Crack Tip Parameters Research Articles

A numerical analysis of the mechanisms behind plasticity induced crack closure: Application to variable amplitude loadings

The effect of loading parameters on fatigue crack growth has been explained using the concept of crack closure. Plasticity induced crack closure (PICC) is linked to the crack tip plastic deformation, which becomes residual with crack propagation. The objective here is to identify the main mechanisms behind PICC, and for that different loading cases were considered namely overloads and load blocks. An analytical model was used to isolate the effect of residual plastic deformation on PICC, however significant differences were obtained relatively to finite element results. A second mechanism, which is crack tip blunting, was used to explain the transient behaviour observed after overloads and load blocks. For overloads and low–high load sequences there is a sudden increase of crack tip blunting with load increase which explains the sudden decrease of crack opening level. For high–low load sequences there is a sudden decrease of crack tip blunting which enhances the effect of residual plastic wake. Finally, the partial closure concept was tested looking to non-linear crack tip parameters but no evidences of Donald’s effect were found for the material studied.

Numerical study of thermo-mechanical coupling effects on crack tip fields of mixed-mode fracture in pseudoelastic shape memory alloys

The thermo-mechanical coupling effects on mixed-mode crack tip parameters in pseudoelastic shape memory alloys are studied by a finite element solution. Different loading rates are applied on the K-dominant part of the small scale transformation region. Both plane strain and plane stress analyses are carried out to study how the coupling between thermal and mechanical regimes alters the near tip fields in the martensitic region. The crack tip energy release rate and the J-integral remain history-dependent. The stress/strain response, the angular distributions of the stress and the released temperature, the shape of the transformation zone and the released temperature are selected as the crack tip fields of interest. Special attention is given to study of how the aforementioned crack tip fields are affected by the increase of applied loading rate. A comparison is also drawn between the crack tip fields in plane strain and plane stress states to complete the discussion.

A numerical study of non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, different authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle, were investigated. It was demonstrated that: i) LEFM concepts are applicable to the problem under study; ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; iii) the ?Keff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level; v) without contact there is no effect of stress ratio on crack tip parameters. Therefore it is proved that the crack closure concept is valid.

Creep relaxation in the presence of residual stress

In this paper, the elastic and elastic–plastic creep behaviour of cracked structures in the presence of a residual stress field have been studied, numerically and analytically. A self-equilibrating residual stress field is introduced by prior mechanical loading. The magnitude of the residual stress field is varied and the corresponding transient crack tip parameter, C(t), is evaluated in single edge notched specimens, using the finite element (FE) method. Since the steady state crack tip parameter, C∗, and redistribution time, tred, are no longer valid for the case of residual stress only (as for this case C∗→0 and thus tred→∞), new normalising factors of Cnorm and tnorm are introduced and used to normalise C(t) and time, respectively. Existing analytical solutions are modified based on these normalising factors, to describe creep relaxation in the presence of a residual stress field. The values of C(t) obtained from FE analysis are compared to those from the proposed equations. It has been found that the transient C(t) value provides an accurate characterisation of the crack tip fields under residual stress only.

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔKeff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.

Study of creep relaxation under combined mechanical and residual stresses

In this work the elastic and elastic–plastic creep behaviour of cracked structures in the presence of residual stress has been studied numerically. The residual stress is introduced by prior mechanical loading and mechanical stress levels are varied to evaluate the transient crack tip parameter, C(t), in single edge notch bend, SEN (B), and tension, SEN (T), specimens, using the finite-element (FE) method. The near tip stress distributions are examined and the influence of residual stress on the evolution of the stress fields, quantified by C(t), is examined. The values of C(t) obtained from the FE analysis are compared to existing analytical solutions. It has been found that the transient C(t) value provides an accurate characterisation of the crack tip fields under combined primary and secondary stress. It has also been found that the level of conservatism of current C(t) estimation schemes, which account for primary and secondary stress, depends on material properties and the level of primary and secondary stress.

A double edge notch specimen design for tension–compression fatigue crack growth testing

Compact, C(T), specimens are commonly used for fatigue and creep-fatigue crack growth testing under constant-load-amplitude conditions. The use of the standard C(T) specimens [ASTM] is limited to positive load ratios. They are also limited in the amount of crack growth data that can be developed at high stress intensity values due to accumulation of plastic and/or creep strains leading to ratcheting in the specimen. Testing under displacement control can potentially address these shortcomings of the load-controlled tests for which the C(T) geometry is unsuitable. A double edge notch tension–compression, DEN(T–C), specimen to perform displacement controlled creep-fatigue crack growth testing is developed and optimized with the help of finite element and boundary element analyses. The specimen has threaded cylindrical ends for applying the loads. The test section is rectangular with a half width, W, and half height, H, and a constant thickness, B. The height to width ratio, H/W, of the specimen must be kept low to avoid buckling during compressive loading while ensuring that the stress-intensity parameter values are not strongly dependent on the chosen H/W value. Simple optimization analysis shows that a H/W ratio of 1.2 is likely to best meet these requirements. However, only performing actual experiments will confirm whether this choice of H/W value is optimum.In the finite element analyses, the specimen is modeled using an effective height (heff) to width (W) ratio, heff/W, of 1.46 to account for the fillet regions on the two ends of the specimens. Accurate expressions for estimating the fracture mechanics crack tip parameters such as the stress intensity parameter, K, the crack mouth opening displacement (CMOD), and the load-line displacement (LLD) are developed over a wide range of crack sizes for the DEN(T–C) specimen. Expressions are also developed for crack size as a function of specimen compliance.

Application of the Θ-Method to 3D BEM Analysis of Cracks in Piezoelectric Components

A general purpose direct BEM code has been developed for three-dimensional crack problems in piezoelectric structures. Special 3D non-continuous crack tip elements and several techniques for determining crack tip parameters were implemented. To calculate the electromechanical energy release rate for a virtual crack extension, the θ-method is employed, which was originally suggested by BONNET for linear elastic materials. The paper presents the generalization and numerical realization of the θ-method to 3D piezoelectric cracks. The great advantage of the θ-method is the direct computation of energy release rate, whereas the way via K-factors and the IRWIN matrix is more complicated. The efficiency and accuracy of the technique are shown for various example problems by comparing with analytical solutions.

Creep Crack Growth Under Complex Loading

Abstract Fitness-for-service assessments of components operating at high temperature often require estimates of creep crack growth in service. Although methods for calculating creep crack growth are given in R5 and other codes, these methods are limited in terms of their range of application and can be over-conservative. This paper extends the current methods in a number of areas. First, a general expression is derived for relaxation of a reference stress for combined primary and secondary loading and significant in-service crack growth. Second, the reference stress history is used to develop an estimate of the transient creep crack tip parameter, C(t) , for elastic-plastic-creep material behaviour for combined loading. This both extends current methods to more complex loading and reduces some known conservatism in these current methods. The general expression for C(t) then enables creep crack growth in service to be estimated using data collected from standard tests under mechanical loading. Finally, the paper presents some finite element calculations for defects in cylinders with welding residual stresses as validation for the new approaches.

Crack tip fracture toughness of base glasses for dental restoration glass-ceramics using crack opening displacements

The critical stress intensity factor, also known as the crack tip toughness K tip , was determined for three base glasses, which are used in the manufacture of glass-ceramics. The glasses included the base glass for a lithium disilicate glass-ceramic, the base glass for a fluoroapatite glass-ceramic and the base glass for a leucite glass-ceramic. These glass-ceramic are extensively used in the form of biomaterials in restorative dental medicine. The crack tip toughness was established by using crack opening displacement profiles under experimental conditions. The crack was produced by Vickers indentation. The crack tip toughness parameters determined for the three glass-ceramics differed quite significantly. The crack tip parameters of the lithium disilicate base glass and the leucite base glass were higher than that of the fluoroapatite base glass. This last material showed glass-in-glass phase separation. The discussion of the results clearly shows that the droplet glass phase is softer than the glass matrix. Therefore, the authors conclude that a direct relationship exists between the chemical nature of the glasses and the crack tip parameter.

Modeling crack in viscoelastic media using the extended finite element method

In this paper, the problem of modeling crack in 2D viscoelastic media is studied using the extended finite element method. The paper focuses on the definition of enrichment functions suitable for cracks assessment in viscoelastic media and the generalized domain integrals used in the determination of crack tip parameters. The opening mode and mixed mode solutions of crack tip fracture problems in viscoelastic media are also undertaken. The results obtained by the proposed method show good agreement with the analytical methods and provide reasonable background information to enhance the modeling of crack growth in viscoelastic media.

Fracture mechanics study on the intermetallic compound cracks for the solder joints of electronic packages

The crack behavior of the intermetallic compounds (IMCs) for the solder joints of electronic packages under the thermal cycling test conditions was analyzed using the finite element method in this research. A flip-chip plastic ball grid array package was selected as the analysis target. The two-dimensional in-elastic finite element method was employed to calculate the fracture mechanics parameters at the crack tip; such as the modes I and II stress intensity factors. Two locations were considered herein to initiate the crack: the first one was on the interface between the IMC and the copper pad (interfacial cracks); and the other one was at the inner part of IMC (IMC cracks). Furthermore, the effects of crack length and thickness of IMC on the crack tip parameters were also studied in this investigation. In the numerical simulation, the properties of the solder joint and the underfill were assumed to be elastic–plastic–creep and viscoelastic, respectively. The sub-modeling technique was used in the finite element analysis to reduce the computational time and the crack tip parameters were obtained using the simulated results of the displacement field near the crack tips. The results show that for both interfacial cracks and the IMC cracks, the modes I and II SIFs decrease as the length of crack increases, and the decreasing trend becomes more stable when the cracks propagate longer except for the variation of the mode II SIF for IMC cracks. Furthermore, the thickness of the IMC has slight effect on the magnitudes of SIFs under the conditions of constant crack lengths.

Determination of crack tip parameters for ASCB specimen under mixed mode loading using finite element method

In this paper, a new asymmetric semicircular bend specimen (ASCB) is presented. Having more geometric parameters in asymmetric bend elements gives the opportunity of covering a wider range of KІ, KІІ and T-stress in comparison with classical SCB specimens. Finite element method is used to obtain these parameters from pure mode I to pure mode II. Extensive numerical calculations are made to get a wide range data for crack tip parameters of this specimen. It is observed that for ASCB specimens with specified geometries under pure mode II loading, one of the bottom supports can move horizontally without significant variation in YI. The complete sets of numerical results are obtained and can be used for verification and interpretation of future experimental results.

The effect of residual stresses on the fracture behaviour of a cracked body under mixed mode loading

Many of engineering structures operate under the presence of residual stresses due to welding or other manufacturing processes. Because of the magnified effects of residual stress on crack growth behaviour, corrections for residual stress are needed for appropriate fatigue life estimation and fracture resistance analysis of cracked structures subjected to mixed mode I and II loading. In this paper, the effect of various residual stress profiles on the crack tip parameters is studied. To make the results more general, two types of butt welds are assumed and the corresponding residual stresses due to the weld are estimated. Than, the effect of residual stress on the crack tip parameters are calculated for complete range of mode mixities from pure mode I to pure mode II and for different crack lengths. It was found that the influence of welding residual stress on the crack tip parameters can be considerable, depending on the stress field, the loading direction, and geometry. In this research, the finite element method is employed to determine the residual stresses and the related stress intensity factors.

Tip Parameter Approximation and Fatigue Growth of Crack Towards Inclined Weld Interface Between Strength Mismatched Steels

A Mode I crack growing at an angle other than 90° with respect to the interface of weld between strength mismatched steels in a bimetallic composite is investigated. The steels and the weld have nearly identical elastic and thermal expansion properties. As the crack in parent steel reaches near the interface of the weld, the plastic strain or yield zone at its tip spreads to the weld, which causes load transfer effect, due to strength mismatch across the weld interface, over the crack tip. Yield zone is modeled as Dugdale’s cohesive zone subjected to constant closing cohesive traction. Geometrical formulations are employed to approximate change in volume of parts of cohesive zone on either side of the interface resulting upon inclining the interface from the vertical. A computational model for crack tip in front of the perpendicular weld interface in linear elastic regime is modified to account for the effect of inclination of weld interface from the vertical. Crack tip stress intensity parameter is approximated from the model, cyclic value of which is used to assess the rate of fatigue crack growth towards the weld interface. The model is validated by experiments. Bimetallic compact tension specimens, prepared by electron beam welding of weak ASTM 4340 alloy and strong MDN 250 maraging steels at interface angles of 10° and 15° with the vertical, are subjected to high cycle fatigue. Growth rate of crack is found to dip substantially when it reaches near the interface of ultra strong weld. The results are compared with those of plain and bimetallic specimens with perpendicular weld interfaces. Inclination of weld interface from the vertical by nearly all the angles changes, albeit marginally, the values of crack tip parameter visà-vis those in the case of perpendicular weld interface. Theoretical and experimental results are in good agreement with each other.

Crack observation methods, their application and simulation of curved fatigue crack growth

Abstract The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples. Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor–corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.

A Simplified Method Study of Aluminium Alloy Fatigue Crack Tip Parameters Computed by Elastic-Plastic Finite Element Model

Fatigue crack propagation of aluminium alloy 7049-OA has been studied by non-linear finite element business-oriented software ABAQUS, and elastic-plastic finite element models of static fatigue crack and dynamic fatigue crack of center crack panel (CCP) specimens are also built. Based on the finite element computation results, the differences of stress and crack opening displacement around crack tip of static crack model have been compared with those of dynamic crack model. The compared results showed that the finite element computation results of dynamic crack model can be replaced by the results calculated by the static crack model. Fatigue crack tip parameters of aluminium alloy CCP specimens can be calculated by elastic-plastic finite element model of static crack. This is an effective method to cut down the computation expense and promote the computational efficiency.

傾斜機能材の高速き裂進展現象に対する移動有限要素法の開発

In the fracture problems in the functionally graded materials (FGMs), singular deformation field near the crack tip is appeared in the gradient field of material properties. In the finite element analyses for the fracture of FGMs, this complex fracture behavior has to be solved by using fine mesh subdivision. In this study, the moving finite element method is devoloped to simulate fracture behavior of four points bending specimen consists of the FGM. In the moving finite element method based on the Delauney automatic triangulation, effective mesh subdivision is updated with crack propagating. The T^* integral is used as criterion to evaluate crack tip condition, because the material properties distribution in FGMs has to be considered to derive exact crack tip parameter. Far-field path independence of the T^* integral is mathematically proved for the fracture in the FGM. The path independence of the T^* integral is also confirmed from the numerical results of the moving finite element analyses. This numerical prediction is demonstrated for four point bending fracture in FGMs. Based on the T^* integral and stress intensity factor, crack propagation path is predicted by the localy symmetry condition. The numerically predicted crack propagation path is compared with experimental result.

Estimation of the transient creep parameter C( t) under combined mechanical and thermal stresses

This paper reports finite element analyses for an axially loaded cylinder with three different types of thermal stress. The magnitudes of the thermal and mechanical loadings are varied and creep crack tip parameters are evaluated for part-through-wall and fully penetrating defects with a range of sizes. The relaxation rate for the creep crack tip parameter is examined in detail and is found to depend on the magnitudes of the mechanical and thermal loads and on whether or not there is plasticity on initial loading. Simplified formulae are developed for describing the rate of relaxation by a modified redistribution time.

Finite Element Analysis of the Effect of the Compressive Loading on Fatigue Crack Growth under Different Loading

In this paper, elastic-plastic finite element analysis has been performed in order to obtain the fatigue crack tip parameters under tension-compression loading. Two centre-cracked high-strength aluminum alloy with a crack length of 2mm under different tension-compression loading are analyzed. The analysis shows that the compressive loading has a significant contribution towards the crack tip plasticity and the crack tip stress. In a tension-compression loading the crack tip displacement increases with the increase of the compressive stress and the crack tip compress stress increases with the increase of the compressive stress. The maximum stress intensity Kmax in the tension part of the stress cycle and the maximum compressive stress in the compression part of the stress cycle are the main factors controlling the near crack tip parameters.