3.6.1 M E T H O D
N o rm a lly the cy clic strain test is used to investigate the response o f a material to cyclic loads. O n e o u tpu t o f these tests is a cyclic stress-strain curv e (C S S C ) which describes the stress-strain relation o f the c y c le d m aterial d u rin g the early stage o f fatigue in clu d in g such p h e n o m e n a as cyclic softening and cyclic hardening.
As m e n tio n e d in C h a p te r 1, the tw o techniques used to d e te rm in e the C S S C arc the in crem ental test and the m ultiple step test. In each test, only the strain in the specim en sho u ld be c o n tro lle d in the in crem ental or step pattern respectively. It is quite difficult to c o n d u c t the increm ental test on an ordin ary m ach ine b e c au s e the strain in the sp e cim en s h o u ld be u n d e r feed b a c k control. H ow ever, if the m ac h in e has a c losed loop control system using the strain signal from the sp ecim en, the increm ental test can be used to obtain the C S S C . Alternatively, a sim ple test like the m ultiple step test can be used to find the C S S C on an ordin ary m achine. In o rd er to apply this test, the strain am p litu d e is increased o n ly after the hysteresis is saturated i.e. after a steady-state stress-strain cy c le is ob tained.
In o rd e r to obtain the cyclic resp o nse o f the present brake disc cast iron m aterial, the m ultiple step test was used. T h e relation betw een the s p ecim en strain and crosshead stroke fro m the strain -stro k e calibration was used to m aintain a constant strain a m p litu d e in both tension and c o m p re s sio n as defined in T a b le 3.2. In these tests, the cyclic strain a m p litu d e started with a low value and then was increased to a h igher value after suc ce ssiv e intervals o f 50 c y c le s as show n in Figure 3.22. T h e sp e cim en w a s
cycled at a fre q u e n c y o f 0.1 H z using a saw tooth w a v e fo rm as indicated in the Figure. In addition lo testing at room tem perature, t h i s m ode o f testing u . i s also used to Imd the
Chapter 3 Material Property Texts and Results
cy clic re sp o n se at e le v a te d tem p e ra tu re s o f 3 00 and 4 0 0 °C using the induction heating system d e scrib ed in section 3.3.2. T herefore, three sp e cim ens in total were required for these tests.
Cycles
Cyclic strain
amplitude
(peak-to-peak)
Stroke (mm)
in
tension
Stroke (mm)
in
compression
First 50 cycles 0 .0 0 1 5 3 6 0 .1 5 8 0 0 0 .1 0 0 0 S e c o n d 50 cycles 0 .0 0 4 5 1 6 0 .3 2 5 5 0 0.2 3 14 T h ird 50 cycles 0 .0 0 7 5 0 0 0 .4 4 5 2 0 0.3 3 09 Fourth 50 c y c le s 0 .0 1 0 4 8 0 0 .5 4 3 5 6 0.4143T able 3.2: R elation betw een the cyclic strain a m plitude and the c ro sshead stroke
3 .6.2 R E S U L T S
All s p e c im e n s broke in tension at the first cycle o f the third strain am p litu d e e x c ep t for the sp e c im e n that w as tested at 4 0 0 °C which broke at the 1 l ' h cy c le o f the secon d strain a m p litu de . T herefore, there were no spe cim ens subjected to the fourth cyclic strain a m p litu d e c o n ditions.
F rom the cy clic stress-tim e histories show n in Figure 3.23, the peak tensile stress d ecreases s ignificantly with increasing cyclic strain am p litu d e w hereas the absolute m ag n itu d e o f the c o m p r e s s iv e stresses increases. This indicates a degree o f cyclic s o fte n ing in ten sio n and cyclic h ard e n in g in c o m p ression . T h e m ag n itu d e o f these effects is also tem p e ra tu re -d ep e n d e n t as can be seen from c o m p a ris o n o f F igure 3.23 (a) and (b). A sim ilar study on the cyclic b e h a v io u r o f cast iron at room tem p erature attributed these c h a ra c te ristic s to the greater o p e n in g o f voids aro und graphite flakes
Chapter 3 M aterial Property Tests and Results
u n d e r cy clic tension and the cyclic strain hardening o f the pearlite m atrix in c o m p re s sio n [16].
In o rd e r to find the hy steresis loops for each strain a m plitude, the cyclic stress-strain c u rv e s w ere g e n e ra te d as sh ow n in Figure 3.24 for tem peratures o f 20, 3(X) and 4(X) r’C. T h e y reveal that the u p p e r (loading in tension) c u rv e s are non -lin ear and the lower (loading in c o m p re s sio n ) c u rv e s are alm ost linear thro ug ho ut all cyclic strain am plitu d es and tem p e ra tu re con d itio n s. T h is is m ainly the result o f the higher plastic d e fo rm atio n a c c o m p a n ie d by voids o p e n in g aro und graphite flakes in tension c o m p a r e d to m uch h igh er strain h a rd e n in g in c o m pre ssion.
T h e peak stress and strain in tension and com p re ssio n at the en d o f each strain cycle can be used to fo rm the C S S C ’s. T h e se c urv es were c o m p a re d to the M S S C 's in Figure 3.25 for tem p e ra tu re s o f 20, 3 0 0 and 4 0 0 °C. T he results show that the M S S C ’s are a bo ve the C S S C ’s in tension due to cyclic s ofte nin g whereas, in c o m p re s sio n , the C S S C ’s give generally h ig h e r stresses for a given level o f plastic strain due to c y c lic hardening. H o w e v er, it sh o u ld be taken into account that the effect o f cyclic load history for these e x p e rim e n ts m ight be a n o ther factor to cause these d ifferen ces in b e h a v io u r b ecau se a single s p e cim en was tested with four different cyclic am p litud es. T h e effect o f dam ag e ac cu m u la tio n du e to p rev io u s loading history is illustrated by the fact that the m a x im u m tensile strain for fracture u n d e r cyclic loading is lower than u n d e r m o n o to n ic loading at all tem p eratures.
3.7 SU M M A R Y
From the FE analysis o f the s p ecim en geom etry, it is c o n c lu d e d that the square s p e cim en with a 4 m m d iam e te r hole can be used for the tensile testing b ecause the stress c o n c en tra tio n at the s h o u ld e r is m in im u m . In addition, the stress co n cen tratio n at the hole is not sign ificantly d e p e n d en t on the d ia m e te r o f the hole.
T h e sp e cim en grips fulfilled all the req uirem ents to m inim ise the backlash for cyclic loading. F u rth e rm o re , they w ere used successfully with the induction coil for testing at e levated tem p e ra tu re s. H o w ev er, a m ore direct m ethod o f m ea su rin g the specim en strain w o uld be d esirable e.g. E tte m e y e r Speckle Interfcronietry (E S P I) [57] in order to e lim in a te the effect o f the pin and w edge displacem ents.
T h e e x p e rim e n tal M S S C ’s at various tem peratu res d e m o n stra te that the stress strain respo n se o f the brak e disc cast iron is tem perature d ep e n d en t both in tension and c o m p re s sio n . F u rth e rm o re , the tem pe ra ture sensitivity increases sig nificantly above 3 00 °C in both tension an d c o m p re ssio n . T herefo re, errors in duced by u sing the room tem p e ra tu re resp onse will be m uch greater above 3 00 °C.
T h e effects o f cy clic load ing ca u se significant differences in the stress-strain response c o m p a re d with m o n o to n ic loading. T h e cyclic load ca u se s the m aterial to harden in co m p re s sio n and to soften in tension esp ecially at high tem peratures. Furtherm ore, cyclic lo ading c a u se s fracture at lo w er strains than und er m o n o to n ic loading at the same tem p eratu re. H o w e v e r, the gen eratio n o f accurate fatigue life d a ta as a function o f stress level and tem p e ra tu re w as co n sid e red outside the scope o f the p rese n t work.
Chapter 3 M aterial Property Tests and Results
Chapter 3 M aterial Property Tests and Results
Figure 3.1: L a y o u t o f sp e cim en s on the rubbing surface