Responses of leaf stomatal and mesophyll conductance to abiotic stress factors

Plant photosynthesis assimilates CO_(2)from the atmosphere,and CO_(2)diffusion efficiency is mainly constrained by stomatal and mesophyll resistance.The stomatal and mesophyll conductance of plants are sensitive to abiotic stress factors,which affect the CO_(2)concentrations at carboxylation sites to control photosynthetic rates.Early studies conducted relevant reviews on the responses of stomatal conductance to the environment and the limitations of mesophyll conductance by internal structure and biochemical factors.However,reviews on the abiotic stress factors that systematically regulate plant CO_(2)diffusion are rare.Therefore,in this review,the rapid and long-term responses of stomatal and mesophyll conductance to abiotic stress factors(such as light intensity,drought,CO_(2)concentration and temperature)and their physiological mechanisms are summarized.Finally,future research trends are also investigated.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

Enhancing Stress Intensity Factor Reduction in Cracks Originating from a Circular Hole in a Rectangular Plate under Uniaxial Stress through Piezoelectric Actuation

Circular holes are commonly employed in engineering designs;however, they often serve as locations where cracks initiate and propagate. This paper explores a novel approach to structural repair by utilizing piezoelectric actuators. The primary focus of this study is to investigate the influence of an adhesively bonded piezoelectric actuator patch placed above a circular hole on the stress intensity factor (SIF) in an aluminium plate. The plate is subjected to uniaxial tensile stress, while the piezoelectric actuator is excited with varying voltage levels. The analysis is conducted using the finite element method (FEM), a powerful numerical technique for simulating complex structures. The study assesses the stress distribution and employs the SIF as an adequate criterion for evaluating the impact of different patch configurations. The results indicate a strong correlation between the applied voltage and the SIF. Whether the SIF increases or decreases depends on the polarization of the piezoelectric actuator. Particularly noteworthy is the finding that rectangular patches in a horizontal orientation significantly reduce the SIF compared to other patch geometries. Moreover, double-sided patches exhibit a pronounced decrease in the SIF compared to single-sided patches. In summary, this research underscores the potential of piezoelectric actuators in mitigating stress intensity in structures with circular hole with crack initiation. It offers valuable insights into the influence of applied voltage, patch geometry, and patch placement on the SIF, thereby contributing to developing effective strategies for enhancing structural integrity.

DETERMINATION OF THE DYNAMIC STRESS INTENSITY FACTORS,K_Ⅰ~d AND K_Ⅱ~d,FOR A MIXED-MODE PROPAGATING CRACK

In this paper,the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics.The initial curve and caustic equations were derived un- der the mixed-mode dynamic condition.A multi-point measurement method for determining the dy- namic stress intensity factors,K_Ⅰ~d and K_Ⅱ~d,and the position of the crack tip was developed.Several other methods were adopted to check this method,and showed that it has a good precision.Finally, the dynamic propagating process of a mixed-mode crack in a three-point bending beam specimen was investigated with our method.

Evaluation of Stress Intensity Factors for Multiple Cracked Circular Disks Under Crack Surface Tractions with SBFEM

Stress intensity factors （SIFs） for the cracked circular disks under different distributing surface tractions are evaluated with the scaled boundary finite element method （SBFEM）. In the SBFEM, the analytical advantage of the solution in the radial direction allows SIFs to be directly determined from its definition, therefore no special crack-tip treatment is necessary. Furthermore anisotropic material behavior can be treated easily. Different distributions of surface tractions are considered for the center and double-edge-cracked disks. The benchmark examples are modeled and an excellent agreement between the results in the present study and those in published literature is found. It shows that SBFEM is effective and possesses high accuracy. The SIFs of the cracked orthotropic material circular disks subjected to different surface tractions are also evaluated. The technique of substructure is applied to handle the multiple cracks problem.

Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods

The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors(SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method,whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials,but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency(less time consuming and less spurious boundary effect).

Evaluation of Stress Intensity Factors Subjected to Arbitrarily Distributed Tractions on Crack Surfaces

The stress intensity factors （SIF） considering arbitrarily distributed surface tractions are evaluated based on the sealed boundary finite element method （SBFEM）. The semi-analytical solving process for the stress intensity factors including the effects of surface tractions is presented. Provided are the numerical examples for the evaluation of mode I and Ⅱ stress intensity factors with linear and non-linear distributing forces loaded on the crack surfaces. The crack problems of anisotropy and bimaterial interface are also studied and the stress intensity factors of single-edge-cracked orthotropic material and bi-material interface problems with surface tractions are calculated. Comparisons with the analytical solutions show that the proposed approach is effective and possesses high accuracy.

THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.

STRESS INTENSITY FACTORS FOR A FINITE PLATE WITH AN INCLINED CRACK BY BOUNDARY COLLOCATION

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.

Simulation Research on Stress Intensity Factors of Different Crack Aspect Ratios on Hollow Axles

Because of the wicked service environment of the high speed train, it is possible that the hollow axle of the train may encounter the foreign object damage and form a sharp notch. Under the fatigue loading a crack can initiate from the notch and propagate to failure. It is noted that the stress intensity factor is the control parameter of the crack propagating, for the purpose of getting the more exact propagation characteristics, the stress intensity factor is studied mainly. The service loads of hollow axles are defined, and the stress distribution of hollow axles is obtained according to the load spectrum. The semi-ellipse crack configuration is defined with three parameters： the aspect ratio, the relative depth and the relative location along the crack front. Quarter point 20-node isoparametric degenerate singular elements are used for the region near the crack tip. The finite element model of crack extension of hollow axle is created, and the crack front is dispersed which can realize orthogonal extension. Based on this the stress intensity factors of crack front were calculated, and the distribution rules of the stress intensity factors of different initial crack shapes are obtained. The conclusions are compared with that of the analytic method and they agree with each other very well, and the calculating results show that there is a close relationship between the stress intensity factor and the initial crack shape. For a round crack the stress intensity factor at the surface point increases faster than the one at the center point with the crock propagation. However, for a narrow crack, the results are in contrast with that of a round one. So, all the cracks with different shapes propagate toward to a similar shape, and they grow at this shape to end. The study may contribute to the crack propagate characteristics research.

SEMI-WEIGHT FUNCTION METHOD ON COMPUTATION OF STRESS INTENSITY FACTORS IN DISSIMILAR MATERIALS

Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.

A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.

STRESS INTENSITY FACTORS CALCULATION IN ANTI-PLANE FRACTURE PROBLEM BY ORTHOGONAL INTEGRAL EXTRACTION METHOD BASED ON FEMOL

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.

Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation

The concept of eigen crack opening displacement （COD） can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix as that in the numerical Green’s function （NGF） approach but without the trouble to determine the complementary solutions since the standard boundary element discretization on the crack surface is no longer required with the proposed approach. Some numerical examples computing the stress intensity factors are presented and compared with those in literature to show the accuracy and the effectiveness of the proposed approach.

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier- Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

Influence of geometric parameters on stress concentration factors of undermatched butt joint with single V-groove under three-point bending load

In order to improve the bending load-carrying capacity （BLCC） of undermatched butt joint under three-point bending load, the influence of joint geometric parameters on stress concentration factors （SCF） at the weld bottom center and the weld toe of uudermatched butt joint with single V-groove are studied respectively based on the finite element method in this paper. Results show that the reinforcement height and the cover pass width play decisive role in the BLCC for undermatched butt joint. BLCC of undermatched butt joint can be improved by choosing the appropriate joint geometric parameters.

Experimental study on failure characteristics of single-sided unloading rock under different intermediate principal stress conditions

Investigation of unloading rock failure under differentσ_(2)facilitates the control mechanism of excavation surrounding rock.This study focused on single-sided unloading tests of granite specimens under true triaxial conditions.The strength and failure characteristics were studied with micro-camera and acoustic emission(AE)monitoring.Furthermore,the choice of test path and the effect ofσ_(2)on fracture of unloading rock were discussed.Results show that the increasedσ_(2)can strengthen the stability of single-sided unloading rock.After unloading,the rock’s free surface underwent five phases,namely,inoculation,particle ejection,buckling rupture,stable failure,and unstable rockburst phases.Moreover,atσ_(2)≤30 MPa,the b value shows the following variation tendency:rising,dropping,significant fluctuation,and dropping,with dispersed damages signal.Atσ_(2)≥40 MPa,the tendency shows:a rise,a decrease,a slight fluctuation,and final drop,with concentrated damages signal.After unloading,AE energy is mainly concentrated in the micro-energy range.With the increasedσ_(2),the micro-energy ratio rises.In contrast,low,medium and large energy ratios drop gradually.The increased tensile fractures and decreased shear fractures indicate that the failure mode of the unloading rock gradually changes from tensile-shear mode to tensile-split one.The fractional dimension of the rock fragments first increases and then decreases with an inflection point at 20 MPa.The distribution of SIF on the planes changes asσ_(2)increases,resulting in strengthening and then weakening of the rock bearing capacity.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.