An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

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.

ANALYSIS OF STRESS FIELD NEAR CRACK TIP BASED ON ELECTRIC SATURATION MODEL

Within the framework of nonlinear eleetroelasticity, the stress field near to the crack tip in an infinite piezoelectric media subject to a far field uniform loading is studied by using an electrical strip saturation model and the complex variable method. And the emphasis is placed on the stress field near to the crack tip. The obtained solutions show that the normalized stress components at an arbitrary point near to the crack tip are determined by the angle of the point. Moreover, the stress components are independent of the distance from the point to the ori- gin of the coordinate. The distributions of in-plane stress components near to the crack tip are analyzed based on numerical results for PZT-SH. Compared with some related solutions, results show that the solutions are valid.

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.

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.

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.

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.

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.

New model of propagation rates of long crack due to structure fatigue

By comparison of the characteristics of existing models for long fatigue crack propagation rates, a new model, called the generalized passivation-lancet model for long fatigue crack propagation rates （GPLFCPR）, and a general formula for characterizing the process of crack growth rates are proposed based on the passivation-lancet theory. The GPLFCPR model overcomes disadvantages of the existing models and can describe the rules of the entire fatigue crack growth process from the cracking threshold to the critical fracturing point effectively with explicit physical meaning. It also reflects the influence of material characteristics, such as strength parameters, fracture parameters and heat treatment. Experimental results obtained by testing LZ50 steel, AlZnMgCu0.5, 0.5Cr0.5Mo0.25V steel, etc., show good consistency with the new model. The GPLFCPR model is valuable in theoretical research and practical applications.

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.

Calculation Model of Equivalent Strength for Induced Crack Based on Double-K Fracture Theory and Its Optimizing Setting in RCC Arch Dam

By means of fracture testing on roller-compacted concrete （RCC） three-point bending beams with two different specimen sizes, the P-CMOD complete curve for RCC was gained. Furthermore, by applying double-K fracture theory, KiniⅠC,KunⅠC, as well as the critical effective crack length and the critical crack tip opening displacement, were evaluated. Based on the double-K fracture parameters above, the calculation model of equivalent strength for induced crack was established, thus the calculation method on its initiation, stable propagation and unstable fracture was ascertained. Moreover, the finite element simulation analysis of stress field in ShaPai arch dam and the on-site observational splaying points of induced crack at different altitudes validated the reliability of the model. Finally, crack inducer′s optimal setting in RCC arch dam was studied. It improves the design level of induced crack in RCC arch dam and satisfies the necessity of engineering practice.

Analytical Modeling for Corrosion-Induced Cover Cracking of Corrosive Reinforced Concrete Structures

An analytical model for predicting the corrosion-induced cracking of concrete cover of reinforced concrete(RC) structures was developed.The effects of influence factors such as practical initial defects,corrosion rate,strength and elastic modulus of concrete on the corrosion-induced cracking of concrete cover were investigated.It was found that the size of practical initial defects was the most effective factor.Therefore,improving the compactness of concrete is an effective way to improve the durability of RC structures.It was also demonstrated that the accelerated corrosion tests may be unfavorable in the study of the relationship between cracking time and crack width.

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.

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.

Estimating the Operation Status of Steam Cracking Furnace Using Numerical Simulation with Combustion Models

An accurate and complete geometric model was constructed to simulate the combustion, flow and temperature environment in the radiant section of the steam cracking furnace. Simulation of flow and radiation status has utilized the standard k-ε model and P1 model. The finite-rate/eddy-dissipation (finite-rate/ED) combustion model and non-premixed combustion model were both used to simulate accurately the combustion and the operation status of the steam cracking furnace. Three different surfaces of the steam cracking furnace were obtained from the simulation, namely:the flue gas temperature field of the entrance surface in long flame burners, the central surface location of tubes, and the crossover section surface. Detailed information on the flue gas temperature and the mass concentration fraction of these different surfaces in the steam cracking furnace can also be obtained by the simulation. This paper analyzed and compared the simulation results with the two combustion models, estimated the operation status of the steam cracking furnace, and reported that the finite-rate/ED model is appropriate to simulate the steam cracking furnace by comparing key simulation data with actual test data. This work has also provided a theoretical basis for simulating and operating the steam cracking furnace.

Knowledge expression,numerical modeling and optimization application of ethylene thermal cracking:From the perspective of intelligent manufacturing

Applications of process systems engineering(PSE)in plants and enterprises are boosting industrial reform from automation to digitization and intelligence.For ethylene thermal cracking,knowledge expression,numerical modeling and intelligent optimization are key steps for intelligent manufacturing.This paper provides an overview of progress and contributions to the PSE-aided production of thermal cracking;introduces the frameworks,methods and algorithms that have been proposed over the past10 years and discusses the advantages,limitations and applications in industrial practice.An entire set of molecular-level modeling approaches from feedstocks to products,including feedstock molecular reconstruction,reaction-network auto-generation and cracking unit simulation are described.Multilevel control and optimization methods are exhibited,including at the operational,cycle,plant and enterprise level.Relevant software packages are introduced.Finally,an outlook in terms of future directions is presented.

7-lump kinetic model for residual oil catalytic cracking

In this paper a novel 7-lump kinetic model is proposed to describe residual oil catalytic cracking, in which coke is lumped separately for accurate prediction. The reactor block is modeled as a combination of an ideal pipe flow reactor (PFR) and a continuously stirred tank reactor (CSTR). Unit factors are designed to correct the deviation between model predictions and practical plant data and tuned by modified Levenberg-Marquardt algorithm. The parameters estimated are reliable and good agreement between the model predictions and plant observations is observed. The model helps us get good insight into the per- formance of an industrial riser reactor that would be useful for optimization of residual oil catalytic cracking.

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.

Data-driven intelligent modeling framework for the steam cracking process

Steam cracking is the dominant technology for producing light olefins,which are believed to be the foundation of the chemical industry.Predictive models of the cracking process can boost production efficiency and profit margin.Rapid advancements in machine learning research have recently enabled data-driven solutions to usher in a new era of process modeling.Meanwhile,its practical application to steam cracking is still hindered by the trade-off between prediction accuracy and computational speed.This research presents a framework for data-driven intelligent modeling of the steam cracking process.Industrial data preparation and feature engineering techniques provide computational-ready datasets for the framework,and feedstock similarities are exploited using k-means clustering.We propose LArge-Residuals-Deletion Multivariate Adaptive Regression Spline(LARD-MARS),a modeling approach that explicitly generates output formulas and eliminates potentially outlying instances.The framework is validated further by the presentation of clustering results,the explanation of variable importance,and the testing and comparison of model performance.

Catalytic cracking mechanisms of tar model compounds

B3LYP/6-31G(d,p) method was used to investigate the catalytic cracking mechanism of biomass tar model compound.Phenol,toluene and benzene were selected as the tar model compounds and CaO was selected as the catalyst.The pathways of tar compound radical absorbed by CaO were determined firstly through comparing enthalpy changes of the absorption,and then Mulliken population changes were analyzed.The results show that the absorption of tar model compound radical and CaO is an exothermic reaction.Formation of C—O—Ca is more easily than that of C—Ca—O and formation of Caromatic—Caromatic—Ca—O is more easily than that of Caromatic—C(O)—Ca—O.The C—C bond Mulliken populations in tar model compound radicals are reduced by 11.9%,10.5% and 15.5% in the case of a hydrogen atom removed,and those are 15.7%,14.3% and 16.3% in the case of two hydrogen atoms removed through the absorption of CaO.Catalytic ability of CaO acting on the tar model compound is in an order of phenol>benzene>toluene.