A B S T R A C T It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic-plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti-6Al-4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.Keywords crack propagation threshold; fatigue crack propagation rate; short fatigue cracks; titanium alloy; unified fatigue life prediction method. N O M E N C L A T U R Ea = the crack length A = a material-sensitive and environmentally sensitive constant of dimensions in the crack growth rate model A 0 , A 1 , A 2 , A 3 = the coefficients defined to calculate the crack opening function f op d = THE intrinsic crack length da/dN = Fatigue crack growth rate f op = a crack opening function defined as the ratio K op /ΔK k = a material constant that reflects the rate of crack closure development with crack advance K cf = the fracture toughness of the material K max = the maximum stress intensity factor K min = the minimum stress intensity factor m = a constant representing the slope of the corresponding fatigue crack growth rate curve dimensions in the crack growth rate model n = the index indicating the unstable fracture in the crack growth rate model r e = an empirical material constant of the inherent flaw length of the order of 1μm R = the stress ratio defined by σ min /σ max Y = a geometrical factor to calculate the stress intensity factor α = a parameter used to calculate the 'virtual strength' of the material α ′ = the plane stress/strain constraint factor ΔK effth = the effective range of the stress intensity factor at the threshold level

Small drug molecules usually bind to multiple protein targets or even unintended off-targets. Such drug promiscuity has often led to unwanted or unexplained drug reactions, resulting in side effects or drug repositioning opportunities. So it is always an important issue in pharmacology to identify potential drug-target interactions (DTI). However, DTI discovery by experiment remains a challenging task, due to high expense of time and resources. Many computational methods are therefore developed to predict DTI with high throughput biological and clinical data. Here, we initiatively demonstrate that the on-target and off-target effects could be characterized by drug-induced in vitro genomic expression changes, e.g. the data in Connectivity Map (CMap). Thus, unknown ligands of a certain target can be found from the compounds showing high gene-expression similarity to the known ligands. Then to clarify the detailed practice of CMap based DTI prediction, we objectively evaluate how well each target is characterized by CMap. The results suggest that (1) some targets are better characterized than others, so the prediction models specific to these well characterized targets would be more accurate and reliable; (2) in some cases, a family of ligands for the same target tend to interact with common off-targets, which may help increase the efficiency of DTI discovery and explain the mechanisms of complicated drug actions. In the present study, CMap expression similarity is proposed as a novel indicator of drug-target interactions. The detailed strategies of improving data quality by decreasing the batch effect and building prediction models are also effectively established. We believe the success in CMap can be further translated into other public and commercial data of genomic expression, thus increasing research productivity towards valid drug repositioning and minimal side effects.

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