轻质泡沫混凝土的劈裂破坏力学行为分析

利用平台巴西圆盘加载方式和钢质压条加载方式,对两种厚度为25mm和50mm、不同密度的轻质泡沫混凝土(400～1000kg/m3)进行巴西圆盘劈裂试验,研究密度和厚度对泡沫混凝土裂纹宽度、劈裂强度、断裂韧度、断裂能的影响规律。结果表明,在橡胶垫平台巴西圆盘和钢质压条加载方式下,其劈裂断裂特征大致分为四个阶段:线性弹性段、非线性弹性段、起裂阶段、失稳阶段。同样加载率下最大裂纹宽度随着泡沫混凝土密度增加逐渐减小,劈裂拉伸强度、断裂韧度、断裂能呈幂函数形式增加。借鉴Reinhardt非线性软化曲线,对不同密度泡沫混凝土的应力软化关系进行曲线拟合,建立基于拉伸强度、断裂韧度等控制参数的应力-裂纹宽度关系三段式模型。基于试验结果,对理想多孔材料细观力学预测模型进行修正,获得泡沫混凝土孔隙率与拉伸强度的半经验公式。     

Compression-shear failure of cementitious materials with oblique weak layers

Compressive/shear failure and strain-softening behavior of a bi-material system consisting of two different mortar compositions are studied. The bulk part of the bi-material specimen was made from the stronger mortar and was cast first, and then an oblique weak layer made from the weaker mortar was introduced in the middle of the specimen. By controlling the weak layer angle, thickness and strength, the compressive/shear failure characteristics and Mode-II shear strain-softening behavior have been determined. A bi-linear strain-softening model is proposed to consider both the Mode-II shear strain-softening behavior and the influence of friction due to compression. A linear softening law for the first part of the bi-linear model is sufficient to describe the softening curve after the peak load, but the second linear ‘softening’ relation is required to explain the influence of friction on the load and displacement curve. With the bi-linear model the Mode-II fracture energy G^f-ll can be separated from the frictional energy dissipation. It is also found that two different frictional coefficients exist if a load and displacement curve has distinct softening and pure frictional regions.     

混凝土拉伸软化曲线折线近似的逆解方法

研究基于Hillerborg的虚拟裂纹模型，利用有限元分析方法，求得折线近似的拉伸软化曲线的逆解方法。对弹性模量，初始开裂应力的决定方法进行了研究。以双直线模型的计算结果为算例进行了逆推分析，算例符合得很好。也较好地从实验得到的荷载位移曲线再现了拉伸软化曲线。这对于研究混凝土的断裂能，尺寸效应等问题很具意义。     

Damage model for viscoplastic-softening behavior: cement paste and concrete

A viscoplastic-softening model is developed; it invokes damage accumulation depending on the viscous strain and stress rates. For deformation beyond the peak on the uniaxial stress-strain curve, the softening behavior is modelled by applying the accounting for loss in stiffness due to localized material damage by cracking. Predicted are the hardening/softening behavior of cement paste. The results for applied strain rates of 3 × 10⁻³, 3 × 10⁻² and 3 × 10⁻¹ s⁻¹ agreed well with the test data. Similar success was obtained for the creep of two types of concrete under compression.     

Strain strengthening effects in Witwatersrand quartzite

A series of uniaxial compression specimens were tested over a range of applied ram displacement rates of 8.9 × 10⁻⁴ to 8.9 mm/sec to elucidate the effects of loading rate on the uniaxial compressive fracture stress of Witwatersrand quartzite. It was demonstrated that even within standard loading rate ranges, considerable scatter in the fracture strength (under uniaxial compression) existed in this particular quartzite rock. Nevertheless, a definite trend of increasing fracture resistance with increasing monotonic loading rate was evident inasmuch that increasing the loading rate (strain rate) by four orders of magnitude increase the fracture strength by almost 2.8 times. Prior fatigue loading also produced a significant strain strengthening as the uniaxial compressive fracture stress tended to increase in a sigmoidal fashion with increasing number of fatigue cycles prior to testing. Indeed, the fracture strength of quartzite was almost doubled in value after 10⁻ cycles. Plane strain fracture toughness tests utilising three point bend specimens were conducted and an average of K_lc = 1.7 MPa√m was realized. In both the uniaxial compression tests and the fracture toughness tests, failure occurred by crack extension predominantly by a transgranular flat cleavage-like mode through pure quartzite (silica) regions. However, crack extension was also observed to occur in an intergranular “ductile-like” mode through areas associated with inclusions prevalent in the quartzite.     

Fracture toughness from the standpoint of softening hyperelasticity

Fracture toughness of brittle materials is calibrated in experiments where a sample with a preexisting crack/notch is loaded up to a critical point of the onset of static instability. Experiments with ceramics, for example, exhibit a pronounced dependence of the toughness on the sharpness of the crack/notch: the sharper is the crack the lower is the toughness. These experimental results are not entirely compatible with the original Griffith theory of brittle fracture where the crack sharpness is of minor importance.¹To explain the experimental observations qualitatively we simulate tension of a thin plate with a small crack of a finite and varying sharpness. In simulations, we introduce the average bond energy as a limiter for the stored energy of the Hookean solid. The energy limiter induces softening, indicating material failure. Thus, elasticity with softening allows capturing the critical point of the onset of static instability of the cracked plate, which corresponds to the onset of the failure propagation at the tip of the crack. In numerical simulations we find, in agreement with experiments, that the magnitude of the fracture toughness cannot be determined uniquely because it depends on the sharpness of the crack: the sharper is the crack, the lower is the toughness.Based on the obtained results, we argue that a stable magnitude of the toughness of brittle materials can only be reached when a characteristic size of the crack tip is comparable with a characteristic length of the material microstructure, e.g. grain size, atomic distance, etc. In other words, the toughness can be calibrated only under conditions where the hypothesis of continuum fails.     

加载速率对40Cr钢Ⅱ型动态断裂特性的影响

采用新型Ⅱ型动态断裂测试技术,对高强钢40Cr在高加载速率下的Ⅱ型动态断裂特性进行了测试研究。基于新设计的Ⅱ型动态断裂试样和分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）技术,通过实验-数值方法确定了裂尖在加载过程中的应力强度因子曲线。采用应变片法确定了试样的起裂时间,最终得到40Cr的Ⅱ型动态断裂韧性值,并对其加载速率相关性和材料的失效机理进行了研究。结果表明,在1.08～5.53 TPa·m1/2/s的加载速率范围内,40Cr的Ⅱ型动态断裂韧性基本表现为与加载速率成正相关的变化趋势。通过对试样断口形貌的分析,确定了材料的失效模式及机理,发现随着加载速率的增加,存在拉伸型失效向绝热剪切型失效模式转变的现象。     

A microsystem for the fracture characterization of polysilicon at the micro-scale

To characterize the effective fracture energy G_IC of polysilicon wafers at room temperature, an on-chip MEMS test structure has been designed and fabricated. The device can provide fatigue pre-cracking at the notch apex and subsequently impose a monotonical load up to failure. The proposed procedure combines the experimental data with outcomes of numerical simulations. A continuously monitored decrease in stiffness of the system is linked to the crack length and the effective fracture energy for the non-standard geometry of the testing device. An average value of G_IC = 12.0 ± 1.8 N m^?1 is found. These values are then used in numerical micro-scale fracture analyses taking into account the material heterogeneity due to the grain structure and reproducing the crack propagation process with a cohesive approach.     

Damage accumulation and crack growth in bilinear materials with softening: Application of strain energy density theory

A pseudo-elastic damage-accumulation model is developed by application of the strain energy density theory. The three-point bending specimen is analyzed to illustrate the crack growth characteristics according to a linear elastic softening constitutive law that is typical of concrete materials. Damage accumulation is accounted for by the decrease of elastic modulus and fracture toughness. Both of these effects are assessed by means of the strain energy density functions in the elements around a slowly moving crack. The rate of change of the strain energy density factor S with crack growth as expressed by the relation dS/da = constant is shown to describe the failure behavior of concrete. Results are obtained for different loading steps that yield different slopes of lines in an S versus a (crack length) plot. The lines rotate about the common intersect in an anti-clockwise direction as the load steps are increased. The intersect shifts upward according to increase in the specimen size. In this way, the combined interaction of material properties, load steps and specimen geometry and size are easily analyzed in terms of the failure mode or behavior that can change from the very brittle to the ductile involving stable crack growth. An upper limit on specimen or structural size is established beyond which stable crack growth ceases to occur and failure corresponds to unstable crack propagation or catastrophic fracture. The parameters that control the failure mode are the threshold values of the strain energy density function (dW/dV)_c and the strain energy density factor S_c.     

Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials

The ferrite and ferroelectric phase of magnetoelectroelastic (MEE) material can be selected and processed to control the macroscopic behavior of electron devices using continuum mechanics models. Once macro- and/or microdefects appear, the highly intensified magnetic and electric energy localization could alter the response significantly to change the design performance. Alignment of poling directions of piezomagnetic and piezoelectric materials can add to the complexity of the MEE material behavior to which this study will be concerned with.Appropriate balance of distortional and dilatational energy density is no longer obvious when a material possesses anisotropy and/or nonhomogeneity. An excess of the former could result in unwanted geometric change while the latter may lead to unexpected fracture initiation. Such information can be evaluated quantitatively from the stationary values of the energy density function dW/dV. The maxima and minima have been known to coincide, respectively, with possible locations of permanent shape change and crack initiation regardless of material and loading type. The direction of poling with respect to a line crack and the material microstructure described by the constitutive coefficients will be specified explicitly with reference to the applied magnetic field, electric field and mechanical stress, both normal and shear. The crack initiation load and direction could be predicted by finding the direction for which the volume change is the largest. In contrast to intuition, change in poling directions can influence the cracking behavior of MEE dramatically. This will be demonstrated by the numerical results for the BaTiO₃–CoFe₂O₄ composite having different volume fractions where BaTiO₃ and CoFe₂O₄ are, respectively, the inclusion and matrix.To be emphasized is that mode I and II crack behavior will not have the same definition as that in classical fracture mechanics where load and crack extension symmetry would coincide. A striking result is found for a mode II crack. By keeping the magnetic poling fixed, a reversal of electric poling changed the crack initiation angle from θ₀=+80° to θ₀=−80° using the line extending ahead of the crack as the reference. This effect is also sensitive to the distance from the crack tip. Displayed and discussed are results for r/a=10⁻⁴ and 10⁻¹. Because the theory of magnetoelectroelasticity used in the analysis is based on the assumption of equilibrium where the influence of material microstructure is homogenized, the local space and temporal effects must be interpreted accordingly. Among them are the maximum values of (dW/dV)_max and (dW/dV)_min which refer to as possible sites of yielding and fracture. Since time and size are homogenized, it is implicitly understood that there is more time for yielding as compared to fracture being a more sudden process. This renders a higher dW/dV in contrast to that for fracture. Put it differently, a lower dW/dV with a shorter time for release could be more detrimental.     

Effects of deformed volume, volume fraction and particle size on the deformation behaviour of W/Cu composites

Tungsten/copper (W/Cu) particle reinforced composites were used to investigate the scaling effects on the deformation and fracture behaviour. The effects of the volume fraction and the particle size of the reinforcement (tungsten particles) were studied. W/Cu-80/20, 70/30 and 60/40 wt.% each with tungsten particle size of 10 μm and 30 μm were tested under compression and shear loading. Cylindrical compression specimens with different volumes (D_S = H) were investigated with strain rates between 0.001 s⁻¹ and about 5750 s⁻¹ at temperatures from 20 °C to 800 °C. Axis-symmetric hat-shaped shear specimens with different shear zone widths were examined at different strain rates as well. A clear dependence of the flow stress on the deformed volume and the particle size was found under compression and shear loading. Metallographic investigation was carried out to show a relation between the deformation of the tungsten particles and the global deformation of the specimens. The size of the deformed zone under either compression or shear loading has shown a clear size effect on the fracture of the hat-shaped specimens.The quasi-static flow curves were described with the material law from Swift. The parameters of the material law were presented as a function of the temperature and the specimen size. The mechanical behaviour of the composite materials were numerically computed for an idealized axis-symmetric hat-shaped specimen to verify the determined material law.     

Fractal geometry concerned with stable and dynamic fracture mechanics

Fractal modeling of the rugged crack geometry is considered for the stable and dynamic fracture mechanics characterizing the morphology of a fracture surface and the influence of its growth. It is shown that the fractal dimension has a strong influence on the rising of the R-curve in brittle materials. For the unstable Griffith–Mott’s approach or dynamical crack growth the fractal dimension has a strong influence on the velocity limit of the crack growth. It is also shown that the limit of crack velocity lowers with increasing surface ruggedness (higher fractal dimension D = 2 − H) explaining the intangibility of the Rayleigh wave velocity by the cracks.     

A centrally cracked thin circular disk, Part I: 3D Elastic–plastic finite element analysis

A full field solution, based on small deformation, three-dimensional elastic–plastic finite element analysis of the centrally cracked thin disk under mode I loading has been performed. The solution for the stresses under small-scale yielding and lo!cally fully plastic state has been compared with the HRR plane stress solution. At the outside of the 3D zone, within a distance of rσ_o/J=18, HRR dominance is maintained in the presence of a significant amount of compressive stress along the crack flanks. Ahead of this region, the HRR field overestimate the stresses. These results demonstrate a completely reversed state of stress in the near crack front compared to that in the plane strain case. The combined effect of geometry and finite thickness of the specimen on elastic–plastic crack tip stress field has been explored. To the best of our knowledge, such an attempt in the published literature has not been made yet. For the qualitative assessment of the results some of the field parameters have been compared to the available experimental results of K, gives a fair estimate of the crack opening stress near the crack front at a distance of order 10⁻² in. On the basis of this analysis, the Linear Elastic Fracture Mechanics approach has been adopted in analyzing the fatigue crack extension experiments performed in the disk (Part II).     

The investigation on dynamic fracture behavour of materials under compressive-shear combined stress waves

In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials, under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt∼10⁸ MPa m^1/2s⁻¹. With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the “momentum trap” technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage failure model. The project supported by the National Natural Science Foundation of China (No. 19672066 and 18981180-4) and the Key Project of Chinese Academy of Sciences (No. KJ951-1-20)     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

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.     

The fragmentation of cementitious composites in a jaw breaker

The paper reports about the fragmentation of cementitious composites in a laboratory jaw breaker. Two types of cement paste and six different concrete materials were investigated. Specific fragmentation energy and size distributions of the generated fragments were estimated. A microscopic inspection of the debris was also performed. Specific energy has values between 5 and 10 J/g. It is highest for a concrete with high porosity and lowest for a mortar. It is also found that the specific fragmentation energy depends on the amount of coarse aggregates in the material. Based on these findings, the specific fragmentation energy is linked to a brittleness parameter of the concrete materials derived from non-linear fracture mechanics. A detailed SEM-study showed features of non-linear fracture, namely crack branching, aggregate bridging, and pore–crack interaction. It was further found that a Rosin–Rammler–Sperling distribution best describes the size distribution of the generated fragments, except the mortar. An approximate estimation of the strain rate during the fragmentation was performed, and a value of s⁻¹ was calculated for concrete.     

Experimental and numerical investigation of concrete properties effects on fracture toughness under complex loading

Abstract

This article is presenting the common experimental specimen for determining the fracture toughness of the first pure mode and second pure mode. The Notched beam is chosen from a presented common specimen in the form of three-point flexure beam and four-point flexure beam that were built in the concrete laboratory. For prevention of cracks growth, a critical load of first pure mode and the second pure mode of each specimen computed. Obtained results are used for computing the fracture toughness. For the purpose of investigating the effective fracture parameters in the suggested specimen, finite element analysis on the mentioned geometry is performed. Obtained results show that different parameters are effective on the fracture toughness including crack length, cement percentage, water and the thickness of biggest used aggregate in the sand. Also with changing each of these parameters, the fracture mechanic properties are changed. Each of these effects is examined separately in this article and the conclusions presented in tables and figures.

Communicated by Dumitru Caruntu.     

Cohesive properties of nickel-alumina interfaces determined via simulation of ductile bridging experiments

A combined experimental and computational study is carried out to characterize a nickel-alumina interface in terms of the two parameter (σ̂, Γ₀) computational cohesive zone (CCZ) model of Tvergaard and Hutchinson. Experiments were performed using a sandwich specimen consisting of a thin nickel foil bonded between two pre-cracked alumina plates. The specimen was loaded in tension with the nickel foil bridging the cracks in the ceramic. Numerical simulations of the experiments were used to extract the parameters for the CCZ model.Effects of various parameters of the CCZ model are investigated and it is found that the most dominant parameter is the interface strength, σ̂. Effects of the residual thermal stresses are also investigated and it is shown that these stresses can enhance the specimen fracture toughness by almost 16%. The parameters for the nickel-alumina interface are found to be σ̂ = 148 MPa and Γ₀ = 11 J m⁻². It is observed that for the foil thicknesses tested, the work of rupture does not vary linearly with the thickness as predicted by many theoretical models. We found that interfaces which are neither too strong nor too weak contribute most to the overall fracture toughness of such a composite. Although the macroscopic loading at the nickel-alumina interface is shear, the failure is primarily tensile due to the thinning that occurs in the metal as it is stretched.