A method to determine the fracture toughness of unidirectional fibre reinforced composites in mode II (forward shear), using a thin tubular specimen

A method has been developed, using thin tubular specimens, to determine the fracture toughness of unidirectional fibre reinforced composites in Mode II. The tubular specimens were loaded under torsion and hence produced pure shear at the crack tips located on the circumference of the tube. The cracks were made parallel to the transverse axis and in the mid-length of the tube. Calibration factors for Mode II were obtained. The stress-intensity factors at instability, K_IIR(INS) were obtained by experiments on thin tubular specimens through a compliance matching procedure. The crack growth resistance at instability and the corresponding initial strain energy release rates were independent of the initial crack in the range of crack length investigated. The stress-intensity factor obtained by the thin torsion tube method is slightly higher than the stress-intensity factor at instability, K_IIR(INS) obtained by the method developed by Giare for end cracked beams [Engng. Fracture Mech. 20, 11–21 (1984)]. This method may be applied to a different geometrical shapes and hence may be useful in determining the fracture toughness of any closed geometrical sections.     

Toughening polymeric composites using nanoclay: Crack tip scale effects on fracture toughness

Fracture behavior of vinyl ester resin and the methods that can be used to toughen vinyl ester resin were studied. Neat resin, 5% by weight nanoclay, 5% by weight core shell rubber (CSR) and hybrid system (3% nanoclay and 2% CSR by weight) were the material systems considered for comparing fracture toughness. Three types of cracks were used to determine the stress intensity factors at failure, viz., sharp crack, blunt crack and notch. The critical stress intensity factor in the case of sharp cracks improved significantly when compared to neat resin. In the case of notched and blunt cracked specimens, a reduction in stress intensity factors (at failure) was observed for reinforced systems. However, for notched and blunt cracked specimens, it was shown from the morphology of the fracture surface that the stress intensity factor calculated by assuming a notch or a blunt crack as an ideal crack was not the controlling parameter for fracture. A method for quantifying the crack tip sharpness using fracture surface roughness has been proposed.     

Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of a tensile crack propagating in a brittle material is studied within Linear Elastic Fracture Mechanics theory. The Griffith energy criterion and the principle of local symmetry provide necessary conditions for the onset of dynamic branching instability and for the subsequent paths of the branches. The theory predicts a critical velocity for branching and a well defined shape described by a branching angle and a curvature of the side branches. The model rests on a scenario of crack branching based on reasonable assumptions and on exact dynamic results for the anti-plane branching problem. Our results reproduce within a simplified 2D continuum mechanics approach the main experimental features of the branching instability of fast cracks in brittle materials.     

Multiscale modeling of dynamic crack propagation

A multiscale approach is employed to investigate a center-cracked specimen with the purpose to redefine fracture toughness from the atomistic perspective and to simulate different modes of crack propagation. The specimen is divided into three regions: (1) far field, modeled by classical fracture mechanics, (2) near field, modeled by a multiscale field theory and analyzed by a generalized finite element method, and (3) crack tip atomic region, modeled by molecular dynamics (MD). The exact and analytical solution of the far field is utilized to specify boundary conditions at the interface between the far field and the near field. The interaction between the near field and the crack tip region is described by full-blown interatomic forces. In this work, crystals of perovskite (Barium Titanate) and rocksalt (Magnesia) have been studied. Fracture toughness is defined as a material property associated with instability of the MD simulation. Mode I, Mode II, and mixed mode fracture have been investigated and numerical results will be presented and discussed.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

单向静压下柱状炮孔端部爆生裂纹的扩展规律

高地应力对岩层地下工程爆破动态断裂过程有重要影响。采用数字激光动态焦散线测试系统,研究了不同单向静压下柱状炮孔端部爆生裂纹动态断裂行为,明确了柱状炮孔端部爆生裂纹的扩展规律。结果表明:单向静压越大,端部裂纹平均扩展长度越短,但单向静压下端部裂纹尖端积聚能量的快速释放会导致裂纹初始扩展速度提升;裂纹尖端应力强度因子基本随单向静压增加而递减,单向静压越大,应力强度因子随时间下降越剧烈,裂纹的止裂韧度越高,止裂时间越早;单向静压作用下的爆生裂纹在整个扩展阶段基本表现为I型裂纹,无静压作用下爆生裂纹在扩展初期表现为I型裂纹,中后期表现为复合型裂纹。研究结果对认识静压作用下的柱状炮孔端部破坏机理具有一定意义。     

Experimental Determination of Fracture Toughness of CFRP in Mode II by Raman Spectroscopy

Fracture toughness of Mode II of carbon fiber reinforced plastic (CFRP) was investigated using end notched flexure (ENF) specimens and a Raman coating method. Distribution of shear strain near the crack tip of CFRP was measured by Raman spectroscopy. A thin film of PbO on the measured surface of the ENF specimen was deposited by physical vapor deposition (PVD) as pretreatment to measure the strain by Raman spectroscopy. Fracture toughness of CFRP in Mode II was determined using the Raman results. The results coincided closely with those measured by the compliance method and FEM analyses (finite element method).     

单边切口薄板研究聚乙烯醇纤维增强水泥基复合材料断裂韧性

利用单边切口薄板对配制的聚乙烯醇纤维增强水泥基复合材料进行单轴直接拉伸试验研究,得到硬化的荷载-裂缝张开位移全曲线。通过试验观察到缺口尖端处出现呈发散状的多条微小裂纹,部分试件在远离切口处还有多条裂缝出现,并不像混凝土或水泥净浆这类半脆性、脆性材料只有单条裂缝并沿着单条路径开裂,因此,适用于应变软化材料的双K断裂理论以及断裂能理论不能直接用在应变已经发生假硬化的材料中。鉴于上述原因,该文提出起裂断裂韧度和耗散能两个韧性评价指标。     

FATIGUE CRACK GROWTH LAWS FOR BRITTLE AND DUCTILE MATERIALS INCLUDING THE EFFECTS OF STATIC MODES AND ELASTIC-PLASTIC DEFORMATION

A fatigue crack growth damage accumulation model is used to derive laws for the fatigue crack growth rates of brittle and ductile materials. The damage accumulated during cyclic loading is assumed to be proportional to the cyclic change in the plastic displacement in the crack tip yielded zone. The static mode contribution to the fatigue damage is assumed to be proportional to some power of the crack tip displacement. The laws are applicable in either the small or large scale yielding regimes provided that the stress ratio remains positive. Static modes are assumed to be controlled by the fracture toughness value in brittle materials, and by the gradient of the crack growth resistance curve in ductile materials. In the analysis of ductile materials it is assumed that the crack growth resistance of the material is not significantly altered by fatigue crack growth.
The growth rate equations are expressed in terms of the near field value of the J -integral, i.e. the value which would be calculated from assuming the material deformed in a non-linear elastic manner during the increasing load part of the fatigue cycle. Examples are given of the predictions of the growth law for ductile materials. It is predicted that after the initiation of stable tearing the crack growth rate, when expressed in terms of the cyclic change in the stress intensity factor, depends on both the structural geometry and the degree of crack tip plastic deformation. In both brittle and ductile materials the fatigue crack growth rate is predicted to accelerate as the failure criteria relevant to static crack instability are approached.     

Brittle fracture in a ductile material with application to hydrogen embrittlement

A physical model of fracture in materials is developed which features a brittle crack imbedded in a plastically deformed medium. This model is presented as an alternative to fully ductile failure by hole growth, and general criteria for the two alternatives are discussed. One of these criteria for the existence of an atomically sharp crack is that the dislocation content near the crack tip be limited by the inhomogeneous character of dislocation slip in the crystal. With the dislocation distribution characteristic of Mode III fracture, we derive expressions for the fracture toughness as a function of material parameters. We have extended the theory to the case of hydrogen embrittlement in steels and compare our theoretical predictions with experimental work by others.     

Cleavage failure of transformer storage tank under dynamic rates of loading: Influence of base plate and weldment microstructure and toughness

A high capacity transformer storage tank that was in service for more than a decade ruptured due to an explosion and a visual examination showed that the fracture facets were essentially brittle in nature with little evidence of plastic deformation. Fracture occurred mainly along weld seam; however, there were sharp cracks even in the base plate. Present study is a focused effort to find reasons for this brittle behavior of normally ductile steel. This entailed an in-depth metallographic examination of samples, selectively cut out from the tank walls and fractured weldments, supplemented by characterization of hardness, tensile, ductility and toughness properties. Results indicate that base plate and weld metal meet the required specifications for static design but not for the dynamic loading experienced under this failure mode (i.e. cleavage). Under dynamic loading conditions, the weld metal is the weakest link in terms of toughness and resistance to crack propagation. The need for adopting modern strong, tough, weldable steels to the construction of these tanks are pointed out.     

Loading Rates and the Dynamic Initiation Toughness in Brittle Solids

The experimentally determined marked rise of the stress intensity factor required to initiate crack propagation in brittle solids under variably high loading rates, is analyzed. This problem of fracture initiation at the tip of a crack is considered in terms of activating a flaw at some distance away from the tip. By using a semi-infinite crack in an unbounded two-dimensional solid subjected to spatially uniform but temporally varying crack-face pressure, we consider the evolution of stress at the failure initiation site. Fracture initiation is assumed synonymous with attaining a critical stress at the fracture site. The results conform to typical experimental data of dynamic crack initiation in brittle solids.     

A Finite Fracture Mechanics approach to the asymptotic behaviour of U‐notched structures

A Finite Fracture Mechanics (FFM) criterion is formalized to predict the critical failure loads of brittle U‐notched specimens, subjected to mode I loading. The criterion, recently applied to V‐notched structures, requires the contemporaneous fulfilment of stress requirements and energy conditions for fracture to propagate: the stress field ahead of the notch tip and the stress intensity factor related to a crack stemming from the root are involved. Both the apparent fracture toughness and the critical crack advancement result to be structural parameters. For sufficiently slender notches, the root radius becomes the only relevant geometric dimension. The consistency of the approach is proved by the comparison with experimental data available in the Literature.     

Fracture behaviour of PC/ABS resin under mixed-mode loading

Fracture behaviour of polycarbonate (PC)/acrylonitrile-butadiene-styrene (ABS) under mixed-mode loading conditions was studied for several weight fractions of PC and ABS. Mode I and mixed-mode fracture tests were carried out by using compact–tension–shear specimens. At a certain value of mixed-mode loading ratio K _II / K _I a crack of the shear type will initiates at the initial crack tip. Fracture toughness increases under mixed-mode loading with an increase in the mode II component, whereas it reduces with the appearance of a shear-type fracture. Fracture toughness and the appearance of a shear-type fracture depends on the blending ratio of PC and ABS. The transition to shear-type fracture occurs at lower value of K _II / K _I for resins with higher fracture toughness.     

Interlaminar fracture toughness of CFRP in Mode I and Mode II determined by Raman spectroscopy

Fracture toughness of multidirectional Carbon Fiber Reinforced Plastics (CFRP) for Mode I and Mode II was investigated using Double Cantilever Beam (DCB), End Notched Flexure (ENF) specimens and Raman Coating Method. The distribution of strain near the crack tip of CFRP was measured by Raman spectroscopy. Thin films of PbO on the measured surface of the DCB and ENF specimens were deposited by physical vapor deposition as the pretreatment to measure the strain by Raman spectroscopy. The fracture toughness of multidirectional CFRP in both Mode I and Mode II was determined using the results measured by Raman spectroscopy. This result coincided with those measured by conventional methods.     

Modes of dynamic shear failure in solids

The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

An explicit elastic solution for a brittle film with periodic cracks

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a “weak form stress boundary condition” at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth’s exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.     

THE PROBLEM OF SCATTER OF FRACTURE TOUGHNESS DATA

The authors studied the influence of the conditions for growing an initial fatigue crack on the scatter of fracture toughness data determined under static loading. It was found that the values of static fracture toughness for cyclically softening steels at temperatures below the brittle-to-ductile transition are essentially dependent on the degree of the material fatigue damage in the vicinity of the crack tip during the final stage of crack initiation. A method is proposed for evaluating the fracture toughness under static loading which makes it possible to take into account the material damage in the vicinity of the crack tip.