Fatigue and fracture of bovine dentin

In this paper, the fatigue and fracture properties of bovine dentin are evaluated usingin vitro experimental analyses. Double cantilever beam (DCB) specimens were prepared from bovine maxillary molars and subjected to zeroto-tension cyclic loads. The fatigue crack growth rate was evaluated as a function of the dentin tubule orientation using the Paris law. Wedge-loaded DCB specimens were also prepared and subjected to monotonic opening loads. Moiré interferometry was used to acquire the in-plane displacement field during stable crack growth, and the instantaneous wedge load and crack length were acquired to evaluate the crack growth resistance and crack tip opening displacement (CTOD) with crack extension. The rate of fatigue crack growth was generally larger for crack propagation occurring perpendicular to the dentin tubules. The Moiré fringe fields documented during monotonic crack growth exhibited non-linear deformation occurring within a confined region adjacent to the crack tip. Both the wedge load and CTOD response provided evidence that a fracture process zone contributes to energy dissipation during crack extension and that dentin exhibits a risingR-curve behavior. Results from this preliminary investigation are being used as a guide for an evaluation of the fatigue and fracture properties of human dentin.     

Correlation of modified crack tip opening distance with heat input to the heat affected zone of high-strength low-alloy steels

Investigated is the dependency of the crack tip opening displacement (CTOD) on the local microstructure of the heat affected zone in high-strength low-alloy (HSLA) microalloyed steel. Since the initiation of the crack tip location could not be controlled in fatigue, any possible correlation between heat iput in welding and fracture toughness could be smeared. Modified CTOD data are defined; they show that the fracture resistance of the weld joint decreased as the heat input increased.     

弯载下位于刚性固定端周向壁穿裂纹的圆柱壳弹塑性解

金属圆柱壳结构常见于大型复杂结构系统中。这类构件在其端部与其它构件相连接是工程上常见的结构形式。由于连接处焊接热影响或实际复杂内力的作用,在连接处产生疲劳裂纹的几率相对增大;另一方面,由于高韧性材料的应用,使得弹塑性裂纹更为常见。然而到目前为止尚无这类问题的弹塑性理论解析。本文针对受弯曲载荷作用下的周向壁穿裂纹位于固定端的圆柱壳,基于半膜力壳理论及Dugdale模型,推导了裂纹尖端张开位移(CTOD)和裂纹尖端张开角度(CTOA)等一套相对完整的弹塑性解析解。该解除少数数值求根外,均为显式表达,可用于裂纹起裂、撕裂计算,追踪此类由弹塑性裂纹的存在所引起的圆柱壳结构的柔度以及裂纹撕裂条件下的极限承载能力等变化过程,弥补了这类工程问题解析解空缺的不足。     

基于CTOD/CTOA管道钢断裂韧性测试方法研究进展

高级别管线钢的一大特点是韧度高,导致管材裂纹尖端周围经常处于大范围屈服状态,现有基于高约束试件的断裂韧性测试方法,很难满足新型管材的断裂韧性测试要求. 本文回顾了基于CTOD 和CTOA的断裂韧度参数,详细介绍了管道钢断裂韧性测试方法的研究现状和发展趋势,分析了影响管道钢断裂韧性测试准确性的各种因素,为管道钢断裂韧性的测试提供帮助.     

Fracture Properties of Concrete–Concrete Interfaces Using Digital Image Correlation

The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete–concrete jointed interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement, crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis matches well with those measured experimentally.     

Equivalence of the notch stress intensity factor,tip opening displacement and energy release rate for a sharp V-notch

For an infinite elastic plane with a sharp V-notch under the action of symmetrically loading at infinity, the length of crack initiation ahead of the V-notch’s tip is estimated according to a modified Griffith approach. Applying a new conservation integral to the perfectly plastic strip (Dugdale model) ahead of the V-notch’s tip, the relationship between notch stress intensity factor (NSIF) and notch tip opening displacement (NTOD) is presented. Also, the relationship between NSIF and perfectly plastic strip size (PPSS) is found. Since there are three fracture parameters (NSIF, NTOD, and PPSS) with changeable notch opening angle in two basic relationships, it is necessary to select one critical parameter with changeable notch opening angle or two independent critical parameters, respectively. With the help of a characteristic length, it is found by this new conservation integral that the NSIF, NTOD and energy release rate are equivalent in the case of small-scale yielding. Especially, the characteristic length possesses clear physical meaning and, for example, depends on both the critical NSIF and SIF or both the NTOD and CTOD, respectively, in which SIF and CTOD are from the tip of a crack degenerated from the sharp V-notch. The dependence of NSIF on NTOD and PPSS is presented according to the equivalence, and the critical NSIF depending on the critical NTOD with a notch opening angle is also predicted.     

Inverse Estimation of Cohesive Fracture Properties of Asphalt Mixtures Using an Optimization Approach

Tensile cracking in asphalt pavements due to vehicular and thermal loads has become an experimental and numerical research focus in the asphalt materials community. Previous studies have used the discrete element method (DEM) to study asphalt concrete fracture. These studies used trial-and-error to obtain local fracture properties such that the DEM models approximate the experimental load-crack mouth opening displacement response. In the current study, we identify the cohesive fracture properties of asphalt mixtures via a nonlinear optimization method. The method encompasses a comparative investigation of displacement fields obtained using both digital image correlation (DIC) and heterogeneous DEM fracture simulations. The proposed method is applied to two standard fracture test geometries: the single-edge notched beam test, SE(B), under three-point bending, and the disk-shaped compact tension test, DC(T). For each test, the Subset Splitting DIC algorithm is used to determine the displacement field in a predefined region near the notch tip. Then, a given number of DEM simulations are performed on the same specimen. The DEM is used to simulate the fracture of asphalt concrete with a linear softening cohesive contact model, where fracture-related properties (e.g., maximum tensile force and maximum crack opening) are varied within a predefined range. The difference between DIC and DEM displacement fields for each set of fracture parameters is then computed and converted to a continuous function via multivariate Lagrange interpolation. Finally, we use a Newton-like optimization technique to minimize Lagrange multinomials, yielding a set of fracture parameters that minimizes the difference between the DEM and DIC displacement fields. The optimized set of fracture parameters from this nonlinear optimization procedure led to DEM results which are consistent with the experimental results for both SE(B) and DC(T) geometries.     

Fracture toughness for CNT specimens from numerically obtained critical CTOD values

Many approaches for estimating mode I fracture toughness (K_IC) using circumferentially notched tensile (CNT) specimen have been demonstrated in the literature. In this paper, an effective approach for estimating fracture toughness from the numerical solution of critical crack tip opening displacement (CTOD) is proposed. An elasto-plastic finite element analysis is used to estimate critical CTOD values for CNT specimens. A number of materials are analysed, and the relationship between K_IC and critical CTOD for CNT specimens is obtained. The proposed relationship is validated by comparing the fracture toughness values obtained from the relationship with those obtained experimentally using CNT specimens. The fracture toughness (K_IC) calculated according to this relationship from numerically obtained critical CTOD is found to be in close agreement with the experimentally obtained fracture toughness for the respective materials.     

RESEARCH PROGRESS OF FRACTURE TOUGHNESS TEST METHOD FOR LOW CONSTRAINT SPECIMENS 1)

低约束试件断裂韧性测试对油气管道安全运营具有重要意义。本文回顾了低约束试件断裂韧性测试方法及发展过程,介绍了裂纹尖端张开位 移(crack tip opening displacement, CTOD)和J积分等常用断裂韧性表征参数,并对断裂韧性测试中应力强度因子、J积分塑性因子、J积分与CTOD转换因子、裂纹尺寸测量方法、数 字图像相关方法等关键问题进行对比分析,总结需要深入研究的问题,为低约束试件断裂韧性测试发展提供一定依据。     

Analysis to the stress and strain structures of mode I 3-D crack in elastic-plastic state

In this paper, the stress and strain structures of Mode I 3-D crack in power hardening material are studied by analyzing the fundamental equations of elastic-plastic mechanics. It is shown that three regions, Z1,Z2 and Z3 can be divided in the thickness direction according to the stress characteristic. In region Z1, the stress components in the plane Perpendicular to z axis (thickness direction) can be solved first using the fundamental equations of plane strain state; in region Z3, they can be solved first by the equations of plane stress state. The region Z2 is defined as a transition layer. It is shown that the transition layer is the characteristic of Mode I 3-D crack in elastic-plastic state, and it is significant to the research on 3-D fracture. The crack tip opening displacement CTOD is chosen to describe the amplitude coefficient of the local stress field, and the distribution of CTOD in 3-D state is investigated.The project supported by National Natural Science Foundation of China.     

低速冲击下混凝土少筋梁断裂性能

动态加载下,混凝土中钢筋的阻裂性能一直是冲击动力学研究领域的难点之一。利用落锤试验机对含缺口的混凝土少筋梁进行三点弯曲试验,分析了不同加载速率下梁的冲击力、跨中挠度、混凝土起裂应变率和钢筋应变。实验结果表明:在一定加载速率范围内（0.885～1.252 m/s）,混凝土预制裂缝尖端的裂纹起裂应变率、冲击力最大值、跨中挠度峰值与加载速率呈线性增长关系,当加载速率增至1.771 m/s时,增长趋势减弱;冲击力卸载时,钢筋部分弹性变形恢复导致裂纹产生闭合,裂纹嘴张开位移逐渐减小至恒定值,对裂纹嘴张开位移峰值前的部分曲线进行拟合后得到裂纹嘴张开位移率,结果表明裂纹嘴张开位移率随加载速率的提高而线性增大。     

Deformation and the strip necking zone in a cracked steel sheet

When a tensile stress is applied to a thin cracked plate, a strip necking region results ahead of a crack tip. The relative opening displacement between the crack surfaces and between the upper and lower boundaries of the strip necking region were measured by the moiré method. The strains ahead of the strip necking region and the thickness reduction (therein) were also measured. The measured relative opening displacements were compared with the calculated values using the Dugdale strip necking model. The thickness reduction in the strip necking region is equal to the relative opening displacement.     

A Zener–Stroh crack interacting with a coated inclusion with generalized Irwin plastic zone correction

The elastic–plastic fracture behavior of a Zener–Stroh crack interacting with a coated inclusion in composite materials has been investigated with crack tip plastic zone corrections. With the distributed dislocation method, the crack problem is formulated into a set of singular integral equations which are solved numerically. The plastic zone sizes at the both crack tips are determined by a generalized Irwin model where Von Mises stress yielding criterion is used. The stress intensity factor (SIF), the plastic zone size (PZS), the crack tip opening displacement (CTOD) and the effective stress intensity factor have been evaluated. In the numerical examples, the influence of the inclusion shear modulus, the coating-layer thickness and shear modulus, as well as the distance between the crack and inclusion, on the SIF, the PZS and the CTOD are discussed in detail. Numerical examples show that increasing the shear modulus or the thickness of the coating phase, the influence of the inclusion on the normalized SIF and the normalized PZS will be shielded.     

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

Analyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J-integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.     

Effects of fractal crack

Experimental results indicate that propagation paths of cracks in geomaterials are often irregular, producing rough fracture surfaces which are fractal. In this paper, crack tip motion along a fractal crack trace is discussed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. The length, velocity and kinking effects of the fractal crack are analysed. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. Finally, expressions of stress and displacement fields near the fractal crack tip are given.     

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

裂纹尖端张开角准则的稳态裂纹扩展实验研究

ASTM和ISO已发布获得低约束条件下断裂性能和裂纹稳态扩展阻力曲线的标准,标准中采用多种试验方法确定临界裂纹张开角度来表征板材的裂纹稳态扩展。本文采用准静态裂纹扩展试验方法,通过摄像技术测定裂纹尖端张开角(CTOA),验证标准对1mm厚度2024-T3铝合金板稳态裂纹扩展行为的有效性。研究了试样构型、裂纹尺寸和是否疲劳预制裂纹对裂纹稳态扩展过程中CTOA的影响。试验结果表明:裂纹扩展2mm后,距离裂纹尖端1mm处的CTOA趋于一个恒定值6°,这个值与试样构型和裂纹长度无关;同时,不预制疲劳裂纹对CTOA值和试样的最大剩余强度影响较小。     

非连续数字图像相关方法在裂纹重构中的应用

数字图像相关方法作为一种新的非接触式位移测量方法,在力学工程中有广泛的应用前景,然而受限于标准方法对图像变形的连续性要求,这种高效的测量方法在断裂力学领域的推广受到了限制. 为解决这一问题,提出采用引入子区分离数学模型,代替标准方法的连续模型,来对非连续区域进行精确识别和匹配的非连续数字图像相关方法. 研究子区被裂纹等非连续分割后原始像素点的位移情况,并引入裂纹张开向量用以表征被分割子区的主区和副区的位移关系;从而建立子区分离模型的数学表达式,并且为所提出的模型设计相应的图像相关算法;然后将所提出的非连续数字图像相关方法应用于重构平板拉伸试验开裂过程中图像的位移. 研究结果表明,相比于标准的数字图像相关方法,所提出的非连续数字图像相关方法解决了图像相关法在非连续区域失效的问题,提高了数字图像相关方法对位移测量的正确率,特别是能够准确重构裂纹面及附近的位移场,其测量精度能够达到亚像素级别.      

Effects of measurement techniques on the experimental characterization of crack tip opening angle-Δ<Emphasis Type="Italic">a</Emphasis> resistance curves

One of the most promising approaches to characterizing the stable tearing process for lower constraint configurations in metallic materials has been indicated to be the crack tip opening angle (CTOA) criterion. In this paper we examine the effect of measurement distance selection and the impact of measurement procedures/analysis on the experimental CTOA-Δa resistance curve behavior of a Ti-6Al-4V and an Al5083 alloy. A new, systematic procedure for carrying out the experimental, surface CTOA measurement process has been used, which has uncovered artifacts of measurement distance selection that have not been presented prior to this study. By studying the CTOA-Δa behavior using a rigidly defined and consistent method, it is apparent that the measurement distance behind the crack tip at which angles are measured has a direct impact on the shape of the early transitional behavior of the CTOA-Δa behavior as well as the critical, experimental CTOA values produced.     

CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of 2.3-mm thick sheets of 2024-T3 aluminum alloy was experimentally investigated for middle crack tension specimens having initial flaws that were: (a) flat fatigue cracks (low fatigue stress) and (b) 45-deg through-thickness slant cracks (high fatigue stress). The critical CTOA values during stable tearing were measured by two independent methods, optical microscopy and digital-image correlation. Results from the two methods agree well.The CTOA measurements and observations of the fracture surfaces have shown that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness (a>B), CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness (a>2B), crack tunneling stabilized. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only slightly higher CTOA values during initial crack growth. The amount of tunneling in the high fatigue stress tests was about the same as that in the low fatigue stress tests after the flat-to-slant transition.This study indicates that stress history has an influence on the initial portion of the stable tearing behavior. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack-tip constraint. The measured CTOA reached a constant value of 6 deg for crack growth of about the specimen thickness. This coincided with the onset of 45-deg slant crack growth and a stabilized, slightly tunneled (about 20 percent of the thickness) crack-front shape. For crack growth on the 45-deg slant, the crack front and local field variables are still highly three dimensional.