Projection-based coupling of infrared thermography and stereocorrelation-based digital image correlation

The gist The study proposes an external projection-based coupling method that uses a pinhole camera model to relate two-dimensional temperature data from infrared thermography to three-dimensional point coordinates from stereocorrelation-based digital image correlation, which is particularly suited for analyzing curved surfaces

How it works

The core of the proposed method involves relating two different measurement modalities: pixel temperatures from infrared thermography and three-dimensional point coordinates from stereocorrelation-based digital image correlation The approach is based on the perspective projection equation, which maps three-dimensional object points to two-dimensional image planes using a pinhole camera model

1. Calibration of the Projection Matrix M: The projection matrix M, which incorporates intrinsic and extrinsic camera parameters, is calibrated using a single image of a three-dimensional reference object, such as an open-book-shaped target This calibration can be performed without prior heating of the reference target.

2. Image Registration: After calibration, the actual image acquisition and evaluation are performed, where point coordinates x are determined by DIC and pixel coordinates xΘ are obtained from the IR image via edge detection. The relationship between these points is governed by the equation xΘ = M x.

3. Interpolation using Radial Basis Functions (RBFs): To compute in-plane temperature gradients and temperature rates on curved surfaces, radial basis functions (RBFs) are utilized as a global interpolation ansatz in both space and time The point coordinates x are projected into the IR image plane using the projection matrix M to evaluate point temperatures on an arbitrarily shaped surface.

4. Computation of Gradients and Rates: The in-plane temperature gradient is expressed as grad Θ = d ∂Θ / ∂Ψα a α, where the total derivative dxˆΘ/dx is computed by differentiating the projection equation (1). The temperature rate is defined as the material time derivative of the temperature, Θ = ˙ dΘˆ / d xˆΘ (xˆ(Ψ, t)), t dt = ∂Θˆ / ∂t + ∂Θˆ / ∂x Θ dx̂/dx∂x̂∂t.

Key Components and Methodology

The methodology is designed to provide a modular approach that is applicable independently of the specific system manufacturer or access to DIC codes, relying instead entirely on (three-dimensional) point coordinates and pixel temperatures The study emphasizes that this external calibration of the projection, while potentially less accurate than hybrid multiview frameworks, allows for straightforward coupling of data from industrial-grade imaging systems.

The reconstruction of a curvilinear surface from discrete pointwise data is achieved using surface parameters Ψ1 and Ψ2, which are then used in the RBF interpolation formula to define the point on the surface x(Ψ, t) The interpolation coefficients a s and b s in Eq. (10) are determined by solving a system of linear equations derived from stereocorrelation-based DIC.

Experimental Validation

The proposed approach was demonstrated through two experiments involving curved and complex surfaces in both purely thermal and thermo-mechanically coupled settings

1. Cylindrical Polymer Half-Shell: This example operated in an entirely thermal setting, where DIC point coordinates were used solely to capture the curved specimen surface. The results showed that temperature increases were observed only in the vicinity of the contact regions with the heat plate due to relatively low thermal conductivity.

2. Tube under Tension-Torsion Load: This thermo-mechanical setup involved a zinc die-casting alloy tube subjected to a proportional tension-torsion load, allowing for the evaluation of full-field data on a curved surface. The results demonstrated that the approach effectively couples point coordinates from stereocorrelation-based DIC with pixel temperatures from IRT, enabling the computation of spatial gradients and temporal rates.

Conclusion

The developed projection approach successfully couples point coordinates from stereocorrelation-based DIC with pixel temperature data from IRT to express the temperature field in the same Lagrangian frame as mechanical fields Furthermore, extending the radial basis function-based evaluation of full-field data to a spatial and temporal interpolation enables the evaluation of in-plane temperature gradients and temperature rates on flat and curved surfaces.

Experimental Validation

The proposed approach was demonstrated through two experiments involving curved and complex surfaces in both purely thermal and thermo-mechanically coupled settings

1. Cylindrical Polymer Half-Shell: This example operated in an entirely thermal setting, where DIC point coordinates were used solely to capture the curved specimen surface.

1. Based on Equation (27) of Section 13, an improved system can perform direct coupling between pixel coordinates and real-world coordinates by reformulating the projection equation as: xΘ = 1/σ(x) 'm˜⊤1 m˜⊤2#x + (m14 m24)! = 1/m˜⊤3 x + m34 'm˜⊤1 m˜⊤2#x + (m14 m24)!. This allows for a more direct, coordinate-based relationship between the Lagrangian material points and the Eulerian pixel temperatures.

2. The system can compute in-plane temperature gradients and temperature rates on flat and curved surfaces by utilizing the derived relations in Equations (6) and (9), which are computed from continuous interpolation of the pixel temperatures with respect to time t and pixel coordinates xΘ and of the point coordinates x with respect to time t and surface parameters Ψ.

3. The improved system can perform strain analysis on curved surfaces by leveraging Equation (25) for computing covariant metric coefficients, allowing for the determination of in-plane temperature gradients (6) which are essential inputs for calculating the deformation gradient Fˆ = ⃗aα ⊗ A⃗α" in Section 13.

Full-field measurement techniques such as digital image correlation and infrared thermography are prevalent in experimental solid mechanics. Digital image correlation is used to analyze surface deformation, while infrared thermography quantifies surface temperature fields. However, sophisticated procedures are necessary to express both datasets in the same Lagrangian frame, especially when analyzing non-flat surfaces. In this study, we propose an external projection-based coupling that uses the pinhole camera model to relate two-dimensional temperature data measured by infrared thermography to three-dimensional point coordinates from stereocorrelation-based digital image correlation. Unlike existing multiview approaches, we utilize two independently calibrated industrial-grade systems and augment the experimental evaluation with the pinhole camera model. The projection matrix of the camera model is calibrated using a single image of a reference object. Through this projection, temperature fields are accurately represented at material points. Our method is particularly suited for, but not restricted to, curved surfaces and is straightforward to embed in existing experimental protocols, as the image registration is kept as is. Additionally, we use radial basis functions as a global interpolation ansatz in both space and time to compute in-plane temperature gradients and even temperature rates on curved surfaces, thereby providing an extensive and information-rich full-field dataset.