二维位错裂纹的稳定性分析

在已有的一维穿透位错裂纹模型及能量计算的基础上，将其推广为二维椭圆盘状裂纹模型，并计算了其能量．根据能量平衡原理，给出了位错裂纹模型的裂纹平衡尺寸、裂纹扩展临界应力．并与不考虑位错影响的宏观断裂力学中Ⅰ型穿透裂纹的Ｇｒｉｆｉｔｈ解及椭圆盘裂纹的Ｇｒｉｆｉｔｈ解加以比较．给出的位错裂纹模型解在位错数目ｎ＝０时与宏观断裂力学解一致     

Dynamic fracture of concrete – compact tension specimen

The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500 m/s.     

Brittle fracture dynamics with arbitrary paths III. The branching instability under general loading

The dynamic propagation of a bifurcated crack under arbitrary loading is studied. Under plane loading configurations, it is shown that the model problem of the determination of the dynamic stress intensity factors after branching is similar to the anti-plane crack branching problem. By analogy with the exact results of the mode III case, the energy release rate immediately after branching under plane situations is expected to be maximized when the branches start to propagate quasi-statically. Therefore, the branching of a single propagating crack under mode I loading should be energetically possible when its speed exceeds a threshold value. The critical velocity for branching of the initial single crack depends only weakly on the criterion applied for selecting the paths followed by the branches. However, the principle of local symmetry imposes a branching angle which is larger than the one given by the maximum energy release rate criterion. Finally, it is shown that an increasing fracture energy with the velocity results in a decrease in the critical velocity at which branching is energetically possible.     

The effect of crack orientation on fracture behavior of tantalum by multiscale simulation

The quasicontinuum (QC) multiscale method is used to investigate anisotropic fracture behaviors of body-centered cubic (BCC) rare metal tantalum (Ta) loaded in Mode I and different fracture mechanisms are discussed from nanoscopic to continuum perspectives to have a deep understanding of brittle and ductile fracture. Initial crack deflection, brittle fracture by cleaving along low surface energy plane, ductile fracture as a result of dislocation emission and fracture accompanied by deformation twinning are all observed near crack tips of different crystal orientations. Particularly, some of these fracture mechanisms are found to be consistent with the latest experimental results. By examining different fracture behaviors, we find the surface energy and the available slip planes play a combined role in determining the fracture mechanisms near a crack tip. Both isotropic and anisotropic critical stress intensity factors are derived and compared for different crack orientations. A straightforward criterion that is proved to be applicable is used to distinguish brittle fracture from ductile fracture.     

Brittle fracture dynamics with arbitrary paths. II. Dynamic crack branching under general antiplane loading

The dynamic propagation of a bifurcated crack under antiplane loading is considered. The dependence of the stress intensity factor just after branching is given as a function of the stress intensity factor just before branching, the branching angle and the instantaneous velocity of the crack tip. The jump in the dynamic energy release rate due to the branching process is also computed. Similar to the single crack case, a growth criterion for a branched crack is applied. It is based on the equality between the energy flux into each propagating tip and the surface energy which is added as a result of this propagation. It is shown that the minimum speed of the initial single crack which allows branching is equal to 0.39c, where c is the shear wave speed. At the branching threshold, the corresponding bifurcated cracks start their propagation at a vanishing speed with a branching angle of approximately 40°.     

Rate effects on toughness in elastic nonlinear viscous solids

A micromechanics-based constitutive relation for void growth in a nonlinear viscous solid is proposed to study rate effects on fracture toughness. This relation is incorporated into a microporous strip of cell elements embedded in a computational model for crack growth. The microporous strip is surrounded by an elastic nonlinear viscous solid referred to as the background material. Under steady-state crack growth, two dissipative processes contribute to the macroscopic fracture toughness—the work of separation in the strip of cell elements and energy dissipation by inelastic deformation in the background material. As the crack velocity increases, voids grow in the strain-rate strengthened microporous strip, thereby elevating the work of separation. In contrast, the energy dissipation in the background material decreases as the crack velocity increases. In the regime where the work of separation dominates energy dissipation, toughness increases with crack velocity. In the regime where energy dissipation is dominant, toughness decreases with crack velocity. Computational simulations show that the two regimes can exist in certain range of crack velocities for a given material. The existence of these regimes is greatly influenced by the rate dependence of the void growth mechanism (and the initial void size) as well as that of the bulk material. This competition between the two dissipative processes produces a U-shaped toughness-crack velocity curve. Our computational simulations predict trends that agree with fracture toughness vs. crack velocity data reported in several experimental studies for glassy polymers and rubber-modified epoxies.     

Pitting formation under rolling contact

The mechanism of pitting caused by rolling contact is analyzed using the fracture mechanics approach. The governing factors are the initial crack length, crack angle, contact force, friction, strain hardened layer, and the hydraulic pressure of trapped fluid acting on the crack surface. Mode I and II stress intensity and the strain energy density factors are calculated by application of the two-dimensional finite element method. The strain energy density criterion is applied to show that shallow angle crack under small rolling contact force and friction enhances the probability of pitting under the roller’s running surface. The presence of a strain hardened surface layer also tends to affect the fracture behavior. The analytical results agree well with the experimental observations.     

Peridynamic modelling of impact damage in three-point bending beam with offset notch

The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics.Based upon the integrodifferential equations,peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching,curving,and arrest.In this paper,the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch,which is widely used to investigate the mixed I-II crack propagation in brittle materials.The predictions from the peridynamic analysis agree well with available experimental observations.The numerical results show that the dynamic fracture behaviors of the beam under the impact load,such as crack initiation,curving,and branching,rely on the location of the offset notch and the impact speed of the drop hammer.     

Influence of domain switching zones on the fracture toughness of ferroelectrics

The paper presents a fracture model for ferroelectric materials taking into account the hysteretic domain switching processes near to the tip of a macroscopic crack. The model is based on the balance of energy supplied by the driving forces, on the one hand, and the total of energies either dissipated by domain switching, stored in the crack wake region or consumed by the formation of new fracture surface, on the other hand. An internal variable theory describes the nonlinear coupled electromechanical material response within the framework of a three-dimensional continuum model. For simplicity, the complex orientation distribution function of domains in a polycrystalline ceramic is approximated by only six representative space orientations. The theory predicts certain dimensionless material parameter combinations which govern the change of fracture toughness under the application of different mechanical and electrical loadings. A comparison with data available in the literature for barium titanate ceramics yields a reasonable coincidence.     

Strain energy density criteria for dynamic fracture and dynamic crack branching

Dynamic extension of Sih's fracture criterion based on strain energy density factor, r_c (dW/dV), is used to analyze dynamic crack propagation and branching. Influence of the nonsingular components, which are known as the higher order terms (HOT) in the crack tip stress field, on the strain energy density distribution at a critical distance surrounding the crack tip moving at constant crack velocity is examined. This r_c (dW/dV) fracture criterion is then used to analyze available dynamic photoelastic results of crack branching and of engineering materials.     

A multiscale model for the ductile fracture of crystalline materials

In this paper, a multiscale model that combines both macroscopic and microscopic analyses is presented for describing the ductile fracture process of crystalline materials. In the macroscopic fracture analysis, the recently developed strain gradient plasticity theory is used to describe the fracture toughness, the shielding effects of plastic deformation on the crack growth, and the crack tip field through the use of an elastic core model. The crack tip field resulting from the macroscopic analysis using the strain gradient plasticity theory displayes the 1/2 singularity of stress within the strain gradient dominated region. In the microscopic fracture analysis, the discrete dislocation theory is used to describe the shielding effects of discrete dislocations on the crack growth. The result of the macroscopic analysis near the crack tip, i.e. a new K-field, is taken as the boundary condition for the microscopic fracture analysis. The equilibrium locations of the discrete dislocations around the crack and the shielding effects of the discrete dislocations on the crack growth at the microscale are calculated. The macroscopic fracture analysis and the microscopic fracture analysis are connected based on the elastic core model. Through a comparison of the shielding effects from plastic deformation and the discrete dislocations, the elastic core size is determined.     

Time-harmonic P-waves engulfing a rectangular limited-permeable crack in piezoelectric medium: Energy density and energy release

The dynamic behavior of a limited-permeable rectangular crack in a transversely isotropic piezoelectric material is impinged by to a P-wave. The generalized Almansi theorem and the Schmidt method are used to determine the stress intensity factor and energy density factor as the primary fracture criterion of failure. The mixed boundary value problem entails the evaluation of the appropriate crack edge stress singularities that are characteristics of the fundamental functions. The stress and electric displacement intensity factors are also used to find the energy release rate that can be computed numerically and compared with the results corresponding to those of the stress intensity factor, and energy density factor. Graphical presentation shows that the energy release rate is always negative for the boundary conditions considered while the energy density factors always remain positive. Under certain conditions, the stress and electric displacement intensity factors can be negative and subject to physical limitations. Piezoelectric material boundary value problem solutions should therefore be qualified by the application of failure criteria by fracture of otherwise, particularly when the mechanical and electrical energy can release by creating free surface at the macroscopic and microscopic scales. Negative energy release rate found for the piezoelectric medium in this work can be a case in point.Positive definiteness of the energy density factor can be applied to mutliscale fracture. This is not true for the stress intensity factor nor the energy release rate. Hence, crack initiation behavior for the permittivity of a rectangular crack due to the wave propagation effects may be studied. In particular, the initiation of micro-cracks may be identified with certain critical stress wave frequency band. Negative stress intensity factor may not enhance macrocracking but it does not exclude microcrack initiation.     

Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging

We demonstrate the use of X-ray phase contrast imaging with sub-microsecond temporal resolution to obtain quantitative visualization of dynamic fracture processes in brittle solids. We examine an amorphous solid (fused silica), a ceramic single crystal (single-crystal quartz), and a polycrystalline ceramic (boron carbide), in the form of single-edge notched specimens loaded using a three-point apparatus at nominal strain rates up to \(\sim \)800 s^?1. We observe that the crack tip speed for boron carbide is relatively independent of mode I stress intensity factor rate (\(\dot {K}_{\mathrm {I}}\)) for these rates of loading, while that of fused silica and single-crystal quartz increases with \(\dot {K}_{\mathrm {I}}\). Further, for the amorphous and single crystal cases, we observe the development of a crack tip instability in the form of crack branching as the crack tip speed approaches 45% of the Rayleigh wave speed. This suggests that strain-rate-dependent mechanisms contribute to crack branching. Such mechanisms may, in turn, affect the macroscopic fracture properties of these materials.     

Crack driving force and energy-momentum tensor in electroelastodynamic fracture

The energy flux integral and the energy-momentum tensor for studying the crack driving force in electroelastodynamic fracture are formulated within the framework of the nonlinear theory of coupled electric, thermal and mechanical fields based on fundamental principles of thermodynamics. This formulation lays a foundation for in-depth understanding of the fracture behavior of piezoelectric materials. Remarkably, the dynamic energy release rate thus obtained has an odd dependence on the electric displacement intensity factor for steady-state propagation of a conventional (unelectroded) crack with exact, electrically permeable, semi-permeable, or impermeable crack surface condition, which is in agreement with experimental evidence.     

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G _max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ _y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

不同加载速率下砂岩弯曲破坏的细观机理

岩石细观破裂形貌是岩石破坏机制的重要反映，为研究不同加载速率对砂岩弯曲破坏的影响，通过三点弯曲实验和扫描电镜方法，对某煤矿关键层砂岩弯曲破断裂纹细观形态以及裂纹的自相似性进行了研究。选取6个不同加载速率对岩样进行三点弯曲实验，观察其宏观断裂情况，并利用扫描电镜对弯曲断裂面表面裂纹细观结构进行观察，并拍摄不同倍数下的扫描电镜图片。对图片进行图像处理后得到砂岩弯曲断裂破坏细观裂纹信息，并计算得到微裂纹的分形盒维数值。结果显示:随着加载速率的提高，砂岩穿晶断裂的比例也随之升高，裂纹分形维数亦随着加载速率的增大而增加，同时，分形维数还与弯曲断裂破坏荷载和抗弯强度成正比。可见，加载速率对断裂方式有一定的影响，且加载速率越大断裂所需的破坏能越大，裂纹分布越广，表明开采速度与岩爆等岩体动力灾变有密切关系。     

Thermodynamics and continuum fracture mechanics for nonlocal-elastic plastic materials

Nonlocal elasticity is used as an improved elasticity model which engenders no crack-tip stress singularities and thus makes applicable the classical stress-based failure criteria. Considering nonlocal-elastic plastic materials exposed to softening by particle decohesion in a process surface and to subsequent surface separation by fracture, fracture mechanics is addressed within the framework of irreversible internal-variable thermodynamics in the hypothesis of small strains and arbitrary (but sufficiently regular) fracture surface (crack surface plus process surface). The state equations and the energy dissipation densities are derived for the bulk material and for the process surface, for both of which thermodynamically consistent evolutive equations are also proposed. The energy consumption for the formation of the unit crack area is evaluated as the sum of two contributions, one as free energy released by the process surface microstructure, the other as mechanical work done by the surrounding bulk material. Basing on the second thermodynamics law, a crack local stability criterion is provided in terms of crack front characteristics, i.e. fracture force vector, fracture resistance vector and fracture (symmetric) stiffness matrix, all defined at the points of the crack front through the response fields and the response sensitivities to virtual crack front advancements. Stability is guaranteed if, at every point of the crack front and for any virtual advancement of the latter, the fracture resistance is greater than the fracture force, or in case of equality, the fracture stiffness matrix is positive definite. The limit case of perfectly brittle fracture is considered, also in the case of local elasticity.     

An In-Situ X-Ray Microtomography Study of Split Cylinder Fracture in Cement-Based Materials

In an effort to quantify microstructure-property relationships, three dimensional imaging experiments were conducted on small cylinder specimens subjected to split cylinder fracture. 3-D images were made using synchrotron-based x-ray microtomography, and the experiments were conducted with an in-situ frame such that a specimen could be examined while under load at varying degrees of damage. The specimens were made of fine-grained portland cement mortar and 0.5 mm glass beads, which served as aggregates. The diameter of the specimens was 5 mm. 3-D image analysis routines were developed or adapted to characterize microstructure and internal damage, which could then be related to bulk splitting strength and fracture energy. For fracture energy calculation, crack surface area could be measured in a way that accounted for roughness, branching, and fragmentation. Results showed that, for the specimens tested, aggregate surface roughness had little effect on strength but significant effect on fracture energy. Split cylinder strength showed correlation with specimen porosity, although there was considerable scatter. Strength did not correlate with maximum flaw size, although flaw location was not evaluated.     

Effects of fillers on fracture performance of thermoplastics: Strain energy density criterion

This paper presents the experimental results on the fracture performance of filled thermoplastics. The emphasis is put on verification of the validity of different fracture criteria. The effects of two- and three-dimensional fillers on the fracture toughness of a representative thermoplastic, polypropylene, are analyzed. It has been found that classical fracture mechanics do not properly describe the fracture behavior of these composites. The strain energy density theory provides a more appropriate criterion for predicting fracture. On the macroscopic scale, the addition of fillers leads to a reduction in the critical strain energy density of thermoplastics. However, on the microscopic level fillers enhance a more wide spread crack-growth and failure by fracture becomes more stable. The material is therefore less prone to shatter in service. This effect of fillers is interpreted in terms of damage development, induced by the debonding at the matrix/fillers interface. A better interfacial adhesion reduces the microscopic damage and the critical increment of crack growth prior to instability. The results explain the negative effect of coupling agent on the impact resistance observed in practice.     

Dynamic fracture instabilities in brittle crystals generated by thermal phonon emission: Experiments and atomistic calculations

Dynamic cleavage fracture experiments of brittle single crystal silicon revealed several length scales of surface and path instabilities: macroscale path selection, mesoscale crack deflection, and nanoscale surface ridges. These phenomena cannot be predicted or explained by any of the continuum mechanics based equations of motion of dynamic cracks, as presumably critical energy dissipation mechanisms are not fully accounted for in the theories. Experimentally measured maximum crack speed, always lower than the theoretical limit, is another phenomenon that is as yet not well understood.We suggest that these phenomena depend on velocity dependent and anisotropic material property that resists crack propagation. The basic approach is that the bond breaking mechanisms during dynamic crack propagation vibrate the atoms at the crack front to generate thermal phonon emission, or heat, which provides additional energy dissipation mechanisms. This energy dissipation mechanism is a material property that resists crack propagation. To evaluate this property, we combined the continuum based elastodynamic Freund equation of motion with molecular dynamics atomistic computer “experiments”.We analyzed the above experimental dynamic fracture instabilities in silicon with the obtained velocity dependent and anisotropic material property and show its importance in cleavage of brittle crystals.