混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

Simulation of crack propagation resistance in brittle media of high porosity

Summary The crack propagation resistance through a porous or microstructurally heterogeneous brittle solid with local variability in strength and stiffness has been simulated. Specifically, the simulation probes the behavior of porous brittle materials in the range of porosity less than those of cellular materials and greater than those of microstructures that are in the category of dilute porosity. The simulation plane consists of a triangular network of points interacting with each other through both linear central force springs and bond angle springs, incorporating an appropriate element of a noncentral force contribution. Explicit microstructural details were incorporated into the model and the simulation was first carried out under conditions of uniaxial tensile strain in order to investigate the mechanisms of subcritical damage evolution, leading to quasi-homogeneous fracture. In order to investigate material strength and stiffness variability on the scale of a representative volume element for coherent fracture events in a crack tip stress gradient, the explicit microstructural results were incorporated into a simulation with boundary conditions characteristic of the displacement field of an infinite Mode I crack. To impart some 3D realism to the primarily 2D simulations a special 2D super-element was devised, which incorporated variability information as might be sampled by a crack front in three dimensions. For a given porosity, in general, only small differences were found between nominally diverse microstructures in terms of their tensile toughness, maximum strength and elastic moduli. The strongest dependence of the overall fracture toughness was found to come from the average porosity. The variability in local element strength and stiffness on the scale of the porosity produced highly tortuous crack paths, roughly on the scale of the chosen representative volume element. The tortuosity of the crack was largest where local variability of strength and stiffness was uncorrelated. Examples of microcrack toughening and crack bridging were observed.     

Simulation of porosity by microballoon dispersion in epoxy and urethane: mechanical measurements and models

Effective mechanical properties of microballoon-dispersed epoxy and urethane are studied under quasi-static and dynamic loading conditions. Elastic modulus measurements of these mixtures over a volume fraction range of 0–0.45 are in good agreement with Hashin-Shtrikman lower-bound predictions for two-phase mixtures comprising of randomly distributed spherical pores in an elastic matrix. The measurements have also been predicted accurately by a LEFM based pore-flaw model for a selected flaw size to pore size ratio. These imply that the microballoons offer negligible reinforcement due to extremely small wall thickness to diameter ratio. Accordingly, feasibility of using these materials to simulate controlled porosity for tensile strength and fracture toughness modeling is explored. Measured tensile strength and fracture toughness values decrease monotonically similar to the Young's modulus variation with volume fraction of microballoons. Guided by the measurements linear elastic models for porous materials that predict tensile strength and fracture toughness of these mixtures are proposed and validated. The tensile strength predictions are in very good agreement with measurements for both epoxy and urethane compositions. The quasi-static crack initiation toughness prediction captures the measurement trends rather well in both cases. The agreement between the measurements and predictions are modest for epoxy matrix while they are good for urethane compositions. Based on fracture surface micrography, an empirical corrective procedure is advanced to improve the agreement between the measurements and the model. The dynamic crack initiation toughness measurements for epoxy, on the other hand, are in excellent agreement with the predictions.     

基于连续球压痕法的45钢强度与韧性测试研究

为研究在役设备的材料强度与韧性测试评价问题,针对工程中常用材料45钢,采用连续球压痕方法,获取了材料的屈服强度、抗拉强度与断裂韧性,通过与常规力学性能试验结果比较,对该方法的可靠性进行了验证。通过研究球压头下压产生的塑性功,与冲击启裂能及断裂韧性之间的关联关系,建立基于仪器化球压痕测试技术的冲击韧性估算评估方法。试验结果表明,利用连续球压痕方法获取的屈服强度、抗拉强度与实际结果的偏差均小于10%,断裂韧性值与试验结果的偏差为12.3%,计算结果在试验值偏差数据范围内。利用连续球压痕技术,建立的断裂韧性与冲击韧性之间的关联公式,所预测的冲击韧性结果与仪器化冲击试验值具有较好的一致性,为在役设备材料的韧性快速评价提供了有效的测试方法。      

Steady-state crack growth in rubber-like solids

The fracture toughness of rubber-like materials depends on several factors. First there is the surface energy required to create new crack surface at the crack tip. Second, a significant amount of energy is dissipated through viscoelastic processes in the bulk material around the crack tip. Third, if the crack propagates very rapidly, inertia effects will come into play and contribute to the fracture toughness. In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to study the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. In addition, the predicted distributions of stress and dissipation around the propagating crack tip are presented.     

Effect of nano-metal particles on the fracture toughness of metal–ceramic composite

A theoretical model is proposed to study the influence of nano-metal particles (NMPs) on the fracture toughness of metal–ceramic composites (MCC). In the framework of the model, the crack tip intersects the grain boundary of the NMPs. Stress concentration at crack tip initiates edge dislocations which makes a shielding effect on the crack and leads to fracture toughness of the MCC. The dependence of critical crack intensity factors on grain size of the NMPs was calculated. The calculation suggested that the existence of the NMPs lead to an increase of critical crack intensity factors by 14%.     

Effect of residual stress on cleavage fracture toughness by using cohesive zone model

This study presents the effect of residual stresses on cleavage fracture toughness by using the cohesive zone model under mode I, plane stain conditions. Modified boundary layer simulations were performed with the remote boundary conditions governed by the elastic K‐field and T‐stress. The eigenstrain method was used to introduce residual stresses into the finite element model. A layer of cohesive elements was deployed ahead of the crack tip to simulate the fracture process zone. A bilinear traction–separation‐law was used to characterize the behaviour of the cohesive elements. It was assumed that the initiation of the crack occurs when the opening stress drops to zero at the first integration point of the first cohesive element ahead of the crack tip. Results show that tensile residual stresses can decrease the cleavage fracture toughness significantly. The effect of the weld zone size on cleavage fracture toughness was also investigated, and it has been found that the initiation toughness is the linear function of the size of the geometrically similar weld. Results also show that the effect of the residual stress is stronger for negative T‐stress while its effect is relatively smaller for positive T‐stress. The influence of damage parameters and material hardening was also studied.     

Experimental and numerical analysis of delamination growth in double cantilever laminated beams

Delamination crack growth in laminated composites is investigated using experiments and finite element (FE) models. Tests are performed on cross-ply graphite/epoxy specimens under static conditions. The load-displacement response is monitored in the tested coupons along with crack length. The FE models employ a cohesive layer that is used to simulate the debonding and crack propagation. The cohesive parameters are calibrated from the experimental load-displacement curves. Crack growth and strain measurements are compared with those from the FE models. The predicted results from the FE models are in good agreement with the test results. The same modeling approach is also used to simulate crack propagation in the transverse direction of a notched laminate. The proposed FE analysis with cohesive layers can simplify fracture toughness assessment in multilayered specimens.     

Crack retardation mechanism due to overload in base material and laser welds of Al alloys

To determine the retardation mechanisms due to overload and to predict the subsequent evolution of crack growth rate, investigations are conducted on crack retardation caused by single tensile overloads in base material and laser-welded sheets of AA6056-T6 Al alloy. The effect of the overload ratio on the fatigue crack propagation behaviour of the C(T) 100 specimens was analysed by using experimental and Finite Element (FE) methods. The crack growth rate and fracture surface features were investigated for both base material and laser-welded sheets. The retardation due to overload is described in terms of the affected regions in front of the crack tip. The size and shape of the crack-tip plastic zone and the damage profile induced during the application of the overload in the base material are predicted by FE analysis in conjunction with a porous-metal plasticity model. The results show that the mechanisms of retardation in under-matched welds are substantially different from that of the homogenous base material. More significant crack retardation due to overload has been observed in the laser weld of AA6056-T6. Based on SEM observations of the fracture surfaces and the damage profiles predicted by the proposed FE model, the shape of the crack front formed during the overload application can be predicted. During the overload, the crack front extends into a new shape, which can be predicted by the ductile damage model; a higher load results in a more curved crack front. These outcomes are used to determine the dominant retardation mechanisms and the significance of retardation observed in each region ahead of the crack tip and finally to define the minimum crack growth rate after overload.     

Approximate stress analysis near crack tip by non-local elasticity

In this paper the non-local elasticity and stress formulae of the classical fracture mechanics are used to analyze the state of stresses in the core region around the tip of a sharp crack, and one-dimensional stress formulae of mode I, II and III problems have been obtained. The results differ from the classical fracture mechanics in that the stresses around the crack tip are finite by using the non-local elasticity, but they are infinite in the classical fracture mechanics. The present calculated results coincide with Eringen's [1] but our model and calculation process is much simpler. At the same time, the maximum tensile stress of the crack tip and fracture toughness are in close agreement with the original experimental results.     

Analysis of mode I delamination of z-pinned composites using a non-dimensional analytical model

We present a non-dimensional analytical model for crack propagation in a z-pinned double cantilever beam specimen (DCB) under mode I loading. Effect of various design parameters on the crack bridging length and apparent fracture toughness are investigated using this model. The efficacy of the analytical model is evaluated by comparing the results with 3D finite element (FE) simulations of the DCB. In the FE model the z-pins are modeled as discrete nonlinear elements. Bi-linear cohesive elements are used ahead of the crack tip to account for the interlaminar fracture toughness of the composite material. The results for load–deflection and crack length obtained from the analytical model and the FE model are compared and found to be in good agreement. The proposed non-dimensional analytical model will be useful in the design and analysis of translaminar reinforcements for composite structures.     

考虑骨料体积含量影响的混凝土准脆性断裂预测模型及应用

基于对准脆性断裂边界影响模型参数的分析,该文将平均骨料粒径d_ave引入模型中,得到了考虑骨料体积含量及尺寸影响的混凝土准脆性断裂预测模型。模型中的有效裂缝与特征裂纹的比值,明确表征了三分点加载单边切口梁(SENB)试件的尺寸及初始缝长度变化时服从的断裂失效准则;模型中d_ave及分散系数β_ave将影响最大荷载P_max作用下临界微裂纹扩展区的平均虚拟裂纹长度Δa_fic。通过SENB试件在P_max时的受力分析,得到了临界正应力σ_n、有效裂缝长度a_e、拉伸强度f_t及断裂韧度K_IC之间的关系式。通过Amparano的试验结果,当a_fic为0.8~1.4倍d_ave时,采用混凝土准脆性断裂模型能较好预测混凝土拉伸强度及断裂韧度。通过对Δa_fic=1.2d_ave时模型得到的预测曲线与试验结果的对比,证明了模型计算结果的可靠性。考虑骨料体积含量影响的混凝土准脆性断裂模型能基于RILEM规范中三分点加载SENB试验预测混凝土断裂韧度与拉伸强度。     

Fracture Parameters for Natural Rubber Under Dynamic Loading

Abstract: An experimental study was conducted to evaluate the tear energy of unfilled and 25 phr carbon black‐filled natural rubber with varying loading rates. The variation of the tear energy with far‐field sample strain rate between 0.01 to 10 s^?1 was found to be different from tensile strip and pure shear specimens. Above a sample strain rate of 10 s^?1, the tear energy calculated from either specimen was comparable. The differences in the tear energy derived from the tensile strip and pure shear specimens were attributed to differences in the local crack tip stress state and strengthening of the material due to strain‐induced crystallisation. Both of these factors resulted in crack speeds 3–4 times higher in the pure shear specimen as compared to the tensile strip specimen. Finite element analysis (FEA) indicated that fracture would initiate at the crack tip either when the strain energy density approached the material toughness or when the maximum principal stress and strain approached the material tensile strength and fracture strain, respectively. It was concluded that these parameters would be better than the tear energy in predicting fracture of natural rubber under dynamic loading.     

Fracture toughness correlation with microstructure and other mechanical properties in near-eutectoid steel

The variation of yield strength and fracture toughness was investigated for four different heat treatments attempted on specimens of a near-eutectoid steel. The aim of this study was to optimize the microstructure for simultaneous improvements in strength and toughness. Further, the fracture toughness deduced through empirical relations from tensile and charpy impact tests was compared with those measured directly according to ASTM Designation: E 399. Among the four different heat treatments attempted in this study, the plane strain condition was valid in the fracture toughness tests for (i) normalized and (ii) hardened and tempered (500°C for 1 h) treatments only. The latter of the two heat treatments resulted in simultaneous improvement of strength and plane strain fracture toughness. The finely-dispersed carbides seem to arrest the crack propagation and also increase the strength. The pearlitic microstructure of the former leads to easy crack propagation along cementite platelets and/or cementite/ferrite interfaces. The nature of variation of empirically determined toughness values from tensile tests for different heat treatments is similar to that measured directly through fracture toughness tests, although the two sets of values do not match quantitatively. On the other hand, the toughness data deduced from charpy impact test is in close agreement with that evaluated directly from fracture toughness tests.     

A new method for evaluating fracture toughness of brittle materials

A new testing procedure is suggested for measuring the fracture toughness of brittle materials as superconductors and ceramics. The idea is to perform a compression test on a subcompact square specimen which contains a central hole. The presence of the hole induces a tensile stress at a certain small region attached to the hole. In this region an artificial notch is introduced such that the fracture path satisfies a pure tensile opening mode (mode I) to which the linear fracture mechanics rules apply. The stress distribution on the fracture plane guarantees a certain amount of stable crack extension. The relationship between the critical compressive load and the stress intensity factor is formulated via an available Green function along with a numerical solution (FEM with ANSYS code). The testing procedure is demonstrated with specimens made of two types of tungsten carbide which differ by their grain size only. Test results are examined via fracture toughness and strength values produced by other conventional methods and the agreement is very good. The geometry and loading direction enable the fracture toughness results to be relatively insensitive to the notch tip radius and the crack length, thereby relaxing the requirements for accurate measurements.The small size of the suggested specimen (12.70mm×12.70mm×5mm) and the avoidance of gripping interfaces provide the major cost-wise advantages.     

Internal hydrogen effects on thresholds for crack growth in the iron-based superalloy IN903

This study of internal hydrogen-induced crack growth in the iron-based superalloy IN903 shows that slow crack growth thresholds are significantly lower than fracture toughness values at the same prechargsd hydrogen concentrations. However, failure in all precharged samples occurred by slip band fracture which differed only in the extent of local surface plasticity. Quantitative fractography of these surface fracture features indicates that the crack tip hydrogen concentrations at threshold were higher than in fracture toughness samples. These higher concentrations are due to crack tip stress enhancement when sufficient time exists for hydrogen redistribution. In addition, continuum models based on mechanisms of failure demonstrate that the matrix carbides control crack growth susceptibility in slow crack growth and fracture toughness samples by establishing the characteristic distance that the crack tip stresses and strains must span to initiate fracture.     

The eigen equation of crack growth to metals

There is an assumption that crack growth is controlled by the high strain area at the very tip of a crack. Based upon the theory of the interaction energy between the inclusion and the applied stress, and the theory of the force acting on elastic singularity, the eigen equation of crack growth is proposed. According to the eigen equation the relation between fracture toughness K_Ic and tensile properties is researched. A general analytical expression for calculation of fatigue threshold values of common metals and alloys is also derived. The fracture toughness and fatigue threshold values for some materials are calculated by the results in this paper. It is found that the theoretical values are in good agreement with the experimental results. A new method predicting the eigen value is also proposed.     

形变孪晶对层状TiAl基合金断裂机制的作用

讨论了形变孪晶在ＰＳＴ晶体断裂过程中的作用,结果表明,裂纹前端形变孪晶对ＰＳＴ晶体的断裂行为具有双重作用。一方面,孪晶致裂是ＰＳＴ晶体断裂的重要方式之一,沿孪晶界面开裂及裂尖开裂是孪晶致裂的两种重要方式。另一方面,形变孪晶能导致主裂纹尖端纯化、分叉等现象,有利于材料断裂韧性的提高。     

Fracture characteristics of Al/zircon particulate composites

A study has been made of the effects of volume fraction and size of zircon particulates on fracture toughness and micromechanisms of fracture in Al/zircon particulate composites. The composites are prepared by a liquid metallurgy technique using volume fractions of zircon in the range 0·06–0·18 and particulate sizes between 75 and 250 μm. The study was conducted on composites in the cast and the forged conditions. The experimental programme included a particle size distribution study, tensile tests, fracture mechanics tests leading to J_1c and crack tip opening displacement evaluation, fractographic investigations, etc. The process zone size at the crack tip was evaluated from crack tip stresses and strains, and compared with the interparticle spacing and particle diameter in order to understand the micromechanics of cracking. The Al/zircon composites were compared with Al/graphite composites in terms of strength and fracture toughness as a function of volume fraction of the filler phase, and regions of optimum performance were identified.     

Prediction of solid block masonry prism compressive strength using FE model

Masonry strength is dependent upon characteristics of the masonry unit, the mortar and the bond between them. Empirical formulae as well as analytical and finite element (FE) models have been developed to predict structural behaviour of masonry. This paper is focused on developing a three dimensional non-linear FE model based on micro-modelling approach to predict masonry prism compressive strength and crack pattern. The proposed FE model uses multi-linear stress–strain relationships to model the non-linear behaviour of solid masonry unit and the mortar. Willam–Warnke’s five parameter failure theory developed for modelling the tri-axial behaviour of concrete has been adopted to model the failure of masonry materials. The post failure regime has been modelled by applying orthotropic constitutive equations based on the smeared crack approach. Compressive strength of the masonry prism predicted by the proposed FE model has been compared with experimental values as well as the values predicted by other failure theories and Eurocode formula. The crack pattern predicted by the FE model shows vertical splitting cracks in the prism. The FE model predicts the ultimate failure compressive stress close to 85% of the mean experimental compressive strength value.