DeterminingK and related stress-field parameters from displacement fields

Interface fracture mechanics is one of the main focuses of electronics reliability research. Determination of fracture mechanical properties of interface cracks is a substantial task for design for reliability comcept. Without experimental determined fracture mechanical parameters such as the critical energy release rate a reliability forecast based on simulation results cannot be given. In fracture mechanics testing often a correct measurement of the crack tip location is needed for the calculation of the energy release rate. The authors present a combined simulative and experimental method for crack tip location determination of typical interface specimens. The specimens are loaded in a newly designed testing apparatus, the Mixed Mode Chisel (MMC) setup, and images of the crack tip at the interface are taken at different load states during the testing procedure. Then images are analyzed by image correlation techniques (DAC, deformation analysis by correlation) and cra ck tip displacement fields are determined. In the next analysis step the displacement fields are compared to fields from finite element analysis of the same specimen geometry with boundary conditions similar to the experimental setup. The point of the best matching of the experimental and simulative field is the actual crack tip location. If finite-element data or analytical solution for the crack tip displacement field is available the method can be applied for a variety of different interface samples.

Fracture of brittle and ductile crystals in the generalized stress state. Strength and strain fracture criteria

A non-uniform temperature rise in the vicinity of crack tip often causes crack propagation. Taking advantage of this phenomenon, some brittle materials can be cleaved without any cutting tools but with an adequate controlling of a temperature distribution in the body.In the present paper, based on the linear fracture mechanics, a possibility of the thermal stress cleaving is discussed for a brittle rectangular plate which is heated along its symmetrical axis. A time dependent thermal stress intensity factor of an edge crack was analyzed systematically by changing the plate dimensions and crack length. Experimental findings were compared with the analytical results and good agreements were found.Especially, the crack extension characteristics in a cleaving test of a lime-soda glass can be well understood through the dependence of stress intensity factor on heating time and crack tip location.

An imaging and a strain mapping in the vicinity of a crack tip in material were investigated using a high energy white X-ray obtained from BL28B2 beam line at SPring-8 in Japan. Low-alloy and high-tensile steel (JIS G3128 SHY685) was used as a specimen prepared in the G-type geometry. A fatigue crack was introduced into the specimen by a cyclic loading. The imaging of the crack in the specimen was carried out by using the X-ray CCD camera that can detect the X-ray transmitted through the specimen. To measure the strain, the synchrotron white X-ray beam, which had a height of 80μm and a width of 300μm, was incident on the specimen with the Bragg angle θ of 5 degrees using the energy dispersive X-ray diffraction technique. The internal strain in the vicinity of the crack tip was mapped out by scanning the irradiated X-ray position around it. As the results, the imaging of the crack, with about 1mm length, in the specimen under the loading of crack opening was practicable by using the synchrotron white X-ray. The map of the internal strain near the crack tip of the steel of 5mm thickness could be obtained using the white X-ray with energy ranging from 50keV to 150keV. The plastic region estimated from the distribution of the FWHM of diffracted X-ray profile almost agreed with the theoretical value calculated by fracture mechanics. It was confirmed that the synchrotron white X-ray is useful for the imaging of the internal crack and the strain mapping near it.

We present a new methodology for the identification of a zone cohesive model that describes material failure. The material under consideration fails by crazing. The study is conducted at the micron scale in order to capture and analyze the fracture mechanism. The crack tip displacement fields are measured optically by Digital Image Correlation. The local stress intensity factors (mode I and II) and the location of the equivalent elastic crack tip are calculated during the loading. The variation of the location of the equivalent crack tip is used to track the initiation and growth of the process zone, up to the onset of crack propagation. These experimental measurements are used to define the appropriate parameters in a cohesive zone model. The methodology addresses the onset of crazing, the traction–separation profile and the maximum opening corresponding to the local nucleation of a crack. The cohesive parameters that are derived from the experimental data are consistent with results available in the literature. In addition, the model enables the characterization of the normal and tangential mode of the cohesive model.

A three dimensional adaptive multiscale method for crack growth in Silicon

Analysis of subsurface crack propagation and implications for wear of elastically deforming materials

Study of quasi-static crack growth in aluminum/alumina functionally graded material using crack gauge

Application of local approach to inhomogeneous welds. Influence of crack position and strength mismatch

The fracture behavior of materials resulting from rapidly applied loads remains poorly understood, and requires consideration of the inertial forces and rapidly changing crack front. At the same time, with the advent of improved high-speed cameras and full-field optical techniques such as digital image correlation (DIC), the spatial and temporal resolution of measurable field data has increased. As such, this thesis presents a novel hybrid experimental-computational technique that extracts dynamic fracture criterion from DIC data using improved, iterative elastodynamic expressions relating stress intensity factors (SIFs) to displacement fields around the crack front. Two variations of the solution are explored: an over-deterministic least squares regression is used when the crack tip location is known, such as at initiation of fracture, and an iterative Newton-Raphson optimization is used when the crack tip location is unknown. Dynamic fracture experiments are conducted on single-edge-notch specimens, impacted on the opposite face by a striker in mode I (or crack opening), to determine the efficacy of the method. Three materials with varying microstructures are studied: brittle polymer polymethyl methacrylate (PMMA), nanolayered metal-ceramic MAX phase Ti₃SiC₂, and human femoral cortical bone, a natural hierarchical ceramic matrix composite. PMMA is a historically well-studied material in classical dynamic fracture mechanics and is chosen as a model material, and when combined with data from literature is used to conduct validation and uncertainty quantification arising from key experimental and numerical parameters. Material rate dependency and the effect of transient wave interactions are investigated in the dynamic fracture behavior of MAX phase Ti₃SiC₂, and found to hold little influence due to the energy absorbing mechanisms of kink banding and delamination unique to the layered microstructure. Mode-mixity arising from an orthotropic microstructure is investigated in human femoral cortical bone, and lead to significant mode II SIFs even in the absence of any applied mode II loading, though mode I fracture remains dominant. These collective results demonstrate the wide variety of material microstructures with varying deformation mechanisms to which the hybrid experimental-computational dynamic fracture analysis is well-suited to handle.

: Crack tip deformations and fracture parameters in functionally graded glass-filled epoxy beams are experimentally evaluated under static and dynamic loading conditions. Beams with unidirectional, monotonic elastic gradients and cracks along the gradient are examined. SEN samples with increasing or decreasing Young's modulus ahead of the crack tip are studied in symmetric four-point bending and one-point impact loading configurations. Optical method of Coherent Gradient Sensing (CGS) is used to measure crack tip deformations prior to crack initiation. For impact loading experiments, CGS is used in conjunction with high-speed photography for recording instantaneous deformation fields. Stress intensity factors (SIF) or SIF-histories in functionally graded materials (FGM) based on locally homogeneous material descriptions in the immediate crack tip vicinity are evaluated and compared with companion finite element simulations. The influence of elastic gradients in FGM samples with cracks on the compliant and stiff sides of the beam are quantified relative to their homogeneous counterparts and with each other. Under static loading conditions, the crack tip located on the compliant side of the beam is elastically shielded when compared to the situation when the crack is on the stiffer side of the same FGM beam. Under dynamic conditions, however, elastic gradients affect crack initiation differently. Crack initiation in an FGM with a crack on the stiff side of the beam and impact occurring on the compliant edge is delayed when compared to the opposite configuration. Independent finite element simulations of FGMs with idealized elastic gradients with identical crack tip elastic properties suggest that lower crack tip loading rate in the former is responsible for the differences.

A two-dimensional (2-D) crack growth measurement method that uses moire fringes generated by circular gratings and pattern matching was developed in this work for application in structural health monitoring. The moire fringe patterns were extracted by transforming the circular gratings into linear gratings using polar-radius transformation and applying a one-dimensional average filter. The filtered image was inversely transformed to recover the moire fringes. Pattern matching was performed by comparing the absolute difference between an input fringe pattern caused by an unknown displacement and a series of reference fringe patterns of known displacements in one direction. The matching of the moire fringes caused by displacement at 90° to that in the reference patterns and combination of the two orthogonal directions was carried out after applying a rotational angle search algorithm. Demonstration using a crack model showed the applicability of the proposed system for the measurement of relative displacement of crack development along two directions with a sensitivity of 0.02 mm. The measured displacements were found to have high correlation with the actual displacements with a R2 value of 0.9985. Copyright © 2010 John Wiley & Sons, Ltd.

Progressive and iterative approximation for least squares B-spline curve and surface fitting

Mechanical damage in transportation pipelines is a threat to their structural integrity. Failure in oil and gas pipelines is catastrophic as it leads to personal fatalities, injuries, property damage, loss of production, and environmental pollution. Therefore, this issue is of extreme importance to pipeline operators, government and regulatory agencies, and local communities. As mechanical damage can occur during the course of pipeline life due to many reasons, appropriate tools and procedures for assessment of severity is necessary. There are many parameters that affect the severity of the mechanical damage related to the pipe geometry and material properties, the defect geometry and boundary conditions, and the pipe state of strain and stress. The main objective of this paper is to investigate the effect of geometry, material, and pressure variability on strain and stress fields in dented pipelines under static and cyclic pressure loading using probabilistic analysis. Most of the published literature focuses on the strain at the maximum depth for evaluation, which is not always sufficient to evaluate the severity of a certain case. The validation and calibration of the base deterministic model was based on full-instrumented full-scale tests conducted by Pipeline Research Council International as part of their active program to fully characterize mechanical damage. A total of 100 cases randomly generated using Monte Carlo simulation are analyzed in the probabilistic model. The statistical distribution of output parameters and correlation between output and input variables is presented. Moreover, regression analysis is conducted to derive mathematical formulas of the output variables in terms of practically measured variables. The results can be used directly into strain based assessment. Moreover, they can be coupled with fracture mechanics to assess cracks for which the state of stress must be known in the location of crack tip, not necessarily found in the dent peak. Furthermore, probabilities derived from the statistical distribution can be used in risk assessment.

Mechanical damage in transportation pipelines is a threat to its structural integrity. Failure in oil and gas pipelines is catastrophic as it leads to personal fatalities, injuries, property damage, loss of production and environmental pollution. Therefore, this issue is of extreme importance to Pipeline Operators, Government and Regulatory Agencies, and local Communities. As mechanical damage can occur during the course of pipeline life due to many reasons, appropriate tools and procedures for assessment of severity is necessary. There are many parameters that affect the severity of the mechanical damage related to the pipe geometry and material properties, the defect geometry and boundary conditions, and the pipe state of strain and stress. The main objective of this paper is to investigate the effect of geometry, material and pressure variability on strain and stress fields in dented pipelines under static and cyclic pressure loading using probabilistic analysis. Most of the published literate focuses on the strain at the maximum depth for evaluation which is not always sufficient to evaluate the severity of a certain case. The validation and calibration of the base deterministic model was based on full-instrumented full-scale tests conducted by Pipeline Research Council International as part of their active program to fully characterize mechanical damage. A total of 100 cases randomly generated using Monte Carlo simulations are analyzed in the probabilistic model. The statistical distribution of output parameters and correlation between output and input variables is presented. Moreover, regression analysis is conducted to derive mathematical formulas of the output variables in terms of practically measured variables. The results can be used directly into strain based design approach. Moreover, they can be coupled with fracture mechanics to assess cracks, for which the state of stress must be known in the location of crack tip, not necessarily found in the dent peak. Furthermore, probabilities derived from the statistical distribution can be used in risk assessment.