Stationary Crack-tip Fields Research Articles

The grain orientation effects on crack-tip fields for additively manufactured titanium alloy: A peridynamic study

In this work, a macroscale description method for grain orientation effects in α-phase additively manufactured titanium alloy is proposed within peridynamic framework, and peridynamic simulations of grain orientation effects on crack-tip fields are performed. The proposed method describes the grain orientation effects by introducing anisotropic peridynamic parameters which are later calibrated according to strain energy density. Then, stationary crack-tip fields in single-crystal model, stationary crack-tip fields in polycrystalline model, and crack-tip fields at branching in polycrystalline model are respectively simulated, whose results are analyzed in detail as well as compared with experimental observations. In the end, some discussions and further considerations are presented, which indicates our efforts to future works. The proposed method may help develop a way to reveal interactive relationships among grain features, crack-tip fields and crack propagation behaviors.

Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity: II. Stationary crack-tip fields

Small-scale yielding around a stationary mode I crack in a cubic single crystal is analyzed in terms of plane-strain elastically anisotropic discrete dislocation plasticity (DDP). Two symmetric crack orientations are considered with two objectives in mind. First, we study the sensitivity to materials aspects such as dislocation source density and elastic anisotropy as well as orientation dependence. Plastic deformation around the crack tip in a single crystal is a patchy field due to the discreteness of the slip systems, as demonstrated in analytical solutions and experimental observations. While these solutions/observations have in common that the plastic zone is composed of sectors with specific slip system(s) active inside each sector, detailed comparisons—recapitulated in this paper—reveal a few, yet significant, discrepancies. In an attempt to resolve these issues, the second objective of this paper is to construct sector arrangements of active slip system(s) from the present DDP simulations and compare those with the analytical solutions. We find that the estimated sector arrangements are in best agreement with the hardening analytical solutions of Saeedvafa and Rice (1989 J. Mech. Phys. Solids 37 673–91); indeed, angular variations of stresses around the crack tip confirm this observation.

Effect of loading rate on crack tip fields in three point bend fracture specimen of FCC single crystal

In this work, the effect of impact loading on mode I stationary crack tip fields in a three point bend FCC single crystal fracture specimen is investigated using plane strain finite element analysis. The behavior of the single crystal is assumed to be elastic-perfectly plastic. The main objective is to examine the role of material inertia in influencing the stress levels as well as the pattern of slip and kink shear bands around the tip. The results show that under quasi-static loading high stress levels prevail ahead of the notch tip. However, the specimen suffers considerable loss of constraint under dynamic loading, particularly during the initial stages. This increases with loading rate J ˙ . Also significant spread of the plastic zone occurs in the forward sector ahead of the tip under impact loading which is akin to isotropic solids. The pattern of shear bands around the tip in the single crystal also changes with impact velocity. In rate dependent single crystals, a competition between rate sensitivity and material inertia is observed. Thus, while the former enhances the stresses near the tip, the latter tends to reduce them.

Higher-Order Terms for the Mode-III Stationary Crack-Tip Fields in a Functionally Graded Material

This paper provides full asymptotic crack-tip field solutions for an antiplane (mode-III) stationary crack in a functionally graded material. We use the complex variable approach and an asymptotic scaling factor to provide an efficient procedure for solving standard and perturbed Laplace equations associated with antiplane fracture in a graded material. We present the out-of-plane displacement and the shear stress solutions for a crack in exponentially and linearly graded materials by considering the gradation of the shear modulus either parallel or perpendicular to the crack. We discuss the characteristics of the asymptotic solutions for a graded material in comparison with the homogeneous solutions. We address the effects of the mode-III stress intensity factor and the antiplane T-stress onto crack-tip field solutions. Finally, engineering significance of the present work is discussed.

Stationary crack tip fields in elastic–plastic solids: an overview of recent numerical simulations

In this paper, an overview of some recent numerical simulations of stationary crack tip fields in elastic–plastic solids is presented. First, asymptotic analyses carried out within the framework of 2D plane strain or plane stress conditions in both pressure insensitive and pressure sensitive plastic solids are reviewed. This is followed by discussion of salient results obtained from recent computational studies. These pertain to 3D characteristics of elastic–plastic near-front fields under mixed mode loading, mechanics of fracture and simulation of near-tip shear banding process of amorphous alloys and influence of crack tip constraint on the structure of near-tip fields in ductile single crystals. These results serve to illustrate several important features associated with stress and strain distributions near the crack tip and provide the foundation for understanding the operative failure mechanisms. The paper concludes by highlighting some of the future prospects for this field of study.

Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones, notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode II component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.

Mode I crack tip fields in amorphous materials with application to metallic glasses

In this work, stationary crack tip fields in amorphous materials such as metallic glasses under mode I loading are studied to understand the factors that control crack tip plasticity and in turn impart toughness to those materials. For this purpose, finite element simulations under plane strain, small scale yielding conditions are performed. A continuum elastic–viscoplastic constitutive theory, which accounts for pressure sensitivity of plastic flow as well as the localization of plastic strain into discrete shear bands, is employed to represent the material behavior. The influence of internal friction and strain softening on the plastic zone, stress and deformation fields and notch opening profile is examined. It is found that higher internal friction leads to a larger plastic zone. Also, it enhances the plastic strain ahead of the notch tip but leads to a substantial decrease in the opening stress. Thus, it appears that a higher friction parameter promotes toughening of amorphous solids. The shear band patterns within the plastic zone and brittle crack trajectories around the notch root generated from the simulations match qualitatively with those observed in experiments.

Asymptotic solutions for tensile crack tip fields without kink-type shear bands in elastic-ideally plastic single crystals

Asymptotic solutions for the near-tip stress fields (and important features of the deformation fields) are derived for stationary plane strain tensile cracks in elastic-ideally plastic single crystals. The cases treated are (0 1 0) cracks pointing in the [1 0 1] direction, and (1 0 1) cracks in the [0 1 0] direction, for both FCC and BCC crystals that yield according to the critical resolved shear stress criterion. The objective is to derive solutions that concur with recent experimental studies and numerical discrete dislocation simulations of stationary crack tip fields in ductile single crystals. The solutions are derived within an extension of the framework laid down in the pioneering analysis of Rice (Mech. Mater. 6 (1987) 317). Rice's solutions for the near-tip fields for cracks of the types considered here are at yield at all angles about the crack tip, and necessarily involve rays of stress and displacement discontinuity, with the latter being of both slip and kink type. His solutions capture several important features of the experiments and discrete dislocation simulations; however, there are significant differences, a key one being that the experiments, and in most cases the discrete dislocation simulations, do not appear to exhibit kink-type shear concentrations for the symmetric crack orientations considered. Thus we seek here asymptotic near-tip solutions that are free of kink-type displacement discontinuities. This necessitates the introduction of sub-yield near-tip sectors to permit derivation of solutions that produce the high stress triaxiality expected ahead of a crack tip under well-contained yielding conditions. The resulting solutions show several interesting differences with Rice's solutions. A major one is that for cracks having the same orientations in FCC and BCC crystals, the near-tip stress fields in Rice's solutions have identical sector assemblies and thus very similar character, whereas the present solutions for the FCC and BCC cases differ substantially. Another difference is that for the two crack orientations noted above in an FCC crystal (or in a BCC crystal), Rice's near-tip stress field solutions are identical, whereas the present solutions differ substantially from one orientation to another. The experimental and discrete dislocation simulations confirm these features of the new solutions.

A finite element analysis of stationary crack tip fields in a pressure sensitive constrained ductile layer

Polymeric ductile adhesive layers joining two elastic adherends is a common feature in various technological applications. Such joints can fail by ductile rupture involving interface debonding and void formation. It has been observed that, unlike in metals, the yield behaviour of polymers is affected by the state of hydrostatic stress. In the present study, the effect of pressure sensitivity of yielding on the stress and deformation fields near a stationary crack tip in a constrained adhesive layer is examined. To this end, finite deformation, finite element analyses of a cracked, sandwiched adhesive layer are carried out under plane strain, small-scale yielding conditions for a wide range of mode mixities. The Drucker–Prager constitutive equations are employed to represent the behaviour of the layer. Both dilational and non-dilational plastic flow are considered. It is found that the stress levels in the layer decrease with increasing pressure sensitivity irrespective of mode mixity. The effect of pressure sensitivity on the notch tip deformation, and near tip plastic mode mixity, is also investigated. Finally, theoretical predictions are made about the variation of fracture toughness with mode mixity due to interface debonding.

Transient effect on ideally plastic stationary crack-tip fields

This paper analyses the transient effect on ideally plastic stationary crack-tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems. of ideally plastic stationary crack-tip fields when the inertia forces are not negligible.

Transient effect on ideally plastic stationary crack tip fields

This paper analyses the transient effect on ideally plastic stationary crack tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack tip fields when the inertial forces are not negligible.

Transient crack-tip fields for mixed-mode power law creep

Mixed-mode stationary crack-tip fields are obtained for an elastic-nonlinear viscous power law creeping solid under conditions of plane strain and small-scale creep. Power law exponents of 2 and 5 are considered which are representative of the creep response of a wide range of ceramics and metals. The imposed far-field mixity ranges from pure mode I to pure mode II. Crack tip fields are calculated during the transient regime using a detailed finite element analysis and are shown to be governed by a Hutchinson-Rice-Rosengren type singularity over the inner one fifth of the creep zone. Dominance of universal mixed-mode near-tip fields within the inner creep zone is found for several mixtures of far-field mode I and mode II. The pronounced effects of the amount of mixity on the size and shape of the creep zone as well as on the time required to reach extensive creep conditions are determined. For a creep exponent of 5, it is estimated that the creep zone grows about seven times faster in mode II than in mode I, with a corresponding decrease in the transition time from small-scale to extensive creep. For a creep exponent of 2, the creep zone grows about six times faster in mode II than in mode I. Finally, the mixed-mode creep fields are used to assess possible beneficial effects of crack deflection or branching in metals and ceramics at elevated temperatures.