The measurement of longitudinal residual stresses in unidirectional glass fibre reinforced plastic
Date
2010-03-23T09:11:37Z
Authors
Reid, Robert Grant
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Abstract
A wide range of experimental methods exist for estimating residual stresses. None
of these methods is suitable, however, for finding the longitudinal residual stresses
that exist in an unloaded unidirectional laminate of glass fibre reinforced plastic.
This work presents a method that enables these stresses to be measured. The method
exploits the substantial reduction in the modulus of a thermoset matrix above its
glass transition temperature, Tg. Restraint forces between the fibres and the matrix
are thereby relaxed. The variation in the longitudinal residual strain of the fibres
with temperature is estimated by gradually heating the laminate above the matrix
Tg whilst monitoring the apparent longitudinal thermal expansion of the laminate.
The longitudinal residual strains in the fibres can be estimated without any knowledge
of the fibre or matrix properties. The consistancy of the measured residual
strains is improved, however, if the known coefficient of thermal expansion of the
fibre is incorporated into the strain calculations. In some situations, the accuracy
of the residual strains can be further improved if temperature-dependent material
properties for the matrix are also used.
The longitudinal residual stress is easily calculated using Hooke’s Law once the
residual strains are known. This approach is simple and very convenient because it
requires no knowledge of any matrix properties. The accuracy of the residual stress
measurements can be improved by considering Poisson’s stresses, however, but this
is not always possible.
The dramatic reduction in matrix modulus during each test prevents the use of
standard methods and so a method to obtain the necessary strain measurements is
developed. Strain-gauges cannot be used and an approach based on dilatometry is
used instead. Displacement measurements taken between the ends of a specimen
give erroneous results, however, and so it is necessary to use reference points that
are located within the specimen length.
Three sets of specimens were manufactured that differ in their longitudinal residual
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stress. The fibres in two specimen sets were significantly strained during manufacture
of the specimens. The stresses in one of these sets were subsequently relaxed
through an annealing process. No substantial fibre preloading was used during the
manufacture of the third specimen set.
Residual strains are measured in the fibres of the three specimen sets. The general
form of the measured strain responses agrees well with the form required by the
theoretical basis of the method. The results are also compared with strains predicted
using the assumption of linear viscoelasticity in the matrix. The correlation is
good except in the case of the annealed specimens. Since these specimens were
subjected to non-linear creep during the manufacturing process, it is probable that
the discrepancies reflect a deficiency in the theory rather than errors in the measured
results.
The residual stresses at ambient conditions are calculated for the three specimen
sets. It is not possible to estimate the Poisson’s stresses in the annealed specimens,
but these stresses do not significantly affect the longitudinal stresses in the other
specimen sets. Although the measured residual stresses are small, the corresponding
strains in the matrix are rather large.