Residual stress contributes to crack deflection, for the present case however the contribution by CNTs is most probably negative (lower CTE than matrix), upon cooling from production temperature they will induce tensile stress into the matrix while the CNTs are in compression. thus they will decrease toughness by this mechanism (Taya, J. Am. Ceram. Soc). the effect scales with delts alpha x delta T. We know the difference of the CTE but not the temperature difference, the relevant temperature is the temperature difference between application temperature and the temperature where the relaxation of residual stress by creep ceases.

Due to the anisotropy the radial contribution will be neglligible along the axis of the CNT the effect may be significant.

This effect is probably offset by the contribution by crack bridging.

The basic analytical models for spherical inclusions are quite old (e.g. Kingery and Bowen). The question that is to be answered is up to which temperature residual stresses build up and from which temperature they relax. The answer to this question can be derived from a creep experiment (see Blendell and Coble)

In case of MWCNTs the slip effect of the layers of the CNT may also be relevant.

If your samples exhibit the cracking mentioned above, then the stress due to the thermal mismatches has been mostly relieved.  However, if you do not see such cracking, then the strain exists and is can be readily measured by taking theta-2 theta x-ray diffraction scans.  By comparing the measured d-spacings of the Al with the published values, you can directly calculate the strain caused by the presence of CNTs following thermal cycling.

Now, if you do see cracking with your thermal cycling, perhaps you can try lowering the temperature sufficiently so that the cracking does not occur.  Then presumably by taking the XRD data following different temperatures, you can map out the evolution of strain as a function of temperature, up to the stress-relaxation temperature which results in cracking.

Good luck.