Hardness testing as a means for creep assessment

ht. J. Pres. Ves. & Piping 66 (1996) 333-339 Copyright Q 1995 Eisexier Science Limited Printed in Great Britain. All rights reserved 0308-0161/96/$15.00

0308-0161(95)00107-7

ELSEVIER

HARDNESS

TESTING

AS

A MEANS

FOR

CREEP

ASSESSMENT

W KOHLHOFER

Peninsula Technicon Mechanical Engineering P 0 Box 1906, Bellville - 7735, South

Africa

R K PENNY

R K Penny & Associates P 0 Box 174, Noordhoek - 7985, South

Africa

ABSTRACT

The mechanics of hardness testing during creep is investigated using Kachanov principles. Time dependent relationships between indenter geometry and load which are derived reveal that the initial indenter velocity is a measurable quantity which enables the rupture characteristics of a creeping material to be determined. Initial experimental results show reasonable agreement with predicted values. INTRODUCTION

The conventional hardness test of Brine11 111 and others have been used consistently in most branches of engineering. The reasons for its success, particularly as a materials characterisation tool, are simplicity, economy (of space, time and material) and, more recently, portability (121 for example). In addition, it is virtually non-destructive. The mechanics of the hardness test is reasonably well understood and relationships with other mechanical properties, such as yield/ultimate strength [ll, elongation (31 and fatigue life [41 have been established for some time. Success in obtaining plastic flow and strain hardening parameters [Sl, gives rise to expectations that similar possibilities exist for creep Several workers in this field have made contributions mainly properties. towards the relation of sub-structures to bulk properties [61, [71 or creep mechanisms [81. In most cases, this is directed towards the determination of constants in Norton’s empirical relationship between strain rate and stress in uniaxially loaded tensile specimens. An analogy has been drawn between indenter impression velocity with strain rate and indenter contact pressure with stress. Comment has been made 181 that to preserve this analogy, the indenter should be flat-ended to ensure constant contact pressure - the conventional creep test being constant stress. However, analogy in the constant stress tests during creep can only rarely be performed in practice so that the standard creep test is constant load in condition anyway. It seems sensible therefore to remove the restriction of a flat-ended indenter in order 333

334

W. Kohlhofer, R. K. Penny

to discover the basic parameters which most affect creep ; and how to vary these so that important deduced. This is the purpose of the present paper.

the impression test during material properties can be

ANALYSIS

Kachanov’s original work 191 on what he called “damage” was phrased of the current (or true) stress for a specimen loaded by constant tension. So, as the specimen elongated during creep, its cross-section - due to any form of load carrying area loss, such as shrinkage or for example and therefore, the current (true) stress correspondingly. The rate of damage growth was then related to the stress. In this way, sufficient equations can be assembled to solve in elasto-plasticity, creep and fracture.

in terms uniaxial changed corrosion changed current problems

Many developments of the original Kachanov concepts have followed, the latest of these being described in 1101. There is now a considerable body of information to show that there is still room for further development on the same themes. What is more, the practical approach and results obtained compared with other more expensive solution procedures have become very appealing. How then can the same concepts be applied to the indentation problem means of obtaining material creep data efficiently, effectively and corresponding reductions in space, time and expense?

as a with

First, we should discard the word “damage” used by Kachanov and which has been mis-interpreted usually ever since, just as a measure of void growth leading to cross-section area loss. This can be the case and, it works well in describing ductile/brittle fracture I101 but there is no need for it to be exclusively the case. Rather, it is perhaps better to think in terms of, what is measurable directly. In the case of a tensile specimen, this would be its which relate to area change and cross-sectional and longitudinal dimensions, to strain increment. Then, bearing in mind two other important factors for namely that during plastic deformation, bodies under tension and compression, there is practically no volume change and also that we are really dealing with it seems reasonable to explore the increments of strain rather than strain, After all, it is use of Kachanov principles in compression during creep. already well-known that the tension and compression behaviours of metals during plastic flow are remarkably similar if proper allowances for geometry changes are made 1111. During

compression,

the

stress

et at time

CT =(Jt

where

A

is the

original

A -=0 oA t

t, in a specimen

of the

Using Kachanov’s expressed by

area

o‘0 the

cross-section

area,

gain

at time

t, when

evaluation

of

approach,

constant

load

ts - 0 (1 +wl

0

is a measure

under

the

the

initial area

term

stress

and

(1 + wl

is At. w

with

time

is

then

Hardness testing as a means for creep assessment

. “0

dw, dt

where

. o

Integrating

0

= B”!

335

(w 2 0)

,

(2)

(1 + WI’ and B, k and r are material

(2) in the range

o 2 0 during (1 + d+’

constants.

t h 0 yields

- 1 = B(1 + r-1 ~7: t

or 1 *t

.A

= (1 + w) = [l + (1 + t-1 iot]‘”

Figure

1. Indenter

(3)

parameters

Considering now the material deformation indenter under constant load P (Fig. 11,

at

time

t resulting

from

a conical

*t I 1 A

where

u

equation:

is the

indented

depth

2

u

-=

ii

0

on first

(4)

0

loading

(t

= 01,

and

then

combining

(3) and (4) 1 u

= [l + (1 + r) bot]2’1+r)

ii For

small

values

of t ;t

U ii

The

interpretation

(5)

0

of

(6)

Iz: 1

+

+

+

ott2,

(6)

. . ..I

0

is that

the

deformation

of

a conical

indenter

under

336

W. Kohlhofer, R. K. Penny

constant rate

load

V. given

will

increase

from

a value

u

any friction

effects

=-

on initial

loading,

at

a uniform

0

w

0 0

and initial

0

8 is the cone half

angle

(7)

2 “bedding”

during

the indentation,

P

o- =

where

0

by

V

Neglecting

u

n(u

0

tar-d2

and then k .

W= B

(8)

0

The indenter

displacement

at small

values

of t is, from

(6):

k

t

with

initial

slope

(9)

V

(IO)

time

Figure

2. Schematic

of indenter

impression

t variation

Allowing for delayed plasticity or initial “bedding” of the indenter (region 1 of the schematic of Fig. 2) when the full load P has been applied, the creep process then takes over (region 2). This process starts with an indenter followed by further initial indentation velocity V and is displacement

at reducing

rates

in ‘accordance

with

equation

(5).

Hardness testing as a means for creep assessment The

important

feature

of

Fig.

2 is the

initial

slope

V

which

337 can be

0

measured and from which the material constants B and k can be determined. This requires several short term-tests in which the cone angle and diameter of the indenter are kept constant. The form taken by (10) is then V 0’) a BPk

(11)

0

Likewise, in optimising the indenter friction effects or the duration of testing, a grven load according to V (e) a cot 0

2k

shape (cone angle) to minimise the cone angle can be varied for 8

(12)

PRELIMINARY EXPERIMENTS The design The results

of an initial must therefore

rest rig is largely be viewed with this

based upon in mind.

available

equipment.

indenter

insulation

3 specimen heater

baseplate Figure

3. Schematic

of experimental

set-up

The rig, shown in Fig. 3, consists of an electric hotplate which is thermostatically controlled. A baseplate, to act as a heat sink was placed on the plate, so that the specimen then rests on the baseplate. Two insulating shells were then placed around the specimen. Since no temperature measuring device was available, it was decided to carry out the tests at 100°C. To achieve this, water was just brought to boil on the hotplate and the The space between the two insulating thermostat was fixed at this setting. was filled with Aerolite glass wool to avoid shells around the specimen fluctuations in temperature caused by atmospheric conditions. Thus, even though the actual temperature of the specimen was not accurately known, it was kept reasonably constant. To ensure that indenter deflection readings were only taken when the system temperature had reached a steady state, the rig was assembled and the heater turned on. After two hours, the indenter was moved to another position on the specimen, the weight was added and the dial gauge only then placed on the free end of the indenter to begin measurement. Readings were then taken every hour. The cover plate of the insulating tube also acted as the guide for the indenter rod. This cover plate was made of asbestos sheeting to cope with any resistance to the movement of the rod, heat loss. It caused some frictional which was minimised but not always eliminated. For this reason, some results had to be disregarded.

338

W. Kohlhofer, R. K. Penny

DISCUSSION In spite of the rather sparse results obtained so far, the form of the predictions (Figure 2) seem to be in agreement with those measured (Figure 4). The main feature which appears to be well demonstrated is that the initial indentation velocity can be measured quite easily. Although only two results are currently available, they are enough to make an assessment of B and k, the characteristics which define the creep characteristics of the material. Using the two velocities obtained experimentally for two different indenter loads applied to an unidentified aluminium alloy in equation (11): x 1O-9

= 5.28 3.5

or, This

result

cannot

be confirmed

x

1o-9

k = 4.5

but is certainly

reasonable.

I-

3.

2.

1 ’

0

0

Figure

I

2

I

4

4. Experimental

I

6

I

I

1

a

10

12

results

for

indenter

I

14

16

velocity

Although substantial evidence in support of these predictions is not available, it is clear that, in principle, the idea works. Of immediate need, is development of the experimental technique using more refined equipment than of the is currently available to the authors for continuous measurement indentation. In the present case, there seems little point in deriving values of the constants B and r which are involved. A discussion of these, for future materials testing is useful though. In Kachanov’s original work, he assumed that k = r since his ideas were based on the premise that the creep process is governed by current stress only. This is largely true for a wide range of materials and, in any case, r is a less dominating factor than k. If more refined estimates of r are needed though, they can be deduced by using the spread-sheet approach given in reference 1101. In the same reference, it is also shown that the more empirical relationship between strain conventional method of using Norton’s rate and stress to determine creep strain variations can be dispensed with. However, it is well known [121 that the Norton exponent m is related to k - as guide. m I* 3/4k + k ; in the present one would expect - and as a reasonable case this would be about 3.4.

Hardness testing as a means for creep assessment

339

CONCLUSIONS So far as we know, the indentation method which has been derived in this paper for the measurement of creep properties is new. The derivation demonstrates, once again, the usefulness of Kachanov principles published 40 years ago. Further experimental effort is needed on a variety of materials to consolidate these ideas. The resources needed for this are elementary and economical in space, time, materials and cost. If this form of short-term testing is to be used for gathering creep data, it is obvious that the results will not include effects of ageing, corrosion and other deteriorating effects ; this applies to any accelerated test. As a preliminary tool or one for in-situ testing, the method described could be useful.

REFERENCES . 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

II. 12.

J A Brinell. Congress International des Methodes d’Essai, Paris, 1900 W Kohlhofer, R K Penny. “Dynamic hardness testing of metals”. Int. J. Pres. Ves. & Piping &l, 1995 cone R Boklen. “A simple method for obtaining ductility from a 100’ impression”. The Science of Hardness Testing, ASM 1971. H O’Neill. “Hardness Measurements of Metals and Alloys”, 2nd ed. Chapman & Hall, London 1967. “Deformation behaviour of neutron irradiated Kazus Furuya, J Moteff. molybdenum in tensile and hardness tests”. J. Nut. Mat. 99, 1981. “Mechanistic approach to remnant creep B J Cane, P F Aplin, J M Brear. life based on hardness measurement. J. Pres. Ves. Tech., 107, 1987. W S Gibbs, S H Wang, D L Olson. “High temperature impression creep testing on weldments”. Welding Research Supplement, W R C June 1985. S N G Chu, J C M Li. “Impression creep : a new creep test”. J. Mat. SC., 12, 1977. L M Kachanov. “Introduction to Continuum Damage Mechanics”. Martinus Ni jhof Publ., Dordrecht, 1986. “The use of damage concepts in component life assessment”. R K Penny. Proc. Cape ‘95, Ageing of Materials and Life Assessment, March, 1995. This volume. “The Mathematical theory of plasticity”. Oxford Univ. Press. R Hill. 1964. R K Penny. “The usefulness of engineering damage parameters during creep”. J. Metals and Materials, 8, May 1974.