample tested at 600

◦

C.

To distinguish the temperature and load effect on hardness evolution, some

special ageing were performed reproducing exactly the time-temperature
history of the fatigue test specimens. It can be seen in Table 2, that the cal-
culated and measured hardness of those fatigue equivalent time-temperature
ageing are very close (that validates again the reliability of the kinetic law).

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6TH INTERNATIONAL TOOLING CONFERENCE

Figure 18.

Relation between test and tempering temperatures and hardness decrease

Figure 19.

Temperature and mechanical hardness decrease.

This allows now to discuss the effect of temperature and cyclic fatigue on

the hardness evolution. Two examples are reported in Fig. 19 for the 45.5
and 50 HRC samples. Three main conclusions can be drawn from these
results:

Tempering Effect on Cyclic Behaviour of a Martensitic Tool Steel

705

if testing temperature is more than 50

◦

Clower than tempering tem-

perature, no temperature ageing happens and hardness is not modified
by fatigue testing,

if testing temperature is close to the tempering one (-50

◦

Cto +50

◦

C),

temperature ageing is limited, but hardness evolution due to cyclic
loading is observed,

if testing temperature is more than 50

◦

Chigher than tempering tem-

perature, hardness variation due to the temperature becomes predom-
inant, but a second evolution related to cyclic fatigue is noticed. It
seems that the amount of hardness decrease due to fatigue is nearly
constant to a value of 50 HV.

In conclusion, it seems that there is a synergetic effect between tempera-
ture ageing and cyclic fatigue only when testing temperature is higher than
tempering temperature. It induces a complementary decrease of hardness of
50 HV, which seems to be a constant whatever the initial tempering state of
the material.

CONCLUSION

The results reported are part of more important research activity that aims

to work out a cyclic constitutive model for tempered martensitic tool steels
[5]. As numerous tempering conditions are used in industry for the same
steel grade, and as in service temperatures may overshoot the tempering one,
at least for short times, a parameter that takes into account the microstruc-
tural evolution has to be added into the model. Microstructural investigation
on various tempered samples have shown that only the intra-laths carbides
undergo changes during tempering (dislocations were not investigated in
this work); a linear relation between hardness and carbides mean size was
established. As a consequence, hardness was chosen to define a temper-
ing ratio parameter. The evolution of this parameter was described with a
Johnson-Mehl-Avrami kinetic law. Cyclic response was discussed with re-
spect to initial hardness. It was shown that if the testing temperature is higher
than the tempering one, samples undergo evolutions, even for short times of
sample heating before testing which may modify the microstructural state
and the resulting mechanical properties. Hardness measurements on fatigue
tested samples have been performed and were analysed in combination with

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6TH INTERNATIONAL TOOLING CONFERENCE

the kinetic law. It was shown that if testing temperature is lower than tem-
pering one, no significant hardness evolution was measured. In other cases,
temperature ageing becomes predominant, and superposed fatigue induces
a synergetic effect which leads to a supplementary hardness decrease of 50
HV, which seems to be a material constant, whatever the hardness and testing
temperature.

ACKNOWLEDGMENT

The authors gratefully acknowledge THYSSEN France for supplying the

steel rods.

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