Fracture and electric-field-induced crack growth behavior in NBT-6BT relaxor ferroelectrics

The fracture properties of 0.94(Na_0.5Bi_0.5)TiO₃-0.06BaTiO₃ (NBT-6BT) relaxor ferroelectrics were investigated using the Vickers indentation method and computation of crack tip opening displacement. It was found that an unpoled sample had a fracture toughness of around 1.35 MPa m^1/2. In contrast, an electrically poled sample exhibited anisotropy with a lower fracture toughness perpendicular to the poling direction and a higher value in the parallel direction, as compared to the unpoled sample. Upon cyclic electrical loading (with applied electric field amplitudes between 0.73E_C and 1.4E_C), the indented surface crack was found to propagate. In general, the crack grew rapidly during the initial cycles followed by crack arrest, and the principal driving force for crack growth was proposed to be residual stress around the indentation, as evidenced by the limited field dependence of crack growth. There was also a contribution from the electromechanical strain, which played a role at high cycles (>100 cycles) and high fields (>1.3 E_C). Evidence of a saturation threshold of crack propagation is an advantage for the electromechanical reliability of relaxor ferroelectrics in devices.     

Fracture Mechanics of High-Toughness Magnesia-Partially-Stabilized Zirconia

Crack growth resistance in MgO-partially-stabilized ZrO₂ (Mg-PSZ) has been studied using notched double-cantilever beams (DCB's). High-toughness Mg-PSZ exhibited nonlinear mechanical behavior in the form of residual displacements, related to the transformation of tetragonal ( t ) ZrO₂ precipitates to monoclinic ( m ) symmetry. The influence of this residual displacement on crack resistance behavior (" R -curve" behavior) was analyzed using several different fracture mechanics approaches. Specifically, the "global" resistance W _R (Δ a ), a J -integral type parameter W _J (Δ a ), were determined as a function of crack extension (Δ a ). Some of these parameters displayed a geometry dependence; their form depended on the initial notch depth and the size of the unbroken ligament. The early stages of crack growth were best described by W _J (δ a ). The residual strains building up in the wake during crack growth and their effect on specimen displacement made the W _R curves (and to some extent the W _J curves) dependent on the ratio between initial notch depth and crack extension. The only curves independent of geometry were the G (δ a ) curves, but only in a restricted range of geometry. However, the material resistance of Mg-PSZ is clearly under-estimated with such a linear elastic approach.     

A quantitative analysis of the indentation fracture of fused silica

It is unclear how the densification of fused silica influences the damage of its precision optics subjected to machining. This paper presents a quantitative analysis of the indentation fracture of fused silica involving densification with the embedded center of dilation (ECD) model. The Hertzian stress field and the ECD-induced stress field were superposed to provide the overall stress distribution in the loading stage. A new method was established to accurately determine the strength of the ECD-induced stress field with densification effects. With the aid of the ECD model, the starting locations, initiation stages and initiation sequence of crack morphologies were predicted by analyzing the stress fields. To quantitatively study the initiation of conical cracks in fused silica, the strain energy release rate was calculated by linear elastic fracture mechanics (LEFM). The predicted minimum threshold load leading to conical cracking was consistent with the measured values.     

Lateral cracks during sliding indentation on various optical materials

A series of static and sliding indentation (ie, scratching) was performed and characterized on a wide range of optical workpiece materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂–Al₂O₃–P₂O₅–Li₂O glass ceramic (Zerodur); and glasses of SiO₂:TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅–Al₂O₃–K₂O–BaO (Phosphate)] at various applied loads using various indenters (Vickers, 10 µm conical, and 200 µm conical). Despite having different load dependencies, the lateral crack depth formed during sliding indentation quantitatively scales with that formed during static indentation, explaining why static indentation has been historically effective in describing various grinding parameters. Depending on the indenter geometry, the amount of residual trench damage (plastic deformation and local fracturing) during sliding indentation was often enhanced by more than an order of magnitude compared with static indentation. A simple ploughing scratch model, which considers both tangential and normal stresses (where the tangential stress is amplified by relatively small tangential contact area), explains this enhancement and other observed trends. Accounting for the high correlation between residual trench depth and volumetric fracturing, the model is extended to estimate the amount of fracture damage as a function of the material properties of the workpiece, indenter geometry, and applied load. Such a model has utility in the design of optimized grinding processes, particularly the abrasive geometry. Finally, at higher loads (>1 N), lateral cracks were often observed to preferentially propagate in the forward scratching direction, as opposed to perpendicular to the scratch as typically observed. High-speed imaging of the scratch process confirms that these cracks propagate ahead of the sliding indenter during the scratching event. Finite element stress analysis suggests the ploughing frictional forces increase the mode I tensile stresses at the leading edge of the sliding indenter explaining the direction of crack propagation of such cracks.     

Fracture mechanics of sharp scratch strength of polycrystalline alumina

The strength of a polycrystalline alumina containing controlled scratches introduced by translated sharp contacts is investigated and described by a multiscale fracture mechanics model. Inert strength measurements of samples containing quasi‐static and translated Vickers indentation contacts showed that scratches degraded the strength at normal contact loads an order of magnitude less than those for quasi‐static indentation. The fracture mechanics model developed to describe strength degradation by scratches over the full range of contact loads included toughening effects by crack‐wake bridging at the microscale and lateral crack‐based residual stress relaxation effects at the mesoscale. A critical element of the model is the nonlinear scaling of the residual stress field of a scratch with the normal contact load acting during scratch formation. The similarities and differences in the scratch model in comparison with prior indentation‐strength fracture mechanics models are highlighted by parallel development of both. Central to the scratch model is the use of easily controlled normal contact load as the scratch‐strength measurement variable. Scratch length and orientation are shown to have significant effects on strength. The distributions of scratch widths controlling the intrinsic strengths of as‐received samples are determined and agreement with the observed scratch dimensions is demonstrated.     

Origin of the Static Fatigue Limit in Oxide Glasses

Oxide glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. The log of crack velocity decreases linearly with decreasing stress intensity factor in Region I. For some glasses, at a lower stress intensity, K_o, log v asymptotically diminishes where there is no measurable crack growth. The same glasses exhibit static fatigue, or a decreasing strength for increasing static loading times, as cracks grow and stress intensity eventually reaches the fracture toughness. In this case, some glasses exhibit a low stress below which no fatigue/failure is observed. The absence of slow crack growth under a low stress intensity factor is called the fatigue limit. Currently, no satisfactory explanation exists for the origin of the fatigue limit. We show that the surface stress relaxation mechanism, which is promoted by molecular water diffusion near the glass surface, may be the origin of the fatigue limit. First, we hypothesize that the slowing down of slow crack growth takes place due to surface stress relaxation during slow crack growth near the static fatigue limit. The applied stress intensity becomes diminished by a shielding stress intensity due to relaxation of crack tip stresses, thus resulting in a reduced crack velocity. This diminishing stress intensity factor should result in a crack growth rate near the static fatigue limit that decreases in time. By performing Double Cantilever Beam crack growth measurements of a soda‐lime silicate glass, a decreasing crack growth rate was measured. These experimental observations indicate that surface stress relaxation is causing crack velocities to asymptotically become immeasurably small at the static fatigue limit. Since the surface stress relaxation was shown to take place for various oxide glasses, the mechanism for fatigue limit explained here should be applicable to various oxide glasses.     

Fracture mechanics of dental adhesives supplemented with Polymethyl-vinyl-ether-co-maleic anhydride

The objective of this study was to determine the effect of Polymethyl-vinyl-ether-co-maleic anhydride (PVM/MA), called Gantrez AN, on interfacial fracture toughness (K_IC) of self-etch and etch-and-rinse dental adhesives. Sixty-five chevron-notched dentin-composite resin specimens were prepared. The following testing groups with different bonding agents were prepared and tested with a cross head speed of 0.1 mm/min: Clearfil SE (CF); Clearfil SE with Gantrez AN in primer (CFGp); Clearfil SE with Gantrez AN in bonding agent (CFG); Prime & Bond (PB); Prime & Bond with Gantrez AN (PBG). The K_IC values were determined and compared. The mode of failure was examined with light microscopy. The mean K_IC (standard deviation) of the Clearfil SE groups were 0.60 (0.09) MPa m^1/2 for CF, 0.64 (0.09) MPa m^1/2 for CFGp and 0.68 (0.16) MPa m^1/2 for CFG. The most common mode of fracture was cohesive. The mean K_IC (standard deviation) of the Prime & Bond groups were 0.63 (0.09) MPa m^1/2 for PB and 0.41 (0.11) MPa m^1/2 for PBG. Adhesive fracture most commonly occurred in the Prime & Bond groups. Gantrez AN did not adversely affect K_IC of the self-etch dental adhesive, but lowered K_IC of the etch-and-rinse adhesive. Addition of Gantrez AN to self-etch adhesive (CF) may be warranted to produce an antibacterial effect. Clinical studies of bacterial attachment and anti-bacterial effects to further justify the use of Gantrez AN in bonding agents are warranted.     

Measurement of the silica glass fatigue limit

The static fatigue limit, or the threshold stress intensity factor, K_o, for first subcritical crack growth has been measured directly in silica glass for T ≥ 600°C using the double cantilever beam (DCB) crack growth technique. Values measured ranged from 0.48 to 0.61 MPa·m^1/2 for a temperature range of 600°C-850°C, respectively. Cracks growing near the static fatigue limit had a time-dependence, where the crack growth decreased and appeared to stop at K ≈ K_o. Slow crack growth curves (K-v) have been measured from room temperature, 50% RH, up to 850°C with subcritical crack growth not measurable for T > 900°C. Increasing temperature was found to first increase, and then decrease the slope of Region I, and a peak in fatigue resistance was found around 150°C-300°C. At T > 600°C subcritical crack growth was observed for K higher than previously measured K_IC values. This observation and the static fatigue limit in silica are explained by a water-assisted stress relaxation mechanism at the crack tip.     

In-Plane Fracture Resistance of a Crossply Fibrous Monolith

The in-plane fracture resistance of a crossply Si₃N₄/BN fibrous monolith in the 0°/90° and ±45° orientations is examined through tests on notched flexure specimens. The measurements and observations demonstrate the importance of fiber pullout following fiber fracture. The mechanical response is modeled using a crack-bridging approach. Two complementary approaches to evaluating the bridging law are developed: one based on a micromechanical model of fiber pullout and the other based on the load versus crack mouth opening displacement response of the flexure specimens following fracture of all fibers. Both approaches indicate that the bridging law follows an exponential form, characterized by a bridging strength and an effective pullout length. An assessment of the bridging model is made through comparisons of simulations of the load–displacement response with those measured experimentally.     

The influence of particle size distribution on rheological properties of fused silica pastes for direct ink writing

Additive manufacturing of ceramics through the direct ink writing method becomes possible when the effective parameters on rheology are optimized accurately. Successful manufacturing first requires the easy flowing of the ink through the nozzle and then a suitable viscoelastic response for the shape retention of the 3D printed structure. In the present study, fused silica pastes with different particle size distributions varying from D₉₀ of 5–50 µm were prepared for direct ink writing of porous structures. The rheological properties of the pastes, including flow behavior and the viscoelastic moduli variations, were investigated to study the influence of particle size and its distribution on fabricating complex structures. Through investigations, it was found that the narrower size distributions were more appropriate for direct ink writing of fused silica pastes. As the distribution became narrow, the shear thinning behavior was intensified, and the pastes showed high elasticity. The sintering procedure was performed using microwave radiation to suggest a fast process for manufacturing fused silica complex parts containing partially crystallized cristobalite phase and providing porosity of about 10% and a relative density of 90%.     

石英陶瓷导弹天线罩材料延迟断裂行为的研究

通过保载试验研究了石英陶瓷导弹天线罩材料延迟断裂行为的特性。试验表明,石英陶瓷材料在低于其断裂强度的恒定载荷作用下,内部微裂纹存在慢速扩展的现象,微裂纹扩展速度与载荷大小密切相关;在低于材料断裂强度约50%左右的载荷下,在300s的保载时间内,石英陶瓷材料试样内部裂纹没有产生明显的裂纹扩展现象。     

Controlled Crack Growth Specimen for Brittle Systems

A pure Mode I fracture specimen and test procedure has been developed which provides extended, stable, through-thickness crack growth in ceramics and other brittle, nonmetallic materials. Fixed displacement loading, applied at the crack mouth, promotes stable crack extension by reducing the stored elastic strain energy. Extremely fine control of applied displacements is achieved by utilizing the Poisson expansion of a compressively loaded cylindrical pin. Stable cracks have been successfully grown in soda-lime glass and monolithic Al₂O₃ for lengths in excess of 20 mm without uncontrollable catastrophic failure.     

在氢环境中2(1/4)Cr-1Mo钢的断裂特性

研究了在模拟加氢反应器工况条件下,国产加氢反应器壁材料2(1/4)Cr-1Mo钢的断裂特性。应用断裂力学方法,分别测定了原始状态、原始＋电化学渗氢、步冷状态、步冷＋热渗氢试样的断裂韧性K_IC;计算了埋入裂纹和表面裂纹的裂纹尖端的应力强度因子K_I。结果表明：步冷处理提高了2(1/4)Cr-1Mo钢的断裂韧性,氢降低了2(1/4)Cr-1Mo钢的断裂韧性;只要反应器内壁无表面裂纹,设备运行是安全的。     

韧性聚合物材料的基本断裂功和变形行为研究

用双边缺口拉伸试样研究了几种聚烯烃塑料薄片在平面应力条件下的破坏行为。从断裂功 -韧带长度关系得到反映断裂韧性的材料常数比基本断裂功和反映材料塑性变形行为的比非基本断裂功 ,藉此分析和解释了这些材料的韧性和塑性特征 ;同时验算处理表明这些材料的试样断裂伸长与韧带长度均呈直线关系 ,线性回归相关系数达到 0 97～ 0 99,由此求得了反映临界裂纹张开位移的材料参数等。这些参数可用于研究材料的变形能力和断裂行为 ,解释材料的破坏机理     

Fracture behavior of epoxy polymers modified with core-shell rubber particles

Physical and thermomechanical properties of BDMA-catalyzed DGEBA/Dicy epoxy toughened with core-shell particles were studied. Relationships between these properties and the level of toughening are reported. The blends have been made in well-defined processing conditions. In fact, the resulting properties depend on the state of dispersion of the particles in the prepolymer matrix before crosslinking and on the cure schedule. The considered core-shell particles were of two types: i) poly(butadiene-co-styrene) core/carboxy-functionalized poly(methyl methacrylate-co-styrene) shell. Such core-shell particles have been dispersed in the epoxy matrix at different volume fractions (from 9.5 to 24%); ii) poly(butyl acrylate) core/carboxy functionalized poly(methyl methacrylate-co-styrene) shell. These particles have been dispersed at a volume fraction of 24%. Static mechanical tests were performed in tension and compression modes on these core-shell polyepoxy blends. A slight decrease of Young's modulus and an increase of the ability to plastic deformation were noticed as the volume fraction of the core-shell particles increased. Using linear fracture mechanics (LEFM), an improvement of the fracture properties (K_IC) was measured. Fatigue crack-growth studied for blends demonstrates that the Paris's law can be used to describe the behavior of the materials. Increasing the volume fraction of core-shell particles leads to an improvement of the resistance to fatigue crack-propagation. The same trend is noted on the impact behavior studied by means of high-speed tests performed in a large range of temperatures. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2419–2431, 1997     

再生混凝土疲劳断裂力学分析

本文在对再生混凝土断裂破坏形态进行分析的基础上,提出了虚拟张开型裂纹模型.由此分析了虚拟张开型裂纹的扩展速率,回归得到了裂纹扩展速率Paris公式的参数.通过对虚拟张开型裂纹的扩展速率理论分析结果进行分析,提出了指数形式的裂纹扩展速率公式,该公式较Paris公式更接近于理论分析的结果.     

压痕法测量ZrO2/Al2O3陶瓷断裂韧性的研究

使用压痕法研究ZrO2/Al2O3陶瓷的断裂韧性,通过实验分析放大倍数和载荷两个因素对试样M31和M34测量结果的影响.放大倍数低于600倍时,很难测量出实际裂纹尺寸,而在6000倍时测得了比较准确的裂纹尺寸.随着载荷的增加,样品M31断裂韧性对比误差逐渐降低,样品M34误差呈波浪式变化.选择最适宜的载荷,可得到最接近实际情况的KIC值;本文通过大量实验数据证实,样品M31最适宜的载荷范围在8～12 kg,M34的载荷范围在6～8 kg.裂纹的扩展形式包括沿相界断裂,沿晶界断裂和潜藏断裂.沿相界断裂消耗能量较低,对陶瓷材料强度和韧性贡献较小;沿晶界断裂消耗能量较高,对陶瓷材料强度和韧性贡献较大.     

Fracture properties of nanoclay‐filled polypropylene

Maleic anhydride‐modified polypropylene was compounded with commercially available surface‐modified montmorillonite in a twin‐screw extruder. Recompounding ensured the removal of visible tactoids from the extrudate but TEM and XRD techniques showed nonuniform dispersion of clay platelets. In this study, we investigated the mechanical and fracture properties of nanoclay‐filled polypropylene. Emphasis was placed on the fracture characterization of the clay‐filled polypropylene. Tensile strength and stiffness increased steadily with an increase in the clay loading. The toughness of compounded materials was characterized using rigorous fracture mechanics. J‐integral fracture resistance decreased with an increase in the clay content. The resistance against stable crack growth was compared using the slopes derived from the J–R curve and the tearing modulus concept. A significant amount of crack growth resistance was evident in the nanoclay‐filled polypropylene as opposed to other brittle nanocomposites such as the nylon–clay systems. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 3298–3305, 2003     

SEM Quantification of Transgranular vs Intergranular Fracture

A SEM procedure for quantifying the percentage area of transgranular fracture and surface roughness was developed to study the fracture morphologies of stable and rapid crack growths in ceramics and ceramic matrix composites. The procedure utilizes software which interprets the SEM line scanning profiles. Results obtained through this procedure were correlated with the visual observation and profilometer measurements of Al₂O₃ and SiC_w/Al₂O₃ fracture specimens.     

Fracture and Subcritical Crack-Growth Behavior of Y-Si-Al-O-N Glasses and Si3N4 Ceramics

Fracture and environmentally assisted subcritical crack-growth processes are examined in bulk Y-Si-Al-O-N oxynitride glasses with compositions typical of the grain boundary phase of silicon nitride ceramics. Both long-crack (in compact tension specimens) as well as short-crack behavior (using indentation techniques) were investigated to establish a reliable fracture toughness and to elucidate the anomalous densification behavior of the oxynitride glass. Environmentally assisted subcritical crack-growth processes were studied in inert, moist, and wet environments under both cyclic and static loading conditions. Behavior is discussed in terms of the interaction of the environment with the crack tip. Likely mechanisms for environmentally assisted crack growth are discussed and related to the subcritical crack-growth behavior of silicon nitride ceramics.