Abstract
Thermoelastic Stress Analysis (TSA) and Digital Image Correlation (DIC) are full-field imagingtechniques that are generally regarded as being capable of providing stress and strain information only
from the surface of components. Both DIC and TSA have been used for in-situ studies on a range of
Carbon Fibre Reinforced Polymer (CFRP) specimens. In TSA the ongoing assumption is that the small
temperature change resulting from the thermoelastic effect occurs under adiabatic conditions, usually
achieved by cyclically loading the materials at a rate that is sufficient to prevent heat transfer. Achieving
such conditions in laminated multiaxial CFRP material is challenging because of ply-by-ply heat
transfer. The aim of the thesis is to investigate if the non-adiabatic thermoelastic response from CFRP
materials and components can be used in a meaningful way to provide a new tool for analysis of material
behaviour. The approach utilises a combination of TSA with DIC, where the data is fused to provide
complementary information about material behaviour. The PhD project supports CerTest (Certification
by Design: Reshaping the Testing Pyramid) which is a 6-year multidisciplinary EPSRC funded
Programme Grant, with the overarching aim to develop new approaches to assess CFRP structures at
the substructural scale to inform the certification process. Therefore, the purpose of the current PhD is
to evaluate if TSA has a role in substructural scale testing of CFRP, with particular focus on deviations
from the desired adiabatic conditions, where the thermoelastic response is not necessarily linearly
dependent on the stresses.
The thesis starts by proposing a novel methodology for the evaluation of the Coefficients of Thermal
Expansion (CTEs) of laminates through a gradient-based optimisation fitting of thermoelastic response
(ΔT) to a numerical model of 1D heat diffusion, which relates ΔT to the loading frequency. The model
includes the contribution of the heat sources generated by each ply and any surface resin-rich layer
(RRL) to the thermoelastic response from the material surface. By minimising the difference between
experimental data and the model it is shown that the two in-plane CTEs for the lamina can be estimated.
The model requires knowledge of the applied strain, which is obtained using the DIC. The new approach
is validated using conventional techniques for obtaining the CTEs, i.e. Thermomechanical Analysis
(TMA) and laser interferometry. Thereby it is demonstrated that TSA has a role in structural analysis
by offering a means to determine the CTEs from an as manufactured component.
Results from multidirectional (MD) CFRP specimens with stacking sequences of [0,45,-45,0,0,0]S,
[0,0,0,45,-45,0]S, [±45]3S, [0,90]3S, [90,0]3S are used to experimentally validate an existing numerical
model that simulates the non-adiabatic thermoelastic response. The model enables the thermoelastic
heat sources to be generated at the lamina level and hence the heat transfer resulting from the laminated
construction of the material in a 3D format. It is shown that the effect of the RRL generated during
manufacturing and the matt black paint applied to prevent reflection can be included in the model and
hence their influence on ΔT established. The validated model is then used in the thesis to support the
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understanding of the TSA results in situations where there is significant departure from adiabatic
conditions. This is particularly important for sub-structural scale testing where loading frequencies of
more than a few Hz cannot be obtained in complex rigs because of significant inertial effects.
The influence of the in-plane and through-thickness heat transfer becomes even more significant
under a 3D stress state, making interpretation of TSA results notably more challenging. Most structural
components are subjected to 3D stress states, and for this reason, this study develops a hybrid approach
integrating TSA, DIC and three numerical thermomechanical modelling approaches to improve stress
analysis in CFRP laminates. Non damaging cyclic tension tests were performed at different frequencies
on [0,45,-45,0,0,0]S and [0,0,0,45,-45,0]S open hole specimens, which revealed that ΔT varies
considerably with loading frequency. Particularly in the vicinity of the hole due to the varying stress
induced temperature change ply by ply. It is shown that the combination of DIC with the numerical
model of ΔT enabled a much-improved interpretation of the thermoelastic response of CFRP
components containing complex 3D stress states. It is demonstrated that creating a model of ΔT,
alongside accurate measures of strain from DIC provides an invaluable tool for selecting the loading
parameters, especially the frequency selection, to support quantitative TSA in CFRP components.
As a result of the different stress states, damage can originate in any ply of the laminate. Hence the
thermoelastic behaviour of [0,90]3S and [90,0]3S laminates at different damage states was investigated.
The aim being to reveal additional subsurface ply information at low frequencies where non-adiabatic
conditions prevail. The research adds to the current knowledge by providing new insights into the interply and intra-ply heat transfer mechanism as damage is induced in the laminate. Moreover, TSA and
DIC are combined to create two thermomechanical models that provide a new inspection tool. It is
demonstrated that the non-adiabatic thermoelastic response can be exploited to obtain full-field
subsurface stress distributions. X-Ray CT is then used to confirm the location of the damage features.
Finally, this thesis builds upon previous TSA research by leveraging the full-field nature of thermal
data to develop a comprehensive damage parametrisation methodology. This is achieved by integrating
data sets obtained from thermal imaging and DIC. A damage parameter, based on a damage theory for
anisotropic materials, is determined using data from [0,45,-45,0,0,0]S and [0,0,0,45,-45,0]S, [0,90]3S and
[90,0]3S specimens. The influence of loading frequency on the accuracy of damage parametrisation is
examined, and for further comparison, a more conventional assessment was conducted using DIC to
estimate stiffness degradation for various damage states.
In conclusion the thesis provides, for the first time, a comprehensive evaluation of the
applicability of TSA to CFRP components. The possibilities of using TSA in a quantitative manner as
a new tool to assess the stress state and the evolution of damage in CFRP components is presented with
a view to application to large scale components.
| Date of Award | 30 Sept 2025 |
|---|---|
| Original language | English |
| Awarding Institution |
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| Supervisor | Ole Thomsen (Supervisor) & Janice M Barton (Supervisor) |