A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

Effect of temperature on the fracture modes of BHW-35 steel under mode-II loading

Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R _o ) exist at an angle of –75. 3° from the original crack plane; the maximum shear stress andR _o = 0 exist along the original crack plane.Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about –90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material.     

Stress intensity factor range and propagation mode of surface cracks under rolling–sliding contact

Finite element analyses were conducted in order to evaluate the mode I and mode II stress intensity factors for inclined edge cracks under cyclic contact load under rolling and rolling–sliding condition. The SIF range depends on crack orientation, crack length to Hertzian contact zone half-width ratio, friction between the crack faces and friction on the contact surface. The results were combined in two compact functions that determine the ΔK_I and ΔK_II values. The crack propagation mode and direction were investigated using both the maximum stress criterion and the minimum strain energy density criterion. The results are displayed in graph form, which allows a fast evaluation of the crack growth condition.     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

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.     

Observations on Mode I and III fracture of steel and PMMA

Considered in this work are the Mode I and III fractures of W18Cr4V steel, 60Si2Mn steel and PMMA specimens. The mixed mode critical stress intensity factor, denoted by K_1f, is shown to be greater than K_1c for Mode I. The ratio K_1f/K_1c depends on the ways in which K₁ and K₃ interact and is affected by the position of the load with reference to the crack position. Analytical and experimental results are presented and discussed in connection with the microfracture surface observed experimentally.     

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.     

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.     

Experimental and Theoretical Assessment of Brittle Fracture in Engineering Components Containing a Sharp V-Notch

A criterion was proposed to predict brittle fracture in engineering components containing sharp V-shaped notches and subjected to mixed mode I/II loading. The criterion, called SV-MTS, was developed based on the maximum tangential stress (MTS) criterion proposed originally for analyzing crack problems. The curves which are obtained from the SV-MTS criterion could be used conveniently to predict the fracture resistance and also the notch bifurcation angle in sharp V-notched components under pure mode II and also mixed mode loading. To evaluate the validity of the proposed criterion, a set of fracture tests were conducted on a new test specimen, called sharp V-notched Brazilian disc (SV-BD), under mixed mode loading conditions. It is shown that the experimental results obtained from PMMA specimens are in very good agreement with the curves of SV-MTS criterion.     

Strip model plasticity analysis of mixed mode crack opening displacement in aluminum alloy LY12

Under mixed mode loading, the crack tip blunts and undergoes displacements in two directions, the normal and shear component corresponding to Mode I and Mode II loading, respectively. These local displacements are determined by the duplicated film method and used to analyze the behavior of mixed mode fracture in aluminum alloy LY12. The mixed mode resultant crack opening displacement (COD) at fracture initiation tends to increase more rapidly with increase of the Mode II shear component. The fracture initiation value of COD for pure Mode II loading is six (6) times greater than that for Mode 1 loading. The same applies to the maximum effective plastic strain crack growth near the crack front. Observed are two typical morphologies, the equal-axes dimples and the parabolic dimples with evidence of slippage as dominated, respectively, by Mode I and Mode II loading.     

A biaxial test specimen for crack arrest studies

A biaxially loaded, single edge notched (SEN) fracture specimen, with mixed modes I and II loading, was used to study the crack arrest capability of a bonded and riveted tear strap without and with simulated multiple site damage (MSD). MSD was modeled by a 50-percent groove without which the running crack would inevitably kink due to K_II loading. A total of thirty-one 2024-T3 aluminum specimens with various crack and MSD configurations were tested. The fracture parameters associated with straight and curved crack paths were determined by using the experimenta results to drive a dynamic finite element model of the specimen in its generation mode. The crack kinking and extension criteria were verified by the excellent agreement between the prediction based on these fracture parameters and the measured crack kinking angles. Comparison between the test results generated by the biaxial stress specimens and by those generated by small- and full-scale pressurized fuselage rupture experiments showed that this specimen can be used to prescreen the effectiveness of tear straps and crack arrestors in an airplane fuselage.     

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.     

Plasticity aspects of interfacial fracture for polymer/glass specimens

Experimental results suggest that the interfacial fracture resistance is minimal for approximate near tip Mode I accompanied by positive and negative near tip Mode II. Finite-strain FE analysis is made for an elastic–plastic medium bonded to an ideally elastic medium with an interface crack. Small-scale plasticity conditions are invoked and examined in relation to the elastic–plastic stress distribution along the bond line. Plasticity engenders a tendency to turn near tip biaxiality towards pure Mode I regardless of the mixed-mode loading. High levels of hydrostatic stress are attained. For different mode mixities of the applied load, the dependence of the elastic–plastic normal bond stress on load level is examined. It is found that under positive Mode II loading, the normal bond stress σ_yy tends to saturate as the load level rises. This does not occur for Mode I and negative Mode II loading. In addition, deformation patterns inside the plastic zone are examined for mixed-mode situations. A displacement criterion based on the normal bond crack opening suggests a dependence of the critical load level on the extent of mixed mode. Under positive mode II fracture, traces of the ductile material are found at the top of the elastic substrate. Some of these conclusions appear to be consistent with the fracture patterns observed for LD-polyethylene/glass interfacial mixed-mode fracture.     

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.     

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK _I , the crack tip biaxiality parameter is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK _I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK _I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.     

Failure modes of specimens containing surface flaws under cyclic torsion

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such a torsional loading may initiate yielding at the outer radius of the shaft or in the fillets. The methods for predicting turbine-shaft fatigue life due to transient loading depent upon the mode of crack growth from an undetected crack. The most common location for the existence of a crack is the fillets or shoulders of the shaft. Specimens were designed from AISI 4340 steel with two diametrically opposed flat surfaces. Initial defect orientations of 0 deg, 45 deg and 90 deg with respect to the sepcimen axis on the fillet were studied. The specimens were subjected to cyclic torsion with zero mean torque and with a torque amplitude necessary to cause yielding at the outer radius of the specimen. When initial defects were aligned with a plane of maximum shear stress (0 deg and 90 deg), the cracks propagated along that plane. For 45-deg defects (aligned to a plane of maximum tensile stress) the crack still propagated along the plane of maximum shear. However, the number of cycles to initiate and to propagate the crack to failure for 45-deg defects were (two to three times) larger than those for 0-deg and 90-deg defects. Mode II and Mode III crack-growth rates were measured from specimens containing 0-deg and 90-deg defects. It was found that the crack-growth rate in Mode II was higher than in Mode III. However, all the specimens failed due to reduction of the net cross section, mostly attributed to Mode III crack growth. Similar results were obtained from specimens of turbine-shaft material (A469 steel), and 2024 aluminum with different rolling directions. Fatigue-crack-growth rates in Mode III were measured from circumferentially notched bar. They were found to be a unique function of ΔK _III alternating stress intensity in Mode III. It was found that the mechanism of crack growth is produced by the formation and linkage of elongated cavities at the crack tip.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material, and to extract the fracture parameters of stress intensity factor K _I and K _II , and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where K _II is not necessarily equal to zero.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.