DIC-IR Analysis of Transient Thermal Stresses

Abstract

This paper shows the feasibility of determining transient thermal strains and stresses using simultaneous time-dependent full-field temperature and displacement measurements along the surface of simple and complex structures. Temperature and displacements were experimentally determined by a set-up composed of a thermographic infrared (IR) micro-bolometer camera coupled to a stereo Digital Image Correlation (DIC) system. A polycarbonate flat disc-shaped specimen was tested under transient thermal inputs. The thermal expansion coefficient of polycarbonate was also measured using the same experimental set up. The mechanical or net strain distributions were determined from the total or gross DIC measured strains by subtracting the free induced temperature strains. The final strain distributions were compared with analytical and finite element solutions determined by using the IR test-measured temperature distributions.

Keywords

Appendices

Appendices

Elasticity equations for a hollow thin disk under thermal loading [6].

$$ {\sigma}_r=\frac{\alpha_TE}{r^2}\left[\frac{r^2-{r}_1^2}{r_2^2-{r}_1^2}\underset{r_1}{\overset{r_2}{\int }}\left(T-{T}_o\right) rdr-\underset{r_1}{\overset{r}{\int }}\left(T-{T}_o\right) rdr\right] $$

$$ {\sigma}_{\theta }=\frac{\alpha_TE}{r^2}\left[\frac{r^2+{r}_1^2}{r_2^2-{r}_1^2}\underset{r_1}{\overset{r_2}{\int }}\left(T-{T}_o\right) rdr+\underset{r_1}{\overset{r}{\int }}\left(T-{T}_o\right) rdr-\left(T-{T}_o\right){r}^2\right] $$

$$ {\varepsilon}_r=\frac{1}{E}\left({\sigma}_r-\nu {\sigma}_{\theta}\right)+{\alpha}_T\left(T-{T}_o\right) $$

$$ {\varepsilon}_{\theta }=\frac{1}{E}\left({\sigma}_{\theta }-\nu {\sigma}_r\right)+{\alpha}_T\left(T-{T}_o\right) $$

= initial temperature; r₁ = a; r₂ = b; E = Young modulus; ν = Poisson’s coefficient, α = thermal expansion coefficient

Finite element axisymmetric solution [7].

The finite element linear-elastic axisymmetric solution employed the software ANSYS^® version 18.1 and used a Poisson’s coefficient μ = 0.36. Tests using different values of μ (from 0.32 to 0.38) showed to cause negligible influence in the numerical and analytic solutions. The applied boundary conditions consisted of zero radial stresses along the internal hole and external disc surfaces. The heating problem was treated as static. A thermal condition was applied to simulate the temperature distribution, obtained from the IR measurement, along the radius of the disc (from r = a to r = b). The model mesh consisted of 9535 SOLID186 elements and a total of 29,308 nodes.