The methodology was applied for the extraction of SIFs for two different sample configurations: a panel with a single edge and a cracked panel with parallel edges. For the estimation of mixed-mode SIFs using DIC, the required displacement data were obtained using 3D-DIC. The presented methodology has been used to extract mixed-mode SIFs for different specimen configurations.
Introduction
These experimental techniques include full-field non-contact optical methods such as holographic interferometry [2], electronic speckle-pattern interferometry (ESPI) [3], moiré interferometry [3-4], coherent gradient sensing [5], method of caustic [6], photoelasticity, digital image correlation, etc. Among these experimental techniques, digital photoelasticity and digital image correlation (DIC) have become the most popular for SIF determination due to their relatively simple sample preparation, ease of use, and requirement of less complicated optics. Thus, digital photoelasticity and DIC have been considered in this work for the estimation of fracture parameters (SIFs).
Literature Review
Evaluation of fracture parameters using digital photoelasticity
They highlighted the influence of initial (starting) estimates for the fracture parameters on the determination of mixed-mode SIFs, which leads to inherent convergence problems. To increase the accuracy of the measurements of SIFs and take advantage of the additional information in the edge contours of the entire field (which may not lie within the singularity-dominated zone), Sanford [13] extended and developed the overdeterministic least squares algorithm the method of local collocation by including some additional lower-order non-singular terms (which can influence the fracture behavior, such as crack branching and crack curvature). They noted that using too large a number of terms in multi-parameter stress field equations does not necessarily improve the estimation of SIFs and that a sensitivity analysis should be performed to determine the number of terms to use in the stress field equations.
Estimation of fracture parameters using digital image correlation (DIC)
22] determined the KI from data points (r, θ and v) collected over the entire field displacement field around the crack tip using 2D-DIC technique. They used a v-displacement field near the crack tip and investigated the effect of using higher order terms on the evaluation of SIF. 24] used 3D-DIC to evaluate the three-dimensional displacement field near the crack tip for compact tension (CT) specimens.
Scope and Motivation
Using the full field displacement data (u, v) obtained with DIC, Zhang and Lingfeng [31] estimated the mixed mode SIFs by linear least squares fitting, the formulation of which was based on multi-parameter displacement field equations derived with William's Eigen function approach. To locate the crack tip, they used trial-and-error technique in coarse-fine form based on minimizing the absolute value of error in the displacement field.
Thesis layout
Introduction
Multi-parameter stress field equations
- Tri-axial state of stress
- Finite slit-tip radius
- Stress-singularity
- Localized crack-tip blunting
- Plastic zone ahead of the crack-tip
It was found that a three-dimensional stress state exists in the immediate vicinity of the crack tip and the assumption of a stress level in this region is no longer valid. Due to the presence of a very high stress concentration, the isochromatic fringe order in the immediate vicinity of the crack tip can exceed the linear limit in the stress-fringe curve of a photoelastic material [32]. The presence of a nonlinear region was predicted [33] in the immediate vicinity of the crack tip due to the end rotations associated with crack tip stiffening.
Digital photoelastic parameter estimation using Ten-step method
2.2), isoclinic phase map is obtained and it needs to be unwrapped using an adaptive quality-controlled approach to remove the inconsistent zone [38]. This continuous fringe order information will be input to SIF estimation using overdeterministic nonlinear least squares technique.
Over-deterministic Non-linear Least Square Methodology
Formulation of equations
Convergence criteria
Implementation
Experimental Validation
Specimen preparation
This is due to the fact that analytical closed-form solution has been obtained by assuming semi-infinite geometry of interacting parallel-edge cracked panel, while the actual sample is of finite geometry. In many cases, there is ambiguity in the location of the crack tip due to low values of scaling factors (pixels/mm). The location of the crack tip can be treated as one of the unknowns to be determined in the overdeterministic least squares technique.
Then, clear high-quality images of the sample surface (with a typical scaling factor of 14-15 pixels/mm). With the increase in the number of parameters, the convergence error is reduced and the coordinates of the crack tip are stabilized to a constant value. It should be noted that the coordinates of the crack tip are relative to the image coordinate system.
This is due to the fact that the analytical closed form solution was derived by assuming semi-infinite geometry of interaction with parallel edge cracked panel and therefore underestimates the influence of finite geometry on the crack tip stress conditions. Data are collected from larger zone along smooth contours of u and v displacements and the coordinates of the crack tip are evaluated automatically. For the validation of the methodology, mixed-mode SIFs were estimated for five different sample configurations with varying mode mixing.
Also, the modified form of the presented algorithm can be used to determine the dynamic mixed-mode SIF for a propagating crack.
Experimental procedure
Photoelastic analysis
The unwrapped isoclinic is used to obtain the isochromatic phase map without any ambiguity and is shown in Fig. The wrapped isochromatic phase map must be unwrapped to get the total fringe order over the model domain, and the unwrapped isochromatic phase map is shown in Fig. The unwrapped isoclinic is used to obtain the isochromatic phase map shown in Fig.
The wrapped isochromatic phase map must be unwrapped to get the total fringe order over the model domain, and the unwrapped isochromatic phase map is shown in Fig. 2.8(d) as gray scale plot and the MATLAB plot of the same is shown in fig. Although data can be collected anywhere from the fringe field, for ease of convergence it has been reported [15] that the fringe order and the corresponding position coordinates should be collected so that when plotted they capture the basic geometric properties of the fringe. field near the crack tip.
Since data must be collected closer to the crack tip for each load step, manual data collection along thin edge skeletons would be not only inaccurate but also tedious. A total of 345 and 393 data points were collected for the SEN specimen and the parallel interacting edge cracked specimen, respectively. For the SEN specimen, the seven-parameter solution is found to be adequate with a convergence error of 0.112, while for the interacting parallel-edge cracked specimen, the twelve-parameter solution is found to model the stress field better with the error of convergence of 0.056.
2.11 (b) shows the magnified image of theoretically reconstructed dark field isochromatic fringe pattern around the lower crack of interaction with parallel edge cracked specimen obtained using a twelve-parameter solution with data points superimposed.
Numerical computation of SIF’s
In both FE models, an 8-node quadrilateral element (PLANE183) is used and the element size at the crack tip is kept at 0.001 mm. 2.12 (a) Two coincident nodes near the crack tip before loading (b) Two closest nodes near the crack tip after loading.
Results and Discussion
For SEN samples, a good agreement can be observed between the results obtained by all three methods. For interaction with parallel edge cracked specimen, results of FEM and experimental method show good agreement; however, analytical results show significant deviation.
Closure
Introduction
This chapter deals with the evaluation of mixed-mode SIFs using whole-field displacement data acquired by 3D-DIC. It also shows the various codes / software used for various purposes in the current work (written out of the box). 29] for the estimation of mixed-mode SIFs of the whole field displacement field, was implemented in modified form to achieve reliable and better rate of convergence.
The required displacement field around the crack tip is obtained by analyzing the acquired images using the commercially available Vic-3D software [47], whose advanced data processing functions are used to collect data (x, y, u and v) along the u and v contours. The number of terms required in the multiparameter displacement field equations to correctly model the displacement field increases until the reconstructed displacement field u and v match the experimental distribution.
Multi-parameter displacement field equations
Over-deterministic nonlinear least squares methodology
Formulation of equations
Although any of the Eq. 3.2) tends to increase the computation time by reducing the rate of convergence since it is non-linear in terms of unknowns Tx, Ty and R. Where i = the iteration step and ∆A is correction added to the previous estimates of A must be To determine the corrections, (hm) i+1 = 0.
Convergence criteria
Implementation
Experimental validation
Specimen preparation
Experimental procedure
To ensure a one-to-one match between the image and the current load, the acquisition of images and load data is synchronized with the direct input of the load signals to VicSnap.
Data analysis
Here too, the data points in both cases coincide reasonably well with the reconstructed displacement field. In both cases, the data points correspond well to the reconstructed displacement contours, ensuring the adequacy of the number of parameters.
Results and Discussion
For both samples, the SIFs are estimated at sufficiently high loads due to the previously mentioned reason of DIC resolution limitation.
Closure
Using this data, a MATLAB program is used to estimate the mixed mode SIF as well as the rigid body motion values and the position coordinates of the crack tip location. The study highlights that DIC can be used as an effective and reliable tool in the field of fracture mechanics to evaluate mixed mode SIF. Tyrer, Phase-stepped ESPI and Moiré interferometry for Measuring Stress-intensity Factor and J-Integral, Experimental Mechanics.
Xu, Mixed-mode crack-tip deformations studied using a modified bending test and coherent gradient sensing, Experimental Mechanics. Dally, A general method for determining mixed strain intensity factors from isochromatic fringe patterns, Engineering Fracture Mechanics. Ravi-Chandar, Experimental determination of the dynamic stress intensity factor using caustics and photoelasticity, Experimental Mech.
Huang, Application of stereo vision to the study of mixed-mode crack-type deformations, Optics and Lasers in Engineering. Kobayashi, Estimation of mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, Engineering Fracture Mechanics. 31] Rui Zhang and Lingfeng He, Measurement of mixed mode stress intensity factors using digital image correlation method, Optics and Lasers in Engineering.
34] Rafael Picon, Federico Paris, Jose Ca|as and Juan Marin, A complete field method for the photoelastic determination of KI and KII in general mixed-mode fractures, Engineering Fracture Mechanics.
![Fig. 1.5 Schematic of deformation process in two dimensions with subsets in deformed and un- un-deformed state [20]](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10557271.0/18.892.225.668.735.1051/schematic-deformation-process-dimensions-subsets-deformed-deformed-state.webp)
