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# OTRC Project Summary

### Project Title: |
Time Dependent Deformation of a Nonlinear Viscoelastic Rubber-Toughened Fiber Composite with Growing Damage |

### Prinicipal Investigators: |
Richard Schapery |

### Sponsor: |
Minerals Management Service |

### Completion Date: |
May, 2001 |

### Final Report ID# |
B113(Click to view final report abstract) |

Review of the literature shows that varying degrees of complexity need to
be incorporated in constitutive models, depending on the composite system
studied. In some studies only the addition of viscoplastic strain was needed to
make good predictions of material behavior. In others, damage only appears
to affect the elastic strain. For certain materials only linear viscoelasticty,
where all nonlinearity came from damage, was needed.

When approaching a new material, one frequently generates stressstrain
data from constant load-rate or strain-rate tests, cyclic load/unload
tests and ramp to failure experiments. A proposed constitutive model is applied
which captures the effects seen for some limited amount of data. Complexity
is built in as necessary to explain results from all of the experiments. Finally, some ‘validation’ experiments are run where the loading history, or perhaps in the case of composites, a different laminate is tested to justify the

constitutive model used.

In terms of durability, material behavior over long times or many fatigue
cycles is needed. Certain material behavior, such as viscoelasticity,
may seem negligible over typical time-frames used for tests in the laboratory
if standard rate-type loadings are used. However, in ten or fifteen years neglected
strains may become significant. The time-dependent microcracking
detected in 90o material, discussed in Chapter 7, is a good example of where
rate-loadings do not give any indication of time-dependent effects.

Here we take the opposite approach and leave as much material complexity
in place as possible so that testing methodologies will have the widest
applicability. Experiments are used that emphasize the time-effect, although
the change in creep strains measured over the short time-frame of testing is
small. These methods are evaluated using a composite which displays all of
the mentioned complexities.

This work uses the theory previously established by Schapery (1999)
to develop experimental and data analysis methods for isolating the softening
effects of nonlinear elasticity, nonlinear viscoelasticity, viscoplasticity and
damage. Damage enters through internal state variables. If all these mechanisms

are significant, the author is not aware of any existing method to
extract both the damage evolution and to differentiate its effect on the material
parameters from that of stress based solely on stress-strain information.
A direct measure of microcracking is needed to help separate these effects.
A major focus, therefore, was to develop relatively short-term experimental
and data analysis methods for determining which material complexities have
a significant effect on material behavior. The major difficulty is separating

the intrinsic effect of stress from that of damage on the nonlinear viscoelastic (NLVE) behavior. This problem was addressed with three concurrent

approaches:

1. Develop experiments and numerical data analysis methods to fit strain

data which are affected by hereditary damage effects.

2. Conduct a Damage Effect Study to identify which nonlinear material

parameters are affected by damage.

3. Develop a real-time nondestructive method to monitor damage growth.

The focus of the first effort was to assess the effect of damage on each
material parameter, in particular the parameter which causes hereditary damage
effects. The material displays a fading memory of the loading path with
which it arrived at a given damage state. Testing methodology and methods
of data analysis were devised without removing any material complexity. The
Damage Effect Study was designed to determine which material parameters
are affected by damage. This information can then be used to simplify the

analysis. Acoustic emission monitoring was used in the third effort to track
how damage evolves with different loading histories and load combinations.
With this knowledge, the state of damage in the material will be known for
any loading and can be used to tie together the first two efforts.

**Related Publications: **Bocchieri, R.T. and Schapery, R.A., “Nonlinear Viscoelastic Constitutive Equations for Carbon/Epoxy Composites and their Correlation through Micromechanics,” Proc. 2nd Int. Conf. on Composite Materials for Offshore Operations, Houston, pp. 513-536, American Bureau of Shipping, 1999.

Bocchieri, R.T. and R.A. Schapery, "Nonlinear Viscoelastic Behavior of Rubber-Toughened Carbon and Glass/Epoxy Composites," *Time Dependent and Nonlinear Effects in Polymers and Composites*, ASTM STP 1357, 2000, pp. 238-265.