Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

巴西圆盘泥岩试件裂纹扩展及应变演化实验研究

为了研究准静态加载条件下岩石试件巴西劈裂裂纹扩展规律,采用MTS试验机进行准静态加载,同时用高速摄像机记录裂纹扩展过程。采用白光数字散斑处理软件对摄像机记录的照片进行处理,得到试件裂纹扩展过程中应变场的演化情况。通过实验和分析可以看出,由于端部效应及加载方式的原因,因此裂纹起裂点在底部加载部位;泥岩试件表面裂纹的平均扩展速度为252m/s;岩石的非均质性即内部微缺陷、微裂纹使得泥岩试样的开裂并不是沿着中心直径方向,而是偏离一定的角度,初始偏离角度约为17°。裂纹扩展过程可以划分为三个阶段:泥岩试件宏观变形阶段(宏观无裂纹)、宏观裂纹稳定扩展阶段、宏观裂纹动态张裂阶段。同时,在裂纹扩展过程中,表面第一主应变场、水平位移场等变化明显,在开裂部位第一主应变最大。通过对圆盘泥岩试件裂纹扩展实验研究,可为研究岩石破裂及其演化规律提供依据。     

Effect of rising elastic modulus in surface layer on stress intensity and gradient

The relaxation element method is applied to obtain the stress field around a crack under normal tension. A surface layer is assumed to surround the crack periphery taken to be in the shape of a narrow ellipse. The elastic modulus within this layer increases from zero to the bulk value of the medium outside. Calculations show that the stresses are finite at the crack tip; they reach a maximum in the layer and then decay to the well known solution of Griffith outside the layer. The influence of plastic deformation on the crack front stresses can also be simulated by the surface layer model. Stress concentration at the crack front is found to be lower when plastic deformation takes place. Sharp decay of stress next to the crack is accompanied by increase of local stress gradients. Severity of the local stress fluctuation depends on the width of the crack surface layer.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

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.     

A Study of Large Plastic Deformations in Dual Phase Steel Using Digital Image Correlation and FE Analysis

Large plastic deformation in sheets made of dual phase steel DP800 is studied experimentally and numerically. Shear testing is applied to obtain large plastic strains in sheet metals without strain localisation. In the experiments, full-field displacement measurements are carried out by means of digital image correlation, and based on these measurements the strain field of the deformed specimen is calculated. In the numerical analyses, an elastoplastic constitutive model with isotropic hardening and the Cockcroft–Latham fracture criterion is adopted to predict the observed behaviour. The strain hardening parameters are obtained from a standard uniaxial tensile test for small and moderate strains, while the shear test is used to determine the strain hardening for large strains and to calibrate the fracture criterion. Finite Element (FE) calculations with shell and brick elements are performed using the non-linear FE code LS–DYNA. The local strains in the shear zone and the nominal shear stress-elongation characteristics obtained by experiments and FE simulations are compared, and, in general, good agreement is obtained. It is demonstrated how the strain hardening at large strains and the Cockcroft–Latham fracture criterion can be calibrated from the in-plane shear test with the aid of non-linear FE analyses. An erratum to this article can be found at     

Strain field associated with brittle-fracture propagation in wide steel plates

The results of an experimental investigation concerned with the study of the strain field surrounding a brittle fracture propagating across a wide steel plate are presented in this paper. The data were obtained from tests of 6-ft wide steel plates that were instrumentated to measure surface strain and crack speed. The plates were tested at an average net applied stress of 19,000 psi, a temperature of about ?5° F, and with the notch-wedgeimpact method for fracture initiation. Several plates were tested under similar conditions and the results were superimposed to give a representative picture of the strain distribution on the surface of a plate in the region of the tip of a propagating fracture. Contours of the maximum principal strain for various lengths of crack are presented. The studies indicate that for this particular specimen geometry and associated test conditions, the strain field surrounding the tip of the advancing fracture remains essentially unchanged after traversing about one-third of the width of a 6-ft wide plate.     

基于数字散斑相关法的紧凑拉伸试样断裂韧性实验研究

本文采用数字散斑相关方法对2A12T4铝合金紧凑拉伸试样的断裂韧性进行了实验研究。应用数字散斑相关方法计算了实验过程中试样的应变场、应力场以及位移场。针对实验所得的结果以及紧凑拉伸试样的裂纹特征,采用了矩形积分路径。选择沿裂纹方向和垂直裂纹方向的J积分路径,并且推导出各方向上J积分的数值计算公式。根据推导得到的公式选择不同的积分路径进行J积分的计算,得到了断裂韧性J0积分路径的合理选择范围,同时验证了J积分的路径守恒性。然后根据所得的路径选择标准,选择合理的积分路径,计算出2A12T4铝合金断裂韧性J0的值。将所得结果与国标计算的J0值对比,误差为1.22%,说明了此种方法的正确性。从而为数字散斑相关方法在紧凑拉伸试样断裂韧性的测试研究中提供参考。     

塑性动态断裂实验研究

本文利用自制的实验装置,对韧性材料在爆炸冲击载荷作用下的塑性动态断裂特性,进行了实验研究,其中包括高塑性应变速率下,塑性区裂纹扩展过程和扩展速度的测试;塑性动态断裂韧性CTOD,及其在不同裂纹扩展速度下变化规律的测试。同时,对不同裂纹扩展速度的试件断口进行微观分析。     

Laser speckle decorrelation as a noncontact method for brittle-ductile fracture differentiation

Quasi-static fracture in four-point-bend specimens of both brittle and ductile materials was examined using a method which required only photographic access to the specimen surface. Decorrelation of laser speckle patterns was used as a means to map out two-dimensional regions of high surface strain associated with crack propagation. ASTM A515 grade 70 steel was tested, at temperatures above and below its brittle-ductile transition temperature, by double-exposure speckle photography of the area ahead of the crack tip. The regions where the two speckle patterns were uncorrelated, determined by pointwise spatial filtering of the speckle interferograms, have been observed and are related to plastic deformation of the specimen surface near the crack tip. A subsequent comparison of the decorrelation zones resulting from brittle versus ductile states showed differences as expected in both zone size and shape.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

Process zone in the Single Cantilever Beam under transverse loading - Part II: Experimental

This paper describes an experimental arrangement to evaluate stress/strain fields in the process zone of asymmetric adhesively bonded joints. A transparent polycarbonate flexible beam was bonded to an aluminium alloy rigid block with an epoxy adhesive in a Single Cantilever Beam (SCB) configuration. The flexible adherend was loaded in the direction parallel to the initial crack front at constant rate. To monitor strains induced by bending and shear along the beam, electric strain gauges were attached to the upper surface of the flexible adherend. Thus strain distribution was measured above the bonded surface, which could be used to monitor crack propagation and investigate stress redistribution in the process zone. A Timoshenko beam lying on a Pasternak elastic foundation model was used for the analysis of experimental findings. Subsequently, the Digital Image Correlation technique was used to measure the flexible substrate in-plane displacement field in the vicinity of the crack front and to assess the specimen kinematics. We found that strain gauge instrumentation of the fracture mechanics specimen was a very sensitive technique for experimental analysis of crack propagation under complex loading, offering fine investigation of stress distribution in the cohesive zone.     

Improved model of the griffith crack

The plane-stress state of a cracked continuous medium in tension is determined using relaxation elements. The stress state is analyzed at the tip of a crack surrounded by a plastically deformed material as a band of localized plastic deformation (LPD) shaped like an elongated ellipse. The plastic deformation considerably decreases the stress concentration at the crack tip. As the localization of the plastic deformation increases, the stresses at the crack sides decrease to zero. The decrease in stresses at the tip is accompanied by an increase in the concentration and gradients of the stresses at the end of theLPD band. Here the region of perturbation of the stress field is comparable with the width of the band. Institute of Physics of Strength and Materials Science, Tomsk 634055. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 132–141, November–December, 1998.     

A multiscale model for the ductile fracture of crystalline materials

In this paper, a multiscale model that combines both macroscopic and microscopic analyses is presented for describing the ductile fracture process of crystalline materials. In the macroscopic fracture analysis, the recently developed strain gradient plasticity theory is used to describe the fracture toughness, the shielding effects of plastic deformation on the crack growth, and the crack tip field through the use of an elastic core model. The crack tip field resulting from the macroscopic analysis using the strain gradient plasticity theory displayes the 1/2 singularity of stress within the strain gradient dominated region. In the microscopic fracture analysis, the discrete dislocation theory is used to describe the shielding effects of discrete dislocations on the crack growth. The result of the macroscopic analysis near the crack tip, i.e. a new K-field, is taken as the boundary condition for the microscopic fracture analysis. The equilibrium locations of the discrete dislocations around the crack and the shielding effects of the discrete dislocations on the crack growth at the microscale are calculated. The macroscopic fracture analysis and the microscopic fracture analysis are connected based on the elastic core model. Through a comparison of the shielding effects from plastic deformation and the discrete dislocations, the elastic core size is determined.     

Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials

The plane strain elastic-plastic state at a crack tip is determined for compact tension, bend, double edge-cracked and centre-cracked specimens using a finite element method with triangular constant-strain elements. The solutions are found to differ by 10 to 30 per cent at the ASTM-limit as regards fracture surface displacement, normal stress and plastic zone size. In order to bring the boundary layer solution for the crack problem into agreement with the solution for a specific specimen one has to modify this solution. The modification consists of an addition to the boundary tractions for the boundary layer problem of tractions corresponding to the non-singular, constant second term in a series expansion of the normal stress parallel to the crack plane.     

一种基于SHTB的Ⅱ型动态断裂实验技术

冲击剪切载荷作用下动态断裂韧性的测定是材料力学性能和断裂行为研究中重要组成部分.为了测定材料的Ⅱ型动态断裂韧性,许多学者采用不同的试样与实验方法进行了实验,但限于实验条件,裂纹断裂模式往往是I+Ⅱ复合型,而不是纯Ⅱ型,因而不能准确测得材料的Ⅱ型动态断裂韧性.鉴于此,本文基于分离式霍普金森拉杆(split Hopkinson tension bar,SHTB)实验技术,提出一种改进的紧凑拉伸剪切(modified compact tension shear,MCTS)试样,通过夹具对MCTS试样施加约束,从而保证试样按照纯Ⅱ型模式断裂.采用实验-数值方法对MCTS试样动态加载过程进行分析,将实验测得的波形输入有限元软件ANSYS-LSDYNA,得到了裂纹尖端应力强度因子-时间曲线,并与紧凑拉伸剪切(compact tension shear,CTS)试样进行了对比.同时采用数字图像相关法进行了实验,验证了有限元分析结果.结果表明,MCTS试样在整个加载过程中K_I K_Ⅱ,裂纹没有张开;而CTS试样在同样的加载过程中K_IK_Ⅱ,出现裂纹张开现象.这说明MCTS试样能够准确地测定材料的Ⅱ型动态断裂韧性,为材料动态力学测试提供了一种有效的实验技术.     

The effect of notches on the fracture behavior in NiTi shape memory alloys

Tensile fracture experiments have been performed on double-notch plate form specimens with different notch types and sizes. Specimen without notch is also studied. The macro-mechanical responses as well as detail examination of the fracture surface have been carried out. The stress, plastic strain and phase transformation fields are analyzed by finite element (FE) simulations using a pseudoelastic constitutive model which considers the permanent plastic deformation. Experimental results show that different type of notches can influence not only the macro-mechanic pseudoelastic but also plastic behaviors of the specimens. Both notch type and notch size affect the mechanism of crack initiation. Notch size influences the specimen behavior in different way for different type of notches. Most of the experimental observations are interpreted properly by the FE results.     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

裂纹动态起始问题的研究进展

力图就前人提出的冲击载荷下裂纹的起始判据进行较全面的综述．这些较著名的判据有：（１）动态应力强度因子判据；（２）动态Ｊ积分判据；（３）最小作用量判据；（４）极小作用时间判据等．简要介绍了近年来有关裂纹在冲击载荷（特别是短脉冲）下动态起始的一些重要实验和实验中所发现的一些重要结论．实验公认，一般对于小范围屈服而言，材料的动态断裂韧性随加载（应变）率的提高而减小，此时材料的断裂形式为解理型；而对于大范围屈服则韧性随加载率的提高而增大，此时材料的断裂形式为纤维型．特别指出，Ｂｒｏｗｎ大学的平板撞击实验表明，裂纹在起始时，观察到一个不再满足二分之一阶奇异性的“尖峰”，按Ｃｌｉｆｔｏｎ和Ｆｒｅｕｎｄ等人所给出的模型，在裂纹起始断裂瞬间，在裂纹顶端会突然形成一个小洞，该洞的半径作为一个参数等于二相粒子的间距．