High-Speed fracture mechanics by photography of polypropylene copolymers

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  • High-speed Fracture Mechanics by Photography of Polypropylene Copolymers


    Monted ison/Hirnont Centro Richerche Giulio N a t t a

    Ferrara. Italy The use of photography applied to stroboscopy in analyzing the processes

    inherent to the starting and propagation of cracks in materials is a technique which has proved to be of great interest, especially since it enables one to check and directly study the evolution of such phenomena. Using fracture mechanics criteria this technique has been applied to the study of the impact behavior of some polypropylene copolymers at different rubber contents obtained either by blending or by synthesis. This technique makes it possible to determine numerous parameters of fracture mechanics, including C.O.D. (crack opening displacement), C.O.A. (crack opening angle), JIc. the plastic work parameter, determined from the resistance curve R, tearing modulus, and crack propagation velocity. Further- more, under high strain rate conditions, the value taken on by the coefficient A relating the J-integral to C.O.D. ( 1 , 2) were checked for those materials using the equation J = X. uy.C.O.D., Hayes and Turner (3) and Boyle (4). From analysis of the materials it was possible to note that the synergetic effect of the EP (ethylene- propylene) rubber increased, especially when present at percentages of more than 10 percent. Annealing the materials, on the other hand, produced a n increase in fracture toughness for those products having a low rubber content; however it did not have any effect on those with an elevated rubber content (26 percent).


    3) 4) 5) 6)

    he use of polymeric materials is ever expanding T into new fields and ever greater performance is being demanded, especially in the field of high strain rate. Arising from the need to predict the processes which cause and propagate cracks in materials re- quiring great resistance reliability (i.e. metals), frac- ture mechanics can prove a valid support in the characterization of polymeric materials intended to withstand great deformation and absorb high impact energies. Little has been written in this field since most fracture mechanics or fracture propagation ve- locity measurements give less problems when per- formed at low strain rates.

    In the present work extremely impact resistant materials such as polypropylene copolymers have been analyzed following the high speed test fracture mechanics principles using two main approaches: crack opening displacement (C.O.D.) (5) and the J- integral (6). This has been done in order to evaluate toughness as a function of EP (ethylene-propylene) rubber content and to experimentally verify the reli- ability of the photographic detection technique by stroboscopy.


    Six polypropylene (PP) products were examined:


    Homopolymer Blend A = 95 percent PP + 5 percent EPR (ethylene-propylene rubber) Blend B = 90 percent PP + 10 percent EPR Blend C = 85 percent PP + 15 percent EPR Blend D = 74 percent PP + 26 percent EPR From synthesis copolymer = 74 percent PP + 26 percent EPR

    The physical properties of the base materials used to obtain these products are given in Table I while Table 2 reports the main physico-mechanical prop- erties according to the ASTM standards. The speci- mens were obtained from injection molded plates according to the diagram in Fig. 1.

    Tests were also performed on specimens which had undergone a 1 4OoC annealing process for 2 h in an oven.


    The machine used for this type of impact testing consisted of an instrumented falling weight which runs between two lateral guides and a support to house the specimen. The force-time curve was re- corded with the following apparatus (see Ffg. 2):

    0 PCB Piezoelectric power transducer with 500 N full

    0 PCB load amplifier (A) scale (FT)


  • M. Brarnuzzo

    Table 1. Physical characteristics ot the Base Materials. ~~~ ~

    Characteristics C.L..I--- in-. Polypropylene


    Polypropylene copolymer

    by synthesis cnlylwll=l rrdpylene

    rubber - - 4.5 g/10 min

    (230C/2.16 Kg) ASTM D1238 (230C/2.16 Kg)

    ASTM D1646 Intrinsic Viscosity (7) 2 dl/g at 135% 2.9 dllg at 135OC 2.1 dl/g at 135OC

    Molecular weight (Mw) . 1 0-3

    Melt flow rate 3.4 9/10 min I

    Mooney at 121 OC I 80 I

    42% I 300 GPC /

    Propylene content I

    Index of molecular weight (MwlMn) 6.9 4.5 I 470 light scattering

    obtained by gel permeation chro- matography

    Density 0.905 g/cm3 0.865 g/cm3 0.887 g/cm3 ASTM-DI 505 Tacticity index 96.6 isotactic insol- I I

    Crystallinity 58% I

    uble in boiling heptane

    X-ray analysis Cp = 14% c3 = 43%

    X-ray analysis

    Table 2. Physical Characteristics of Polypropylene Copolymers.

    Pohrprowlene -. . - Blend A Blend B Blend C Blend D copolymer

    Characteristics Method Unit Polwropy'ene 95% PP 90% PP 85% PP 74% PP by synthesis homopo'ymer 5% EPR iw0 EPR i50/~ EPR 26y0 EPR (26% Ethylene

    content) Melt flow rate (230C/2.16 Kg) Densitv

    ASTM 1238 g/10 min 3.4 3.1 2.9 2.8 2.4 4.5

    ASTM 1505 g/cm3 0.905 0.902 0.899 0.893 0.887 0.887 Notched lzod ASTM D-256 J/m 25 65 105 230 no break no break (23OC) Flexuial modulus ASTM 0-790 MN/m2 (23OC)

    1660 1600 1460 1330 1000 740

    Yield strength ASTM D-638 MN/m2 36 32 29 26 19 15 (23OC)

    0 Could transient storage oscilloscope OS4040 (TR) 0 Linseis pen recorder LY 18 100 (PR)

    The system set up by F. Polato (7) was used for photography and consisted of a Pentax MX camera (C), Gen Rad Stroboscope GR1538-A (SU), and Cam- era and stroboscope control unit (CSCU).

    As outlined in Fig. 2, this apparatus functioned as follows:

    Fig. 1 . Position for withdrawal of the specimen In respect to the plate injection direction.

    I 1 Fig. 2. Schematic diagram of set up of the apparatus to record impact testing and single or multipleflash photo- graphic detection.


    a) The hook freeing the fall weight, FW, is released b) The first switch, SW1, is turned on by passage of

    the magnetic bar, MR, linked to the falling weight and timer, T, is activated which, in turn, controls the electromagnet, E. The latter opens the camera diaphragm, C. Timer, T, serves to keep the camera diaphragm open for approximately 500 ms.

    c) The second switch, S2, is turned on by passage of the magnetic bar, MR, and the delay circuit, DT, for the strobe flash is activated.

    d) The falling weight hits the specimen making im- pact and the storage circuit of the transient re- corder-oscilloscope, TR, is activated by means of the power transducer, FT.

    e) The delay circuit, DT, simultaneously sends the flash activating signal to the stroboscope unit, SU, and the transient recorder-oscilloscope.


  • High-speed Fracture Mechanics by Photography of Polypropylene Copolymers

    f ) The impact force-time curve is recorded as well as the flash command and the image is recorded on film.

    The delay circuit, DT, (of the camera and the stro- boscope control unit, CSCU) is preset by means of a potentiometer in order to cut in the flash at the desired moment. Thus, the load level and image pho- tographed will coincide (see Fig. 3 ) .

    The CSCU unit is also able to emit signals in se- quence in order to produce the same number of flashes at times preestablished by the circuit PT; thus one may obtain several images in a single photogram (see Fig. 4 ) . The train of pulses is stopped by the digital counter, CT.

    An Apple I1 Plus personal computer with 48 Kbytes of memory was used to calculate and diagram the data obtained.

    Test geometry Three point bending geometry was used. Plane

    strain conditions theory (8) requires that the follow-


    1 ;!E FORCE-TIME Pretrigger time1


    U N I T

    X Fig. 3. Example of the force-time curve and single pulse to control the stroboscope unit (single image in the pho- togram).


    I Pretrigger time

    -~ X

    Fig. 4. Example of the force-time curve and multiple pulses controlling the stroboscope unit [different images in the same photogram).


    ing inequality be satisfied for specimen size:

    Jlc a, B , (W - a) -> a*- u flow

    where a = Crack length B W cr Jlc

    = Breadth of specimen cross-section = Height of specimen cross-section = Coefficient variable between 25 and 50 = Critical strain energy release rate in the

    plastic field o flow = (oy + uu)/2 uy = Yield strength u u = Tensile strength

    If one assumes a value of Jlc = 20 KJ/m2 and u flow = 60 MN/m2 (under impact conditions), and taking a = 25, the result of the inequality (Eq 1 ) is 8.3 mm. For polymeric materials, molding of plates with a thickness of more than 3 to 4 mm leads to a progressive increase in inhomogeneity with an in- crease in thickness. In fact, if the thickness is great, the difference between the cooling time on the sur- face of the material and within the sample will lead to different crystallization kinetics and thus to a different number and size of the spherulites within the thickness. This is likewise influenced by the type of material used.

    Keeping these problems in mind and considering that most injection molded polymeric items have a thickness on the order of 3 to 4 mm the following dimensions were chosen:

    B = 3.2 mm

    W = 1 5 m m

    a = 7.5 mm

    Notches, to a depth of 7 mm, were first made using a tool in accordance with the ASTM-D256 standard. A razor blade was then used to a depth of 0.5 mm. This was in agreement with the rules of fracture mechanics requiring the curve radius of the apex notch to tend toward 0.

    Other test conditions were as follows:

    Impact rate (Vo) = 2 m/s

    Span (S) = 60 mm

    S I W = 4


    Ftgures 5 and 6 exemplify the results obtained by application of the photographic technique to impact testing. The negatives of the photograms were en- larged by means of a slide projector in order to take measurements with the least possible margin of error.

    G & J measurements The procedure proposed by Landes and Begley (8)

    based on the method developed by Rice (10) for meas-


  • M. Brarnuzzo


    Fig. 5. Photographic sequence of the fracturing of Blend A. Impact speed 2 m/s at +23"C.

    urements on deeply cracked specimens was used to determine the J-integral:

    In the case of specimens notched on only one edge (SEN) and under three point bending conditions, hav- ing an a/ W ratio > 0.15 it has been demonstrated that the coefficient, 8. under plastic conditions is equal to 2. This is so, even when these specimens

    (2) 8 . A

    B(W - a) J =


  • High-speed Fracture Mechanics b y Photography of Polypropylene Copolymers

    200. 1

    Y 0 . e , Y

    11 timm hsl

    f ] Y b

    '2 timo h.1

    t4 tima (msl

    Fig. 6. Photographic sequence of the fracturing of the copolymer obtained from synthesis. Impact speed 2 mls at +23"C.

    have been analyzed at a span greater than 4 W and

    present case span = 4W and a / W = 0.5 have been

    A is the absorbed energy corresponding to a certain displacement. In the case of impulsive stress, calcu-


    lation has been made using the following equation when they have 0.45 c a / W c 0.65 (11). In the (12):

    used. A=U(l--&-) (3)

    where U is the impact energy which has not been


  • M . Bramuzzo

    corrected by the deceleration effect of the falling mass which takes place during impact:

    U = Vo s F ( t ) d t (4) In fact, the impact speed Vo taken into consideration in this equation is constant.

    K e = Yzm. Vo2

    (kinetic energy of the falling mass) (5)

    Vo = (impact speed at time to) (6) g = acceleration due to gravity

    h = height of fall

    Equat ion 2 was, thus, used to obtain the resistance curve (R) by plotting the J-integral as a function of the corresponding crack advancement, Aa.

    One must recall, as has been shown in a previous work (1 3). that under plane strain conditions the crack begins in the point of maximum specimen stress; that is, on the inside. It then proceeds main- taining a propagation front similar to the initial one. Therefore the effective Aa value will be the value revealed externally through photography plus the internal value within the specimen. In order to meas- ure the dimensions of the crack on the inside, some specimens of each material were subjected to impact with deflection preset by steel retainers. This was done so as to achieve slight, controlled advancement of the crack (13). Thereafter, the crack thus obtained was made more evident by staining the crack with red ink. The specimen was then opened (at the tem- perature of liquid nitrogen) thus making it possible to photograph the surfaces and take the necessary measurements.

    Figure 7 gives an example of what has been de- scribed above. Internal advancement of the crack was approximately 0.5 mm for almost all the mate- rials examined. In Fig. 8 an example of the J-integral trends is shown as a function of Aa for the nonan- nealed polypropylene obtained from synthesis and after annealing. The intersection point between the straight regression line of the experimental points and the blunting line (where J = 2uy. Aa) gives the Jlc value ( 13, 14).

    Another important parameter describing the ma- terials ability to resist crack propagation is the tear- ing modulus (1 4):

    dJ E da uy2

    T = -.- (7) This depends solely on the slope of curve R (dJ/da), on stiffness (modulus of elasticity, E ) and on tensile properties (yield strength, uy).

    Observing the JZc values and tearing modulus data reported in Table 3 one will note that annealing no longer exerts any influence over the materials with a high EP rubber content (26 percent). This is most likely because, after the morphological resettling due to annealing, the contribution of the polypropylenic

    a = a a by photography b=Aa inside the specimen

    c = a + b ( t r u e a a ) Fig. 7 . Example of the advancement front of the crack within a specimen.

    140 , 7

    I P o l y p r o p y l e n e C o p 0 l ymer [ b y s y n f hesisl

    0 1 2 3 4 5 6 7 Aa( m m 1

    Fig. 8. Resistance curve R with blunting line and regression line. non annealed specimen, A annealed specimen.

    matrix is of little relevance in comparison to the impact-resistant contribution of the rubber.

    In the equations used, it is of utmost importance that the modulus of elasticity be determined at the same strain rate as the impact tests. Since the poly-


  • High-speed Fracture Mechanics b y Photography of Polypropylene Copolymers


    CQ S'z-00

    mer is not perfectly elastic, but is rather a viscoelastic material, its mechanical properties change markedly with strain rate. This happens especially in deter- mining the modulus of elasticity [ 15). The technique for determining this parameter under dynamic con- ditions, small ball...


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