Micromechanics Of Fatigue Crack-Growth At Low Stress Intensities In A High-Strength Steel

An attempt to systematically investigate the effects of microstructural parameters in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels has been made for a high strength low alloy steel to observe in general, widely different trends in the dependence of both the total threshold stress intensity range, DELTA-K(th) and the intrinsic or effective threshold stress intensity range, DELTA-K(eff-th) on the prior austenitic grain size (PAGS). While a low strain hardening microstructure obtained by tempering at high temperatures exhibited strong dependence of DELTA-K(th) on the PAGS by virtue of strong interactions of crack tip slip with the grain boundary, a high strength, high strain hardening microstructure as a result of tempering at low temperature exhibited a weak dependence. The lack of a systematic variation of the near-threshold parameters with respect to grain size in temper embrittled structures appears to be related to the wide variations in the amount of intergranular fracture near threshold. Crack closure, to some extent provides a basis on which the increases in DELTA-K(th) at larger grain sizes can be rationalised. This study, in addition, provides a wide perspective on the relative roles of slip behaviour embrittlement and environment that result in the different trends observed in the grain size dependence of near-threshold fatigue parameters, based on which the inconsistency in the results reported in the literature can be clearly understood. Assessment of fracture modes through extensive fractography revealed that prior austenitic grain boundaries are effective barriers to cyclic crack growth compared to martensitic packet boundaries, especially at low stress intensities. Fracture morphologies comprising of low energy flat transgranular fracture can occur close to threshold depending on the combinations of strain hardening behaviour, yield strength and embrittlement effects. A detailed consideration is given to the discussion of cyclic stress strain behaviour, embrittlement and environmental effects and the implications of these phenomena on the crack growth behaviour near threshold.

A spiral growth model for quasicrystals in two dimensions

Spiral space filling geometrical constructions using rhombuses in two dimensions are considered as plausible mechanisms for quasicrystal growth. These models will show staircase-like features which may be observed experimentally.

Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK th , and the intrinsic threshold stress intensity range, ΔK eff, th , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK th and ΔK eff, th on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK th and ΔK eff, th on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔKth and ΔKeff, th with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning, J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago.

Fatigue crack growth under an eqivalent falstaff spectrum

Optical fractography was used to estimate growth of small cracks at notches under programmed FALSTAFF loading in an Al-Cu alloy. Crack sizes as low as 25 microns and growth rates over two orders of magnitude could be resolved using this technique. Randomized MiniFALSTAFF load sequence was modified into a programmed load equivalent with major loads either preceding or following marker loads. Crack growth rate under programmed FALSTAFF spectrum as estimated by optical fractography conformed to compliance based estimates on a SE(T) specimen. Long crack growth rates under programmed and randomized MiniFALSTAFF spectrum were essentially similar. Spectrum load fatigue crack growth was studied in central hole coupons under notch inelastic conditions. Scatter in growth rates for small notch cracks was found to be of the same magnitude as that of long cracks. Multiple fatigue cracks are observed at the notch root, and they appear to influence each other.

The fatigue crack growth rate in L-72 Al-alloy plate specimens with cold worked holes

A fatigue crack growth rate study has been carried out on L-72 aluminium alloy plate specimens with and without cold worked holes. The cold worked specimens showed significantly increased fatigue life compared to unworked specimens. Computer software is developed to evaluate the stress intensity factor for non-uniform stress distributions using Green's function approach. The exponents for the Paris equation in the stable crack growth region for cold worked and unworked specimens are 1.26 and 3.15 respectively. The reduction in exponent value indicates the retardation in crack growth rate. An SEM study indicates more plastic deformation at the edge of the hole for unworked samples as compared to the worked samples during the crack initiation period.

Autocalibration of dynamic bacterial growth model for water distribution system using GA

The presence of residual chlorine and organic matter govern the bacterial regrowth within a water distribution system. The bacterial growth model is essential to predict the spatial and temporal variation of all these substances throughout the system. The parameters governing the bacterial growth and biodegradable dissolved organic carbon (BDOC) utilization are difficult to determine by experimentation. In the present study, the estimation of these parameters is addressed by using simulation-optimization procedure. The optimal solution by genetic algorithm (GA) has indicated that the proper combination of parameter values are significant rather than correct individual values. The applicability of the model is illustrated using synthetic data generated by introducing noise in to the error-free measurements. The GA was found to be a potential tool in estimating the parameters controlling the bacterial growth and BDOC utilization. Further, the GA was also used for evaluating the sensitivity issues relating parameter values and objective function. It was observed that mu and k(cl) are more significant and dominating compared to the other parameters. But the magnitude of the parameters is also an important issue in deciding the dominance of a particular parameter. GA is found to be a useful tool in autocalibration of bacterial growth model and a sensitivity study of parameters.

Re-examination of crack opening model of interface fracture

The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts, such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. To avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singularity at an interface crack. International Journal of Fracture 1980;16(2):111-9) assumed a finite crack opening angle (COA) such that the singularity lambda became real equal to 1/2. This paper extends the COA model by considering real singularities not necessarily equal to 1/2. When COA is 0 degrees: the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields. (C) 1999 Elsevier Science Ltd. All rights reserved.

The effect of T-stress on plane strain dynamic crack growth in elastic-plastic materials

In this paper, the effects of T -stress on steady, dynamic crack growth in an elastic-plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J (2) flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T -stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T -stress for both ductile and cleavage mode of crack growth.

Fatigue crack growth studies on lug joints

Pin loaded lug joints fitted with different types of pins are analysed in the presence of cracks at pin-plate interface. An algorithm for finite element contact stress analysis of joints developed earlier to deal with varying partial contact/separation at the pin-plate interface using a marching solution is used in the present analysis. Stress Intensity Factors (SIF) at the crack tips are evaluated using Modified Crack Closure Integral (MCCI) method within the realm of Linear Elastic Fracture Mechanics (LEFM) assumptions. A comparison of fatigue crack growth lives between interference and push fit pin joints is carried out using these SIF's. Results from a finite element analysis on a push fit pin joint are used to fit experimental fatigue crack growth data.

Use of acoustic emissions in flexural fatigue crack growth studies on concrete

The acoustic emission technique is used for monitoring the fatigue crack growth in plain concrete beams under three-point loading. Variable amplitude loading with step-wise increase in the maximum load is applied. The fatigue crack growth is continuously monitored using six acoustic sensors. The results of load, displacement, crack mouth opening displacement, acoustic events, and acoustic energy are simultaneously acquired during the test. It is seen that a Paris law type of relationship exists between the rate of increase of acoustic emission count per cycle and the stress intensity factor range. Using b-value analysis, different stages of fatigue fracture is explained. (C) 2012 Elsevier Ltd. All rights reserved.

An automatic algorithm for mixed mode crack growth rate based on drop potential method

A new automatic algorithm for the assessment of mixed mode crack growth rate characteristics is presented based on the concept of an equivalent crack. The residual ligament size approach is introduced to implementation this algorithm for identifying the crack tip position on a curved path with respect to the drop potential signal. The automatic algorithm accounting for the curvilinear crack trajectory and employing an electrical potential difference was calibrated with respect to the optical measurements for the growing crack under cyclic mixed mode loading conditions. The effectiveness of the proposed algorithm is confirmed by fatigue tests performed on ST3 steel compact tension-shear specimens in the full range of mode mixities from pure mode Ito pure mode II. (C) 2015 Elsevier Ltd. All rights reserved.