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.

ON CRACK-TIP STRAIA ENERGY RELEASE RATE IN NON-PRINCIPAL DIRECTIONS OF ELASTICITY FOR SIMPLE LAYER PLATE OF COMPOSITE MATERIALS

In this paper,the fracture problem in non-principal directions of elasticity for a simple layer plate of linear-elastic orthotropic composite materials is studied.The formulae of transformation between characteristic roots,coefficients of elastic compliances in non-principal directions of elasticity and corresponding parameters in principal directions of elasticity are derived.Then,the computing formulae of strain energy release rate under skew-symmetric loading in terms of engineering parameters for principal directions of elasticity are obtained by substituting crack-tip stresses and displacements into the basic formula of the strain energy release rate.

Deformation and damage properties of rock-like materials subjected to multi-level loading-unloading cycles

In the process of engineering construction such as tunnels and slopes,rock mass is frequently subjected to multiple levels of loading and unloading,while previous research ignores the impact of unloading rate on the stability of rock mass.A number of uniaxial multi-level cyclic loading-unloading experiments were conducted to better understand the effect of unloading rate on the deformation behavior,energy evolution,and damage properties of rock-like material.The experimental results demonstrated that the unloading rate and relative cyclic number clearly influence the deformation behavior and energy evo-lution of rock-like samples.In particular,as the relative cyclic number rises,the total strain and reversible strain both increase linearly,while the total energy density,elastic energy density,and dissipated energy density all rise nonlinearly.In contrast,the irreversible strain first decreases quickly,then stabilizes,and finally rises slowly.As the unloading rate increases,the total strain and reversible strain both increase,while the irreversible strain decreases.The dissipated energy damage was examined in light of the aforementioned experimental findings.The accuracy of the proposed damage model,which takes into account the impact of the unloading rate and relative cyclic number,is then confirmed by examining the consistency between the model predicted and the experimental results.The proposed damage model will make it easier to foresee how the multi-level loading-unloading cycles will affect the rock-like materials.

Research on the energy evolution characteristics and the failure intensity of rocks

It is pretty challenging and difficult to quantitatively evaluate the intensity of dynamic disasters in deep mining engineering.Based on the uniaxial loading-unloading experiments for five types of rocks,this paper investigated the energy evolution characteristics,and identified the damage and crack propagation thresholds.Also,the fragment size distributions of the rocks after failure were analyzed.The energy release rate(Ge)and energy dissipation rate(Gd)were then proposed to describe the change of energies per unit volume and per unit strain.Results demonstrated that the more brittle rocks had the shorter stage of unstable crack growth and the lower induced damage at crack damage thresholds.The evolution characteristics of the strain energy rates can be easily identified by the crack propagation thresholds.The failure intensity index(FId),which equals to the values of Ge/Gd at the failure point,was further put forth.It can account for the brittleness of the rocks,the intensity of rock failure as well as the degree of rock fragmentation.It was revealed that a higher FId corresponded to a lower fractal dimension and stronger dynamic failure.

Mechanical and energy dissipation characteristics of granite under cyclic impact loading

This study investigated the effect of repeated blasting on the stability of surrounding rock during the construction of a tunnel or city underground engineering.The split Hopkinson pressure bar(SHPB)was used to carry out cyclic impact tests on granite samples,each having a circular hole,under different axial pressures,and the cumulative specific energy was proposed to characterize the damage characteristics of the rock during the cyclic impact.The mechanical properties and the energy absorbed by the granite samples under cyclic impact loads were analyzed.The results showed that under different axial pressures,the reflected waveform from the samples was characterized by“double-peak”phenomenon,which gradually changed to“single-peak”wi th the increase in damage value.The dynamic peak stress of the sample first increased and then decreased with an increase in impact times.The damage value criterion established based on the energy dissipation could well characterize the relationship between the damage and the number of impacts,which showed a slow increase,steady increase,and high-speed increase,and the damage value depended mainly on the last impact.Under the action of different axial pressures,all the failure modes of the samples were axial splitting failures.As the strain rate increased,with an increase in the dimension of the block,the sizes of the rock fragments decreased,and the fragmentation became more severe.

基于能量原理不同含水率下煤岩体变形破坏能量损伤演化机制

为探究不同含水率下煤岩体在变形破坏过程中的能量演化规律与损伤演化特征,对双马一矿煤岩体开展了在不同含水率条件下单轴压缩试验,基于能量计算及最小耗能原理,分析不同含水率下煤岩体能量耗散特征及损伤演化机制,结果表明:不同含水率下煤岩体力学性质不同,峰值应变与含水率呈正相关,抗压强度、弹性模量与含水率呈负相关;煤岩体含水率越高,其在峰值处弹性应变能及破坏吸收总应变能越小,耗散能占总应变能比例越高;基于最小耗能原理建立的损伤本构模型表明:随着煤岩体含水率增加,损伤门槛值逐渐降低;干燥状态下,煤岩体在应力峰值处损伤变量分别为0.36、0.28,当含水率增至自然状态时,煤岩体在应力峰值处损伤变量值分别下降0.09、0.18,但当含水率增至饱水状态时,煤岩体在应力峰值处损伤变量值反而分别大幅度上升0.102、0.49,总体呈先减后增的发展趋势;进一步建立了不同含水率煤岩损伤应变能释放率演化模型,低含水率煤岩较干燥煤岩的最大损伤应变能释放率大幅度下降,降幅分别为45.61%、31.29%,而随着含水率增加至饱水状态,其最大损伤应变能释放率增大幅度较平缓,分别为3.08%、8.80%,表明煤岩破坏剧烈程度并未大幅度增加。研究成果对煤岩矿柱水害预测评价与岩石损伤评估具有一定参考意义。

磁电弹性体中正三角形孔口快速传播裂纹问题分析

目的探索含运动缺陷的磁电弹性材料的力学性能和断裂机理。方法基于磁电弹性材料断裂理论和广义复变函数理论展开力学行为研究,通过作伽利略变换,将磁电弹性材料的断裂问题转化为稳定裂纹动力学问题进行解答。结果获得了磁电非渗透边界条件下裂纹尖端处动态应力强度因子以及机械应变能释放率的解析表达式。结论磁电弹性材料损伤、断裂现象的发生不仅受缺陷的几何参数和损坏载荷的影响,还与缺陷的运动速度有密切关系。

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.

基于态基近场动力学的碳化硅陶瓷圆柱壳体断裂损伤分析

碳化硅(SiC)陶瓷材料具有优异的力学性能,广泛应用于各种工程部件中.然而,陶瓷是脆性材料,当发生脆断时会造成巨大的危害.因此对其断裂行为的准确预测显得极为重要.为了研究SiC陶瓷壳体在外载荷作用下的断裂损伤机理,首先通过准静态拉伸和压缩实验获得SiC陶瓷的临界能量释放率,建立了适用于拉伸和压缩损伤分析的常规态基近场动力学模型.然后,采用Fortran语言编程实现了陶瓷壳体在线性递增外载荷作用下断裂损伤行为的数值仿真,并将所获得的仿真值与理论预测值进行对比,验证了所建模型的准确性.最后,对仿真结果进行详细分析,揭示了壳体结构的损伤扩展演化规律.仿真结果表明:初始损伤区源于壳体内壁面的压缩断裂,且沿环向呈90°均匀分布.随着载荷的逐渐增加,壳体外壁面出现拉伸断裂损伤区,内外壁面的损伤区先沿着周向扩展,再向着壳体中面缓慢延伸,并在厚度方向贯穿整个壳体.随后,在壳体轴线方向出现拉-压损伤混合区,该损伤区沿着轴向扩展,最终将壳体分成4个断裂区.所建模型能够有效地描述复杂载荷作用下SiC陶瓷结构的断裂损伤演化过程,同时弥补了态基近场动力学在断裂分析方面的不足.

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。

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.

FRACTURE ANALYSIS OF A FUNCTIONALLY GRADED STRIP UNDER PLANE DEFORMATION

In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.

Anti-plane analysis of semi-infinite crack in piezoelectric strip

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

MICROMECHANICAL DAMAGE MODEL FOR ROCKS AND CONCRETES SUBJECTED TO COUPLED TENSILE AND SHEAR STRESSES

Based on the analysis of the deformation in an infinite isotropic elastic matrix with an embedded elliptic crack under far field coupled tensile and shear stresses, the energy release rate and a mixed fracture criterion are obtained using an energy balance approach. The additional compliance tensor induced by a single opening elliptic microcrack in a representative volume element is derived, and the effect of microcracks with random orientations is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes is obtained and is verified with experimental results.

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Study of Debond Fracture Toughness of Sandwich Composites with Metal Foam Core

Two types of experiments were designed and performed to evaluate the adhesive bond in metal foam composite sandwich structures. The tensile bond strength of face/core was determined through the flatwise tensile test （FWT）. The test results show that the interfacial peel strength is lower than the interlaminar peel strength in FWT test. The mode I interracial fracture toughness （GIC） of sandwich structures containing a pre-crack on the upper face/core interface is determined by modified cracked sandwich beam （MCSB） experiment. It is found that the crack propagates unsynchronously on the two side of the specimen and the propagation of interfacial debonding always stays on the face/core interface during the MCSB tests. In order to simulate the failure of metal foam composite sandwich structures, a computational model based on the Tsai-Hill failure criterion and cohesive zone model is used. By comparing with experiment results, it can be concluded that the computational model can validly simulate the interracial failure of metal foam composite sandwich structures with reasonable accuracy.

Coupling damage and reliability model of low-cycle fatigue and high energy impact based on the local stress–strain approach

Fatigue induced products generally bear fatigue loads accompanied by impact processes,which reduces their reliable life rapidly. This paper introduces a reliability assessment model based on a local stress–strain approach considering both low-cycle fatigue and high energy impact loads.Two coupling relationships between fatigue and impact are given with effects of an impact process on fatigue damage and effects of fatigue damage on impact performance. The analysis of the former modifies the fatigue parameters and the Manson–Coffin equation for fatigue life based on material theories. On the other hand, the latter proposes the coupling variables and the difference of fracture toughness caused by accumulative fatigue damage. To form an overall reliability model including both fatigue failure and impact failure, a competing risk model is developed. A case study of an actuator cylinder is given to validate this method.

An Elastoplastic Damage Constitutive Model for Concrete

An elastoplastic damage constitutive model to simulate nonlinear behavior of concrete is presented. Similar to traditional plastic theory, the irreversible deformation is modeled in effective stress space. In order to better describe different stiffness degradation mechanisms of concrete under tensile and compressive loading conditions, two damage variables, i.e., tension and compression are introduced, to quantitatively evaluate the degree of deterioration of concrete structure. The rate dependent behavior is taken into account, and this model is derived firmly in the framework of irreversible thermodynamics. Fully implicit backward-Euler algorithm is suggested to perform constitutive integration. Numerical results of the model accord well with the test results for specimens under uniaxial tension and compression, biaxial loading and triaxial loading. Failure processes of double-edge-notched （DEN） specimen are also simulated to further validate the proposed model.

A micromechanical damage model for rocks and concretes under triaxial compression

Based on analysis of deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.

PEELING-OFF PHENOMENON IN FRP STRENGTHENED CONCRETE BEAMS DUE TO THERMAL RESIDUAL STRESS

Peeling-off phenomena in FRP strengthened concrete beams are investigated in this paper. Based on the beam theory and the fracture mechanics, a new theoretical model is proposed to analyze the peeling-off behavior near FRP-concrete interfaces, which is governed by residual thermal stresses. Numerical examples are presented to provide a clear insight into the failure mechanism. Some suggestions are provided for the optimal design of FRP strengthened structures.