Crack-Tip Toughness Measurements on a Sintered Reaction-Bonded Si3N4

An evaluation of measurements of crack opening displacements (CODs) on a commercial sintered reaction-bonded silicon nitride (SRBSN) was performed. To determine the intrinsic fracture toughness of this material, a new evaluation method is presented, which takes into account not only the near tip CODs, but the CODs of the complete crack profile. The method is applied on through-thickness cracks in bend bars and contrasted to CODs of Vickers radial cracks. A crack-tip toughness of ∼1.7 MPa·m^1/2 is obtained.     

Measurement of Crack Tip Toughness in Alumina as a Function of Grain Size

Crack profile measurements near the crack tip in the SEM were used to measure crack tip toughness of alumina as a function of grain size (average grain size 0.9–16 μm). For comparative tests, two crack configurations were included in the present study: straight cracks (CT specimen) loaded with an in situ device; and radial indentation cracks. The measured crack tip toughness values were independent of crack geometry, and no grain size dependence could be discerned. A mean crack tip toughness of 2.3 MPam^1/2 was evaluated. The crack tip toughness determined from crack profile measurements is significantly lower than the toughness evaluated with conventional indentation techniques (e.g., indentation strength bending).     

High-Temperature Crack Growth in Monolithic and SiCw-Reinforced Silicon Nitride under Static and Cyclic Loads

Experimental results are presented on subcritical crack growth under sustained and cyclic loads in a HIPed Si₃N₄ at 1450°C and a hot–pressed Si₃N₄–10 vol% SiC_w composite in the temperature range 1300°–1400°C. Static and cyclic crack growth rates are obtained from the threshold for the onset of stable fracture with different cyclic frequencies and load ratios. Fatigue crack growth rates for both the monolithic and SiC_w-reinforced Si₃N₄ are generally higher than the crack growth velocities predicted using static crack growth data. However, the threshold stress intensity factor ranges for the onset of crack growth are always higher under cyclic loads than for sustained load fracture. Electron microscopy of crack wake contact and crack–tip damage illustrate the mechanisms of subcritical crack growth under static and cyclic loading. Critical experiments have been conducted systematically to measure the fracture initiation toughness at room temperature, after advancing the crack subcritically by a controlled amount under static or cyclic loads at elevated temperatures. Results of these experiments quantify the extent of degradation in crack–wake bridging due to cyclically varying loads. The effects of preexisting glass phase on elevated temperature fatigue and fracture are examined, and the creep crack growth behavior of Si₃N₄–based ceramics is compared with that of oxide-based ceramics.     

Temperature dependence of craze shape and fracture in polycarbonate

The shape of the craze at the tip of a loaded crack has been determined by optical microscopy for polycarbonate. The effect of temperature was examined, and measurements were made on samples of different molecular weight. In all cases the craze shape can be described to a good approximation by the Dugdale model for the plastic zone at a crack tip. The crack opening displacement depended on sample molecular weight, but was independent of temperature. Fracture toughness values deduced from the craze shape were in good agreement with plane strain fracture toughness obtained from direct cleavage fracture measurements, on the assumption that failure occurs by combined plane strain and plane stress fracture modes.     

Crack‐tip toughness of lead‐free (1−x)(Na1/2Bi1/2)TiO3–xBaTiO3 piezoceramics

Crack opening displacements were evaluated on semi‐elliptical indentation cracks in lead‐free (1?x)(Na_1/2Bi_1/2)TiO₃–xBaTiO₃ piezoceramics and a commercially available PZT ceramic. The observed crack‐tip toughness of NBT‐xBT was found to be substantially higher than for PZT. Two evaluations for the crack opening displacement were demonstrated and contrasted: A more elaborate three‐term‐approximation and a pragmatic utilization of the Irwin parabola.     

Piezospectroscopic measurement of the stress field around an indentation crack tip in ruby using SEM cathodoluminescence

Piezospectroscopy using stress-sensitive lines in the cathodoluminescence (CL) spectrum generated in response to excitation by the electron beam of an SEM has recently been shown to be a promising technique for submicron resolution stress measurements in alumina and other ceramics. This paper develops and applies the technique by mapping the wavelength shifts of the R₁ CL line around the tip of an indentation crack in a ruby single crystal. Accounting for crystallographic anisotropy, the shifts observed were quantitatively consistent with the classical crack tip stress field for all polar angles ahead of the crack tip and indicated a crack tip stress intensity factor of 1.0 MPa m^1/2. This is significantly lower than the fracture toughness of the crack plane (4.5 MPa m^1/2), and indicates the post-indentation development of lateral cracks and slow crack growth. The spatial resolution of the stress measurements was measured as 550 nm and the effects of specimen heating by the electron beam were shown to be negligible.     

聚碳酸酯／弹性体合金的断裂过程形貌研究

采用扫描电子显微镜 (SEM)和长距离显微镜 (LDM)对PC/弹性体共混体系试件中的裂纹在平面应变和平面应力下发展的形貌进行观察。结果表明 :弹性体的加入影响了材料断裂的各个过程。在平面应变下 ,裂纹尖端出现超钝化现象 ;平面应力下 ,第一次观察到裂纹后岸两侧出现副裂纹的现象。采用透射电子显微镜 (TEM )观察慢速加载时裂纹前沿各区的形貌 ,从微观上解释弹性体增韧PC的原因     

Fracture toughness of random fibrous materials with ultrahigh porosity at elevated temperatures

The fracture toughness of three‐dimensional random fibrous (3D RF) material was investigated from room temperature to 1273 K by virtue of experimental method, theoretical model and Finite Element Method (FEM) in the through‐the‐thickness (TTT) and in‐plane (IP) directions. The experiments showed that the fracture toughness in the TTT and IP directions increases (from 0.0617 to 0.0924 Mpa·m^1/2 and from 0.2958 to 0.3982 Mpa·m^1/2 for the TTT and IP directions, respectively) as the temperature until reaching a transition temperature (1123 K and 1223 K for the TTT and IP directions, respectively), then the fracture toughness decreases from 0.0924 to 0.0393 Mpa·m^1/2 and from 0.3982 to 0.3106 Mpa·m^1/2 for the TTT and IP directions, respectively. The fracture behavior was related to the bulk microstructures, the mechanical properties of fibers and the blunting of crack tip. The crack tip blunting affected the fracture toughness at elevated temperatures which was verified using the theoretical model. A FEM model with a single edge crack where special attention was drawn to the influence of the morphological characteristic was developed to simulate the fracture behavior of 3D RF material. Numerical results from the FEM modeling along with a theoretical model with crack tip blunting mechanism incorporated agreed well with the experimental results.     

Anisotropy of Fracture Toughness of Piezoelectric Ceramics

The anisotropy of fracture toughness of PZT- and barium titanate-based piezoelectric ceramics was studied using doubletorsion and indentation methods. The influence of elastic anisotropy and the piezoelectric effect in calculating the K_c value are discussed. The fracture toughness in the polarization plane is greater than that in the perpendicular plane. A model is suggested to explain the observed anisotropy; it is based on assumption of a stress-induced domain reorientation zone near the crack tip.     

Evaluation of Electric Fracture Properties of Piezoelectric Ceramics Using the Finite Element and Single-Edge Precracked-Beam Methods

Single-edge precracked-beam (SEPB) tests were performed on a commercial lead zirconate titanate (PZT) ceramic. Mechanical loading was applied by the crosshead displacement control of a screw-driven electromechanical test machine. The fracture toughness parameter K _C was determined for various electric fields. A finite element analysis was also done to calculate the total potential energy release rate, mechanical strain energy release rate, and stress intensity factor for three-point flexure piezoceramic specimens with permeable and impermeable cracks under displacement and load control conditions. Numerical investigation and comparison with test data indicate that the energy release rate, upon application of the permeable model, is useful for predicting crack growth in PZT ceramic under electromechanical loading. Based on current findings, we suggest that the energy release rate criteria for the permeable crack are superior to fracture criteria for the impermeable crack.     

Fracture toughness and crack instability in tough polymers under plane strain conditions

The plane strain fracture toughness and fracture mechanisms of several tough engineering plastics have been studied and compared with poly(methyl methacrylate) (PMMA), a relatively brittle polymer. The tough polymers all are observed to form a multiple craze zone at the crack tip, which is shown to be the primary source of plane strain fracture toughness in these materials. The multiple craze zone is retained during slow crack growth but is metastable, and at a critical stress intensity and associated crack velocity, the system passes through a transition to a greatly accelerated single craze mode of unstable propagation.     

用J积分法表征聚碳酸酯／弹性体合金的韧性

采用Ｊ积分法表征聚碳酸酯（ＰＣ）／弹性体共混体系的韧性。结果表明，当加入弹性体后，体系断裂韧性ＪＩＣ明显提高，提高了约８０％。在弹性体含量为５－１５％时，断裂韧性ＪＩＣ变化不大，撕裂量Ｔｍ随着弹性含量的增加而增大，在弹性体含量为１０％时增加了１２．５倍。弹性体增韧ＰＣ的原因主要在于提高其抗 扩展能量。采用ＳＥＭ观察材料中的裂纹在平面应变下的发展过程发现，起裂前裂尖出现钝化和靴状超钝化现象，从微观上     

R-curves of lead zirconate titanate (PZT)

R-curves were measured for ferroelectric ceramic lead zirconate titanate (PZT) using surface cracks in flexure (SCF) in a single composition of unpoled, ferroelastic PZT. The effects of several parameters on the R-curves were experimentally determined. These included grain size, indentation load, polishing away the residual stress zone associated with the Knoop indentation, and thermal depolarization after indentation. The larger grain size resulted in a higher plateau value of the R-curve, a result consistent with the larger amount of ferroelastic switching observed in the stress/strain curve. Increasing the indentation load from 10 to 50 N resulted in larger initial crack sizes. This had some effect on the early part of the R-curve, but did not much affect the plateau value. Polishing away the residual stress zone eliminated the residual stress contribution of the Knoop indentation to the stress intensity factor. This resulted in the most accurate measurement of the intrinsic toughness (0.4 MPa m^1/2). Thermal depolarization to remove any potential ferroelastic crack tip switching zone associated with the indentation had little or no effect on the measured R-curves.     

Anisotropic Fracture Behavior in Ferroelectric Relaxor PZN–4.5%PT Single Crystals

The anisotropic fracture behavior in unpoled and poled (1− x )Pb(Zn_2/3Nb_1/3)− x PbTiO₃ ( x =0.045) (PZN–4.5%PT) single-crystal relaxor ferroelectrics cut along the crystal planes, [010] and [001], was characterized. The crack tip toughness ( K _tip) determined from Vickers indentations was compared with the R -curve behavior measured using the single-edge V-notch beam (SEVNB) method. Several of the SEVNB fracture experiments resulted in cracks forming and propagating under mixed mode loading ( K _I and K _II) along the [110] crystal plane. Other specimens formed cracks at 0° along the [010] plane. To assess the anisotropic fracture behavior, the local and global critical energy release rates were determined using Stroh's formalism.     

In Situ Measurement of Bridging Stresses in Toughened Silicon Nitride Using Raman Microprobe Spectroscopy

Bridging stresses that result both from elastic tractions and frictional interlocking in the wake of an advancing crack have been evaluated quantitatively via in situ Raman microprobe spectroscopy in a toughened Si₃N₄ polycrystal. Crack opening displacement (COD) profiles of bridged cracks also have been measured quantitatively via scanning electron microscopy to substantiate the piezospectroscopic determination of microscopic stresses via Raman spectroscopy. The highest spatial resolution of the stress measurement in the Raman apparatus was 1 µm, as dictated by the optical lens that was used to focus the laser on the sample. Measurements of the bridging stresses were performed both at fixed sites (as a function of the applied load) and along the profile behind the crack tip (under a constant load). Rather high stress values (i.e., 0.4-1.1 GPa) were measured that corresponded with unbroken ligaments that bridged the crack faces in elastic fashion, whereas frictional sites were typically under a lower tensile stress (0.1-0.5 GPa). Mapping the near-tip COD profile and the bridging stresses at the (normal) critical load for catastrophic fracture enabled us to calculate the crack-tip toughness and to explain the rising R -curve behavior of the material. From a comparison with conventional fracture-mechanics data, a self-consistent view of the mechanics that govern the toughening behavior of the Si₃N₄ polycrystal could be obtained. In particular, crack bridging is proven to be, by far, the most important mechanism that contributes to the toughening of polycrystalline Si₃N₄ materials.     

Raman Microprobe Evaluation of Bridging Stresses in Highly Anisotropic Silicon Nitride

The microscopic bridging stress distribution developed behind the crack tip of a highly anisotropic silicon nitride has been measured along the crack profile using Raman microprobe spectroscopy with a micrometer spatial resolution. The near-tip rising R -curve behavior and the crack-opening displacement (COD) profile of the material were also determined and discussed in comparison with the Raman microstress data. A comparison with the fracture behavior of a previously investigated silicon nitride material with a three-dimensional random microstructure is also proposed. According to this set of micro/macroscopic fracture characterizations, a self-consistent view of toughening behavior in silicon nitride ceramics is obtained, and the role on toughness of anisotropically oriented acicular grains clarified. In agreement with previous studies, it is confirmed that crack-face bridging is the most effective mechanism for toughening silicon nitride ceramics.     

Effect of Bond Thickness on Fracture Behaviour in Adhesive Joints

To study the effects of bond thickness on the fracture behaviour of adhesive joints, experimental investigation and finite element analysis have been carried out for compact tension (CT) and double-cantilever-beam (DCB) specimens with different bond thickness. Fractography and fracture toughness exhibited apparent variations with bond thickness. Numerical results indicate that the crack tip stress fields are affected by bond thickness due to the restriction of plastic deformation by the adherends. At the same J level, a higher opening stress was observed in the joint with a smaller bond thickness (h). Beyond the crack tip region, a self-similar stress field can be described by the normalized loading parameter, J/hσ₀. The relationship between J and crack tip opening displacement, δ, is dependent on the bond thickness. The strong dependence of toughness upon bond thickness is a result of the competition between two different fracture mechanisms. For small bond thickness, toughness is linearly proportional to bond thickness due to the high constraint. After reaching a critical bond thickness, the toughness decreases with further increase of bond thickness due to the rapid opening (blunting) of the crack tip with loading. A simple model has been proposed to predict the variation of toughness with bond thickness.     

Fabrication, Sinterability, and Mechanical Properties of Lead Zirconate Titanate/Silver Composites

High-toughness and high-strength lead zirconate titanate (PZT) composites that contain fine silver particles were successfully fabricated at low sintering temperatures. Addition of silver to a PZT matrix did not result in unwanted reaction phases; however, some silver diffused toward the perovskite crystal structure. A small quantity of silver accelerated the sinterability of the PZT composites. The formation of oxygen vacancies due to the partial substitution of silver appeared to enhance the sinterability of the PZT. Fracture toughness depended on the size and degree of sphericity of the silver particles, and SEM observations on crack propagation suggested that the toughening mechanism in the PZT/Ag composites involves crack bridging resulting from the ductile behavior of silver particles. It is proposed that high fracture strength in PZT/1 to 5 vol% Ag composites results from the relaxation of transformation-induced internal stress by the silver particles.     

Effect of Surface Tension on the Toughness of Glass

Mechanical stresses (i.e., surface tension) inherently exist on a general free surface because its atomic structure differs from its bulk counterpart. The effect of surface tension is amplified at a crack tip because of curvature enhancement. An integral equation describing this effect on the toughness of glass is derived and first-order approximations using a weight function technique were made. The qualitative results indicate that the geometry-induced toughening is linearly proportional to surface tension and crack tip curvature and to the square root of crack tip zone size. An illustrative example of a recently observed crack tip in SiO₂ glass is given which shows that toughness is enhanced by ∼3 times the intrinsic K _1C value.     

Simultaneous Enhancement of Fracture Toughness and Unipolar Strain in Pb(Zr,Ti)O3‐ZrO2 Composites Through Composition Adjustment

The influence of second phase zirconia particles on the electrical properties and fracture behavior of various polycrystalline soft Pb(Zr_1?xTi_x)O₃ (PZT) compositions was investigated. PZT composites with yttria‐stabilized tetragonal zirconia particles exhibited enhanced crack resistance in comparison to monolithic compositions, regardless of the PZT composition. The addition of zirconia, however, was found to change the PZT composition through the diffusion of zirconium, resulting in variations in the observed piezoelectric and ferroelectric responses. Through the tailoring of the PZT matrix composition, the large electromechanical response and enhanced fracture toughness could be retained. The variation in both small and large signal properties is contrasted to fracture results and crystal structure changes, as determined by X‐ray diffraction.