Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.     

Fracture toughness determination for compact tension specimens

An analysis of determining the plane stress fracture toughness based on a beam-on-elastic foundation model for compact tension specimens (CTS) covering a wide range of a/2H and d/W ratios is presented. The solution is achieved by using the Timoshenko beam theory and Pasternak foundation with alternative formulations of the foundation modulus and the shear parameter to reflect more accurately the stress-strain distributions at the crack tip.The solution applicable to a wider range of a/2H and d/W ratios becomes desirable for practical reasons. For instance, the determination of plane-strain fracture toughness from the CTS specimens at higher a/W ratios enables the reduction of loading capacity from a testing machine which may become prohibitively high for medium strength engineering materials. Maximum fatigue crack growth data to be measured from a CTS specimen also becomes possible when the validity of fracture toughness can be ensured at the extended a/W ratios.The computed fracture toughness from the present analysis are compared with those measured experimentally and found to be satisfactory not only for high a/W ratios but also for a wide range of a/2H ratios commonly used in double-cantilever beam specimens.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

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.     

Fracture toughness for CNT specimens from numerically obtained critical CTOD values

Many approaches for estimating mode I fracture toughness (K_IC) using circumferentially notched tensile (CNT) specimen have been demonstrated in the literature. In this paper, an effective approach for estimating fracture toughness from the numerical solution of critical crack tip opening displacement (CTOD) is proposed. An elasto-plastic finite element analysis is used to estimate critical CTOD values for CNT specimens. A number of materials are analysed, and the relationship between K_IC and critical CTOD for CNT specimens is obtained. The proposed relationship is validated by comparing the fracture toughness values obtained from the relationship with those obtained experimentally using CNT specimens. The fracture toughness (K_IC) calculated according to this relationship from numerically obtained critical CTOD is found to be in close agreement with the experimentally obtained fracture toughness for the respective materials.     

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.     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

Unsteady Dynamic Crack Propagation in a Brittle Polymer

Dynamic crack propagation in a brittle polymer, poly(methyl-methacrylate) (PMMA), was studied using the method of caustics in combination with a Cranz–Schardin high-speed camera. Four different types of specimen geometry and loading method were employed to achieve the crack acceleration, deceleration, and/or reacceleration processes in one fracture event. The dynamic stress intensity factor K _ID and crack velocity were obtained in the course of the crack propagation and the corresponding relationship was determined. The effect of the crack acceleration and deceleration on the K _ID-velocity relationships was as follows: (1) the variations of K _ID and the velocity were strongly influenced by the specimen geometry and loading method; (2) the velocity change was qualitatively in accord with K _ID; (3) K _ID for a constant crack velocity was larger when the crack decelerated than it was when the crack accelerated or reaccelerated; (4) K _ID for an acceleration-free crack was uniquely related to the velocity; and (5) K _ID could be expressed as two parametric functions of the velocity and acceleration.     

Effect of T-stress on crack growth under mixed mode I–III loading

For a crack subjected to combined mode I and III loading the influence of a T-stress is analyzed, with focus on crack growth. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyzes are carried out for conditions of small scale yielding, with the elastic solution applied as boundary conditions on the outer edge of the region analyzed. For several combinations of the stress intensity factors K_I and K_III and the T-stress crack growth resistance curves are calculated numerically in order to determine the fracture toughness. In all situations it is found that a negative T-stress adds to the fracture toughness, whereas a positive T-stress has rather little effect. For given values of K_I and T the minimum fracture toughness corresponds to K_III = 0.     

Critique on fracture criteria in mixed-mode-loading

The paper presents an improved formulation of mixed-mode fracture criteria. Both the fracture toughness K_IC and K_IIC are taken into account. Consequently, the crack propagation direction and the fracture envelope in the and plane depends on the toughness ratio . In the plane only one envelope for each criterion is obtained.     

Computer simulated analyses on deformation and fracture of non-cracked and cracked specimens

A unified damage and fracture model, the combinatory work density model, which is suitable for either non-cracked body or cracked body has been suggested^[t−7]. In the present paper, the deformation and fracture of the two kinds of tensile spceimen and TPB specimen made of 40Cr steel have been simulated by using the new model together with the large elastic-plastic deformation finite element method. The results give a good picture of the whole deformation and fracture processes of the specimens in experiments; especially, the results on the TPB specimen can be used to obtain the relationship between load and displacement at the loading pointP-Δ, and between crack extension and displacement at the loading point Δa-Δ, the resistance curveJ _R -Δa and the fracture toughnessJ _1C . All the results are in remarkable agreement with those obtained by experiments. Therefore the model suggested here can be used to simulate crack initiation and propagation in non-cracked body and fracture initiation and crack stable propagation in cracked body. The project supported by National Natural Science Foundation of China     

采用压缩单裂纹圆孔板确定岩石动态起裂、扩展和止裂韧度

爆炸、冲击、地震等人为或自然灾害不可避免,经常造成大量土木工程设施的破坏,因此岩石在动态载荷作用下的行为受到特别关注.岩石动态断裂韧度是评价岩石抵抗裂纹动态起裂、扩展和止裂性能的材料参数,开展岩石动态断裂韧度测试方法的研究对相关理论基础和实验技术的要求较高.岩石动态断裂韧度分为动态起裂、动态扩展、动态止裂三种,虽然关于动态起裂和动态扩展的研究已有一些成果,对岩石动态止裂的研究仍是一个难题,至今几乎无人问津.研究表明,在分离式霍普金森压杆撞击压缩单裂纹圆孔板岩石试样的I型动态断裂试验中,动态起裂、扩展、止裂的全过程可以由黏贴在压缩单裂纹圆孔板试样上的裂纹扩展计监测,岩石的动态起裂、扩展、止裂韧度可以用实验-数值-解析法确定.特别值得一提的是首次测出了岩石的动态止裂韧度.裂纹扩展计信号还显示,压缩单裂纹圆孔板在止裂后,停止的裂纹还会再次动态起裂、扩展并超出裂纹扩展计的检测范围.从能量的角度分析了动态止裂的过程,指出测试动态止裂韧度时要注意的一些问题.结果显示,岩石动态起裂韧度和动态扩展韧度分别随动态加载率和裂纹扩展速度的增大而增大,岩石动态起裂韧度略大于动态止裂韧度.      

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

Fracture toughness of CIP-HIP Beryllium at elevated temperatures

The fracture toughness of CIP-HIP Beryllium was determined using the short bar fracture toughness (K_IcSB) method. The K_IcSB value measured was 10.96 MPa√m at room temperature. This falls well within the expected range of 9 to 12 MPa√m as observed from previous fracture toughness measurements of beryllium. Toughness increased rapidly between 400°F and 500°F reaching a value of 16.7 MPa√m at 500°F.     

Mode II fracture behavior of a Zr-based bulk metallic glass

Shear band formation and fracture are characterized during mode II loading of a Zr-based bulk metallic glass. The measured mode II fracture toughness, K_IIc=75±4 MPa√m, exceeds the reported mode I fracture toughness by ∼4 times, suggesting that normal or mean stresses play a significant role in the deformation process at the crack tip. This effect is explained in light of a mean stress modified free volume model for shear localization in metallic glasses. Thermal imaging of deformation at the mode II crack tip further reveals that shear bands initiate, arrest, and reactivate along the same path, indicating that flow in the shear band leads to permanent changes in the glass structure that retain a memory of the shear band path. The measured temperature increase within the shear band is a fraction of a degree. However, heat dissipation models indicate that the temperature could have exceeded the glass transition temperature for less than 1 ms immediately after the shear band formed. It is shown that this time scale is sufficient for mechanical relaxation slightly above the glass transition temperature.     

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.     

Dynamic mechanical and fracture properties of an infiltrated TiC-1080 steel cermet

The dynamic mechanical and fracture properties of a TiC porous network infiltrated with1080 steel are reported. Following infiltration, the cermet is subjected to various heat treatments that affect essentially the steel matrix. Dynamic compression tests show that the heat treatments increase the fracture strength of the cermet. The quasi-static fracture toughness (K_Ic) is also increased by the heat treatments. The dynamic (initiation) fracture toughness (K_Id) is substantially higher (by about a factor of 3) than its static counterpart. Failure mechanisms consist mainly of cleavage of the TiC and matrix grains, along with minor interfacial decohesion. However, dynamic loading induces substantial damage around the crack tip, consisting essentially of cleavage of TiC grains. Microcrak toughnening is believed to be responsible for the high dynamic toughness of the material. The critical microstructural fracture event is thus identified as the spreading of TiC cleavage microcracks into the neighboring steel grains.     

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

IntroductionStudy on the model of fatigue crack growth rate (da/dN) and measurement of theprobabilistic curves of the model are a basis of the fatigue damage tolerate design and theprobabilistic safety assessment. Some benefit efforts have been made in th…     

Dynamic fracture behavior of ceramics at elevated temperatures by caustics

The fracture behavior of partially stabilized zirconia (PSZ) and silicon-nitride ceramics (Si₃N₄) is investigated under dynamic loading at elevated temperatures up to 1200°C using the caustic method combined with an ultra high-speed camera. The values of the dynamic fracture toughnessK _Id and the crack-propagation fracture toughnessK _ID are obtained, and it is shown that a dynamic effect on these values is observed in PSZ but not in Si₃N₄. The dynamic crack arrest toughnessK _Ia is found to exist for PSZ.