Crack Growth Criterion Research Articles

Typical Calculation Method of Stress Intensity Factors and Crack Growth Criterions on Infinite Plate Containing Hole-Edge Cracks

This paper introduces a finite element analysis software FRANC2D/L to calculate the stress intensity factor (SIF) and simulate the crack growth. Samples with infinite plate containing center crack, one hole-edge crack and two symmetrical hole-edge cracks were analyzed by this software. Comparing the SIF calculation results of the three samples based on displacement correlation method, J-integral method and virtual crack closure integral method, the results show that the three methods are all suitable for calculating the SIF problems, and the calculation precision of J-integral method and virtual crack closure integral method are better. Comparing the three crack growth criterion of maximum circumferential stress, maximum strain energy release rate and minimum strain energy density, the calculation velocity and precision of maximum circumferential stress criterion and minimum strain energy density criterion are prior to maximum strain energy release rate criterion. The calculating time and angle error of maximum strain energy release rate criterion is larger than that of the other two criterions．

Effect of KIII on Fatigue Crack Growth Behavior

In this study, mixed-mode fatigue tests are conducted using surface-cracked specimens. Slant surface-cracked specimens are prepared with crack angles of 15 deg, 30 deg, 45 deg, and 60 deg. It is shown that a “factory roof” fracture is formed at the deepest point of the surface crack due to ΔKIII and causes the crack growth rate to decrease. Additionally, fatigue crack growth is simulated using the superposition finite element method (FEM) with crack growth criteria. It is shown that conventional crack growth criteria are not applicable to factory roof fractures. Finally, a modified criterion for the prediction of crack growth rate is proposed, fatigue crack growth simulation is conducted using this criterion, and the results are compared with experimental results.

Conditions for Mode I crack deviation in orthotropic plane subjected to biaxial loading

A problem of a Mode I crack deviation is considered. It is assumed that a crack is located initially on a symmetry axis of an orthotropic plane and subjected to biaxial loading. A crack is modeled as a thin elliptical hole. The maximal tensile stresses are taken as a crack growth criterion. To stress the role of elastic anisotropy for a crack rotation, the strength properties of the material are assumed to be isotropic. Conditions for a crack deviation and stability of a straight crack path are obtained. The obtained results generalize previous results of the authors, where an analogical problem was considered for the case of uniaxial tension. Presented results are compared with the results following from the traditional model of the crack, considering a crack as an ideal cut.

Simulation of the shear-tensile mode transition on dynamic crack propagations

We propose an approach to the simulation of the shear-tensile transition in dynamic crack growth based on two points: a new crack propagation criterion which is suitable for shear, and an algorithm which is capable of handling the transition from shear mode to tensile mode and back in the same simulation. The new crack propagation criterion for brittle crack growth is based on the maximum shear stress rather than the maximum hoop stress. The shear stress direction becomes the new crack’s direction in which propagation is initiated for shear-type failure. The stress state at the crack’s tip is obtained through a local approach which can be used even in the case of extensive plasticity. Additionally, we propose to control the transition from shear mode to tensile mode during the simulation of crack propagation using an equivalent strain estimated at the crack’s tip. Depending on a threshold strain, the propagation direction is predicted using the maximum shear stress (in the shear case) or the maximum hoop stress (in the tensile case).

Improvement of the extended finite element method for ductile crack growth

The continuum damage mechanics (CDM) model is added to the extended finite element method (XFEM) to provide a model of ductile crack growth. In this model, the criterion for crack growth in the evaluation of ductile materials is the critical damage parameter obtained from continuum damage mechanics. Numerical implementation of the CDM–XFEM model was used to simulate crack growth modeling in comparison with experimental results, and the results are presented in this paper. The CDM–XFEM model was experimentally validated by the ductile damage evolution measured in A533B1 steel through three-point bending and compact tension tests. The identification of damage parameters was performed under various conditions. The critical load at crack growth initiation, the ductile behavior of cracks and the fracture toughness, JIc, were also predicted with the CDM–XFEM model simulations. The results confirm the potential of the CDM–XFEM model for predicting crack growth in ductile materials. Using the proposed model, crack propagation has been simulated within two examples; center inclined crack and single edged notched beam for A533B1 steel.

Special criterion for crack path prediction at micro-structural scale based on dominate slip system and grain boundary

This study develops a new method for the analysis of fatigue crack growth at micro-structural scale. Proposed model was constructed based on material anisotropic properties and crystallographic planes. In this research, it has been attempted to suggest an accurate and precise criterion for the prediction of crack growth path at micro-structural scales by the study of various criteria for crack growth. For this purpose, considering fracture energy for trans-granular and inter-granular fracture as well as dominant slip planes, a criterion was proposed to predict crack growth. In the current research, fatigue tests were performed on two different alloys and the real path of the crack growth was obtained. Next, by the simulation of tested pieces through finite element software (ABAQUS) and using extended finite element method, various criteria to predict crack growth path were studied. The microstructures of both specimens tested in considered areas were modelled with an anisotropic behaviour and their crystal orientations were gained using electron-back-scattering-diffraction-pattern (EBSP) method. The results suggest the accuracy and precision of proposed criterion with minor error in single-phase alloys and major difference in two-phase alloys.

Three-dimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique

In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz–Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa–Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm. The predicted crack growth simulation and corresponding load-displacement curves are compared with the experimental and other numerical results reported in literature.

Crack growth modeling via 3D automatic adaptive mesh refinement based on modified-SPR technique

In this paper, the three-dimensional automatic adaptive mesh refinement is presented in modeling the crack propagation based on the modified superconvergent patch recovery technique. The technique is developed for the mixed mode fracture analysis of different fracture specimens. The stress intensity factors are calculated at the crack tip region and the crack propagation is determined by applying a proper crack growth criterion. An automatic adaptive mesh refinement is employed on the basis of modified superconvergent patch recovery (MSPR) technique to simulate the crack growth by applying the asymptotic crack tip solution and using the collapsed quarter-point singular tetrahedral elements at the crack tip region. A-posteriori error estimator is used based on the Zienkiewicz–Zhu method to estimate the error of fracture parameters and predict the crack path pattern. Finally, the efficiency and accuracy of proposed computational algorithm is demonstrated by several numerical examples.

Crack Propagation in Honeycomb Cellular Materials: A Computational Approach

Computational models based on the finite element method and linear or nonlinear fracture mechanics are herein proposed to study the mechanical response of functionally designed cellular components. It is demonstrated that, via a suitable tailoring of the properties of interfaces present in the meso- and micro-structures, the tensile strength can be substantially increased as compared to that of a standard polycrystalline material. Moreover, numerical examples regarding the structural response of these components when subjected to loading conditions typical of cutting operations are provided. As a general trend, the occurrence of tortuous crack paths is highly favorable: stable crack propagation can be achieved in case of critical crack growth, whereas an increased fatigue life can be obtained for a sub-critical crack propagation.

Ratchetting strain as a driving force for fatigue crack growth

Ratchetting deformation has significant implications on material damage and fatigue life of components under service loading conditions. In this work, we explore the concept of ratchetting strain as a driving force in controlling crack growth, both time-independent and time-dependent, utilising elasto-plastic, visco-plastic and crystal-plasticity constitutive models. Characteristics of crack tip deformation were examined for both stationary and growing cracks using the finite element method. Whilst the strain range and the stress range remained largely unchanged throughout the loading cycles, distinctive strain ratchetting behaviour near the crack tip occurred in all cases, leading to progressive accumulation of tensile strain normal to the crack growth plane. It seems plausible that this tensile strain, or ratchetting strain, may be responsible for material separation leading to crack growth. The effects of material constitutive model, grain orientation and loading frequency on the development of ratchetting strain were also examined. Ratchetting strain was found to be related to accumulated plastic strain; and both were used in a crack growth criterion with which the crack growth rates of a nickel alloy were predicted. The preliminary results seem to be encouraging.

Crack growth simulation of bulk and ultrafine grained 7075 Al alloy by XFEM

In the present work, the effect of cryorolling on tensile strength, impact toughness and fracture energy of 7075 Al alloy has been studied experimentally, and quasi-static crack growth simulation has been performed by extended finite element method (XFEM) for both UFG and bulk Al Alloys. The 7075 Al alloy is rolled for 40% and 70% thickness reduction at cryogenic temperature. The microstructural characterisation of the alloy was carried out by using field emission scanning electron microscopy (FESEM). The cryorolled Al alloy after 70% thickness reduction exhibits fully formed ultrafine grain structure (grain size 600 nanometres) throughout the cross section as observed from FESEM micrographs. The mechanical properties of both alloys are obtained by tensile and Charpy impact testing. In XFEM simulations, this impact energy is used as a crack growth criterion for elastic-plastic ductile fracture. In XFEM, a discontinuous function is used to model the region behind the crack tip, whereas a crack tip is modelled by near-tip asymptotic functions.

An Experimental Evaluation of Material Properties and Fracture Simulation of Cryorolled 7075 Al Alloy

This work presents an experimental evaluation of yield strength, tensile strength, and impact toughness of 7075 Al alloy. The extended finite element method (XFEM) has been chosen for quasi-static crack growth simulations using Charpy impact energy as the crack growth criterion for both Bulk and ultrafine-grained (UFG) 7075 Al alloy. The 7075 Al alloy is rolled for different thickness reductions (40 and 70%) at cryogenic (liquid nitrogen) temperature, and its mechanical properties are studied by performing the tensile and Charpy impact testing. The microstructural characterization of the alloy was carried out using field emission scanning electron microscopy (FE-SEM). The rolling of the Al alloy at cryogenic temperature suppresses dynamic recovery, and dislocation cells formed during processing, transformed into fully formed ultrafine-grains (600 nm) at 70% thickness reduction. The impact energy used as the crack growth criterion under quasi-static loading condition based on the Griffith energy concept. The elastic-plastic ductile fracture simulations are performed by XFEM using ABAQUS Software (Version 6.9). For crack modeling, two different types of functions are used to model a crack based on partition of unity concept. A discontinuous function is used to model the portion behind the crack tip, whereas crack tip is modeled by near-tip asymptotic functions. This permits the crack is to be represented explicitly without meshing the crack surfaces, thus crack propagation simulations can be carried out without a need of re-meshing. Strain energy release and stress distribution ahead of the crack tip is found for some practical crack problems. The numerical examples indicate a significant improvement in crack growth properties of UFG 7075 Al alloy as compared to its bulk form due to an effective grain refinement.

Studies on the effect of compliance on fracture behaviour of carbon steel pipes with circumferential through-wall crack

The design of Nuclear Power Plant piping is based on Leak-Before-Break (LBB) design philosophy. The integrity of cracked nuclear piping system in LBB is often examined from conventional fracture mechanics. Conventionally the fracture analysis is performed by assuming infinite compliance of the piping system, which means that the stiffening effect of the connected uncracked piping system is fully neglected. However, in reality the ends of the pipe are connected to the rigid pressure vessels, primary coolant pipes, etc. In order to study the effect of compliance on the fracture behaviour of pipes, fracture studies were carried out on fourteen specimens of 219 mm outer diameter carbon steel pipes having circumferential through-wall crack. The fracture tests were conducted under four point bending. Out of the fourteen specimens, twelve specimens were tested in fixed end condition (finite compliance) and the remaining two specimens were tested in simply supported condition (infinite compliance). These pipes were made of SA 333 Gr. 6 carbon steel. Extensive instrumentation was carried out on these pipes to collect various data, e.g., load, load-line displacement (LLD), crack mouth opening displacement (CMOD), rotation at the ends (flanges), deflection at critical locations and surface crack growth. Surface crack growth was monitored using Image Processing Technique (IPT). The investigations have shown that the load carrying capacity of the pipes under finite compliance condition (fixed end condition) increases when compared to infinite compliance (simply supported condition). The load carrying capacity of the pipes under finite compliance weakly depends on the initial crack angle where as the load carrying capacity of the pipes under infinite compliance strongly depends on the initial crack angle. The safety margin is quite large particularly with a stiff piping system. This benefit in terms of increase in safety margin from LBB point of view is due to the moment redistribution. This paper discusses the effects of notch angle, span and the support conditions on the fracture behaviour of pipes with circumferential through-wall crack.

Estimation of dynamic fatigue strengths in brittle materials under a wide range of stress rates

This paper aims to statistically estimate the dynamic fatigue strength in brittle materials under a wide range of stress rates. First, two probabilistic models were derived on the basis of the slow crack growth (SCG) concept in conjunction with two-parameter Weibull distribution. The first model, Model I, is a conventional probabilistic delayed-fracture model based on a concept wherein the length of the critical crack growth due to SCG is enough larger than the initial crack length. For the second model, Model II, a new probabilistic model is derived on the basis of a concept wherein the critical cracks have widely ranging lengths. Next, a four-point bending test using a wide range of stress rates was performed for soda glass and alumina ceramics. We constructed fracture probability–strength–time diagrams (F–S–T diagrams) with the experimental results of both materials using both models. The F–S–T diagrams described using Model II were in good agreement with plots of the fracture strength and the fracture time of both materials more so than Model I.

Crack propagation in multilayer thin-film structures of electronic packages using the peridynamic theory

This paper presents an application of the peridynamic theory to predict crack paths in multilayer thin-film structures of electronic packages. The peridynamic theory is a nonlocal continuum theory that has an inherent crack initiation and growth criterion. Specifically, the peridynamic theory is employed to model cross-sectional nanoindentation, an experimental technique used for characterizing interfacial adhesion and observing crack paths. Cross-sectional indentation experiments previously conducted on blanket and patterned thin-film structures were simulated. The predicted crack propagation paths in both blanket and patterned multilayer thin-film structures compare well with the results from cross-sectional nanoindentation experiments.

J– Q characterized stress fields of surface-cracked metallic liners – II. Composite overwrapped pressure vessels

Two-parameter J– Q elastic–plastic crack front fields are developed for surface-cracked metallic liners of composite overwrapped pressure vessels (COPV). Uniaxial tensile data from 6061-T6 aluminum coupon specimens for the metallic liner and anisotropic elastic material properties for the filament wound carbon fiber epoxy are used in three-dimensional finite element models. Modified boundary layer (MBL) finite element solutions are used to evaluate near tip dominance and parameterization limits. Semicircular surface cracks of varying depths inserted in the inner liner surface are investigated. J and Q crack front distributions, and the corresponding parameterization limits, and near tip triaxiality trends are obtained and the effects of elastic–plastic material discontinuity of the heterogeneous joint and the biaxiality of stresses are evaluated. J– Q predicted fields maintain accuracy for higher far-field loads and lower near tip deformations compared to the liner only models for angles near the free surface. However, for the critical crack growth region, Q does not maintain a radially independent measure of constraint for loads seen in a typical COPV; therefore, these fracture predictors may not be applicable. In the COPV, large-scale yielding marks a transition where triaxiality is higher as a function of constraint compared to the linear relationship common to homogeneous structures. Results from this study will facilitate the implementation of proof test logic and accurate fracture prediction of COPV liners with emphasis on geometric limits and fracture specimen applicability.

A further insight into spherical indentation: Ring crack formation in a brittle La 0.8Sr 0.2Ga 0.8Mg 0.2O 3 perovskite

It is known that theoretical considerations of fracture under loading by a spherical indenter are based on the concept of pre-existing cracks. However, nucleation and growth of the critical crack could occur during indentation, as happens during microcracking. The goal of the presented research is to develop a new concept of fracture under spherical indentation in a brittle elastic material taking into account the possibility of critical crack nucleation and growth during loading. La 0.8Sr 0.2Ga 0.8Mg 0.2O 3 (LSGM) perovskite has been chosen as a polycrystalline elastic low fracture toughness ceramic to perform indentation using a tungsten carbide spherical indenter. Experimental measurements of ring crack radii for well-polished LSGM cannot be explained within the framework of the pre-existing crack hypothesis. The local risk calculated using the concept of pre-existing cracks gives a most probable range of ring crack radii that does not match the radii measured experimentally. However, the local risk calculated using the assumption of critical crack nucleation and formation during spherical indentation results in a most probable range of ring crack radii which exhibits good agreement with the experimental data.

Characterization of fracture processes by continuum and discrete modelling

A large number of methods to describe fracture mechanical features of structures on basis of computational algorithms have been developed in the past due to the importance of the topic. In this paper, current and promising numerical approaches for the characterization of fracture processes are presented. A fracture phenomenon can either be depicted by a continuum formulation or a discrete notch. Thus, starting point of the description is a micromechanically motivated formulation for the development of a local failure situation. A current, generalized method without any restriction to material modelling and loading situation in order to describe an existing crack in a structure is available through the material force approach. One possible strategy to simulate arbitrary crack growth is based on an adaptive implementation of cohesive elements in combination with the standard discretization of the body. In this case, crack growth criteria and the determination of the crack propagation direction in combination with the modification of the finite element mesh are required. The nonlinear structural behaviour of a fibre reinforced composite material is based on the heterogeneous microstructure. A two-scale simulation is therefore an appropriate and effective way to take into account the scale differences of macroscopic structures with microscopic elements. In addition, fracture mechanical structural properties are far from being sharp and deterministic. Moreover, a wide range of uncertainties influence the ultimate load bearing behaviour. Therefore, it is evident that the deterministic modelling has to be expanded by a characterization of the uncertainty in order to achieve a reliable and realistic simulation result. The employed methods are illustrated by numerical examples.

Fatigue crack growth model for assessing reliability of box-girders for cable-stayed bridge combining SHMS with strain data

Enhancement of the computer algorithm developed for the Runyang cable-stayed bridge (RYCB) in China is made by incorporating the fatigue crack growth analysis in contrast to the SN curve approach. Strain data obtained from the structural health monitoring system (SHMS) and finite element calculations are used. This provides the application of a deterministic method in addition to the probabilistic approach with the added feature of crack growth. The choice of selecting the two-parameter fatigue crack growth criterion was based on the definition of reliability index β such that the new results can be compared with those using the SN curves. A gradual drop of the reliability index β with time with an upper limit was obtained for the crack growth model in contrast to the linear time relation for the SN curve model that had no upper limit. This difference is significant and reveals the importance for selecting the fatigue failure criterion. Deterministic and probabilistic crack growth models are used to assess the differences. The results are based on the box-girder component strain history data of the Runyang Cable-stayed Bridge (RYCB) in China, stress history recorded by structural health monitoring system (SHMS) is analyzed using the monitored stress amplitude, mean stress and stress ratio. Finite element calculations are used to supplement data at locations not accessible for measurements. Additional improvement with reference to damage accumulation and the physical meaning of the reliability index will be studies in relation to the fatigue damage of box-girder of long cable-stayed bridges.

Effect of KIII on Fatigue Crack Growth Behavior (2nd Report, Verification of Crack Growth Criterion)

Mixed mode fatigue tests are conducted using through cracked specimen. Slant through cracked specimens are made where crack angle is 15°, 30° and 45°. It is shown that factory roof is made in all crack tips due to ΔKIII, and crack growth rate decreases by the factory roof. Fatigue crack growth is simulated using S-version FEM( Finite Element Method) using crack growth criteria. It is shown that conventional crack growth criteria are not available to predict fatigue crack growth with factory roof. In authors' previous study, modified new criterion for the prediction of crack growth rate is proposed. In this study, by using new criterion, fatigue crack growth simulation is conducted, and results are compared with those of experiments and discussed.