br Experimental work br Results br Discussion br Conclusions

Experimental work
Results
Discussion
Conclusions In this paper, the effect welding consumables and welding processes on fatigue crack growth behaviour of armour grade Q&T steel joints was analysed in detail. From the above illustrations, the following conclusions are derived:
Acknowledgements The authors are thankful to M/s Combat Vehicle Research Development Establishment (CVRDE), Avadi, Chennai for providing notch signaling pathway material and extending fabrication facility for joint fabrication, M/s Defence Metallurgical Research Laboratory (DMRL), Hyderabad for providing characterization facility and Department of Manufacturing Engineering, Annamalai University for providing testing facility for this investigation. The authors are also thankful to Armament Research Board (ARMREB), New Delhi for funding this project work (Project No MAA/03/41).
Introduction Interception of high-speed exo-atmospheric targets with angular constraint is a challenging task since the speed of target is higher than that of interceptor in the exo-atmosphere. Recently, several guidance laws using proportional navigation (PN)-based methods have been proposed, which are used to intercept the targets with angular constraint. However, most of the guidance laws are only for intercepting low-speed targets (Ref. [1] and [2]) or stationary targets (Ref. [3] and [4]). A biased PN (BPN) guidance law which can be used for intercepting low-speed targets with angular constraint was proposed in Ref. [1]. The BPN [5] is one such scheme, in which a fixed angular rate is superimposed on the measured LOS rate before computing the commanded projectile turn rate (or lateral acceleration). Because of the introduction of an extra parameter (i.e., rate bias), BPN can achieve an interception with a desired impact angle. This is an important advantage for enhancing warhead effectiveness. When the guidance laws are used to intercept the high-speed targets without angular constraint, they can be classified as two cases: head-on and tail-chase engagements. In the case of head-on engagement, three-dimensional pure PN (PPN) guidance law [6] is used for engaging the high-speed targets, and a capture + region is obtained. In the case of tail-chase engagement, the retro-PN (RPN) guidance law [7] for interception of high-speed targets without angular constraint uses a negative navigation ratio. Prasanna et al. demonstrated that the capture region of RPN is larger than that of PN for intercepting high speed target, and reported that Stop codons is valuable to incorporate the useful features of both the PN and RPN guidance laws in the future work [7]. In this paper, a guidance law, called biased retro-proportional navigation (BRPN), is proposed. BRPN has a very larger capture region compared to BPN.
Definition of BRPN guidance law In this work, the planar motions of interceptor and target are considered. In order to facilitate the whole analysis, some general assumptions are introduced as follows. Under the above assumptions, a planar engagement geometry, as shown in Fig. 1, can be described by the following nonlinear differential equations. The rotation rate of the line of sight (LOS) at any time is given by the following equation The velocity component along LOF is given by the following equationwhere R is the range between interceptor and target, Vm is the interceptor missile velocity, Vt is the horizontal velocity of target, λ is the LOS angle, and γ is the flight path (or heading) angle of missile. Note that, in order to show the impact angle clearly, here the final path angle γf is defined to be the impact angle. The rate of change of the interceptor heading is defined aswhere N is the navigation ratio, is the LOS rate, and is a rate bias at LOS turn rate. Differentiating Eq. (1), we havesubstituting Eqs. (2) and (3) into Eq. (4), we have Note thatwhere tf is the total intercept time. Defining , Vc > 0 (Vc is the approaching velocity of interceptor [8]). Eq. (7) can be derived from Eqs. (6) and (5), yieldingusing Eq. (8) proposed in Ref. [8]substituting Eq. (8) into Eq. (7), we havewhere is commonly called the effective navigation ratio [8] and is a constant in this paper.