3D imaging has become popular for analyzing material microstructures. When time lapse series of 3D pictures are acquired during a single experiment, it is possible to measure displacement fields via digital volume correlation (DVC), thereby leading to 4D results. Such ForewordThe present paper aims at reviewing the major developments in Digital Volume Correlation (DVC) over the past ten years. It follows the first review on DVC that was published in 2008 by its pioneer [11]. In the latter, the interested reader will find all the general principles associated with what is now called local DVC. They will not be recalled hereafter. In such approaches the region of interest is subdivided into small subvolumes that are independently registered. In addition to its wider use with local approaches, DVC has been extended to global approaches in which the displacement field is defined in a dense way over the region of interest. Kinematic bases using finite element discretizations have been selected. To further add mechanical content, elastic regularization has been introduced. Last, integrated approaches use kinematic fields that are constructed from finite element simulations with chosen constitutive equations. The material parameters (and/or boundary conditions) then become the quantities of interest.These various implementations assume different degrees of integration of mechanical knowledge about the analyzed experiment. First and foremost, DVC can be considered as a stand-alone technique, which has seen its field of applications grow over the last ten years. In this case the measured displacement fields and post-processed strain fields are reported. With the introduction of finite element based DVC, the measured displacement field is continuous. It is also a standalone technique. However, given the fact that it shares common kinematic bases with numerical simulations, it can be easily combined with the latter. One route is to require local satisfaction of equilibrium via mechanical regularization. Another route is to fully merge DVC analyses and numerical simulations via integrated approaches. Different examples will illustrate how these various integration steps can be tailored and what are the current challenges associated with various approaches.

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Fast 4D tensile test monitored via X-CT: Single projection based Digital Volume Correlation dedicated to slender samples. AbstractThe measurement of 4D (i.e., 3D space and time) displacement fields of in situ tests within X-ray Computed Tomography scanners (i.e., lab-scale X-CT) is considered herein using projection-based Digital Volume Correlation. With one single projection per loading (i.e. time) step, the developed method allows for loading not to be interrupted and to vary continuously during the scan rotation. As a result, huge gains in acquisition time (i.e., more than two orders of magnitudes) to be reached. The kinematic analysis is carried out using predefined space and time bases combined with model reduction techniques (i.e., Proper Generalized Decomposition with space-time decomposition). The accuracy of the measured kinematic basis is assessed via gray level residual fields. An application to an in situ tensile test composed of 127 time steps is performed. Because of the slender geometry of the sample, a specific beam space regularization is used, which is composed of a stack of rigid sections. Large improvements on the residual, whose SNR evolves from 9.9 dB to 26.7 dB, validate the procedure.

Abstract. The question of registering two images (or image volumes) acquired with different modalities, and thus exhibiting different contrast, at different positions is addressed based on an extension of global Digital Image (or Volume) Correlation. A specific comparison metric is introduced allowing the signature of the different phases to be related. A first solution consists of Gaussian mixture to describe the joint distribution of gray levels, which not only provides a matching of both images, but also offers a natural segmentation indicator. A second 'self-adapting' solution does not include any postulated a priori model for the joint histogram and leads to a registration of the images based on their initial histograms. The algorithm is implemented with a pyramidal multiscale framework for robustness. The proposed multiscale technique is tested on two 3D images obtained from X-ray and neutron tomography respectively. The proposed approach brings the two images to coincidence with a sub-pixel accuracy and allows for a "natural" segmentation of the different phases.

An online calibration procedure for X-ray lab-CT is developed using projection-based digital volume correlation. An initial reconstruction of the sample is positioned in the 3D space for every angle so that its projection matches the initial one. This procedure allows a space-time displacement field to be estimated for the scanned sample, which is regularized with i) rigid body motions in space and ii) modal time shape functions computed using model reduction techniques (i.e., proper generalized decomposition). The result is an accurate identification of the position of the sample adapted for each angle, which may deviate from the desired perfect rotation required for standard reconstructions. An application of this procedure to a 4D in situ mechanical test is shown. The proposed correction leads to a much improved tomographic reconstruction quality.

A recently proposed "Projection-based Digital Volume Correlation" (P-DVC) method is extended in this work to a cone-beam lab-tomograph in which a mechanical test is performed. This consists of a crack propagation test in an elasticbrittle gypsum specimen. Kinematic analysis is performed based on a reduced finite element modeling for which the appropriate boundary conditions and crack propagation stage are determined from the radiographs. By considering only two projections per loading step, an integrated model-based analysis of the entire test provides a full space and time identification of the kinematics, including the crack position and the determination of two material parameters. This is achieved with a drastic reduction in the acquisition time compared to classical digital volume correlation analysis. In the examples presented, the acquisition time was reduced by a factor of 350.

The motion of a sample while being scanned in a tomograph prevents its proper volume reconstruction. In the present study, a procedure is proposed that aims at estimating both the kinematics of the sample and its standard 3D imaging from a standard acquisition protocol (no more projection than for a rigid specimen). The proposed procedure is a staggered two-step algorithm where the volume is first reconstructed using a “Dynamic Reconstruction” technique, a variant of Algebraic Reconstruction Technique (ART) compensating for a “frozen” determination of the motion, followed by a Projection-based Digital Volume Correlation (P-DVC) algorithm that estimates the space/time displacement field, with a “frozen” microstructure and shape of the sample. Additionally, this procedure is combined with a multi-scale approach that is essential for a proper separation between motion and microstructure. A proof-of-concept of the validity and performance of this approach is proposed based on two virtual examples. The studied cases involve a small number of projections, large strains, up to 25%, and noise.