On assumptions associated with ΔKeff and their implications on FCG predictions

In this paper, an assessment of commonly used assumptions associated with ΔK_eff and their implications on FCG predictions in light of existing experimental and numerical data is presented. In particular, the following assumptions are examined: (1). ΔK_eff fully describes cyclic stresses and strains at the crack-tip vicinity. (2). K_op can be determined experimentally or numerically with certain accuracy. (3). Overload alters K_op but not K_max and associated σ_max at the crack-tip ‘process zone’. (4). Contact of crack faces curtails the crack driving force in terms of ΔK_eff.The analysis indicates that there is insufficient support to justify the above assumptions. In contrary, the analysis demonstrates that a two-parameter fatigue crack driving force in terms of ΔK and K_max, which accounts for both applied and the internal stresses should be used in FCG analyses and predictions.     

Solutions of the second elastic-plastic fracture mechanics parameter in test specimens

Extensive finite element analyses have been conducted to obtain solutions of the A-term, which is the second parameter in three-term elastic-plastic asymptotic expansion, for test specimens. Three mode I crack plane-strain test specimens, i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analyzed included shallow to deep cracks. Solutions of A-term were obtained for material following the Ramberg-Osgood power law with hardening exponent of n = 3, 4, 5, 7 and 10. Remote tension loading was applied which covers from small-scale to large-scale yielding. Based on the finite element results, empirical equations to predict the A-terms under small-scale yielding (SSY) to large-scale yielding conditions were developed. In addition, by using the relationships between A and other commonly used second fracture parameters such as Q factor and A₂-term, the present solutions can be used to calculate parameters A₂ and Q as well. The results presented in the paper are suitable to calculate the second elastic-plastic fracture parameters for test specimens for a wide range of crack geometries, material strain hardening behaviors and loading conditions.     

Three-dimensional cracks with Dugdale-type plastic zones

A general method for the determination of three-dimensional crack-front plastic zones is presented. The crack-model utilised is of the Dugdale-type, that is a plastic zone is assumed to spread in front of the crack, in the plane of the crack. The solution method relies on the eigenstrain approach to crack-problem solving. Using this approach, the elastic and plastic regions of the crack are first discretised into triangular elements and the stress arising over the crack due to a constant or linear crack-surface displacement in each element is obtained. The stresses are given in terms of hyper-singular integrals, which may be solved numerically. The boundary conditions in the elastic portion (traction-free) and in the plastic zones (Tresca or some other yield condition) are encompassed in an object function in such a way that the boundary conditions are satisfied if and only if the object function is zero. The resulting quadratic programming problem is solved numerically, and hence the crack displacements, and other important quantities, are obtained. Results agree well with some known analytic results regarding the penny shaped crack in tension.     

Dynamic crack propagation in matrix involving inclusions by a time-domain BEM

The dynamic crack propagation in composites with inclusions is analyzed by a time-domain boundary element method (BEM) in conjunction with the sub-region technique. The crack-growth direction and the crack-tip instantaneous velocity are determined by the maximum circumferential stress criterion. The instantaneous velocity is well smoothed by a bisection technique. New crack-tip elements of inconstant length are added to the active crack-tip to simulate the fast crack growth. Square root shape functions are adopted as to describe the proper asymptotic behavior in the vicinity of the crack-tips. The computation time for the dynamic fracture problems in composites with multiple inclusions is reduced by a numerical method. The influences of the inclusions on the shielding ratio, the crack growing path and the crack-tip instantaneous speed are well investigated.     

An approximation for the cyclic state of stress ahead of cracks and its implications under fatigue crack growth

Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J-integral solutions to be employed in damage tolerance analysis of cracked components. In this frame, simple assumptions about material properties are taken into account.More refined approaches try to describe the plasticity-induced crack closure in order to account for retardation effects under variable amplitude loading. In these approaches, the cyclic plasticity is used and cyclic finite element analyses are carried out.In the present work, a novel strategy is presented for the calculation of the relevant parameters to the fatigue crack growth, based on the evaluation of local field parameters (J-integral, T-stress) and cyclic material properties. It is demonstrated that, in case of mild steels and under the assumption of a stress ratio R = −1, the global constraint factor α_g widely employed in fatigue crack growth algorithms such as the strip-yield model, can be calculated in a closed-form on the basis of the expression of the crack-tip fields. Moreover, α_g provides a reasonable explanation of the fatigue crack growth behaviour of the A1N steel for different geometrical and loading configurations. Further investigations carried out on different medium and high strength steel grades show that the plastic radius ahead of small and long cracks at their fatigue limits can be considered as a constant for the material.     

Mode I solution for micron-sized crack

The feature size of micro-electronic, optoelectronic and biomedical devices is in the sub-micron scale and is pushing toward the nanometer scale. Defects in these small structures are correspondingly smaller such that small crack behavior is becoming an important design consideration for reliability and performance of such devices. Analyses of small cracks are complicated by the rapid variation in the deformation in the crack tip zone. Strain gradients in the near tip zone, which can be ignored in large cracks, will influence the small crack behavior when the crack tip zone is in the order of the crack size. In this paper, we consider two-dimensional crack deformations with strain gradient effect and establish the dual formulations in terms of potentials. The formulations reduce to the conventional linear elastic fracture theory, when the material length scale parameters for the higher order deformation measures are zero. One of the formulations is in terms of two complex stress functions and two pseudo potentials. The complex stress functions are harmonic and the governing equations for the pseudo-potentials are two uncoupled second order partial differential equations. The solutions for these equations are coupled through the boundary conditions.A perturbation method is used to construct the solution for mode I cracks under a K-field when only the effect of the rotational gradient is included. The perturbation solution has induced singularity for the stresses. The induced deformation decays exponentially away from the crack tip. The induced stresses become insignificant beyond 3ε, the typical characteristics of a boundary layer type. To a first order approximation, the induced deformation energy normalized by that of the classical solution under constant applied crack opening load is linearly proportional to ε. This implies that the induced energy release rate is linearly proportional to the length scale parameter. The induced energy release rate under a fixed crack opening load is negative indicating that the rotational gradient shields the crack and lowers the total deformation energy release rate for small crack.     

Characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique

This work presents a novel methodology for characterising fatigue cracks under biaxial conditions on a low carbon steel. It allows both short crack and early propagation stages to be studied in tubular specimens. Short crack growth is studied with a long-distance microscope acquiring images of the bare metal surface. Results showed oscillations in crack growth rate due to microstructure. Early propagation stage is studied with high magnification Digital Image Correlation (DIC) technique for measuring displacement and strain crack-tip fields. By applying micro-speckle pattern on the metal surface it is possible to achieve high magnification for DIC technique. Ultra-fine black and white speckles were created by electro-spray technique. The validity of this novel technique is demonstrated by direct comparison with extensometer measurements, under combined tension–compression and torsion conditions. It was also possible to estimate satisfactorily the mixed-mode stress intensity factor.     

Effect of grain disorientation on early fatigue crack propagation in face-centred-cubic polycrystals: A three-dimensional dislocation dynamics investigation

Three-dimensional dislocation dynamics simulations are used to study micro-crack interaction with the first micro-structural barrier, in face-centred-cubic bi-crystals loaded in high-cycle fatigue conditions. In the examined configuration, we assumed that micro-crack transmission occurs due to surface relief growth in the secondary grain ahead of the primary crack. This indirect transmission mechanism is shown to strongly depend on grain-1/grain-2 disorientation. For instance, small grain disorientation induces plastic strain localization ahead of the crack and therefore, faster transmission through the first barrier. Conversely, large grain-1/grain-2 disorientation induces plastic strain spreading similar to crack tip blunting, yielding slower indirect transmission. A semi-analytical micro-model is then proposed based on the present simulation results and complementary experimental observations, highlighting the original notion of first-barrier compliance. The model captures well-known experimental trends, including the effects of grain-size, grain disorientation and micro-crack retardation at the first barrier.     

Automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method

In this paper, automated simulation of multiple crack fatigue propagation for two-dimensional (2D) linear elastic fracture mechanics (LEFM) problems is developed by using boundary element method (BEM). The boundary element method is the displacement discontinuity method with crack-tip elements proposed by the author. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Local discretization on the incremental crack extension is performed easily. Further the new adding elements and the existing elements on the existing boundaries are employed to construct easily the total structural mesh representation. Here, the mixed-mode stress intensity factors are calculated by using the formulas based on the displacement fields around crack tip. The maximum circumferential stress theory is used to predict crack stability and direction of propagation at each step. The well-known Paris’ equation is extended to multiple crack case under mixed-mode loadings. Also, the user does not need to provide a desired crack length increment at the beginning of each simulation. The numerical examples are included to illustrate the validation of the numerical approach for fatigue growth simulation of multiple cracks for 2D LEFM problems.