Near-tip Stress Intensity Research Articles

Modeling fatigue crack growth in a bimaterial specimen with the configurational forces concept

A two-dimensional finite element analysis is performed to model the behavior of fatigue cracks in bimaterial specimens made of diffusion-bonded ARMCO-iron and SAE 4340 steel with an interface perpendicular to the crack plane. The numerical analyses are based on experiments conducted by Pippan et al. [Mater. Sci. Eng. A 283 (2000) 225–233]. The concept of configurational forces is used to evaluate by post-processing the crack-tip shielding and anti-shielding effects that occur due to the differences in yield stress, hardening and coefficients of thermal expansion of ARMCO-iron and SAE 4340 steel. For given values of applied stress intensity range Δ K app and applied load ratio R app, the near-tip J-integral J tip is calculated at the maximum and minimum load. To allow for crack closure, the effective near-tip stress intensity range Δ K eff,tip is evaluated from the near-tip stress intensity range Δ K tip and the near-tip load ratio R tip. Calibration curves for homogeneous ARMCO-iron and SAE 4340 steel are used to calculate the crack growth rate da/ dN from the values of Δ K eff,tip. The distance between interface and crack tip L is varied to simulate the behavior of a growing crack. The computed curves da/ dN versus L curves are in good agreement with the experimental results.

The Near-Tip Stress Intensity Factor for a Crack Partially Penetrating an Inclusion

When a crack is lodged in an inclusion, the difference between the elastic modulus of the inclusion and matrix material will cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous material. A method is derived for calculation of the near-tip stress intensity factor for the inclusion with arbitrary shape. The derivation of the fundamental formula is based on the transformation toughening theory. The equivalent transformation strain contributed from modulus difference between inclusion and matrix is calculated from Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formula has excellent accuracy.

The lowest order solution of the crack–inhomogeneity interaction for mode I crack

The lowest order solution to crack–inhomogeneity interaction is derived for mode I crack. The basic solution evaluates the variation of near-tip stress intensity factors induced by an inhomogeneity of arbitrary shape. A set of simplified forms of the basic solution is also obtained for several special inhomogeneity shapes. As validated by numerical examples, the approximate solutions have good accuracy.

The application of the Eshelby equivalent inclusion method for unifying modulus and transformation toughening

When a crack is lodged in an inclusion, both difference between the modulus of the inclusion and matrix material and stress-free transformation strain of the inclusion will cause the near-tip stress intensity factor to be greater (amplification effect) or less (shielding or toughening effect) than that prevailing in a homogeneous material. In this paper, the inclusion may represent a second phase particle in composites and a transformation or microcracked process zone in brittle materials, which may undergo a stress-free transformation strain induced by phase transformation, microcracking, thermal expansion mismatch and so forth. A close form of solution is derived for predicting the toughening (or amplification) effect. The derivation is based on Eshelby equivalent inclusion approach that provides rigorous theoretical basis to unify the modulus and transformation contributions to the near-tip field. As validated by numerical examples, the developed formula has excellent accuracy for different application cases.

SUBCRITICAL CRACK GROWTH IN GLASSES UNDER CYCLIC LOADS: EFFECT OF HYDRODYNAMIC PRESSURE IN AQUEOUS ENVIRONMENTS

The effect of hydrodynamic pressure developed in the wake of a crack growing in a brittle material under cyclic loads in an aqueous environment is considered. The pressure acts in opposition to the movement of the crack faces, thus shielding the crack tip from the applied loads. A general hydrodynamic fluid pressure relation based on a one-dimensional Reynolds equation, which is applicable to a crack with an arbitrary crack opening profile, is developed. The model is modified to account for side flow through the thickness of the sample and cavitation near the crack tip. Both effects significantly modify the hydrodynamic pressure distribution. Finally, the resulting hydrodynamic pressure relations are combined with a fracture mechanics model to account for the change in the near-tip stress intensity. Resulting predictions of the cyclic crack-growth rate are found to be in good agreement with measured values for a borosilicate glass tested at various frequencies in a water environment. © 1997 Acta Metallurgica Inc.

Shielding due to aligned microcracks in anisotropic media

Abstract This work presents a continuum damage analysis of the effect of aligned microcracks on a dominant crack in an otherwise anisotropic medium. This geometry is particularly relevant for composite media with an aligned reinforcement phase, where aligned cracking can change the magnitude and principal axes of anisotropy. Provided that the density of aligned microcracks reaches a stable saturation value near the crack tip, the near-tip stress intensity factor, K I s , may be related to the remote value, K I 0 , in terms of the anisotropic properties of the undamaged and saturated media. Results show that of all types of damage, that which increases compliance in a direction normal to the crack plane typically reduces K I s / K I 0 near the crack tip most significantly, while comparable increases in compliance parallel to the crack growth direction produce a relatively small change. Reduction in K I s K I 0 due to increased shear compliance may be 80% of that due to increased compliance normal to the crack plane. For damage consisting of aligned microcracks, the most effective reduction in K I s / K I 0 occurs when the microcracks are oriented parallel, rather than perpendicular to the main crack. This conclusion holds even for alumina/aluminum and graphite/epoxy systems that display large anisotropy. In those cases, optimal reduction in K I s / K I 0 occurs when in addition to parallel macro and microcracks, the stiffer direction is perpendicular to the crack surfaces. This case corresponds, for example, to macrocrack extension perpendicular to aligned fibers or layers in composite materials, with pinned microcracking through fiber or layer cross sections.

Effects of interface degradation on fiber bridging of composite fatigue cracks

This paper presents a theoretical analysis that examines the effects of cyclic degradation of interface on fiber bridging of fatigue cracks in metal-matrix or intermetallic-matrix composites. Using fiber bridging models and crack-tip micromechanics results available in the literature, the frictional stresses on individual fiber/matrix interfaces located within the bridging zone in the wake of a fatigue crack in a SCS-6/Ti-6Al-4V composite are calculated. The results are used to demonstrate that a reduction of the interface friction stress by fatigue can lead to a decrease of the fiber bridging stress, and an increase in the near-tip stress intensity range. The consequence is that the near-tip stress intensity range and, thus, the crack growth of a bridged fatigue crack are sensitive to cyclic interface degradation and the distribution of the frictional stress within the bridged zone.

A Semi-Infinite Crack Partially Penetrating a Circular Inclusion

When a crack is lodged in an inclusion, differences between the moduli of the inclusion and the bulk material can cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous body. To study the influence of such moduli differences, we solve the problem of a semi-infinite crack half-way penetrating a circular inclusion. The field equations are automatically satisfied by choosing appropriate series expansions for the complex stress potentials; a doubly-infinite system of linear algebraic equations for the series coefficients then enforces continuity of traction and displacement at the inclusion boundary. Results for the reduction (or enhancement) of the stress intensity factor are given for the entire range of material parameters.

Shear, shape and orientation effects in transformation toughening

The continuum mechanics is formulated for the inelastic behavior of a ceramic material containing particles of a second phase ceramic which undergo a martensitic phase transformation when a function of the macroscopic stress state attains a critical value. A constitutive law is derived which is applicable to such materials viewed as composites. The constitutive law is similar in structure to the incremental (or flow) theories of metal plasticity in that it is characterized by a yield function (relating the critical values of the components of the stress state), a loading criterion (specifying the condition for continued deformation) and a set of flow equations (relating the increments of inelastic strains to the macroscopic stress state). Explicit forms of the constitutive law are presented for the cases in which the second phase particles are either spheres or thin oblate spheroids. The inelastic constitutive law is used to predict the toughness enhancement measured in ceramics which are strengthened by second phase particles (usually ZrO2) which undergo both dilatational and shear irreversible transformations in the presence of a macroscopic crack. The neartip stress intensity factor is related to the applied stress intensity factor for stationary and growth macroscopic cracks. Toughening is associated with crack growth and is due to the wake of transformed particles which are left behind a growing crack. The results show the importance of accounting for both the shear and dilatational components of the transformation as well as the importance of orientation effects on the values of the toughness enhancement.

High strain-rate crack growth in rate-dependent plastic solids

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10 3 s −1 to 10 5 s −1. At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.

Continuum theory of dilatant transformation toughening in ceramics

A continuum description is introduced for an elastic solid which contains particles that undergo an irreversible stress-induced dilatant transformation. The behaviors of the composite solid considered range from abrupt complete transformation at a critical mean stress to strain controlled transformation at constant stress. It is useful to define and distinguish between super-critically and sub-critically transforming materials. Stress and strain fields in the transformation zone at the tip of a macroscopic crack are determined for stationary and growing cracks. The near-tip stress intensity factor is related to the applied stress intensity factor. Toughening is associated with crack advance and is due to the wake of transformed particles which are left behind a quasi-statically advancing crack-tip. Detailed calculations for the toughening are made over a wide range of possible material parameters.