Printer Friendly

Fatigue crack propagation behavior of cellulose esters.

INTRODUCTION

Cellulose is an abundant, naturally occurring polymer found in the cell walls of all plants. It can be modified by relatively simple chemistry to form a variety of cellulose esters including cellulose acelate, cellulose propionate, and the mixed esters cellulose acetate-propionate and cellulose acetate-butyrate (1). A plasticizer such as dioctyl adipate is often added to the cellulose esters to improve their moldability. In most commercial systems, plasticizer concentration. as well as ester concentration and type, can have a dramatic effect on the mechanical properties of the cellulose ester. Cellulose esters are used for such diverse applications as toothbrush handles, tool handles, and eyeglass frames, where resistance to fatigue crack propagation (FCP) can be of critical importance. The objective of this work is to determine the effect of plasticizer concentration on FCP response of a particular cellulose ester, cellulose acetate-propionate.

EXPERIMENTAL

Sample Preparation

The cellulose acetate-propionate (CAP) used in this study was a product of Eastman Chemical Co., Kingsport. Tenn. The degrees of esterification (number of groups per glucose residue) for propionate, acetate, and hydroxy were 2.65, 0.1, and 0.25, respectively. The CAP was plasticized with dioctyl adipate at four loading levels. The plasticizer concentration, yield strength, and elastic modulus of each sample are listed in Table 1.

Compact tension specimens were machined from 6.2-mm-thick injection molded plaques. Two specimens were obtained from each plaque, as shown in Fig. 1. The specimen width, W, defined as the distance from the center of the loading pin holes to the back face of the specimen, was equal to 50.8 mm for all specimens used in this work. The specimens were notched with a band saw. The notch root was sharpened by tapping on a razor blade. The specimens were subsequently fatigue precracked prior to any data acquisition. The notch length, a, is defined as the distance from the center of the loading pin holes to the tip of the notch. All specimens were notched along the mold-flow direction.

Fatigue Tests

Fatigue tests were performed at room temperature on an MTS closed-loop servohydraulic testing machine using a sinusoidal waveform with a frequency of 1 Hz. The tests were conducted in load-control using a minimum-to-maximum load ratio of 0.1. Crack length was measured by computer using an elastic compliance technique. Crack length was related to the compliance by the following relationship

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [c.sub.o], [c.sub.1], [c.sub.2] [c.sub.3], [c.sub.4], and [c.sub.5] are compliance coefficients and [u.sub.x] is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where B is the specimen thickness, E is tensile modulus, and V/P is the slope of the load-displacement data recorded during the experiment. Displacement data were recorded using a clip gage mounted to the front face of the compact tension specimen. Compliance coefficients for this mounting geometry are given in Table 2.

Table 2. Compliance Coefficients (6)
[c.sub.0] 1.0010
[c.sub.1] -4.6695
[c.sub.2] 18.460
[c.sub.3] -236.82
[c.sub.4] 1214.9
[c.sub.5] -2143.6


Fatigue crack propagation rate per cycle, da/dN, was computed using an incremental polynomial method that fits a second-order polynomial to sets of seven successive data points. Details of this method can be found in ASTM Standard E647-91 (2). The stress intensity factor range for Mode I loading of a compact tension specimen is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where P is load and [alpha] equals a/W. FCP rate is plotted vs. [Delta] K according to the well-known Paris law, which is

da/dN = a [Delta] [K.sup.m] (4)

where A and m are constants (3)

Fractography

Fracture surfaces were examined by optical microscopy by using a Wild M400 optical microscope and by scanning electron microscopy by using a Cambridge Instruments Stereoscan 200 scanning electron microscope. Specimens were coated with a thin layer of gold in a sputtering chamber before the SEM observations. The accelerating voltage for the SEM observations ranged from 10 to 20 kV.

RESULTS AND DISCUSSION

Fatigue crack propagation rates for each CAP composition are plotted vs. stress intensity factor range in Fig. 2. The initial linear regime of each CAP composition falls on the straight line given by

log(da/dN) = 6.85log([Delta]K) - 1.66 (5)

Similarly, the final linear regime of each CAP composition falls on the straight line given by

log(da/dN) = 5.56log([Delta]K) - 2.88 (6)

For each composition, these two linear regimes are joined by a continuous curved transition regime. The location of the transition regime, however, varies with plasticizer content; as plasticizer concentration increases, the value of [Delta] K at the onset of the transition regime decreases.

These observations suggest that the mechanism that controls FCP in CAP changes as [Delta] K increases. An examination of the fracture surfaces confirms this hypothesis. A low magnification optical micrograph of the fracture surfaces of the four CAP compositions is shown in Fig. 3a. A sketch of a typical fracture surface is shown in Fig. 3b. Each fracture surface exhibits a V-shaped feature. The value of the crack length, and consequently the value of the [Delta] K, at the tip of the V-shaped feature decrease as plasticizer concentration increases. Thus, it is presumed that the linear regime of the FCP curve described by Eq 5 occurs to the left of the V-shaped feature (see Fig. 3b), the transition regime coincides with the development of the V-shaped feature, and the linear regime described by Eq 6 occurs after the V-shaped feature has fully formed.

At first glance, the area to the right of this V-shaped feature appears to be reminiscent of shear lip formation. Under plane stress conditions, the plane of the crack may assume a 45[degrees] angle relative to the xz- and xy-planes, creating so-called shear lips (see Fig. 1 for definition of axes). Under plane strain conditions, the plane of the crack remains in the xz-plane. Shear lip width, D, then, is a function of the prevailing stress conditions at the crack tip and can be related to the plane stress plastic zone radius, [r.sub.y], by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [omega] is the yield strength (4, 5). According to Eq 7, shear lip width increases with increasing stress intensity and crack length (see Fig. 5). Using the value of [Delta] K at the tip of the V-shaped feature, where D should equal B/2 = 3.1 mm, the value of D for each CAP composition was calculated from Eq 7 and is listed in Table 3. It is clear from Table 3 that Eq 7 severely underestimates the size of the "apparent" shear lips.

In addition, the fracture surfaces shown in Fig. 3 differ distinctly from typical shear lip formation in that the plane of the crack remains in the xz-plane both to the left and to the right of the V-shaped feature. This is clearly illustrated in Fig 4. A specimen was sectioned in the yz-plane, mounted in epoxy, and metallographically polished. The specimen was tilted slightly in the micrograph to reveal the V-shaped feature. The arrowheads delineate the fracture surface. As can be seen, the crack front remains flat throughout the specimen thickness. This observation and the fact that Eq 7 does not adequately predict shear lip width suggest that the V-shaped feature does not arise from normal shear lip formation.

An alternative explanation for the V-shaped feature is that crack growth proceeds by a plane strain crazing at lower [Delta] K values (to the left of the V-shaped feature) and by plane strain shear yielding at higher [Delta] K values (to the right). As Table 3 shows, there is a correlation between [Delta] K and yield strength, indicating an influence of yield strength on the formation of the V-shaped zone. It is not surprising that this change in mechanism would produce an improvement in FCP resistance; shear yielding absorbs more energy per unit crack length than a single craze. Note that similar improvements in FCP resistance are observed when FCP mechanisms change from single craze to multiple craze formation (7).

If we assume that fatigue crack propagation is controlled by simple rule-of-mixtures from plane strain crazing, Eq 5, and from plane strain shear yielding, Eq 6, we may be able to predict the overall FCP response for each CAP using the data in Fig. 5 to weight the relative contributions from each crack growth mechanism. The predicted FCP curves for CAP 14, CAP 12, and CAP 9 are compared with the experimental curves in Figs. 6, 7, and 8, respectively. The FCP curves for CAP 14 and CAP 12 are modeled well by this approach. Unfortunately, the same is not true for the FCP curve for CAP 9.

The lack of fit for the CAP 9 data may be a result of crack tunneling (i.e., crack front curvature). Crack tunneling was observed visually during the FCP tests, and the severity of the tunneling increased with increasing crack length. In CAP 9, the tip of the V-shaped feature is found at a longer crack length than in CAP 14 and CAP 12 and hence would be subjected to greater crack tip tunneling. Consequently, the crack length computed by compliance will be less than that measured at the tip of the crack front. The crack lengths shown in Fig. 5 were measured directly from the fracture surface and hence will not agree closely with that computed by compliance, particularly at longer crack lengths where tunneling becomes more severe. Naturally, the data for CAP 9 and CAP 6 will be most affected by tunneling because the V-shaped features occur at longer crack lengths.

Scanning electron microscopy of the fracture surfaces confirms the existence of tunneling. A scanning electron micrograph of a typical fracture surface is shown in Fig. 9. The bands in Fig. 9 are fatigue striations and correspond to the increment of crack growth that occurs per stress cycle. Figure 9 also shows an area of severe beam damage. The CAP materials were particularly susceptible to damage by the electron beam because of the presence of the volatile plasticizer. Thus, the SEM observations were limited to rather low magnifications. The rate of crack growth per cycle determined from the striations is compared to that obtained by compliance measurements for CAP 14, CAP 12, and CAP 9 in Fig. 10, 11, and 12, respectively. The value of [Delta] K at the end of the craze zone (tip of V-shaped feature) is labeled in each Figure. The crack growth rates agree well at low values of [Delta] K, where tunneling is minimal, but deviate substantially at the larger values of [Delta] K, where tunneling is significant. If tunneling is severe during the transition from plane strain craze formation to plane strain shear yielding, as is the case for CAP 9, the approach described above for modeling FCP behavior will not be successful. Tunneling is most severe in CAP 6 and is easily observed by optical microscopy, as shown in Fig. 13. The crack front for a particular striation near the tip of V-shaped region is highlighted for clarity.

CONCLUSIONS

Two mechanisms of fatigue crack propagation were identified in CAP a crazing mechanism, which dominated at low values of [Delta] K, and a shear yielding mechanism, which dominated at high values of [Delta] K. Increasing the concentration of plasticizer in CAP caused both the yield strength and the value of [Delta] K at the onset of the transition from the crazing mechanism to the shear yielding mechanism to decrease. The transition in crack propagation mechanism crated a V-shaped feature on the fracture surface. The FCP rate in CAP during the transition was modeled by using the width of the V-shaped feature to weight the contributions from the crazing and shear yielding crack growth mechanisms to the overall FCP rate. This approach was successful provided that crack tip tunneling was limited.

ACKNOWLEDGMENTS

The authors wish to thank G. Ruth and S. Gilliam for preparing the fatigue specimens. The authors also wish to thank R. McGill and L. Roberson for their assistance with the microscopy and metallographic polishing.

NOMENCIATURE

a = Notch length. [c.sub.x] = Compliance coefficient. da/dN = Fatigue crack growth rate. m = Paris law constant. [r.sub.y] = Plane stress plastic zone radius. A = Paris law constant. B

= Specimen thickness. CAP = Cellulose acetate propionate. CAP 14 = Cellulose acetate propionate containing 14

wt% plasticizer. CAP 12 = Cellulose acetate propionate containing 12

wt% plasticizer. CAP 6 = Cellulose acetate propionate containing 6

wt% plasticizer. D = Shear lip width. E = Tensile modulus. FCP = Fatigue crack propagation. [Delta] K = Stress intensity factor range. P = Load. V = Displacement. W

= Specimen width. [alpha] = Ratio of specimen thickness to specimen

width. [[omega].sub.ys] = Yield strength.

REFERENCES

[1.] K. J. Saunders, Organic Polymer Chemistry, Chapman and Hall, London (1976).

[2.] ASTM Standard E647-91, Standard Test Method of Fatigue Crack Growth Rates, Volume 3.01, 654, American Society for Testing Materials, Philadelphia (1991).

[3.] P. C. Paris and F. Erdogan, J. Bas. Eng. Trans. ASME Ser D, 85, 528 (1963).

[4.] R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York (1976).

[5.] R. W. Hertzberg and J. A. Manson, Fatigue of Engineering Plastics, Academic, New York (1980).

[6.] A. Saxena and S. J. Hudak, Intern J. Fract, 14, 453 (1978).

[7.] M. T. Takemori, T. A. Morelli, and J. McGuire, J. Mater. Sci., 24, 2221 (1989).
COPYRIGHT 1994 Society of Plastics Engineers, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1994 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Moskala, Eric J.; Pecorini, Thomas J.
Publication:Polymer Engineering and Science
Date:Sep 1, 1994
Words:2256
Previous Article:A numerical model for single screw extrusion with poly(vinyl chloride) (PVC) resins.
Next Article:Three-dimensional modeling of reaction injection molding.
Topics:


Related Articles
The effect of specimen thickness and stress ratio on the fatigue behavior of polycarbonate.
Synthesis and properties of new esters of cellulose and inorganic polyacids containing phosphorus, molybdenum, tungsten and vanadium.
Kinetics of fatigue failure in polystyrene.
Impact fatigue of a polycarbonate/acrylonitrile-butadiene-styrene blend.
Environmental stress cracking (ESC) of plastics caused by non-ionic surfactants.
The effects of frequency on fatigue threshold and crack propagation rate in modified and unmodified polyvinyl chloride.

Terms of use | Privacy policy | Copyright © 2020 Farlex, Inc. | Feedback | For webmasters