Dwell sensitivity Part I. Behavior and modeling

imalllmll illlllluAl ELSEVIER

Mechanics of Materials 22 (1995) 105-130

Dwell sensitivity Part I. Behavior and modeling * Tarun Goswami 3209 Merrill Engineering Building, Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah 84112, USA

Received 14 October 1994; revised version received 17 August 1995

Abstract This paper examines tile dwell sensitive behavior of materials subjected to creep-fatigue deformation. A study of published creep-fatigue data on seventeen materials was conducted to investigate the dwell sensitivity for different materials under different hold times applied in tension and compression. The seventeen materials selected were such that their melting temperatures varied from 250 to 1700°C, and the test temperatures ranged from 0.4 to 0.75 of the homologous temperature, where creep and fatigue interact. The dwell sensitivity was found to depend upon the test temperature, period of hold time, and hardening and softerfing phenomena of the materials subjected to a particular cyclic waveform. Since no previous model exists for the prediction of dwell sensitivity, it is conceptualized in a cycle in terms of hardening (H) and softening (S) and their combinations in tension (T) and compression (C) directions. Thus, for a cycle (TC), there are four possible combinations namely HS, HH, SH and SS. A demonstration of such combinations with H and S was made for a tensile dwell sensitive material where cycles produced tensile hardening and compressive hardening or HH were found to cause dwell sensitivity. However, for a compressive dwell sensitive material, the combinations were tensile hardening and compressive softening or HS. This study on dwell sensitivity attempts to address an important material behavior which is not very well understood and may initiate further research interests. Keywords: Tensile and corrtpressivedwell sensitivity; Hardening; Softening; Normalized cycle ratio; Strenght ratio; Creep-fatigue; Strain range; Hold times

1. Introduction Study of high te~aaperature, low cycle fatigue ( H T L C F ) failure mechanisms became important only after service failure occurred in power plants and commercial aviation during the 1950s. Though there were distinct examples of fan disk failures due to "dwell sensitivity" in the 1970s (Wilkinson, 1973; Stubbington and Pearson, 1978), the study of the * This paper is dedicated to Professor David W. Hoeppner on the occasion of his 60th birthday in December 1995 and his early contribution on this topic.

mechanics and modeling of dwell sensitivity has not progressed at the required pace. Only mechanistic explanations were reported for a particular behavior in terms of secondary cracks, oxidation, cavitation and other metallographic and fractographic features. No conceptual models were developed to address dwell sensitivity for high temperature materials. This paper, while briefly examining the mechanistic features, mainly focuses on the dwell sensitive behavior of seventeen materials and the development of a conceptual framework for modeling dwell sensitivity. These concepts will be developed further in Parts II and III,

0167-6636/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved SSDI 0167-6636(95)00028-3

T. Goswami/Mechanics of Materials 22 (1995) 105-130

106

CONTINUOUS STRAIN CYCLING 0/0

TENSION STRAIN HOLD

"£rl'

t/0

t" a

r

!

COMPRESSION STRAIN HOLD 0 / t

TENSION AND COMPRESSION STRAIN HOLE) t / t

'E

Fig. I. Waveformsused in creep-fatiguetesting, strain and stress range versus cycle time and resulting hysteresis loops. respectively. Laboratory tests are conducted to generate data, document damage development and investigate hardening and softening behavior of the materials subjected to different cyclic waveforms. Fig. 1 describes the conventional waveforms that are used in HTLCF testing. A trapezoidal cycle which has, in addition to a loading and an unloading path, a period of hold applied at either constant stress or strain at the peak loading conditions, which simulates the operating conditions of a power plant turbine disk or a gas turbine disk component. Usually the period of hold varies from application to application. For example, hold periods of a few minutes to several hours are applied in the case of gas turbine disks (Cowles et al., 1978; Stub-

bington and Pearson, 1978) which corresponds to a week or more for power plant components (Gangadharan et al., 1973) located in the peak tensile direction. When the hold time (t) is applied in one direction, it is known as either tensile (t/O) or compressive hold (0/t), whereas, if the same hold time is applied in both directions it is known as balanced hold ( t / t ) a n d when different hold times in tension and compression are applied it is known as unbalanced (tl It2) cycles. The HTLCF life of materials is different under continuous fatigue when no hold was applied and with hold times. In cases where a tension hold (t/O) or a compression hold (O/t) is applied at the same test conditions, for example, temperature, strain range and strain rate, the life is different under different test con-

T. Goswami/Mechanics of Materials 22 (1995) 105-130

ditions. A material is dwell sensitive in a direction which produces a lower life. Creep-fatigue data were collected for seventeen materials which were widely used in electronic packaging, space shuttle nozzle liners, power plant components and gas turbines and which experience HTLCE They range from solder alloy, copper alloys, low alloy steels, stainless steel, titanium alloys and superzlloys. Since creep-fatigue tests are expensive and cast specific, statistical viability of the data and experiments is not possible since tests are conducted based upon only one test for every test condition.

1.1. Data collection Published data on the following materials were collected: solder alloy (96.5%Pb-3.5%Sn), copper alloys (NARIoy and A/VIZIRC), low alloy steels (1CrMo-V, 1.25Cr-Mo, 2.25Cr-Mo), stainless steel (SS 316), titanium alloys (IMI 318 and IMI 829) and superalloys (MAR M 002, waspaloy, Rend 95, Rend 80, inconel 617, In 100, PWA 1480 and MA 754 in two orientations) subjected to creep-fatigue deformation. A summary of materials, hold times, test temperatures and references is provided in Table 1. It is evident from Table 1 that the hold times varied from a few seconds to as long as 47 hours for these materials and different cycle types such as (t/O, O/t, tit and tl It2) were applied. The mechanical properties of these seventeen materials are tabulated in Table 2. The ductility was determined from the percentage reduction in area following 1:heAmerican Society of Metals Handbook (Vol. 8) for both room and high temperature. Ductility in fatigue and creep are two different terms which cannot bc determined accurately, if concepts such as tensile and compressive ductilities are taken into account. Therefore, though ductility models in HTLCF life prediction have been developed in the past, namely: ductility exhaustion (Edmund and White, 1966; Priest and Ellison, 1981), and Code R5 (Goodall and Thomas, 1990) to predict life, use of such models must be raade carefully to predict the life under balanced, unbalanced and compression hold cycles.

1.2. Normalized cycle' ratio A new term, the "normalized cycle ratio" (NCR), was evolved in this study to quantify the dwell sensi-

107

tivity, and the way in which the NCR was determined is described below.

1.3. Data fitting: total strain and life The creep-fatigue data were generated at a random order in total strain ranges for continuous fatigue as well as for hold times. Continuous fatigue data were fitted with a least square best fit equation in the following form:

Act = A ( N f ) m

(1)

where A and m are material parameters. The values of log A, m and the correlation coefficient of (R) are tabulated in Table 3 for the data analyzed. The reduction in life caused by a particular hold was determined in terms of the number of cycles to failure under hold time waveform divided by the number of cycles to failure under same conditions by continuous fatigue. This ratio, evolved in this study as "normalized cycle ratio" (or NCR), which measures the dwell sensitivity if the NCR is less than 1 for different hold time cycles. However, when the NCR is higher than 1, hold times were causing beneficial effects, thereby improving the fatigue resistance of the material. Therefore, the total strain and life extrapolation equation ( 1) will be used to extrapolate continuous fatigue behavior under the test conditions of hold time cycles to determine the NCR.

1.4. Cyclic hardening and softening Majumdar (1987) conducted a few tests under isothermal and thermo-mechanicai fatigue where the cycle began in compression rather than, as usual, in tension and found that the stress-strain behavior and deformation features as a result of the compressiontension cycle were different and enhanced life. The interactions of creep and fatigue have been explored in terms of intergranular creep cavity generation and transgranular fatigue crack growth in the materials that are being examined in this paper. A combination of critical stress and strain rate produces the cavitation under creep-fatigue tests which varies in tension and compression directions. The critical strain rate in compression for SS 304 was found (Majumdar, 1987) to be at least five times slower than in the tension, as a result, it produced a tensile dwell sensitivity. However, this aspect has not been sufficiently

T. Goswami/Mechanics of Materials

108

22

(1995) 105-130

Table 1 Summary of the materials studied Materials

Hold Times

Temperature

Reference

t/O

25°C

Vaynman et al. (1987)

same

538°C same

Stentz et al. (1978) same

large data bank large data bank large data bank

540-565°C 550-600°C 540-600°C

Goswami (1995a) Goswami (1995a) Goswami (1995a)

Solder Alloy (96.5%Pb-3.5Sn)

10 min

Copper alloys t/O, O/c, t/c

(a) NARIoy Z (b) AMZIRC

of 5 min.

bin, alloy steels (a) I C r - M o - V (b) 1.25Cr-Mo (c) 2.25Cr-Mo

Stainless steel SS 316

Yamaguchi et al. (1980)

Titanium alloys IMI 829 IMl 318 (Ti-6AI-4V)

3 to 15 min t, c and

t/c

600°C

Plumbridge et al. (1986)

t/O, O/c

and

tic

unequal

450°C

Drapier et al. (1979)

MAR M 002

t/O, O/c

and

t/c

of 20 s

MAR M 002 Waspaloy Ren6 95 Ren6 80 Inconel 617 IN 100 PWA 1480

t/O, t/O, t/O, t/O, t/O,

MA 754 L and LT orientations,

t/O, O/t

750, 850 950, 1040°C 750, 850, 1000°C 750°C 650°C 871 and 1000°C 650°C 925°C 10t5°C 1050°C 850°C

Antunes et al. (1978) Ellison et al. (1984) Asquith et al. (1978) Hyzak et al. (1978) Kortovitch et al. (1978) Rao et al. (1988) Halford et al. (1978) Miner et al. (1988) same Nazmy (1988).

Stq~eralloys O/c and tic of 5 min O/c and t/c unequal O/c and t/c unequal O/c, and t/c unequal. O/c and t/c unequal.

unbalanced t/O, O/t and

t/t

Table 2 Summary of mechanical properties of the materials investigated Material

NARIoy Z AMZIRC 1CrMoV 1.25CrMo 2.25CrMo

SS 316 Ti6AI4V MarM 002 Waspaloy Ren6 95 Ren6 80 IN 100

Temp. ( ° C )

538 538 565 600 500 593 600 600 700 450 500 1040 750 650 1000 649

¢ry/O'u

Creep ductility %

Ductility

RT

HT

RT %

HT %

0.62 0.89 0.79 0.62 0.78 0.79 0.67 0.34 0.34 0.98 0.87 0.87 0.70 0.80 0.86 0.69

0.85 0.99 0.71 0.67 0.86 0.86 0.91 0.29 0.35 0.87 0.82 0.71 0.70 0.84 0.67 0.86

0.7 I 1.66 1.02 1.30 1.34 1.50 1.51 1.66 1.66 0.54 0.28 0.125 0.06 0.12

0.53 1.83 1.6 2.30 1.6 2.04 2.40 1.2 1.10 0.67 1.21 1.4 0.38 0.133 0.396 0.22

unknown unknown unknown unknown unknown unknown unknown 0.4 1.07 unknown unknown unknown unknown 0.112 0.10

T. Goswami/Mechanics of Materials 22 (1995) 105-130 Table 3 Material parameters of the total strain versus life equation Material

m

logA (%)

R

NARIoy Z (538°C) AMZIRC (538°C) Ti-6AI-4V (450°C) Ren6 95 (650°C a) Ren6 95 (650°C b) Waspaloy (750°C) MAR M 002 (750°C) MAR M 002 (850°C) MAR M 002 (1040°C) Ren6 80 (871°C) Ren6 80 (1000°C) IN 100 (925°C) PWA 1480 (1015°C) PWA 1480 (1050°C) MA 754 (850°C c) MA 754 (850°C d)

-0.459 -0.58 -0.256 -0.375 -0.135 -0.4 -0.127 -0.271 -0.205 -0.209 -0.253 -0.273 -0.332 -0.247 -0.248 -0.387

1.478 2.20 0.96 1.198 0.524 0.99 0.262 0.608 0.38 0.529 0.563 0.58 1.04 0.797 0.618 0.883

0.966 0.78 0.82 0.974 0.965 0.985 0.905 0.987 0.983 0.952 0.984 0.945 0.958 0.951 0.88 0.983

a Strain rate of 1.5%/s. b strain rate 5.9 x 101%/s. c Orientation: longitudinal. a Orientation: longitudinal-transverse.

investigated for most materials and no argument can be provided for the materials studied in this paper. The cyclic action ot' fatigue produced a microscopic change in copper (Gough and Hansen, 1923; Gough et al., 1926; Gough, 1933). Slip systems were generated that caused hardening in the material and progressively resulted in failure when a critical strain was reached. A stress level below which no fatigue cracks formed had a limiting value of strain hardening. Ludwik (1919) concluded that monolonic torsion tests were independent of prior cycles, however, the fracture ductility decreased with increasing number of cycles. Ewald and Polanyi (1925) observed that previously strained materials exhibited strain softening. Coffin (1954) observed that prior cold work plays an important role in the life to failure as the total plastic strain absorbed for a particular number of cycles to failure is reduced as the amount of work increased. Under strain control tests mean stresses develop or diminish depending upon the frequency, ramp rates or hold times applied. A combination of strain range, frequency, ramp rates, hold times andL temperatures governs the failure mode by either intergranular or mixed intergranular and transgranular fracture. Therefore, in a CoffinManson curve, the c]hange in the failure mechanism

109

from one mode to the other caused a bi-linearity in the behavior. There are also other mechanisms, such as oxidation, which have not been accounted for in the creep-fatigue interactions and their models. Therefore, mechanistic investigations of creep-fatigue deformation behavior also are not fully equipped to address dwell sensitivity and predict it.

2. Dwell sensitive behavior The mechanistic features of damage development are due to activation of slip systems, microstructural effects and cracking and to address dwell sensitivity under every test condition need to be investigated by metallographic and fractographic means. The evolution of stresses, stress range effects, strain rate effects, relaxation and increases in the inelastic strain per cycle which cause a decrease in the life if test parameters selected favor occurrence of one or more of the above mechanisms. Hence, study of mechanistic features and stress evolution for seventeen materials under different waveforms is a topic of Parts II and III (Goswami, 1996a,b). This paper focuses on the discussion of the dwell sensitive behavior and an attempt to model that behavior.

2.1. Dwell sensitivity maps The dwell sensitivity maps were constructed for every material studied in this paper. A dwell sensitive map describes the effects of dwell times on the life of a material with respect to its continuous fatigue behavior at the same test parameters. Test parameters for all the conditions studied in this paper are summarized in Table 1. In this paper continuous fatigue life was taken as a reference to determine whether or not a material is dwell sensitive. This was achieved in terms of total strain range and NCR data plotted in dwell sensitivity maps, Discussed below is the dwell sensitive behavior of seventeen materials under the test parameters summarized in Table 1.

3. Materials studied Normal alloys 1. Solder alloy, 96.5% Pb-3.5%Sn, tested at 25°C (Vaynman et al., 1987) This particular material was found to be both tensile dwell sensitive as well as unbalanced dwell sensitive

110

T. Goswami/Mechanics of Materials 22 (1995) 105-130

at the test parameters described in Table 1, for which no data were reported. The compressive dwells (O/t) show similar life to that of continuous fatigue (0/0). However, when the same dwell time is applied in tension, the life reduced by 1/5 compared with the O/t cycle. When a small dwell time applied in compression together with a tensile dwell (tl/t2), life was reduced drastically. When unbalanced dwell times were applied (360/120 and 120/360 s) the cyclic lives were almost the same (130 and 140 cycles, respectively).

2. Copper alloy AMZIRC tested at 538°C (Stentz et al., 1978) The AMZIRC alloy, developed for use in the space shuttle's engine nozzle liner (Stentz et al., 1978), was found to be a tensile dwell sensitive material tested under the conditions listed in Table 1. Fig. 2 indicates the effect of dwell times in either direction of the AMZIRC alloy. The normalized cycle ratios (NCR = Ny(hold time)/Nf(O/O) at the same strain level) of t/O cycles were in all cases less than O/t cycles. However, the NCR improved with increases in tensile hold time at higher strain levels (for example at 5%). The O/t lives were higher than 0/0 lives at 5% strain and 300 s hold, whereas, at lower strains (1.4%) the t/OO/t lives were nearly same in Fig. 2. At lower strain levels, where elastic strains dominate, tensile mean stresses develop which reduce the life, as a result the NCR observed is less than that at higher strain levels. As the strain level increased, the NCR also increased for dwell containing cycles.

3. Copper alloy NARIoy-Z tested at 538°C (Stentz et al., 1978) The NARIoy-Z alloy, which was also developed for use in the nozzle liners of the space shuttle's main engine, was found to be tensile dwell sensitive under the test parameters listed in Table 1, and the hold times applied are listed in Fig. 3. The NCRs were plotted against total strain ranges for this material at 538°C as shown in Fig. 3. At lower strain levels (0.9%) the life of a t/O cycle was nearly 10% of the same O/t cycle. However, at higher strain levels (2.6%) t/O cyclic lives were 25% of the O/t cyclic lives. As the strain level increases, the NCR also increases for t/O and O/t cycles, however, as is to be expected since it is a tensile dwell sensitive material, the improvement is larger for compression dwell cycles.

4. Low alloy steel ICr-Mo-V (Goswami, 1995a-c) Low alloy steels are used in components of power equipment. This particular steel is used in forged condition for turbine disks. It is found to be a tensile dwell sensitive material. The creep-fatigue data, behavior and life prediction of low alloy steels such as 1.25Cr-Mo, 2.25Cr-Mo and 9 C r - l M o are described elsewhere (Goswami, 1995a-c) and will be discussed briefly here. Since the data reported (Goswami, 1995a) have a range of variables and hold times from a few minutes to as long as 47 hours, only limited data containing longer holds are used to construct a "typical" dwell sensitive map to show the pronounced effects displayed in Fig. 4. Few compressive dwell tests were performed on this grade of alloy, however, the most widely referred data source is that of Ellison and Paterson (1976). Fig. 4 shows the total strain range (%) versus NCR of various hold cycles in tension and compression and in both directions. This plot includes the data generated under Metal Properties Council Inc. of the American Society of Mechanical Engineers (ASME) assignment with combined cycles with t/O of 23 and 47 hours. Life of compressive dwell cycles are higher than those under 0/0 behavior. Tensile holds are more damaging than all other hold combinations. Unbalanced dwell cycles (tl/t2), where tl >> t2, caused a healing action and life improved compared with t l / 0 cycles reported by Ellison and Patterson (1976).

5. Low alloy steel 1.25Cr-Mo Tensile dwell data from two sources were analyzed. In a tensile dwell, the NCR is always less than one, this material may be expected to be t/O sensitive. Data at two temperatures (550 and 600°C) were analyzed and, as shown in Fig. 5, that with an increase in hold time, the NCR decreased. Reduction in life is larger at lower strain levels than at higher strains. A comparison of.Figs. 4 and 5 shows that in the case of 1.25Cr-Mo steel, lower hold time cycles (0.167 hour t/O) produce lower dwell sensitivity, whereas, in I C r - M o - V the opposite trend is seen. This behavior is due mainly to the application of a number of fatigue cycles ( N = 1.5 to 22.5) at the end of dwell time, known as combined cycles. Such cycles altered the damage mechanisms in low alloy steels and enhanced the fatigue resistance under specific conditions. A discussion on this behavior is reported elsewhere (Goswami 1995a).

T. Goswami/Mechanics of Materials 22 (1995) 105-130

I II

10 1 o o o

N f(hold time) = N f (010)

A -l~e x Keys: time in soe.,

=UD ¢g L.

"t-

300/0

&

200/0

0

56•0

•

0/200

x

0/300

.=. ¢_

o

D u e

•

10 0

n

0•56

•

300/300

i i I

0-1

10 0

1

Normalized cycle ratio (NS hold time/Ny0/0) Fig. 2. Dwell sensitive behavior of copper alloy AMZIRC at 538°C. '10 1 i J i i o

N f (hold time) =NJ(O/O) =

¢1 L.

.=.

10 0

t_

p.

Keys: time in sec.. m

300/0

•

0/300

10 -1 0-1

60

Normalized cycle ratio (NS hold time/N~f 0/0) Fig. 3. Dwell sensitive behavior of NARALOY-Z at 538°C.

10 1

I 12

T. Goswami/Mechanics of Materials 22 (1995) 105-130

10 1

Nf (hold time) = N/ (0/0) ! !

10 0

N

O ¢m el n-

O

)&

•

On CI

•

~,

•

O 23 I-It(frO)540" C • 47 l-h"(t/0)540" C o I/2 Hr (frO)565" C.

c

10 "1

I/2 I-~ (0/t)565"C.

O

I-•

.

0.5/0.5 Hr (fit) 565" C. 3 Hr (t/0) 565" C.

Keys: time in hours. 10-2

.

0-3

.

.

.

.

.

.

!

.

.

.

.

.

.

.

10"2

!

.

.

.

.

10"1

.

.

.

m

.

.

.

.

.

.

.

10 0

10 1

Normalized cycle ratio ( N f hold time / N.f 0/0) Fig. 4. Dwell sensitivebehavior of ICr-Mo-V steel. 101 + n

0.0166 Hr (t/0) 550 ° C. 0.167 Hr (t/0) 550 ° C.

• x

0.5 Hr (t/0) 550 ° C. 0.03 Hr (t/0) 600 ° C.

J &

10 0

&O

mid

0

0

x

xA

+a

b

a

o

0.08Hr(t/0)600°C. 1 • 0.167Hr (frO)600° C.

0

O • A

-I-

Nf (hold time)= Nf (0/0)

>

0.5 Hr (frO) 600 ° C. 1Hr (frO) 600 ° C.

Keys: time in hours. 10-1 10 0

10-1 N o r m a l i z e d cycle r a t i o ( N f h o l d t i m e / N y Fig. 5. Dwell sensitive behavior of 1.25Cr-Mo steel.

0/0)

T. Goswami/Mechanics of Materials 22 (1995) 105-130

6. Low alloy steel 2.25Cr-Mo One set of data is widely referred (Brinkman et al., 1976) to describe the creep-fatigue behavior of this material which is observed to be compressive dwell sensitive under varying dwell times of several minutes. The mechanical properties improved with temperature within a temperature range. Within that range, the fatigue properties were also found to be superior. Some data containing large (23 to 47 hours) tensile hold times are plotted in Fig. 6. This figure shows that as the total strain range reduces to 0.55% the NCR also reduces considerably. The NCR was much lower at the 0.55% toted strain range and 23 hour hold in annealed condition than in all other types of data analyzed. Therefore, it may be concluded that other factors, such as material condition, also influence the dwell sensitivity. It was also seen that the NCR decreases with lower strain levels (0.55%) than higher strain ranges ( > 1.5%) which indicates that with the increase in strain there is strain saturation, which raises the fatigue life.

7. Stainless steel SS 316 (Yamaguchi and Kanazawa, 1980) The SS 316 is found to be a t/O sensitive material. Balanced and tensile dwell data were compared for 600°C and 700°C. At 600°C the NCR was 0.45 at the lower strain range (1%) compared to 0.35 at 2% total strain. Higher NCR observed at higher strains also observed in this case. At 700°C there was more strain saturation and h~old time had a less detrimental effect than at 600°C. Also creep ductility improved by 260% at 7000C from 600°C, which explains the observation of superior life at 700°C in Fig. 7. The observations made for low alloy steels are in contrast to those found for SS 316. One may speculate why such a contrast Ilas not been found in the literature; this may be to be due, however, to the strain saturation, which occurs after a dwell is applied. Since dwell times were much longer in low alloy steels, the interactions among damage mechanisms are higher. As a result the cyclic lives were on the order of a magnitude lower in ICr-lVlo-V and 2.25Cr-Mo steels than in SS 316. Figs. 4 and 6 show that the NCR values varies from 0.004 to 0.008 at 0.55% total strain range for low alloy steels rather than 0.4 and higher when extrapolated at the same strain for SS 316 at 6000C and 700°C.

113

8. Titanium alloys Ti-6AI-4V (Drapier and Hirschberg, 1979) The Ti-6A1-4V alloy has a wide range of applications ranging from aviation, off-shore, medical science, human implants, chemical plants to shipbuilding, It is also used as fan disk material for various gas turbines used to power civil and military aircraft. Since this is a compressive dwell sensitive material, the NCR is expected to increase with hold times in tension as shown in Fig. 8. There was an intermediate range of hold times from 300 to 420 s, where the NCR increased with an increase in hold time. However, with a further increase in hold time to 990 s, the NCR became larger than l, which offers a higher than 0/0 life. Application of compressive dwell causes the NCR to reduce. With a 3.6 s O/t cycle, the NCR was 0.39, however, as the O/t dwell time increased to 687 s, the NCR was nearly unchanged until a 3000 s, O/t hold was applied. The life of the 3000 s hold, O/t cycle ( N C R = 0.61, Nf = 142 and et = 2.29%) was twice as much as with the 117 s, O/t hold, at half its strain range ( N C R = 0.33%, Nf = 698 and et = 1.304%) in Fig. 8. Unbalanced dwell cycles (tilt2), showed a trend that with a small fraction ( 1/3000) of tensile hold as in the case of 1800/0.6 at 0.45% strain, when applied in compression, the NCR was quite high (0.7-0.8). However, when compressive dwell increased as in the case of 15/510 the NCR decreased. The lowest NCR was observed when 150% of tensile dwell was applied in the compression direction, as shown in Fig. 8.

9. Titanium alloy IMI 829 (Plumbridge and Stanley, 1986) Three strain levels were examined with hold times of 2, 5 and 15 min in tension, compression and in both directions. Fig. 9 illustrates the NCR with respect to the total strain range. The NCR of a O/t cycle with 2 min hold was less than those of the t/O and tit combinations. With 15 rain compressive dwell, the NCR was the least, compared with the other two possible combinations. As the strain ranges rose to 2.5%, the NCR of the O/t cycle improved. The same trend that the NCR lowered at lower strain ranges, was observed.

I 14

T. Goswami/Mechanics of Materials 22 (1995) 105-130 10 1

'~A 47 Hr (t/0) 540" C. Annealed [] 23 Hr (frO) 540"C. Annealed

)

J 0

-i~O

+ e~

¢1 L. == °~

10 0

t_

n

Z¢) N f (hold time) = N f ( 0 / 0 ) ~ ' )

p. Keys: time in hours.

O 47 Hr (t/0) 540" C.Normalized & Tempered ) + 23 Hr (t/0) 540" C. Normalized & Tempered

J

10"1 10"2

10-3

10 "1

10 0

Normalized cycle ratio (NS hold time/ NS 0/0) Fig. 6. Dwell sensitive behavior of 2.25Cr-Mo steel.

101

>

Nf(hold time) = N f (0/0)

+

0

•

°~

¢/)

10 0

+

0

•

x

n

o p, Keys:

•

time in minutes.

5/0 (600-C)

s/5 (700"c)

5/0 (700"C) t" 10

60/0(600*)

"1

0-1

1

Normalized cycle ratio (N5 hold time/Nf 0/0) Fig. 7. Dwell sensitive behavior of SS 316 at different temperatures.

0

T. Goswami/Mechanics of Materials 22 (1995) 105-130

I 15

101

Nf(hold time) = Nf (0/0) Keys: time in sec..

+

II

N

0

1= ¢1 L.

..=

&

10 0

r~

0

10"1 0-1

lO 0

• • A [] • • + O o X A N

16810 300/0 990/0 420/0 0/3.6 0/117 0/687 0/3000 151510 6/9 1356/0.8 108010•5 1800/0.6

101

Normalized cycle ratio (Ny hold time/Ny 0/0) Fig. 8. Dwell sensitive behavior of Ti-6AI-4V at 450°C.

Superalloys

10. MAR M 002 (Ellison et al., 1984; Antunes and Hancock, 1978) Fig. 10 describes the dwell sensitive behavior of MAR M 002 at 750°(2, 850°C, 1000°C and 1040°C. Hold times of 20 to 300 s, were examined at 750°C, 850°C, 1000°C and 1040°C where the following were observed: 750°C: The NCR of a 0/20 s hold was 0.25 compared with t/O of 0.8 and t/t of 0.71. 850°C: Tensile dwell or t/O cycles produced an NCR in the range of 0.92 to 2.66, which is obviously up to 2.66 times higher than 0 / 0 life. The NCR of O/t cycles was similar to those of t/t cycles. The balanced dwell cycles were most damaging. 1040°C: Compressive hold cycles or O/t cycles were at the right hand extreme where they acted similar to 0 / 0 fatigue life. Tensile dwell cycles were

more damaging than O/t and t/t cycles at the same strain levels• As the strain range decreases, with the increase in hold time, a drop in the NCR is observed.

11. Waspaloy tested at 750°C (Asquith and Springthall, 1978) Fig. 11 shows the t/O combinations at the right hand side of the plot. Tensile dwell cycles were 1/3 of 0 / 0 fatigue, where the NCR maintained nearly 0•35 at all strain levels. Compressive dwell cycles were more damaging than t/O and t/t cycles. Unbalanced dwell (tj It2) data contained a large scatter and had values between those of O/t and t/t cycles.

12. Ren~ 95 tested at 650°C (Hyzak and Bernstein, 1978) This particular superalloy, which has been developed for use in the gas turbine blades, is found to be a compressive dwell sensitive material• The test

I 16

T. Goswami/Mechanics of Materials 22 (1995) 105-130

10 1

I~0

AcOrn

/

A Keys:

¢I I:I

Nf (hold time)=Nf(O/O)

10 0

nA

•

time in min.

~0 m

2/0

•

012

0

A2/2 0

1510

•

15/15

[]

0/15

10-1 0-1

10 0

101

Normalized cycle ratio (Ny hold time/Nf 0/0) Fig. 9. Dwell sensitive behavior of IMI 829 at 600°C.

parameters employed are described in Table 1. The NCR was lowest with O/t cycles (Fig. 12) for different hold times. Compared to the same tensile and balanced dwells, compressive dwell cycles were producing a larger decrease in the life. The NCR dropped with higher strain ranges, as shown in Fig. 12.

with 47 s hold at 0.907% strain range was nearly three times more damaging than a 65 s hold at 0.995%. At 1000°C: Fig. 14 shows the NCRs versus total strain range of Rent 80 at 1000°C. A 120 s t/O hold cycle was most damaging. Other hold cycles with t/O, O/t and tl/t2and t/t appear in the same region.

13. Rend 80 tested at 871°C and IO00°C (Kortovitch and Sheinker, 1978) At 871°C: Tensile dwell of 47 and 190 s were most

14. INCONEL 617 tested at 950°C (Rao et al., 1988)

damaging as these periods have the lowest NCR. Compressive dwells of 80 and 195 s were next damaging compared with t/O cycles. Balanced dwell cycles exhibited higher lives than t/O and O/t combinations. A large scatter was observed in Fig. 13. A t/O cycle

The NCRs were calculated at one strain level of 0.6% with different hold times and strain rates. Hold time in each cycle was different where longer t/O produced the smallest NCR. Data on other cycle types such as t/t and O/t were not available. In summary, balanced dwell cycles were least damaging compared with O/t and t/O, as shown in Fig. 15.

T. Goswami/Mechanicsof Materials 22 (1995) 105-130

117

101 Keys: hold times in sec.. []

0/300 850"C

,ll

300/300 850°C 0/20 850°C

o 20/0 850°C A 20/20 850°C

20/0 1040*C 20/20 1040"C

[] 0/300 750*C [] 300/0 750*C

0/20 1040°C

• •

qD

+

N

[] 300/0 850"C

II L,

0/300 1000*C 300/0 1000*C

10 o

N° •

0

0

+

A

N

o

+x X

Nf (hold time) = Nf (0/0)

10"1

.

10-2

.

.

.

.

.

.

i

10 "1

.

.

.

.

.

.

.

10 0

10 1

Normalized cycle ratio (Ny hold time/Ny 0/0) Fig. 10. Dwell sensitive behaviorof MAR M 002 at different temperatures.

15. IN 100 tested at 925°C (Halford and Nachtigall, 1978) The creep-fatigue data contained several variables such as coated, uncoated, cast and powder, Gatorized IN 100. These were a]Lso tested under different temperatures and hence i,;olation of such variables was not possible, instead only one set of data was analyzed for a cast IN 100 at 925°C. Under coated condition at 1000°C, the ratio of NCR of compressive to tensile hold of 330 s at the same strain level was 1.67. Several unbalanced dwell sequences were analyzed at three strain levels. Dwell combinations with 6/116 and 116/6 s at two strain levels above 0.82% had identical lives (17, 84 and 15, 79), respectively, whereas the life shortening effect of 6/116 was more than 3 times that of the 116/6 cycle at the lower strain

of 0.5% (454 and 1400), respectively. For both unbalanced cycles the NCR were less than 1, meaning that such unbalanced cycles were more damaging than 0 / 0 cycles. Longer tensile dwell cycles were more damaging than other cycles, as shown in Fig. 16.

16. PWA 1480 single crystal tested at 1015 and 1050°C (Miner et al., 1988) This is a tensile dwell sensitive material. Total strain range versus NCR data are plotted in Fig. 17. The NCR were minimum values at lower strain levels. With increasing hold time of the t/O cycle and strain range, the NCR were observed to be increasing. The compressive dwells were next damaging. At higher strain levels the NCR were constant for cycles containing 877 and 1315 s hold times. Lives of balanced dwell

118

T. Goswami/Mechanics of Materials 22 (1995) 105-130 10 1

Keys: hold time in sec..

30/0 0/30

N.f(hold time) = N f (0/C;

f

30/30 100110

L

10 0

•

o~

• o

¢_

oo

•

*u

a

o

o

8

o •

0

•

0

10"1 0-1

Normalized cycle ratio (Ny hold time/Ny 0/0) Fig, I 1. Dwell sensitive behavior of Waspaloy at 750°C. 10 1

Nf hold time=N.f(0/0)

V !

p~

; |

A c r_

+O

o+

._=

•

== 10 0

x

x

• on u ', em • x • I~ •

x

A

t_

[]

m

q r'l . i

, ; i ; i

A=I.5E00 %/sec. I B=6-9E- 1%/sec.

'

!

;;

: ! ,!

Keys: how times in .~c.. •

60/01A)

0

60/01B1 600/0 (B)

• • o

0/60 (A) 0/60 (BI 0/600 (A)

• • A +

60/60 (B) 600~001A) 600/600 (B)

x

60/60 (A)

; I

10"1 0-1

10 o

Normalized cycle ratio (Ny hold time/NS 0/0) Fig, 12. Dwell sensitive behavior of Ren~ 95 at 650°C.

10 1

T. GoswamilMechanics of Materials 22 (1995) 105-130 10 1

119

! !

N.f(hold time) = Nf (0/0) Keys: time in sec.. ! |

!

o 10 0

eoa A/~ C! ex

D4D e~

!

o • A a • O [] + 0 x a A

!

•

!

O | |

it

f,.

t

.E

! ! |

[-o

I

10 "1

! t t

! |

0/103(871"C) 0/80(871"C) 0/84(871"C) 0/128(871"C) 190/0(871"C) 47/0(871"C) 65/0 (871"C) 95.7/0 (871"C) 66.5/0 (871"C) 140/140 (871"C 100/100 (871"C 110/110 (871"C 200/200 (87 I'C 0/195 (871"C)

I

!

10 "2 10 "1

10 0

101

Normalized cycle ratio (N.f hold time/NJ" 0/0) Fig. 13. Dwell sensitive behavior of Ren~ 80 at 871°C.

101

¢= f,,,,

11) 0

• •

0/215 190/0 47•0 65/0

• A + • x

95.710 66.5/0 40•0 55/0 120/0

" •

55/0

N/(hold time) = N f (0/0/

23/0

o~ ¢tl L

[]

0/77

=

100/100

÷

=,.=

• 160/80 -t- 90•90

¢=

•"O

p.,

•

/1

Keys: time in see..

10" 1 4 _ _ _ lO-2

10-1

Normalized cycle ratio (N~ hold time/NS 0/0) Fig. 14. Dwell sensitive behavior of Ren6 80 at 1000°C.

10 0

120

T. Goswami/Mechanics of Materials 22 (1995) 105-130

10 0

=

n,

==*•

•

o

A

Keys: hold times in sec.. Z--

5/0

"

•

°m

60/0

x

L.

180/0

• • a • • O +

60010 180010 7200•0 0•60 0•600 30/30 300/300

10"1

Nf(hold time) = N f (0iG)

.

.

.

.

.

.

.

I

.

.

.

.

.

.

.

10 0

10-1

0-2

Normalized cycle ratio (NS hold time/NS O/O) Fig. 15. Dwell sensitive behavior of Inconel 617.

lO 1 N.f(hold time) = N.f(0/0)

A

[]

O

L

¢=

"3

10 0

t..

O

[]

o

F-

[]

Keys: time in sec.. O

6/116

1

[]

116/6

J

lO-1 1 0

lO-1

Normalized cycle ratio (Nf hold time/NS 0/0) Fig. 16. Dwell sensitive behavior of 1N 10O.

T. Goswami/Mechanics of Materials 22 (1995) 105-130

121

10 1

N.f(hold time)=Nf(0/0).

/

[]

o == ¢1 t_.

.=

& O

X 4.

10 0

o Keys: time in sec. rm

900/0

•

0/871

•

275/0

A

0•225

• A

265/0 130/0

O 0/63 + 0/65

•

890•0

O

I~ 8.4/8.4 1 12.6/12.6 0/1315

216/216

10"1 10 -1

10 0

1

Normalized cycle ratio (Nf hold time/N~f 010) Fig. 17. Dwell sensitive behavior of PWA 1480 (single crystal) at I015°C.

cycles were more damaging than those of 0/0 fatigue. Fig. 18 shows the total strain range versus NCR at 1050°C. With increasing t/O time the NCR decreased and the minimum lif,~ was observed for a 66 s t/O cycle. The next dama~ging cycles were the tit cycles, where the NCR decreased as the hold time of the t/t cycle increased. The cyclic lives of the O/t cycles were found to be five times that of continuous fatigue lives.

17. MA 754 tested at 850°C (Nazmy, 1988) Two orientations, @scussed below, have been tested to quantify the effects of orientation on life. LT-orientation: This is also a t/O sensitive material where total strain range versus NCR data are plotted in Fig. 19. For a 300 s hold in t/O and O/t, the difference in NCR was nearly two magnitudes. The same trend of PW 1480 was obse,rved also for this material; with

increasing strain range the NCR was increasing. T-orientation: Fig. 19 shows the NCRs with the total strain range for this material. This is a tensile dwell sensitive material. Endurance with balanced dwells of 30 s was nearly four times the endurance with continuous fatigue. With the increasing strain range the NCR were found to be increasing. The dwell sensitivity, as stated earlier, depends upon the combinations of test parameters selected. In the case of superalloys, as evident from the behavior of MAR M 002, the dwell sensitivity depends upon test temperature, which has a threshold value, that, if exceeded, causes the transition from compressive to tensile dwell sensitivity. The threshold temperature appears to.be nearly 1000°C for the MAR M 002. The waveforms investigated for seventeen materials in this paper were random and not standardized. Therefore,

122

T. Goswami/Mechanics of Materials 22 (1995) 105-130 10 1

N f(hold

time)=N.f(O/O)

/ In:

0 0o

==

: A

10 0

x

x

Keys: hold times in sec.

0

"B • [] •

15115 20/0 1410 0•25

x x • o

0/14 0/4 18/18 8/0

~,

0/20

•

1(3/0

•

0•27 0•25 []

0 h

66•0 10/10

0/14

10"1 10 0

10"

10 1

Normalized cycle ratio (Ny hold time/Ny 0/0) Fig. 18. Dwell sensitive behavior of PWA 1480 (single crystal) at 1050°C.

to investigate the dwell sensitivity of various high temperature materials there is a need to follow standardized test waveforms in material testing• Such data will help to examine mean stress development, stress range effects, strain rate effects and the resulting dwell sensitivity of materials. Mechanistic features under similar tests in different materials will contribute to the development of the knowledge in this area of research. In this respect, no study on the dwell sensitivity for the seventeen materials will be decisive since the test parameters in the creep-fatigue tests are not standardized. The continuation of this study on dwell sensitivity will be published in the subsequent Part II and III. In Part II the mechanistic aspects under different test conditions for the seventeen materials will be examined• Various deformation mechanisms, crack

paths, microstructural changes, damage due to creepfatigue and oxidation will be discussed• In Part III the trends found for IMI 829, i.e., compressive dwell cycles raised positive mean stresses and tensile dwells caused tensile softening and raised compressive mean stresses at higher plastic strain ranges (Goswami, 1995d), will be validated for other materials. In addition, evolution of stresses, mean stresses, stress range effects, strain rate effects and other stress-strain behaviors will be discussed more fully•

4. Modeling dwell sensitivity In the past no models have been developed to either predict the dwell sensitivity or to present a quantitative analogy that explains why under a selected set of

T. Goswami/Mechanics of Materials 22 (1995) 105-130

123

10 1

Keys: time in sec. Nf(hold time)=Nf(0/0)

=

I

I I

r,,

50/OL

•

300/0 L

A

• •

300/0 L 30/30 L 30/30 L

[]

0/100 L

r'l 0/50 L

10 0

[] •

° ~

ell

A

t..

÷

m

o

•

o

!

L: Longitudinal direction. LT: Longitudinal-Transverse direction. 10-1

•

.

.

.

0-2

.

.

.

.

!

.

10 -1

.

.

.

.

.

.

.

• + O = M •

t

0/300 L 50/0 LT 300/0 1T 300/0 LT 0/50 LT 0/300 LT 0/300 L'I

i i !

•

.

.

10 0

10 1

Normalized cycle ratio (N.f hold time/N,f 0/0) Fig. 19. Dwell sensitive behavior of MA 754 (ODS) at 850°C.

test parameters materials either tend to behave as tensile dwell sensitive or as compressive dwell sensitive. Hence, in this paper an attempt was made to study the mechanical properties of materials and therefrom conduct data synthesis to develop conceptual models of dwell sensitivity. Therefore, one must realize that the conceptual model:~ have limited applications and should be used with caution. Two types of data that exist are tensile and fatigue. These data are analyzed to develop models four dwell sensitivity that are discussed below.

4.1. Modeling with tensile properties The data used (sttch as yield strength, ultimate strength, percentage reduction in area and ductility) were available for both room temperature and the temperature at which the creep-fatigue tests were conducted. The yield strength to tensile strength ratio, known as strength ratio (Or) was used by Smith et al. (1963) to predict the work hardening behavior of the

material. Within a range of strength factor greater than 0.8 the materials softened and below that range materials hardened. This trend was observed for numerous materials a few of them are being examined in this paper. Hence, strength ratio at both room temperature and test temperature was determined for the materials where data were available. The ductility at room and test temperatures was determined using the percent reduction in area following the ASM procedures. It was also pointed out by Dieter (1985) that ductility is a qualitative subjective property of a material and no direct relationship exists between the ductility measurement and performance in actual service. A relationship was developed with the strength factor (O'r) which is a ratio of strength ratio (o-r u x ) a t high temperature to room temperature (O'r RT) and the ductility ratio (Dr) which is a ratio of high temperature ductility (DHT) with room temperature ductility (DRT). It was observed that a balance between the two terms determines whether or not a material be dwell sensitive. The values of strength ratio and ductility un-

124

T. Goswami/Mechanics of Materials 22 (1995) 105-130 10 1

Compressive dwell sensitive line

tO

==

Tensile dwell sensitive

y

\y,..

10 0

r,~

Tensile dwell sensitive

10"1, 10 "1

10 0

10 1

Ductility ratio Fig. 20. Strength factor and ductility ratio distribution and dwell sensitivity.

der different conditions are tabulated in Table 2 where strength factor and ductility ratio improved with an increase in temperature. An analogy was made with the values of strength factor and ductility ratio which result in tensile and compressive dwell sensitivity. Fig. 20 shows the limits of strength factor and ductility ratio and it can be concluded that as long as the strength factor is not equal to the ductility ratio the material was tensile dwell sensitive. However, as the two terms become the same the material was found to be compressive dwell sensitive. The line in Fig. 20 indicates that the ductility ratio and strength factor values are the same along this line and any deviations from this line is the region where tensile dwell sensitivity occurred. Based upon this criterion, a prediction of the dwell sensitive behavior of the materials is given in Table 4, where observed and predicted dwell sensitivity are summarized. Why this trend is observed with the values of the strength factor and the ductility ratio needs to be explored further and this mechanism needs to be investigated. Since there is a lack of knowledge

on this topic, such an interpretation of the material behavior is highly qualitative and care needs to be taken to predict the dwell sensitive behavior of materials. Also, one needs to relate the microstructural evolution during the test, aging characteristics of these materials to the dwell sensitivity.

4.2. Modeling with fatigue properties The cyclic deformation under creep-fatigue causes progressively a material to either soften or harden. Usually tests are conducted in tension-compression waveforms which result in either retention or relaxation of stress/strain ranges. However, if tests began in a compression-tension pattern the hardening and softening phenomena that result are not the same as for tension-compression. Therefore, conceptually either hardening (H) or softening (S) result in either tension (T) or compression (C) directions. Usually one term, % hardening, is used to describe the material behavior in both directions. When the % hardening

T. Goswami/Mechanics of Materials 22 (1995) 105-130

125

Table 4 Tensile strength and ductil:ity ratios of materials Materials

Strength factor HTtrr/RTtrr

Ductility ratio Dr HT(D)/RT( D )

Predicted DS

Observed DS

NARIoy-Z AMZIRC 1Cr-Mo-V 1.25Cr-Mo 2.25Cr-Mo SS 316

1.37 1.12 0.89 1.08 1.08-1.35 0.85 1.02 0.887 0.81 1 1.05 0.77 1.24

0.74 1.10 1.6 1.76 1.19-1.56 0.34 0.97 1.24 1 1.06 6.6 1.83

t/O O/t t/O t/O

t/O t/O t/O t/O

0/t

0/t

t/O O/t t/O O/t O/t O/t t/O t/O

t/O t/O O/t O/t O/t O/t t/O t/O

Ti-6AI-4V MAR M 002 Waspaloy Ren6 95 Ren6 80 IN 100

is positive, materials ]aarden, when negative materials soften. Conceptually it is proposed that there are two independent hardening or softening phenomena in two directions. It is recognized that there exists no parameter which can be used to express hardening or softening behavior, due mainly to the fact that such a relationship depends upon many test parameters. In that, plastic strain rate under dwell varies with respect to time as the stress changes, as well as measure of stress ranges in tension and compression changes. Hence, several expressions have been proposed in the literature (Plumbridge et al., 1980; Kremple and Walker, 1969; Swindeman et al., 1983; Kuwabara and Nitta, 1977) which have been used with specific materials and test conditions. Ill this study, the cyclic hardening coefficient (%) was determined from the following expression (Plumbridge et al., 1980); tl = ( ( A O r s a t . - AO'ini.)/AO'ini.) X 100,

(2)

where the initial stress (Ao'ini.) is the value of first full-cycle stress and (AO'sat.) is the saturation stress at half-life, determine t!he % hardening coefficient (n). When the value of n is negative, it indicates softening. This equation may be used to represent independent hardening/softening behavior by replacing the saturation stress range at half-life in tension and compression, respectively. Similarly, the initial stress range in tension or compression directions must be computed to determine tensile/compressive hardening or softening.

Thus, the four mechanisms conceptually possible are: 1) Tensile hardening reversed by compressive hardening (HH). 2) Tensile hardening reversed by compressive softening (HS). 3) Tensile softening reversed by compressive hardening (SH). 4) Tensile softening reversed by compressive softening (SS). Thus a cycle consists of the following: Cycle = Tension part 4- Compression part ---- [ (O. t" -- O.ini.)/O.ini. ] S/H 4- [ (O'sat. -- O'ini. )/O'ini. ] S/H

(3)

where o'~t. occurs for each tension and compression direction, respectively. The changes that accrue inside materials as a result of cyclic loading are very difficult to model. Hardening in tension or compression raises the stress range in that direction, as a result tensile or compressive mean stresses develop. Softening in tension or compression is associated with relaxation of stresses. Where a particular combination of H and S will take place is determined by test parameters such as hold times. In general, dwell cycles consist two of the following four combinations as follows: HH: develop tensile and compressive mean stresses, HS: develop tensile mean stresses,

126

T. Goswami/Mechanics of Materials 22 (1995) 105-130

SH: develop compressive mean stresses, SS: produce stress relaxation in both tension and compression. A schematic model of the above possible combinations (HH, HS, SH and SS) is shown in Fig. 21. The stresses in tension (Fig. 21 (a)) and compression (Fig. 21 ( b ) ) are represented in a X - Y plot. The Xaxis plots the "cycle time" which is the ratio of total strain range to strain rate. The horizontal line which indicates that there is no hardening or softening represents a stable material. The arrows indicate whether there is evolution of mean stresses and, accordingly, the softening and hardening lines shift. If the cycle has no dwell time in tension or compression, the resulting stress response will be determined by the stress ranges in tension and compression from Eq. (2). Data on several materials have been analyzed with the limitation of no known compressive data. Compressive behavior was determined from the data that contained the tensile and compressive stresses at halflife, with the stress range at half-life and with the expression for cyclic hardening coefficient (%). This coefficient was assumed to be the same for the tensile and compressive parts, and stresses were determined from Eq. (2). When the tensile and compressive stresses so determined have values less than half the stress range, stress relax or mean stresses develop if exceeded. A demonstration of H and S combinations in tension and compression directions was made with Ti6A1-4V and AMZIRC, NARIoy-Z and PWA 1480. An interesting trend in the stress envelopes was observed for various materials drawn schematically in Fig. 22. Fig. 22(a,b), in which the y-axis plots the stresses and x-axis shows the zero stress level, shows the stress envelopes for compressive and tensile dwell sensitive materials. For a compressive dwell sensitive material, for example, Ti-6AI-4V the following combinations were found: I) HS: Very high tensile stresses compared with HH, SH and SS where compressive stresses were minimum. Lowest life and O / t sensitive as in the case of Ti-6AI-4V. 2) HH: Tensile stresses drop and compressive stresses increase compared with HS combinations. Continuous fatigue 0 / 0 of Ti-6AI-4V behaves in this manner. 3) SH: Tensile stresses further drop followed by gains in the compressive stresses and better fatigue

life compared with HS and HH combinations. Tensile hold times or with balanced dwells behaves in this manner (for compressive dwell sensitive material). 4) SS: Tensile stresses are less than half the compressive stresses. Combinations of hold times in tension and compression direction at a strain range offer the best fatigue resistance. A demonstration is given in Fig. 22(a) with only one compressive dwell sensitive material and the concepts developed in this paper will be explored more fully for the seventeen materials individually in Part III (Goswami, 1996b). Similarly, a demonstration was made for a tensile dwell sensitive material PWA 1480 in Fig. 22(b) where reversed stress envelopes in terms of following HH, HS, SH and SS combinations were observed. The tensile and compressive stresses continuously drop as the combination change from HH to HS, SH and SS in this case. A dwell sensitive map for a PWA 1480 single crystal has been constructed in Fig. 18 which shows tensile dwells are producing reduced life compared with the 0/0 condition. Though tensile and compressive behaviors were determined from one % hardening coefficient, use of tensile and compressive properties to determine the exact combination will be more realistic. The above pattern of stress envelopes for tensile and compressive dwell sensitive materials is very important since it establishes the stress directions and their magnitudes and resulting hardening or softening behavior. Further work is needed to determine a range of stresses where HH, HS, SH and SS combinations exist that may help in the interpretation of dwell sensitive behavior of materials.

5. Concluding remarks This examination on dwell sensitive behavior for seventeen materials resulted in the following conclusions: Solder alloy (96.5Pb-3.5Sn), AMZIRC, NARIoyZ, 1Cr-Mo-V, 1.25Cr-Mo, SS 316, MAR M 002 at 1040°C, Ren6 80, Inconel 617, IN 100, PWA 1480 and MA 754 were observed to be tensile dwell sensitive. However, 2.25Cr-Mo, Ti-6AI--4V, IMI 829, MAR M 002 below 1040°C, Waspaloy, Ren6 95 were compressive dwell sensitive.

T. Goswami/Mechanics of Materials 22 (1995) 105-130

127

Positive m e a n s t r e s s ~ ~ f s t : b l a r e

denlng Tensile part

Total s t r a i n range / s t r a i n rate = cycle time

(a) Possible t r e n d s In the s t r e s s e s in t e n s i o n direction.

••

Total s t r a i n range / s t r a i n rate = cycle time

~

~

softening

hardening

Compressive m e a n s t r e s s e s 0

0

(b) Possible t r e n d s in c o m p r e s s i o n direction. Fig. 21. Schematic representation of stresses in two directions.

Mechanical properties such as strength factor and ductility ratio play a role in predicting the material behaviors such as hardening/softening and dwell sensitivity. When the strength factor increases at high temperatures and is accompanied by a decrease in ductility, the materials tend to strain-harden which results in a tensile dwell sensitivity. However, a compressive dwell sensitivity resu]Ltswhen the strength factor is approximately similar to the ductility ratio. Material behavior, such as hardening (H) or soft-

ening (S), conceptually occurs in two possible loading directions. Thus there are four possible mechanisms involving HH, HS, SH and SS combinations. They determine the fatigue resistance of a material. Creep-fatigue test parameters determine a particular combination of H and S to occur and these combinations need to be established for such tests. Tensile hardening, which has higher detrimental effects, is determined by test parameters such as hold time, its direction, strain rate, strain range and temperature em-

128

T. Goswami/Mechanics of Materials 22 (1995) 105-130

HS

Positive m e a n s t r e s s e s

HH

SH

H

SS ~

S

Tensile s t r e s s e s

S

Zero level

r~

S H

Compressive stresses

H Negative m e a n s t r e s s e s

(a) D e m o n s t r a t i o n for c o m p r e s s i v e dwell sensitive m a t e r i a l (TI-6AI-4V) I-IH HS SS

SH

S

S

H

H

Positive m e a n s t r e s s e s

t

Tensile s t r e s s e s

Zero level

S

S H

H

Compressive stresses Negative m e a n s t r e s s e s

(b) D e m o n s t r a t i o n for tensile dwell sensitive m a t e r i a l PWA 1480. Fig. 22. Stress envelopes and the hardening of dwell sensitive materials.

T. Goswami/Mechanics of Materials 22 (1995) 105-130

ployed. Compressive dwell sensitive material has a stress envelope where t,~nsile stresses decrease with an increase in compressive stresses with HS, HH, SH and SS combinations, respectively. As a result, tensile fatigue resistance improves. Tensile dwell sensitive material has a stress envelope in the reversed order from compressive dwell sensitive material, where the tensile stresses increase accompanied by maximum compressive stresses under the HH combinations. However, both the tensile and compressive stresses decrease with HS, SH and SS combinations. Thereby tensile fatigue resistance deteriorates under HH conditions and under those test parameters promote HH combinations. Further work is needed to extend and assess these conceptual models in the prediction of dwell sensitivity for other materials.

Acknowledgements The author would hke to thank senior researchers for their contributions which inspired this effort are Professors W.J. Evans, W.J. Plumbridge, D.W. Hoeppner and E.G. Ellison and Dr. G.R. Halford, Dr. G.E Harrison, Dr. T. Nicholas, Dr. G.R. Leverant, Dr. C.R. Brinkman, Mr. R. Jeal, and Dr. N. Paton. The work reported in this paper is a part of authors' private research carried out in the Materials Discipline, Faculty of Technology, Open University, Milton Keynes, England. The author woudd like to thank the reviewers who contributed significantly in the interpretation of some of the results. Dr. C. Elliot read the manuscript and helped in the English write up and presentation.

References Antunes, V.T.A. and P. Hancock (1978), Advisory Group on Aerospace Research & Development CP 243, paper no. 5. Asquith, G. and S.H. Springthall (1978), Advisory Group on Aerospace Research & Development CP 243, paper no. 7. Brinkman,C.R., J.P. Strizak, M.K. Brookerand C.E. Jaske (1976), J. NucL Mater. 62(2/3) 181. Cowles, B.A., D.L. Sims and J.R. Warren (1978), NASA Report No. CR 159409. Coffin, LE (1954), Trans. ASME 76, 931. Dieter, G.E. (1985). Meta!s Handbook, Vol. 8, AmericanSociety of Metals. Drapier, J.M. and M.H. Hirschberg (1979), Advisory Group on Aerospace Research & Development AR 130.

129

Edmunds, H.G. and D.J. White (1966), J. Mech. Eng. Sci. 8(3), 310. Ellison, E.G. and A.J.E Patterson (1976), Proc. Int. Mech. Eng. 190, 321. Ellison, E.G., W.J. Plumbridgeand M.S. Dean (1984), Research Report 327, Departmentof MechanicalEngineering,University of Bristol. Ewald, W. and M. Polanyi (1925), Z. Phys, 31, 139. Gangadharan, A.C., D.H. Pai and I. Berman (1973), Int. Mech. Eng, paper no. 215. Goodall, I.W.and D.L. Thomas (1990), An Assessment Procedure for High Temperature Response of Structures, Nuclear Electric Plc. U.K.. Goswami, T. (1995a), Creep Fatigue, Part I, Int. J. High Temp. Mater. Processes 14(1), I.

Goswami, T. (1995b), Creep Fatigue, Part II, Int. J. High Temp. Mater. Processes 14(1), 21. Goswami, T. (1995c), Creep Fatigue, Part III Int. J. High Temp. Mater. Processes 14(1), 35. Goswami, T. (1995d), Int. Z High Temp. Mater. Processes, in print. Goswami, T. (1996a), Dwell sensitivity,Part If, Mech. Mater., to be submitted. Goswami, T. (1996b), Dwell sensitivity,Part III, Mech. Mater. to be submitted. Gough, H.J. (1933), Proc. ASTM 33 3. Gough, H.J. and D. Hanson (1923), Proc. R. Soc. bmdon A 104, 539. Gough, H.J., D. Hansen and S.J. Wright (1926), Philos. Trans. R. Soc. London A 226, 226. Halford, G.R. and A.J. NachtigaU (1978), Advisory Group on Aerospace Research & Development CP 243, paper no.2. Hyzak, J.M. and H.L. Bernstein (1978), Advisory Group on Aerospace Research & Development CP 243, paper no. I 1. Kortovitch, C.S. and A.A. Sheinker (1978), Advisory Group on Aerospace Research & Development CP 2fl3, paper no. I. Kremple, E. and C.D. Walker (1969), Fatigue at Elevated Temperature, ASTM STP 520, p. 75. Kuwabara, K. and A. Nitta (1977), Isothermal and thermal fatigue strength of Cr-Mo-V steel )'or turbine rotors, CRIEPI Report E277005. Ludwik, P. (1919), Z. Metallkunde 11 157. Majumdar, S. (1987), ASME Conf. Thermal Stress, Material Deformation and Thermo-Mechanical Fatigue, eds. H. Sehitoglu and S.Y. Zamrik, pp. 37. Mann, S.D. (1989), M.Sc, Thesis, Monash University,Australia. Miner, R.V., J. Gayda and M.G. Hebsur (1988), ASTM STP 942, 371. Nazmy, M.Y. (1988), ASTM STP 942, 385. Plumbridge, W.J. and M. Stanley (1986), Int. J. Fatigue 8, 209. Plumbridge, W.J., M.E. Dalski and P.J. Castle (1980), Fatigue Eng. Mater. Struct. 3, 177. Priest, R.H. and E.G. Ellison (1981),.Mater. Sci. Eng. 49, 7. Rao, K.B., H.P. Meurer and H. Schuster (1988), Mater. Sci. Eng. A 104, 37. Smith, R.W., M.H. Hirschberg and S.S. Manson (1963), NASA Technical Note D-1574.

130

T. Goswami/Mechanics of Materials 22 (1995) 105-130

Stentz, R.H., J.T. Berling and J.B. Conway (1978), Advisory Grcnq~ on Aerospace Research & Development CP 243, paper no. 12. Stubbington, C.A. and S. Pearson (1978), Eng. Fracture Mech. 10(4), 723. Swindeman, R.W., K. Farreli and J.B. Conway (1983), Proc. Thermal and Environmental Effects in Fatigue: Research Design hltetfuce, ASME PVP, vol. 71, pp. 121.

Vaynman, S., M.E. Fine and D.A. Jeannotte (1987), TMS AIME Annual Meeting, Denver, eds. EK. Liaw and T. Nicholas. Wilkinson, K.G. (1973), Tech. Air, 2 November issue. Yamaguchi, K. and K. Kanazawa (1980), Metall. Trans. A I1 2019.