Viscoelastic Behavior of a Rubber-Toughened Composite

One important factor in the durability of polymeric composites is their loss in stiffness over time. At the fiber and ply-level, this softening is primarily due to viscoelasiticity and viscoplasticity of the polymer matrix and time-dependent damage growth. Damage refers to all microstructural changes such as matrix cracking, fiber/matrix debonding and shear yielding (Time-Dependent Microcracking). An understanding of this softening behavior is needed to make reliable predictions of more serious larger-scale damage, such as transverse cracking, delamination, fiber breakage, and catastrophic failure. We have developed and demonstrated a damage effect study which identifies the effects of damage on the constitutive behavior of a nonlinear viscoelastic material.

Characterizing the constitutive behavior of composites with nonlinearity and time-dependence is complicated by the variety softening mechanisms which may evolve concurrently. Frequently a constitutive model is chosen and fit to a limited set of experimental data. However, for many standard experiments (e.g. constant rate or creep), a variety of models can be successfully fit. There is no assurance that subsequent predictions for more complicated load histories will be successful.

In this study, the opposite approach was taken and all possible softening mechanisms were considered. The objective was to develop an experimental program to determine which softening mechanisms have a significant effect on strain for a given material. A constitutive theory which includes elastic, nonlinear viscoelastic and viscoplastic strains, with effects of growing damage, was used to develop a Damage Effect Study. The major focus is separating the intrinsic effect of stress from that of damage on the nonlinear viscoelastic behavior. This approach can be used as a screening process of candidate materials for a given application. Upon selecting a material, the study will also provide the necessary data for the selection, development, or validation of a constitutive theory.

With constant stress rate testing all softening mechanisms grow concurrently, resulting in nonlinear rate-dependent behavior as shown in Figure 1.By performing creep and recovery experiments the effect of the damage growth and viscoplastic strain are more apparent. The creep response, shown in Figure 2(a), changes form cycle to cycle due to damage growth and viscoplastic strains. These mechanisms eventually become constant during subsequent cycles as the conditioned response is repeatable and represents an average of multiple cycles. In the conditioned response, the change in strain is only due to viscoelasticity. The viscoplastic strain is most evident in recovery and is mostly responsible for the difference between the first and the conditioned cycles, as shown in Figure 2(b).

A general loading history for The Damage Effect Study is shown in Figure 3. The study effectively examines snapshots of the viscoelastic material behavior at different constant damage states. The material is first conditioned at one stress level until damage growth and the growth of viscoplastic strains become negligible. A few creep/recovery cycles are then performed at the same stress to get an average response. This process is then repeated at a higher stress, except the conditioned response is also found at the previous stress level and so on. In the example shown, data can be compared for three damage states at the lower stress level and two damage states at the higher. This study was then implemented on unidirectional 90, 45, and 30 degree off-axis samples of a rubber-toughened carbon/epoxy composite. The viscoelastic creep and recovery response in shear from a 30 degree sample are shown in Figure 4. Two significant simplifications are found for the material studied; damage does not affect the time scale of the viscoelastic strains and enters through only one parameter in the transverse strain. Viscoelastic shear strain requires two parameters, however. The elastic component of the modulus is also found to stiffen with increased damage.model.

References

• Schapery, R.A., "Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage," International Journal of Fracture, Vol. 97, 1999, pp. 33-66.
• R.T. Bocchieri, "Time-Dependent Deformation of a Nonlinear Viscoelastic Rubber-Toughened Fiber Composite with Growing Damage," Ph.D. Dissertation, Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 2001.

For inquiries or comments, please contact:
Dr. Robert T. Bocchieri
Principal Engineer
e-mail: rbocchieri@ara.com

This research program was sponsored by the National Science Foundation through the Offshore Technology Research Center and The University of Texas at Austin by Dr. Robert T. Bocchieri as his PhD Thesis. The University of Texas at Austin advisor for this research was Prof. Richard Schapery who heads the Composite Materials Laboratory in the Dept. of Aerospace Engineering and Engineering Mechanics.

Figure 1. Constant Stress Rate Experiments

Figure 2. Cyclic Creep/Recovery Experiments

Figure 3. Damage Effect Study
General Load History

Figure 4. Damage Effect Results Shear compliance from a 30 degree sample