Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites

Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the brittle layer and the poroelastic substrate, such a composite can develop a toughening mechanism that relies on the simultaneous growth of multiple cracks. Here, we study this remarkable behaviour by means of a detailed model, and explore how the material and loading parameters concur in determining the macroscopic toughness of the system. By extending a previous study, our results show that rapid loading conveys material toughness by promoting distributed cracking. Moreover, our theoretical findings may suggest innovative architectures of flaw-insensitive materials with higher toughness.     

On the toughening of brittle materials by grain bridging: Promoting intergranular fracture through grain angle, strength, and toughness

The structural reliability of many brittle materials such as structural ceramics relies on the occurrence of intergranular, as opposed to transgranular, fracture in order to induce toughening by grain bridging. For a constant grain boundary strength and grain boundary toughness, the current work examines the role of grain strength, grain toughness, and grain angle in promoting intergranular fracture in order to maintain such toughening. Previous studies have illustrated that an intergranular path and the consequent grain bridging process can be partitioned into five distinct regimes, namely: propagate, kink, arrest, stall, and bridge. To determine the validity of the assumed intergranular path, the classical penetration/deflection problem of a crack impinging on an interface is re-examined within a cohesive zone framework for intergranular and transgranular fracture. Results considering both modes of propagation, i.e., a transgranular and intergranular path, reveal that crack-tip shielding is a natural outcome of the cohesive zone approach to fracture. Cohesive zone growth in one mode shields the opposing mode from the stresses required for cohesive zone initiation. Although stable propagation occurs when the required driving force is equivalent to the toughness for either transgranular or intergranular fracture, the mode of propagation depends on the normalized grain strength, normalized grain toughness, and grain angle. For each grain angle, the intersection of single path and multiple path solutions demarcates “strong” grains that increase the macroscopic toughness and “weak” grains that decrease it. The unstable transition to intergranular fracture reveals that an increasing grain toughness requires a growing region of the transgranular cohesive zone be near the cohesive strength. The inability of the body to provide the requisite stress field yields an overdriven and unstable configuration. The current results provide restrictions for the achievement of substantial toughening through intergranular fracture.     

共晶基陶瓷复合材料的断裂韧性

应用细观力学方法研究了由具有随机尺寸和方位的棒体共晶体构成的共晶基陶瓷复合材料的断裂韧性.首先根据棒状共晶体的细观结构特性,考虑共晶体边界处的微观滑移确定共晶陶瓷复合材料的开裂应力,当外载荷达到开裂应力时,裂纹开始扩展.然后分析裂纹表面处的棒状共晶体桥联力使裂纹产生闭合效应,减小裂纹尖端的应力集中,建立棒状共晶体桥联增韧机制;再依据棒状共晶体拔出过程中摩擦力做功,建立棒状共晶体拔出增韧机制.最后在棒状共晶体的桥联与拔出增韧机制的基础上,得到了共晶基陶瓷复合材料断裂韧性的理论表达式.结果表明共晶基陶瓷复合材料的断裂韧性与棒状共晶体的长径比密切相关.     

Toughening analysis of mode III crack in transformation toughened ceramics

The fracture toughness enhancement of mode III crack in transformation toughened ceramics such as Ce-TZP and Mg-PSZ is predicted by using a pressure sensitive transformation criterion and the weight function method. The theoretical analyses of the toughening effect for both stationary and steady-state growing crack are given, respectively. The results show that the toughening is only associated with crack growth and there is no toughening effect for stationary crack.The project was supported by the National Science Foundation of China     

Crack deflection occurs by constrained microcracking in nacre

For decades, nacre has inspired researchers because of its sophisticated hierarchical structure and remarkable mechanical properties, especially its extreme fracture toughness compared with that of its predominant constituent, \(\hbox {CaCO}_{3}\), in the form of aragonite. Crack deflection has been extensively reported and regarded as the principal toughening mechanism for nacre. In this paper, our attention is focused on crack evolution in nacre under a quasi-static state. We use the notched three-point bending test of dehydrated nacre in situ in a scanning electron microscope (SEM) to monitor the evolution of damage mechanisms ahead of the crack tip. The observations show that the crack deflection actually occurs by constrained microcracking. On the basis of our findings, a crack propagation model is proposed, which will contribute to uncovering the underlying mechanisms of nacre’s fracture toughness and its damage evolution. These investigations would be of great value to the design and synthesis of novel biomimetic materials.     

Ductile reinforcements for enhancing fracture resistance in composite materials

Ductile reinforcements can supply fracture toughness to a polymer matrix by pulling out and by plastically deforming. In the case of metal reinforcements that are not in a toughened condition, there may be more toughening to be gained when the fibers remain in the matrix and plastically deform rather than pulling out. These fibers can be said to have an unused plastic potential. When these fibers bridge a crack, their plastic deformation causes a rise in the force which is trying to pull out the fiber. Because of this, the shape of the fiber must be adjusted along its length if it is to remain anchored and contribute its plastic work. The use of anchored, ductile fibers provides a new design axis that brings new possibilities not achievable by the current research focus on the fiber–matrix interface. This paper describes the experimental pullout of aligned ductile fibers from a polymer matrix, and indicates the effect of the shape and embedded length of the fiber on the toughness increase of the composite. Anchored, plastically deforming fibers are shown to provide a major improvement to the toughening. Even for unoptimized ductile fibers, the calculated toughening improvement equals or exceeds the toughening available from current short glass or graphite fibers. In addition, pullout values are obtained for fibers that are embedded at an angle, simulating fiber bridging from fibers not perpendicular to the crack surface. These results further demonstrate the toughening efficiency of ductile fibers.     

Crack buckling in soft gels under compression

Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior. The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping. In this paper, we study a possible fracture mechanism of soft gels under uni-axial compression. We show that the surfaces of a pre-existing crack, oriented parallel to the loading axis, can buckle at a critical compressive stress. This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip, which can lead to crack growth. We show that the onset of crack buckling can be deduced by a dimensional argument com- bined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space. The critical compression for buckling was verified for a neo-Hookean material model using finite element simulations.     

Small-scale crack bridging and the fracture toughness of particulate-reinforced ceramics

Theoreticalanalyses of small-scale bridging of crack surfaces by elastic-ideally plastic springs are presented and applied to the study of the fracture toughness of ceramics reinforced by small particles. The dependence of toughening on particle size, concentration, strength, and ductility is explored, and relations between toughening and bridge length at fracture are given. Available experimental information is examined in the light of the analyses.     

Toughening by Phase Boundary Propagation

Transformation toughening has enhanced the fracture toughness of certain Zirconia-Toughened Ceramics (ZTC) by factors of 2–4. The primary explanation of toughening, by McMeeking and Evans [1] and Budiansky et al. [2], suggests that the main source of toughening is the energy stored by the transformed inclusions in the wake of a propagating crack. In the case of supercritical ZTC where the boundary of the transformed zone is a phase boundary (surface of strain discontinuity), this paper suggests an additional source of toughening – that due to propagation of the phase boundary. By extending the J-integral to cracked bodies containing surfaces of strain discontinuity, the transformation toughening for a steady Mode I crack is evaluated.     

Interaction of fiber and transformation toughening

B small scale bridging (SSB) assumption, a theoretical study is made of the interaction between the fracture toughening effects of transforming particles and crack bridging fibers which are aligned in the direction perpendicular to the crack surfaces. The fibers bridging the crack are assumed to undergo large amounts of slipping inside the matrix. It is found that the interaction can be synergistic over a parametric range of material properties of the ceramic composite system. The Mode-1 plane-strain fracture toughness of the ceramic composite system is determined in terms of fiber strength, transformation toughening parameters and interaction parameters. The results obtained here are qualitatively similar to those for the interaction between the fracture toughening effects of transforming particles and crack-bridging ductile particles by A and B (1988a, J. Mech. Phys. Solids 36, 581).     

任意加载模式下含裂纹超弹性体的能量释放率

能量释放率是表征断裂性能的一个重要指标, 在经典的断裂力学中, 只给出在恒力或恒位移加载情形下通过柔度标定来确定材料能量释放率的公式, 而且仅限于线弹性材料. 但是近年来生物材料和高分子材料(如橡胶) 等超弹性材料的断裂韧性和增韧机理越来越受到研究人员的关注, 该文旨在导出一个更加通用的柔度标定公式, 从而可以确定非线性弹性材料在任意加载模式下的能量释放率, 并能判断裂纹扩展的稳定性. 在推导的过程中, 对一些重要而容易被错误理解的概念做了进一步论述.     

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.     

On the effect of nano-particle clustering on toughening of nano-composite ceramics

In this paper, two and three-dimensional clustering models are developed to characterize the effect of nano-particle clustering on toughening of nanocomposite ceramics. It is found that crack pinning toughens the nano-composite ceramics because a higher stress intensity factor is needed for crack to propagate around or to pull-out the nano-particle. The nano-particle along the grain boundary steers the crack into the matrix grain due to the strong cohesion between the nanoparticle and the matrix. Since the fracture resistance of the grain boundary is lower than that of the grain lattice, the higher the probability of transgranular fracture induced by nano-particles, the tougher is the nano-composite. However, both crack pinning and transgranular fracture are affected by nano-particle clustering. Nanoparticle clustering, which increases with increasing volume fraction of nano-particles, leads to reduction of both the strength and toughness of the nano-composite ceramics. The larger the size of the clustered particle, and the more defects it contains, the easier it is for the crack to pass through the clustered particle, which means that the nano-particle clustering can reduce toughening induced by crack pinning and transgranular fracture. The theoretical prediction, based on the combination of the three mechanisms of nano-particles, is in agreement with the experimental data. The project supported by the National Natural Science Foundation of China (19891180) and the Research Grants Council of the HKSAR, China(HKU7081/00E)     

Separating viscoelasticity and poroelasticity of gels with diferent length and time scales

Viscoelasticity and poroelasticity commonly coexist as time-dependent behaviors in polymer gels.Engineering applications often require knowledge of both behaviors separated;however,few methods exist to decouple viscoelastic and poroelastic properties of gels.We propose a method capable of separating viscoelasticity and poroelasticity of gels in various mechanical tests.The viscoelastic characteristic time and the poroelastic difusivity of a gel define an intrinsic material length scale of the gel.The experimental setup gives a sample length scale,over which the solvent migrates in the gel.By setting the sample length to be much larger or smaller than the material length,the viscoelasticity and poroelasticity of the gel will dominate at diferent time scales in a test.Therefore,the viscoelastic and poroelastic properties of the gel can be probed separately at diferent time scales of the test.We further validate the method by finite-element models and stress-relaxation experiments.     

Influence of relative humidity on fracture toughness of rock: Implications for subcritical crack growth

Information relating to the fracture toughness of geomaterials is critical to our understanding of tensile fracturing, and in particular in geological and rock engineering projects that are subjected to elevated moisture levels. In this study, we conducted a comprehensive set of fracture toughness tests on a suite of key rock types in air under different relative humidities and at constant temperature in order to investigate the influence of relative humidity on fracture toughness. Three sandstones and two igneous rocks were chosen for this purpose. We show that the value of fracture toughness decreases with increasing relative humidity. In addition, we find that the decrease in fracture toughness was more significant when the expansive clay such as smectite was included in rock. Since smectite is prone to expanding in the presence of water, the strength and thus crack growth resistance decrease when relative humidity is high. Therefore, we interpret the decreasing fracture toughness upon the degradation of expansive clays with increasing water content. It was also shown that the decrease of the fracture toughness with increasing humidity is less significant than the concomitant decrease in the measured value of the subcritical stress intensity factor. This was likely as a result of stress corrosion having little influence on the fracture toughness. We conclude that crack growth in rock is affected by humidity, and that clay content is an important contributing factor to changes in fracture toughness and subcritical stress intensity factor.     

Helical Fiber Pull-out in Biological Materials

Many biological materials, such as wood and bone, possess helicoid microstructures at microscale, which can serve as reinforcing elements to transfer stress between crack surfaces and improve the fracture toughness of their composites. Failure processes, such as fiber/matrix interface debonding and sliding associated with pull-out of helical fibers, are responsible mainly for the high energy dissipation needed for the fracture toughness enhancement. Here we present systemic analyses of the pull-out behavior of a helical fiber from an elastic matrix via the finite element method(FEM) simulation, with implications regarding the underlying toughening mechanism of helicoid microstructures. We find that, through their uniform curvature and torsion, helical fibers can provide high pull-out force and large interface areas, resulting in high energy dissipation that accounts, to a large extent, for the high toughness of biological materials. The helicity of fiber shape in terms of the helical angle has significant effects on the force-displacement relationships as well as the corresponding energy dissipation during fiber pull-out.     

Role of the polymer phase in the mechanics of nacre-like composites

Although strength and toughness are often mutually exclusive properties in man-made structural materials, nature is full of examples of composite materials that combine these properties in a remarkable way through sophisticated multiscale architectures. Understanding the contributions of the different constituents to the energy dissipating toughening mechanisms active in these natural materials is crucial for the development of strong artificial composites with a high resistance to fracture. Here, we systematically study the influence of the polymer properties on the mechanics of nacre-like composites containing an intermediate fraction of mineral phase (57 vol%). To this end, we infiltrate ceramic scaffolds prepared by magnetically assisted slip casting (MASC) with monomers that are subsequently cured to yield three drastically different polymers: (i) poly(lauryl methacrylate) (PLMA), a soft and weak elastomer; (ii) poly(methyl methacrylate) (PMMA), a strong, stiff and brittle thermoplastic; and (iii) polyether urethane diacrylate-co-poly(2-hydroxyethyl methacrylate) (PUA-PHEMA), a tough polymer of intermediate strength and stiffness. By combining our experimental data with finite element modeling, we find that stiffer polymers can increase the strength of the composite by reducing stress concentrations in the inorganic scaffold. Moreover, infiltrating the scaffolds with tough polymers leads to composites with high crack initiation toughness K_IC. An organic phase with a minimum strength and toughness is also required to fully activate the mechanisms programmed within the ceramic structure for a rising R-curve behavior. Our results indicate that a high modulus of toughness is a key parameter for the selection of polymers leading to strong and tough bioinspired nacre-like composites.     

冲击载荷作用下黑砂岩动态断裂参数的分形修正

基于分形理论研究了偏折裂纹扩展路径对动载荷作用下黑砂岩的动态断裂力学参数的测试误差影响作用,采用传统的分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验装置对修正侧开单裂纹半孔板（improved single cleavage semi-circle specimen, ISCSC）试样进行动态冲击实验,随后采用裂纹扩展计进行裂纹起裂时间与裂纹扩展速度等动态断裂力学参数测试,采用分形理论对测试的裂纹扩展速度与动态应力强度因子进行修正,利用实验-数值法对黑砂岩的动态断裂韧度进行计算。研究结果表明,ISCSC构型构件能够有效应用于岩石材料动态裂纹扩展行为的研究,并发生了止裂现象,经分形修正的裂纹扩展速度与动态断裂韧度更接近实际裂纹动态扩展情况,修正前后得到黑砂岩材料的裂纹扩展速度误差为33.51%,动态断裂韧度最大误差为7.68%,说明利用分形理论对动态断裂韧度等动态断裂参数计算更合理。

     

用焦散线法研究PP/PA6/POE-g-Ma的动态断裂性能

研究了由直接共混法制备而成的聚丙烯/尼龙6/马来酸酐接枝乙烯-辛烯共聚物(PP/PA6/POE-g-MA)三元共混体系的静、动态力学性能,并采用反射型动态焦散线方法对其动态断裂性能进行了实验研究。根据动态断裂实验过程中得出的I型裂纹尖端的焦散斑,测得PP/PA6/POE-g-Ma共混高聚物的动态断裂韧性和裂纹扩展速度。此外,本文通过扫描电镜对动态断裂截面的细观观测,进一步分析了材料损伤破坏的机理,并探讨了共混高聚物方法对材料抗断裂性能的影响。实验结果表明,动态焦散线方法为高聚物复合材料的动态断裂实验研究提供了一种可行的方法,并可为高聚物复合材料性能的改进提供依据。     

相变增韧陶瓷Ⅱ型裂纹增韧分析

本文采用压力敏感和权函数法，对相变增韧陶瓷Ⅱ型裂纹的增韧效应进行了理论预测。分别给出了静止裂纹和定常扩展裂纹相变性屏蔽的理论表达式，结果表明；相变对静止裂纹无增韧效应，纹尖端屏蔽来自于裂纹扩展尾区的贡献。