Fatigue Crack Growth and Fracture of 30 wt% B4C/6061Al Composites

This paper focuses on studying the fatigue crack growth (FCG) characteristics and fracture behaviours of 30 wt% B₄C/6061Al composites fabricated by using powder metallurgy and hot extrusion method. Compact tension (CT) specimens having incisions parallel to the extrusion direction (T‐D) and perpendicular to the extrusion direction (E‐D) were investigated through FCG tests. Results show that, at low/medium stress‐intensity factor range levels (ΔK ≤ 9), crack propagation rate in E‐D specimens is lower than that in T‐D specimens because the elongated B₄C particles parallel to the extrusion direction in E‐D specimens can deflect the crack. The scanning electron microscope micrographs of the fractured surface illustrate that crack mainly propagates in the matrix alloy at the initial stage of its propagation and propagates more remarkably near the particle‐matrix interface with the increase of ΔK value. B₄C particles are also found to be easy to fracture during the rapid crack propagation. Based on fracture analyses, considering the impacts of factors like crack deviation, plastic zone size at the crack tip, and crack driving force, a 2‐D crack propagation model was developed to study the fatigue crack propagation mechanism in the 30 wt% B₄C/6061Al composite.     

Mixed-Mode Crack Propagation in Cruciform Joint using Franc2D

The focus of this research was on determining the cracking behavior when parameter such as the biaxiality ratio was varied. The crack propagation under mixed-mode loading was simulated by means of finite element method. The stress intensity factors have been calculated by the linear elastic fracture mechanics approach using fracture analysis code-2D (Franc2D). The crack growth under opening mode-I was considered because the crack growth occurs mainly along the direction where the mode-I stress component becomes the maximum. The numerical integration of Paris’ equation was carried out. The effect of normal and transverse applied load (σ _x, and σ _y, respectively) on crack propagation was presented. It was found that the fatigue crack growth was faster at a smaller biaxial stress ratio (λ), i.e., higher σ _y on the horizontal crack plan. Moreover, fatigue strength values decrease as λ decreases. The results confirm the use of fracture mechanics approach in biaxial fracture.     

Fatigue Propagation of Fibre-Bridged Cracks in Unidirectional Polymer-Matrix Composites

In order to improve the fatigue resistance of polymer-matrix composites by materials design, or to conceive micromechanics based models for life predictions, the underlying micromechanisms must be understood. Experimental investigations have revealed fibre-bridged cracking as a toughening micromechanism that retards further fatigue crack growth in a unidirectional 0° carbon-fibre-reinforced epoxy. The bridging fibres exert a closing traction on the crack surfaces, thereby reducing the driving force for crack growth. In this study, the growth of bridged cracks has been quantified by a surface replication technique. The da/dN–K curve defined in terms of nominal stress-intensity factors shows a crack retarding behaviour. The crack growth curve can be replotted in terms of the effective stress-intensity factor where the contribution of the cohesive crack surface forces from the bridging fibres are taken into account. This curve falls somewhat closer to that of the neat matrix material, but the difference is still considerable, and it shows a decelerating propagation. Therefore, there must be other active toughening mechanisms besides fibre bridging, that slow the crack propagation down, and account for the fatigue resistant behaviour of the tested material. Ways by microstructural design to promote the fatigue resistant mechanisms are discussed.     

Numerical and experimental investigations of the influence of corner singularities on 3D fatigue crack propagation

In the case of surface breaking cracks, the typical square-root stress singularity is generally not sustainable and a 3D corner singularity in the vicinity of the intersection of crack front and free surface has to be considered. Only the crack front intersection under a special angle γ_r ensures a valid square-root stress singularity and the applicability of the classical SIF-concept. In this paper, the theory of the numerical determination of the intersection angle γ_r is briefly described and the influence of the 3D corner singularity on fatigue crack growth is experimentally investigated. Therefore, 3D fatigue crack propagation experiments under pure mode-I are performed. Transparent specimens of PMMA are used, in order to be able to observe and to document accurate sequences of real 3D crack front evolution profiles via in situ photographic measurement.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method

This paper presents a new fractal finite element based method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and two-dimensional linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predicts the first-order sensitivity of J-integral or mode-I and mode-II stress-intensity factors, K_I and K_II, more efficiently and accurately than the finite-difference methods. Unlike the integral based methods such as J-integral or M-integral no special finite elements and post-processing are needed to determine the first-order sensitivity of J-integral or K_I and K_II. Also a parametric study is carried out to examine the effects of the similarity ratio, the number of transformation terms, and the integration order on the quality of the numerical solutions. Four numerical examples which include both mode-I and mixed-mode problems, are presented to calculate the first-order derivative of the J-integral or stress-intensity factors. The results show that first-order sensitivities of J-integral or stress-intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.     

A mathematical equation relating low cycle fatigue data to fatigue crack propagation rates

A mathematical equation is derived to predict fatigue crack growth rates on the basis of a J integral analysis from the fatigue fracture behaviour of low cycle fatigue samples. According to this equation, the fatigue crack propagation curves can be predicted if low cycle fatigue data and an initial microcrack size are available. The results obtained from this study show that the predicted fatigue crack propagation rates for Ti-24V, Ti-6Al-4V and Al-6Zn-2Mg alloys are very close to experimental values.     

Study of the fatigue failure of an anti-return valve of a high pressure machine

This paper presents a study of the fatigue failure of an anti-return valve, designed to work in the high pressure system (500 MPa) of a high pressure processing machine. To do this, the crack propagation has been simulated by means of the linear-elastic fracture mechanics approach under mixed-mode loading conditions. From an initial crack, which size is related with the microstructure and superficial finish, the crack growth has been simulated using the stress intensity factors K_I and K_II of the cracked valve axisymmetric geometry. The crack propagation path has been obtained step by step, applying the criterion of the maximum circumferential stress at the crack tip. The experimental and simulated crack propagation paths have been compared and, as a consequence of the reliable results obtained, the fatigue life of the valve has been calculated using the Paris law of the material with an effective stress intensity factor K_eff. The good agreement with experimental fatigue life allows to perform new improved designs using the methodology presented.     

Fatigue crack growth acceleration due to intermittent overstressing in adhesively bonded CFRP joints

Double cantilever beam joints were used to investigate cohesive and interlaminar crack growth in bonded composite joints under constant and variable amplitude (VA) loading. Numerical crack growth integration was used to predict the VA fatigue life using constant amplitude data. This underestimated the fatigue crack growth rate for interlaminar cracks, indicating crack growth acceleration due to load interactions. This was also the case for cohesive cracks subjected to a moderate initial strain energy release rate (G_max). An unstable crack growth regime was also identified for the case of high initial G_max cohesive crack propagation. This behaviour is attributed to the development of a damage zone ahead of the crack tip.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

Fatigue crack propagation damaging micromechanisms in ductile cast irons

Ductile iron discovery in 1948 gave a new lease on life to the cast iron family. In fact, these cast irons are characterized both by a high castability and by high toughness values, combining cast irons and steel good properties. Ductile cast irons are also characterized by high fatigue crack propagation resistance, although this property is still not widely investigated.In the present work, three different ferritic–pearlitic ductile cast irons, characterized by different ferrite/pearlite volume fractions, and an austempered ductile cast iron were considered. Their fatigue crack propagation resistance was investigated in air by means of fatigue crack propagation tests according to ASTM E647 standard, considering three different stress ratios (R = K_min/K_max = 0.1; 0.5; 0.75). Crack paths were investigated by means of a crack path profile analysis performed with an optical microscope. Crack surfaces were extensively analysed by means of a scanning electron microscope both considering a traditional procedure and performing a quantitative analysis of 3D reconstructed surfaces, mainly focusing graphite nodules debonding.     

Alloy induced inhibition of fatigue crack growth in age-hardenable Al–Cu Alloys

Environmental fatigue crack propagation (EFCP) is alloy-inhibited in under aged Al–Cu–Mg and peak aged Al–Cu–Li alloys stressed in pure aqueous chloride solution. Counter to H diffusion and H-embrittlement rate limited step considerations which predict fatigue crack growth rate (da/dN) to be either independent of fatigue loading frequency (f) or increase with decreasing f, da/dN declines with decreasing f. The mechanism for such alloy induced inhibition and decreasing da/dN with decreasing f is reduced crack tip H production and uptake due to stabilization of the native aluminum passive film resulting from: (1) dissolution of anodic Cu-containing GP zones or precipitates (Al₂CuLi or Al₂CuMg) by dealloying, (2) crack surface Cu enrichment, and (3) enhanced crack wake cathodic reaction kinetics on Cu enriched sites that increase crack solution pH. Peak aged Al–Zn–Mg–Cu alloy 7075 does not exhibit alloy induced inhibition because the predominant anodic phase, Mg(Cu,Zn)₂, does not provide a source for Cu surface enrichment. Alloy induced inhibition is similar to ion-assisted inhibition by molybdate or chromate addition into bulk chloride solution which provides an alternate path to stabilize a crack tip passive film. Both alloy-induced and ion-assisted inhibition of EFCP are promoted by reduced f and crack tip strain rate which favor repassivation of the crack tip passive film over film rupture.     

Comparison of the simulation and experimental fatigue crack behaviors in the nanoseconds laser shocked aluminum alloy

This investigation was performed to compare the simulation and experimental results of the fatigue crack growth rates and behaviors of the 7050-T7451 aluminum alloy by nanoseconds laser shock processing (LSP). Forman–Newman–deKoning (FNK) model embedded in the Franc2D/L software was utilized to predict fatigue crack growth rate, which was conducted to weigh the stress intensity factor (SIF) changing on the surface cracks. LSP induced high compressive residual stresses that served to enhance fatigue properties by improving the resistance against fatigue crack initiation and propagation. The circulating times of crack growth obtained from the simulation and experimental values indicated a slower fatigue crack growth rates after LSP. The relationships between the elastic–plastic materials crack growth rates and the SIF changing after LSP are resolved.     

Fatigue analysis of non-load-carrying fillet welded cruciform joints

The goal of this investigation was to study the effect of local geometrical variations of the weld on the fatigue strength. Therefore the fatigue behaviour of non-load-carrying cruciform fillet welded joint under tensile loading has been studied parametrically. Several two-dimensional (2D) finite element models of the joint were analysed using plane strain linear elastic fracture mechanics (LEFM) calculations in order to get the magnification function M_k. A maximum tangential stress criterion was used to predict the crack growth direction under mixed mode K_I-K_II conditions. The derived M_k solution was then applied both for continuous weld toe cracks and also for semi-elliptical toe cracks at the deepest point of the crack front. An experimental crack aspect ratio development curve was used for propagating semi-elliptical cracks. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. The Paris crack growth law was used to predict the growth rate. The effects of weld toe radius, flank angle and weld size on the fatigue strength were systematically studied. Finally, predicted fatigue strength values corresponding to different assumed crack sizes were compared with the available test results.     

A durability model incorporating safe life methodology and damage tolerance approach to assess first inspection and maintenance period for structures

This paper outlines a new durability model to assess the first inspection and maintenance period for structures. Practical scatter factor formulae are presented to determine the safe fatigue crack initiation and propagation lives from the results of a single full-scale test of a complete structure. New theoretical solutions are proposed to determine the s_a−s_m−N surfaces of fatigue crack initiation and propagation. Prediction techniques are then developed to establish the relationship equation between safe fatigue crack initiation and propagation lives with a specific reliability level using a two-stage fatigue damage cumulative rule. A new durability model incorporating safe life and damage tolerance design approaches is derived to assess the first inspection and maintenance period. Finally, the proposed models are applied to assess the first inspection and maintenance period of a fastening structure at the root of helicopter blade.     

Computer simulation of fatigue crack propagation under random loading conditions

The aim of this study is to simulate fatigue crack propagation under random loading conditions using a simple algorithm based on the Wheeler model [Wheeler O. Spectrum loading and crack growth. J Basic Eng D 1972;94:181–86]. To create the computer simulation, a model based on the mechanical properties of the material has been used. These properties include the yield stress (σ_y) and Paris’s constants C and m. The loading conditions (baseline loading ratio R, baseline stress intensity factor range ΔK and overload stress intensity factor K_ol, R_ol) are also required. The present model is validated with fatigue crack growth test data conducted on 12NC6 steel samples with four different heat treatments in order to have different types of mechanical behavior. The computer simulation and experimental results for crack propagation for different overload distributions (a single overload, a repeated overload, different overload magnitudes, random overload) are in good agreement.     

Two parameter fracture mechanics: Fatigue crack behavior under mixed mode conditions

The fatigue crack path has been studied on a tensile specimen with holes. The experimental crack path trajectories were compared with those calculated numerically. To incorporate the influence of constraint on the crack curving, we predicted the fatigue crack path by using the two-parameter modification of the maximum tensile stress (MTS) criterion. The values of the mixed-mode stress intensity factors K_I, and K_II as well as the corresponding constraint level characterized by T-stress were calculated for the obtained curvilinear and reference crack path trajectories. It is shown that in the studied configuration the effect of T-stress on the crack path is not significant. On the other hand the effect of constraint on the fatigue crack propagation rate is more pronounced.     

Fatigue assessment using an integrated threshold curve method - applications

This paper deals with the analysis and prediction of a high-cycle fatigue behaviour in notched and damaged specimens, as well as butt-welded joints by using a threshold curve for fatigue crack propagation that includes the short crack regime (a function of crack length, a). The approach regards the effective driving force applied to the crack as the difference between the total applied driving force defined by the applied stress distribution corresponding to a given geometrical and loading configuration, ΔK(a), and the threshold for crack propagation, ΔK_th(a). Chapetti’s model is used to estimate the threshold for crack propagation by using the plain fatigue limit, Δσ_eR, the threshold for long cracks, ΔK_thR, and the microstructural characteristic dimension (e.g. grain size). Applications, predictions and results, in good agreement with experimental results from the literature, demonstrate the ability of the method to carry out quantitative analyses of the high cycle fatigue propagation behavior (near threshold) of short cracks in different geometrical, mechanical and microstructural configurations.     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

Strain-energy-density factor applied to mixed mode crack problems

This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k ₁,k ₂ are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S _cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS _cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS _cr is related tok _1c alone asS _cr = (κ ? 1)k ₁ ² /8μ. In general,S takes the quadratic forma _{1 1} k ₁ + 2a _{1 2} k ₁ k ₂ +a _{2 2} k ₂ whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.