Multiscale strain measurements of plastically deforming polycrystalline titanium: Role of deformation heterogeneities

The purpose of this work was to characterize the spatial distribution of residual deformation at the mesoscale (a few grains) and at the macroscale (hundreds of grains) in titanium subjected to cyclic tensile loading. Using ex situ digital image correlation, we compared the axial residual strain fields obtained at optical magnifications ranging from 3.2× to 50×. To compare the results obtained at different optical magnifications, numerous images at higher magnification had to be assembled to encompass the same field-of-view observed at lower magnifications. The strain fields at the highest optical magnification revealed deformation patterns that were not detectable at lower magnifications. These deformation patterns appeared as inclined slip bands near grain boundaries and grain boundary triple points, with the bands sometimes crossing into neighboring grain interiors. Measurements made at optical magnifications greater than 10× captured an underlying deformation pattern, however, considerably more detail within grains was obtained at 50× magnification. The strain fields obtained at 10× and 50× magnifications were subsequently used to estimate the length scale of a representative volume element (RVE) based on the standard deviation of the average residual strain. The estimated RVE length scale was nearly three times the average grain diameter if extracted from the 50× results. The estimate of the RVE length scale was smaller at lower magnification which was due to a homogenizing effect caused by the low measurement resolution. Thus, care must be taken when experimentally obtaining RVE length scale estimates.     

Ductile–brittle transitions in the fracture of plastically deforming,adhesively bonded structures. Part II: Numerical studies

To enable the effective and reliable use of structural adhesive bonding in automotive applications, the cohesive properties of a joint need to be determined over a wide range of loading rates. In this paper, a strategy for determining these properties has been described and used to analyze a set of experimental results presented in a companion paper. In the particular system studied, a crack growing in a toughened quasi-static mode could make a catastrophic transition to a brittle mode of fracture. The cohesive parameters for both the toughened and brittle modes of crack growth were determined by comparing numerical predictions from cohesive-zone simulations to the results of experimental tests performed using double-cantilever beam specimens and tensile tests. The cohesive parameters were found to be essentially rate-independent for the toughened mode, but the toughness dropped by a factor of four upon a transition to the brittle mode. The results of wedge tests were used as an independent verification of the cohesive parameters, and to verify that the quasi-static properties remained rate-independent to very high crack velocities corresponding to conditions of low-velocity impact. The effects of friction, and the use of the wedge test to determine cohesive parameters, were also explored.     

Analysis of spherical indentation of materials with plastically graded surface layer

In the present work, a comprehensive parametric study for establishing contact mechanics of instrumented normal spherical indentation on homogeneous materials and materials with plastically graded surface layer (PGSL) was undertaken by dimensional analysis and finite element modeling. The spherical indentation response for homogeneous materials can be described only by two dimensionless parameters: strain hardening exponent and a unified parameter that can describe effects of both the normalized yield strength and the normalized indentation depth. The influences of these two parameters were investigated for a wide range of engineering materials, and the results may be used as an estimate of loading response and pile-up/sink-in behavior when the material properties are known. In the materials with PGSL, a linear gradient in yield strength, and no variation in elastic modulus and strain hardening exponent were explored. The indentation response of the materials with PGSL can be described only by three dimensionless parameters: the normalized indentation depth, the dimensionless strength gradient parameter, and the normalized PGSL thickness. The effects of these three parameters were studied systematically. The normalized pile-up/sink-in parameter is found to be an increasing function of the strength gradient parameter. The normalized pile-up/sink-in parameter increases (decreases) with increasing PGSL thickness for a fixed positive (negative) gradient case at large indentation depth. The results also indicate that the materials with positive PGSL can bear more loads and have significantly more resistance to contact crack formation.     

Analysis of surface cracks by holography

Presented here is a combination of holographic interferometry with a smoothing numerical method taking into consideration the balance of momentum. The method permits the experimental determination of strains, stresses as well as related quantities in fracture mechanics. An edge cracked beam subjected to three-point bending and a double torsion specimen have been selected as the specimens for illustrating the hybrid method.     

Elastic-plastic models of surface cracks in tensile panels

The surface crack is a common flaw in structures and vessels, and its elastic characterization has been studied extensively as reviewed in Ref. 1 and its references. Elastic-plastic fracture-mechanics (EPFM) technology can be used to characterize surface cracks in tough materials. Two EPFM aprameters are commonly used: the crack-tip-opening displacement (CTOD) and the three-dimensionalJ integral. This paper draws on a series of studies^2–11 at the National Bureau of Standards related to the development and verification of analyticalmodels for the calculation of EPFM parameters in surface-cracked tensile panels. The models previously verified for pipeline steel plates^4–7 are used to calculate the crack-mouth-opening displacement (CMOD) andJ for surface cracks in welded-steel specimens.     

Morphological evolution during diffusive healing of internal cracks within grains of α-iron

Micron-sized internal cracks were introduced into rounded bars of pure iron by low cycle fatigue, and the cracks had irregular penny-shaped morphology with the critical diameter of about 30μm and the thickness of 0.5–1.5μm. The initiation and propagation of the cracks were investigated quantitatively as well as their location and geometry. After vacuum annealing of the samples fatigued, the morphology in a two-dimensional longitudinal section of cracks within grains had evolved from initially elliptical one into arrays of spherical voids controlled by surface diffusion. Furthermore, a typical morphology for a broken crack with a center spherical void surrounded by outer doughnut-like cavities was observed along a perpendicular section of the specimen. Subsequently the spherical voids shrink and diminish gradually dominated by bulk diffusion. A physical model to heal an internal microcrack was proposed, in particular for the various healing stages controlled by the related dominant diffusion mechanism and their dependencies upon the morphology and geometry of an original micro-crack in materials. The project supported by the National Outstanding Young Investigator Grant of China (59925104) and the National Natural Science Foundation of China (59889101)     

A new method of analyzing surface cracks

The authors have developed a new line-spring boundary element method in thepresent paper,which combines the advantage of the line-spring model with that of theboundary element method.This method reduces the three-dimension problem of thesurface cracks into a quasi-one-dimension problem and can be used to analyze thesurface cracked plate under various loading conditions.In this paper theoreticalanalyses and numerical verifications are carried out.The calculated results arereported,which indicate that the present method is efficient and can be used to analyzethe surface crack problem on a personal computer.     

Fatigue crack growth of surface cracks in the rail web

The analytical prediction of surface cracks in the rail web is investigated by two different approaches. The first approach uses engineering fracture mechanics principles with elementary beam theory (i.e., one dimensional) stress analysis. The second approach applies the strain energy density criterion to a three dimensional finite element stress analysis of the rail web. Results are presented in terms of crack size as a function of accumulated tonnage for variations in loading (tangent or curved track), support conditions (foundation modulus), and assumed levels of residual stress. The results of both models are consistent in that the predicted growth rates are fairly slow when compared to other types of rail defects (for example, the detail fracture in the rail head).     

Variation in stress-intensity factor and back-surface displacement for surface cracks

Knowledge of the magnitude and variation in the stress-intensity factor (SIF) around the perimeter of a surface crack is essential for an accurate analysis of a flawed component. SIFs for surface flaws of various semi-elliptical geometries were analytically determined. Three-dimensional linear-elastic finite-element analysis was performed to determine the maximum SIF for bending and tension for each of 12 crack geometries which represent deep surface flaws in finite-thickness plates. Experimental verification of one of the crack geometries was performed. Interferometry techniques were used to determine the actual variation in SIF along the curve crack front due to bending. In addition to the SIF calculations, physical characteristics are noted as observed in the analytical and experimental evaluations.     

Segmental orientation in plastically deformed glassy PMMA

In this study, spatial orientational distribution functions of labeled chain segments of cross-linked and linear PMMA were obtained by solid-state NMR as a function of finite deformation (far) below and (far) above the glass transition temperature T_g. The applied data analysis allows comparison of theoretical predictions and experimental data, both in terms of the orientational probability distributions as a function of two polar angles, as well as in terms of moments of the distribution. Orientation-strain relationships of chain segments agreed above and below T_g with predictions from the rubber-elastic affine network model, but suggests a much denser network below T_g than given by the cross-link density or the entanglement density in the melt. This suggested network structure is believed to be the generator of segmental orientation during plastic deformation in the glassy state, independent of the range of applied cross-link densities and deformation rates used in this study.     

Environmentally assisted initiation and growth of multiple surface cracks

The initial stages of stress corrosion on an amorphous polymer is investigated. This is done by exposing stressed specimens of polycarbonate to an acetone and water solution. The surface develops two distinct features of degradation that appear on different length scales when subjected to tensile stress. Small pits form on the surface and make it rough. These pits are in the order of micrometers, and are found to be randomly distributed. They occur even without load and seem to slightly increase in number with increasing stress. In the millimeter domain, visible to the bare eye, surface cracks are formed transverse to the direction of loading. The occurrence of cracks is seen to have a positive stress threshold value, exceeding which, a linear increase of number of cracks with stress is found. The manners in which the cracks grow and coalesce on the surface are examined. It is seen that they do not meet crack tip to crack tip. Instead, they avoid each other initially and coalesce crack tip to crack side. The results are discussed in the light of mechanical considerations. A stress analysis for a few configurations of meeting cracks supports the experimental observations. With assumptions of stress corrosion crack growth and coalescence, a simulation of cracks growing from randomly distributed initiation sites is performed. Similar crack patterns as obtained in the experiments are found.     

A simple method for measuring surface strains around cracks

A simple system has been developed to measure surface strains that occur during in situ deformation of mechanical test specimens. The system uses photolithographically deposited displacement markers and computer image recognition routines to determine in-plane displacements and strains from digital images. The strain calculating routines are integrated into a simple mouse-driven software package that facilitates the transformation from digital images to useful strain field information. Additional routines have been developed to determine crack tip stress fields and J integrals. Crack tip stress intensities have been calculated from strain maps obtained for traction-free cracks in stainless steel. The J integrals were found to be independent of contour and consistent with applied stress intensities. Crack tip stress intensities were calculated for bridged cracks in lamellar TiAl. The toughening effect of the bridging zones was determined by including the bridged region in the contours. Resistance curves generated from strain maps were consistent with those measured during mechanical testing.     

Local weight functions for semi-elliptical surface cracks in finite thickness plates

Weight functions for any local point, 0 < Φ < π/2 along a semi-elliptical surface crack in finite thickness plates were derived from an assumed approximate general weight function and two reference stress intensity factors. The resulting weight functions were verified using available finite element results for two nonlinear stress fields and good agreement was achieved. When used together with weight functions for Φ = 0 and Φ = π/2 the weight functions are suitable for the calculation of stress intensity factors anywhere along the crack front for semi-elliptical surface cracks in complex stress fields with aspect ratios in the range 0 ≤ a/c ≤ 1 and relative depths 0 ≤ a/t ≤ 0.8.     

Propagation of surface breathing cracks in shafts under quasi-static rotary bending

Nonlinear Dynamics -     

Wave dynamics of cracks and multiple contact surface interaction

This work considers the numerical simulation of crack behavior involving contact surfaces. A surface-slipping algorithm is developed to obtain the deformation of solids containing one or several cracks under dynamic loading. A shear-loading-induced crack is also considered.     

Collinear periodical cracks with surface separation and frictional sliding

Using the method of Muskhelishvili, an exact solution is obtained for the problem of collinear, periodical cracks whose surface undergo separation and frictional sliding.