Effect Of Crack Size Research Articles

Novel Concepts on the Growth of Corrosion Fatigue Small and Short Cracks

Corrosion fatigue small, short and long crack growth rates have been determined for a 12Cr steam turbine steel in aerated 300 ppb Cl- + 300 ppb SO42- solution and in air at 90 °C. The crack growth rate for short and long cracks was monitored by direct current potential drop (DCPD) and for the small cracks by combining high resolution optical microscopy and DCPD. Comparison of the fatigue growth rate demonstrated that in solution the short crack growth rate was remarkably enhanced in comparison to long cracks, when the crack size is smaller than 250 μm. This enhancement was attributed to the electrochemical crack size effect associated with greater anodic polarisation of the short crack in such low conductivity solution. However, such enhanced growth was not observed for small cracks, which was rationalised on the basis of additional contribution of current from the pit limiting crack-tip polarisation.

Corrosion pitting and environmentally assisted small crack growth

In many applications, corrosion pits act as precursors to cracking, but qualitative and quantitative prediction of damage evolution has been hampered by lack of insights into the process by which a crack develops from a pit. An overview is given of recent breakthroughs in characterization and understanding of the pit-to-crack transition using advanced three-dimensional imaging techniques such as X-ray computed tomography and focused ion beam machining with scanning electron microscopy. These techniques provided novel insights with respect to the location of crack development from a pit, supported by finite-element analysis. This inspired a new concept for the role of pitting in stress corrosion cracking based on the growing pit inducing local dynamic plastic strain, a critical factor in the development of stress corrosion cracks. Challenges in quantifying the subsequent growth rate of the emerging small cracks are then outlined with the potential drop technique being the most viable. A comparison is made with the growth rate for short cracks (through-thickness crack in fracture mechanics specimen) and long cracks and an electrochemical crack size effect invoked to rationalize the data.

An alternating current electric flux leakage testing methodology and experimental research for metallic materials

This paper proposes an alternating current electric flux leakage (AC-EFL) testing method, which was verified by a series experiments. The inspection ideal and its feasibility research were detailedly presented on the basis of electric field (E-Field) theory. The inspection principle, which is to evaluate surface defect in AC-carrying metallic components using a coplanar capacitive sensor, was briefly described. Physical experiments with a prototype capacitive probe were also carried out to observe and analyze the detection performance of AC-EFL. Effects of crack size of the conducting specimen, through holes size, flat-bottom holes depth, insulation thickness between the probe and the conducting specimen, and exciting signal frequencies were studied. The proof-of-concept results indicated that the AC-EFL testing method could be used to detect surface defect for metallic specimen, and of complete feasibility and the potential of great practical value as a supplement of conventional NDT methods.

Stress Distribution in Single Lap Joints with a Cracked Composite Adherend—Part II: Laminated Adherends

The effect of a crack in the overlap region of an adhesive single lap joint is studied on the shear stress distribution in adhesive layer. Each adherend is considered to be a laminated composite material with unidirectional fibers aligned in the direction of the applied load. Crack location is selected to be in the top adherend laminate, in the form of cut fibers and matrix bays. The crack can occur in any layer. The shear-lag model is used to derive the equilibrium equations which are then solved by means of eigenvector expansion. The effects of adhesive thickness, crack size, and location in the adherend, total number of layers in each adherends, volume fraction of fibers, and type of fibers are investigated on the shear distribution in the adhesive as well as load distribution in the intact fiber at the crack tip located in the top adherend. The effect of dissimilar laminated adherends is also investigated on the adhesive shear stress distribution. According to the results, in the presence of a crack, the peak shear stress in the adhesive layer and load concentration in the fibers are very susceptible to the adhesive thickness and number of layers in laminated adherends.

Interpreting some experimental evidences of fatigue crack size effects through a kinked crack model

AbstractThreshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection. In the present paper, a theoretical model of a periodically kinked crack is proposed to describe the influence of the crack deflection degree on the fatigue behaviour. The kinking of the crack is due to a periodic self‐balanced microstress field having length scale d. By correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate size in concrete), the present model is applied to interpret some experimental findings related to crack size effects in fatigue of materials. Well‐known experimental results concerning three different situations (fatigue threshold, fatigue short crack growth and fatigue crack growth in the Paris regime) are analysed.

The effect of crack size and specimen size on the relation between the Paris and Wöhler curves

Paris and Wohler’s fatigue curves are intimately connected by the physics of the process of fatigue crack growth. However, their connections are not obvious due to the appearance of anomalous specimen-size and crack-size effects. In this study, considering the equations for a notched specimen (or for a specimen where failure is the result of the propagation of a main crack) and the assumption of incomplete self-similarity on the specimen size, the relations between the size-scale effects observed in the Paris and Wohler’s diagrams are explained. In the second part of the work, the behaviour of physically short cracks is addressed and, considering a fractal model for fatigue crack growth, the crack-size effects on the Paris and Wohler’s curves are discussed.

Elastic analysis of a circumferential crack in an isotropic curved beam using the modified mapping–collocation method

The modified mapping-collocation (MMC) method was applied to the boundary value problem (BVP) of a circumferential crack in an isotropic elastic curved beam subjected to pure bending moment loading. The stress correlation technique is then used to determine opening and sliding mode stress intensity factor (SIF) values based on the computed stress field near the crack tip. The MMC method aims at solving two-dimensional BVP of linear elastic fracture mechanics (LEFM) circumventing the need for direct treatment of the biharmonic equation by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and continuation arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. A good qualitative agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. A quantitative comparison with FEM results is also made using ANSYS. The effect of crack size, crack position and beam thickness variation on SIF values and mode-mixity is investigated.

Environmentally Assisted Small Crack Growth

Corrosion fatigue small crack growth rates have been determined for a 12Cr steam turbine steel in a simulated condensate solution under conditions representing repetitive turbine start-up and shut-down. Cracks were grown from a single corrosion pit generated electrochemically using the droplet technique and the crack length monitored optically and by direct current potential drop (DCPD). A comparison is made with growth rates for short and long cracks determined using fracture mechanics specimens. The enhanced crack growth rate observed for a short crack (relative to that for a long crack) but not realised for the small crack is rationalized on the basis of an electrochemical crack size effect.

On the dependency of the parameters of fatigue crack growth from the fractal dimension of rough crack profiles

A theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1 < D < 2) and the parameters defining the fatigue crack propagation rate. The exponent m of the Paris’ law is found to be an increasing function of the fractal dimension of the crack profile, m = 2 D/(2 − D). This trend is confirmed by a quantitative analysis of fractographic images of titanium alloys with different grain sizes (different roughness of crack profiles), by a new experimental test and by an indirect estimation of D from crack growth equations accounting from crack-size effects in steel and aluminum. The present study can be considered as the first quantitative analysis of fractographic images aiming at relating the morphological features of cracks to their kinetics in fatigue.

Study of Tower Surface Crack Size Effect Based on Weibull Theory

This paper presents the evaluation of safety state of for tower surface with Weibull and Fractal theory which simulate stress situation of the different scales on the cable-stayed tower surface with PFC. The combination of the Weibull theory and the Fractal theory evaluated the crack condition on the surface of the cable-stayed tower. Calculation results of three specimens showed that the number of the cracks increased when the load step and surface size increased. At the same time, the largest size of specimen had the biggest fractal dimension. The discrete element numerical simulation shows that Weibull modulus was successfully used to evaluate the crack extension of the cable bent tower.

A simple model to account for the role of microtexture on fatigue and dwell fatigue lifetimes of titanium alloys

A deterministic model to account for the effect of initial crack size, microtextured region size and aspect ratio on the mean cyclic and dwell fatigue lifetimes of titanium alloys is described. The model also quantifies variability in lifetime from sample to sample due to differences in the position of subsurface crack initiation. The results indicate that dwell fatigue life and cyclic fatigue life depend most on microtexture region size and initial crack size, respectively.

Analytical estimation of natural frequencies and mode shapes of a beam having two cracks

Abstract In this paper, an analytical estimation based on the Rayleigh's method is extended for a beam having one or two cracks to find natural frequencies and mode shapes in order to overcome weakness of solving eigenvalue problem. Weakness of solving eigenvalue problem to obtain exact natural frequencies and mode shapes is that, an algebraic equation must be solved numerically and then coefficients of trigonometric and hyperbolic terms in mode shapes will be found using matrices obtained from compatibility conditions at each point of cracks and boundary conditions. So this method does not show effects of crack size and location in the explicit form. The advantage of analytical estimation based on the Rayleigh's method over the eigen analysis method is that, the Rayleigh method obtains explicit expression for both natural frequencies and mode shapes in which effect of parameters such as crack size and location on natural frequencies and mode shapes can be investigated analytically. In the analytical estimation method, mode shapes of cracked beam are constructed by adding a polynomial function which shows effect of cracks, to mode shape of undamaged beam. The coefficients of the polynomial function are obtained by using boundary conditions and compatibility equations at the point of cracks. However in this paper it is shown that the accuracy of this estimation decreases when crack depth increases. Therefore, this paper also investigates on the upper limit of crack depth in which natural frequencies have error less than 5% and mode shapes have error less than 7% obtained by analytical estimation in compare to the exact solution. In the literature, it is shown that, analytical estimation based on the Rayleigh's method can predict only the first natural frequency of a simply supported cracked beam with sufficient accuracy, but no more investigation reported for finding the reliable range of crack depth natural mode shapes or higher natural frequencies. So, in this study, upper limit of crack depth has been found for both cases of beam with one or two cracks for first three natural frequencies and mode shapes.

Instability of cracked CFRP composite cylindrical shells under combined loading

Numerical analysis of cracked composite cylindrical shells under combined loading is carried out to study the effect of crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, torsion, internal pressure and external pressure are obtained, using the finite element method. In general, the internal pressure increases the critical buckling load of the CFRP cylindrical shells while torsion and external pressure decrease it. Numerical analyses show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell while for cylindrical shells under combined external pressure and axial load, the global buckling shape is insensitive to the crack length and crack orientation.

Experimental Finding Of Initiation Fracture Toughness And FEM Simulation Of Fracture Behaviour Of UFG 7075 Al Alloy

The present work describes an experimental evaluation of yield strength, tensile strength, initiation fracture toughness and Finite element simulations of fracture behaviour for both bulk and ultrafine-grained (UFG) 7075 Al Alloy. The 7075 Al alloy has been rolled for different thickness reductions (40%, 70% and 90%) at cryogenic (liquid nitrogen) temperature, and its mechanical properties and microstructural morphology have been investigated. Rolling of the Al alloy at cryogenic temperature suppresses the dynamic recovery and grain growth, which leads to grain fragmentation. Dislocation cells formed during consecutive rolling passes, transformed into fully formed UFG (600 nm) up to 70% thickness reduction. Grain size gets reduced further when 90% thickness reduction is achieved. Incremental crack growth simulations have been carried out by commercial software ABAQUS under quasi-static loading using deformation plasticity theory based on Griffith energy concept. J-integral, stress along crack path, effect of crack and specimen size over J-integral, stress distribution and plastic dissipation ahead of the crack tip have been investigated for some practical crack problems under mechanical and thermo-mechanical loading. The numerical examples indicates a significant enhancement in crack arrest capabilities of UFG alloys for the same boundary conditions because of decreasing J values with increasing % thickness reduction. This is attributed to the improved mechanical properties (UTS: 625 MPa and YS: 610 MPa) of the cryorolled alloy which hinders the onset of plasticity, results from ultrafine-grain formation.

Transient thermal cracking of a brittle half space medium with a semi-elliptical surface crack

The paper conducts the cracking study of a brittle half space medium with a semi-elliptical surface crack. The transient thermal stress intensity factors are obtained and are graphically presented. Effects of thermal shock time, crack size, and crack shape on the crack growth and thermal shock resistance behavior of the medium are investigated in details. A thermal shock resistance analysis methodology is established, allowing us to study the fracture strength of brittle media subjected to thermal shock.

Crack propagation and size effect in concrete using a non-local damage model

Size effect is a major issue in concrete structures. Experimental and numerical investigations on the influence of size effect on crack opening, crack length and crack propagation are presented in this paper. An isotropic non-local strain softening damage constitutive law is adopted for the numerical model. The material characteristic length is calibrated using an optimization algorithm and a post-processing method is chosen to obtain information on cracking. Numerical global and local results are compared with the experimental data and conclusions are drawn on the advantages and limitations of the adopted modelling strategy to reproduce size effect in concrete structures.

Prediction of size effect and non-linear crack growth in plain concrete under fatigue loading

A new method is proposed that uses inverse analysis to calculate cyclic induced bridging stresses along a dominant crack face in a plain concrete three-point bending single edge notch specimen. Peak to peak low cycle fatigue data is used to back-calculate the bridging stresses and an equivalent crack resistance curve is derived with a weight function. Fourteen specimens were tested under low cycle fatigue and two were tested under high cycle fatigue. The results of this study indicate that the equivalent cyclic crack resistance curve obtained under low cycle fatigue can be used to predict the equivalent cyclic crack resistance under high cycle fatigue and explain the decelerating crack growth phenomenon and size effect in plain Portland cement concrete.

On a kinked crack model to describe the influence of material microstructure on fatigue crack growth

Threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection. In the present paper, a theoretical model of a periodically-kinked crack is presented to describe the influence of the degree of crack deflection on the fatiguebehavior. The kinking of the crack is due to a periodic self-balanced microstress field having a length scale, d.By correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate dimension in concrete), the possibility of using the present model to describe some experimental findings related to crack size effects in fatigue of materials is explored. Well-known experimental results concerning two different situations (fatigue threshold and fatigue crack growth in the Paris regime) are briefly analysed.

Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading

A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.

Equivalent CTOD Ratio β for Engineering Assessment of CTOD Correction for Constraint Loss

The critical CTOD δWP for structural components associated with plastic constraint loss in case of the brittle fracture over small-scale yielding condition can be corrected from CTOD fracture toughness δ by means of the “equivalent CTOD ratio β” defined as δ/δWP, which is based on the Weibull stress criterion. In this study, taking the case of specific wide plate components subjected to uni-axial tensile load, the effect on β is analyzed taking account of Weibull shape parameter m, loading level, constraint effect that can be influenced by material work-hardening and crack type/size in structural components, etc., and volumetric effect. It is found that the β-value is almost constant beyond the applied CTOD level that is lower than CTOD of small-scale yielding limit (SSY-limit) for 25 mm thick toughness specimen. From an engineering point of view, the β-value at the CTOD level of 0.01 mm is used in the whole loading range beyond SSY-limit CTOD, which provides to some extent conservative measure of fracture toughness of structural components. The defined β is found to decrease with increasing Weibull shape parameter m and yield-to-tensile ratio YR of steel for all type of wide plates concerned. The crack length effect on β is quasi-theoretically formulated, which can convert the β for the wide plate with reference crack size to β for target crack size. These β and quasi-theoretical equations for the correction of crack size effect can be utilized for estimating the CTOD for wide plate in consideration of constraint loss effect without numerical calculation of the Weibull stress.