Characterizing the content of geometrically necessary dislocations (GNDs) in crystalline materials is crucial to understanding plasticity. Electron backscatter diffraction (EBSD) effectively recovers ...local crystal orientation, which is used to estimate the lattice distortion, components of the Nye dislocation density tensor (α), and subsequently the local bulk GND density of a material. This paper presents a complementary estimate of bulk GND density using measurements of local lattice curvature and strain gradients from more recent high resolution EBSD (HR-EBSD) methods. A continuum adaptation of classical equations for the distortion around a dislocation are developed and used to simulate random GND fields to validate the various available approximations of GND content.
•Classical dislocation distortion fields are adapted for continuum simulation.•These fields are used to evaluate EBSD dislocation microscopy techniques.•An estimate of GND density based on the one-norm of the Nye tensor is introduced.
Electron backscatter diffraction (EBSD) dislocation microscopy is an important, emerging field in metals characterization. Currently, calculation of geometrically necessary dislocation (GND) density ...is problematic because it has been shown to depend on the step size of the EBSD scan used to investigate the sample. This paper models the change in calculated GND density as a function of step size statistically. The model provides selection criteria for EBSD step size as well as an estimate of the total dislocation content. Evaluation of a heterogeneously deformed tantalum specimen is used to asses the method.
•The GND to SSD transition with increasing step size is analytically modeled.•Dislocation density of a microindented tantalum single crystal is measured.•Guidelines for step size selection in EBSD dislocation microscopy are presented.
•Advanced DIC techniques applied to HREBSD.•New method (ICGN HREBSD) validated using dynamically simulated patterns.•DIC-based HREBSD method compared with existing state of the art (remapping).
...Conventional high angular resolution electron backscatter diffraction (HREBSD) uses cross-correlation to track features between diffraction patterns, which are then related to the relative elastic strain and misorientation between the diffracting volumes of material. This paper adapts inverse compositional Gauss Newton (ICGN) digital image correlation (DIC) to be compatible with HREBSD. ICGN-based works by efficiently tracking not just the shift in features, but also the change in their shape. Modeling a shape change as well as a shift results in greater accuracy. This method, ICGN-based HREBSD, is applied to a simulated data set, and its performance is compared to conventional cross-correlation HREBSD, and cross-correlation HREBSD with remapping. ICGN-based HREBSD is shown to have about half the strain error of the best cross-correlation method with a comparable computation time.
•New noise reduction method for HREBSD.•HREBSD correlated with TEM and ECCI dislocation micrographs.•Single dislocations visible in HREBSD.
High resolution electron backscatter diffraction (HREBSD), ...an SEM-based diffraction technique, may be used to measure the lattice distortion of a crystalline material and to infer the geometrically necessary dislocation content. Uncertainty in the image correlation process used to compare diffraction patterns leads to an uneven distribution of measurement noise in terms of the lattice distortion, which results in erroneous identification of dislocation type and density. This work presents a method of reducing noise in HREBSD dislocation measurements by removing the effect of the most problematic components of the measured distortion. The method is then validated by comparing with TEM analysis of dislocation pile-ups near a twin boundary in austenitic stainless steel and with ECCI analysis near a nano-indentation on a tantalum oligocrystal. The HREBSD dislocation microscopy technique is able to resolve individual dislocations visible in TEM and ECCI and correctly identify their Burgers vectors.
In many applications of digital image correlation (DIC), it is advantageous to have measurements at multiple scales. Because it is rare to have natural features that can be used for DIC at multiple ...magnifications, an appropriately multiscale DIC pattern is needed. This work develops a multiscale DIC pattern that (1) contains features appropriate for both high and low magnification, (2) does not need to know the location of high magnification
a priori
, and (3) does not require specialized DIC equipment beyond what is necessary to achieve the two magnifications. The pattern is developed based on an optimization framework that minimizes expected DIC error while constraining sub-regions of the pattern to biased average grayscale values. The inclusion of local grayscale biases in the pattern has the effect of introducing resolvable features at a length scale much larger than the speckles of which the pattern is composed. Numerical and physical experiments were performed to illustrate the functionality and utility of the designed patterns. Notable among the findings is the trade off between DIC accuracy at the two scales and how it is controlled by grayscale bias.
Summary
The effects of using a traction‐free (plane‐stress) assumption to obtain the full distortion tensor from high‐resolution EBSD measurements are analyzed. Equations are derived which bound the ...traction‐free error arising from angular misorientation of the sample surface; the error in recovered distortion is shown to be quadratic with respect to that misorientation, and the maximum ‘safe’ angular misorientation is shown to be 2.7 degrees. The effects of localized stress fields on the traction‐free assumption are then examined by a numerical case study, which uses the Boussinesq formalism to model stress fields near a free surface. Except in cases where localized stress field sources occur very close to sample points, the traction‐free assumption appears to be admirably robust.
Lay description
High‐resolution electron backscatter diffraction (HR‐EBSD) enables one to measure the orientations of crystals in a material with extreme precision. This data is then frequently used to estimate residual strain values and dislocation (defect) densities within the material. However, such estimates require assumptions to be made about the microscopic stress state of the material being examined. This paper examines the validity of the assumption of a traction‐free state (zero stress vector on the surface of the sample). The assumption is found to hold over inaccurate measurement of the actual sample surface orientation (measurements not occurring along the desired plane are valid as long as they are within a few degrees of the desired plane). The assumption is also found to hold even though the measurements actually occur in material just below the surface where the traction can be non‐zero, rather than on the surface. This assumption hold as long as there are no significant stress concentrations close to the surface. In short, the traction‐free assumption appears to be robust and is therefore a valid assumption to use when estimating strain values and dislocation densities.
This paper describes a model of tumor-induced bone destruction and hyperalgesia produced by implantation of fibrosarcoma cells into the mouse calcaneus bone. Histological examination indicates that ...tumor cells adhere to the bone edge as early as post-implantation day (PID) 3, but osteolysis does not begin until PID 6, correlating with the development of hyperalgesia. C3H/He mice exhibit a reproducible hyperalgesia to mechanical and cold stimuli between PID 6 and 16. These behaviors are present but significantly reduced with subcutaneous implantation that does not involve bone. Systemic administration of morphine (ED(50) 9.0 mg/kg) dose-dependently attenuated the mechanical hyperalgesia. In contrast, bone destruction and hypersensitivity were not evident in mice implanted with melanoma tumors or a paraffin mass of similar size. A novel microperfusion technique was used to identify elevated levels of the putative algogen endothelin (ET) in perfusates collected from the tumor sites of hyperalgesic mice between PID 7 and 12. Increased ET was evident in microperfusates from fibrosarcoma tumor-implanted mice but not from melanoma tumor-implanted mice, which are not hyperalgesic. Intraplantar injection of ET-1 in naive and, to a greater extent, fibrosarcoma tumor-bearing mice produced spontaneous pain behaviors, suggesting that ET-1 activates primary afferent fibers. Intraplantar but not systemic injection of the ET-A receptor antagonist BQ-123 partially blocked tumor-associated mechanical hyperalgesia, indicating that ET-1 contributes to tumor-induced nociception. This model provides a unique approach for quantifying the behavioral, biochemical, and electrophysiological consequences of tumor-nerve interactions.
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