Hardness Uts Relationsip

M. Gaško, G. Rosenberg: Correlation between hardness and tensile properties

in ultra-high strength dual phase steels – short communication

Materials Engineering - Materiálové inžinierstvo 18 (2011) 155-159

155

CORRELATION BETWEEN HARDNESS AND

TENSILE PROPERTIES IN ULTRA-HIGH STRENGTH

DUAL PHASE STEELS – SHORT COMMUNICATION

Martin Gaško1,*

, Gejza Rosenberg1

1Institute of materials research, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice - Slovakia

*corresponding author: Tel.: +421 55 729 2473, e-mail: [email protected]

Resume The possibility to predict yield strength, strength limit, fatigue live

estimation as well as other mechanical properties depending on values of

materials hardness is commonly known and it is often used in practice.

The main aim of this contribution is to review the possibilities of

application of correlation relationships between hardness and ultimate

tensile strength of steel sheets in various structural states. The

experiments were performed on advanced steels with structure which is

composed from ferrite and martensite (dual phase steels).

Available online: http://fstroj.uniza.sk/PDF/2011/27-2011.pdf

Article info

Article history:

Received 27 May 2011

Accepted 28 July 2011

Online 3 November 2011

Keywords:

Dual phase steel

Vickers hardness

Mechanical properties

ISSN 1335-0803

1. Introduction

Although, basically the hardness test of

the metal materials evaluates only surface

resistance of the material against the plastic

deformation, the hardness test is frequently used

because it represents cheap non-destructive and

simple method for assessment of various

material properties like yield strength, tensile

strength, fatigue limit, but also distribution of

residual strains and, in a case of brittle materials,

fracture toughness [2-4]. In order to determine

the relationship between the ultimate tensile

strength (UTS) and hardness (H) a number of

relations were established [2-4]. In practice, the

simplest equation is most often used:

kHUTS .= (1)

where k is coefficient. In contribution [1], the

coefficient was in range from 3.38 to 3.55 for

steel, from 3.48 to 3.21 for brass and from 2.86

to 3.63 for nodular iron (the hardness was

measured according to Brinell, HB). Fig. 1

shows the progress of UTS in dependence on

HB for different materials [1-3]. For aluminium

alloys, in comparison with steels, generally the

smaller values of coefficient k are observed

(Fig.1). This can be well seen from results

mentioned in Fig. 1 based on work [3]. In this

contribution the fact that the value of coefficient

k, in dependence on microstructure state (SDAS

secondary dendrite arm spacing), is in the range

from 2.63 to 2.88 was found. At the steels, the

coefficient k ranges the most frequently in the

interval from 3.0 to 3.6.

According to standard ČSN 420379,

which is replaced now by STN EN ISO 18265, in

dependence on applied heat treatment or heat

mechanical treatment, the influence of

microstructure on correlation of TS-HB is

reflected by the ratio of yield strength and

tensile strength of steel. By this standard [2], for

the ratio YS/TS in range from 0.5 to 0.9 the

coefficient k in the range from 3.54 to 3.21 (with

increase the ratio YS/TS low value of k is

recommended to use) is recommended to use. In

present, there exist a number of correlation




156

relationships HB – UTS a HB – YS type, where

besides the empirical coefficients, many other

material characteristics are involved. For

example, the equations by Cahoon et al. are

among the most known which include the strain

hardening exponent [3].

The utilizing of the high strength steels

constantly increases in the entire area of

industry. The high demands on strength and

plastic properties of the steel sheets for

automotive industry intended for the autobody

are placed. Among all advanced high strength

steels the dual phase steels (DP) are most often

used for automotiv industry. By comparison to

conventional steels, DP steels have significantly

better combination values of strength versus

ductility and a very good compressibility. The

high plasticity of DP steels is given by

microstructure consisting of soft ferrite and hard

martensite. In consequence of this, these steels

are also known by low value of YS/TS ratio

(mostly YS/TS = 0.6 to 0.7, valid even for steels

with strength over the 1000 MPa) [5,6].

The main aim of this work was to find out

how the individual composition of

microstructure and low ratio YS/TS results in

value of coefficient k and, at the same time, with

which accuracy it is possible to predict YS and

TS of these steels, by the Vickers hardness

testing.

2. Experimental material

For experiments five low carbon steels

with carbon content C = 0.07 - 0.15 % and

manganese content Mn = 1.0 - 1.8 % were used.

All steels were processed with two modes of

intercritical annealing consisting of heating on

750 °C or 800 °C (10 minutes hold) and

consequential quenching in water. The volume

fraction of martensite was in range from 20 to 60

%.

The tensile properties was measured on

specimens, which were 120 mm long, and

10 mm wide, with starting measured length

L0 = 50 mm (thickness of specimens was in

range from s = 1.0 to s = 1.2 mm). In this study

the correlation of relationship in form TS - HV,

YS - HV, YS/TS - HV5 as well as the

correlation between strain hardening exponent

and hardness: n - HV was examined.

3. Results and discussion

Among the all studied correlations, as

expected, the highest coefficient of correlation

was found between hardness and strength.

However, also in this case, the correlation

coefficient did not attain the value R2

= 0.9,

therefore the interdependence between strength

and hardness is relatively low. The results show

that the prediction of UTS value based on the

measurement of values of HV5 could be loaded

UTS - HB

Steel [2]

Steel[1]

Brass

Cast iron

(nodular)

Al-Si-Mg (A356)

f ine SDAS

Al-Si-Mg

large SDAS200

400

600

800

1000

1200

1400

90 140 190 240 290 340

HB

UT

S

[MP

a]

Fig. 1. Plot of ultimate tensile strength of various materials as a function of hardness [1-3]




157

by considerable error. The biggest scatter of data

is observed in the range from 270 to 325 HV5.

The anticipated strength (UTS calculated from

equation on Fig. 2) is in comparison with the

strength based on tensile test measurement in the

range UTS ±125 MPa.

When we take into account all measured

values mentioned in Fig.1, and the shape of

correlation equation (1) then we detect that the

coefficient k is in the range from 2.8 to 3.6. The

correlation coefficient for the relation YS = f

(HV5) is less than R2 = 0.8.

This result clearly shows that the

prediction of the yield stress of steel through the

measured values of hardness is loaded with

larger error as it was in the case of strength

prediction. Measured results in Fig. 3 indicate

that the relation YS = f (HV5) at hardness over

the 325 units HV5 is steeper.

The slope in the established equations

reaches more than three times higher values

(Fig. 3). It is likely that for the YS - HV5

correlation using the equation in exponential

form would be more suitable.

Also in the relation YS / UTS = f (HV5),

for the same hardness, it is possible to observe

the break. From the set of correlation

equations it is clear that, for the hardness of

about 330 units HV5, the relation shows a

minimum (Fig. 4). In practical terms we

cannot speak about correlation of YS / UTS -

HV5, because correlation coefficient is low.

The data in Fig. 4 show that in the range from

210 to 330 units of HV5 the values of ratio

YS / UTS are in the range from 0.5 to 0.7, and

the hardness from 370 to 430 units

of HV5 results in the ratio YS / UTS = 0.7 to

0.85.

Fig. 2. Ultimate tensile strength as a function of hardness HV5

UTS - HV5

y = 2,77x + 92,754

R2 = 0,8786

600

700

800

900

1000

1100

1200

1300

1400

200 250 300 350 400 450

HV5

UT

S

Fig. 3. Yield strength as a function of hardness HV5

YS - HV5

y = 2,5009x - 181,44

R² = 0,7695y = 1,5703x + 76,165

R² = 0,5694

y = 5,4035x - 1312,5

R² = 0,736

200

400

600

800

1000

1200

200 250 300 350 400 450

HV5

YS




158

Fig. 5 shows the dependence of strain

hardening exponent for hardness HV5. Unlike

Fig. 3 and Fig. 4 it is possible to describe the

measured data by one equation, but with low

correlation coefficient R2 = 0.55. The practical

use of correlation equation n - HV5, referred in

Fig. 5, is limited. It is proved by the fact that for

the steels with n = 0.14 hardness from 225 up to

320 units HV5 was measured.

From the measured results in this work it

is evident that the possibility to predict

mechanical properties of dual phase steels by

means of the measured values of hardness is

very limited, if not impossible.

As seen in the Table 1, from known

hardness of steels, also in this case it is possible

to predict the strength of steel with the accuracy

about ±10 % UTS. Also we can see the correlation

coefficients and relationships among the hardness

and other mechanical properties which suggest the

possibility of using the hardness measurements. On

the other hand, it should be noted that the

measured data (in the case of relationship

between hardness and ultimate tensile strength)

are not very different from the results measured

for different steels and different structural states

observed by other authors [4, 7].

Table 1

Table of regression analysis for all data sets

Relationship Best fit equation Coefficient of

determination

UTS= f (HB) y = 2.77x + 92.754 R2 = 0.8786

YS = f (HB) y = 2.5009x – 181.44 R² = 0.7695

YS/UTS=f(HB) y = 0.0006x + 0.417 R2 = 0.2303

n = f(HB) y = -0.0003x + 0.2344 R² = 0.5518

Fig. 4. The yield strength to tensile strength ratio, as a function of hardness (HV5)

Fig. 5. The strain hardening exponent as a function of hardness (HV5)

YS/UTS - HV5

y = 0,0006x + 0,417

R2 = 0,2303y = -0,0003x + 0,6852

R2 = 0,0562

y = 0,0027x - 0,3592

R2 = 0,5422

0,4

0,5

0,6

0,7

0,8

0,9

200 250 300 350 400 450

HV5

YS

/UT

S

n - HV5

y = -0,0003x + 0,2344

R² = 0,5518

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

200 250 300 350 400 450

HV5

n




159

Evidence of this is Fig. 6 that is identical to

Fig. 1, but complemented with the data

measured in this work (values of HV5 were

converted using the table of values for HB).

4. Conclusions

In this work the possibility of prediction

of selected mechanical properties of dual phase

steels by means of Vickers hardness tests was

verified. It was shown that from all correlation

relations established in the work it is practically

applicable only the correlation between hardness

HV5 and UTS (on the basis of known values

HV5 it is possible to predict the strength with an

accuracy of ± 10%). Results of work clearly

shows that for the prediction of mechanical

properties of dual phase steels with higher

accuracy the influence of the microstructural

parameters in the correlation equations is

necessary to include. That is the aim of our

further research.

Acknowledgements

The authors are thankful to grant agency

VEGA of SR for financial support of this work, which

was realized within the frame of project with No.

2/0195/09.

References

[1] http://www.calce.umd.edu/TSFA/Hardness_ad_.

htm#6 [1 November 2011].

[2] ČSN 42 0379 (in Slovak)

[3] L. Ceschini, A. Morri, A. Morri, G. Pivetti:

Mater Des 32 (2011) 1367-1375.

[4] E.J. Pavlina and C.J. Van Type: J. Mater. Eng.

Perform, 17 (2008) 6 888-893.

[5] G. Rosenberg, K. Buríková, Ľ. Juhár: Manufact.

Eng. 3 (2009) 49-52.

[6] Xin-sheng Liao, Xiao-dong Wang, Xu-fei Li,

Yheng-hong Guo, Yong-hua Rong: Adv. Mater.

Res. 97-101 (2010) 728-732.

[7] J. Pavlina, C.J. Van Tyne: J. Mater. Eng.

Perform. 17(6) (2008) 888-893.

Fig. 6. Dependence of ultimate tensile strength of various materials as a function of hardness [1-3]

UTS - HB

Steel [2]

Steel[1]

Brass

Cast iron

(nodular)

Al-Si-Mg (A356)

f ine SDAS

Al-Si-Mg

large SDAS

DP

200

400

600

800

1000

1200

1400

90 140 190 240 290 340

HB

UT

S

[MP

a]

Documents

Hardness Uts Relationsip