Estimation of Fracture Toughness of Metallic Materials Using Instrumented Indentation: Critical Indentation Stress and Strain Model

We propose a generalized approach based on fracture mechanics and contact mechanics to estimate the fracture toughness in metallic materials from instrumented indentation testing. Models were developed for brittle and ductile fracture. Different criteria were applied to each model to determine the critical fracture point during indentation. For brittle fracture, the critical fracture point was defined in terms of the critical mean pressure; for ductile fracture, the critical fracture point was derived from fracture strain and critical plastic zone size. Each fracture criterion was used to determine the indentation fracture energy corresponding to the fracture energy required for crack extension. The fracture toughness was estimated for various metallic materials using each model and compared with standard fracture toughness tests.     

金属材料脆性断裂机理的实验研究

材料的脆性断裂有许多准则和模型,但对脆断机理和变化规律缺乏合理的描述,给工程应用带来不便。本文对典型脆性材料球墨铸铁、灰铸铁分别进行了拉扭双轴断裂实验和常规拉伸、扭转破坏实验;对韧性金属材料合金钢进行了单轴拉伸颈缩破坏实验。通过上述实验分析了脆性材料和韧性材料发生脆性断裂的机理特征并选择应力三维度作为应力状态参数描述危险点的应力状态,同时考察了脆性材料和韧性材料发生脆性断裂的主导因素。结果表明:韧性材料45#钢和14CrNiMoV合金钢在颈缩断面心部应力三维度值较大时发生脆性拉断,而在颈缩断面边缘处应力三维度值较小时发生剪断;脆性材料球墨铸铁在应力三维度值为0.0～0.33之间变化时均发生脆性断裂;灰铸铁在应力三维度值大于0.0时发生脆性拉断,而在应力三维度值小于0.0时发生剪断。因此可以认为,材料的细观组织结构和危险点应力状态是影响断裂机理及变化规律的主要因素。对于同种材料,随着应力三维度代数值从小向大变化材料的断裂机制由塑性剪切断裂逐渐转变为脆性断裂。本文通过对几种材料的脆性断裂危险点和断裂方向的研究给出了脆断宏观破坏条件。     

The brittle fracture criterion based on the maximum tensile stress on the surface of blunt crack tip

The brittle fracture criterion is developed for a blunted crack. The curvature radius of the blunt crack tip is suggested as a characteristic length for brittle materials, and then the fracture toughness of the brittle materials can be determined from the cohesion strength and the characteristic length of the materials.     

On a model of structured medium fracture under compression conditions

Extension is necessary in order to initiate brittle fracture in a structured medium. One possible version of the fracture scenario under compression conditions is the development of extension near local concentrators. The dimensions of such regions depend on the level of hydrostatic compression (pressure). As the hydrostatic compression increases, these dimensions decrease approaching the dimension of individual structure elements of the medium (e.g., grains or pores). Under these conditions, the mechanisms of brittle fracture of the medium differ from those in ordinary structural materials. We consider mechanisms of brittle fracture in compression. It is assumed that the sources of the local extension required for the development of discontinuities are the response of the heterogeneous structure elements of the medium (pores) at which the external compressive stresses can transform into local extensions sufficient for crack propagation. In this case, a characteristic cell representing the scale of the leading process of local fracture is a volume containing two pores. The coalescence of these pores is an elementary fracture process. An increase in the pressure level increases the role of such fracture processes and leads to the development of ordered fracture structures. Several examples of fracture scenarios under loads that are combinations of homogeneous compression and a concentrated action are used to illustrate the conditions for the development of discontinuities, in whose end regions an elementary act of pore coalescence takes place, and to demonstrate the appearance of linear structures such as curtains or echelons of microcracks.     

缺陷对脆性材料碎裂过程的影响

采用特征线方法模拟脆性材料中应力波的传播过程,采用内聚力模型模拟断裂点的断裂过程,运用C++语言开发了一个模拟脆性圆环发生一维膨胀碎裂过程的实用工具ExpRing,简要给出了该程序的理论基础和使用说明。采用此程序模拟了具有初始缺陷的脆性圆环在均匀膨胀作用下的碎裂过程,探讨了不同应变率下,缺陷分布特征对碎裂过程和平均碎片尺寸的影响。计算结果表明:(1)在一定的应变率范围内,等间距分布的点缺陷会控制断裂点的位置及碎片个数,在碎片尺寸 应变率曲线上形成一个缺陷控制碎裂平台;(2)点缺陷的间距和弱化程度将影响缺陷控制碎裂平台的宽度和位置;(3)具有缺陷的脆性材料的表观强度呈现应变率硬化特征;(4)在一定的应变率范围内,正弦分布型缺陷同样导致缺陷控制碎裂的现象。     

Energy consumption for creep fracture of metallic materials

The energy conservation law is applied to formulate the ductile and brittle creep fracture criterion for metallic materials. The criterion contains a summary of heat and latent energies. Assuming that the heat energy is given out so it has no effect on the fracture process, the ductile creep fracture criterion is simplified. To take into account the evaluation of the damage state of materials the compressibility condition is introduced and the brittle creep fracture law is formulated.     

金属材料中低加载速率下的动态韧脆转变及断裂韧性测量

金属材料在冲击下的韧脆转变现象和动态断裂韧性的测量是金属材料冲击力学性能研究的重要组成部分.针对金属材料在冲击下的韧脆转变现象认识不足和韧性材料在较低加载率下动态$J$-$R$阻力曲线难以测量的现状,提出了采用高速材料试验机, 设计专用试验夹具,测量15MnTi钢和11MnNiMo钢在不同加载速率下的韧脆转变过程,以及裂尖约束对其动态韧脆转变速率变化的影响.在高速材料试验机上采用上夹具辊刹车,通过调节压缩杆长度改变试验中裂纹扩展量的试验方法,测量了15MnTi钢三点弯曲试样件在较低加载率下的动态断裂韧性.试验发现15MnTi钢CT试验件加载速率低于0.025 m/s时呈现出韧性断裂的特点,加载速率在0.1,$\sim$,0.5 m/s时为韧脆结合型断裂,加载速率高于0.5 m/s后进入脆性断裂区; 11MnNiMo钢CT试验件加载速率大于1.5 m/s后,分层断裂过程中出现先脆断后韧段的现象;发现15MnTi钢和11MnNiMo的动态韧脆转变速率受裂尖约束的影响非常明显,面内约束和面外约束的升高都会导致材料动态脆断速率出现明显降低;还发现三点弯曲试验中, 15MnTi钢在8788 MPa$\cdot$mm/s加载率内断裂韧性随加载率的提升呈现出缓慢下降的趋势.      

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

Effect of microstructure on fracture of brittle materials: Unified approach

A theoretical approach to the fracture of brittle solids based on crack opening displacement and energy rate criterion is presented. The approach allows for the prediction of elastic (Young’s modulus) and fracture (fracture strength and thermal shock) response of a brittle material containing spherical pores and polycrystalline solids containing anisotropic residual stresses.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

脆塑性岩石破坏后区应力跌落效应数值模拟

采用三轴试验和数值模拟研究了岩石类脆塑性材料的应力跌落效应,并用塑性流动因子λ来描述应力跌落效应。为简化计算,给出了一种应力陡降过程中伴随的非零应变增量的工程近似处理方法,基于此针对性地编制了处理脆塑性材料应力跌落的有限元分析程序代码。数值模拟结果验证了塑性流动因子λ以及该近似处理方法的有效性。     

固体力学中侵入问题的若干新进展

本文主要介绍了固体力学中侵入问题近10余年来的发展情况。重点综述了侵入断裂实验及理论研究的新成果;讨论了动静态侵入断裂的关系;简述了侵入方法在测定材料断裂韧性方面的应用。      

脆性断裂的非局部力学理论

本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。     

PMMA膨胀环动态拉伸碎裂实验研究

在强动载作用下, 脆性材料的碎裂问题是一个重要的研究课题, 而脆性材料在冲击拉伸载荷下的力学行为的实验研究相对较匮乏. 提出了一种动态拉伸断(碎)裂的液压膨胀环实验技术, 可用于准脆性/脆性材料的动态拉伸. 利用该技术对有机玻璃(PMMA)圆环试件进行了不同膨胀速度下的动态碎裂实验研究. 从回收碎片的断口形貌和碎片内部残余裂纹观察可知试件的破碎由环向拉伸应力造成, 碎片断口处发出的稀疏波会将周围的拉伸应力卸载, 从而抑制其他裂纹的进一步发展. 利用超高速相机记录了试件的膨胀碎裂过程, 利用DISAR激光速度干涉仪获得了试件外表面粒子的径向膨胀速度历史, 通过试件上的应变片获得了试件的应变历史和断裂应变. 实验结果表明: 在拉伸应变率150\mathrm{~}500s^{-1}范围, 材料的动态断裂应变低于准静态加载下的断裂应变, 体现出“动脆”现象; 随着加载应变率的提高, PMMA 材料的碎片尺寸减小; 无量纲化的PMMA圆环的平均碎片尺寸介于韧性碎裂模型和脆性碎裂模型的预测数值之间, 反映出材料的准脆性特性.      

Failure resistance of intermetallic matrix reinforced by wires

Composite materials with brittle matrices such as ceramics and intermetallic compounds have gained increased importance in application. Ceramics and intermetallic compounds possess unique heat-resistance at high temperatures. They are, however, vulnerable to brittle fracture. This problem can be overcome by reinforcing the intermetallic compounds with wires. NiAl-tungsten composite wire was manufactured by hot diffusion welding of alternate layers of the matrix and wires. These specimens were subjected to a three-point bending in the temperature range from 20° to 1000°C. Temperature dependence of the bending strength exhibited brittle to ductile transition behavior. At room temperature, unstable failure by bending is terminated in a stable fashion. Brittle fracture of the matrix and wire were observed. For text temperatures of 300°, 500° and 700°C, subcritical crack growth occurred where the matrix and wire showed brittle and ductile fracture, respectively. A pronounced necking of the specimen was observed as the temperature is increased. Substantial plastic deformation occurred when the test is performed at 1000°C. The critical stress intensity factor K_1c and specific work of fracture were measured and found to be two to three times larger than the intermetallic compounds without wire reinforcement.     

Influence of the Longitudinal Shear Crack Tip Radius on the Feathering Structure

The initial phase of feather joint development in the vicinity of a turnpike longitudinal shear vertex is analyzed. Experiments with model materials demonstrate that the crack parameters and the distance between the cracks along the shear front in the primary echelon brittle fracture structure linearly depend on the shear radius. A model for the development of the primary echelon structure along the longitudinal shear front is proposed.     

A nonlocal theory for brittle fracture

In this paper, a nonlocal theory of fracture for brittle materials has been systematically developed, which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-I, II and III, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion for brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I–II, I–III are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.     

3-D numerical simulation of fracture processes in heterogeneous brittle materials

By using the lattice model combined with finite element methods and statistical techniques, a numerical approach is developed to establish mechanical models of three-dimensional heterogeneous brittle materials. A special numerical code is introduced, in which a lattice model and statistical approaches are used to simulate the initial heterogeneity of material properties. The size of displacement-load step is adaptively determined so that only few elements would fail in each load step. When the tensile principal strain in an element exceeds the ultimate strain of this element, the element is considered broken and its Young's modulus is set to be very low. Some important behaviors of heterogeneous brittle materials are indicated using this code. Load-displacement curves and figures of three-dimensional fracture patterns are also numerically obtained, which are similar to those observed in laboratory tests.     

Determination of Mechanical Properties of Sand Grains by Nanoindentation

Determination of the mechanical properties of individual sand grains by conventional material testing methods at the macroscale is somewhat difficult due to the sizes of the individual sand particles (a few μm to mm). In this paper, we used the nanoindentation technique with a Berkovich tip to measure the Young’s modulus, hardness, and fracture toughness. An inverse problem solving approach was adopted to determine the stress-strain relationship of sand at the granular level using the finite element method. A cube-corner indenter tip was used to generate radial cracks, the lengths of which were used to determine the fracture toughness. Scatter in the data was observed, as is common with most brittle materials. In order to consider the overall mechanical behavior of the sand grains, statistical analysis of the mechanical properties data (including the variability in the properties) was conducted using the Weibull distribution function. This data can be used in the mesoscale simulations.     

Fracture energy based constitutive models for tensile fracture of metal powder compacts

Diametral compression test or the Brazilian disc test is commonly used to characterise the tensile strength of brittle materials. A general fracture model based on energy assumptions is proposed for simulation of the discrete and localised tensile fracturing process in metal powder. The characteristics of the tensile fracture development of the central crack in diametral tested specimen is numerically studied. The softening rate of the model is obtained from the corresponding rate of the dissipated energy. Finite element simulations of the diametral compression test are performed with the proposed tensile fracture model used in conjunction with a Cap model for the deformation of the powder material. The results agree reasonably with experiments.