ductile-brittle transition behavior of short-chain branched polyethylenes at 80°c

Macromol, Chem. Phys. 196,3353 -3368 (1995) 3353

Ductile-brittle transition behavior of short-chain branched polyethylenes at 80 OC

Jen-taut Yeht Wen-Shuan Lee

Graduate School of Textile and Polymer Engineering, Department of Textile Engineering, National %wan Institute of Technology, Taipei, Taiwan

(Received November 21, 1994; revised manuscript of February 21, 1995)

SUMMARY: A systematic study on the ductile-brittle transition of short-chain branched polyethylenes

(SBPEs) is reported. The values of threshold stress intensity, the time corresponding to the point of ductile-brittle transition and the failure time (tf) of samples which failed in ductile and brittle regions were found to increase significantly with increasing branch length of the SBPEs. The fracture kinetics and the morphology at the notched root were distinguished for SBPE samples that failed in ductile and brittle regions. The values of (CC(notch opening displacement at the root of notch) - BB(the thickness of the craze))/(AA(notch opening displacement at the surface of the specimen) - CC) are less than or equal to about 0.3 for all samples which failed in the brittle region, and these values are only about 20- 30% of those of the samples which failed in the ductile region. Finally, an equation was developed to predict if of SBPEs which failed in the ductile and brittle region in terms of stress intensity, branch length and other material and experimental parameters.

Introduction

Short-chain branched polyethylenes (SBPEs) have been widely used as gas and water pipes during the last decades. In service, most of these SBPE pipes fail in a brittle manner by slow crack growth near room temperature. In the laboratory, the behavior of slow crack growth is commonly studied by the static fatigue test which can produce the same type of brittle fracture that occurs in gas pipes after long time in service and which can provide a reliable way for evaluating the performing lifetime of SBPE l-*).

The static fatigue test is usually analyzed by plotting loading stress (a) vs. the failure time of static fatigue (tf), which typically displays a shallow-sloped region followed by a more steeply sloped region. As reported by Brown and co -au thor~~*~) , brittle-type failure occurs in the region of lower stress levels and longer failure times, which is characterized by little deformation at the point of failure and corresponds to the region of the curve where the slope is steeper. In contrast, ductile-type failure shows large deformation and necking, and occurs in the shallow-sloped region, which is corresponding to relatively higher stress levels and short failure times. The point at which the slope changes can be characterized as a type of “ductile-brittle tran~ition”~). More detailed observation3) at the root of the notch indicates that brittle-type failure is associated with a small difference between the thickness of the craze (BB) and notch opening at the root of the notch (CC), and the difference becomes large in the ductile region. They also showed that the most distinguishing feature of slow crack growth is the formation of a craze-like damage zone which consists of fibrils and voids at the defect tip‘l). However, the time to failure in the brittle mode of many SBPE resins may

0 1995, Hiithig & Wepf Verlag, Zug CCC 1022-1 352/95/$1O.O0

3354 J. Yeh, W.-S. Lee

be extremely long at low temperature below about 50°C. Therefore, a higher temperature, 80 “C, was often used to study the slow crack growth behavior of SBPEs, which allows to study the “ductile-brittle transition” in a reasonable period of time.

Few investigations have reported the criteria for determining whether the failure mode is ductile or brittle for a given p~lyethylene~*’~). In general, for all polyethylenes, the most widely used criterion for determining whether the failure is ductile or brittle is based on the curves of stress (a) against time to failure (tf) (i. e., t , - o - * ) ~ ) . If n is appreciably greater than about 20, the behavior is ductile, if n is definitely less than about 6 the behavior is brittle. Most recently, it was demonstrated ‘‘1 that there is a threshold stress intensity (Kth ) for polyethylene below which purely brittle-type failure occurs. This threshold stress intensity increases with decreasing temperature. However, as far as we know, no study has ever been reported on the effect of material parameters on the behavior of the ductile-brittle transition of SBPEs. The purpose of this study is to investigate the effect of short-chain branch length on the ductile-brittle transition behavior of SBPEs at 80°C. The effects of branch length on Kth, and the time corresponding to the point of ductile-brittle transition are reported. In addition, several distinguishing features were observed on the fracture kinetics and on the morphology at the notched root of SBPEs that failed in ductile and brittle regions. Finally, an equation was developed to predict t , of SBPEs that failed in ductile and brittle regions in terms of stress intensity, branch length and other material and experimental constants. The tolerance of C, obtained from experiments and predicted from this equation is within about G ? 5 % .

Experimental part

Three commercial short-chain branched polyethylene (SBPE) resins prepared from ethylene-butene, ethylene-hexene and ethylene-octene copolymers were used in this study, which will be referred to as samples A, B and C, respectively. These resins were used in our previous investigations ’* 12, 13). Their molecular parameters and crystalline microstructuure were determined before and summarized in Tab. 1. Within experimental error, these resins have similar weight-average molecular wekht (aw), molecular weight distribution (MWD), branch frequency, degree of crystallinity (Wc), lamellar thickness (L), size of supermolecular structure (D), tie molecular density cfT) but different branch length (see Tab. 1). The molecular weight and its distribution associated with the SBPEs were determined with a Viscotek gel permeation chromatography (GPC) model 1 .O. n o 5 pm highly crosslinked ST-DVD copolymer columns (lo3 + lo4 nm) were chosen and slowly conditioned from toluene to decahydronaphthalene (C,,H The samples were prepared by dissolving in decahydronaphthalene at 135°C to reach a final concentration of 1.0 mg/mL. Specific molecular weights of narrow fractions of polystyrene were used to calibrate the instrument. The branch length and frequency of each sample were measured from 13C NMR spectra using the method proposed by Pooter et al. 14) Results obtained from 13C NMR spectra of these samples suggested that samples, A, B and C are associated with eighteen ethyl, butyl and hexyl short-chain branches per thousand carbon atoms, respectively”). The thermal behaviors of all samples were performed on a Dupont differential scanning calorimeter (DSC) model 2000. Lamellar thickness of each sample was not measured directly but estimated from the observed melting temperature using the Gibbs- Thomson equation Is). The supermolecular structure of all samples was viewed through crossed polarizers with an Olympus BHSP-300 optical microscope. As indicated from these

?lab

. 1.

Sam

ple

Com

ono-

M

w M

WD

=

Bran

ch fr

eque

ncy

Ther

mal

hist

ory

W, i

n Vo

fT

in Y

o L

/nm

D

/pm

Mol

ecul

ar p

aram

eter

s and

cry

stal

line m

icro

stru

ctur

e ass

ocia

ted

with

eac

h sa

mpl

e 1

3.

Mw

/Mn

v) 0,

mer

s P

u 1

*

h 18

bra

nche

s 1

A

ethy

lene

/ 9.

2 x

lo4

3.4

- iso

ther

mal

cry

stal

li-

40.1

6.

3 13

.0

15 +

3 bu

tene

1 O

OO C

atom

s za

tion

at 1

00°C

/12

h E.

R 5

B et

hyle

ne/

9.4

x lo

4 3.

3 - 1

8 br

anch

es

isoth

erm

al c

ryst

alli-

40

.6

6.2

14.1

17

f 3

3 E

zatio

n at

90°

C/1

h

1 000

C at

oms

18 b

ranc

hes

1 000

C at

oms

hexe

ne

C

ethy

lene

/ 9.

7 x

lo4

3.6

- iso

ther

mal

cry

stal

li-

41.7

6.

0 13

.2

16 f 3

za

tion

at 1

00°C

/l h

oc

tene


photographs, these samples exhibited the well-known banded-ring structure, which are the standard characteristics of polyethylene spherulites. The spherulite size distribution of these samples was represented by the average spherulite size together with its standard deviation. Tie molecule densities were evaluated from their measured brittle fracture stress ’@. More detailed characterization of the molecular parameters and crystalline microstructure are described in our previous studies ‘ 9 12). A DMA (dynamic mechanical analysis) unit model Eplexor 150N (GAB0 Qualimeter Testanlagen GmbH) was used to study the mechanical relaxation of all samples. All DMA experiments were operated at a frequenccy of 3.5 MHz, a heating rate of 3 “C/min and in a temperature range from - 150 to 100 “C.

The single-edge notched specimens were sectioned and polished from the injection- molded plaques. Thhe dimensions of the single-edge notched tensile specimens are shown in Fig. 1. Specimens were notched with a razor blade to a required depth of 2 to 4 mm. Increasing the notch’s depth in the thickness direction was utilized to minimize the time to failure while ensuring that the fracture mode was brittle. The specimens have side grooves which are 1 mm in depth. The side grooves reduce the amount of plane stress fracture that occurs at the edge of the crack. Each notch was carefully made by pressing a fresh razor blade into the inside surface of the specimens at a constant notching speed of 50 pm/min. The specimens were then loaded under a constant stress at 80°C. The notch opening displacements (NOD) at the following three locations were measured with an Olympus SZ40 optical microscope: (1) at the surface of the specimen (AA), (2) at the root of the notch as formed by the razor blade (CC), and (3) at the base of the craze (BB) (see Fig. 2). The loading stress, a, used in this study was calculated as follows

F A

a = - ,

where F is the applied load and A is the unnotched cross-sectional area. The morphological changes of all samples fractured in air were observed using an

Olympus SZ40 optical microscope from the outlook of the roots (see Fig. 2). Photographs were made during the fracture process to observe possible changes in the morphology of the roots. The top view of the fractured surface was examined using a scanning electron microscope (SEM).

Results and discussion

Analysis of the ductile-brittle transition

Fig. 3 shows the plots of failure time versus stress of all samples notched at different depths. The curves generated typically display a shallow-sloped region followed by a more steeply sloped region for all samples. The values of n (cf. Introduction) in the shallow-sloped region are approximately 29.4, 34.8 and 37.5 for samples A, B and C, respectively, which is corresponding to a behavior of ductile-type failure. In the steeply slope region, the values of n are approximately 5.8, 4.0 and 3.3 for samples A, B and C, respectively, and the failure behavior is brittle-type. As shown in Fig. 3, samples A notched at 2, 3 and 4 mm depths underwent “ductile-brittle transition”. However, within experimental time, the point of “ductile-brittle transition” was not observed on the plots of 0 vs. t , for sample B notched at 2 mm and sample C notched at and 3 mm depths. It is interesting that the threshold stress intensity (Kth) values remained unchanged for samples A notched at various depths (see lkb. 2). As reported by Brown

Ductile-brittle transition behavior of short-chain branched . . .

a

3357

70 mm

1 t U

Fig. 1.

sidenotch(1mm)

i I damaeed

A L C notch

Fig. 2.

Fig. 1. Shape and dimensions of the single-edge notched tensile specimen

Fig. 2. Experimental measurements of notch opening displacements

Fig. 3. Loading stress plotted against time to failure (tf) at 80°C for all samples notched at different depths: sample A at 4 mm (O) , 3 mm (A) and 2 mm (A), sample B at 4 mm (o), 3 mm (A) and 2 mm (A), and sample C at 4 mm (0 ) and 3 mm (A)

U 1 J ' .."'.'I ' . ." ' . ' I ' """. '"..-I 10 100 1000 10000 100000

Time to failure in min

and Lua, pure brittle behavior occurs if the value of stress intensity is below Kth and the value of Kth remains unchanged for samples tested at a given temperature regardless of the notched depth. On the other hand, the threshold stress intensity values of all samples notched at 4 mm depth increased from sample A to B and C, and the


lkb. 2. Threshold stress intensity values (&) at 80 "C of all samples

Samples Notched depth Kth in mm

tdb/min

A

B C

0.43 0.43 0.43 0.59 0.70

4900 3 100 3000

1 1 000 30 000

time of ductile-brittle transition (tdJ of samples A, B and C notched at 4 mm depth occurs at about 4900, 1 I OOO and 30000 min, respectively. As described previously, samples A, B and C are associated with approximately the same weight-average molecular weight, molecular weight distribution, branch frequency and microstructural parameters (i. e., degree of crystallinity, lamellar thickness, supermolecular structure and tie molecule density). Thus, it is reasonable to suggest that the significant increase in the values of t& and K,,, from sample A to B and C is due to the increasing branch length of the short-chain branched polyethylenes.

Morphology of notched roots, fracture surfaces and kinetics of damage of samples that failed by brittle and ductile modes

The kinetics of damage and the morphology changes at the roots of all samples that failed by brittle and ductile modes were observed using an optical microscope by looking directly into the notch. Figs. 4-6 show the typical kinetics of damage of samples A, B and C failed by a brittle mode, where the notch openings AA, CC and BB are plotted against time. These fracture kinetics are nearly the same for all samples and several features were observed and reported before7.'*): The notch openings grew

0' 1 10 100 1000 10000 100000

Time in rnin

Fig. 4. and CC plotted against loading time of sample A notched at 4 mm depth and tested at 80 "C and 1.2 MPa. The arrow indicates that the fibrils begin to break

Notch openings AA. BB

Ductile-brittle transition behavior of short-chain branched . . . 3359

Fig. 5 . Notch openings AA, CC and BB plotted against loading time of sample B notched at 4 mm depth and tested at 80 "C and 1.4 MPa. The arrow indicates that the fibrils begin to break

'i 1,": 0 AA 0

0 1 . ..... "I . .... "I ...... "I . .......I 1 10 100 1000 10000 100000

Time in min

u) rn C C 0)

0

.- n

z 0 0 10

4-

Fig. 6. Notch openings AA, BB * and CC plotted against loading time of sample C notched at 4 mm depth and tested at 80°C and 1.9 MPa. The arrow indicates that the fibrils begin to break 0

0

-I- 1 10 100 1000 10000 100000

Time in rnin

immediately upon loading and then grew at a slow but nearly constant rate up to a critical value (63, at which fibrils begin to break at the bottom of the notch. However, it is interesting to note that 6, increases somewhat with increasing branch length (see Figs. 4-6). As shown in Figs. 7-9, a more detailed characterization on the morphological changes at the notched roots indicates that a bright zone was observed under reflected light shortly upon loading the specimens, the fibrils broke and the film shred at a time near the time required to reach 6, (tJ and many voids were observed on the film. After t,, the film damaged completely and the notch openings jumped to another "step", and which another bright film under reflected light was formed at the notch roots of all samples that failed by a brittle mode. The notch openings of these samples continued to grow "stepwise" before ultimate failure and, during each step, the notch opened very slowly (see Figs. 4-6). The corresponding fracture surfaces of these samples that failed in the brittle region are shown in Fig. 10a-IOc. Several "arrest lines" were observed on these fracture surfaces, and the numbers of arrest lines


(x BB

I 2 m m I

Fig. 7. Optical views into the root of notch of sample A notched at 4 mm and tested at 80 “C and 1.2 MPa after (a) 6 min, (b) 92 min, (c) 209 min

are corresponding to the numbers of “stepwise fracture” observed in Figs. 4-6. This type of “stepwise fracture” became obscured on the plot of 0 vs. t , for samples that failed in the ductile region and disappeared completely as the loading stress continued to increase (see Figs. 11 - 13). Therefore, the corresponding arrest line due to stepwise fracture disappeared on the fracture surfaces of these samples that failed by a ductile mode. Furthermore, it is interesting to note that the voids observed on the film at the notched roots for samples associated with brittle-type failure became obscured and, in fact, no clear voids can be found on the film during the fracture process for many of the samples that failed in the ductile region. Fig. 14 shows the typical optical micrograph of the notched root morphology of sample C that failed in the ductile region. In addition, as reported by Lu and Brown3), another distinguishing feature between samples thaht failed by ductile and brittle modes is that brittle-type failure is associated with a small difference between the values of the notch openings BB and CC, and the difference becomes large in the ductile region. In fact, as shown in ’Itlb. 3, the values of CC-BB divided by the values of AA-CC are less or equal than about 0.3 for


AACC BB

CC BB

CC BB

Fig. 8. Optical views into the root of notch of sample B notched at 4 mm and tested at 8OoC and 1.4 MPa after (a) 1098 min, (b) 19872 min, (c) 24889 min

all samples that failed in the brittle region. These values are only about 20-30% of those of samples that failed in the ductile region.

Relationship between short-chain branch length and failure time of SBPEs

As shown in Fig. 3, the failure time (t,) of samples tested under the same conditions increased significantly as the short-chain branch length increased from two to four and six carbon lengths. A similar result was found in our previous paper I ) for samples tested at 25 "C; it was suggested that this dramatic improvement in t f was due to the increasing sliding resistance of the polymer chains through the crystal and through the entanglements in the amorphous region as the branch length of SBPEs increases. It has been suggested by Bassini and co-workers'') that the stress intensity factor (K) is a good correlating parameter for predicting t , of SBPEs. Since samples A, B and C show about the same material parameters (i. e., I%&, MWD, branch frequency, W,, 0, L and f T ) but different short-chain branch length, it is suggested that t , can be expressed as a function of the stress intensity (K) and the short-chain branch length (B) as represented by Eq. (62)


t f = A Bm K-“ (2)

where A and m are constants depending on material parameters (excluding the branch length) and the type of failure mode, and n equals (29.4,34.8, 37.5) and (5.8,4.0, 3.3) for samples A, B and C that failed in ductile and brittle regions, respectively.

K is defined as follows 171:

K = Y*a.ab’2

Y = X’’2[1.12 - 0.231(Uo/b) + 10.55(ao/b)’ - 21.72(~o/b)~ + 30.39(Q0/b)~]

a,: the initial notch depth b: the sample thickness u: the loading stress as defined in Eq. (1)

The failure times obtained from experiments and predicted from Eq. (2) are shown in Fig. 15; the agreement is within about t-25% and should be considered to be good.

CC BB

-7-

CC BB

Fig. 9. Optical views into the root of notch of sample C notched at 4 mm and tested at 80°C and 1.9 MPa after (a) 8 min, (b) 10577 min, (c) 18007 min


lJa!uLl Fig. 10. Fracture surfaces of samples (a) A failed at 1.2 MPa, (b) B failed at 1.4 MPa and (c) C failed at 1.9 MPa (notched depth: 4 mm, testing temperature: 80 "C). The arrows indicate arrest lines

Relationship between thermal molecular motion and the process of slow crack growth of SBPEs

The temperature dependence of the storage modulus E and t ans for samples A, B and C are shown in Fig. 16a- 16c. No significant difference was found in the nature of these curves. Three distinct transitions are observed as tans peaks at temperatures near - 120 "C (y-transition), -20 "C @-transition) and 45 "C (a-transition) in all of these three curves. These relaxation processes have been extensively studied 18-20). It is generally desribed that the p- and y-transitions are due to the motion of branches 21-24)

and due to the crankshaft motion of short polymer segments requiring a minimum of three methylene units20*25s26) in the amorphous matrix, respectively. In contrast, the


.E I" 1 ° 1 8

A A AA 0

. . '....'I . . . . . . . . I .c1

1 10 100 1000

Time in rnin

lo 1 0

1 10 100 1000 10000

Time in min

. . ...__1____... . . .-.7

0.1 1 10 100 1000 10000 Time in rnin

Fig. 11. Notch openings plotted against loading time of sample A notched at 4 mm depth and tested at 1.8 MPa: ( 0 ) AA, ( 0 ) CC,

( 0 ) CC, (.) BB; and 2.0 MPa: (A) AA, (A) CC, (4 BB

(.) BB; 1.9 MPa: (0) AA,

Fig. 12. Notch openings plotted against loading time of sample B notched at 4 mm depth and tested at 2.0 MPa: ( 0 ) AA, ( 0 ) CC, (.) BB; 2.2 MPa: (0) AA, ( 0 ) CC, (.) BB; and 2.3 MPa: (A) AA, (A) CC, (4 BB

Fig. 13. Notch openings plotted against loading time of sample C notched at 4 mm depth and tested at 2.3 MPa: ( 0 ) AA, ( 0 ) CC,

( 0 ) CC, (.) BB; and 2.5 MPa: (A) AA, (A) CC, (4 BB

(.) BB; 2.4 MPa. (0) AA,

a-transition is attributed to motions or deformations in the interfacial region (tie molecules, loops, folds, etc.) which originate from chain mobility in the crystalsm). These molecular motions originated from the crystalline and amorphous regions

Ductile-brittle transition behavior of short-chain branched 3365

tr CC BB

IT CC BB

T BB

Fig. 14. Optical views into the root of notch of sample C notched at 4 mm and tested at 80 "C and 2.3 MPa after (a) 10 min, (b) 160 min, and (c) 2 150 min

should all be activated at a temperature of 80°C. With the aid of these activated molecular motions, the disentanglement of tie molecules during the process of slow crack growth becomes easier than those of samples tested at temperatures lower than these transition temperatures. For instance, the activated tie molecule and loop motions originated from the crystalline region should certainly help these SBPE samples to fail by a brittle manner, since it was reported that the disentanglement of tie molecules during the process of slow crack growth is the fundamental failure process that

3366 J. Yeh, W.4. Lee

CC - BB AA- cc 'Rib. 3. The values of AA-CC, CC-BB and (cf. Fig. 2) of samples notched

at 4 mm depth and tested at various stresses and 80 "C

Sample Fracture Stress AA- cc CC - BB CC - BB AA- cc mode in MPa in mm in mm

A ductile 2.0 2.24 1.57 0.78 1.9 2.18 1.44 0.66 1.8 2.36 1.37 0.58

brittle 1.6 2.13 0.46 0.22 1.4 1.95 0.51 0.26 1.2 1.99 0.47 0.24

B ductile 2.3 1.33 1.45 1.10 2.2 1.31 1.44 1.15 2.2 1.34 1.41 1.05 2.0 1.35 1.47 1.09

brittle 1.9 1.78 0.33 0.19 1.7 2.27 0.41 0.19 1.4 2.03 0.35 0.17

C ductile 2.5 2.06 2.19 1.06 2.4 2.15 2.23 1.04 2.3 2.08 2.27 1.09

brittle 2.1 2.82 0.87 0.31 1.9 2.80 0.71 0.25

0.4 :::m 0.3

10 100 1000 10 1000 1000001000000 Failure time in min

Fig. 15. The stress intensity versus failure time for samples A (A), B (A) and C (0) notched at 4 mm depth. The solid line re- presents the failure time predicted from Eq. (2)

determines the failure time of polyethylenes that failed in the brittle region2). Therefore, the time to failure in the brittle mode of these SBPE samples was obtained in a reasonable period of time at 80 "C, while it was normally not obtained at room temperature.


Fig. 16. Plots of E’ and tan6 as a function of temperature for samples (a) A, 01) B, and (c) C

a .0.3 C 0 I

0.2

0.1

0

ton 6 r LOO0

3000

2000

a

Lu

1000

0 -150 -50 50

Temperature in O C 0.3 - lbl -LOO0

0.2 - C - ton6 a

- 3000 5 I - € Lu - 2000

- 1000

0

0.1 - 0 . 0 -150 -50 50

a 0.3

0.2 C CI

0.1

0

Temperature in O C - (c) - - ton6 - E ‘

-

4000

3000 5 Lu

2000

a

1000

0 -150 -50 50

Temperature in O C

Conclusions

The values of threshold stress intensity, the time corresponding to the point of ductile-brittle transition and the failure time of samples that failed in ductile and brittle regions were found to increase significantly for SBPE samples with the same weight- average moleular weight, molecular weight distribution, branch frequency, microstructural parameters but longer branch lengths. These significant increases in Kth, t,, and t, are attributed to the increasing branch length of the SBPEs. The notch openings grew stepwise for samples that failed by a brittle mode. However, this type of “stepwise fracture” became obscured for samples that failed in the ductile region and disappeared completely as the loading stress continued to increase, and, hence, the corresponding arrest lines due to stepwise fracture disappeared on the fracture surfaces of these samples that failed by a ductile mode. In addition, the values of (CC- BB)/(AA-CC) are less than or equal to about 0.3 for all samples that failed in the brittle region, and these values are only about 20-30% of those of samples that failed in the ductile region. Finally, an equation was developed to predict t, of SBPEs that failed in ductile and brittle regions in terms of stress intensity, branch length and other material and experimental constants. The agreement of measured t , values with those predicted by this equation is within about +25%.

3368 J. Yeh, W.3. Lee

The authors express their appreciation to the National Science Council (Grant NSC 81-0405-E011-536) and the Industrial Development Bureau for support of this work. Thanks are also extended to Mr. C. H. Hsu, Miss I: C Cheng and Mr. Yu-Lung Lin for their assistance in the preparation of this manuscript.

I ) J. T. Yeh, C. Y. Chen, H. S. Hong, 1 Muter. Sci. 29, 4104 (1994) ’) N. Brown, X. Lu, Y. Huang, R. Qian, Makromol. Chem., Macromol. Symp. 41, 55

3, X. Lu, N. Brown, .I Muter. Sci. 25, 411 (1990) 4, X. Lu, R. Qian, N. Brown, J. Muter. Sci. 26, 917 (1991)

X. Lu, N. Brown, 1 Muter. Sci. 26, 612 (1991) 6, Y. L. Huang, N. Brown, J. Muter. Sci. 23, 3648 (1988) ’) X. Lu, N. Brown, 1 Muter. Sci. 21, 2423 (1986) *) N. Brown, J. Donofrio, X. Lu, Polymer 28, 1326 (1987) ’) A. Lustiger, R. D. Corneliussen, 1 Muter. Sci. 22, 2470 (1987)

lo) N. Brown, X. Lu, Y. L. Huang, R. Qian, Makromol. Chem., Macromol. Symp. 41,55

(1991)

(1991) Y. L. Huang, N. Brown, J. Polym. Sci., Part B: Polym. Phys. 29, 129 (1991)

”) J. T. Yeh, J. H. Chen, H. S. Hong, 1 Appl. Polym. Sci. 54, 2171 (1994) 13) J. T. Yeh, H. S. Hong, Macromol. Chem. Phys. 196, 705 (1995) 14) M. De Pooter, P. B. Smith, K. K. Dohrer, K. F. Bennett, M. D. Meadows, C. G. Smith,

15) J. D. Hoffman, G. T. Davis, J. I. Launtzen, “Treatise on Solid State Chemistry”, Vol. 3,

16) N. Brown, I. M. Ward, 1 Muter. Sci. 18, 1405 (1983) 17) J. L. Bassani, N. Brown, X. Lu, Znt. 1 Fract. 38,43 (1988) Is) R. Popli, M. Glotin, L. Mandelkern, J. mlym. Sci., Polym. Phys. Ed. 22, 407 (1984) 19) R. H. Boyd, Polymer 26, 1123 (1985) m, Y. P. Khanna, E. A. Turi, T. J. Taylor, V. V. Vickroy, R. F. Abbot, Macromolecules 18,

’I) D. R. Saini, A. V. Shenoy, Polym. Commun. 26, 50 (1985)

u, D. E. Kline, J. A. Saver, A. E. Woodward, 1 Polym. Sci. 22, 455 (1956)

H. P. Schouwenarrs, R. A. Geerards, 1 Appl. Polym. Sci. 42, 399 (1991)

Plenum Press, New York 1975

1302 (1985)

F. C. Stehling, L. Mandelkern, Macromolecules 3, 242 (1970)

L. E. Nielson, “Mechanical Properties of Polymers’: Reinhold, New York,

25) S. D. Clas, D. C. McFaddin, K. E. Russell, 1 Polym. Sci., PartB: Polym. Phys. 25, 1057

%) N. G. McCrum, B. E. Read, G. Williams, ‘Xnelastic and Dielectric Effect in Polymeric

pp. 180- 182, 209-210 (1962)

(1987)

Solids”, Wiley, New York 1967

ductile-brittle transition behavior of short-chain branched polyethylenes at 80°c

Documents