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.

SlGH9-15 regulates tomato fruit cracking with hormonal and abiotic stress responsiveness cis-elements

Fruit cracking occurs easily during the late period of fruit development when plants encounter an unsuitable environment,dramatically affecting fruit production and marketing.This study conducted the bulked segregant RNA-Seq(BSR)to identify the key regulatory gene of fruit cracking in tomatoes.BSR-Seq analysis illustrated that two regions associated with irregularly cracking were located on chromosomes 9 and 11,containing 127 candidate genes.Further,through differentially expression analysis and qRT-PCR in cracking-susceptible and cracking-resistant genotypes,the candidate gene SlGH9-15(Solyc09g010210)with significantly differential expression levels was screened.Bioinformatics analysis of the GH9 gene family revealed that 20 SlGH9 genes were divided into three groups.The phylogenetic analysis showed that SlGH9-15 was closely related to cell wall construction-associated genes AtGH9B1,AtGH9B6,OsGH9B1,and OsGH9B3.The cis-acting elements analysis revealed that Sl GH9-15 was activated by various hormones(ethylene and ABA)and abiotic stresses.The expression pattern indicated that 13 SlGH9 genes,especially SlGH9-15,were highly expressed in the cracking-susceptible genotype.Its expression level gradually increased during fruit development and achieved maximum value at the red ripe stage.Additionally,the cracking-susceptible tomato showed higher cellulase activity and lower cellulose content than the cracking-resistant tomato,particularly at the red ripe stage.This study identified SlGH9-15 as a key gene associated with fruit cracking in tomatoes for the first time and gives new insights for understanding the molecular mechanism and complex regulatory network of fruit cracking.

CRACK TIP FIELD AND J-INTEGRAL WITH STRAIN GRADIENT EFFECT

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani.The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory.No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required.The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus.The strain gradient measures are included into the tangent modulus as internal parameters.Therefore the boundary value problem is the same as that in the conventional theory.Two typical crack problems are studied:(a)the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and(b)the complete field for a compact tension specimen.The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory.The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it.Consequently,the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.

接触面倾角对干燥及饱和砂岩-混凝土组合体力学性能的影响

为研究两种含水状态下不同接触面倾角对砂岩-混凝土组合体的强度和变形特性的影响,分别对干燥与饱和状态下不同倾角的组合体开展了单轴压缩试验.结果表明:两种状态下组合体的峰值强度均随着倾角的增大先增大后减小再增大,且分别在倾角为30°和60°时取得最大值和最小值;饱和状态下不同倾角组合体弹性模量整体略高于干燥状态,而峰值应变小于干燥状态,曲线近似成W型分布;60°组合体均出现整体滑移裂纹,其余试样多为整体张拉破坏,表现出一体两介质连续性力学特性,饱水状态下试样劈裂裂纹数量少于干燥状态;对两种状态下组合体裂纹闭合压密阶段的曲线进行拟合,组合体轴向裂纹闭合应变的演化趋势能较好地贴合其演化方程.

NUMERICAL SIMULATION OF STRESS-STRAIN DISTRIBUTIONS FOR WELD METAL SOLIDIFICATION CRACKING IN STAINLESS STEEL

This paper analyzed the characteristics of welding solidification crack of stainless steels,and clearly re- vealed the the of the deformation in the molten - the pool and the solidification shrinkage on the stress - strain fields in the trail of molten - weld pool.Moreover, rheologic properties of the alloys in solid - liquid zone were also obtained by measuring the hading and unloading deform curves of the steels.As a result, a numerical model for simulation of stress - strain distributions of welding solidifi- cation crack was developed. On the basis of the model,the thesis simulated the driving force of solidifi- cation crack of stainless steels, that is, stress - strain fields in the trail of molten-weld pool with fi- nite element method.

ELASTIC-PLASTIC CRACK GROWTH ON PLANE STRAIN BIMATERIAL INTERFACE

Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish technique introduced by Tvergaard et al.are used to model the final formation of an open crack.It is found from the calculation that the critical fracture toughness for crack growth is much low- er in bimaterials than that in homogeneous material.The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads.The interface crack grows in the more compliant(lower hardening)material or in the weaker(lower yield strength)material.In Mode-Ⅰ loading,the crack grows zigzag along the interface.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

Analytical solution for a strained reinforcement layer bonded to lip-shaped crack under remote modeⅢuniform load and concentrated load

In this paper, the analytical solution of stress field for a strained reinforcement layer bonded to a lip-shaped crack under a remote mode III uniform load and a concentrated load is obtained explicitly in the series form by using the technical of conformal mapping and the method of analytic continuation. The effects of material combinations, bond of interface and geometric configurations on interfaciai stresses generated by eigenstrain, remote load and concentrated load are studied. The results show that the stress concentration and interfaciai stresses can be reduced by rational material combinations and geometric configurations designs for different load forms.

RESEARCH FOR THE STRAIN ENERGY RELEASE RATE OF COMPLEX CRACKS BY USING POINT-BY-POINT CLOSED EXTRAPOLATION APPROACH

A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsistency in some published papers can be avoided. The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two, the displacement of nodes behind the crack tip that is multiplied by nodal forces, the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly. A DCB (double cantilever beam) specimen was calculated and compared with other theoretical results, it is shown that a better coincidence is obtained. In addition the same results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.

Multiscale Study on Low Temperature Crack Resistance Mechanism of Steel Slag Asphalt Mixture

The objective of this paper was to study low temperature crack resistance mechanism of steel slag asphalt mixture(SAM).Thermal stress restrained specimen test(TSRST)and three-point bending test were carried out to evaluate the low-temperature crack resistance of SAM and basalt asphalt mixture(BAM).Based on the digital image correlation technique(DIC),the strain field distribution and crack propagation of SAM were analyzed from the microscopic point of view,and a new index,crack length factor(C),was proposed to evaluate the crack resistance of the asphalt mixture.The crystal phase composition and microstructure of steel slag aggregate(SA)and basalt aggregate(BA)were studied by X-ray diffraction(XRD)and scanning electron microscopy(SEM)to explore the low-temperature crack resistance mechanism of SAM.Results show that the low-temperature crack resistance of SAM is better than that of BAM;SAM has good integrity and persistent elastic deformation,and its bending failure mode is a hysteretic quasi-brittle failure;The SA surface is evenly distributed with pores and has surface roughness.SA has the composition phase of alkaline aggregate-calcite(CaCO3),so it has good adhesion to asphalt,which reveals the mechanism of excellent low-temperature crack resistance of SAM.

装配式BFRP型材-混凝土新型组合梁受弯性能研究

为分析装配式BFRP型材-混凝土新型组合梁的受弯性能,文中对比不锈钢管梁、玄武岩纤维钢管梁以及复合钢管梁的箍筋应变、混凝土正截面应变以及最大裂缝宽度。结果表明,复合梁承受的荷载水平大于玄武岩纤维梁以及不锈钢管梁的承载水平,且对应的箍筋应变值小于玄武岩纤维梁以及不锈钢管梁的应变值;随着荷载水平的增加,相同位置不锈钢管梁、玄武岩纤维钢管梁以及复合钢管梁的混凝土应变值不断增加;复合钢管梁的裂缝宽度最小,分别比不锈钢管梁及玄武岩纤维钢管梁的最大裂缝宽度减少7.1%、50%,由此证明复合钢管梁具有最佳的承载能力、抗变形能力、抗裂性能及抗弯性能。

A new method--the inverse strain method(ISM)for preventing welding hot cracking of high strength aluminium alloy LY12CZ

In this paper a new method for preventing welding hot cracking—the inverse strain method(ISM)is developed on the principle of welding mechan- ics.Effectiveness and feasiblity of method in preventing welding hot cracking of high strength aluminum alloy LY12CZ by synchronous rolling during welding (SRDW)along both sides of the weld at a suitable distance behind the welding arc are examined.Experimental resulte indicate that welding hot cracking of LY12CY can be effectively prevented and the mechanical properties of welded joint can also be improved by the method.It is an important new solution for preventing hot cracking in welding of sheet metal.

THE ASYMPTOTIC SOLUTION TO THE ANTIPLANE SHEAR DYNAMICCRACK-TIP FIELD IN AN ELASTIC STRAIN-SOFTENING VISCOPLASTIC MATERIAL

The elastic strain softening-viscoplastic model is given in this paper. Using this model, the asymptotic stress and strain equations surrounding the tip of a propagating crock are given and numerical results ale obtained under antiplane shear. The analysis and calculation show that at the crack tip the strain possesses logarithmic singularity (ln(R/r))(1/(n+1)) while the stress is like (ln(R/r))(-n/(n+1)), therefore the asymptotic behaviour of the elastic strain-softening viscoplastic field is revealed under the antiplane shear.

Effect of pre-strain on fatigue crack growth of 2E12 aluminum alloy

The influences of pre-strain on the mechanical property and fatigue crack growth of 2E12 aluminum alloy were evaluated by SEM,TEM,mechanical property and fatigue tests. The axial fatigue tests were conducted under a constant amplitude sinusoidal wave loading at stress ratio of 0.1 in laboratory air and salt fog at room temperature. The results show that the yield stress of pre strain material is higher than that of the material without undergoing pre-strain,but pre-strain can not make the increase of the growth rate of fatigue crack. Fatigue crack growth rates of the alloy in salt fog are higher than those in air. The increased fatigue crack growth of the alloy in a given environment and more brittle striations can be observed in salt fog.

EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)--THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper,three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program.The results reveal that the constraints along the thickness direction are obviously separated into two parts:the keeping similar high constraint field(Z_(1))and rapid reducing constraints one(Z_(2)).The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively.So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively.The distribution of the Crack Tip Opening Displacement(CTOD)along the thickness direction and the three dimensional distribution of the void growth ratio(V_(g))near the crack tip are also obtained.The two fracture parameters are in similar trends along the thickness direction,and both of them can reflect the effect of thickness and that of the loading level to a certain degree.

AN APPROACH TO THE ELASTIC-PLASTIC ANALYSIS OF THE PLANE STRAIN MODE-I CRACK

This paper presents an approach to the solution of the approximate elastic-plastic analysis for the plane strain mode-1 crack.

GFRP-轻木夹芯结构Ⅰ/Ⅱ混合型界面剥离试验研究

为研究工程适用性轻木夹芯复合材料结构的界面粘结性能及剥离破坏机制,对不同跨高比的玻璃纤维增强复合材料-Balsa轻木(GFRP-Balsa)夹芯结构进行了单臂弯曲试验(SLB),得到了此种界面的I/II混合型剥离破坏模式、荷载-位移变化规律及裂纹扩展长度曲线,计算了界面裂纹应变能释放率,验证了界面裂纹线性扩展准则的适用性。结果表明:裂纹发展过程中会破坏玻璃纤维面层,界面剥离后芯材表面出现玻璃纤维的分层和断裂;试件跨高比越小,界面剥离裂纹萌生所需时间越长,裂纹扩展速率越小,且剥离极限荷载也越大;发生界面剥离后,随着裂纹的持续扩展,剥离荷载呈下降趋势;剥离界面应变能释放率随裂纹扩展呈上升趋势,且随跨高比的减小而显著增加。

Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.