After a description of each measurement technique is given, stress intensity factor measurements made on 12.7 mm thick pre-cracked 6Al-4V titanium specimens are compared. Side grooves are required for the more ductile 6Al-4V titanium ELI and Timetal 5111 materials to obtain plane strain fracture toughness values.
Fracture Mechanics Preliminaries
- Fracture Mechanics
- Linear Elastic Fracture Mechanics
- Quasistatic and Dynamic Stress Intensity Factors
- Small Scale Yielding
- Failure Criterion
- Elastic–Plastic Fracture Mechanics
- Research Goal
Because of this dominance, the coefficient (or magnitude) of the leading term can serve as a single parameter description of the stress state at the crack tip. The left side is the stress intensity applied to the crack tip and depends on the geometry and loading history.
Four Fracture Toughness Measurement Techniques
Overview
Side grooves are necessary to obtain plane strain fracture toughness values from specimens that are otherwise insufficiently thick.
BoundaryLoad Measurement Calculation
The first is the three-point bending geometry, where the stress intensity factor KI is given by. 2 (2.2) where P is the applied load and all other variables are derived from the specimen geometry as shown in Figure 2.1.
Crack Opening Displacement (COD)
- Overview and Governing Equations
- Implementation
However, the opening measurements made on the EDM cut are at least 2 mm from the crack tip and not at the location specified in the definition of δ. Using this constitutive approximation, the COD analysis is greatly simplified and the opening at the EDM point can be easily related to the crack tip.
Strain Gage Measurement
- Overview and Governing Equations
- Measuring K I d with One Strain Gage
- Measuring T Stress with One Strain Gage
A resistance meter forms one leg of the bridge, and three resistors of the same value fill the remaining legs. Often the gradient error correction will be smaller than the uncertainty in the strain gauge position.
Coherent Gradient Sensing (CGS)
- CGS Overview
- CGS Setup
- Implementation
After the laser beam reflects off the surface of the deformed sample, it passes through two diffraction gratings which process the beam to give fringes of constant out-of-plane displacement gradient. 2 The beam splitter can be removed by reflecting the beam off the sample at an angle sufficient to avoid blocking the incoming beams by the gratings.
Experimental Comparison of Measurement Techniques
- Material System and Geometries
- Test Results
CGS provides the location of the crack tip (Figure 2.14), which indicates an initiation time that matches well with the strain gauge initiation time. The position of the zeroth order edge is indicated by a “0”. The first image shows that the sample surface has a slight curvature before loading, which manifests as a wide horizontal dark ridge above the crack tip. Figure 2.18 shows four COD profiles for the lateral groove sample, each at the same time as the four CGS edge patterns.
For COD measurements on ungrooved and grooved specimens, crack initiation was indicated by a jump in the crack opening angular velocity (Figure 2.21). The same for specimens with side grooves are shown in Figure 2.24, all at the same time as the CGS edge patterns.
Conclusions
Analysis of many consecutive fringe pattern images is performed almost entirely objectively, so the level of noise in measured values is an indication of the amount of random measurement error. The implementation also uses a measure of fit error that describes how well the edge patterns of the crack tip mechanical field correlate with the LEFM crack tip asymptotic solution terms used. The abundance and correlation of information obtained by CGS helps to build confidence in its measurement results and establish it as the benchmark for evaluating the other two methods in this case where all three methods can be used.
The use of opening measurements behind the crack tip in the EDM notch is essential because light only penetrates the fatigue crack after crack initiation has already occurred. Although strain gauges can be used to detect initiation in ungrooved samples, samples with side grooves may require the development of an alternative method.
Improvements in Implementation of Coherent Gradient Sensing
Technique
Historyand Overview
Using higher-order fitting terms allows data further from the crack tip to be used for the determination of K. This condition requires, first, that sufficiently general crack tip solutions be used for the current analysis and, second, that the edge data used for adaptation, is within the dominance of the solution concepts used. This package highly automates the analysis of CGS fringe patterns to obtain objective results, including immediate crack tip location1, which is automatically organized and stored.
Next, the relationship between a general asymptotic LEFM crack tip solution and CGS edge patterns is developed. Other implementation advances are then detailed, including the use of edge data within the three-dimensional zone, the objective localization of the crack tip within the dark shadow spot caused by large deformations around the crack tip, and the visualization of fitting results.
CGS Governing Equations
Finally, a comparison of stress intensity results for different choices of fitting terms on experimental data is made to illustrate the usefulness of the analysis package. Next, the conditions under which the superposition of the two shifted images produces interference are investigated, given that the interrogation beam is coherent. Constructive interference between the superimposed points of the two images occurs when their ray path difference is an integer number of the light's wavelength.
In particular, the small angle at which the first deviated images pass through the second grating is ignored, and in equation (3.4) it is assumed that there is only a difference in out-of-plane displacement and no rotation of the reflecting surface, which is left generally a sufficiently accurate approximation. Here is the undeformed material's refractive index and D1 is the coefficient of the strain-optical law.
Crack Tip Asymptotic Equation
As previously mentioned, this two-dimensional plane stress assumption is valid for the interpretation of edge data taken at least a sample half-thickness distance from the crack tip. As the crack tip is approached, the stress state transitions from plane stress to plane strain in a complex three-dimensional manner. Because of the coupling, the solution of the differential equations for successive terms of the potential expansion is increasingly complex.
Typically, limiting assumptions, such as a constant crack tip velocity, are made to simplify the process by reducing the number of coefficients depending on time or space. The equations depend heavily on the crack tip velocity and acceleration, which are very difficult to determine, hence the quantities in parentheses.
Interpretation of CGS Fringe Patterns
Because of measurement error, it seems best to treat all β as variables for fitting and then later check for consistency if desired.
Fitting Data
Implementation in Matlab
- Matlab Implementation Overview
- Digitizing the CGS Fringe Patterns
- Utilizing Fringe Data Inside the Three-Dimensional Zone
- Fitting CGS Fringe Data with Asymptotic Terms
- Evaluating and Optimizing Fit and Locating Crack Tip
- Visualizing and Interpreting Results
- Comments
Before digitizing, the following must be determined: First, the location of the crack tip must be estimated and specified. The extent of the three-dimensional area is shown (the green oval, which should have the same shape and orientation as the beam image). one more directly in front of the crack tip. Matlab has a useful zoom feature that allows the higher density edges near the crack tip to be accurately digitized.
This technique eliminates the need to know absolute edge numbers and uses data very close to the crack tip. After finding the crack tip location with minimum error, a surface plot of error versus position (Figure 3.7) can be created.
A Comparison of Results Obtained byDifferent Fits
- Overview and Experiment Details
- Comparison of Stress IntensityValues
- Comparison of Fit Error
- Comparison of Crack Tip Locations
- Comments
Since the perfect fit does not indicate the presence of significant mode II components in the crack tip field (Fig. 3.13), this difference must be due to the contribution of higher-order terms. Finally, the crack tip location for each fit is considered to be the location estimated during digitization, improved by changing the crack tip location found during the crack tip search. The crack tip data is not as smooth as would be expected from the objective location method.
In any case, crack tip location data are useful for determining initiation and sufficient to estimate crack velocity. Other items of possible interest may include higher order term coefficients, digitizer-indicated crack tip location corrections found from crack tip searches in both directions normal and tangent to the crack plane, as well as changes in the angle of the crack plane.
Conclusions
Dynamic Crack Initiation
Toughness in Titanium Alloys
- Introduction
- Experimental Setup
- Quasistatic Setup
- Dynamic Test Setups
- Experimental Observations and Results
- Overview
- Initiation Toughness
- Quasistatic Load-Displacement Data
- Examination of Fracture Surfaces
- Other Results for 6Al-4V Titanium
- Other Data for 6Al-4V Ti ELI
- Conclusions
The hardness of 6Al-4V Ti was measured by all techniques using both side grooved and irregularly grooved specimens. For 6Al-4V Ti ELI (Figure 4.3) the h/rp ratio is about 2.1 for quasi-static loading, so the disparity between the starting resistance values from specimens with and without side grooves is expected to be significant. Thus unlike 6Al-4V Ti, 6Al-4V Ti ELI shows a less pronounced thickness effect compared to aluminum.
Using average plane strain values for the data obtained, the 6Al-4V Ti ELI is 53% stronger than. All fracture surfaces exhibit a granular appearance much coarser than that of the 6Al-4V Ti ELI material.
Comparison of Dynamic Stress IntensityFactor Measurement
Comparison of Techniques
Equipment Lasers, high-speed cameras, Lasers, high-speed electronics Measurement challenge Required diffraction gratings and cameras, and some and high-speed data.
CGS Data Fitting in the Three-Dimensional Zone
Overview
Calculation of Conversion Factor
If we have equations for u3 for both the three-dimensional crack tip region and the leading term of the asymptotic solution (the KI field), it is easy and useful to compare the two for r/h < 0.5. The two plots match well at the perimeter or boundary of the three-dimensional region, as expected. However, as the crack tip approaches, the contour density increases to infinity at the crack tip for the KI-field (only contours up to −3.0 are shown), while the maximum displacement contour for the three-dimensional crack is −2.2.
For the three-dimensional field, the curvature in the same region is high but measurable. The contours for the three-dimensional crack are similar, but the inner back lobe only has a magnitude of 5.
Obtaining K I from Curvature
Although the three-dimensional zone conversion factor has been successfully applied, this method has not yet been systematically tested. With the three-dimensional field contour plot in Figure B.4 in mind, the goal is to find the proportionality functiong(∆x1/h, x2/h) such that. Crack propagation generated by a horizontally polarized shear wave.Journal of the Mechanics and Physics of Solids.
On the extent of dominance of asymptotic elastodynamic fields of the crack tip: II. part – numerical investigation of three-dimensional and transient effects. Determination of the dynamic fracture toughness of AISI 4340 steel using the shadow point method.
