Calculation of Autocatalytic Phase Transformation Zones in Cracked and Uncracked Zirconia Ceramics

Stabilized zirconia ceramics can undergo a stress-induced tetragonal-to-monoclinic phase transformation. A transformation zone with compressive stresses develops at crack tips, leading to an increased fracture toughness which depends on the size and geometry of the transformation zone. In this paper, transformation zones in cracked and uncracked bodies for the case of autocatalytic phase transformation are computed using the weight function method and Eshelby's method. The results are compared with experimentally observed transformation zones.     

R-curve behaviour of 9Ce-TZP zirconia ceramics

Stabilised zirconia ceramics may undergo a stress-induced tetragonal-to-monoclinic phase transformation. At crack tips, a transformation zone with compressive stresses develops, leading to an increase in fracture toughness, which depends on the size and geometry of the transformation zone. The influence of grain size on the R-curve behaviour and transformation zone size is investigated for five 9Ce-TZP zirconia ceramic materials of variable grain size.     

Effect of martensite transformation on fracture behavior of shape memory alloy NiTi in a notched specimen

In this paper, the finite element calculation of the stress–strain distribution in front of a notch tip were carried out for two materials. One is a shape memory alloy NiTi with the stress-induced martensite transformation, and another is a fully transformed martensite NiTi without the transformation. Based on the results obtained, and combining a model of the fracture process zone, effect of martensite transformation on the fracture behavior of the shape memory alloy NiTi in a notched specimen of plane stress state is comparably analyzed. The results show that the martensite transformation increases the load to produce plastic deformation in the transformed martensite at the notch tip and decreases the maximum normal stress and plastic strain near the notch tip, and tends to suspend the crack nucleation and propagation in the fully transformed martensite in front of the notch tip, and thus increases the fracture load and improves the toughness. A quantitative analysis based on the model of the fracture process zone shows that the martensite transformation in the SMA NiTi causes about 47% increase in the apparent fracture toughness.     

Increased fracture toughness of ceramics by energy-dissipative mechanisms

A theoretical model for the fracture toughness of ceramics is developed which takes into account such energy-dissipative mechanisms as stress-induced microcracking or phase transformation. To establish the general fracture criterion, a Griffith-type energy balance is employed. This energy balance comprises the elastic energy, the fracture surface work consumed in the process zone at the crack tip, the energy dissipated in the dissipation zone and the energy stored by residual stresses. Stress-induced microcracking is considered in more detail. An expression for the dependence of the fracture toughness on the density of microcracks, the amount of residual stresses caused by thermal expansion mismatch between the ceramic matrix and small particles embedded in it and the volume fraction of these particles is derived. The final results are used to state conditions necessary for the fracture toughness to be increased. The theory agrees well with experimental results taken from literature (alumina with zirconia particles).     

Crack growth in non-homogeneous transformable ceramics. Part II: Crack deflection

Crack growth in transformation toughened ceramics is studied using a micromechanics based continuum model which accounts for both dilatant and shear transformation strain components. In the computations, the transformable phase is taken to be distributed non-homogeneously in order to model Zirconia Toughened Aluminas that have not been optimally mixed, or Duplex Ceramics in which large zirconia inclusion are dispersed in an untransformable matrix. The small scale transformation problem is solved using a finite element approach. The influence of the transformation strains around the propagating crack on the stress intensity at the crack tip is computed using the transformation domain integral. The crack is modelled as a missing row of mesh elements and crack growth is simulated by nullifying the stiffness of a crack tip element. In contrast to Part I of this paper [1], this part is concerned with cases where the transformable phase is not distributed symmetrically with respect to the x ₁-axis, which causes the crack to deflect from its original crack path due to a local shear stress intensity factor at the crack tip. A computational method is developed which is capable of simulating this, assuming that the deflections from the original crack path are small. A parametric study is carried out of the effect of crack deflection and crack meandering on the overall crack growth resistance.     

陶瓷材料断裂韧性与缺口半径 Ⅱ 断裂韧性估算方法

在陶瓷材料裂纹尖端存在一个断裂过程区，当断裂过程区内平均应力达到断裂强度时，裂纹扩展。本文由理论推导结合实验数据，得到了新断裂过程区的大小是平均晶粒直径的四倍。并由平均应力断裂模型，给出了陶瓷材料断裂韧性和缺口半径及平均晶粒直径之间的关系式，由此关系式可以用宽缺口试件测出的断裂韧性去估算陶瓷材料的本质断裂韧性。     

Transformation toughening behavior of two edge cracks emanating from a circular hole in zirconia ceramics

The growth and fracture toughening behavior of two edge cracks emanating from a circular hole in zirconia toughened ceramics is analyzed in this paper. The supercritical model is adopted in this study to simulate the stress-induced phase transformation. The two edge cracks are of equal length and located symmetrically at the edge of the circular hole. The initial transformation zone is assessed with the model proposed by David. M. Stump. Then the growth of the two edge cracks in supercritical zirconia ceramics is simulated with computational methods. Numerical examples on the enhanced fracture toughness due to phase transformation are given under different material and geometry parameters.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

Stable crack growth,instability, fatigue and fracture of a 50/50 blend of poly(2,6-dimethyl-1,4-phenylene oxide) and polystyrene

The fracture behaviour of a 50/50 blend of poly(2,6-dimethyl-1,4-phenylene oxide)/poly-styrene has been studied. The crack propagation behaviour is strongly influenced by the temperature, crack driving force and the nature of the crack tip craze zone. A fracture map outlining the regions of stable crack growth as a function of temperature, crack velocity and crack driving force has been determined. At high temperatures and low crack growth velocities, stable crack propagation proceeds through a single-craze crack tip damage zone, while at lower temperatures and high crack velocities, a multiple-craze crack tip zone is observed. Corresponding behaviour can be observed under fatigue loading conditions. An instability leading to very high-speed fracture occurs at a critical crack velocity, thus limiting the stable crack propagation regime to lower velocities. The various reported measures of fracture toughness, such as those based on crack initiation, peak load and the onset of crack instability, are discussed.     

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。     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Some recent developments in numerical modelling of fracture toughness in brittle matrix composites

Finite element analysis was used to study the fracture toughening of a ceramic by a stress induced dilatant transformation of second phase particles. The finite element method was based on a continuum theory which modelled the composite as subcritical material. Transient crack growth was simulated in the finite element mesh by a nodal release technique. The crack's remote tensile opening load was adjusted to maintain the near-tip energy release rate at the level necessary for crack advance. The transformation zone surrounding the crack developed as the crack propagated through the composite. Resistance curves were computed from the analysis; and the results show that during crack advance maximum toughness is achieved before a steady state is reached. The toughening effect of a crack-bridging ductile phase in a brittle material may be predicted if ligament deformation is characterized. A plastically deforming ligament constrained by surrounding elastic matrix material is modelled using finite elements and the relevant toughness enhancement information extracted. Comparison is made to model experiments as well as to toughness measured for technologically important materials. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.     

氮化硼纳米管增强氮化硅复合材料的裂纹扩展阻力行为

用氮化硼纳米管(BNNT)增强氮化硅(Si₃N₄)陶瓷制备了BNNT/Si₃N₄复合材料, 利用三点弯曲强度及单边切口梁(SENB)法测定了BNNT/Si₃N₄复合材料的弯曲强度和断裂韧性。通过SEM观察了BNNT/Si₃N₄复合材料微观形貌。基于BNNT增强Si₃N₄陶瓷复合材料的裂纹扩展阻力计算公式, 构建了BNNT对Si₃N₄陶瓷裂纹屏蔽区的裂纹扩展阻力的数学模型。用该模型的计算结果与Si₃N₄陶瓷的裂纹扩展阻力进行了对比。结果表明: BNNT/Si₃N₄复合材料的弯曲强度和断裂韧性明显高于Si₃N₄陶瓷, 说明BNNT对Si₃N₄陶瓷的裂纹扩展有阻力作用, 摩擦拔出是Si₃N₄陶瓷抗裂纹扩展能力提高的主要原因; BNNT对Si₃N₄陶瓷有明显的升值阻力曲线行为。通过有限元模拟裂纹尖端应力分布, 发现BNNT使Si₃N₄陶瓷裂纹尖端的最大应力转移到纳米管上, 而且BNNT降低了Si₃N₄陶瓷裂纹尖端的应力, 对Si₃N₄陶瓷尖端的裂纹有屏蔽作用, 从而提高了Si₃N₄陶瓷的裂纹扩展阻力。     

原奥氏体晶粒尺寸对珠光体钢组织及韧性的影响

探索了奥氏体晶粒尺寸对珠光体等温转变组织特征以及对韧性性能的影响规律.研究表明,在相同等温转变温度下,珠光体片层间距无明显变化,随奥氏体晶粒尺寸的增加,先共析铁素体量减少而珠光体团尺寸增加.珠光体断裂韧性受控于裂纹前沿塑性影响区尺寸(1～2)δc,其中δc为临界裂纹张开位移,当原奥氏体晶粒大于(1～2)δc时,裂纹扩展阻力主要来自穿越珠光体片层α、θ相的颈缩、破断.当原奥氏体晶粒尺寸接近或小于(1～2)δc时,裂纹主要沿晶界、珠光体团界、α+θ片层界面扩展,通过扩展路径发生多次弯折消耗能量,随原奥氏体晶粒尺寸增加,准静态断裂韧度J变化幅度较小.而冲击韧性缺口前沿塑性影响区远大于原奥氏体晶粒,大角度晶界将促使裂纹的转折而提高扩展阻力,提高裂纹前沿塑性区大角度晶界密度有利于提高冲击功,冲击韧性A随晶粒尺寸的增加显著下降.     

Computational analysis of dynamically propagating cracks in axisymmetric solids

Dynamic crack propagation behavior in axisymmetric solids is investigated using an effective computational procedure. First, an accurate method to extract energy release rate of a dynamically propagating crack from finite element solutions is formulated for axisymmetric geometries. The method is applied to an analysis of a radially growing circular crack under remote tension in an infinite medium. The computed dynamic energy release rate shows an excellent agreement with the exact solution. Next, we have developed an iterative technique to propagate a crack whose velocity history is initially unknown. With the iterative procedure, the crack propagates according to a condition specified by a dynamic fracture criterion. At each increment of crack growth, an optimum velocity at which the crack growth condition satisfies is obtained by the iterative scheme. This procedure requires no artificial input or no preset crack tip speed in a simulation study. The iterative scheme is employed in a dynamic fracture analysis of ceramics. The computational analysis is carried out for simulation of fracture experiments using circumferentially notched round bars. In the test, a ceramic specimen is subjected to tensile stress wave loading and after crack growth initiation, the external crack propagates to tear the specimen. The computational simulation is carried out for the entire fracture process including the crack growth initiation and the dynamic propagation. The iterative procedure enables us to predict the crack tip velocity which is unmeasurable in the experiment. Suitabilities of proposed fracture toughness criteria for the ceramics are investigated by comparing measured and computed transmitted pulses through the uncracked ligament. This study proves the usefulness of the computational procedures for dynamic fracture analysis. It is most effective in characterizing dynamic fracture toughness where determination of every relevant parameter is difficult in the experiments.     

Failure prediction in toughened epoxy resins

In order to improve the damage tolerance of composites and the performance of adhesives, one of the methods being considered is toughened or modified epoxy resins. The modifiers which are commonly used are CTBN rubber and inorganic fillers. A major toughening mechanism causing the increased toughness is the shear deformation process occurring near the crack tip. The effect of such a deformation process is to blunt the crack tip and increase the size of the plastic zone. Several models are available to predict the toughness on the basis of plastic zone size, crack tip opening displacement or crack tip radius, but these are only applicable to Mode I crack extension. Also, most of these approaches use only one stress component which is normal to the crack plane to predict the fracture toughness. The present paper reviews the existing models and suggests a criterion based on the phenomenological approach to failure in order to study the yielding and fracture toughness behavior of both unmodified and modified epoxies. The proposed yield and fracture criteria give predictions in good agreement with experimental results.     

Fracture characteristics of Al/zircon particulate composites

A study has been made of the effects of volume fraction and size of zircon particulates on fracture toughness and micromechanisms of fracture in Al/zircon particulate composites. The composites are prepared by a liquid metallurgy technique using volume fractions of zircon in the range 0·06–0·18 and particulate sizes between 75 and 250 μm. The study was conducted on composites in the cast and the forged conditions. The experimental programme included a particle size distribution study, tensile tests, fracture mechanics tests leading to J_1c and crack tip opening displacement evaluation, fractographic investigations, etc. The process zone size at the crack tip was evaluated from crack tip stresses and strains, and compared with the interparticle spacing and particle diameter in order to understand the micromechanics of cracking. The Al/zircon composites were compared with Al/graphite composites in terms of strength and fracture toughness as a function of volume fraction of the filler phase, and regions of optimum performance were identified.     

Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.