SEMI-ANALYTICAL FINITE ELEMENT METHOD FOR FICTITIOUS CRACK MODEL IN FRACTURE MECHANICS OF CONCRETE

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.

DYNAMIC CRACK MODELS ON PROBLEM OF BRIDGING FIBER PULL-OUT OF COMPOSITE MATERIALS

An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was performed. A dynamic model of bridging fiber pull-out of composite materials was presented. Resultingly the fiber failure is governed by maximum tensile stress, the fiber breaks and hence the crack extension should occur in self-similar fashion. By the methods of complex functions, the problem studied can be transformed into the dynamic model to the Reimann-Hilbert mixed boundary value problem, and a straightforward and easy analytical solution is presented. Analytical study on the crack propagation subjected to a ladder load and an instantaneous pulse loading is obtained respectively for orthotropic anisotropic body. By utilizing the solution, the concrete solutions of this model are attained by ways of superposition.

Application of flow driven pore-network crack model to Zipingpu reservoir and Longmenshan slip

The study has analyzed the relationship between the water-drainage sluice process of reservoir, stress triggers and shadows of earthquake and porosity variability of fault slip zone. First, the pore pressure, pressure gradient, viscous stress and Reynolds stress to reservoir-earthquake fault slip problem are analyzed, and these are un-negligible factors of the extended coulomb failure stress under ultra-high temperature and pressure condition. Second, the porosity tensor and permeability tensor are studied, the relationship between Zipingpu reservoir and Longmenshan slip has been analyzed, and the extended viscous stress and Reynolds stress as function of time and infiltration process are obtained. Last, some primary conclusions about the flow-solid coupled facture mechanism to the Zipingpu reservoir and Longmenshan slip problem are presented, which can help understand the flow-solid coupled facture mechanism of reservoir-coseismic fault slip problem.

An Extended Dielectric Crack Model for Fracture Analysis of a Thermopiezoelectric Strip

An extended dielectric crack model is proposed to capture the effects of the physical properties of crack interior on crack-tip thermoelectroelastic fields.The typical crack-face boundary conditions can be retrieved by considering the limiting cases of electrical permeability and thermal conductivity inside a crack.Making use of the Fourier transform technique,the problem of a thermopiezoelectric strip weakened by a Griffith crack is investigated and transformed to solve the system of the second kind Fredholm integral equations with Cauchy kernel.The Lobatto-Chebyshev collocation method is used to form a nonlinear system of algebraic equations,which is solved by elaborating on an algorithm.The crack-tip thermoelectroelastic fields are determined by using the approximate solutions.Numerical simulations are carried out to show the variations of the fracture parameters of concern under applied thermoelectromechanical loads,the physical properties of the dielectric medium inside the crack and the geometry of the cracked thermopiezoelectric strip.Some comparisons with the experimental results are reported to reveal the effectiveness of the extended dielectric crack model.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Crack evolution behavior of rocks under confining pressures and its propagation model before peak stress

The understanding of crack propagation characteristics and law of rocks during the loading process is of great significance for the exploitation and support of rock engineering.In this study,the crack propagation behavior of rocks in triaxial compression tests was investigated in detail.The main conclusions were as follows:1)According to the evolution characteristics of crack axial strain,the differential stress?strain curve of rocks under triaxial compressive condition can be divided into three phases which are linear elastic phase,crack propagation phase,post peak phase,respectively;2)The proposed models are applied to comparison with the test data of rocks under triaxial compressive condition and different temperatures.The theoretical data calculated by the models are in good agreement with the laboratory data,indicating that the proposed model can be applied to describing the crack propagation behavior and the nonlinear properties of rocks under triaxial compressive condition;3)The inelastic compliance and crack initiation strain in the proposed model have a decrease trend with the increase of confining pressure and temperature.Peak crack axial strain increases nonlinearly with the inelastic compliance and the increase rate increases gradually.Crack initiation strain has a linear relation with peak crack axial strain.

Coupled simulation of recirculation zonal firebox model and detailed kinetic reactor model in an industrial ethylene cracking furnace

A coupled system simulating both firebox and reactor is established to study the naphtha pyrolysis in an industrial tubular furnace.The firebox model is based on zone method including combustion,radiation,and convection to simulate heat transfer in the furnace.A two-dimensional recirculation model is proposed to estimate the flow field in furnace.The reactor model integrates the feedstock reconstruction model,an auto-generator of detail kinetic schemes,and the reactor simulation model to simulate the reaction process in the tubular coil.The coupled simulation result is compared with industrial process and shows agreement within short computation time.

A Proposed Systemic Modeling Software for Jujube Fruit Cracking

Jujube fruit cracking has become a major concern in jujube production. It can affect fruit quality and yield and crop productivity, resulting in significant economic loss. Recent advances in jujube fruit cracking research provide opportunities to improve our understanding of the impacts of environmental factors and plant physiological metabolism on jujube fruit cracking. In this article, we have developed a novel systemic modeling software for jujube fruit cracking. The potential function and value of this modeling software are presented. Current issues and future research directions in the modeling of jujube fruit cracking system are also discussed. To our knowledge, this is the first functional and/or integrated modeling software developed for the management of jujube fruit cracking.

Catalytic Cracking of Cycloparaffins Admixed with Olefins:1. Single-Event Microkinetic(SEMK) Modeling

Single-event microkinetic(SEMK) model of the catalytic cracking of methylcyclohexane admixed with 1-octene over REUSY zeolites at 693 K—753 K in the absence of coke formation is enhanced. To keep consistency with the wellknown carbenium ion chemistry, hydride transfer forming and consuming allylic carbenium ions in the aromatization of cycloparaffins are further investigated and differentiated. The reversibility of endocyclic β-scission and cyclization reactions is refined by accounting explicitly for the reacting olefins and resulting cycloparaffins in the corresponding thermodynamics. 24 activation energies for the reactions involved in the cracking of cycloparaffins are obtained by the regression of 15 sets of experimental data upon taking the resulting 37 main cracking products, i. e., responses into account. The enhanced SEMK model can adequately describe the catalytic behavior of 37 main products with conversion and temperature.

U-model Enhanced Dynamic Control of a Heavy Oil Pyrolysis/Cracking Furnace

This paper proposes a case study in the control of a heavy oil pyrolysis/cracking furnace with a newly extended U-model based pole placement controller(U-PPC). The major work of the paper includes: 1) establishing a control oriented nonlinear dynamic model with Naphtha cracking and thermal dynamics; 2) analysing a U-model(i.e., control oriented prototype) representation of various popular process model sets; 3)designing the new U-PPC to enhance the control performance in pole placement and stabilisation; 4) taking computational bench tests to demonstrate the control system design and performance with a user-friendly step by step procedure.

DISLOCATION EMISSION AND EQUATION OF ENERGY BARRIERS AT MODEL I CRACK TIP

The propagation for the model I crack in aluminum single crystal has been directly studied by in-situ TEM observation.The equation of energy barrier of the dislocation building-up and emission at the model I crack tip has been established by means of Peierls-Nabarro dislocation model and starting from angle of energy.By means of calculation,the critical value of spontaneous emission of the dislocations from tip of the model I crack was obtained.

A Model for Diagnosing the Formation of Internal Cracks in Continuously CastSlabs

The internal cracks in continuously cast slabs are attributed to the excessive tensile strain occurring at the solidifying frontduring the continuous casting process. Based on the understanding, a model for diagnosing the formation of the internal cracks was established, in which the strains at the solidifying front caused by' bulging, straightening or unbending, and roll misalignment were calculated and compared with a critical strain value to estimate whether the internal cracks form. Moreover, the established model was appliedto a real slab caster to reveal the distribution of the strains in casting direction and its effect on the internal cracks. It was proved that themodel was reliable and useful for optimizing the operation of continuous casting.

Crack Prediction Model for Concrete Affected by Reinforcement Corrosion

The purpose of this study was to develop an analytical model to predict the time required for cracking of concrete due to corrosion of the iron reinforcement. The concrete and cement specimens used for this study were batched with cover material ranging from 0.75 to 1.3 in (1.91 to 3.30 cm). The extent of cover material was not formulated into the model under the assumption that crack initiation would tend to produce visible cracking within a relatively short time period. The model was derived using both Hooke’s Law and the volume expansion induced by the corrosion oxides. Correlation achieved with specimen cracking data from the literature was relatively good with a 95% level of confidence. This model presents a key benefit to facility and infrastructure managers by enabling them to plan the time when corrosion mitigating actions are required. It also provides a significant convenience as the condition of the concrete structure or its environment changes over time. The only parameter that needs to be updated over time is the corrosion rate measurement. This single parameter captures the most influential impact that stems from several other parameters which tend to be required in models that are more mechanistically definitive.

A new generic reaction for modeling fluid catalytic cracking risers

A new generic reaction in the form of PC_i→PC_m+[i,m]→PC_m+λi,m coke+surplusage has been proposed for describing the catalytic cracking behavior of petroleum narrow cuts or pseudo-components(PCs),where the rate constant formula is derived from the transition state theory and the coking amount is correlated to the properties of the intermediate substance [i,m].In composing the cracking reaction network for feedstock and product oils,only the product PC m of the proposed generic reaction is used,which together with a criterion for excluding exothermic reactions,distinctly reduces the number of reactions in the network.With the proposed cracking reaction scheme coupled with special pseudo-components,a predictive one-dimensional steady state model for fluid catalytic cracking risers is formulated in the sense that for a given riser and given catalyst,the model parameters are independent of stock oils,product schemes and other operational conditions.The great correlating and predicting capability of the resulted model is tested with production data in different scenarios of four commercial risers.

Metallurgical modeling of microcrack repairment during welding nonferrous materials: non-equilibrium solidification behavior of weld pool (Ⅰ)

Metallurgical modeling of synergistic microcrack self-repairmen during welding single crystal and polycrystalline superalloys of high-temperature aerospace materials has been properly established. The idea of improvement of nickel-based superalloys weldability through non-equilibrium solidification behavior of backfill to self-repair arterial crack network is usefully proposed. Crystallographic control strategy of crack self-repairmen of fusion zone interdendritic solidification cracking and heat-affected zone （HAZ） intergranular liquation cracking is technically achievable, indicating that optimal niobium alloying beneficially refines weld microstructure, stabilizes the primary solidification path, increases the solidification temperature and concomitantly decreases the weld pool geometry. High-carbon grain boundary is more thermal stable and less contributes to incipient intergranular liquid film than that of low-carbon grain boundary. The theoretical predictions of cracking susceptibility are indirectly verified in a rather satisfactory manner. Additionally, the metallurgical modeling enhances predicative capabilities and thereby is readily applicable for other alloy systems.

Four-Beam Model for Vibration Analysis of a Cantilever Beam with an Embedded Horizontal Crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton＇s principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior＇s material properties （e.g. strain rate sensitivity） characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

Effect Analysis of Gurson Model Parameters on Crack Extension of Pipeline

Leakage-before-break technique is widely used in high energy pipeline of nuclear plant, for which crack stability of pipeline under complex loading condition is a key issue, and crack growth resistance curve of pipeline material is the important foundation for crack stability analysis. In this paper, ferritic steel A533B is studied, Gurson damage model is used to simulate crack process of contact tension specimen under unitension, and effect of Gurson model parameter on simulation result is discussed. The following results are found during simulation: initial porosity factor is the main parameter, when it increases gradually, unstable crack extension will be observed;however, only initial J toughness is affected by critical porosity factor;the minor parameter is load step control, when it increases, stable and convergent result is obtained. All results in this paper can be used to determine parameters in Gurson mode, which will be foundation for crack extension analysis of pipeline.

Application of a Geometric Similar Model in Structure Crack Diagnosis

As the working condition of the large arm on the steel package rotating station is serious, it is very difficult to test on the spot. In order to simplify the study process, a geometric similar modal is designed and made. During the study, the same element partition method and boundary condition are used in both the large arm and its similar model. The result shows that the numerical solution of the lar-ge arm is verified well indirectly by validating the numerical solution of the similar model.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates （da/dN） of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-△K relations, the confidence-based da/dN-△K relations, and the probabilistic- and confidence-based da/dN-△K relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.