Virtual hybrid test control of sinuous crack

TLDR: A new generation of experimental protocol for analysing crack propagation in quasi brittle materials that exhibits a much improved sensitivity to the sought parameters such as internal lengths as assessed from the comparison with other available experimental tests is proposed.

Abstract: The present study aims at proposing a new generation of experimental protocol for analysing crack propagation in quasi brittle materials. The boundary conditions are controlled in real-time to conform to a predefined crack path. Servo-control is achieved through a full-field measurement technique to determine the pre-set fracture path and a simple predictor model based on linear elastic fracture mechanics to prescribe the boundary conditions on the fly so that the actual crack path follows at best the predefined trajectory. The final goal is to identify, for instance, non-local damage models involving internal lengths. The validation of this novel procedure is performed via a virtual test-case based on an enriched damage model with an internal length scale, a prior chosen sinusoidal crack path and a concrete sample. Notwithstanding the fact that the predictor model selected for monitoring the test is a highly simplified picture of the targeted constitutive law, the proposed protocol exhibits a much improved sensitivity to the sought parameters such as internal lengths as assessed from the comparison with other available experimental tests.

Figures

Table 2: Parameters for the analysis of noise sensitivity

Figure 4: Target point with the two proposed methods, (a) at a distance dr from the previous measured point, and (b) at a projected distance dx on the x-axis

Figure 12: Maximum applied displacement at the top left and right corners of the sample vs. step number. (a) Tension on the top left corner (positive values) and on the top right corner, and (b) shear (uniform)

Figure 13: Total crack length vs. step number

Figure 5: Example of a rotational loading stabilising crack propagation. The distance ∆x between the crack tip and the projected instantaneous centre of rotation (ICR) is introduced in the studied case

Table 1: Parameter values

Frequently asked questions

Q1. What is the advantage of this simplified procedure?

The advantage of this simplified procedure is that the algorithm does not fail,225even though the determined crack orientation angle is restricted to cracks whose propagation never recedes along the x-axis. 

Q2. What is the method for measuring crack tip?

The crack tip measurement may rely on Integrated Digital Image Correlation (I-DIC) using, for example, Williams’ series [44, 45, 42], or any other suitable technique. 

Q3. What are the other parts that are referred to as physical sub-domains?

The other parts, which are critical and complex (e.g., involving non-linearities, irreversibility), the so-called physical sub-domains, are kept as substructures actually tested in the laboratory. 

Q4. How can the two SIFs that control crack propagation be bijective?

the two SIFs that control crack propagation are linearly dependent on the sample boundary conditions,250and can be bijectively related to two degrees of freedom. 

Q5. What is the correlation code for the measured displacement field?

Since the measured displacement field is corrupted by noise, the DIC matrix is related to the covariance matrix [Cu] of the measured degrees of freedom by [60][Cu] = 2γ 2 f [M ] −1 (20)Once a discretization has been chosen for displacement field measurements, and the level of acquisition noise is known, this derivation gives access to the470sensitivity of the measured degrees of freedom to acquisition noise [62]. 

Q6. What is the correlation matrix for the sinusoidal crack path?

The corresponding correlation matrix is formed (with no index summation)[H̃−1u ]ij = [H−1u ]ij√[H−1u ]ii √ [H−1u ]jj(26)For the sinusoidal crack path the correlation matrix shows an anti-correlationbetween the Poisson’s ratio and the scale parameter p. 

Q7. How many degrees of freedom are used to keep the experiment without significant out-of-plane?

In the following test-case with a hexapod, three degrees of freedom are used to keep the experiment without significant out-of-plane motion. 

Q8. What is the correlation matrix for the Nooru-Mohammed test?

The correlation matrix520for the Nooru-Mohammed test (obtained with the same mesh) appears to be strongly coupled whereas the sinusoidal experiment is less coupled (Figure 16). 

Q9. how to calculate internal length scales of damage models?

achieving real 3rd generation tests is the next560step of the present study to calibrate internal length scales of damage models, which are very difficult to estimate with current tests and procedures. 

Q10. What is the effect of the low level model on the crack path?

However the inaccuracies of this low level model produce spurious damage patterns from which a secondary crack may branch whenever the main crack path reaches some unfavourable direction. 

Q11. What is the way to determine the path of the crack?

the crack will follow230in the best case a path that will be called the command crack path, namely, the discretised version of the initial input path. 

Q12. What is the way to determine the influence of elementary loading on the SIFs?

The easy way to establish all sensitivity matrix elements SiI,II is to perform numerical simulations to assess the influence of each elementary loading on the SIFs. 

Q13. How is the crack path sensitivity to the length scale parameter?

As shown455in Figure 14 the crack path is sensitive to the length scale parameter p, but it is difficult to assess its best fit value, as its variation is really important (i.e., a factor of 3).