Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

涡轮盘篦齿裂纹扩展的有限元数值模拟

为了详细考察篦齿裂纹的扩展规律,对篦齿裂纹从齿尖一直扩展到即将完全穿透篦齿环的过程进行了数值模拟.含篦齿裂纹的涡轮盘有限元模型采用子模型法建立,使用M积分计算裂纹前沿的应力强度因子;在确定篦齿裂纹前沿每一节点处的局部扩展方向及距离后,通过样条曲线拟合出新裂纹前沿,并依靠自适应网格划分实现裂纹区有限元网格的更新.数值模拟结果表明,篦齿根部过渡圆角顶部可以视为裂纹缓慢扩展阶段与快速扩展阶段的分界点,在此之前篦齿裂纹以穿透型裂纹的形态以较低的速度进行扩展,在此之后篦齿裂纹开始向表面裂纹进行转化,并且平均扩展速度大大增加,分界点前的裂纹扩展寿命是之后的数倍.此外,由数值模拟结果还可以发现,增大篦齿根部过渡圆角半径以及减小相邻篦齿的间距,均有助于延缓篦齿裂纹的扩展.     

高温合金的裂纹扩展与强韧化

用直接流位法研究了高温合金涡轮材料的裂纹扩展速率，结果表明，高温合金涡轮盘材料的裂纹扩展速率快不完全取决于材料强度，更主要地取决于持久塑性，在考察高温合金涡轮盘材料的裂纹扩展时，不能仅以速率ｄａ／ｄｔ的绝对值来衡量，还应看裂纹扩展速率曲线的斜率是否锐减或曲线出现明显的拐点，以及曲线所对应的应力强度因子△Ｋ的范围。     

Comparison of cohesive zone parameters and crack tip stress states between two different specimen types

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality.     

任意分布参数的涡轮盘裂纹扩展寿命可靠性分析

讨论了某型涡轮盘随机参数服从任意分布时的可靠性问题.在基本随机参数前四阶矩已知的情况下,以Pairs-Erdogan裂纹扩展模型为基础,应用随机摄动理论和Edgeworth 级数技术,采用疲劳寿命模型对某型涡轮盘随机参数服从任意分布时的可靠性进行分析,建立了涡轮盘疲劳寿命可靠性分析模型,并求得了涡轮盘裂纹扩展寿命的可靠度.模型计算结果与Monte-Carlo仿真结果非常接近,文章提出的方法对涡轮盘可靠性设计具有一定的参考价值.     

Cell model for nonlinear fracture analysis – II. Fracture- process calibration and verification

A cell endowed with the micro-separation characteristics of the material is critical to formulating a predictive tool for nonlinear fracture mechanics analysis. This companion article addresses the second step in a two-step calibration scheme, namely, the calibration of the fracture-process parameters D and f0. The discrete, three-dimensional nature of a cell element enables it to capture important features of (i) interaction between the cell elements forming the fracture process zone and the crack including a single cavity-crack tip interaction and (ii) interaction between the fracture process and the plastic dissipation in the background material. The full three-dimensional computational model is applied to two crack geometries known to give rise to significantly different crack tip constraints and crack growth resistance behavior. Details of the load, displacement and crack growth histories in these specimens including the measured three-dimensional crack profiles are accurately predicted by the computational model. The comparison of model predictions and test data of surface cracked plates loaded by different combinations of tension and bending is reported in the third paper (Gao et al., 1997) in this series. This revised version was published online in July 2006 with corrections to the Cover Date.     

A high-cycle fatigue accumulation model based on electrical resistance for structural steels

For high-cycle fatigue of metals, the DC electrical resistance is a more sensitive parameter to the initiation of micro-cracks during the irreversible fatigue damage accumulation process. This implies that the electrical resistance is a suitable parameter that can be consistent with the fatigue damage physical mechanism. The relation between the ratio of electrical resistance changes and the cyclic fraction of the fatigue specimen may reasonably represent deterioration in mechanical properties of structural steels during the high-cycle fatigue process. The high-cycle fatigue damage accumulation model based on electrical resistance for structural steels was proposed. The model was verified by some experimental data for three structural steels; normalized 45C steel, 20 Mn steel and 16 Mn steel, and good agreement was obtained. The corresponding fatigue lifetime on the basis of the electrical resistance model was also performed. The results show that the approach to fatigue lifetime prediction and failure based on the electrical resistance is a good non-destructive technique.     

Alloy design for fracture resistance

Several methods for improving the strength of metallic materials are available and correlations between strength and various microstructural features have been established. The purpose of this paper is to review parallel developments favouring improved fracture resistance. Resistance to fracture in monotonie loading, cyclic loading and when fracture is environment-aided have been considered in steels, aluminium alloys and anisotropic materials. Finally, the question of optimising alloy behaviour is discussed.     

The influence of material mismatch on the evaluation of time-dependent fracture mechanics parameters

The influence of material mismatch on the stress field of uniaxial specimens and the time-dependent fracture mechanics parameters is studied in the present work. The applicability of the conventional C^* equation based on the load line displacement is re-examined by using the finite element method. It is found that under the extensive creep condition the C^* value of hard weld/soft parent metal specimen can be significantly higher than that of a single weld metal specimen, and the material mismatch has little influence on C(t) in small scale creep in the studied cases. It is proposed that the C^* formula based on the load line displacement recommended by ASTM E1457 needs to be modified to interpret the CCG behaviour of welded specimens. Candidate modification factors have been proposed.     

Proposal of a new concept on creep fracture remnant life for a precracked specimen

Abstract

The creep life time of a smooth specimen can be predicted using existing laws for creep deformation and steady state creep rate. When crack growth behaviour is involved, it is necessary to construct a law of creep crack growth rate to predict creep fracture life. Creep fracture life can be measured by integrating the law of creep crack growth rate. One example is the creep crack growth rate, represented by the parameter Q*. In this study, we investigated the applicability of this prediction method to creep fracture remnant life for a cracked specimen. The Ω criterion is proposed to predict creep fracture remnant life for a smooth specimen for creep ductile materials. In this study, the correlation between Q*_L derived from the paremeters Q* and Ω is investigated. The correlation between Q_L* and Ω provided a unified theoretical prediction law of creep fracture remnant life for high-temperature creep-ductile materials in the range from smooth to precracked specimens.     

Determination of fracture parameters for crack propagation in concrete using an energy approach

Double-G fracture model, a new analytical model describing fracture behaviour on cracked concrete, was recently proposed by Xu and Zhao based on the conception of energy release rate. This model couples the Griffith brittle fracture theory with the bridging softening property of concrete, and it is an extension of double-K fracture model proposed by Xu and Reinhardt. In this model, two fracture parameters, i.e., the initiation fracture energy release and the unstable fracture energy release , are termed to distinguish the different crack propagation stages undergoing during the whole fracture process in concrete. The difference between the two parameters, written as , is assumed to come from the contribution by aggregate bridging interlock, which results in the presence of fracture process zone. In our present work, firstly, the new model is elaborately introduced. Then, fracture tests are conducted, where besides three-point bending beams, a new testing method, called wedge-splitting on compact tension is adopted. In the experiments, electrical strain gauges are used to measure initial cracking load. Based on recorded load-crack mouth opening displacement curve (P-CMOD) or load-displacement curve (P-δ) and load-strain curve (P-ε), double-G fracture parameters are experimentally determined. Further more, based on the assumed three parameters relationship among , and , unstable fracture energy release are calculated. A comparable result between the measured and the calculated confirms this assumption. In order to verify the feasibility of this new model, the effective double-K fracture parameters converted by double-G fracture parameters using are compared with the double-K fracture parameters calculated by double-K fracture model. It is found that there is a good agreement. Another two series of different initial crack-depth ratios three-point bending beams carried out by Refai and Swartz are also collected to provide more experimental verification. It shows that the results obtained from the double-G fracture model agree well with those of double-K fracture model.     

Level-set topology optimization for maximizing fracture resistance of brittle materials using phase-field fracture model

Fracture is one of the most common failure modes in brittle materials. It can drastically decrease material integrity and structural strength. To address this issue, we propose a level-set (LS) based topology optimization procedure to optimize the distribution of reinforced inclusions within matrix materials subject to the volume constraint for maximizing structural resistance to fracture. A phase-field fracture model is formulated herein to simulate crack initiation and propagation, in which a staggered algorithm is developed to solve such time-dependent crack propagation problems. In line with diffusive damage of the phase-field approach for fracture; topological derivatives, which provide gradient information for the topology optimization in a LS framework, are derived for fracture mechanics problems. A reaction-diffusion equation is adopted to update the LS function within a finite element framework. This avoids the reinitialization by overcoming the limitation to time step with the Courant-Friedrichs-Lewy condition. In this article, three numerical examples, namely, a L-shaped section, a rectangular slab with predefined cracks, and an all-ceramic onlay dental bridge (namely, fixed partial denture), are presented to demonstrate the effectiveness of the proposed LS based topology optimization for enhancing fracture resistance of multimaterial composite structures in a phase-field fracture context.     

Review of new formats for fracture mechanics parameters

New methods to formulate fracture mechanics parameters are presented. These include the common format that relates the deformation behavior of a cracked structure or specimen to the deformation behavior of a tensile test and the concise format that suggests a shortened form of common fracture mechanics parameters to replace the usual polynomial formulations. These forms may give an easier way to use the fracture mechanics parameters in analytical calculations. __________ Translated from Problemy Prochnosti, No. 4, pp. 39–45, July–August, 2006.     

On the determination of the cohesive zone parameters for the modeling of micro-ductile crack growth in thick specimens

The paper deals with the determination of the cohesive zone parameters (separation energy, , and cohesive strength, T _max) for the 3D finite element modeling of the micro-ductile crack growth in thick, smooth-sided compact tension specimens made of a low-strength steel. Since the cohesive zone parameters depend, in general, on the local constraint conditions around the crack tip, their values will vary along the crack front and with crack extension. The experimental determination of the separation energy via automated fracture surface analysis is not accurate enough. The basic idea is, therefore, to estimate the cohesive zone parameters, and T _max, by fitting the simulated distribution of the local crack extension values along the crack front to the experimental data of a multi-specimen J _IC-test. Furthermore, the influence of the cohesive zone parameters on the crack growth behavior is investigated. The point of crack growth initiation is determined only by the magnitude of . Both and T _max affect the crack growth rate (or the crack growth resistance), but the influence of the cohesive strength is much stronger than that of the separation energy. It turns out that T _max as well as vary along the crack front. In the center of the specimen, where plane strain conditions prevail, the separation energy is lower and the cohesive strength is higher than at the side-surface.     

Analysis of crack growth rate based on rotation at the crack tip plastic zone

The crack growth rate of a line crack is obtained from a linear elastic analysis of work required in the formation of a crack tip plastic zone. Equations of crack growth rate are derived from rigid body rotation at the root of Dugdale's plastic zone. The proposed relations are used to study the fracture behaviour of materials in tension tests and the three point bending tests. This revised version was published online in August 2006 with corrections to the Cover Date.     

海上风机单桩基础受船舶撞击的数值研究

目前国内没有海上风机受船舶撞击的相关规范和损伤评估标准,以国内某单桩基础海上风机为例,运用LS-DYNA软件从能量变化、最大撞击力和风机响应角度对风机受船舶撞击过程进了分析,并提出面积受损率来评估风机受损程度。分析结果显示:船舶初始动能在分别不超过约35 MJ、35 MJ、25 MJ时,最大撞击力与船舶质量的1/3次方、速度、撞击角度的正弦值成线性关系,超过时线性关系不再明显;面积受损率能合理反映单桩基础的受损区域和受损面积。     

A framework for fracture modelling based on the material forces concept with XFEM kinematics

A theoretical and computational framework which covers both linear and non‐linear fracture behaviour is presented. As a basis for the formulation, we use the material forces concept due to the close relation between on one hand the Eshelby energy–momentum tensor and on the other hand material defects like cracks and material inhomogeneities. By separating the discontinuous displacement from the continuous counterpart in line with the eXtended finite element method (XFEM), we are able to formulate the weak equilibrium in two coupled problems representing the total deformation. However, in contrast to standard XFEM, where the direct motion discontinuity is used to model the crack, we rather formulate an inverse motion discontinuity to model crack development. The resulting formulation thus couples the continuous direct motion to the inverse discontinuous motion, which may be used to simulate linear as well as non‐linear fracture in one and the same formulation. In fact, the linear fracture formulation can be retrieved from the non‐linear cohesive zone formulation simply by confining the cohesive zone to the crack tip. These features are clarified in the two numerical examples which conclude the paper. Copyright © 2005 John Wiley & Sons, Ltd.     

Simplified equations for determining double‐K fracture parameters of concrete for 3‐point bending test

The paper presents simplified polynomial equations for determining the double‐K fracture parameters of concrete for 3‐point bending beams with variable strengths and material properties of concrete. The derived equations avoid complexities involved in computations of fracture parameters using existing analytical methods. The input data required for systematic computation in the study for deriving the nondimensional fracture parameters are obtained using a fictitious crack model. It is inferred that for a relative size of initial crack length, critical load and corresponding crack opening displacement maintain a linear relationship in their nondimensional forms. The value of critical mouth opening displacement can also be determined for known value of peak load using the derived nondimensional equation, thus avoiding the measurement of the crack mouth opening displacement in the experiment. Further, the derived polynomial equations predict the double‐K fracture parameters of concrete with negligible error as compared to those obtained based on experimental results.     

In-service fatigue fracture mechanisms in covered disks of a TV3-117VK helicopter turbine engine

In-service propagating fatigue cracks were examined in EI-698VD superalloy thin turbine covered disks of the first, second, and third stages of a TV3-117VK helicopter engine within service lifes of 200–1800 h. To reveal causes of early crack initiation and estimate a propagation time, metallographic and fractographic analyses were performed. The sequence of events during fatigue cracking of the disks was established. A block of striations on the fracture surface was discovered, which characterized fatigue crack propagation during one flight of a helicopter under different operating conditions. The number of striations in each block varied over the range of 4–20, being much more than those used to design covered disks. Fractographic results were used to estimate fatigue crack growth in covered disks of different stages using data on different operating conditions of helicopters. __________ Translated from Problemy Prochnosti, No. 1, pp. 171–174, January–February, 2008.     

Prediction of the Work of Separation and Implications to Modeling

Following Barenblatt's idea about the modeling of cracks by the use of a cohesive zone has attracted considerable attention. Recently, this model has also been applied to the prediction of ductile crack growth. For this case the present investigation aims to compare the predictions of a cohesive zone model with the predictions of the more physically based modified Gurson relation. The results demonstrate that in case of ductile fracture the parameters cohesive strength and energy may only be regarded as material properties within a small range of stress triaxialities. This finally leads to the conclusion that special care has to be taken if a cohesive zone model is used for the analysis of ductile fracture. The use of the modified Gurson relation predicts that the cohesive energy and strength do not remain constant throughout a crack growth analysis and their change is not known a priori. Improved cohesive zone models that take a coupling to the surrounding material into account may overcome this problem. This revised version was published online in July 2006 with corrections to the Cover Date.