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Determination of fracture toughness in rubber modified glassy polymers under impact conditions.

INTRODUCTION

The use of polymers is expanding into new fields and ever greater performance is demanded, especially on exposure to high strain rate. The measurements and analysis of the impact properties of polymers are still a controversial subject. The amount of energy absorbed by the polymer during impact depends on many variables, such as sample geometry, test temperature, impact velocity, and striker shape; relatively minor changes in any of these factors may induce the material to undergo a brittle-ductile transition. (1-3)

Conventional Izod and Charpy impact tests The Charpy impact test is a standardized high strain-rate test which determines the amount of energy absorbed by a material during fracture. This absorbed energy is a measure of a given material's toughness and acts as a tool to study brittle-ductile transition.  involve the measurement of the energy to break a notched specimen, generally divided by the ligament ligament (lĭg`əmənt), strong band of white fibrous connective tissue that joins bones to other bones or to cartilage in the joint areas. The bundles of collagenous fibers that form ligaments tend to be pliable but not elastic.  area. It is well known that such an analysis is not satisfactory, particularly since the parameter has a strong geometry dependence and doesn't provide a measurement of a critical initiation parameter. Fracture mechanics Fracture mechanics is a method for predicting failure of a structure containing a crack. It uses methods of analytical Solid mechanics to calculate the driving force on a crack and those of experimental Solid mechanics to characterize the material's resistance to fracture.  theory provides the necessary theoretical framework to overcome these disadvantages. However, to employ this theory under impact conditions is not simple, because of dynamic effects, and because it requires sophisticated acquisition data instrumentation. That is one reason why industry does not usually incorporate fracture analysis as a routine test.

Several methods have been developed for the analysis of impact data depending on whether the material undergoes brittle (jargon) brittle - Said of software that is functional but easily broken by changes in operating environment or configuration, or by any minor tweak to the software itself. Also, any system that responds inappropriately and disastrously to abnormal but expected external stimuli; e. , ductile ductile /duc·tile/ (duk´til) susceptible of being drawn out without breaking.

duc·tile
adj.
Easily molded or shaped.



ductile

susceptible of being drawn out without breaking.
 (3), or some intermediate mode of fracture. In our view, in aiming to change industry habits, the most appealing approaches are those that put the fracture mechanics problems in terms of energy rather than in terms of the maximum load. These methods involve the measuring of the energy consumed in the impact fracture by a pendulum impact machine, and the use of Charpy or Izod type specimens with sharp notches to suit the requirements of fracture mechanics. Early test programs demonstrated the utility of the approach when applied to brittle fracture (4-10). Data from these programs of work showed that for brittle fracture behavior, a basically linear relationship exists between the impact fracture energy and the specimen dimension and compliance function BW[Phi] (11). The slope of this relationship defines the critical strain energy release rate [G.sub.c] for unstable fracture. This assumption cannot be made where similar tests are carried out on materials showing nonlinear-elastic behavior. As Hodgkinson proposed (11), the fracture energy measured by an impact pendulum is a combination of crack initiation and propagation The transmission (spreading) of signals from one place to another.  energies, including any energy to deform the material.

ABS (Automatic Backup System) See backup program.  (acrylonitrile-butadiene-styrene) and HIPS (butadiene butadiene (byt'ədī`ēn), colorless, gaseous hydrocarbon. There are two structural isomers of butadiene; they differ in the location of the two carbon-carbon double bonds in the  rubber-modified polystyrene polystyrene (pŏl'ēstī`rēn), widely used plastic; it is a polymer of styrene. Polystyrene is a colorless, transparent thermoplastic that softens slightly above 100°C; (212°F;) and becomes a viscous liquid at around 185°C; ) are well-known rubber-modified thermoplastics. The most important characteristics of these multiphase Mul´ti`phase

a. 1. (Elec.) Having many phases;

Adj. 1. multiphase - of an electrical system that uses or generates two or more alternating voltages of the same frequency but differing in phase angle
 products are the molecular weight of the matrix; phase-volume ratio; type of particle, particle size Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. , and size distribution; interfacial bonding; and rubber crosslink density. Different combinations of these properties will lead to materials exhibiting different behaviors. Under the testing conditions used in this paper, all materials displayed nonlinear A system in which the output is not a uniform relationship to the input.

nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input.
 ductile behavior, with the sole exception of one modified polystyrene that displayed semiductile behavior.

Different approaches have appeared in the literature to provide an answer to the problem of testing materials exhibiting nonlinear effects: the elastic corrected method and [J.sub.c] analysis (1). The applicability of these methods to polymers has been questioned, and new approaches have been proposed (2, 3) that will also be considered in this paper.

These investigations aim to analyze the applicability of simple indirect methods for determining the impact fracture toughness In materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications.  of ductile polymers on ABS and modified PS and to compare the equivalence between the different critical parameters calculated from those methods.

EXPERIMENTAL

Materials

Four commercial grade materials have been investigated: two injection grade ABS type resins, mainly differing in rubber content (Monsanto Lustran ABS 240 and Lustran ABS 740); and two rubber-modified polystyrenes (PS) (Monsanto Lustrex 2220, medium impact, and Lustrex 4300, high impact), which also mainly differ in the rubber content. (Materials were kindly provided by Unistar Argentina S Argentina (ärjəntē`nə, Span. ärhāntē`nä), officially Argentine Republic, republic (2005 est. pop. 39,538,000), 1,072,157 sq mi (2,776,889 sq km), S South America. .A.)

Pellets of ABS resins were dried at 85 [degrees] C for 2 h under vacuum and then compression molded at 190 [degrees] C into thick plates 5, 6, 11 and 16 mm thick. Pellets of modified PS resins were dried at 65 [degrees] C for 2 h under vacuum and then compression molded at 180 [degrees] C into thick plates 5 and 6 mm thick. To release the residual stresses Residual stresses are stresses that remain after the original cause of the stresses (external forces, heat gradient) has been removed. They remain along a cross section of the component, even without the external cause.  generated during molding, all plaques were submitted to a post-molding thermal treatment Thermal treatment is a term given to any waste treatment technology that involves high temperatures in the processing of the waste feedstock. This commonly, although not exclusively involves the combustion of waste materials.  in which the samples were kept for 1 h at 120 [degrees] C for ABS and at 110 [degrees] C for PS under a slight pressure, and then slowly cooled to room temperature within the oven.

Ultrathin sections ul·tra·thin section
n.
See thin section.
 of compression molded specimens stained by Os[O.sub.4] were examined by transmission electron microscopy “TEM” redirects here. For other uses, see TEM (disambiguation).

Transmission electron microscopy (TEM) is an imaging technique whereby a beam of electrons is transmitted through a specimen, then an image is formed, magnified and directed to appear either
 (TEM TEM

1. transmission electron microscope.

2. triethylenemelamine.

3. transmissible encephalopathy of mink.
), and the numerical average diameter of the rubber subinclusions was calculated from the micrographs by means of a processing image PC software. ABS displayed a unimodal Adj. 1. unimodal - having a single mode
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
 rubber-particle distribution while HIPS displayed a bimodal bi·mod·al  
adj.
1. Having or exhibiting two contrasting modes or forms: "American supermarket shopping shows bimodal behavior
 submicron rubber-particle distribution.

Table 1 and Table 2 display the materials' molecular and morphological mor·phol·o·gy  
n. pl. mor·phol·o·gies
1.
a. The branch of biology that deals with the form and structure of organisms without consideration of function.

b.
 data and conventional mechanical properties, respectively.

Impact Fracture Measurements

Impact experiments were carried out using a conventional ASTM ASTM
abbr.
American Society for Testing and Materials
 D 256 non-instrumented Charpy Pendulum Instrument at an impact velocity of 3.5 m/s at 23 [degrees] C and at 80 [degrees] C. In the experiments carried out at 80 [degrees] C, ABS specimens were simply preheated in an oven at the desired temperature for at least 20 min and then quickly placed in the pendulum grips and impacted immediately.

Bars for impact characterization were cut from the compression molded plaques and then machined to reach the final dimensions and improve edge surface finishing Surface finishing is used to describe a number of industrial processes that can be applied to improve the surface of a manufactured item. The major reason to apply these processes is to improve appearance, improve adhesion or ink wettability, corrosion protection, wear resistance and . Tests were performed on samples with two different span lengths: 57 and 95 mm.

Sharp notches were introduced by scalpel-sliding a razor blade ra·zor·blade also ra·zor blade  
n.
A thin sharp-edged piece of steel that can be fitted into a razor.

razor blade nhoja de afeitar

razor blade 
 having an on-edge tip radius Tip radius is the radius of the circular arc used to join a side-cutting edge and an end-cutting edge in gear cutting tools. Edge radius is an alternate term.1

Notes
1. ANSI/AGMA 1012-G05, "Gear Nomenclature, Definition of Terms with Symbols".
 of 13 [[micro]meter]. The notch depth (a/W) was varied from 0.1 to 0.9. The thickness-to-depth ratios (B/W B/W Black and White
B/W Between
B/W be with
B/W Bundled With
B/W Backed With (recording industry)
B/W backwash
B/W B-Wing (Star Wars)
B/W Back of Walk
) were 0.5 and 1. For Lustran ABS 240 and for Lx 2220 resins, "V" and "U" side-grooved specimens were also tested. The reduction of thickness was 20% and the angle of "V" side grooves was 45 [degrees].

The impact fracture energy was taken directly from the scale on the machine. The energy values reported here were corrected by kinetics kinetics: see dynamics.
Kinetics (classical mechanics)

That part of classical mechanics which deals with the relation between the motions of material bodies and the forces acting upon them.
 effects using the following equation:

[Mathematical Expression A group of characters or symbols representing a quantity or an operation. See arithmetic expression.  Omitted]

where g is the acceleration due to gravity Acceleration due to gravity can refer to:
  • Gravitational acceleration, the acceleration due to the gravitational attraction of massive bodies, in particular that due to the Earth's gravity
  • Standard gravity, or g
, h is the height of fall (12), U[prime] is the uncorrected energy displayed by the instrument, and [K.sup.e] is the kinetic energy kinetic energy: see energy.
kinetic energy

Form of energy that an object has by reason of its motion. The kind of motion may be translation (motion along a path from one place to another), rotation about an axis, vibration, or any combination of
 of the falling mass.

RESULTS AND DISCUSSION

Fracture Propagation Modes

Rubber toughening is one of the most successful methods of modifying the properties of brittle polymers. [TABULAR tab·u·lar
adj.
1. Having a plane surface; flat.

2. Organized as a table or list.

3. Calculated by means of a table.



tabular

resembling a table.
 DATA FOR TABLE 1 OMITTED] Toughening mechanisms include crazing craze  
v. crazed, craz·ing, craz·es

v.tr.
1. To cause to become mentally deranged or obsessed; make insane.

2. To produce a network of fine cracks in the surface or glaze of.

v.
 and shear yielding, both of which involve localized deformation deformation /de·for·ma·tion/ (de?for-ma´shun)
1. in dysmorphology, a type of structural defect characterized by the abnormal form or position of a body part, caused by a nondisruptive mechanical force.

2.
 of the brittle matrix associated with stress concentrations initiated by the rubber inclusions. Dispersed dis·perse  
v. dis·persed, dis·pers·ing, dis·pers·es

v.tr.
1.
a. To drive off or scatter in different directions: The police dispersed the crowd.

b.
 rubber particles toughen the matrix mainly by promoting multiple crazing in PS and by inducing an extensive combined crazing and yielding in SAN.
Table 2. Materials Conventional Mechanical Properties.


                    Impact Strength      [[Sigma].sub.y]       E
Material             (KG/[m.sup.2])         (MPa)            (MPa)


Lustran ABS 240         5.3                  47.5            2859.5
Lustran ABS 740        20.7                  27.1            1823.4
Lustrex 2200            4.9                  21.9            2608.1
Lustrex 4300            8.2                  20.6            1936.7


The presence of ductile fracture may be determined by the naked eye from the appearance of the fracture surface. The surface exhibits a whitening whit·en·ing  
n.
1. An agent used to make something white or whiter.

2. The act or process of making white or whiter.

Noun 1.
 effect or becomes bright, reflecting light, due to craze formation (13). Another behavior was reported by Vu-Khanh and De Charentenay (2), a complex mode of fracture combining stable and unstable crack propagation mode: fracture initiates in a stable manner and at some point becomes unstable. They called it "semi-ductile" behavior. In these cases the fracture surfaces have different zones: shiny zones interspersed with dull zones. Figures 1a and b show macrophotos of typical fracture surfaces of ABS 240 and HIPS samples, respectively. Consistent with other authors' findings (1), all the broken samples appeared completely stress whitened, suggesting stable propagation. The surfaces of the broken samples of medium impact polystyrene, shown in Fig. 1c, exhibited a typical combined stable and unstable crack propagation mode displaying shiny and dull zones.

Wu (14) stated that the brittle-ductile (craze-yield) behavior of polymers and blends depends on both extrinsic EVIDENCE, EXTRINSIC. External evidence, or that which is not contained in the body of an agreement, contract, and the like.
     2. It is a general rule that extrinsic evidence cannot be admitted to contradict, explain, vary or change the terms of a contract or of a
 and intrinsic variables. Extrinsic variables include rate, temperature, stress state, notch, and specimen geometry. Intrinsic variables include phase morphology morphology

In biology, the study of the size, shape, and structure of organisms in relation to some principle or generalization. Whereas anatomy describes the structure of organisms, morphology explains the shapes and arrangement of parts of organisms in terms of such
 and chain structure. Under a given extrinsic condition, different polymers or blends behave differently, because they have different chain structures and phase morphologies. The maximum responsiveness of a brittle polymer to rubber toughening occurs at an entanglement density close to 0.1 mmol/[cm.sup.3] in the matrix (14). In this range of entanglement density (such as SAN) the matrix can undergo massive combined crazing and yielding, as induced by rubber particles. In contrast, rubber particles mainly promote multiple crazing in brittle polymers having entanglement density [much less than] 0.1 mmol/[cm.sup.3] (such as PS).

The two rubber-modified polystyrenes investigated here displayed submicron particle diameters, which has been reported to be inefficient in toughening (15). However, Keskkula (16) reviewed the role of submicron particles in toughening in PS, reporting excellent impact strength in HIPS with bimodal rubber particle distribution and with the majority of the particles below the minimum critical rubber particle-size diameter. He suggested that a high concentration of small particles (small interparticle distance) controls the growth and termination of crazes. The crazes are initiated at large particles, and the small particles control the ductile PS ligament thickness in the fracture zone A fracture zone is a linear oceanic feature--often hundreds, even thousands of kilometers long--resulting from the action of offset mid-ocean ridge axis segments. They are a consequence of plate tectonics.  by a cooperative mechanism.

In light of the above discussion, the semiductile-ductile transition, which modified polystyrene has undergone through these investigations, may be justified in terms of the presence of a critical interparticular distance mainly associated with the difference in rubber content between Lustrex 2220 and 4300.

Data Analysis

Data points were analyzed following the different procedures proposed in the literature depending on the type of fracture exhibited by the materials, ductile or semiductile.

Ductile fracture with a stable crack propagation occurs with a continuous supply of energy from the striker to the specimen. Ductile effects during fracture, as suggested by Hodgkinson (11), are stress whitening, surface distortion, or hinging. In such cases the fracture energy measured by an impact pendulum is a combination of crack initiation and propagation energies. The latter includes any energy to deform the material. Regarding "semiductile" behavior, Vu-Khanh and De Charentenay (2) proposed that in the first zones the propagation of the crack is stable, that is, it develops on the basis of a continuous supply of additional energy from the external forces. In the second zone type, the fracture is unstable and the crack speed is very high in relation to that of the hammer. Fracture occurs with the aid of the strain energy stored in the sample.

Plati and Williams, corrected elastic method (1):

In the case of completely elastic behavior, the critical strain energy release rate [G.sub.c] can be expressed as follows (1):

[G.sub.c] = U/C U/C Under Construction
U/C Upper Case
U/C unit cost (US DoD)
U/C upconverter (US DoD)
U/C Unapplied Cash
 dC/dA (2)

where C is the compliance of the specimen, U is the energy absorbed by the specimen during fracture, and A is the ligament area: B.(W - a). The factor C/(dC/d(d(a/W))) = [Phi], which depends on the length of crack size of the sample, can be calculated from the following equation (17):

[Phi] = [integral of] [Y.sup.2](x) xdx/[Y.sup.2](x)x + 1/18W 1/[Y.sup.2](x) x (3)

Y is computed from the equation given by Williams (18):

Y = [summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument)  of] An[(a/W).sup.n] where 0 to 4

When the effects of plastic yielding are not negligible, Plati and Williams (1) proposed that LEFM LEFM Linear Elastic Fracture Mechanics  could be extended by using an effective crack length, [a.sub.f] = a + [r.sub.p], where a is the original crack length and [r.sub.p] is the plastic zone length; [r.sub.p] is obtained iteratively by varying its value to give the best linear fit to the U vs. BW[Phi] plot.

The polynomial polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a  coefficients for the span-to-width ratios (S/W See software. ) used here were interpolated interpolated /in·ter·po·lat·ed/ (in-ter´po-la?ted) inserted between other elements or parts.  from the corresponding ones for S/W equal to 8 and 4 tabulated in Williams (18).

Plati and Williams, J analysis method:

Plati and Williams (1) also made a parallel proposal that under fully yielding conditions, as the elastic analysis is not still valid, the concept of [J.sub.c] should be used. In bending, [J.sub.c] can be determined as the double of the slope of the plot of the energy absorbed in the fracture U vs. the cross-sectional area of the ligament behind the notch, B.(W - a).

[J.sub.c] = 2U/B(W - a) (5)

For this expression to be valid, the energy absorbed, U, is that appropriate to the onset of crack propagation, which is not necessarily that under the complete load-deflection curve since this may represent extensive crack propagation (19).

Method of Vu-Khanh and De Charentenay:

Vu-Khanh and De Charentenay (2) proposed a model for the combined mode of fracture, called "semiductile."

They assumed that the fracture process takes place as ff there was only one stable crack propagation zone ([A.sub.1]), afterward af·ter·ward   also af·ter·wards
adv.
At a later time; subsequently.

Adv. 1. afterward - happening at a time subsequent to a reference time; "he apologized subsequently"; "he's going to the store but he'll be back here
, the remaining fractures are entirely brittle. The energy balance is therefore:

U = [G.sub.st][A.sub.1] + [G.sub.inst]BW[[Phi].sub.1] (6)

where [[Phi].sub.1] is [Phi] evaluated at the instability and [G.sub.st] is the mean value of the energy absorbed during the stable stage of propagation, obtained under the assumption that the variation in [G.sub.c] during stable propagation is linear.

From a plot of (U/[A.sub.1]) vs. (BW[Phi]/[A.sub.1]), [G.sub.st] and [G.sub.inst] can be obtained from the intercept intercept

in mathematical terms the points at which a curve cuts the two axes of a graph.
 and the slope of this straight line, respectively.

Vu-Khanh's method:

Recently, Vu-Khanh (3) proposed a new model for ductile impact fracture, assuming that the fracture energy [G.sub.r] varies linearly with crack extension following the expression:

[G.sub.r] = [G.sub.i] + [T.sub.a]A (7)

where [G.sub.i] is the fracture energy at crack initiation and [T.sub.a] is a material constant equivalent to the material tearing modulus See modulo.  that describes stable crack propagation.

The fracture energy, [G.sub.i], can be obtained from the U/A U/A
abbr.
urinalysis
 vs. A plot at the intercept of the curve.

ABS at Room Temperature

Hodgkinson (11) applied the elastic corrected method to highly ductile materials, proposing that ductile effects stem from plane stress, finding a certain dependence upon thickness in the measurements that supported his hypothesis. Figure 2 shows ABS 240 energy data points, corrected by plastic radius, against BW[Phi] obtained for samples having different thicknesses, with and without sidegrooves and tested with two different spans.

Figure 3 shows ABS 240 and 740 energy data fitted against ligament area. The linear correlation was found to be good.

Table 3 shows [r.sub.p] that leads to the best linear fit, the corresponding [G.sub.c] value; [J.sub.c] value and the correlation coefficients Correlation Coefficient

A measure that determines the degree to which two variable's movements are associated.

The correlation coefficient is calculated as:
 obtained for each analysis.

For both fittings, the results appeared to be independent of the B/W ratio and the span used as shown in Figs. 2 and 3. The critical initiation values calculated from the elastic corrected method are larger than that obtained from J method.

Results seem to have no influence of thickness, suggesting a plane strain condition at the crack tip; as confirmed by the minimum dimension calculated from ASTM E813 plain strain thickness requirements:

B, W - a [greater than] = 25([J.sub.c]/[[Sigma].sub.y]) (8)

assuming that [[Sigma].sub.y] in impact is equal to 80 MPa (this value was calculated by extrapolation (mathematics, algorithm) extrapolation - A mathematical procedure which estimates values of a function for certain desired inputs given values for known inputs.

If the desired input is outside the range of the known values this is called extrapolation, if it is inside then
 at 3.5 m/s of the Eyring equation The Eyring equation in chemical kinetics relates the reaction rate to temperature. It was developed by Henry Eyring. This equation follows from his transition state theory and contrary to the empirical Arrhenius equation this model is theoretical.  from [[Sigma].sub.y] values measured at different crosshead cross·head  
n.
A beam that connects the piston rod to the connecting rod of a reciprocating engine.

Noun 1. crosshead - a heading of a subsection printed within the body of the text
crossheading
 displacements).

Consistent with Newman's findings, our results were independent of the span, suggesting no rate effects at the testing conditions used here (20).

As shown in Table 3, [J.sub.c] increases with rubber content, consistent with the idea that at these rubber contents no important overlapping effects of stress fields are present. Dynamic [J.sub.c] appeared extremely higher than the ones obtained in static conditions (21).

ABS 240 data points were also fitted following Vu-Khanh's recommendations (3), [ILLUSTRATION FOR FIGURE 4 OMITTED]. In a later paper (22), Mai criticized some aspects of Vu-Khanh's model, stating that his model is equivalent to the "essential work of fracture" method, first developed by Broberg (23). This theory (24) was originally designated for plane stress ductile fracture of metals. For ductile materials with appropriate ligament length, the ligament will undergo full necking before crack initiation. Under this assumption, [W.sub.f] is the total work to fracture the specimen, We is the work for crack to growth inside the end zone, and [W.sub.p] is the work for plastic deformation plastic deformation,
n any irreversible deformation of tissues.
 that is not necessary condition for crack growth. In such conditions, for a given thickness, only the intercept value at A = 0, [W.sub.e], results to be a real material property, while [Beta]. [W.sub.p] is dependent on geometry. Cotterell (25) stated that We is equal to [J.sub.c], and the state of plane stress may arise from the usual size requirements for plain strain (Eq 8).

In the extreme case in which the plastic contribution [W.sub.p] is negligible respect to the "crack growth" work, if [W.sub.e] exists, it would be expected that Vu-Khanh's plots or "essential work of fracture" lead to a constant U/A value with respect to ligament area.

However, as it emerges from the results shown in Fig. 4, there is a decreasing trend between specific fracture energy and ligament area. Under impact bending conditions, the velocity of the crack varies during its propagation and the fracture energy cannot remain constant. Consequently, the concept of "essential work of fracture" does not appear to be applicable for the impact fracture characterization of rate-dependent materials like polymers.

[TABULAR DATA FOR TABLE 3 OMITTED]

The larger scatter scat·ter
v.
1. To cause to separate and go in different directions.

2. To separate and go in different directions; disperse.

3. To deflect radiation or particles.

n.
 found for data points [ILLUSTRATION FOR FIGURE 4 OMITTED] corresponding to small areas can be justified ff one considers that the absolute error in area determination is constant. This fact gives rise to an increasing relative error for small areas, which negatively affects the calculated U/A values.

Rubber Modified Polystyrene at Room Temperature

Figure 5 shows energy data points corrected by plastic radius against BW[Phi], and Fig. 6 shows energy data points vs. ligament area for Lustrex 4300 and Lustrex 2220. Critical values and statistics are displayed in Table 3.

In the case of the J method, the goodness of the fitting was excellent, and in the case of HIPS led to the same value of [J.sub.c] first published by Plati and Williams (1) for a high impact polystyrene of similar characteristics. Again, [G.sub.c] values were larger than [J.sub.c] ones, and large [r.sub.p] were necessary to reach an acceptable linear fitting. As an example, in the case of Lustrex 2220, Table 4 illustrates how the fitting is improved with the [r.sub.p] up to a maximum where the fit quality diminishes again. Obviously [G.sub.c] increased with the increase in [r.sub.p].

Figure 7 shows Vu-Khanh's plots for Lustrex 4300. The same considerations made with ABS are valid in this case.

For Lustrex 2220, as fracture surface revealed a semiductile behavior, data points were also fitted, following rigorously the method of Vu-Khanh and De Charentenay (2) Fig. 8. An acceptable fitting was found. Instability values resulted very close to the apparent [J.sub.c] value obtained without considering semiductile behavior. The [G.sub.inst] value that resulted was larger than the [G.sub.st] value. A similar result was reported by Vu-Khanh for PA11 (2) and was explained in terms of crack tip blunting before unstable crack propagation.

Consistent with fracture surface observations denoting a transition in the propagation mode, independently of the method used to evaluate the initiation criterion chose, a clear increasing trend with the rubber content was verified.
Table 4. [G.sub.c] as a Function of Plastic Radio for LX 2220.


[r.sub.p]                [G.sub.c]
mm                     mJ/[mm.sup.2]           [r.sup.2]


0.0                          6.2                0.8831
1.0                          8.6                0.9762
2.0                         10.3                0.9932
2.2                         10.6                0.9943
2.3                         10.8                0.9947
2.4                         10.9                0.9950
2.5                         11.1                0.9952
2.6                         11.3                0.9953
2.7                         11.4                0.9952
3.0                         11.9                0.9947


ABS Data at 80 [degrees] C

In room temperature tests, the extent of the craze whitening zone outside the process zone was inappreciable in·ap·pre·cia·ble  
adj.
Too small to be noticed or make a significant difference; negligible: inappreciable fluctuations in temperature.
, while in the tests at higher temperatures, with the same characteristics stated before (17) a larger plastic zone appeared.

We assayed Lustran ABS 240 and 740 at 80 [degrees] C; the plots of energy data points against ligament area are shown in Fig. 9. In contrast to the findings of Newman and Williams (20), no negative intercept was found, even if the plastic zone depth was of the same order of penetration reported by these authors. The J method still showed a good correlation coefficient.

CONCLUDING REMARKS

The applicability of simple indirect methods for determining the impact fracture toughness of ductile polymers was analyzed with several commercial rubber modified thermoplastics (two injection grade ABS type resins and two rubber modified polystyrenes).

ABS and high impact polystyrene samples exhibited a whitening effect due to craze formation through the whole fracture surface, indicating that stable crack propagation was occurring. Medium impact polystyrene, however, exhibited a combined stable and unstable crack propagation mode, displaying shiny and dull zones on the surfaces of the broken samples.

Linear fittings between energy and ligament area (J method) always displayed high correlation coefficients.

The elastic corrected method gave somewhat complicated results because of the iterative it·er·a·tive  
adj.
1. Characterized by or involving repetition, recurrence, reiteration, or repetitiousness.

2. Grammar Frequentative.

Noun 1.
 calculations necessary to find [r.sub.p]. Relatively large [r.sub.p] values were calculated, leading to high critical values ([G.sub.c]).

The J method provides more conservative critical values than the elastic corrected method, especially at high toughness levels. This latter statement has serious implications for safety engineering design. However, both methods predict the same qualitative trends against rubber content.

At room temperature, plain strain conditions were always met. Results were independent of thickness and span-to-depth ratio.

For materials displaying ductile fracture, the essential work of fracture was also tried. Results suggested a rate effect that impeded im·pede  
tr.v. im·ped·ed, im·ped·ing, im·pedes
To retard or obstruct the progress of. See Synonyms at hinder1.



[Latin imped
 the application of the essential work of fracture under impact conditions in bending.

The "semiductile" model of Vu-Khanh and De Charentenay (2) fitted Lustrex 2220 data points reasonably well. Instability values resulted that were very close to the apparent [J.sub.c] (2) value obtained in a simpler manner, without considering semiductile behavior.

Regarding studies carried out at 80 [degrees] C, the d method still accurately fit data points; showing a trend toward an increase in critical initiation value with the increase in temperature. Even if under this last condition the materials showed a considerable plastic zone, data points did not exhibit a negative intercept in the energy vs. ligament area plots. Therefore, the Williams' method (26) was inapplicable in·ap·pli·ca·ble  
adj.
Not applicable: rules inapplicable to day students.



in·ap
.

Further work will be done to determine impact J-R curves and initiation values by measuring J vs [Delta] a. This will allow us to compare the actual critical values with the ones obtained by indirect methods.

REFERENCES

1. E. Plati and J. G. Williams, Polym. Eng. Sci., 15, 470 (1975).

2. T. Vu-Khanh and F. X. de Charentenay, Polym. Eng. Sci., 25, 841 (1985).

3. T. Vu-Khanh, Polymer, 29, 1979 (1988).

4. J. G. Williams in Fracture Mechanics of Polymers, p. 237, Ellis Horwood, London (1984).

5. G. P. Marshall, J. G. Williams, and C. E. Turner, J. Mater. Sci., 8, 949 (1973).

6. M. Bramuzzo, Polym. Eng. Sci., 29, 1077 (1989).

7. C. E. Turner, Mater. Sci. Eng., 11, 275 (1973).

8. Y. Nakamura, M. Yamaguchi, and M. Okubo, Polym. Eng. Sci., 33, 279 (1993).

9. R. Greco and G. Ragosta, J. Mater. Sci., 23, 4171 (1988).

10. S. W. Koh, J. K. Kim, and Y. W. Mai, Polymer, 34, 3446 (1993).

11. J. M. Hodgkinson, K. H. L. Chow and J. G. Williams, 8th Intern intern /in·tern/ (in´tern) a medical graduate serving in a hospital preparatory to being licensed to practice medicine.

in·tern or in·terne
n.
. Conf Deform. Yield Fracture Polymers, 43/1, Churchill College, Cambridge, U.K. (April 1991).

12. D. R. Ireland, Instrumented Impact Testing, ASTM-STP 563, p. 7 (1973).

13. C. B. Bucknall, Plast., November 1967, 118.

14. S. Wu, Polym Intern, 29, 229 (1992).

15. C. B. Bucknall in Toughened Plastics, Applied Science, London (1977).

16. H. Keskkula, "Optimum Rubber Particle Size in High-Impact Polystyrene: Further Considerations," in Rubber-Toughened Plastics, C. K. Riew, Am. Chem. Soc. Series 12, 290 (1989).

17. J. G. Williams, in Fracture Mechanics of Polymers, p. 69, Ellis Horwood Limited, London (1984).

18. J. G. Williams, in Fracture Mechanics of Polymers, p. 67, Ellis Horwood Limited, London (1984).

19. A. J. Kinloch and R. J. Young in Fracture Behavior of Polymers, p. 196, Applied Science Publishers Ltd., England (1983).

20. L. V. Newman and J. G. Williams, Polym. Eng. Sci., 18, 893 (1978).

21. C. R. Bernal and P. M. Frontini, Polym. Testing, 11, 271 (1992).

22. Y.-W. Mai, Polymer Commun., 36, 330 (1989).

23. K. B. Broberg, J. Mech. Phys. Solids, 23, 215 (1975).

24. Y.-W. Mai and B. Cotterell, Int. J Fracture, 32, 105 (1986).

25. B. Cotterell and J. K. Reddel, Int. J. Fracture, 13, 267 (1977).

26. J. G. Williams, in Fracture Mechanics of Polymers, p. 262, Ellis Horwood Limited, London (1984).
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Author:Bernal, Celina R.; Frontini, Patricia M.
Publication:Polymer Engineering and Science
Date:Nov 15, 1995
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