Physical interpretation of fracture-toughening mechanisms

The basic idea behind the toughening of materials by the introduction of energy-absorbing or dissipating artefacts is critically re-examined. It is shown that energy dissipation by plastic deformation or other dissipative processes at the tip of a growing crack does not contribute to increasing the effective surface energy or the crack resistance of the material. Erroneous interpretations of toughening by the presence of fibres or by phase transformations occuring at the tip of a growing crack are discussed. It is argued that all processes which dissipate energy at the crack tip produce crack shielding and that this effect must be an important contribution to toughening. It is concluded that most of the features and properties embodied in methods of toughening can be explained by shielding effects and that the increase in toughness is due to a reduction in the local value of the crack extension force, or its equivalent stress intensity factor, and not to an increase in energy dissipated.     

基于扩展有限元的陶瓷复合材料多重增韧机制

为了提高陶瓷材料的断裂韧性和可靠度,改善材料抵御破坏的能力,将优化的多重增韧机制应用到氧化铝基陶瓷材料的开发中。相变增韧机制可以耗散部分能量,降低裂纹尖端处的应力集中程度,阻止或延缓裂纹扩展速率。当增强相分布较为合理、材料的致密度较高时,裂纹偏转与桥接增韧机制可以有效地削弱裂纹扩展动力,提高材料的断裂韧性。利用扩展有限元（X-FEM）手段讨论了裂纹扩展问题,为分析陶瓷复合材料的多重增韧机制提供了新思路。     

生物陶瓷增韧前后的比较研究

通过扫描电子显微镜对氧化锆增韧的羟基磷灰石和纯羟基磷灰石的裂纹扩展和断口形貌特征的观察，发现增韧的羟基磷灰石是以沿晶方式断裂，而纯羟基磷灰石是以解理方式断裂。本文分析了造成增韧前后两种材料不同断裂方式的机制，并讨论了颗粒增韧生物陶瓷的机理。     

晶须增韧陶瓷基复合材料裂纹扩展行为模型

在考虑晶须桥联和裂纹转两种增韧机理的基础上，建立了晶须增韧陶瓷复合材料裂纹扩展行为的理论模型，利用该型计算了单边切口梁三点弯曲的Ｒ－阻力曲线和载荷－位移曲线。     

SiC_w/ZrO_2(6mol%Y_2O_3)陶瓷中晶须增韧的数值模型

SiCw／ZrO2（6mol％Y2O3）陶瓷的实验研究表明，晶须桥联和裂纹偏转是其主要增韧机制在两种机制协同增韧的基础上，建立了晶须增韧的数值模型，对材料的三点弯曲断裂过程的计算结果表明：载荷／位移曲线呈锯齿状，是由于晶须桥联作用使得裂纹扩展与停止这一过程反复出现而引起的；随晶须含量增加，复合材料韧性提高，晶须桥联和裂纹偏转两种增韧贡献都增加，但是占主导地位的增韧机制由裂纹偏转机制逐步过渡到裂纹桥联机制．计算结果与材料的测试结果很吻合．     

Fracture process in cortical bone: X-FEM analysis of microstructured models

Bones tissues are heterogeneous materials that consist of various microstructural features at different length scales. The fracture process in cortical bone is affected significantly by the microstructural constituents and their heterogeneous distribution. Understanding mechanics of bone fracture is necessary for reduction and prevention of risks related to bone fracture. The aim of this study is to develop a finite-element approach to evaluate the fracture process in cortical bone at micro-scale. In this study, three microstructural models with various random distributions based on statistical realizations were constructed using the global model’s framework together with a submodelling technique to investigate the effect of microstructural features on macroscopic fracture toughness and microscopic crack-propagation behaviour. Analysis of processes of crack initiation and propagation utilized the extended finite-element method using energy-based cohesive-segment scheme. The obtained results were compared with our experimental data and observations and demonstrated good agreement. Additionally, the microstructured cortical bone models adequately captured various damage and toughening mechanisms observed in experiments. The studies of crack length and fracture propagation elucidated the effect of microstructural constituents and their mechanical properties on the microscopic fracture propagation process.     

硅碱钙石微晶玻璃的析晶特性及其增韧机理研究

通过调整热处理工艺制备了不同结构的R₂O-CaO-SiO₂-F系硅碱钙石微晶玻璃, 分析了析晶特性和力学性能, 重点研究以硅碱钙石为主晶微晶玻璃的裂纹扩展机制及增韧机理。结果表明, 基础玻璃在低温处理时首先析出CaF₂微晶作为异质晶核, 一步法处理后得到岛屿状硬硅钙石/硅碱钙石复相微晶玻璃, 两步法处理后得到了力学性能优异、具有板条交错结构的硅碱钙石微晶玻璃。研究发现, 硅碱钙石微晶玻璃的裂纹扩展受到周围板条晶体取向及晶界影响, 存在穿晶断裂和沿晶断裂两种模式扩展, 呈现出随机取向的折线或台阶状裂纹路径。其中具有一定长径比的板条状硅碱钙石具有较好的桥联作用, 承载补强效果显著, 此外硅碱钙石晶体与玻璃相之间存在的残余应力, 有利于缓解裂纹应力集中以及增加裂纹扩展能。即, 硅碱钙石微晶玻璃优异的力学性能是各种增强和增韧机制综合作用的结果。     

Orientation dependent fracture toughness of lamellar bone

The critical energy release rate of human bone was determined for different crack propagation directions with three-point-bending tests using controlled crack extension. The local structure was characterised by small-angle X-ray scattering, SEM and polarised light microscopy and related to the energy required for crack extension. It turns out the collagen angle is decisive for switching the fracture behaviour of bone from brittle to quasi-ductile. A significant increase in the critical energy release rate as well as a change of the appearance of the crack path from straight and smooth to deflected and zig-zag is observed.     

SiCw/ZrO2(6mol%Y2O3)陶瓷中晶须增韧的数值模型

ＳｉＣｗ／ＺｒＯ２（６ｍｏｌ％Ｙ２Ｏ３）陶瓷的实验研究表明，晶须桥联和裂纹偏转是其主要增韧机制。在两种机制协同增韧的基础上，建立了晶须增韧的数值模型，对材料的于点弯曲断裂过程的计算结果表明：载荷／位移曲线呈锯齿状，是由于晶须桥联作用使得裂纹扩展与停止这一过程反复出现而引起的，；随晶须含量增加，复合材料韧性提高，晶须桥联和裂纹偏转两种增韧贡献都增加，但是占主层地位的增韧机制由裂纹偏转机制逐步过渡到裂     

Crystal orientation,toughening mechanisms and a mimic of nacre

Based on the investigations of crystal structure of nacre using SEM, TEM and XRD, it is proposed that there exists a domain structure of crystal orientation in the nacre. The orientation domain consists of continuous 3–10 tablets along the direction perpendicular to nacreous plane, and 1–5 tablets in a single lamina. The tablets in a domain are crystallographic identical in three dimensions. From the crack morphologies, it is found that the crack deflection, fibre pull-out and organic matrix bridging are the three main toughening mechanisms acting on nacre. The organic matrix plays an important role in the toughening of this biological composite. The biomimetically synthesized composite made of alumina and kevlar showed significant increase in the fracture energy compared with the single ceramics. The soluble proteins extracted from nacre can induce aragonite and the one from prism can induce calcite grown with a preferred orientation of [104]. The insoluble proteins control the nucleation site and thus lead to a finer crystallization of CaCO₃.     

Combined modelling and experimental studies of rubber toughening in polymers

When researching the effect of rubber toughening in acrylonitrile-butadiene-styrene (ABS) copolymer and high-impact polystyrene (HIPS) and also toughening methods used in other materials, then, often comparisons are needed between materials with and without the toughening agents over the full crack velocity range. This is from the threshold stress to just maintain crack propagation up to the limiting crack velocity conditions. However, the toughening of materials can change other material properties including, for example, the onset of yield in the material under static stress. The result can be that a crack velocity versus stress curve cannot be obtained by experiment over the full crack velocity range for some toughened materials. However, as used in this study, combined experimental and computer simulations can provide for a meaningful and informative comparison between crack velocity versus stress curves for materials with and without toughening agents over the full crack velocity range.     

半圆盘构件冲击断裂特性的动态焦散线实验研究

采用动态焦散线实验系统,对有机玻璃（PMMA）在冲击载荷下的I型和I-II混合型裂纹在起裂和扩展时的动态断裂特性进行了研究。结果表明：随着PMMA由I型断裂转变为I-II混合型断裂,从落锤作用在试件上到裂纹起裂所需时间不断增加,说明裂纹起裂需要的能量有所增加,同时从裂纹起裂到最终贯通所需时间不断减少,说明裂纹平均扩展速度也不断增大;在I型断裂中,PMMA的断裂韧度KIC为2.04 MN/m3/2,而在I-II混合型断裂中,PMMA的断裂韧度KIC低于I型断裂时的断裂韧度KIC,但是KIIC有所增大;对于I-II混合型断裂,PMMA极限扩展速度约为366m/s,当达到极限扩展速度后,裂纹尖端出现微裂纹增韧现象,使裂纹的表面能迅速增大,随后裂纹的扩展速度迅速减小。     

FEA of crack-particle interactions during delamination in interlayer toughened polymer composites

A numerical analysis was conducted, using previously obtained experimental results, to establish basic toughening mechanisms and fracture behaviour of an interlayer-toughened composite material, containing particulate modified interlayers. Aims of the analysis were to examine the influence of the particles on the plastic zone size that develops in front of the crack tip and to investigate interactions between the particles and the crack tip during elastic-plastic crack propagation. Under both loading modes particles did not promote yielding but induced micro-cracking. This was concluded to be the most dominant toughening mechanism within high particle content interlayers.     

Al_2O_3-ZrO_2-SiCw陶瓷复合材料的断裂特点和韧化机理

本文通过 XRD,SEM,TEM 以及三点弯曲试验技术研究了 Al_2O_3-25 v.-%ZrO_2(2mol%Y_2O_3)-25v.-% SiCw(AZS)三元陶瓷复合材料的断裂特点和韧化机理。结果表明,该材料的载荷-位移曲线因晶须的反复阻止作用呈锯齿状,ZrO_2与 SiC 晶须同时起增韧作用,材料的良好韧性是 ZrO_2的相变增韧、微裂纹增韧和裂纹偏转与分枝增韧以及 SiC 晶须的裂纹桥接与拔出效应共同作用的结果,但其综合效果不是简单叠加。本文还建立了 ZrO_2-SiC_W 的复合韧化模型,并进行了讨论。     

Fracture and tearing in oriented polyethylene

Measurements of energy for crack propagation (fracture surface energy) have been made on low-density and high-density polythenes both in the undrawn state and in different states of orientation produced by drawing under various conditions. Both cleavage and tear tests were employed. For the unoriented materials the values of fracture surface energies were in the range 10⁴ to 10⁵ J m^–2.With increasing orientation (represented by birefringence) the energy for crack propagation parallel to the direction of orientation fell by a factor of approximately 100. The differences between the low-density and high-density polymers, and between the different types of low-density polymers examined, were comparatively slight.Measurements of crack tip diameter showed a direct relation between this quantity and fracture surface energy. From their comparable studies of the tearing of rubbers Rivlin and Thomas have interpreted such a relationship as implying that the high values of fracture surface energy arise from the work required to deform the material in the crack tip up to the point of rupture. On this basis the reduction in fracture surface energy with increase in orientation is a direct result of the reduction in the diameter of the crack tip.     

Multiscale Toughening Mechanisms in Biological Materials and Bioinspired Designs

Biological materials found in Nature such as nacre and bone are well recognized as light‐weight, strong, and tough structural materials. The remarkable toughness and damage tolerance of such biological materials are conferred through hierarchical assembly of their multiscale (i.e., atomic‐ to macroscale) architectures and components. Herein, the toughening mechanisms of different organisms at multilength scales are identified and summarized: macromolecular deformation, chemical bond breakage, and biomineral crystal imperfections at the atomic scale; biopolymer fibril reconfiguration/deformation and biomineral nanoparticle/nanoplatelet/nanorod translation, and crack reorientation at the nanoscale; crack deflection and twisting by characteristic features such as tubules and lamellae at the microscale; and structure and morphology optimization at the macroscale. In addition, the actual loading conditions of the natural organisms are different, leading to energy dissipation occurring at different time scales. These toughening mechanisms are further illustrated by comparing the experimental results with computational modeling. Modeling methods at different length and time scales are reviewed. Examples of biomimetic designs that realize the multiscale toughening mechanisms in engineering materials are introduced. Indeed, there is still plenty of room mimicking the strong and tough biological designs at the multilength and time scale in Nature.     

Microstructure and fracture in three dimensions

A high resolution three dimensional (3D) scanning technique called X-ray microtomography was used to measure internal crack growth in small mortar cylinders under compressive loading. Tomographic scans were made at different load increments in the same specimen. 3D image analysis was used to measure internal crack growth during each load increment. Load–deformation curves were used to measure the corresponding work of the external load on the specimen. Fracture energy was calculated using a linear elastic fracture mechanics approach using the measured surface area of the internal cracks created. The measured fracture energy was of the same magnitude that is typically measured in concrete tensile fracture. A nominally bilinear incremental fracture energy curve was measured. Separate components for crack formation energy and secondary toughening mechanisms are proposed. The secondary toughening mechanisms were found to be about three times the initial crack formation energy.     

Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method

The interaction of a crack with perfectly bonded rigid isolated inclusions and clusters of inclusions in a brittle matrix is investigated using numerical simulations. Of particular interest is the role inclusions play on crack paths, stress intensity factors (SIFs) and the energy release rates with potential implications to the fracture behavior of particulate composites. The effects of particle size and eccentricity relative to the initial crack orientation are examined first as a precursor to the study of particle clusters. Simulations are accomplished using a new quasi-static crack-growth prediction tool based on the symmetric-Galerkin boundary element method, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating SIFs, and the maximum principal stress criterion for crack-growth direction prediction. The numerical simulations demonstrate a complex interplay of crack-tip shielding and amplification mechanisms leading to significant toughening of the material.     

Ductile Phase Toughened Brittle Materials

Toughening of brittle materials by the inclusion of ductile phases is governed by several important factors which include ceramic-ductile phase interfacial bond strength, physical and chemical compatibility between ceramic and ductile phase, geometry and mechanical properties of ductile phase. The present understanding of the effect of these factors on toughening is reviewed and clarified. Continuous ductile phases (network, fibre or plate) are found to be more efficient for the toughening of brittle materials than discrete ductile particles. However, ductile particle toughened brittle materials have the advantages of material homogeneity isotropy and particularly better high temperature properties. It has been demonstrated that the influence of interfacial bond strength is determined by the geometry of the ductile phase in the composites. For the comparatively continuous ductile phase, such as ductile network, fibre or plate, comparatively weak inteffocial bond strength can promote partial debonding of the brittle matrix-ductile phase intedece during crack propagation and is beneficial for toughening. For discrete particulate ductile phase toughened brittle materials, the small gauge length of the ductile phase often results in the ductile phase pull-out during crack propagation which is the main limitation to toughening.Thus strong bond strength is required to ensure the bridging of the crack by the ductile phase.The coefficient of thermal expansion (CTE) mismatch between matrix and ductile phase has also been correlated with the geometry of the ductile phase. In most of the ceramic/metal systems,the CTE of the ductile metal phase is greater than that of the ceramic matrix. In the case of ductile network, fibre or plate, the residual stress created by the CTE mismatch can contribute to toughening through its influence on the initial crack opening stress while the bridging of the crack by the ductile phase is still ensured. However, for discrete ductile particles, the residual stress created by CTE mismatch is liable to cause cracks to by-pass the spherical particles, limiting the efficient use of the inherent toughness of the ductile phase. Low-modulus ductile inclusions are beneficial for the bridging of cracks by the ductile phase. Softer, more ductile inclusions are more effective for the toughening of brittle materials by particulate ductile phase     

Finite Element Analysis of the Competition Between Crack Deflection and Penetration of Fiber-Reinforced Composites Using Virtual Crack Closure Technique

Crack deflection along the fiber/matrix interface for fiber-reinforced composites is an important condition upon which the toughening mechanisms depend. Sound control for the interface debonding of composites contributes to improving the fracture toughness of composites. Combined with the virtual crack closure technique, a finite element model of composites is proposed to predict the competition between the matrix crack deflection along the interface and the matrix crack penetration into the fibers under the thermomechanical coupling fields. For C/C composites, the effects of the geometry size, fiber volume fraction, fiber coating materials and thermal mismatch on the energy release rate and the crack deflection mechanisms are studied. Results show the fiber coating increases the ability to deflect at large thermal mismatch and small crack sizes, and the TaC coating shows larger effect than the SiC coating. The research provides fundamental method for promoting the toughening design of C/C composites.