Critical thrust and feed prediction models in drilling of composite laminates Navid Zarif Karimi a,⇑ , Hossein Heidary b , Giangiacomo Minak a a Alma Mater Studiorum, Università di Bologna, Department of Industrial Engineering DIN, Viale del Risorgimento 2, 40136 Bologna, Italy b University of Tafresh, Department of Mechanical Engineering, First of Tehran Road, 7961139518 Tafresh, Iran article info Article history: Received 4 March 2016 Accepted 29 March 2016 Available online 30 March 2016 Keywords: Composite laminates Analytical modeling Delamination Drilling Oblique cutting Linear elastic fracture mechanics abstract Drilling induced delamination has been recognized as a major problem during drilling of composite materials. The size of the delamination zone has been shown to be related to the thrust force. However, thrust force strongly depends on drilling parameters and it is not possible to control it directly. Thrust force can be correlated with feed rate, the most important parameter affecting thrust force. This paper presents analytical models to predict critical thrust force and feed rate at the onset of delamination. The model proposed is based on elastic fracture mechanics, classical plate bending theory and the mechanics of oblique cutting. An advantage of this model over other proposed models is that to avoid delamination via thrust monitoring, the thrust force will need to be sensed and used in adaptive control, while optimal feed rate can be used directly in CNC command generation to maximize productivity. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Among various drilling processes for fiber reinforced composite laminates, conventional drilling with twist or special drill bits has remained the most frequently and economically used machining operation in industry. Drilling of FRPs is a complex process and it differs significantly in many aspects from machining of conventional metals and alloys due to the anisotropic and non-homogeneous characteristics of these materials. During the drilling of composite materials many problems arise which do not occur in other materials. Among various defects caused by dril- ling, delamination is known as the most prevalent life limiting damage growth mode [1–4]. Delamination is an inter-ply failure phenomenon, which is a highly undesirable problem and occurs due to localized bending in the zone sited at the point of drill contact. At the beginning of the drilling process, the thickness of the composite laminate is able to withstand the cutting force. As the drill bit approaches the hole’s exit side, the cutting force applied to the uncut laminae of the workpiece exceeds the inter-ply bonding strength and results in delamination [5–8]. It has also been observed that drilling-induced delamination is directly related to the component of cutting force along the drill axis known as thrust force, and it is reported that there is a critical value for thrust force below which delamination is negligible [9]. Analytical study of this thrust force is thus interesting in order to reduce delamination. Several researchers attempted to model critical thrust force for delamination propagation. The first analytical model was proposed by Hocheng and Dharan [10]. They employed linear elastic fracture mechanics (LEFM), classical plate bending theory and energy con- servation theory to formulate an analytical model to predict the critical thrust force at the onset of delamination during drilling of composite materials. This model predicts a critical thrust force (the minimum force above which delamination is initiated) as a function of composite properties and drilled hole depth. The isotro- pic behavior and pure bending of laminate are assumed in their model. Jain and Yang [11,12] developed this model, considering the anisotropy of the material and hypothesizing that the cracks are elliptical. They also observed that the chisel edge has a greater contribution to the thrust force than cutting lips. In their model, the drilling thrust force is simplified by a representative single con- centrated central load. Hocheng and Tsao [9,13–15] extended this model, taking into consideration a series of loading types such as circular load, concentrated centered load associated with circular load, distributed circular load and stepwise distributed circular load for various drill types such as saw drill, candle stick drill, core drill and step drill, respectively. In this analysis, the critical thrust force at the onset of delamination is predicted and compared with the twist drill. http://dx.doi.org/10.1016/j.compstruct.2016.03.059 0263-8223/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: navid.zarif@unibo.it (N. Zarif Karimi), heidary@tafreshu.ac.ir (H. Heidary), giangiacomo.minak@unibo.it (G. Minak). Composite Structures 148 (2016) 19–26 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct