Fracture mechanics applications of absorbed specific fracture energy: Notch and unnotched specimens

The Absorbed Specific Fracture Energy (ASFE)^* is an energy criterion that may be applied to evaluate the embrittlement and fracture properties of low and medium strength structural materials. Some new results are presented to illustrate the application of ASFE, and relating them to the other fracture criteria such as J_1c and K_1c. A comparison of results is made for static and dynamic loading, and the influence of neutron irradiation.     

中子辐照金属材料的脆化模型研究

金属材料的辐照脆化问题一直以来都是核能安全领域亟待解决的关键问题之一.为了更准确地预测金属材料的辐照脆化行为,基于Johnson-Cook本构模型,将未辐照金属材料的断裂真应力取作辐照材料的断裂真应力,建立了通过辐照退火态金属材料屈服强度就能够预测其整个真应力$\!$-$\!$-$\!$应变曲线,以及断裂真应变的辐照脆化模型.实验研究了不同中子剂量辐照退火态高纯铝的准静态拉伸真应力$\!$-$\!$-$\!$应变曲线、断裂真应力和断裂真应变随辐照剂量的变化规律.结果表明,辐照剂量越高,高纯铝的屈服强度越高,断裂真应变越低,但断裂真应力几乎不变.通过TEM显微分析获得了高纯铝内部辐照缺陷的尺寸和数密度随辐照剂量的变化规律,结果表明,辐照剂量越高,孔洞的尺寸和数密度越高,但位错环尺寸和数密度始终很小,难以准确统计.由辐照高纯铝实验数据拟合得到了辐照脆化模型所需参数,并检验了该模型的预测效果.结果表明,无论是通过实验还是显微分析得到辐照高纯铝的屈服强度,模型的预测结果均能够与实验结果较好地吻合,且模型对退火态高纯铝临界中子剂量的预测值也与文献结果一致.      

A model of the viscous-brittle transition upon fracture of metals and alloys

A model of the viscous-brittle transition upon fracture of metals and alloys that is based on the competition of the processes of microcrack development and dislocation generation is proposed. Micropores which occur in the region of stress concentration in the coagulation of vacancies are regarded as defects of one or another type. The kinetics of development of a micropore and the micropore-assisted generation of microcracks or prismatic dislocation loops are estimated quantitatively. The temperature dependence of the embrittlement of metals and alloys and also the influence of the loading rate and doping on the embrittlement temperature are considered. Institute of Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634021. 1996. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 158–162, May–June, 1998.     

预应变对中子辐照高纯铝拉伸性能的影响

金属材料的中子辐照硬化和脆化一直都是核能安全领域十分关注的重要问题之一. 为了进一步认识预应变对中子辐照金属材料塑性形变和最终断裂特性的影响规律, 及其微观机理, 本文研究了10%拉伸预应变高纯铝的拉伸应力-应变曲线、失稳应力和失稳应变等随辐照剂量的变化规律. 结果表明, 辐照剂量越高, 预应变高纯铝内部孔洞的尺寸和数密度越高, 导致屈服强度和极限拉伸强度越高, 均匀延伸率和失稳应变越小, 表现出典型的辐照硬化和脆化效应, 但失稳应力与辐照剂量几乎无关. 相同辐照剂量条件下, 预应变引入的高密度位错能够显著降低辐照孔洞的尺寸和数密度, 加之辐照退火效应的综合影响, 导致预应变能够降低高纯铝屈服强度的增长率和失稳应变的下降率, 从而表现出一定的抑制辐照硬化和脆化的能力, 预应变还能够提高高纯铝的失稳应力, 但整体而言预应变并不能提高高纯铝的延性. 最后, 基于J-C本构模型的中子辐照退火态金属材料的脆化模型能够直接应用于预应变金属材料, 且模型预测结果与实验结果吻合较好.      

Prediction of diffusion assisted hydrogen embrittlement failure in high strength martensitic steels

A stress assisted hydrogen diffusion transport model, a dislocation-density-based multiple-slip crystalline plasticity formulation, and an overlapping fracture method were used to investigate hydrogen diffusion and embrittlement in lath martensitic steels with distributions of M₂₃C₆ carbide precipitates. The formulation accounts for variant morphologies based on orientation relationships (ORs) that are uniquely inherent to lath martensitic microstructures. The interrelated effects of martensitic block and packet boundaries and carbide precipitates on hydrogen diffusion, hydrogen assisted crack nucleation and growth, are analyzed to characterize the competition between cleavage fracture and hydrogen diffusion assisted fracture along preferential microstructural fracture planes. Stresses along the three cleavage planes and the six hydrogen embrittlement fracture planes are monitored, such that crack nucleation and growth can nucleate along energetically favorable planes. High pressure gradients result in the accumulation of hydrogen, which embrittles martensite, and results in crack nucleation and growth along {110} planes. Cleavage fracture occurs along {100} planes when there is no significant hydrogen diffusion. The predictions indicate that hydrogen diffusion can suppress the emission and accumulation of dislocation density, and lead to fracture with low plastic strains.     

Combined analysis of fracture under stresses acting along cracks

A joint approach to the study of two non-classical fracture mechanisms, namely fracture of cracked materials with initial (residual) stresses acting along the crack planes and fracture under compression along parallel cracks, is considered in the framework of three-dimensional linearized solid mechanics. Mathematical statements of problems for pre-stressed solids that contain interacting circular cracks are given. Problems for an infinite solid containing two parallel co-axial cracks and for a space with the periodical set of co-axial parallel cracks as well as for a half-space with near-the-surface crack are solved. Several patterns of loading on the crack faces (normal loading, radial shear and torsion) are considered. The effects of initial stresses on stress intensity factors are analyzed for highly elastic materials with some types of elastic potentials. Formulation of fracture criteria accounting effect of initial (residual) stresses is given. Critical parameters of fracture of solids containing interacting cracks under compression along the cracks are calculated. The influence of geometrical parameters of the problems as well as physical and mechanical properties of materials on these critical parameters is analyzed.     

The trousers test for tearing of soft biomaterials

The mechanical modeling of rubber-like materials within the framework of nonlinear elasticity theory is well established. The application of such modeling to soft biomaterials is currently the subject of intense investigation. For soft biomaterials it is well known that exponential strain energy density models are particularly useful as they reflect the typical J-shaped stress-stretch stiffening response that is observed experimentally. The most celebrated of these models for isotropic hyperelastic materials are those of Fung and Demiray which depends only on the first strain invariant and its generalization by Vito that depends on both strain invariants. In the limit as the strain-stiffening parameter tends to zero, one recovers the neo-Hookean and Mooney–Rivlin models that are linear functions of the invariants. Here we apply these models to the analysis of the fracture or tearing of soft biomaterials. Attention is focused on a particular fracture test namely the trousers test where two legs of a cut specimen are pulled horizontally apart out of the plane of the test piece. It is shown that, in general, the location of the cut in the specimen plays a key role in the fracture analysis, and that the effect of the cut position depends crucially on the constitutive model employed. This dependence is characterized explicitly for the strain-stiffening exponential constitutive models considered. In contrast to the situation for rubber, our findings show that the critical driving force and fracture toughness in tearing of some soft biomaterials in the trousers test are virtually independent of the cut position.     

A statistical, physical-based, micro-mechanical model of hydrogen-induced intergranular fracture in steel

Intergranular cracking associated with hydrogen embrittlement represents a particularly severe degradation mechanism in metallic structures which can lead to sudden and unexpected catastrophic fractures. As a basis for a strategy for the prognosis of such failures, here we present a comprehensive physical-based statistical micro-mechanical model of such embrittlement which we use to quantitatively predict the degradation in fracture strength of a high-strength steel with increasing hydrogen concentration, with the predictions verified by experiment. The mechanistic role of dissolved hydrogen is identified by the transition to a locally stress-controlled fracture, which is modeled as being initiated by a dislocation pile-up against a grain-boundary carbide which in turn leads to interface decohesion and intergranular fracture. Akin to cleavage fracture in steel, the “strength” of these carbides is modeled using weakest-link statistics. We associate the dominant role of hydrogen with trapping at dislocations; this trapped hydrogen reduces the stress that impedes dislocation motion and also lowers the reversible work of decohesion at the tip of dislocation pile-up at the carbide/matrix interface. Mechanistically, the model advocates the synergistic action of both the hydrogen-enhanced local plasticity and decohesion mechanisms in dictating failure.     

Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009.     

Evaluation of fracture behavior of iron aluminides

Comparative fracture tests of three Fe-28%Al iron aluminides showed that alloys with Zr and C addition (FA-187) or with B, Zr, and C addition (FA-189) are extrinsically more susceptible to environmental embrittlement than the base ternary alloy (FA-186) under constant tensile loading condition. This may be caused by the variations of grain boundary morphology (i.e. changes of grain size and grain boundary cohesive strength) caused by the alloy addition. The effect of grain boundary size and cohesive strength are further investigated with reference to the susceptibility of hydrogen embrittlement. Finite element simulation of initial intergranular fracture of two iron aluminides (FA-186 and FA-189) are made. The computational scheme involves coupling the stress and mass diffusion analyses to determine crack-tip stress state and the crack tip hydrogen diffusion. Maximum strain failure criteria was adopted to simulate intergranular fracture. The numerical modeling results correlated well with the experimental data. The result further confirmed that the grain boundary morphology is important as it appears to control the intrinsic and extrinsic fracture behavior of iron aluminides.     

On the threshold force pulses for spall fracture of materials

Spall fracture is considered using the classical one-dimensional model. Results of the analysis are used to predict the dynamic strength properties of some structural materials, in particular, rail steels. The dependence of the time of fracture of the material on the threshold amplitude and time of loading is obtained. A model for the comparative estimation of the dynamic strength of materials is proposed, and corresponding diagrams are constructed. It is shown that the fracture process can be optimized by choosing the duration of loading of the material. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 97–106, September–October, 2006.     

Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.     

有限宽板中心裂纹断裂过程区的长度和位移公式

对岩石、混凝土和陶瓷等准脆性材料进行断裂分析,有必要研究裂纹前端的断裂过程区所起的作用以及各种因素对它的影响。本文提出分析有限宽中心裂纹板剪切断裂过程区的方法,此方法基于D－B模型的叠加原理,考虑了压剪断裂的摩擦阻力,并将有限板宽影响简化为载荷的修正,以非常简便的方法推导出计算断裂过程区长度和位移的公式,这些公式补充了现有文献只有“无限大”板的解的不足。利用这些公式,分析各种参数对断裂过程区长度和位移的影响变得非常方便。     

A multiaxial criterion for crack nucleation in rubber

The present paper is a first step towards the definition of a new multiaxial fracture criterion for rubber-like materials. Assuming that elastomers are subjected to a uniform distribution of intrinsic flaws, the framework of Eshelbian mechanics is considered. More precisely, the properties of the energy-momentum tensor are thoroughly studied to derive the criterion. A basic numerical example is presented and the qualitative discrepancy between the results obtained with this criterion and those relative to more classical approaches is highlighted.     

Hydride-induced embrittlement and fracture in metals—effect of stress and temperature distribution

A mathematical model for the hydrogen embrittlement of hydride forming metals has been developed. The model takes into account the coupling of the operating physical processes, namely: (i) hydrogen diffusion, (ii) hydride precipitation, (iii) non-mechanical energy flow and (iv) hydride/solid-solution deformation. Material damage and crack growth are also simulated by using de-cohesion model, which takes into account the time variation of energy of de-cohesion, due to the time-dependent process of hydride precipitation. The bulk of the material, outside the de-cohesion layer, is assumed to behave elastically. The hydrogen embrittlement model has been implemented numerically into a finite element framework and tested successfully against experimental data and analytical solutions on hydrogen thermal transport (in: Wunderlich, W. (Ed.), Proceedings of the European Conference on Computational Mechanics, Munich, Germany, 1999, J. Nucl. Mater. (2000a) 279 (2-3) 273). The model has been used for the simulation of Zircaloy-2 hydrogen embrittlement and delayed hydride cracking initiation in (i) a boundary layer problem of a semi-infinite crack, under mode I loading and constant temperature, and (ii) a cracked plate, under tensile stress and temperature gradient. The initial and boundary conditions in case (ii) are those encountered in the fuel cladding of light water reactors, during operation. The effects of near-tip stress intensification as well as of temperature gradient on hydride precipitation and material damage have been studied. The numerical simulation predicts hydride precipitation at a small distance from the crack-tip. When the remote loading is sufficient, the near-tip hydrides fracture. Thus a microcrack is generated, which is separated from the main crack by a ductile ligament, in agreement with experimental observations.     

2%氢气含量对X80管线钢断裂韧性和缺陷容限的影响

氢气的存在会劣化金属材料的力学性能,导致材料发生氢脆断裂,严重影响含氢天然气输送管线的安全输送,为此本文开展X80 管线钢在含氢环境中的断裂韧性试验,通过对比无氢环境,评定氢气的存在对X80管线钢断裂韧性和缺陷容限的影响规律,利用扫描电镜对断口进行观察分析,判断其在不同条件下的断裂模式。结果表明,在12 MPa的输送压力环境中掺入2% H₂,X80管线钢的断裂韧性比氮气环境有一定程度的下降,X80管线钢在氮气中的裂纹尖端张开位移 (crack tip opening displacement, CTOD)值为0.42 mm,在氢气中的值为0.33 mm,2% H₂使X80的断裂韧性下降21.42%,相应地氢气降低了管线钢允许的缺陷尺寸。从断口的形貌来看,氢气并没有改变材料的断裂模式,仍表现出明显的韧性断裂的特征,但局部有少量微裂纹存在。

     

On the path of a crack near a graded interface under large scale yielding

The trajectory of a crack lying parallel to a thin graded layer between two plastically dissimilar materials is studied using the exclusion region (ER) theory of fracture. The ER theory is a theoretical framework for surface separation within which a broad range of fracture phenomenologies can be represented. In the present study, the direction of crack advance is determined by maximizing the resolved normal-opening force on the near-tip region, whereas separation itself is governed by the intensity of plastic deformation near the tip. A computational study was undertaken using the ER theory. The special-purpose finite element analysis platform accommodates arbitrary––and a priori unknown––crack trajectories. The model problem considered herein involves two plastically dissimilar, but elastically identical, materials joined by a thin, graded interface layer. The initial crack lies parallel to the interface layer, and crack advance occurs under conditions of extensive plastic flow. It is found that the position of the initial crack relative to the interface layer has a strong influence on the fracture behavior. In general, the crack trajectories tend to curve toward the less-ductile material. Also, the presence of the interface layer leads to fracture toughnesses that significantly exceed those of either material individually for the configurations studied.     

Discrete fracture modeling of asphalt concrete

A heterogeneous fracture approach is presented for modeling asphalt concrete that is composed of solid inclusions and a viscous matrix, and is subjected to mode-I loading in the fracture test configuration. A heterogeneous fracture model, based on the discrete element method (DEM), is developed to investigate various fracture toughening mechanisms of asphalt materials using a high-resolution image processing technique. An energy-based bilinear cohesive zone model is used to model the crack initiation and propagation of materials, and is implemented as a user-defined model within the discrete element method. Experimental fracture tests are performed to investigate various fracture behavior of asphalt concrete and obtain material input parameters for numerical models. Also, bulk material properties are necessary for each material phase for heterogeneous numerical models; these properties are determined by uniaxial complex modulus tests and indirect tensile strength tests. The main objective of this study is to integrate the experimental tests and numerical models in order to better understand the fracture mechanisms of asphaltic heterogeneous materials. Experimental results and numerical simulations are compared at different test conditions with excellent agreement. The heterogeneous DEM fracture modeling approach has the potential capability to understand various crack mechanisms of quasi-brittle materials.     

Introducing Heterogeneity into the Micro-Scratch Test Fracture Toughness Relation for Brittle Particle Composites

Existing analysis methods of scratch test data are limited in their application to composite materials since they are built on the assumption of homogeneous material. In this study, the heterogeneity of the composite material is considered for analysis of scratch data on a resin and glass bead particle composite. Experiments are conducted using two approaches: macroscale three-point single edge notch and micro-scratch. An analysis method is presented which introduces a region in front of the crack tip to calculate the energy release rate during the fracture process which accounts for the heterogeneity of this region. By comparing with the experimental results, it is observed that this analysis method reduces the difference in fracture toughness derived from macroscale and microscale tests, and matches the trend of fracture toughness values as a function of particle volume fraction. This observation provides the insight that the local microstructure of the material needs to be considered in the scratch test analysis of particle composites.     

Amplitude-distribution analysis of acoustic emission

Amplitude distribution of acoustic-emission events generated during fracture of materials contains the potential information about the fracture mechanisms. A methodology is developed for the analysis of acousticemission burst signals. Based on this, the amplitude distributions can be characterized from the cumulative counts and events data alone. This simplifies the equipment as well as the data analysis. A model for amplitude distribution is proposed here, which can potentially identify two mechanisms operating simultaneously. It is also shown analytically that cumulative counts (N) are linearly related to summation of amplitudes of events and thatN can be considered a measure of the total energy of acoustic emission only if the amplitude distribution does not change significantly.