In this model the growth of a crack is analysed in terms of the successive blocking of the plastic zone by slip barriers (e.g. grain boundaries) and the subsequent initiation of the slip in the next grain. The discontinuous character of the slip process (slip jumps) plays a fundamental role in the model. The factor governing the transfer of slip across a grain boundary is considered to be the stress concentration ahead of the plastic zone which, for a constant applied stress τ, is found to be dependent only on a parameter n = a/c defining the position of the crack tip relative to the grain boundary. The discrete behaviour of the slip has a strong influence in the short-crack period and hence cannot be neglected in the analysis of the crack growth rate. This period is characterized by large variations in the parameter n. In the long-crack period the slip jumps do not influence the overall description of the growth and the parameter n is almost constant. By making the crack extension per cycle prop...

Short and long fatigue crack growth: A unified model

http://qmxmt.com/scans/dave/other/papers/xmt%20applications/xmt_metalfatigue.pdf

Study of the interaction of a short fatigue crack with grain boundaries in a cast Al alloy using X-ray microtomography

— Recent experimental work on the growth of small fatigue cracks is surveyed and critically analyzed. It is shown that microcracks grow at anomalous rapid rates relative to large ones only when certain criteria, involving crack size, plastic zone size, and micro-structural element size, are met. Retardation and arrest of microcracks is found to correlate with microstructural element size, hence with crystallographic influence.

The influence of microstructure on the growth of small fatigue cracks

A study of nucleation and fatigue behavior of an aerospace aluminum alloy 2024-T3

The behaviour of short cracks approaching growth barriers (eg grain boundaries) is considered The crack model of Bilby, Cottrell and Swinden is applied to simulate the blocking of the plastic zone at the grain boundary and to obtain the stress concentration ahead of the crack as it approaches the barrier The idea of the Hall-Petch type relationship that the transmission of slip across grain boundaries needs the previous achievement of a critical stress has been used By making the crack growth rate proportional to the plastic displacement at the root of the crack the deceleration behaviour of short cracks and the existence of non-propagating cracks may be explained The fatigue limit is related to the stress below which a crack growing in a single grain is unable to promote slip in the neighbouring grain The different behaviour in the so-called long crack period has been rationalized in terms of the plastic zone exceeding the grain size For this case, and in the grain completely included within the plastic zone, the Hall-Petch analysis must be applied Hence the maximum back-stress sustained by this grain cannot exceed the yield stress After this point the Bilby et al model is used with uy as a friction stress (ie the Dugdale model) Finally use is made of Fracture Mechanics to correlate the results in the long crack phase

A model for short fatigue crack propagation with an interpretation of the short‐long crack transition

The influence of alloy grain size on growth rates of surface cracks 20 to 500 μm in length was studied in Al 7075-T6 specimens prepared in 12 and 130 μn grain sizes. Grain boundaries temporarily interrupt the propagation of cracks shorter than several grain diameters in length. Linear elastic fracture mechanics is inadequate to describe resulting average growth rates which must instead be characterized as a function of cyclic stress amplitude, σa, and alloy grain size as well as stress intensity range, σK. These observations are rationalized using two models, one that relates crack closure stress to alloy grain size, and a second that relates the development of microplasticity in a new grain in the crack path to grain size. In addition, growth rates were found to be faster in fully reversed loading than in tension-tension loading, especially in the large grained material. Evidence is presented to demonstrate that this is a consequence of the fatigue induced development of a compressive residual surface stress during tension-tension loading. These complex effects, and the role of grain size in determining short crack growth, are discussed.

The Effect of Grain Size on Fatigue Growth of Short Cracks

— Evidence is presented that the cyclic stress intensity threshold for fatigue crack growth in A1 2219-T851 is associated with a critical maximum value of stress intensity, Kc. This relationship is discovered by measuring the local value of stress intensity at the crack tip which is less than the applied stress intensity because of fatigue induced compressive residual stresses in the plastic zone. Crack growth rates and values of the crack tip residual stress are measured as functions of load ratio. For local stress intensities greater than Kc, the growth rate follows a power-law relationship, increasing monotonically with δK. For local stress intensities below Kc, growth rates are also sensitive to the cyclic stress range, δσ. If the stress range is small, a threshold to growth, typical of long cracks, is seen. When the cracks are short and δσ exceeds a critical value, growth rates are a complex function of both δσ and δK. This behavior is attributed to the effect of δσ on the propagation of the crack front past obstacles such as grain boundaries.

On the transition from near‐threshold to intermediate growth rates in fatigue

The extent of crack tip plasticity for short fatigue cracks

Alloy grain size is known to influence both the propagation path and the closure stress of surface fatigue cracks in many alloys. The general trend is for the path to be more tortuous and the closure stress to be larger, the larger the grain size. By use of Ti Al-4V and Al 7075-T6, the effects of grain size on the nondestructive detection of surface cracks which might arise from closure stress and path irregularity variables were evaluated. Titanium specimens were inspected using an acoustic harmonic generation technique, and it was discovered that the major source of harmonic signals was grain sized crystallographic cracks. Harmonic signals were larger during fatigue in an 8-µm compared to a 4-µm grain sized alloy, as there were more grain sized cracks in the large grain material. Crack closure was found to be extremely important in determining the reflected acoustic amplitude obtained in inspecting small (100–1000 µm) cracks in Al 7075-T6 using a critical angle technique. Average received amplitudes were an order of magnitude smaller for cracks at zero load than for those opened by a tensile stress. The scatter in the reflected amplitude was also large, apparently as the result of variations in the degree of the closure from crack to crack. For the 7075 material, the important effect of larger grain size was to increase the irregularity of the crack path, making the small cracks more visible acoustically at azimuthal angles not normal to the crack plane.

A. K. Zurek

Papers

The Effect of Grain Size on Fatigue Growth of Short Cracks

On the transition from near‐threshold to intermediate growth rates in fatigue

The extent of crack tip plasticity for short fatigue cracks

Relationships between crack opening displacement, alloy variables, and crack detection sensitivity