J O U R N A L OF M A T E R I A L S SCIENCE LETTERS 4 (1985) 125-128
Tertiary ductile fracture process in polycarbonate (PC) specimens O. S. LEE Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California 91125, USA
The tertiary fracture process in 1.6mm thick polycarbonate (PC) single edge notch (SEN) and centre notch (CN) specimens, which were annealed at 320°F for 2 h and furnace cooled, differs considerably from the brittle fracture process. We observed the cup-and-cup fractured section as shown in Fig. 1 which resembles the double cup fracture in a single crystal which was reported by Orowan in 1948 [1]. Orowan's slip mechanism can be used to explain qualitatively the final section configuration of double cup fracture in PC specimen even though it has a different microstructure from fcc metals. Rogers [2] also reported such fracture in face centred cubic (fcc) metals such as gold, silver, copper, aluminium and nickel. Highly deformed tertiary fracture process in a PC CN specimen as shown in [3] has been interpreted by adopting Onat and Prager's [4] plain strain slip line theory. Accurate crack tip opening displacement (CTOD) was obtained by using this slip line theory and the modified Dugdale model [51. The modified Dugdale model which was compatible with the experimentally determined stress field surrounding a rapid propagating
Figure 1 Cup-and-cup fractured section in a polyearbonate
(PC) single edge notch (SEN) specimen (sectioned in the direction perpendicular to the sheet thickness). 0261-8028/85 $03.00 + .12
ductile crack provided the means for computing the ductile fracture parameters which cannot be measured directly. The optical stress-analysis such
Figure 2 Highly deformed
tertiary fracture in a polycarbonate (PC) single edge notch (SEN) specimen (sectioned in the direction perpendicular to the sheet thickness).
© 1985 Chapman and Hall Ltd.
125
Figure 3 Schematics of tertiary
ductile fracture process. -.'
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' '
,1
J// /
/
,'<, /•
L,
first
%"%
d
stage
js
,%
ff ...... ," second
(a)
stage
(b)
I
,.:--;:;,
":...2",
third
(c)
stage fourth
stage
(dl
as the photoelasticity of PC fracture specimens augmented with a suitably modified Dugdale model provided a unique tool of hybrid
experimental-model analysis for investigating'the complex elastic-plastic field surrounding a rapidly extending ductile crack. The measured and,
Figure 4 Mating surface of a rapid teared polycarbonate (PC) single edge notch (SEN) specimen. 1 26
W
O
O [6]
~'
t"-I T H I S S T U D Y
10 -2
I
J
J
I
"'1
I
I
J' 10 -1
P H Y S IC A L CRACK TI P
log
[/-(inch)]
D UG DALE CRACK TIP
Figure 5 Strains, eyy, along the modified Dugdale strip yield zone.
calculated CTODs determined from this hybrid experimental-model analysis were found to be within 10% with each other. Another type of tertiary fracture, as shown in Fig. 2, was observed. The final stage of this tertiary fracture process was different from that based on [1, 4]. By examining the sectioned fractured surface configuration of a PC SEN specimen, as shown in Fig. 2, the following tertiary fracture process was deduced (see also Fig. 3). (a) First stage: 45 ° slip lines occur and some microcracking take place along these characteristic slip lines during the plastic deformation. (b) Second stage: The specimen is elongated in the loading direction with velocity which is essentially the same as that of perpendicular to the loading direction. (c) Third stage: A crack initiates from one specimen surface side while the other side sustains the external loading under further deformation. (d) Fourth stage: The crack propagates toward
the other specimen surface side in the direction perpendicular to the thickness of the specimen to fracture in the configuration shown in Fig. 2 and which is presented schematically in Fig. 3. The tertiary fracture process of PC SEN specimens is a complex ductile tearing involving combined modes I and III crack deformation as discussed above. Fig. 4 shows the mating fracture surfaces viewed in the direction of D~ and D2 in Fig. 3d. The tertiary fracture process with accompanying mode III crack deformation is clearly seen by noting the fractured ligament direction in Fig. 4. It is noted that the ligaments decline about 25 ° from the perpendicular which is for pure mode I crack propagation. This angle of decline of the ligaments was found to be varied during the crack propagation period. Equation 1 defines the modified Dugdale crack tip profile in which the constants were determined through the hybrid experimental model analysis [51. 127
8 Yr~ Modified Dugdale crack profile = ~-
-- ~ry (ry --r) log t r + ry + 2rrv J
x
+ Z
8 (--1)nr(2~-l>/ZD2n-I-~
(1)
n=2,3
where Di are constants determined by the optimization process used in evaluating the dynamic photoelastic data, Y is the yield stress in the uniaxial tension test, E is Young's modulus, ry is the modified Dugdale strip yield zone, and r is the axial position measured from the modified Dugdale crack tip. The measured CTOD, however, defined as the length AB and not A'B', as indicated in Fig. 2, agreed within 10% with the calculated CTOD using Equation 1. Furthermore, strains, eyy, in the loading direction can be estimated by using the crack opening along the crack profile of the modified Dugdale strip yield zone and the tertiary ductile fracture process as
The 100% shear lip fractured surface has not revealed the 45 ° slip line fracture because of the large deformation which follows the initial 45 ° slip line deformation. This large deformation phenomenon defined as the tertiary ductile fracture process cannot be neglected in highly ductile material and thus a ductile fracture criterion should incorporate the detailed deformation and/or the reduction area across the yielding zone ahead of the physical crack tip.
Acknowledgements The results of this investigation were obtained through a research grant funded by the US NSF Grant No. CME-792 507 to the University of Washington. The author wishes to acknowledge the support and encouragement of Dr C. J. Astill of NSF during the course of this investigation.
References 1. E. OROWAN,Rep. Prog. Phys. 12 (1948) 185. 2. H.C. ROGERS, Trans. Metall. Soe. AIME 218 (1960). 3. O.S. LEE,
eyy
=
Modified Dugdale crack profile Original thickness of the specimen
Fig. 5 shows two estimations of strains which were obtained by using a tertiary ductile fracture model and a model proposed by Achenbach and Dunayevsky [6], respectively, in the loading direction along the modified Dugdale strip yield zone. The critical strain at the small distance ahead of the physical crack tip based on this study differs from that derived by Achenbach and Dunayevsky [6] within approximately 10% as shown in Fig. 5.
128
A . S . KOBAYASH1
and
A. KOMINE
5th International Congresson Experimental Mechanics, Montreal, Canada, June 1984. 4. E. T. ONAT and W. P R A G E R , J. AppL Phys. 25 (1954) 491. 5. O. S. LEE
and
A.S. KOBAYASHI,
Fraet.
Mech.
U6th), ASTM STP submitted. 6. J. D. ACHENBACH and V. DUNAYEVSKY J. Mech Phys. Solids 32 (1984) 89.
Received 1 May and accepted 31 May 1984
