Arbitrarily oriented microcracks near the tip of an interface macrocrack in bonded dissimilar anisotropic materials

It is well known that microcracking in brittle materials results in a reduction of the stress intensity factor (SIF) and energy release rate (ERR). The reduced SIF or ERR represents crack tip shielding which is of significant interest to micromechanics and material science researchers. However, the effect of microcracking on the SIF and ERR is a complicated subject even for isotropic homogeneous materials, and becomes much more formidable in case of interface cracks in bonded dissimilar solids. To unravel the micromechanics of interface crack tip shielding in bonded dissimilar anisotropic solids, an interface crack interacting with arbitrarily oriented subinterface microcracks in bonded dissimilar anisotropic materials is studied. After deducing the fundamental solutions for a subinterface crack under concentrated normal and tangential tractions, the present interaction problem is reduced to a system of integral equations which is then solved numerically. A J‐integral analysis is then performed with special attention focused on the J₂‐integral in a local coordinate system attached to the microcracks. Theoretical and numerical results reassert the conservation law of the J‐integral derived for isotropic materials 1 , 2 also to be valid for bonded dissimilar anisotropic materials. It is further concluded that there is a wastage when the remote J‐integral transmits across the microcracking zone from infinity to the interface macrocrack tip. In order to highlight the influence of microstructure on the interfacial crack tip stress field, the crack tip SIF and ERR in several typical cases are presented. It is interesting to note that the Mode I SIF at the interface crack tip is quite different from the ERR in bonded dissimilar anisotropic materials.     

K Variations and Anisotropy: Microstructure Effect and Numerical Predictions

Computer experiments were performed on simulated polycrystalline material samples that possess locally anisotropic microstructures to investigate stress intensity factor ( K ) variations and anisotropy along fronts of microcracks of different sizes. The anisotropic K , arising from inhomogeneous stresses in broken grains, was determined for planar microcracks by using a weight function-based numerical technique. It has been found that the grain-orientation-geometry-induced local anisotropy produces large variations in K along front of microcracks, when the crack size is of the order of few grain diameters. Synergetic effect of grain orientation and geometry of broken grains control K variations and evolution along the microcrack front. The K variations may diminish at large crack sizes, signifying a shift of K calculation to bulk stress dependence from local stress dependence. Local grain geometry and texture may lead to K anisotropy, producing unusually higher/lower K at a segment of the crack front. Either K variation or anisotropy cannot be ignored when assessing a microcrack.     

A simulation on growth of multiple small cracks under stress corrosion

In order to keep high reliability of components in a nuclear power plant, it is important to understand the damaging process due to multiple small cracks. The growth shows random behavior because of the microstructural inhomogeneity and the interaction between cracks. The former includes the effects of crack kinking and anisotropic deformation in each crystal of polycrystalline. In this study, a Monte Carlo simulation method is developed in order to analyze the random behavior, taking into account the their influences on the stress intensity factor. The damaging process of mill-annealed alloy 600 in the primary water stress corrosion cracking (PWSCC) is numerically simulated by the proposed method. The crack size distribution obtained agrees well with the experimental observation, and the maximum crack size is statistically estimated on the basis of the Gumbel statistics.     

BIEM for 2D steady-state problems in cracked anisotropic materials

The two-dimensional ‘in-plane’ time-harmonic elasto-dynamic problem for anisotropic cracked solid is studied. The non-hypersingular traction boundary integral equation method (BIEM) is used in conjunction with closed form frequency dependent fundamental solution, obtained by Radon transform. Accuracy and convergence of the numerical solution for stress intensity factor (SIF) is studied by comparison with existing solutions in isotropic, transversely-isotropic and orthotropic cases. In addition a parametric study for the wave field sensitivity on wave, crack and anisotropic material parameters is presented.     

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading*

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.     

The influence of crystal anisotropy on mechanical behaviour

Anisotropy of crystal structure leads to complications in mechanical behaviour. Robert Cahn, 50 years ago, made valuable contributions through determination of crystallographic features of plastic deformation in large crystals in polycrystalline -uranium. This research area has become increasingly linked with the effects of internal and external stresses on many materials in polycrystalline form comprised of grains with anisotropic crystal structure. The extent of irreversibility of deformation when such materials are subjected to thermal cycles leads to the significance of crystallographic textures but major effects on mechanical behaviour are often apparent where grains are randomly aligned without preferred crystal orientation when small external stresses are imposed. The importance of these features, their main characteristics and their analysis are briefly reviewed     

Computational modeling of strong and weak discontinuities using the extended finite element method

In this article, the extended finite element method is employed to solve problems, including weak and strong discontinuities. To this end, a level set framework is used to represent the discontinuities location, and the Heaviside and Branch function are included in the standard finite element method. The case of two arbitrary curved cracks is solved numerically and stress intensity factor (SIF) values at the crack tips are calculated based on the evaluation of the crack tip opening displacement. Afterwards, J-integral methodology is adopted to evaluate the SIFs for isotropic and anisotropic bi-material interface crack problems. Numerical results are verified with those presented in the literature.     

Effects of notch radius and anisotropy on the crack tip plastic zone

Factors which influence the shape and size of the plastic zone in the immediate vicinity of a crack tip in isotropic materials at small loads are investigated. The plastic zone dimensions for the opening mode (Mode I) have been calculated over a range of values for the crack tip radius. An increase in tip radius results in an increase in the plastic zone dimension. In anisotropic materials, the orientation of crack slit and the anisotropic yield constants are other factors that affect the plastic zone size and shape. In this paper, typical curves for the shape and size of plastic zone are given to illustrate the influence of normal or shear anisotropic yield constants. For sheet metals the effects of anisotropy on the plastic zone dimensions can be evaluated in terms of R values. Suggested values of constant b for isotropic materials are given if the “radius” approximation is employed for small applied stresses.     

A new analytical method for stress intensity factors based on insitu measurement of crack deformation under biaxial tension

A new approach for the calculation of stress intensity factors (SIF) for isotropic and orthotropic materials under biaxial tension loading was proposed in this paper. In order to determine SIF from the full-field displacement data, an asymptotic expansion of the crack tip displacement field was performed. The deforming shape and surface residual stress of the crack tip was obtained at the early extended stage of the loading process by using optical microscope and X-ray diffraction measurement. During this stage, a modified Dugdale Model, which takes into account the coupled effect at the crack tip, was proposed for the open displacement of the crack tip. In this paper, the SIFs of two types of silicon steel sheet with isotropic and orthotropic properties were calculated using the modified Dugdale Model based on the biaxial tension experimental data. From the results, it was found that analysis using the modified Dugdale Model is an effective way to evaluate SIF under biaxial stress.     

Fracture analysis of anisotropic materials using enriched crack tip elements

Enriched finite element methodology, which employs special crack tip elements, is extended for cracks in anisotropic materials. Enrichment formulation is described briefly and three validation examples using single crystal, directionally solidified, and orthotropic material properties are presented to demonstrate the accuracy and effectiveness of the methodology. In addition to validation examples, the effect of material anisotropy on stress intensity factors is investigated using the common compact tension specimen and the results are compared to the ASTM solution for isotropic materials. It is shown that the effect of anisotropy on the computed stress intensity factors can be significant, depending on the degree of anisotropy, material orientation, and a/W ratio in the compact tension specimen geometry.     

Dynamic fracture analysis of a smoothly inhomogeneous plane containing defects by BEM

In this work, the dynamic interaction between defects of different types such as cracks and cavities in a smoothly inhomogeneous, elastic anisotropic plane subjected to incident SH-waves is investigated.Solution of the ensuing boundary-value problem is numerically realized using the non-hypersingular, traction boundary element method (BEM). By employing a special functional transform, the wave equation for inhomogeneous media is reduced to one with constant coefficients and the relevant frequency-dependent fundamental solution for graded anisotropic continua is obtained by the Radon transform. All surface discretizations are then done by standard collocation procedure with a parabolic type of approximation of all field variables. Next, validation of the numerical method is carried out through comparisons with available solutions for crack stress intensity factors (SIFs) and for cavity stress concentration factors (SCF).A detailed parametric study is then undertaken for a circular cavity interacting with a stationary, mode III crack in the presence of a propagating SH-wave. In sum, the key parameters of the simulation study are the characteristics of the incident wave, the geometry and configuration of the defects, the material inhomogeneity, and the dynamic interaction between the defects. The influence of all these key parameters on the dynamic SIF and SCF for different defects is finally discussed.     

Phase‐field‐crystal study on deformation behavior of nanoscale monocrack system in the ductile‐to‐brittle transition region

Phase‐field‐crystal method is applied to study deformation behavior in the ductile‐to‐brittle transition region of the nanoscale monocrack system in this work. The influence of temperature, crystal orientation angle, and crack shape on the deformation behavior is investigated. Temperature can induce fracture mode change, while crystal orientation angle and crack shape can only affect the specific evolutionary behavior. In the ductile region, if the orientation of a vertex is approximately aligned with a certain close‐packed direction, crack extends shortly in cleavage mode at this vertex, which means cleavage crack propagation can be promoted in a particular range of crystal orientation angle. Additionally, the influence of crack shape is achieved by varying the orientation relationship between crack and lattice structure. In the brittle region, crystal orientation angle impacts on the specific cleavage evolution process, and crack shape can promote or hinder plastic deformation by affecting stress concentration.     

Stress intensity factors of square crack inclined to interface of transversely isotropic bi-material

This paper analyzes a square crack in a transversely isotropic bi-material solid by using dual boundary element method. The square crack is inclined to the interface of the bi-material. The fundamental solution for the bi-material solid occupying an infinite region is incorporated into the dual boundary integral equations. The square crack can have an arbitrary angle with respect to the plane of isotropy of the bi-material occupying either finite or infinite regions. The stress intensity factor (SIF) values of the modes I, II, and III associated with the square crack are calculated from the crack opening displacements. Numerical results show that the properties of the anisotropic bi-material have evident influences on the values of the three SIFs. The values of the three SIFs are further examined by taking into account the effect of the external boundary of the internally cracked bi-material.     

A theoretical investigation into the nucleation of stable crack precursors in polycrystalline ice

The possible formation of small stable cracks (crack precursors) at grain triple points in polycrystalline S2 ice subjected to stresses below that required to nucleate grain-size cracks is examined theoretically at –10° C. The investigation is based on the theory that stress concentrations can arise from the crystal elastic anisotropy and the pile-up of grain boundary dislocations at the triple point. Using an energy approach, numerical simulations of a model show that (i) small stable cracks can initiate from triple points under small stresses, (ii) unstable Griffith cracks can also nucleate, (iii) the smallest nucleation stresses are weakly dependent on hydrostatic compression and crystal orientation, and obey approximately the Hall-Petch relation with respect to the mean grain size, (iv) the crack to grain boundary length ratios are statistically distributed rather than constant, and (v) crack nucleation is strongly influenced by the orientations of the grain boundaries with respect to the applied stress and by the grain boundary dislocation configurations (positive or negative).     

Microstructure and load sensitive fatigue crack nucleation in Ti-6242 using accelerated crystal plasticity FEM simulations

This paper investigates microstructure and load sensitive fatigue behavior of Ti-6242 using cyclic crystal plasticity finite element (CPFE) simulations of statistically equivalent image-based microstructures. A wavelet transformation induced multi-time scaling (WATMUS) method [1], [2] is used to perform accelerated cyclic CPFE simulations till crack nucleation, otherwise infeasible using conventional time integration schemes. A physically motivated crack nucleation model in terms of crystal plasticity variables [3] is extended in this work to predict nucleation. The crack nucleation model is based on dislocation pile-up and stress concentration at grain boundaries, caused by inhomogeneous plastic deformation in the polycrystalline microstructure. The model is calibrated and validated with experiments. The dependence of yield strength on the underlying grain orientations and sizes is developed through the introduction of an effective microstructural parameter Plastic Flow Index or PFI. To determine the effects of the microstructure on crack nucleation, a local microstructural variable is defined in terms of the surface area fraction of soft grains surrounding each hard grain or SAFSSG. Simulations with different cyclic load patterns suggest that fatigue crack nucleation in Ti-6242 strongly depends on the dwell cycle hold time at maximum stress.     

Fatigue crack initiation in AA2024: A coupled micromechanical testing and crystal plasticity study

A new combined experimental and modelling approach has been developed in order to understand the physical mechanisms that lead to crack nucleation in a polycrystalline aluminium alloy AA2024 undergoing cyclic loading. Four‐point bending low‐cycle fatigue tests were performed inside the chamber of a scanning electron microscope on specimens with a through‐thickness central hole, introduced to localize stresses and strains in a small region on the top surface of the sample. Fatigue crack initiation and small crack growth mechanisms were analyzed through high‐resolution scanning electron microscope images, local orientation measurements using electron‐back‐scattered‐diffraction, and local strain measurements using digital image correlation. A crystal plasticity finite element model was developed to simulate the cyclic deformation behaviour of AA2024. Two‐dimensional Voronoi‐based microstructures were generated, and the material parameters for the constitutive equations (including both isotropic and kinematic hardening) were identified using monotonic and fully reversed cyclic tests. A commonly used fatigue crack initiation criterion found in the literature, the maximum accumulated plastic slip, was evaluated in the crystal plasticity finite element model but could not predict the formation of cracks away from the edge of the hole in the deformed specimens. A new criterion combining 2 parameters: The maximum accumulated slip over each individual (critical) slip system and the maximum accumulated slip over all slip systems were formulated to reproduce the experimental locations of crack nucleation in the microstructure.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.     

A wedge crack in an anisotropic material under antiplane shear

A crack emanating from the apex of an infinite wedge in an anisotropic material under antiplane shear is investigated. An isotropic wedge crack subjected to concentrated forces is first solved by using the conformal mapping technique. The solution of an anisotropic wedge crack is obtained from that of the transformed isotropic wedge crack based on a linear transformation method. Expressions for the stress intensity factor for the anisotropic wedge crack with both concentrated and distributed loads are derived. The stress intensity factors are numerically calculated for generally orthotropic wedge cracks with various crack and wedge angles as well as anisotropic parameters.     

The limits of Poisson's ratio in polycrystalline bodies

While it has been established that the elastic moduli and compliances of anisotropic and isotropic materials should be positive for thermodynamic reasons, no condition related to the values of Poisson's ratio has yet been established. However, it is generally accepted that for isotropic materials Poisson's ratio should vary between — 1.0 and 0.5, whereas for orthotropic materials various conditions have been introduced relating the different components of the anisotropic Poisson's ratio with the remaining elastic constants of the material. In this paper, limits for Poisson's ratio of body-centred cubic (bcc) polycrystalline materials are determined, based on the modes of deformation of a typical unit cell of the material subjected to a uniform external loading arbitrarily oriented relative to the principal axes of the crystal. It is shown that the values of Poisson's ratio thus established correlate satisfactorily with experimental values of this constant. The procedure can be readily applied to other structural units of polycrystalline bodies.