Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method

A new experimental technique has been developed to investigate the onset of fracture in metals at low and intermediate stress triaxialities. The gage section of a flat specimen has been designed such that cracks are most likely to initiate within the specimen center, remote from the specimen boundaries. Along with the specimen, a biaxial testing device has been built to apply a well-defined displacement field to the specimen shoulders. The stress state within the specimen is adjusted by changing the biaxial loading angle. Using this new experimental technique, the crack initiation in metals can be studied experimentally for stress triaxialities ranging from 0.0 to 0.6. The stress and strain fields within the specimen gage section are determined from finite element analysis. The reliability of the computational model of the test set-up has been verified by comparing the simulation results with laser speckle-interferometric displacement measurements during testing. Sample experiments have been performed on the Al-7Si-Mg gravity die casting alloy. A three-step hybrid experimental–numerical calibration procedure has been proposed and applied to determine a phenomenological crack formation criterion for the Al-7Si-Mg alloy.

Non-local theory solution for in-plane shear of through crack

A non-local theory of elasticity is applied to obtain the plane strain stress and displacement field for a through crack under in-plane shear by using Schmidt's method. Unlike the classical elasticity solution, a lattice parameter enters into the problem that make the stresses finite at crack tip. Both the angular variations of the circumferential stress and strain energy density function are examined to associate their stationary value with locations of possible fracture initiation. The former criterion predicted a crack initiation angle of 54° from the plane of shear for the non-local solution as compared with about 75° for the classical elasticity solution. The latter criterion based on energy density yields a crack initiation angle of 80° for a Poisson's ratio of 0.28. This is much closer to the value that is predicted by the classical crack tips solution of elasticity.     

Measurement of the Residual Stress Tensor in a Compact Tension Weld Specimen

Neutron diffraction measurements have been performed to determine the full residual stress tensor along the expected crack path in an austenitic stainless steel (Esshete 1250) compact tension weld specimen. A destructive slitting method was then implemented on the same specimen to measure the stress intensity factor profile associated with the residual stress field as a function of crack length. Finally deformations of the cut surfaces were measured to determine a contour map of the residual stresses in the specimen prior to the cut. The distributions of transverse residual stress measured by the three techniques are in close agreement. A peak tensile stress in excess of 600 MPa was found to be associated with an electron beam weld used to attach an extension piece to the test sample, which had been extracted from a pipe manual metal arc butt weld. The neutron diffraction measurements show that exceptionally high residual stress triaxiality is present at crack depths likely to be used for creep crack growth testing and where a peak stress intensity factor of 35 MPa√m was measured (crack depth of 21 mm). The neutron diffraction measurements identified maximum values of shear stress in the order of 50 MPa and showed that the principal stress directions were aligned to within ~20° of the specimen orthogonal axes. Furthermore it was confirmed that measurement of strains by neutron diffraction in just the three specimen orthogonal directions would have been sufficient to provide a reasonably accurate characterisation of the stress state in welded CT specimens.     

Stress intensity factors and crack initiation directions for ceramic/metal joint

Four points bending tests for Si₃N₄/Cu/S45C joint specimen showed that the bending strengths depend on the residual stresses that originated from joining process. The residual thermal stresses caused an edge sub-interface crack to initiate in the ceramic. The stress intensity factors (SIFs) of the edge sub-interface crack located at distance h from the interface with or without interlayer metal were calculated by the Green's function obtained from a finite element analysis. The crack path at the joint specimen under four points bending loading with the influence of residual stresses was also evaluated by the maximum tensile stress criterion. Finally the effect of residual stress on the crack path was found numerically; the interlayer metal decreases the deflection angle of crack from interface by reducing the residual stress.     

Numerical study of contact forces for crack closure analysis

Plasticity induced crack closure (PICC) has been widely studied using numerical models. Different numerical parameters can be considered to quantify the opening level, namely one based on the analysis of contact stresses at minimum load. A modified version of this parameter is proposed here, based on nodal contact forces instead of contact stresses. The predictions were found to be similar to those obtained from the contact status of 2nd node behind crack tip. The PICC_contact parameter was also found to be very consistent and adequate for parametric studies of the influence of different physical parameters. The contributions to the opening stress intensity factor of different points along crack flank were found to strongly decrease with distance to crack tip. The cumulative K_open between the crack tip and a distance of 0.1 mm was found to vary from 30% to 100%, increasing with stress ratio, R. Finally, a K solution was developed for punctual forces applied on crack flank and compared with a literature solution for infinite plates. A good agreement was found for plane strain state but significant differences of about 10% were found for plane stress state.     

基于圆弧底试件的动态裂纹扩展及止裂规律研究

为了研究脆性材料的动态裂纹扩展及止裂规律，设计了一种带圆弧形底边的梯形开口边裂纹（trapezoidal opening crack with arc bottom，TOCAB）构型的试件。在落锤冲击设备加载下，对圆心角为0°、60°、90°和120°的TOCAB试件进行了冲击实验，并采用裂纹扩展计(crack propagation gauge，CPG)监测裂纹起裂和扩展时间，从而获得裂纹扩展速度。采用有限差分软件AUTODYN对落锤冲击设备和试件进行数值模拟，研究了裂纹的动态扩展过程及止裂规律。还基于实验和数值方法，计算了裂纹的临界动态应力强度因子。实验和数值结果均表明:3种弧度的TOCAB试件都可以实现运动裂纹止裂，该构型可用于研究动态裂纹止裂问题；数值计算的裂纹扩展路径与实验结果基本一致，验证了数值模型的有效性；裂纹起裂和止裂时刻的临界动态应力强度因子大于裂纹动态扩展过程中的临界动态应力强度因子。     

Assessing the effect of residual stresses on the fatigue behavior of integrally stiffened structures

Residual stresses emerge quite often in real structures due to the various manufacturing processes such as, welding, forming, cutting, milling, etc. In such cases, development of cracks at regions influenced by manufacturing operations demand additional attention. In the present work a numerical methodology has been developed, based on three-dimensional Finite Element Analysis, for the calculation of Stress Intensity Factors at cracks in welded components. The residual stress fields, which are used in SIF calculations, have been computed by the numerical simulation of the thermo-mechanical process. A numerical algorithm based on interpolation principles is developed, in order to introduce the three-dimensional field in the computational model of the cracked structure. The SIF calculation methodology is initially validated for the case of a welded plate by comparison of numerical results with existing analytical solutions. A cracked stiffened panel is analysed afterwards and the calculated fatigue crack propagation results are compared to experimentally measured data. Finally, the numerical procedure is applied to study the effect of more complicated residual stress fields on SIF values developing at cracks located in stiffened panels.     

Measurement of Torsionally Induced Shear Stresses in Shrink-Fit Assemblies

Shear stresses along the shaft/hub interface in shrink-fit components, generated by torsional loads, can drive premature failure through fretting mechanisms. It is difficult to numerically predict these shear stresses, and the associated circumferential slip along the shaft/hub interface, due to uncertainties in frictional behaviour and the presence of steep stress gradients which can cause meshing problems. This paper attempts to provide validation of a numerical modelling methodology, based on finite element analysis, so the procedure may be used with confidence in fitness-for-purpose cases. Very few experimental techniques offer the potential to make measurements of stress and residual stress interior to metallic components. Even fewer techniques provide the possibility of measuring shear stresses. This paper reports the results of neutron diffraction measurements of shear stress and residual shear stress in a bespoke test specimen containing a shrink-fit. One set of measurements was made with a torsional load ‘locked-in’. A second set of measurements was made to determine the residual shear stress when the torsional load had been applied and removed. Overall, measurement results were consistent with numerical models, but the necessity for a small test specimen to allow penetration of the neutron beam to the measurement locations meant the magnitude of shear stresses was at the limits of what could be measured experimentally.     

爆炸荷载下青砂岩动态起裂韧度的测试方法

为了研究爆炸荷载下青砂岩I型裂纹动态断裂韧度的测试方法，利用内部中心单裂纹圆盘（internal center single crack disc，ICSCD）试样进行了爆炸试验研究。试样由外径为400 mm、内部加载孔径为40 mm、预制裂纹长为60 mm的青砂岩制成。利用同步触发器实现圆盘中心起爆，并同步触发超动态应变仪，通过径向应变片获取爆炸应变曲线、裂纹尖端的环向应变片获取裂纹起裂时刻。以实测爆炸应变曲线为参量，应用Laplace变换推导出试样加载孔壁应力时程曲线表达式，并用数值反演法得出其数值解。利用ANSYS有限元软件，建立数值计算模型，通过相互作用积分法得出了在爆炸荷载作用下砂岩的I型动态应力强度因子曲线。研究结果表明:（1）ICSCD试件能够很好地用来测试岩石的动态起裂韧度；（2）炮孔周边的应力可以通过拉普拉斯变换的数值反演方法得到；（3）通过试验-数值法能稳定计算出ICSCD砂岩构型的动态起裂韧度，其最大误差仅为7%。     

Meshless simulation of crack propagation in multiphase materials

The material body considered in this work consists of multiphases. Digital imaging data are taken as the input to specify the configuration and composition of the specimen. Meshless method is demonstrated as a superior numerical tool to analyze crack initiation and propagation in multiphase material. A fracture criterion, based on the ratio of the opening stress over the material toughness distributed in front of the crack tip, is proposed to determine the direction of crack propagation of mixed mode fracture problem in multiphase material. Numerical results are presented and discussed.     

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。     

Characterization of crack tip stresses in plane-strain fracture specimens having weld center crack

Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (I_p) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation.     

An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression

Strength and deformability characteristics of rock with pre-existing fissures are governed by cracking behavior. To further research the effects of pre-existing fissures on the mechanical properties and crack coalescence process, a series of uniaxial compression tests were carried out for rock-like material with two unparallel fissures.In the present study, cement, quartz sand, and water were used to fabricate a kind of brittle rock-like material cylindrical model specimen. The mechanical properties of rock-like material specimen used in this research were all in good agreement with the brittle rock materials. Two unparallel fissures(a horizontal fissure and an inclined fissure) were created by inserting steel during molding the model specimen.Then all the pre-fissured rock-like specimens were tested under uniaxial compression by a rock mechanics servocontrolled testing system. The peak strength and Young's modulus of pre-fissured specimen all first decreased and then increased when the fissure angle increased from 0?to 75?.In order to investigate the crack initiation, propagation and coalescence process, photographic monitoring was adopted to capture images during the entire deformation process.Moreover, acoustic emission(AE) monitoring technique was also used to obtain the AE evolution characteristic of prefissured specimen. The relationship between axial stress, AE events, and the crack coalescence process was set up: when a new crack was initiated or a crack coalescence occurred, thecorresponding axial stress dropped in the axial stress–time curve and a big AE event could be observed simultaneously.Finally, the mechanism of crack propagation under microscopic observation was discussed. These experimental results are expected to increase the understanding of the strength failure behavior and the cracking mechanism of rock containing unparallel fissures.     

A combined fatigue crack initiation and propagation specimen—its initial development

The investigation detailed in this paper involves the initial design and development of a specimen geometry, designated as a BN(T) specimen, that is suitable for the combined determination of: (a) the fatigue crack initiation; and (b) the fatigue crack propagation, characteristics of materials. The experimental procedure developed during the course of this investigation is applied to a Ti---6Al-4V titanium alloy. This crack initiation and propagation test involves the use of the BN(T) compact-tension specimen with a polished notch root that facilitates an in-situ replication technique for the detection of crack initiation, and a modification of the ASTM-E647 Standard for crack growth data acquisition. The stress intensity factors, K_I, associated with the BN(T) specimen are established in this paper by means of a numerical finite element investigation. The use of this unique specimen for fatigue testing gives very satisfactory results and its extended use is expected.     

Application of material forces to fracture of inhomogeneous materials: illustrative examples

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.     

CTOD试验焊缝表面开缺口试样裂纹前沿平直度研究

对于裂纹尖端张开位移(CTOD)试验,焊缝试样中预制疲劳裂纹前沿平直度直接影响了试样制备的合格率,是试验的关键难题之一．试验中常对试样进行预处理以提高裂纹前沿平直度,但由此也使试验结果与实际情况产生一定差异．本文深入研究规范BS7448: Part2中对焊缝试样取样方向的规定,对表面开缺口试样裂纹尖端焊接残余应力进行分析,运用大型有限元软件ANSYS模拟90mm厚钢板焊接过程,求解了横向残余应力沿板厚方向及焊缝方向的分布规律,研究出横向残余应力分布是影响焊缝试样预制裂纹前沿平直度的主要原因,并通过试验进行验证．试验结果表明,表面开缺口试样可不经过局部韧带压缩等预处理而得到合格的裂纹前沿平直度,试验不改变原焊缝残余应力,可测得更加接近焊缝实际情况的CTOD韧度值,给CTOD试验中合理选取焊缝试样取样方向提供了新思路．     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

Cohesive-zone laws for void growth — I. Experimental field projection of crack-tip crazing in glassy polymers

A hybrid framework for inverse analysis of crack-tip cohesive-zone model is developed in this two-part paper to measure cohesive-zone laws of void growth in polymers by combining analytical, experimental, and numerical approaches. This paper focuses on experimental measurements of the cohesive-zone laws for two nonlinear fracture processes in glassy polymers, namely multiple crazing in crack-growth toughening of rubber-toughened high-impact polystyrene (HIPS) and crazing of steady-state crack growth in polymethylmethacrylate (PMMA) under a methanol environment. To this end, electronic speckle pattern interferometry (ESPI) is first applied to measure the crack-tip displacement fields surrounding the fracture process zones in these polymers. These fields are subsequently equilibrium smoothed and used in the extraction of the cohesive-zone laws via an analytical solution method of the inverse problem, the planar field projection method (P-FPM) [Hong, S., Kim, K.-S., 2003. Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method. Journal of the Mechanics and Physics of Solids 51, 1267-1286]. Results show that the proposed framework of the P-FPM could provide a systematic way of finding the shape of the cohesive-zone laws governed by the different micro-mechanisms in the fracture processes. In HIPS, inter-particle multiple crazing develops and the craze zone broadens ahead of a crack-tip under mechanical loading. The corresponding cohesive-zone relationship of the multiple-craze zone is found to be highly convex, which indicates effectiveness of rubber particle toughening. It is also observed that the effective peak traction, 7 MPa, in the crack-tip cohesive zone of HIPS (30% rubber content) is lower than the uniaxial yield stress of 9 MPa, presumably due to stress multi-axiality effects. In contrast, in PMMA, methanol localizes the crack-tip craze, weakening the craze traction for craze-void initiation to about 9 MPa and the fibril pull-out stress to less than 6 MPa. This reduction in cohesive traction, coupled with a strongly concave traction-separation cohesive-zone relationship, signifies environmental embrittlement of PMMA. These experimentally determined cohesive-zone laws are compared with detailed numerical analyses of effective microscale-void growth ahead of a crack tip in Part II.