Critical thrust force at delamination propagation during drilling of angle-ply laminates

A new formulation for the critical thrust force necessary to propagate the delamination generated during the drilling operation of an antisymmetric angle-ply laminate is proposed by modeling the delamination zone as an elliptical shape. The critical thrust force is analytically derived with the consideration of bending, twisting and mid-plane extension of the delamination zone. And then to maximize the critical thrust force, the optimal design of an angle-ply laminate is performed to find the optimal number of fiber per millimeter, optimum diameter of fiber and optimum lamination angle using ADS (Automated Design Synthesis).     

Reinforcement delamination of metallic beams strengthened by FRP strips: Fracture mechanics based approach

The delamination failure of metallic beams reinforced by externally bonded fibres reinforced polymers (FRP) is addressed in this paper and a simplified fracture mechanics based approach for the edge delamination of the reinforcement strips is illustrated. The criterion is based on the evaluation of the energy release rate (ERR) using both analytical and numerical models. The analytical models consist of a simplified version of a “two parameters elastic foundation” and “transformed section” model while the numerical analyses refer to the modified virtual crack closure technique (MVCCT). The main aim of the paper is to establish a fracture mechanics failure criterion based on the ERR and the specific fracture energy of the bonded strips. The criterion is an alternative approach to the well known stress based method to asses the load carrying capacity of the adhesive joint. The accuracy of the simplified approaches is shown through a numerical example which refers to a steel beam strengthened by carbon fibres reinforced polymers (CFRP).     

Numerical prediction of the thrust force responsible of delamination during the drilling of the long-fibre composite structures

In this paper, a numerical FE analysis is proposed to calculate the thrust forces responsible for the defect at the exit of the hole during the drilling phase of long-fibre composite structures, within a quasi-static framework. This numerical model – compared with the analytical models studied in the literature – takes into account the tool point geometry as well as the shear force effects in the laminate. The validation of this numerical model is carried out thanks to punching tests conducted at low speed on two types of semi products in carbon/epoxy long fibre manufactured by Hexcel composites. The numerical results provide the right correlation with the experimental values. Moreover, the comparison between the numerical thrust forces and those provided by the analytical models of the literature is called into question.     

考虑刀具磨损影响的CFRP复合材料钻削轴向力预测

在碳纤维增强树脂(CFRP)复合材料钻削过程中,随着刀具磨损量的累积,轴向力会逐渐增加,轴向力过大会导致CFRP复合材料一系列的加工缺陷.为实现在CFRP复合材料钻削过程中随刀具磨损量的累积轴向力变化的有限元分析及预测,建立了CFRP复合材料钻削仿真模型,通过对ABAQUS仿真软件二次开发,利用python语言开发子程...     

基于CFRP层合板钻削轴向力时变曲线的钻头几何形状分析

为探索能够实现碳纤维增强复合材料（CFRP）层合板低损制孔的钻头几何形状,采用4种不同几何形状的钻头,对T800级CFRP层合板进行钻孔实验研究,分析了钻头几何形状对钻削轴向力的影响,探讨了钻削轴向力与分层损伤之间的关系。结果表明:轴向力归零速度与出口分层因子有较好的正相关性,可采用钻削轴向力归零速度来表征钻头几何形状对CFRP层合板钻孔的适用性能。同时,实验发现切削区域具有多阶段几何特征的钻头,在钻出工件底部时轴向力是分阶段缓慢归零,出口分层因子较小。      

Tool geometry based prediction of critical thrust force while drilling carbon fiber reinforced polymers

Carbon fiber reinforced polymers(CFRPs) are known to be difficult to cut due to the abrasive nature of carbon fibers and the low thermal conductivity of the polymer matrix.Polycrystalline diamond(PCD) drills are commonly employed in CFRP drilling to satisfy hole quality conditions with an acceptable tool life.Drill geometry is known to be influential on the hole quality and productivity of the process.Considering the variety of CFRP laminates and available PCD drills on the market,selecting the suitable drill design and process parameters for the CFRP material being machined is usually performed through trial and error.In this study,machining performances of four different PCD drills are investigated.A mechanistic model of drilling is used to reveal trade-offs in drill designs and it is shown that it can be used to select suitable feed rate for a given CFRP drilling process.     

Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, \(K_{\mathrm{IE},}\) was evaluated numerically as \(K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)\), where \(\upmu \) is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, \(K_{\mathrm{IE,d}}\), was observed to vary as \(K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}\). Consistent with the FEM simulation, experiments conducted using \(12\,\upmu \hbox {m}\) thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of \(\ge \) \(1.85\times 10^{9}\,\hbox {A/m}^{2}\) for \(a/w = 0.5\). Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.     

Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM).A finite element model considering solid elements of the ABAQUS^® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.     

A nonlinear viscoelastic fracture analysis of concrete/FRP delamination in aggressive environments

In this paper, the durability of the bondline between concrete and FRP reinforcement was characterized at various temperature and humidity levels. The linear and nonlinear viscoelastic constitutive behavior of the epoxy bondline was characterized and used for a nonlinear viscoelastic fracture analysis of delamination. A hygrothermal nonlinear viscoelastic pseudo-stress model was developed and calibrated in order to compute a generalized J integral. Driven wedge tests were conducted for examining the fracture behavior of the interface. A finite element analysis was developed for determining the cohesive zone size and the generalized J integral at various temperature and humidity levels. The fracture energy obtained from these parameters greatly depended upon crack growth rate, temperature and humidity.     

Investigation on cutting mechanism in small diameter drilling for GFRP (thrust force and surface roughness at drilled hole wall)

This study describes the relation between the cutting force and the surface roughness of a drilled hole wall in small-diameter drilling of GFRP for a printed wiring board. In order to investigate the characteristics of small diameter drilling for GFRP, the surface of the drilled hole wall is observed by SEM, and the surface roughness along the feed direction is measured at various edge position angles of the drilled hole. The cutting force during drilling is measured. Moreover, the thrust force is devided into two components (the static component and the dynamic component). It is shown that the dynamic components are related with the surface roughness of the drilled hole wall. In conclusion, it is found that the major cutting edge of the drill is more influential in the quality of the drilled hole wall than the chisel edge of the drill in small diameter drilling of PWB.     

The effect of constraints due to fibres on the delamination of composites

Stress criteria and energy criteria for crack propagation are examined. It is shown that attempts to improve the delamination resistance of composites are inevitably hampered by fibre constraints on matrix yield and flow. The toughness of the matrix in the absence of fibres is very roughly equal to twice the product of the matrix yield stress, the strain in the plastic zone, , and the thickness of the yield zone at the crack faces, t. For ductile matrices with a given yield stress, then, it is probable that toughness is very roughly proportional to t (i.e. ductile matrices are expected to have fairly uniformly high values of ). However, when fibres are present (e.g. in a laminate) they severely restrict t, and hence the resistance to delamination. While t is less than the interfibre spacing, making the matrix tougher through increasing t directly affects composite toughness. Hence the resistance of the composite to delamination is directly proportional to matrix toughness. However, when t becomes so large as to equal the interfibre spacing, the development of matrix toughness is inhibited, and composite delamination resistance is little affected by further increases in matrix toughness. At this stage, additional increases in delamination resistance depend on increasing the matrix yield stress, rather than increasing the toughness of the matrix.     

A shell element for the prediction of residual load-carrying capacities due to delamination

This paper deals with layered plates and shells subjected to static loading. The kinematic assumptions are extended by a jump function in dependence of a damage parameter. Additionally, an intermediate layer is arranged at any position of the laminate. This allows numerical simulation of onset and growth of delaminations. The equations of the boundary value problem include besides the equilibrium in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, and a constraint which enforces the correct shape of a superposed displacement field through the thickness as well as boundary conditions. The weak form of the boundary value problem and the associated finite element formulation for quadrilaterals is derived. The developed shell element possesses the usual 5 or 6 degrees of freedom at the nodes. This is an essential feature since standard geometrical boundary conditions can be applied and the elements are applicable to shell intersection problems. With the developed model, residual load-carrying capacities of layered shells due to delamination failure are computed.     

Stress gradient due to incremental forming of bonded metallic laminates

The residual stress and associated gradient can affect the performance of a material/component during service. Sheet-metal in incremental sheet forming (ISF) due to missing back support may experience high stress gradient across the thickness. The current work is aimed at experimentally analyzing the through-thickness stress gradient in the Cu/steel bonded laminates after ISF deformation. It is found that ISF induces compressive stress gradient, which can be a way greater (about 18 times) than that the rolling process induces in the parent laminates while bonding, specifically when the deformation angle is high. Further, the tool imposes more stress gradient (1–50% depending on the forming conditions) in its motion direction than that in the transverse (or stretching) direction. Moreover, un-strained Cu/steel laminated sheet experiences higher (25%–68%) gradient than that the pre-strained/rolled sheet endures. Regarding the role of technological parameters, high angle, small tool, average step-size and spindle rotation, and low flow-stress induce high stress gradient. The tension tests of the ISFed samples reveal that the post-ISF tensile strength of laminated sheet increases as the stress gradient increases, thus showing a direct relationship between stress gradient and strain hardening in ISF. Finally, models are proposed to predict the stress gradient in the ISFed Cu/steel components.     

Analysis of crack propagation due to rebar corrosion using RBSM

Cracking behavior due to rebar corrosion in concrete specimens having a single rebar is evaluated experimentally and analytically. In the experiments, in which corrosion was induced electronically, the propagation of cracks (including internal crack patterns and surface crack widths) was monitored. In addition, deformation of the specimen surface was measured using a laser displacement meter. In the analysis, a three-dimensional Rigid-Body-Spring Method (RBSM), combined with a three-phase material corrosion–expansion model, is proposed to simulate crack propagation due to rebar corrosion. The effects of the properties of corrosion products such as elastic modulus, penetration of corrosion products into cracks, and local corrosion after cracking of the concrete are investigated. Cracking behavior due to rebar corrosion is simulated reasonably well. The simulations using RBSM provide insight into the mechanisms of crack initiation and propagation due to rebar corrosion.     

Stresses in an elastic cone due to an axial force at a point on the axis

Summary The solution to the problem of an isolated force acting along the axis of a cone at its vertex is known [1]. In the present problem the force is assumed to act on the axis at a distancec from the vertex. This greatly complicates the problem. An exact analytical solution is given in terms of integrals which are all convergent. Their order of convergence is given. For some cases these integrals are evaluated numerically. When the force acts very close to the vertex of the cone, stresses are compared with those obtained fromLove's solution for the point force acting at the vertex. The results agree very closely.The solution is obtained by superposition of two stress systems. The first system corresponds to a point force in an infinite medium. This solution is known in the literature [1]. The second system is obtained by applying on the surface of the cone, normal and shearing forces opposite to those obtained in the first system. The method applied to the solution of the latter problem is that of theMellin transform.

---

Zusammenfassung Die Lösung des Problems einer axialen Einzelkraft, die im Scheitel eines Kegels angreift, ist bekannt [1]. Im vorliegenden Problem wird angenommen, daß die Einzelkraft im Abstandc vom Scheitel auf der Achse angreift. Dies erschwert das Problem beträchtlich. Eine exakte analytische Lösung wird durch Integrale angegeben, welche überall konvergieren. Die Ordnung der Konvergenz wird angegeben, und für einige Fälle werden die Integrale numerisch ausgewertet. Für einen Kraftangriff nahe am Kegelscheitel werden die Spannungen mit jenen aus derLoveschen Lösung verglichen, bei der die Kraft im Kegelscheitel angreift. Die Ergebnisse liegen nahe beieinander.Die Lösung wird durch Überlagerung zweier Spannungssysteme erhalten. Das erste System entspricht der Wirkung einer Einzelkraft in einem unendlich ausgedehnten Medium. Diese Lösung ist in der Literatur bekannt [1]. Das zweite System wird dadurch erhalten, daß am Kegelmantel Normal- und Schubspannungen in der Gegenrichtung zu jenen des ersten Systems angebracht werden. Das letzte Problem wird mit Hilfe derMellin-Transformation gelöst.

---

---

With 4 Figures     

Critical stresses and strains at the spall edge of a case hardened bearing due to ball impact

Short spall propagation times of failing main shaft ball bearings of aircraft engines are a serious safety concern for single engine aircraft. Bearing designers would like to understand the impact of four variables namely (i) ball material density, (ii) subsurface residual stress, (iii) gradient in yield strength with depth (case hardening), and (iv) raceway surface hardness/yield strength that are thought to affect spall propagation. Extensive spall propagation experiments have been conducted at AFRL, Ohio in the past few years to address this issue. However, a detailed mechanistic analysis of these experiments has not been performed. This work presents an elastic–plastic finite element (FE) model that simulates a ball impacting a spall edge to determine the relative contributions of the four material variables on spall propagation. The magnitude and extent of damage of the spall edge material is determined based on critical stresses and plastic strains induced by the ball impact. The results indicate that the influence of ball density is greatest on inducing damage at the impacted spall edge when compared to the other three properties, which also agrees with the hybrid bearing spall propagation tests conducted at AFRL.     

Suppression of ice adhesion force to cooling wall due to voltage application

For ice storage, one of the authors has previously reported on the ice slurry formed by cooling water–silicone oil mixture with stirring. When the mixture is stirred in a vessel, the oil is charged due to static electricity. If the vessel can attract the charged oil, suppression of ice adhesion force to a cooling wall may be possible. In this study, therefore, a certain voltage was applied to the vessel filled with the mixture with cooling and stirring simultaneously, and water was frozen in the vessel. Then, the ice adhesion force to the cooling vessel wall was measured under a constant apparent adhesion area between the ice and cooling vessel wall. From the measurement results, optimal conditions of the oil viscosity, rotation speed and applied voltage to suppress the ice adhesion force effectively were clarified. Moreover, the factors governing suppression of the ice adhesion force were clarified.