<Emphasis Type="Italic">In-situ</Emphasis> AFM Experiments with Discontinuous DIC Applied to Damage Identification in Biomaterials

Natural materials (e.g. nacre, bone, and spider silk) exhibit unique and outstanding mechanical properties. This performance is due to highly evolved hierarchical designs. Building a comprehensive understanding of the multi-scale mechanisms that enable this performance represents a critical step toward realizing strong and tough bio-inspired materials. This paper details a multi-scale experimental investigation into the toughening mechanisms in natural nacre. By applying extended digital image correlation and other image processing techniques, quantitative information is extracted from otherwise prodominantly qualitative experiments. In situ three point bending fracture tests are performed to identify and quantify the toughening mechanisms involved during the fracture of natural nacre across multiple length scales. At the macro and micro scales, fracture tests performed in situ with a macro lens and optical microscope enable observation of spreading of damage outward from the crack tip. This spreading is quantified using an iso-contour technique to assess material toughness. At the nanoscale, fracture tests are performed in situ an atomic force microscope to link the larger-scale damage spreading to sliding within the tablet-based microstructure. To quantify the magnitude of sliding and its distribution, images from the in situ AFM fracture tests are analyzed using new algorithms based on digital image correlation techniques which allow for discontinuous displacement fields. Ultimately, this comprehensive methodology provides a framework for broad experimental investigations into the failure mechanisms of bio- and bio-inspired materials.     

Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging

We demonstrate the use of X-ray phase contrast imaging with sub-microsecond temporal resolution to obtain quantitative visualization of dynamic fracture processes in brittle solids. We examine an amorphous solid (fused silica), a ceramic single crystal (single-crystal quartz), and a polycrystalline ceramic (boron carbide), in the form of single-edge notched specimens loaded using a three-point apparatus at nominal strain rates up to \(\sim \)800 s^?1. We observe that the crack tip speed for boron carbide is relatively independent of mode I stress intensity factor rate (\(\dot {K}_{\mathrm {I}}\)) for these rates of loading, while that of fused silica and single-crystal quartz increases with \(\dot {K}_{\mathrm {I}}\). Further, for the amorphous and single crystal cases, we observe the development of a crack tip instability in the form of crack branching as the crack tip speed approaches 45% of the Rayleigh wave speed. This suggests that strain-rate-dependent mechanisms contribute to crack branching. Such mechanisms may, in turn, affect the macroscopic fracture properties of these materials.     

An Experimental Investigation of Deformation and Fracture of Nacre–Mother of Pearl

Nacre, also known as mother-of-pearl, is a hard biological composite found in the inside layer of many shells such as oyster or abalone. It is composed of microscopic ceramic tablets arranged in layers and tightly stacked to form a three-dimensional brick wall structure, where the mortar is a thin layer of biopolymers (20–30 nm). Although mostly made of a brittle ceramic, the structure of nacre is so well designed that its toughness is several order of magnitudes larger that the ceramic it is made of. How the microstructure of nacre controls its mechanical performance has been the focus of numerous studies over the past two decades, because such understanding may inspire novel composite designs though biomimetics. This paper presents in detail uniaxial tension experiment performed on miniature nacre specimens. Large inelastic deformations were observed in hydrated condition, which were explained by sliding of the tablets on one another and progressive locking generated by their microscopic waviness. Fracture experiments were also performed, and for the first time the full crack resistance curve was established for nacre. A rising resistance curve is an indication of the robustness and damage tolerance of that material. These measurements are then discussed and correlated with toughening extrinsic mechanisms operating at the microscale. Moreover, specific features of the microstructure and their relevance to associated toughening mechanisms were identified. These features and mechanisms, critical to the robustness of the shell, were finely tuned over millions of years of evolution. Hence, they are expected to serve as a basis to establish guidelines for the design of novel man-made composites.     

Toughness amplification in natural composites

Natural structural materials such as bone and seashells are made of relatively weak building blocks, yet they exhibit remarkable combinations of stiffness, strength and toughness. This performance can be largely explained by their “staggered microstructure”: stiff inclusions of high aspect ratio are laid parallel to each other with some overlap, and bonded by a softer matrix. While stiffness and strength are now well understood for staggered composites, the mechanisms involved in fracture are still largely unknown. This is a significant lack since the amplification of toughness with respect to their components is by far the most impressive feature in natural staggered composites such as nacre or bone. Here a model capturing the salient mechanisms involved in the cracking of a staggered structure is presented. We show that the pullout of inclusions and large process zones lead to tremendous toughness by far exceeding that of individual components. The model also suggests that a material like nacre cannot reach steady state cracking, with the implication that the toughness increases indefinitely with crack advance. These findings agree well with existing fracture data, and for the first time relate microstructural parameters with overall toughness. These insights will prove useful in the design of biomimetic materials, and provide clues on how bone fractures at the nano and microscales.     

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s~(-iε), so that K = ■ s~(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.     

Discontinuous crack-bridging model for fracture toughness analysis of nacre

Studying the structure–property relation of biological materials can not only provide insight into the physical mechanisms underlying their superior properties and functions but also benefit the design and fabrication of advanced biomimetic materials. In this paper, we present a microstructure-based fracture mechanics model to investigate the toughening effect due to the crack-bridging mechanism of platelets. Our theoretical analysis demonstrates the crucial contribution of this mechanism to the high toughness of nacre. It is found that the fracture toughness of nacre exhibits distinct dependence on the sizes of platelets, and the optimized ranges for the thickness and length of platelets required to achieve higher fracture toughness are given. In addition, the effects of such factors as the mechanical properties of the organic phase (or interfaces), the effective elastic modulus of nacre, and the stacking pattern of platelets are also examined. Finally, some guidelines for the biomimetic design of novel materials are proposed based on our theoretical analysis.     

Numerical computation of central crack growth in an active particle of electrodes influenced by multiple factors

Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithium-ion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles \((\hbox {LiMn}_{2}\hbox {O}_{4})\) by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages: no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling.     

Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Dynamic fracture initiation toughness of marble was tested using two types of the holed-cracked flattened Brazilian disc (HCFBD) specimens, which were diametrically impacted at the flat end of the disc by the split Hopkinson pressure bar (SHPB) of 100 mm diameter. One type of the discs is geometrically similar with different outside diameter of 42 mm, 80 mm, 122 mm and 155 mm respectively, and with crack length being half the diameter; another type of the discs has identical 80 mm diameter and different crack length. Issues associated with determination of the stress wave loading by the SHPB system and the crack initiation time in the disc specimen were resolved using strain gage technique. The stress waves recorded on the bars and the disc failure patterns are shown and explained. The tested dynamic fracture toughness increases obviously with increasing diameter for the geometrically similar HCFBD specimens. It changes moderately for the one-size specimens of identical diameter and different crack length. The size effect of rock dynamic fracture toughness is mainly caused by the fracture process zone length l and fracture incubation time τ, the latter being an additional influencing factor for the dynamic loading as compared with the counterpart static situation. Hence a method is proposed to determine a unique value for the dynamic fracture initiation toughness, the approach takes average of the local distribution and time history for dynamic stress intensity factor in the spatial-temporal domain, which is defined by l and τ jointly. In this way the dynamic size effect is minimized.     

Fracture-toughness testing of limestone

Fracture-toughness measurements were made on standard three-point-bend fracture specimens of Indiana limestone. Specimen dimensions, experimental techniques, and methods of data reduction were chosen to comply as closely as possible to the Tentative Method of Test for Plane Strain Fracture Toughness of Metallic Materials (ASTM Designation: E399-72T). Typical strain-gage-type clip-in displacement gages were found to lack the necessary sensitivity for measuring the crack-opening displacement while an LVDT displacement transducer having a linear range of ±0.25 mm (±0.010 in.) was found to be ideal.Fatigue cracks were successfully introduced by repeated cycling to 85 percent of the fracture load. Load vs. crack opening-displacement records indicated that crack closure occurred in these tests. Effective crack lengths were determined using an experimental compliance calibration that was checked analytically. Final fracture was stable when using displacement control in a stiff load frame. Some size effects were noted, with toughness increasing with specimen size. Values ofK _c, fracture toughness, were found to approach 990 kNm^–3/2 (900 .) for the largest specimens.Paper was presented at 1975 SESA Spring Meeting held in Chicago, IL on May 11–16.Work was supported by the U.S. Energy Research and Development Administration.     

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.     

Identification of multiple open and fatigue cracks in beam-like structures using wavelets on deflection signals

A novel method for damage detection of multi-cracked beam-like structures by analyzing the static deflection is presented. The damage incurred produces a change in the stiffness of the beam. This causes a localized singularity which can be identified by a wavelet analysis of the displacement response. The existence and location of the cracks can be revealed by positions of the peaks in the continuous wavelet transform (CWT). To achieve this, the static profile of beams is analyzed with Gauss2 wavelet to identify the cracks. Beams under some ideal boundary and prescribed load conditions are considered. The deflected shape of the beam with open and fatigue cracks has been simulated under static loading using lumped crack models adopted from fracture mechanics and involving various degrees of complexity. The deflection of cracked beam in closed form for several cases of loads, crack sizes, and crack locations is calculated, and an explicit expression for the damage index (DI), based on CWT, is developed; it is demonstrated that the proposed damage index does not depend on mechanical properties of a homogeneous beam, and that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. Numerical results show that the method can detect cracks of small depth and is also applicable under the presence of measurement noise.     

Dynamic mechanical and fracture properties of an infiltrated TiC-1080 steel cermet

The dynamic mechanical and fracture properties of a TiC porous network infiltrated with1080 steel are reported. Following infiltration, the cermet is subjected to various heat treatments that affect essentially the steel matrix. Dynamic compression tests show that the heat treatments increase the fracture strength of the cermet. The quasi-static fracture toughness (K_Ic) is also increased by the heat treatments. The dynamic (initiation) fracture toughness (K_Id) is substantially higher (by about a factor of 3) than its static counterpart. Failure mechanisms consist mainly of cleavage of the TiC and matrix grains, along with minor interfacial decohesion. However, dynamic loading induces substantial damage around the crack tip, consisting essentially of cleavage of TiC grains. Microcrak toughnening is believed to be responsible for the high dynamic toughness of the material. The critical microstructural fracture event is thus identified as the spreading of TiC cleavage microcracks into the neighboring steel grains.     

Fracture Paths from Front Kinetics: Relaxation and Rate Independence

Crack fronts play a fundamental role in engineering models for fracture: they are the location of both crack growth and the energy dissipation due to growth. However, there has not been a rigorous mathematical definition of crack front, nor rigorous mathematical analysis predicting fracture paths using these fronts as the location of growth and dissipation. Here, we give a natural weak definition of crack front and front speed, and consider models of crack growth in which the energy dissipation is a function of the front speed, that is, the dissipation rate at time t is of the form

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.     

Effect of dislocation structure on fracture toughness of strained BCC-metals

Mechanical properties of materials depend on their structure. Examined are the effects of dislocation structure on fracture toughness and mechanisms of fracture of BCC-metals. Fracture toughness was determined by depending specimens with cracks introduced into the plane perpendicular to the plane of rolling. Fracture toughness increases with decreasing yield stress (for =15–25%). This is due to instability of slightly misoriented cell structure under repeated loading. The peak of fracture toughness at the temperature 77 K was not observed. The increase of fracture toughness for high strained metals (>60% for Mo, and >85% for Cr) corresponds to cell size reduction and the change of fracture mechanisms.     

Crack growth in concrete slab resting on steel beam: softening and damage accumulation

Analyzed in this work is the four-point bending of a concrete slab supported by a steel beam. An edge crack is assumed to prevail on the tension side of the concrete that would grow gradually while the overall stiffness and local fracture toughness of the concrete would also degrade as damage accumulates. The latter two quantities are assumed to decrease with increasing deflection of the composite system. These effects are incorporated into the strain energy density criterion that can simultaneously predict crack initiation and growth including the event of final termination. Numerical results on load and deflection are obtained for two different composite concrete/steel beam systems such that the prevailing geometric material and loading parameters are accounted for as a combination. The distances between the local and global stationary values of the volume energy density are also determined as an indication of fracture instability. An edge crack tends to extend more stably as the compressive zone ahead increases with deflection of the composite beam.     

Fracture in Microscale SU-8 Polymer Thin Films

In this work, the fracture of spin coated SU-8 epoxy thin films was investigated under mode I loading using in situ optical experiments on specimens with double edge notched tensile geometry. A method was developed to fabricate 3 μm thick SU-8 films with tapered Chevron type notches using a combination of electron beam and ultra-violet lithography techniques. Subsequently, through speckle patterning under tensile loading, the local deformation fields around the crack tip were extracted using digital image correlation. Since the notches were tapered through the thickness, a crack nucleated from them and grew stably until it spanned the entire thickness before propagating unstably leading to catastrophic failure. As SU-8 underwent brittle fracture with no evidence of a large process zone, the critical energy release rate, J _{I C} was computed from deformation fields, and was found to be 106.6 ± 12.03 J /m ². As the film thickness was small compared to lateral dimensions, assuming plane stress conditions, the critical stress intensity factor was calculated as 0.57 ± 0.03 MPa\(\sqrt {m}\). Furthermore, to assess the validity of the experimental method, a finite element simulation on the exact specimen geometry was conducted with experimentally evaluated far field displacement boundary conditions. The strain fields and J-integral value obtained from the simulation were in good agreement with the experimental results, implying the validity of the in situ experimental method proposed given the challenges of small scale specimens. Furthermore, using fractography and optical imaging it was confirmed that the unstable crack propagation started once the crack front reached full thickness, thereby providing sharp crack at the time of failure, which is necessary for brittle materials for valid fracture toughness experiment. It is expected that the proposed methods of specimen preparation and fracture experiments on microscale polymer thin films can be used on other materials.     

伴随微孔洞生长的裂纹弹塑性定常扩展

裂纹在韧性材料中扩展时,将们随着微孔洞的萌生和生长,孔洞的萌生和深化将直接影响着材料的总体断裂韧性和强度,以往的研究主要集中在将裂纹的扩展刻划为微孔洞的萌生、生长和汇合这样一个过程。从传统的断裂过程区模型出发研究微孔洞的萌生和生长对材料总体断裂韧性的影响,通过采用Ｇｕｒｓｏｎ模型,建立塑性增量本构关系,然后针对定常扩展情况直接进行分析,孔洞对材料断裂韧性的影响由本构关系刻划,而在孔洞汇合模型中,上     

A Robust <Emphasis Type="Italic">in situ</Emphasis> TEM Experiment for Characterizing the Fracture Toughness of the Interface in Nanoscale Multilayers

A novel in situ transmission electron microscopy (TEM) bending method using a nano-cantilever specimen that includes a naturally sharp pre-crack at the interface between a 500 nm-thick SiN layer and a 200 nm-thick Cu layer on a Si substrate is developed in order to precisely characterize the fracture toughness of the interface in nanoscale multilayers. By fabricating a perpendicular nanoscale notch in the SiN layer close to the horizontal Cu/SiN interface, a sharp pre-crack is successfully introduced at the Cu/SiN interface. In addition, by changing the relative position of the notch with respect to the fixed end of the specimen, both the instant and continuous interface crack propagation behaviors could be in situ observed using TEM. Finite element analysis shows that the crack propagation from the sharp pre-crack is dominated by a singular stress field within a region 100 nm from the crack tip under a mixed-mode state in all specimens. On the other hand, the fracture toughness represented by the critical energy release rate for the start of crack propagation along the Cu/SiN interface in all specimens is determined through a compliance method and shows good agreement with an average value of 7.1 J/m². This indicates the robust reliability and high precision for characterizing the fracture toughness of the interface in nanoscale multilayers.     

冲击载荷作用下圆孔缺陷对裂纹动态扩展行为的影响规律

空腔和裂纹缺陷通常共存于深部地下岩体中,它们共同影响着岩体的结构安全性与稳定性。为了探究动力扰动载荷下圆形空腔对裂隙岩体内裂纹扩展行为的影响规律,提出了不同圆孔倾角的直裂纹空腔圆弧开口试件（circular opening specimen with straight crack cavity, COSSCC）,利用自制大型落锤冲击实验装置进行动态加载实验,同时采用裂纹扩展计系统测试了裂纹的动态起裂时刻与裂纹扩展速度等各种断裂力学参数,随后采用有限差分软件Autodyn进行裂纹扩展路径与圆孔周围应力场的数值分析,并采用有限元软件Abaqus计算裂纹的动态起裂韧度与裂纹扩展过程中的动态扩展韧度。结果表明:（1）当圆孔倾角θ小于10°时,裂纹扩展路径会偏折并穿过圆孔表面;当圆孔倾角θ为20°与30°时,裂纹扩展路径向圆孔方向发生偏折但不会穿过圆孔,圆孔具有明显的裂纹扩展引导作用; 当圆孔倾角θ为40°与50°时,裂纹扩展路径不会发生偏折,圆孔引导作用明显减弱。（2）当裂纹扩展路径达到圆孔空腔附近时,裂纹尖端的拉伸应力区与圆孔边缘的拉伸应力区发生重合,此时裂纹扩展速度显著增大,裂纹动态断裂韧度显著减小。（3）裂纹的偏折方向与裂纹尖端最大周向应力的方向基本一致。（4）裂纹动态断裂韧度始终小于裂纹起裂韧度,且裂纹动态断裂韧度与裂纹动态扩展速度呈负相关关系。裂纹动态扩展速度越大,裂纹动态断裂韧度越小。