Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen

A brittle fracture criterion is proposed for predicting fracture toughness of U-shaped notches under pure mode II loading. The criterion, called UMTS, is developed based on the maximum tangential stress (MTS) criterion. The UMTS criterion can be generally used for determining the mode II fracture toughness of U-notched components as well as the fracture initiation angle in U-shaped notches under pure mode II loading. To verify the validity of the proposed criterion, a set of experiments were carried out on the U-notched Brazilian disc (UNBD) specimens made of PMMA and also soda-lime glass. It is shown that there is a good agreement between the results of the UMTS criterion and the experimental results both for fracture toughness and for the fracture initiation angle under pure mode II conditions.     

用短棒试件测试无烟煤的动态断裂韧度

介绍了设计的新型圆台式压头及配套的衬片加载部件,推导了采用新的加载部件进行冲击断裂实验时的断裂韧度计算公式。采用SHPB实验装置,用新加载部件对带有V形切口的无烟煤短棒试件的裂纹尖端施加拉伸载荷,测定了无烟煤的动态断裂韧度。结合准静态实验数据得到了无烟煤断裂韧度随加载率lg(dF/dt)的总体变化规律:当lg(dF/dt)6时,无烟煤的断裂韧度缓慢上升,但当lg(dF/dt)6以后,无烟煤的断裂韧度随加载率的增加快速增大。实验表明:圆台式加载比刀刃式加载更具优越性和适应性,是测试岩石类材料短棒试件动态断裂韧度较好的方法。     

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.     

An analytical and experimental stress analysis of a practical mode II fracture test specimen

A boundary-collocation method has been employed to determine the Mode II stress-intensity factors for a pair of through-the-thickness edge cracks in a finite isotropic plate. An elastostatic analysis has been carried out in terms of the complete Williams stress function employing both even and old components. The results of the numerical analysis were verified by a two-step procedure whereby the symmetric (Mode I) and antisymmetric (Mode II) portions of the solution were independently compared with existing solutions. Since no previous analytical solutions existed for the asymmetric loading of an edge-cracked plate, the complete solution was verified by comparison with a photoelastic analysis. A compact shear (CS) specimen of Hysol epoxy resin was loaded in a photoelastic experiment designed to study the isochromatic-fringe patterns resulting from the Mode II crack-tip stress distribution. The experiment verified that a pure mode II stress distribution existed in the neighborhood of the crack tips, and confirmed the accuracy of the boundary-collocation solution for the Mode II stress-intensity factors. Specimen center-line stress-distribution data were obtained photoelastically and employed to refine the boundary-collocation analysis. Agreement between the analytically and experimentally determined Mode II stress-intensity factors was excellent.     

An edge-cracked Mode II fracture specimen

A proposed edge-cracked Mode II fracture specimen is analyzed using an extended photoelastic-numerical procedure. It is shown that the Mode II stress-intensity factor is significantly higher for the longest edge-crack considered and the Mode I deformation is negligible, demonstrating the merits of this specimen for Mode II fracture-toughness testing.     

Material fracture toughness determination for polyethylene pipe materials using small scale test results

The Small-Scale Steady State (S4) test has been recently developed in order to assess the fracture behaviour of polyethylene (PE) gas distribution pipe material during rapid axial crack propagation. Based on an investigation of the S4 test, a simulation model of S4 test has been developed. This paper describes the use of the results obtained from the S4 test and program modified from PFRAC (Pipeline Fracture Analysis Code) to evaluate the fracture toughness of the material,G, which could not be directly obtained from the test, and to predict critical pressure,p _c , for rapid crack propagation (RCP) in a full scale PE pipe. The algorithms for contact conditions are developed to consider the opening pipe wall impact against a series containment rings and the capabilities of PFRAC are also extended. WhenG _d is evaluated, investigations are made on the effect of temperature, wall thickness and crack velocity. In addition, procedures to evaluate the critical pressure for the S4 test pipe are also discussed.     

Computation of V-notch shape factors in four-point bend specimen for fracture tests on brittle materials

Four-point bend (FPB) specimen is an important test sample in mixed mode fracture study of notched components made from brittle materials like rocks, brittle polymers, ceramics, etc. On the other hand, the notch stress intensity factors (NSIFs) are vital parameters in brittle fracture assessment of V-notched structures. Therefore, computation of NSIFs in FPB specimens is of practical interest to engineers and researchers. Since the available methods for calculating the NSIFs are often cumbersome and need complicated calculations, it is preferred to show them as a set of dimensionless parameters for the FPB specimen. In this research, the finite element method coupled with a recently developed algorithm called FEOD is employed to calculate the NSIFs of a FPB specimen for several V-shape notches and for different combinations of mode I and mode II. The obtained NSIFs are then converted to dimensionless parameters called notch shape factors and are illustrated in a number of figures. It is shown that depending on the notch depth and the location of loading points, full mode mixity from pure mode I to pure mode II can be provided in the FPB specimen. The numerical results obtained in this research are verified by using very limited results reported earlier in literature.     

On the fracture toughness of ferroelastic materials

The toughness enhancement due to domain switching near a steadily growing crack in a ferroelastic material is analyzed. The constitutive response of the material is taken to be characteristic of a polycrystalline sample assembled from randomly oriented tetragonal single crystal grains. The constitutive law accounts for the strain saturation, asymmetry in tension versus compression, Bauschinger effects, reverse switching, and strain reorientation that can occur in these materials due to the non-proportional loading that arises near a propagating crack. Crack growth is assumed to proceed at a critical level of the crack tip energy release rate. Detailed finite element calculations are carried out to determine the stress and strain fields near the growing tip, and the ratio of the far field applied energy release rate to the crack tip energy release rate. The results of the finite element calculations are then compared to analytical models that assume the linear isotropic K-field solution holds for either the near tip stress or strain field. Ultimately, the model is able to account for the experimentally observed toughness enhancement in ferroelastic ceramics.     

Crack-stability analysis and fracture toughness of ceramic bend bars with a modified circular cross section

Previous analysis has shown that the round bend bar is more stable than the rectangular bend beam. The geometry of the round bend bar was slightly modified to permit precracking of ceramic bars for subsequent fracture-toughness testing. Stability solutions of this new modified round bend bar were found as a function of precrack length for several machine-compliance values. A threshold crack length was determined which predicted the transition from unstable to stable fracture behavior. Experiments with silicon nitride and alumina specimens verified the results of the analysis.     

Experimental determination of fracture toughness of CFRP by Raman Coating Method

Summary  Strain distribution near the crack tip of Raman-inactive Carbon Fiber Reinforced Plastics (CFRP) was measured by Raman spectroscopy. A PbO thin film was deposited on the measured surface of the specimen by physical vapor deposition (PVD). The results agree well with those obtained by conventional experimental methods and FEM analysis. The proposed method allows to investigate fracture toughness of Raman-inactive materials. Received 8 December 1999; accepted for publication 28 March 2000     

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.     

Empirical assessment of ductile fracture initiation in steel bars with notch and three-point bend specimen with edge crack

Proposed is a parameter defined to characterize the onset of macrocrack initiation in notched steel bars and cracked three-point bend specimens. It accounts for stress triaxiality and damage by plasticity reflected via the effective plastic strain. Results are obtained for notched round bars made of 20#, A3, DE36I and DE36II steel by assuming that the stress triaxiality increases with increasing effective plastic strain; they are compared with the results by letting the stress triaxiality to be constant. Use are made of experimental data on the necking of tensile bars. The parameter corresponding to the onset of ductile fracture were found to be nearly constant. Since the local effective plastic stress can be related to the crack tip opening (COD) distance, the same procedure can be applied to evaluate fracture initiation in three-point bend specimens with an edge crack. It is found that the COD in AS1204-350 and AS1405-180 structural steels decreased with increasing stress triaxiality.     

CTS试样I/II混合型断裂特性数值计算研究

采用CTS试样研究I/II混合型断裂特性计算裂纹前缘应力强度因子时可采用解析公式,一旦裂纹发生扩展,解析公式便不再适用。文中采用有限元法研究紧凑拉伸剪切（CTS）试样在I/II平面混合型加载下的裂纹扩展行为。采用ANSYS建立CTS试样I/II混合型测试系统有限元模型,为模拟真实受力状态,在CTS试样-销-扇型夹具以及扇型夹具-销-U型夹具之间分别建立接触对进行接触力学分析。通过与解析公式结果进行对比验证了该数值方法的可靠性。采用最大环向应力准则（MTS）,模拟了CTS试样不同加载角度下的裂纹扩展路径,获得了裂纹扩展路径中应力强度因子随裂纹长度的变化曲线,解释了裂纹扩展路径不与外载荷方向垂直的原因。结合文中计算结果,在CTS试样I/II混合型裂纹扩展速率实验测得裂纹长度与寿命的关系曲线a-N的基础上,便可得到材料I/II型混合型裂纹扩展速率曲线。     

On fracture toughness of orthotropic metallic materials under cyclic loading

AVT-6 titanium alloy rolled sheet, which is initially isotropic and subject to kinematic hardening, is used as an example to analyze the effect of kinematic hardening on crack growth resistance under uniaxial cyclic loading. Crack growth resistance is characterized by the number of cycles to failure, critical crack length, and critical stress intensity factor. The subject of study is plane specimens with an edge notch. It is shown that prestrain changes the anisotropy of the specimens, which is determined as the ratio of the crack growth resistance in the rolling direction to that in the transverse direction. The crack path under a load applied at an angle to the axes of anisotropy is studied     

Pure mode II fracture characterization of composite bonded joints

A new data reduction scheme is proposed for measuring the critical fracture energy of adhesive joints under pure mode II loading using the End Notched Flexure test. The method is based on the crack equivalent concept and does not require crack length monitoring during propagation, which is very difficult to perform accurately in these tests. The proposed methodology also accounts for the energy dissipated at the Fracture Process Zone which is not negligible when ductile adhesives are used. Experimental tests and numerical analyses using a trapezoidal cohesive mixed-mode damage model demonstrated the good performance of the new method, namely when compared to classical data reduction schemes. An inverse method was used to determine the cohesive properties, fitting the numerical and experimental load–displacement curves. Excellent agreement between the numerical and experimental R-curves was achieved demonstrating the effectiveness of the proposed method.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

On the temperature dependence of fracture toughness in the brittle-to-ductile transition region

A method for calculation of fracture toughness in the brittle-to-ductile transition region is proposed for a known fracture toughness at a given temperature and a known temperature dependence of the yield point. A two-parameter quasi-brittle fracture criterion proposed earlier is employed. This criterion contains in explicit form a plastic constraint factor that is sensitive to temperature variation under plane strain conditions. The obtained calculation dependence is compared with experimental data for four structural steels. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 80–86, April, 1999.