Stress Detection of Conical Frustum Windows in Submersibles Based on Polarization Imaging

Abstract

Stress detection of the conical frustum window is a very important issue to ensure the safety of deep manned submersibles. In this paper, we propose a method based on polarization imaging to evaluate the stress accumulation and recovery in the conical frustum window. An experimental setup of Mueller matrix polarimetry is built, and the samples are made by referring to the typical conical frustum windows in submersibles. By pressurizing different pressures on the samples, we can find the changes of their Mueller matrix images and further derived polarization parameters. The results show that the polarization parameters can characterize the stress transfer process and the elastic-plastic transformation process of the window under different pressurization pressures. We also use a two-layered wave plate model to simulate the stress distribution in the window, which reveals different performances of the former and latter layers of the window under pressurization. Finally, we use a finite element model to simulate and understand some of the above experimental results. This proposed method is expected to provide new possibilities for monitoring the window stress and further ensure the safety of deep manned submersibles.

Keywords: PMMA; conical frustum window; polarization imaging; stress detection.

Figure 1

Structural parameters of sample.

Figure 2

Schematic configuration (a) and photograph (b) of the experiment setup. P1, polarizer; R1 and R2, achromatic quarter-wave plates.

Figure 3

Results of the correction method. (a) Original image without pressure; (b) distorted images with 120 MPa pressure; (c) merged image of (a,b) with false-color algorithm; (d) merged image of original and corrected images with false-color algorithm. Red dots in (a,b) are the feature points.

Figure 4

b, $t_3$,${\alpha }_r$,$\delta$ images of sample after 0 MPa, 72 MPa and 144 MPa pressure and those after 24 h recovery. (a–d): b images; (e–h): $t_3$ images; (i–l):${\alpha }_r$ images; (m–p):$\delta$ images.

Figure 5

γ images under different pressures and recovery times. (a–f): γ images under different pressures; (g–i): γ images under different recovery times.

Figure 6

(a) V for different pressurization pressures; (b) V for different recovery times.

Figure 7

Two-layered difference of retardance parameters $\Delta {\theta }_1,\Delta {\theta }_2,\Delta {\delta }_1,\Delta {\delta }_2$. (a)$\Delta {\theta }_1$ image; (b) $\Delta {\theta }_2$ image; (c) $\Delta {\delta }_1$ image; (d)$\Delta {\delta }_2$ image.

Figure 8

Fast axis orientation flow diagram of two-layered simulation. (a) initial image of former layer; (b) initial image of latter layer; (c) after loading image of former layer; (d) after loading image of latter layer.

Figure 9

Relationship of the clear aperture of the sample with the pressurization surface.

Figure 10

Boundary constraint and mesh division of finite element model. (a): boundary constraint image; (b): mesh division image.

Figure 11

Mises stress diagram of sample.

Figure 12

The stress along x-axis of sample as different distances to the central line.

Figure 13

A,$m_{33}, \Psi$ images of sample at 0 MPa, 72 MPa, 144 MPa and images after 24 h recovery. (a–d): A images; (e–h): $m_{33}$ images; (i–l): $\Psi$ images.