Predictive process mapping for laser powder bed fusion: A review of existing analytical solutions

One of the main challenges in the laser powder bed fusion (LPBF) process is making dense and defect-free components. These porosity defects are dependent upon the melt pool geometry and the processing conditions. Power-velocity (PV) processing maps can aid in visualizing the effects of LPBF processing variables and mapping different defect regimes such as lack-of-fusion, under-melting, balling, and keyholing. This work presents an assessment of existing analytical equations and models that provide an estimate of the melt pool geometry as a function of material properties. The melt pool equations are then combined with defect criteria to provide a quick approximation of the PV processing maps for a variety of materials. Finally, the predictions of these processing maps are compared with experimental data from the literature. The predictive processing maps can be computed quickly and can be coupled with dimensionless numbers and high-throughput (HT) experiments for validation. The present work provides a boundary framework for designing the optimal processing parameters for new metals and alloys based on existing analytical solutions.     

Analytical modeling of complex contact behavior between rock mass and lining structure

Based on the nondestructive test data of operating railway tunnels in China, this paper summarizes the basic characteristics of the complex contact behavior between the rock mass and lining structure. The contact modes are classified into dense contact, local non-contact, and loose contact. Subsequently, the corresponding mechanical model for each contact mode is developed according to its mechanical characteristics using the complex variable method. In the proposed mechanical model, a special algorithm is introduced to detect whether the local non-contact zone is re-contacted. Besides, a novel conformal mapping method is also proposed to accurately calculate the mechanical response of the concrete lining. Finally, the accuracy of the proposed method is verified by comparing it with the finite element method (FEM). Several parameter investigations are conducted to analyze the effects of different contact modes on the rock–lining interaction. The results show that: (i) the height of the local non-contact area does not have a significant effect on the contact stress distribution if no re-contact occurs; (ii) backfill grouting can reduce the local stress concentration caused by poor contact modes; and (iii) reducing the friction coefficient of the interface can lead to a more uniform distribution of internal forces in the concrete lining.     

基于ELM的英语教学质量评价研究

对英语教学质量实施科学化的评价关系到英语教学质量的提升,为减少主观因素的影响,本文提出一种ELM的教学质量评价方法,该种方法将可以在很大程度上提高教学质量评价的精度。对影响英语教学质量的12个指标进行打分,以此作为ELM的输入,同时将英语教学质量的综合得分作为ELM的输出。评价结果表明,基于EIM的英语教学质量评价结果比SVM、BP具有了很大程度的提升,为实施英语教学质量的评价提供了参考。     

What makes an elongated lake ‘large’? Scales from wind-driven steady circulation on a rotating Earth

When investigating wind-induced steady circulation, the effect of the acceleration due to Earth’s rotation is often neglected in narrow lakes, but the argument behind this assumption is blurred. Commonly, when the horizontal dimension is smaller than the Rossby radius, the Coriolis force is considered unimportant, but this is correct only for inertial currents and barotropic and baroclinic waves. In this work, we revisit the classical Ekman transport solution for wind stress acting along the main axis of an elongated lake in steady-state conditions. We demonstrate that a secondary circulation develops and that the resulting crosswise volume transport, constrained in the closed domain, produces downwelling and upwelling that cannot be predicted by the standard Ekman formulas. We claim that the Rossby radius does not play any role in this process, which on the contrary is governed by the ratio between the actual depth and the thickness of the Ekman layer. The theoretical analysis is supported by numerical experiments to show the dependence on latitude, width, depth and turbulence closure.     

A study of the load transfer behavior of fully grouted rock bolts with analytical modelling

Fully grouted rock bolts have been used in mining industry for many years. Much research has been conducted to evaluate the load transfer behavior of fully grouted rock bolts with experimental programs.However, compared with that, less work has been conducted with analytical modelling. Therefore, in this paper, the authors used an analytical model to study the load transfer behavior of fully grouted rock bolts.To confirm the credibility of this analytical model, an in-situ pull-out test was used to validate this model.There was a close match between the experimental result and the analytical result. Following it, a parametric study was conducted with this analytical model. The influence of coefficients, Young's modulus of the rock bolt and the diameter of the rock bolt on the load transfer performance of rock bolts was studied.Furthermore, the load distribution along the fully grouted rock bolt was analytically studied. The results show that the axial load in the rock bolt decayed from the loaded end to the free end independent of the pull-out load. However, the trend of the load distribution curve was influenced by the pull-out load. This paper was beneficial for better understanding the load transfer mechanism of fully grouted rock bolts.     

Static stress analysis of carbon nano-tube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields

Static stresses analysis of carbon nano-tube reinforced composite (CNTRC) cylinder made of poly-vinylidene fluoride (PVDF) is investigated in this study. Non-axisymmetric thermo-mechanical loads are applied on cylinder in presence of uniform longitudinal magnetic field and radial electric field. The surrounded elastic medium is modeled by Pasternak foundation because of its advantages to the Winkler type. Distribution of radial, circumferential and effective stresses, temperature field and electric displacements in CNTRC cylinder are determined based on Mori–Tanaka theory. The detailed parametric study is conducted, focusing on the remarkable effects of magnetic field intensity, elastic medium, angle orientation and volume fraction of carbon nano-tubes (CNTs) on distribution of effective stress. Results demonstrated that fatigue life of CNTRC cylinder will be significantly dependent on magnetic intensity, angle orientation and volume fraction of CNTs. Results of this research can be used for optimum design of thick-walled cylinders under multi-physical fields.     

Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its influence on creep

A model to predict time-dependent evolution of simultaneous transverse cracking developed in multiple plies during creep loading and its effects on creep of multidirectional polymer matrix composite laminates is presented. The stress states in the intact regions of the plies are determined using the lamination theory during an incremental change in time. The stored elastic energy, determined using this stress state, is compared with a critical stored elastic energy value for damage to determine if a ply would fracture after the increment. If fracture is predicted, variational analysis is used to determine the perturbation in ply stresses due to cracking. This procedure is repeated to determine the crack evolution and creep strain. Model predictions compared well with experimental results for a [±θ_m/90_n]_s laminate.     

An investigation of the mechanical fatigue behavior of low thermal expansion lattice structures

A study of the mechanical fatigue behavior of a Ti–6Al–4V lattice structure designed to exhibit controlled thermal expansion has been performed. Comparison of S–N curves generated under both zero-tension and fully reversed cyclic loading has determined that the fatigue resistance of the lattice is substantially poorer than that of the constituent Ti–6Al–4V material for the same remote applied (macroscopic) stress. In addition, the effect of beta annealing the as-received mill-annealed alloy was also to reduce fatigue life in both the lattices and parent material. This effect is due to significant microstructural changes that occurred during heat treatment. Increasing the stress ratio (σ_min/σ_max) of the cyclic waveform from −1 to 0 had a similar effect. An analytical model has been developed to predict the fatigue life of the lattice structures from the S–N curves of the parent material, by determining the relationship between the macroscopic stresses acting on the lattice structure and the local stresses. The local stresses were then used in a multiaxial fatigue model to determine the fatigue life. The analytical model is able to predict the fatigue life with reasonable accuracy and minimal cost. The Findley multiaxial fatigue parameter for the parent material and lattice structures can be fitted with a power law equation and appears to fall onto a single curve, suggesting the local behavior within the lattice material is similar to the parent material. The analytical tools developed in this study can be hugely beneficial to the design of these lattice structures in the aerospace and communications industries.     

Effects of nonlinear strain components on the buckling response of stiffened shear-deformable composite plates

A detailed investigation of the weight of each non linear term of the Green–Lagrange strain displacement equation is presented, with reference to the buckling of orthotropic, both flat and prismatic, Mindlin plates. Usually in the literature, in buckling analysis only the second order terms related to the out-of-plane displacement are considered. Such heuristic simplification, known as von Kármán hypothesis, starts by the consideration that the buckling mode of a flat plate is described by dominant out-of-plane displacement and disregards the non-linear terms of the Green–Lagrange strain tensor depending on the in plane displacement components, whose role is confined to first order, say pre-critical, deformation. The present paper shows that disregarding the non linear terms related to the in-plane strain–displacement is equivalent to neglect shear induced rotation. In the work, the governing equations are derived using the principle of strain energy minimum and the differential equations solution is gained by using the general Levy-type method. The obtained results show that the von Kármán model overestimates the critical load when, in buckling mode, magnitudes of shear rotation, in-plane and out-of-plane displacements are comparable.     

Assessment of the effectiveness of steel fibre reinforcement for the punching resistance of flat slabs by experimental research and design approach

The present paper deals with the experimental assessment of the effectiveness of steel fibre reinforcement in terms of punching resistance of centrically loaded flat slabs, and to the development of an analytical model capable of predicting the punching behaviour of this type of structures. For this purpose, eight slabs of 2550 × 2550 × 150 mm³ dimensions were tested up to failure, by investigating the influence of the content of steel fibres (0, 60, 75 and 90 kg/m³) and concrete strength class (50 and 70 MPa). Two reference slabs without fibre reinforcement, one for each concrete strength class, and one slab for each fibre content and each strength class compose the experimental program. All slabs were flexurally reinforced with a grid of ribbed steel bars in a percentage to assure punching failure mode for the reference slabs. Hooked ends steel fibres provided the unique shear reinforcement. The results have revealed that steel fibres are very effective in converting brittle punching failure into ductile flexural failure, by increasing both the ultimate load and deflection, as long as adequate fibre reinforcement is assured. An analytical model was developed based on the most recent concepts proposed by the fib Mode Code 2010 for predicting the punching resistance of flat slabs and for the characterization of the behaviour of fibre reinforced concrete. The most refined version of this model was capable of predicting the punching resistance of the tested slabs with excellent accuracy and coefficient of variation of about 5%.