Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen

A brittle fracture criterion is proposed for predicting fracture toughness of U-shaped notches under pure mode II loading. The criterion, called UMTS, is developed based on the maximum tangential stress (MTS) criterion. The UMTS criterion can be generally used for determining the mode II fracture toughness of U-notched components as well as the fracture initiation angle in U-shaped notches under pure mode II loading. To verify the validity of the proposed criterion, a set of experiments were carried out on the U-notched Brazilian disc (UNBD) specimens made of PMMA and also soda-lime glass. It is shown that there is a good agreement between the results of the UMTS criterion and the experimental results both for fracture toughness and for the fracture initiation angle under pure mode II conditions.     

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.     

基于GMTS准则的岩石复合型断裂机理研究

使用国际岩石力学协会规定的半圆盘岩石试件,加工不同倾角的直裂纹试样,通过三点弯曲加载试验得到不同I-II复合比断裂的断裂韧性和初始断裂角．传统裂纹扩展准则忽视了常数项即T应力及更高阶项的影响,导致该扩展准则的理论预测结果存在较大缺陷,本文通过考虑常数项,建立广义最大周向应力准则(GMTS)．在此基础上,分别采用传统的裂纹扩展准则和考虑T应力的裂纹扩展准则预测不同复合比裂纹的断裂韧性和初始扩展角,然后对比理论预测结果和实验结果．分析可得：常数项即T应力对断裂的临界应力强度因子和初始断裂角的影响是不可忽略的,且II型断裂占比较大时影响更大,广义最大周向应力准则预测值与实验测试结果之间的误差最小．     

Fracture strength for a high strength steel bridge cable wire with a surface crack

In this paper, the fracture strength of a cracked suspension bridge wire is determined based on linear elastic fracture mechanics (LEFM). The wire is 5 mm in diameter, with an original ultimate strength of 1725 MPa and ultimate elongation that ranges between 5.5% and 6%. The average value of for the wire fracture toughness, K_C, was recently evaluated by the author. The state of practice is to use the ultimate strength of the cracked wire as obtained from tensile tests. This approach may overestimate the strength of the wire due to possible delamination and crack tip plasticity. A case study for a group of in situ wire breaks retrieved from a suspension bridge cable is presented. The failure analysis is performed based on both the fracture toughness criterion and the net section theory. The fracture toughness criterion produced more realistic results for the fracture strength of the wire. The decline in the fracture toughness and the corresponding reduction in the fracture strength of cracked degraded wire are predicted making use of the strain energy density criterion.     

Toughness characterization of iron-based powder material

Fracture mode dependence on the material structure is applied to characterize the fracture toughness of iron-based powder material. The porosity parameter is varied to exhibit the change in the observed fracture mechanism and hence the fracture toughness of powder materials. Useful information is obtained to enhance the production technology in terms of porosity content and inter-particle contacts. The proposed simulation procedure provides data that are in good agreement with experiments and makes it possible to predict the mechanical behavior of powder materials with different structures. Complex dependence of fracture toughness on the porosity of powder materials is reflected by competing microfracture mechanisms and inherent peculiar behavior of the compacting powder.     

Investigation of the elastoplastic deformation and the fracture criterion of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane

The stress-strain state and fracture of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane is studied. The deformation theory of the plasticity of a transversally isotropic body was used to analyze the stress-strain state. The fracture analysis of the material is carried out using a proposed variant of the strain-strength criterion. Theoretical and experimental data on the stress-strain state and the strength of a transversally isotropic material are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 67–71, March, 2000.     

基于线法的U形切口混凝土梁断裂参数研究

混凝土的断裂韧度是重要的材料参数，本文利用含U形切口的三点弯曲梁试验结合临界距离线法来获得混凝土的断裂韧度．理论推导了含断裂韧度与不同根部半径的断裂失效方程，采用有限元法计算了切口应力集中系数．根据断裂失效方程和试验中的材料几何参数，利用最小二乘法拟合计算得到混凝土材料的断裂韧度和抗拉强度．对小切口半径情形，采用双K断裂准则分析计算了混凝土起裂韧度和失稳断裂韧度，分析结果表明：临界距离线法得到的材料断裂韧度与双K断裂准则中的失稳断裂韧度吻合，同时获得相应临界距离值．     

基于临界距离点法的混凝土Ⅰ型断裂韧度的预测

混凝土的断裂韧度是极为重要的断裂力学材料参数，本文利用临界距离理论(TCD)中的点法和混凝土标准断裂梁试样裂缝尖端应力场的近似解，提出了一种对混凝土断裂问题按临界距离的点法进行分析的方法．基于已有文献的试验材料及其实验结果，分析了这种断裂研究分析方法的可行性．将临界距离点法与双K断裂准则应用于几何相似的混凝土梁的断裂韧性和断裂过程区分析，验证了TCD点法的可靠性．实验表明：临界距离理论的点法能够获得比双K断裂准则相对安全的失稳断裂韧度，利用临界距离法还可得到相应断裂过程区长度的极限估算值．     

Equivalent thickness conception for corner cracks

Thickness dependence of the one-parameter-based fracture toughness has been well recognized and widely studied. However, it is still a challenge to predict the fracture of structures with curved cracks from the fracture toughness data obtained from the standard through-the-thickness cracked specimens. The complicated three-dimensional (3D) stress fields near the crack front play a vital role in the fracture strength of materials. Based on a systematical numerical study of the 3D stress fields near the crack tip of quarter elliptic corner cracks and comparison with that of ideal through-the-thickness cracks, an equivalent thickness conception for curved cracks is proposed from the viewpoint of out-of-plane constraint, and a semi-analytical solution for the equivalent thickness of corner cracks is obtained. With the evaluated equivalent thickness, the fracture toughness of corner cracked specimens is predicted efficiently by the plane-strain toughness value of the material obtained from the standard through-the-thickness specimen.     

Effect of constraint on fracture controlled by stress or strain

To interpret fracture of solids, an appropriate fracture criterion is required. It is often believed that the level of strain ahead of a crack tip controls the fracture event for materials exhibiting high ductility, e.g. ductile fracture of A533B steel in the upper shelf regime. And the level of stress ahead of a crack tip controls the brittle fracture event, e.g. cleavage fracture of A533B steel in the lower shelf regime. Within each regime (ductile or brittle), the level of constraint of a specimen or structure determines the magnitude of the apparent fracture toughness. In this paper, we address the difference in the effect of constraint on the stress- or strain-controlled fracture. It is found that the constraint plays an opposite role to the apparent fracture toughness values for strain-controlled vs. stress-controlled fracture.     

Fracture toughness of cast ferritic steel applying local approach

Fracture characteristics prediction with temperature dependence has been made and experimentally proved for cast manganese steel. The approach is based on computer simulation of the crack nucleus formation and unstable microcrack equilibrium in polycrystalline metal. Results of low-temperature tests of smooth tensile specimens, tensile specimens with circumferential U and V notches, pre-cracked bend specimens and tensile specimens with circumferential shallow crack have been applied. A good agreement of predicted and experimentally determined fracture toughness temperature dependence for the tested steel has been obtained.     

U形切口的有限断裂准则

有限断裂力学准则综合了应力和能量参数,假设裂纹或切口端部有限裂纹长度的增长．特别地,该有限裂纹的长度不是材料的基本常数,而是与构件的结构有关．基于U形切口两种形式：点方式和线方式有限断裂准则,对文献中的铝合金U形切口三点弯曲断裂实验进行了分析验证．一方面基于材料的断裂韧度和抗拉强度,预测切口件断裂载荷;另一方面根据几组不同的切口根部半径及其对应的临界切口应力强度因子,同时估算材料的断裂参数：断裂韧度和抗拉强度．将点方式和线方式两种不同形式有限断裂准则的预测结果,与平均周向应力准则、最大周向应力准则以及文献中相关结果进行了比较得出：无论是预测断裂载荷还是估算材料断裂参数,线方式有限断裂准则,与文献中相关结果比较吻合,尤其是估算的断裂韧度精度较高．     

A new ductile fracture theory and its applications

This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characterize various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness valuesJ _1c and δ _c with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameterJ _dc and δ _dc are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.     

Effects of static electric field on the fracture behavior of piezoelectric ceramics

The paper gives an overview on experimental observations of the failure behavior of electrically insulating and conducting cracks in piezoelectric ceramics. The experiments include the indentation fracture test, the bending test on smooth samples, and the fracture test on pre-notched (or pre-cracked) compact tension samples. For electrically insulating cracks, the experimental results show a complicated fracture behavior under electrical and mechanical loading. Fracture data are much scattered when a static electric field is applied. A statistically based fracture criterion is required. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate ceramics and that the concepts of fracture mechanics can be used to measure the electrical fracture toughness. Furthermore, the electrical fracture toughness is much higher than the mechanical fracture toughness. The highly electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under purely electric loading, which is impossible under mechanical loading in the brittle ceramics. The project supported by an RGC grant from the Research Grant Council of the Hong Kong Special Administrative Region, China     

高强混凝土热-力响应的断裂相场分析方法研究

高强混凝土(High-Strength Concrete, HSC)的力学性能受温度影响较大,尤其在高温环境下性能衰退剧烈,因此在结构分析中宜采用随温度变化的材料性能参数．断裂相场方法基于Griffith变分断裂准则,无需复杂的裂纹拓展追踪技术便可处理多裂纹的问题,可方便地模拟裂纹的萌生、扩展、分岔及汇合过程．本文采用适宜进行结构断裂分析的断裂相场方法,基于能量泛函变分原理,将温度对混凝土材料弹性模量及断裂能的影响引入断裂相场分析方法中,用于高强混凝土高温环境下的强度和破坏分析．以高温作用下高强混凝土梁三点弯曲试验为算例,进行方法验证,通过与实测结果对比,证实了算法的有效性．     

Brittle fracture of precompressed steel as affected by hydrostatic pressure,temperature and strain concentration

Highly precompressed 1020 HR steel, 0.65 prestrain at 400°F (204°C), tested in nominally uniform tension at ?80°F (?62°C) fractures at about 110,000 psi (760 MN/m²) with less than 0.02 plastic strain. Yet the addition of a hydrostatic pressure of less than 7000 psi (48 MN/m²) converts this visually brittle fracture to a ductile one with appreciable necking. The explanation of this surprising experimental result is shown to follow directly and simply from the combination of a tensile stress criterion of fracture, strain concentration and the low tangent modulus of the stress-strain curve in tension beyond the Bauschinger transition region of a few percent of plastic strain. Temperature dependence and strain-rate dependence of brittle fracture similarly are predictable in an almost trivial manner from the appropriate stress-strain curves for different amounts of precompression. So also is the amazingly high ductility or fracture toughness of the most complex of perforated or notched statically loaded structures of mild steel in an undamaged or fully annealed state.     

一种表面裂纹高温断裂韧性测试方法

提出了一种表面裂纹高温断裂韧性测试方法，包括试样加热、温控和裂纹嘴张开位移测试方法．该方法适合于在相对简单的条件下测试表面裂纹高温断裂韧性．最后给出了铝合金焊缝表面裂纹高温断裂韧性的测试结果．     

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。     

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.     

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.