Near-tip Deformation Fields Research Articles

Characterisation of fatigue crack tip field in the presence of significant plasticity

Characterisation of a fatigue crack tip in the presence of significant plasticity has been challenging due to the lack of suitable tools and lack of knowledge of material constitutive information under cyclic loading. In this paper, Digital Image Correlation (DIC) and integrated finite element (FE) analyses have been used to characterise the crack-tip field beyond the small-scale yielding (SSY) regime in a stainless steel 316L of a compact-tension (CT) specimen under mode I loading conditions. The non-linear characteristics of the near-tip deformation field were verified by the poor fit to the William’s regression and the overestimation of the stress intensity factor K. The extent of the crack tip plasticity was estimated using a detailed constitutive material model and compared with the estimated by Irwin. The displacement fields local to a stationary fatigue crack were mapped using DIC, and inputted into the FE model as boundary conditions so that an integrated FE analysis was carried out. Fatigue pre-cracking was simulated in the FE analysis prior to the full-field analysis of the fatigue crack tip, including stress/strain distributions ahead of the crack tip and the crack opening displacement (COD) under selected loading conditions. Although a distinct “knee” was captured as an indication of crack opening from the compliance curves in both the DIC measurements and the FE analyses, consistent with the existing knowledge on the phenomenon of crack closure, it does not appear to correlate with the crack driving force measured by the J-integral.

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic-perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near-tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T-stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T-stress becomes more negative irrespective of lattice orientation. Also, the near-tip field for a range of constraint levels can be characterized by two-parameters such as K-T or J-Q as in isotropic plastic solids.

Observation of kink shear bands in an aluminium single crystal fracture specimen

The near-tip deformation field in a high-constraint three-point bend specimen of pure aluminium single crystal is studied using in situ electron back-scattered diffraction and optical metallography. The orientation considered has the notch lying on the (0 1 0) plane and the notch front along direction. Results clearly show the occurrence of a kink shear sector boundary at 90° to the notch line on the specimen free surface as predicted by the analytical model of Rice [J.R. Rice, Mech. Mater. 6 (1987) 317].

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.

Asymptotic analysis of growing crack stress/deformation fields in porous ductile metals and implications for stable crack growth

Asymptotic stress and deformation fields near a quasi-statically growing plane strain tensile crack tip in porous elastic-ideally plastic material, characterized by the Gurson-Tvergaard yield condition and associated flow rule, are derived for small uniform porosity levels throughout the range 0 to 4.54 percent. The solution configuration resembles that for crack growth in fully dense, elastically compressible, elastic-ideally plastic Huber-Mises material for this porosity range, except that the angular extents and border locations of near-tip solution sectors vary with porosity level, as do the stress and deformation fields within sectors. Increasing porosity is found to result in a dramatic reduction in maximum hydrostatic stress level, greater than that for a stationary crack; it also causes a significant angular redistribution of stresses, particularly for a range of angles ahead of the crack and adjacent to the crack flank. The near-tip deformation fields derived are employed to generalize a previously-developed, successful ductile crack growth criterion. Our model predicts that for materials having the same initial slopes of their crack growth resistance curves, but different levels of uniform porosity, higher porosity results in a substantially greater propensity for stable crack growth.

Shear dominated transonic interfacial crack growth in a bimaterial I-II. Asymptotic fields and favorable velocity regimes

Motivated by experimental observations of transonic crack tip speeds (Lambros and Rosakis, 1994c, J. Mech. Phys. Solids 43(2), 169–188), the problem of intersonic interfacial crack growth in an elastic-rigid bimaterial system is analysed. Following the analytical procedure employed in Liu et al. (1993, J. Mech. Phys. Solids 41, 1887–1954), the two-dimensional in-plane asymptotic deformation field surrounding the tip of a crack propagating intersonically along an elastic-rigid bimaterial interface, is obtained. The theoretical results show that the near-tip stress field does not exhibit oscillations, while a stress singularity weaker than 0.5 still exists and is a function of the crack tip speed. In addition, due to the intersonic nature of crack growth, a singular line emanating from the moving crack tip is present in the near-tip field. Across this line, stresses and particle velocities suffer infinite jumps. The theoretical analysis also shows that the near-tip deformation field is shear dominated. It is also shown that in the velocity range c s < v < √2 c s , either crack face contact or negative normal tractions ahead of the crack tip exist. Visual evidence of such contact is reported in Part I of this study. These observations, together with additional experimental results of Part I, lead to the conclusion that crack growth is favorable in the velocity regimes 0 < v < c s and √2 c s < v < c 1.

The interpretation of optical caustics in the presence of dynamic non-uniform crack-tip motion histories: A study based on a higher order transient crack-tip expansion

The optical method of caustics is re-examined by considering the presence of dynamic non-uniform crack-tip motion histories. Based on the higher order transient expansion obtained by Freund and Rosakis (1990, Eleventh National Congress of Applied Mechanics; 1992, J. Mech. Phys. Solids40(3), 699–719) and Rosakis et al. (1991, Int. J. Fract. 50, R39–R45), in which dynamic transient effects were included in the near-tip deformation field, the exact mapping equations of caustics are derived for non-uniformly propagating cracks. The resulting equations indicate that the classical analysis of caustics based on the assumption of KId-dominance, is inadequate to interpret the experimental caustic patterns when dynamic transient effects become significant. In this paper, an explicit relation between the instantaneous value of the dynamic stress intensity factor KId(t) and the geometrical characteristics of the caustic is established. This relation shows that for the case of non-uniformly propagating cracks, the relation between the dynamic stress intensity factor and the geometrical characteristics of the caustic pattern depends on the crack-tip acceleration and on KId(t). It also reduces to the classical relation between KId(t) and the caustic diameter for the case of KId-dominance (when the crack-tip fields are well described by the r−½ singularity in stresses). The Broberg problem is used as an example problem to check the feasibility of analysing caustics in the presence of higher order transient terms. It is shown the value of the dynamic stress intensity factor obtained by the proposed method agrees remarkably well with the exact analytical value while large errors are introduced when the classical analysis (KId-dominant) of the method of caustics is used.

The [formula omitted] integral analysis for implant specimens: A comparison for some notch geometries

Application of Rice's path-independent J integral and its extended formulations is now well established to correlate the crack growth initiation for materials under extensive plastic deformation. An elastic-plastic finite element analysis suitably formulated to admit linear work hardening of materials for a circumferentially notched axisymmetric implant specimen, commonly used to determine the fracture resistant parameters of welded joints, has been carried out under contained yielding and monotonically increasing tensile loads. The direct procedure for estimating J around the smoothly blunted notch of two different shapes has been followed to examine the role of J as a notch tip characterizing parameter and to establish a possible relationship between J and other specimen parameters. The numerical results include notch tip parameters and near-tip deformation fields. Also, the effects of the difference in weld and base metal properties on J have been investigated here. Even though the results do not predict a unique J value, they may still be employed confidently for engineering purposes in view of the justification demonstrated by the nearly path-independent J solutions obtained from a rather crude finite element formulation based on linear displacement distributions. In the present paper, an attempt has been made to predict the specimen response with the available J relations and to explore the numerical solution sensitivity to the changes in notch parameters. The problem has been decomposed into two models; one representing the circumferential notch having its faces inclined to the axis of notch symmetry while the other refers to a parallel sided flat notch in the implant specimen. An axisymmetric FE analysis that employs linear displacement distributions of the elements, suitably modelled to admit linear work hardening of the materials for incremental flow theory, has been carried out under axisymmetric tensile loads. The numerical results include notch tip parameters and near-tip deformation fields for both cases. Also, the effects of the difference in weld and base metal properties on various J relations have been investigated for a typical notch geometry. We first consider the inclined notch test specimen where both elastic and elastic-plastic analyses have been performed, yielding some approximate expressions between J and other relevant specimen parameters. In the same way, relationships between the various J formulations, the applied loads and the various geometric parameters have been studied for the flat notched specimen. The advantage in the use of such unique expressions is that only one specimen variable is sufficient to determine the J integral and therefore the elaborate numerical procedures are avoided.

Thickness effect of notched metal sheets on deformation and fracture under tension

The deformation field in notched metal sheets stretched under tension was analysed experimentally. The results of strain distribution were explained by using the result of the near-tip deformation field of non-linear elastic material, combined with a simple model of the plastic state under a mixed plane stress and plane strain condition. Next, the relationship among fracture mechanics parameters, i.e. the notch-tip opening displacement, the notch-tip contraction and J- integral was established based on the rigid plastic strip model. Finally, the effect of the specimen thickness on the toughness value at crack initiation and instability was discussed by improving Bluhm's idea that the total fracture resistance was the sum of the fracture work for slant and flat fractures.

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

A nalyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J-integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.