SUMMARYThe cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction-separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack-tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi-phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross-triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al 2 O 3 ceramic and in an Al 2 O 3 /TiB 2 ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour.
Dynamic fracture in two-phase Al 2 O 3 /TiB 2 ceramic composite microstructures is analyzed explicitly using a cohesive finite element method (CFEM). This framework allows the effects of microstructural heterogeneity, phase morphology, phase distribution, and size scale to be quantified. The analyses consider arbitrary microstructural phase morphologies and entail explicit tracking of crack growth and arbitrary fracture patterns. The approach involves the use of CFEM models that integrate cohesive surfaces along all finite element boundaries as an intrinsic part of the material description. This approach obviates the need for any specific fracture criteria and assigns models the capability of predicting fracture paths and fracture patterns. Calculations are carried out using idealized phase morphologies as well as real phase morphologies in actual material microstructures. Issues analyzed include the influence of microstructural morphology on the fracture behavior, the influence of phase size on fracture resistance, the effect of interphase bonding strength on failure, and the effect of loading rate on fracture.
Dynamic crack propagation in ceramic composites is analyzed numerically. The simulations concern the effects of microstructural morphologies on fracture. The analysis coniders arbitrary phase distributions in the actual microstructures of alumina/titanium diboride (Al2O3/TiB2) composites. The microstructures analyzed have different phase morphologies and different phase sizes over an order of magnitude in length (from 1–2 to 10–20 μm). A micromechanical model that provides explicit account for arbitrary microstructures and arbitrary fracture patterns is developed and used. The approach uses both a constitutive law for the bulk solid constituents and a constitutive law for fracture surfaces. The model is based on the cohesive surface formulation of Xu and Needleman and represents a phenomenological characterization for atomic forces on potential crack/microcrack surfaces. This framework of analysis does not require the use of any fracture criteria. Instead, fracture evolves as an outcome of bulk material response, interfacial behavior, and applied loading. This approach provides a unified and self-consistent treatment of mixed mode fracture. The evolutions of crack lengths in different phases and along interphase interfaces are calculated to track crack growth. The overall local crack speed, defined as the time rate of change of arc length along zigzagging crack paths, is found to reach the intersonic range, i.e., greater than the shear wave speeds and smaller than the longitudinal wave speeds in the constituent phases. The model also allows the energy release rate to be evaluated easily. For the same amount of crack surfaces generated, the average energy release rates for fracture patterns in four microstructures analyzed differ by up to 25%. The results demonstrate that larger TiB2 reinforcements significantly impede crack propagation and increase the fracture resistance of the composites, as indicated by higher average energy release rate values.
With the CFD calculation software FLUENT, numerical simulation has been conducted to study the surface flow and heat transfer in inclined wave fin-and-tube heat exchanger, including uniform angle wave fin and inclined increase-angle wave fin. Velocity field, pressure field and the distribution of temperature field on the air side of fin surface were obtained. Heat transfer performance of the two kinds of fin were discussed and the curve of both heat exchange and pressure drop related to the inlet velocity were analyzed. The results indicates that in the same conditions, heat transfer effect is better than uniform angle wave fin. When the inlet velocity is 4 m/s ,the heat transfer of inclined increase-angle wave fin is about 1.1 times higher than that of uniform angle wave fin meanwhile the pressure resistance is as much as around 1.2 times, which provides a theoretical basis on heat transfer enhancement of wave finned tube.
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