Compressive failure of microcracked porous brittle solids

Constitutive equations for porous, brittle solids are developed based on the damage mechanics of elastic materials containing cavities and microcracks. For homogeneous deformation modes, microcrack growth from pores causes changes in the average elastic compliance of the material. Failure criteria in terms of bifurcations of the constitutive paths are established by examining the properties of the evolving tangent stiffness tensor. Limit points as well as localized shear band failure modes are addressed. The influence of moderate levels of lateral stresses is studied for biaxial stress states.     

Defect propagation at a circular interface

In this paper a nonlinear, nonuniform cohesive zone is employed to study the detailed features of quasi-static defect evolution in a simple, planar elastic system consisting of a circular inclusion embedded in an unbounded matrix subject to different remote loading configurations. The inclusion–matrix interface is assumed to be described by Needleman-type force-separation relations characterized by an interface strength, a characteristic force length and a shear stiffness parameter. Interface defects are modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body inclusion displacement, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. For equibiaxial tension, quasi-static defect initiation and propagation occur under increasing remote load. For decreasing characteristic force length, a transition occurs from more or less uniform decohesion along the bond line to propagation of a crack-like defect. In the later case a critical failure load is well defined and interface failure is shown to be defect dominated (brittle decohesion). For interfaces with large characteristic force length, the matrix “lifts off” the inclusion accompanied by a delay in defect propagation (ductile decohesion). The decohesion modes ultimately give rise to a cavity with the inclusion situated within it on the side opposite to the original defect. Results for small characteristic force length show consistency with England’s results for the sharp arc crack on a circular interface (England AH (1966) ASME J Appl Mech 33:637–640) Stress oscillation and contact at the tip of the defect are observed primarily for small characteristic force lengths under extremely small loading. Results for remote tension, compression and pure shear loading are discussed as well. In the final section of the paper the results obtained in the first part are utilized to estimate the plane effective bulk response of a composite containing a dilute distribution of inclusions with randomly oriented interface defects.     

Interfacial cracking of a composite

The interfacial cracking, or debonding, of a composite has been studied both in tension and interlaminar shear, the fracture force being applied parallel to the interfaces in both cases. Application of the energy balance theory of brittle fracture has provided theoretical criteria for debonding failure. These equations have been verified experimentally using polymethylmethacrylate models. There were three conclusions: (1) interfacial cracks can propagate along the direction of the applied force in a theoretically predictable manner; (2) these interfacial cracks must be triggered by flaws, either edge cracks or internal defects; (3) it is wrong to characterise brittle interfacial adhesion by means of an interlaminar shear strength. Instead, the interfacial fracture energy should be used.     

Finite element analysis of micromechanical failure modes in a heterogeneous ceramic material system

A micromechanical model that provides explicit accounts for arbitrary microstructures and arbitrary fracture patterns is developed and used. The approach uses both a constitutive law for the bulk solid constituents and a constitutive law for fracture surfaces. The model is based on a cohesive surface formulation of Xu and Needleman and represents a phenomenological characterization for atomic forces on potential crack/microcrack surfaces. This framework of analysis does not require the use of continuum fracture criteria which assume, for example, the existence of K-fields. Numerical analyses carried out concern failure in the forms of crack propagation and microcrack formation. Actual microstructures of brittle alumina/titanium diboride (Al₂O₃/TiB₂) composites are used. The results demonstrate the effects of microstructure and material inhomogeneities on the selection of failure modes in this material system. For example, the strength of interfaces between the phases is found to significantly influence the failure characteristics. When weak interfacial strength exists, interfacial debonding and microcrack initiation and growth are the principal mode of failure. When strong interfacial strength is derived from material processing, advancement of a dominant crack and crack branching are observed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computational modeling of debonding behavior at the bone/cement interface with experimental validation

Both clinical examinations and in vitro physical experiments have shown that the fixation interfaces of cemented components are actually critical sites affecting the long-term stability and survival of prosthetic implants after implantation. This study aims to investigate the interfacial debonding behavior of bone/cement composite structures and attempts to establish an analysis model for clinical applications involving cemented prosthetic components. The mechanical properties of the bonded interface were characterized by interfacial strength, interfacial stiffness, and fracture toughness; the measured values of tensile strength, shear strength, and fracture toughness were 4.94 MPa, 5.94 MPa, and 0.34 MN/m^3/2, respectively. The measured strengths of the different configurations from this study are in good agreement with the experimental results available in the literature. In addition, we generated a finite element model with the same geometry as that of the experimental specimen used in the fracture test. The extent of interfacial debonding was further determined by means of the surface damage criteria and the fracture characteristics of the interface crack. The finite element model with an elastic interface predicted that the stress intensity factor (SIF) at the bone/cement interface crack varies nonlinearly with the applied load, which shows that the interface disintegrates at the load level, as was measured in the fracture experiments. It was possible to verify that the proposed simulation model was capable of describing the interfacial mechanical behavior of cemented components.     

Ice/metal interfaces: fracture energy and fractography

Results are presented of the fracture tests of ice/metal interfaces in an attempt to utilize fracture mechanics to characterize the failure of ice/solid adhesion. The four-point bending delamination specimen was used to measure the fracture energy of ice/aluminium and ice/steel joints at — 15 °C. The interfacial fracture energy was found to be dependent on ice type and formation procedure of the ice/metal composites. Crack growth was in a manner of asymmetrical bursting, and both cohesive and adhesive failure mechanisms were observed. Although the fracture of ice/metal interfaces was brittle in nature, the evidence of dislocation slip in ice crystals, as revealed by etching and replicating, suggests that microplastic deformations occur in the ice component.     

Extension of fibre bundle models for creep rupture and interface failure

We present two extensions of the classical fibre bundle model to study the creep rupture of heterogeneous materials and the shear failure of glued interfaces of solid blocks. To model creep rupture, we assume that the fibres of a parallel bundle present time dependent behaviour under an external load and fail when the deformation exceeds their local breaking threshold. Assuming global load sharing among fibres, analytical and numerical calculations showed that there exists a critical load below which only partial failure occurs while above which the system fails globally after a finite time. Approaching the critical point from both sides the system exhibits scaling behaviour which implies that creep rupture is analogous to continuous phase transitions. To describe interfacial failure, we model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. In the framework of global load sharing, we obtain analytically the macroscopic constitutive behaviour of the system and describe the microscopic process of the progressive failure of the interface.     

On the failure of a brittle material by high velocity gas jet impact

Failure of brittle solid bodies due to the impingement of a high velocity air jet on the body surface is studied, experimentally and theoretically. Using the linear elastic theory and stress distribution analysis, a general criterion for the failure of brittle materials impacted by a gas jet is derived. Several special cases of jet–solid body interaction including failure of thin and thick layers and cylindrical objects immersed in a crossflow gas stream are investigated and proper material failure criteria are developed. These criteria correlate the minimum jet peak impact pressure (PIP) required to break the material to the material's tensile strength and Poisson's ratio. A series of experiments were performed using a laboratory-scale apparatus. Gypsum cast on steel tubes forming cylindrical samples was used as the model brittle material. Experimental data and high-speed breakup movies are employed to understand the gas jet–solid body interaction and to validate the theoretical criteria developed for the material failure. It is deduced that the failure of cylindrical samples impacted by a gas jet is by the formation and propagation of cracks. However, when the impact jet diameter is small, the cracks cannot propagate, and the material is failed due to localized surface pitting. One of the practical applications of this research is in Kraft recovery boilers, where high velocity supersonic steam jets are employed to remove deposits accumulated on the outer surfaces of the steam tubes.     

Micromechanical modeling of interface damage of metal matrix composites subjected to transverse loading

A three-dimensional finite element micromechanical model was developed to study effects of thermal residual stress, fiber coating and interface bonding on the transverse behavior of a unidirectional SiC/Ti–6Al–4V metal matrix composite (MMC). The presented model includes three phases, i.e. the fiber, coating and matrix, and two distinct interfaces, one between the fiber and coating and the other between coating and matrix. The model can be employed to investigate effects of various bonding levels of the interfaces on the initiation of damage during transverse loading of the composite system. Two different failure criteria, which are combinations of normal and shear stresses across the interfaces, were used to predict the failure of the fiber/coating (f/c) and coating/matrix (c/m) interfaces. Any interface fails as soon as the stress level reaches the interfacial strength. It was shown that in comparison with other interface models the predicted stress–strain curve for damaged interface demonstrates good agreement with experimental results.     

Combination of biological mechanisms for a concept study of a fracture-tolerant bio-inspired ceramic composite material

The biological materials nacre and wood are renowned for their impressive combination of toughness and strength. The key mechanisms of these highly complex structures are crack deflection at weak interfaces, crack bridging, functional gradients and reinforcing elements. These principles were applied to a more fracture-tolerant model material which combined porous stiff ceramic layers, manufactured by freeze casting, infiltrated and bonded by a polymer phase reinforced with fabric layers. In the hybrid composites, crack deflection occurred at the ceramic–fabric interface and the intact fabric layers served as crack-bridging elements. Fabric-reinforced epoxy layers stabilized the fracture behaviour and delayed catastrophic failure of the material. The influence of the different components was analysed by varying the ceramic, fabric and interface properties. More ductile fabrics lead to larger strain to failure and more crack bridging but reduced the composite strength and stiffness after initial cracking. Higher elastic mismatch between the components improved crack deflection and bridging but resulted in deterred load transfer and a lower strength. The stiffness and strength of the ceramic layers influenced the elastic properties of the laminar composite and the initial crack resistance. Flaw tolerance was increased with polymer infiltration. We show with our hybrid ceramic–fabric composite as a bio-inspired concept study how fracture toughness, work of fracture and tolerance for cracking can be tailored when the contributing factors, i.e. the ceramic, the fabric and their interface, are modified.     

Ultrasonic Characterisation of Porous Biomaterials Across Different Frequencies

Abstract:  Mechanical testing is the most common experimental technique to determine elastic stiffness of materials. In case of porous materials, especially such with very high porosity, the determination of material stiffness may be strongly biased by inelastic deformations occurring in the material samples, especially in the vicinity of the load transfer devices, such as loading platens. In contrast, ultrasonic waves propagating through a material generate very small stresses and strains (and also strain rates lying in the 'quasistatic' regime). Thus, they enable the direct determination of the components of elastic stiffness tensors of materials, and also of those with a very high porosity. We shortly revisit from the theoretical basis of continuum (micro)mechanics that, depending on the frequency of the employed acoustical signals, the investigated materials are characterised at different observation scales, e.g. the elasticity of the overall porous medium, or that of the solid matrix inside the material are determined. We here report the elastic properties of biomaterials and biological materials at different length scales, by using ultrasound frequencies ranging from 100 kHz to 20 MHz. We tested isotropic scaffolds for biomedical engineering, made up of porous titanium and two different bioactive glass–ceramics, and we also determined the direction-dependent normal and shear stiffness components of the anisotropic natural composite 'spruce wood'.     

双向耦合地震作用下含软弱层岩质边坡锚固界面剪切作用

为研究地震作用下锚固岩质边坡锚杆-砂浆界面和砂浆-岩体界面上的剪切作用,利用FLAC~(3D)软件构建锚固含软弱层岩质边坡数值模型,对水平向和竖向地震波耦合作用下的全长黏结锚杆锚固边坡两锚固界面上的剪切作用进行了深入研究。研究结果表明:两锚固界面上的剪应力分布很不均匀,界面处于弹性变形阶段时,两峰值剪应力紧邻中性点,随锚固界面脱黏破坏的发展,两峰值剪应力不断地向锚杆两端转移;双向耦合地震波较单向和双向未耦合地震波对锚固界面剪应力影响更为显著。考虑双向地震波耦合作用的锚固边坡抗震设计更为合理。研究结果可为边坡锚固抗震设计提供参考。     

Antiplane shear crack problem in bonded materials with a graded interfacial zone

In this paper the interface crack problem for two elastic half spaces bonded through a nonhomogeneous interfacial zone is considered. It is assumed that the medium is under antiplane shear loading. The problem is solved for two different interfacial zone models that may approximate the actual diffusion bonded materials or homogeneous solids bonded through a functionally gradient material. Extensive results are obtained by varying the stiffness and the interfacial zone thickness to crack length ratios. Also, for various limiting cases the behaviour of the stress intensity factors and the strain energy release rates are studied.     

Shear band formation in polycarbonate-glass bead composites

The shear band formation at glass beads embedded in a polycarbonate matrix subjected to a uniaxial tension has been investigated by microscopic in situ observation. The degree of interfacial adhesion was varied by different glass surface treatments. To gain insight into the three-dimensional stress field requirement for shear band formation, the distributions of several elastic failure criteria around an isolated adhering glass sphere in a polycarbonate matrix have been computed with the aid of finite element analysis. It was found that the mechanism for shear band formation is fundamentally different for adhering and non-adhering glass beads. In the case of excellent interfacial adhesion, the shear bands form near the surface of the bead in regions of maximum principal shear stress and of maximum distortion strain energy. In the case of poor interfacial adhesion, shear band formation is preceded by dewetting along the interface between bead and matrix.     

Effect of interfacial thickness and stiffness on the stress distributions in fibre reinforced cementitious composites

The different microstructure of the fibre–cement interface might result in different failure mechanisms. It is expected that improvement of strength and toughness in fibre-reinforced cementitious composites will depend on their interfacial thickness and stiffness. A three-phase model, subject to a transversely uniform tensile stress, was utilized to investigate the effect of interfacial thickness and stiffness on the stress distributions near the fibre–cement interface and the corresponding failure mechanism. The results suggest that optimum interfacial microstructure of fibre-reinforced cementitious composites can be tailored to obtain a higher strength and toughness. Optimum interfacial thickness and stiffness was evaluated for various reinforcements, including steel, carbon, glass and polypropylene fibres. This revised version was published online in November 2006 with corrections to the Cover Date.     

On Elastic Compliances of Interfacial Cracks

Results for elastic compliances of interfacial cracks — quantities that determine change in the overall elastic compliances of a material due to interfacial cracks — are obtained. Such cracks may develop in composite materials as a result of debonding at inclusion/matrix interfaces or at boundaries between layers in layered materials, for example, at film/substrate interfaces. Our method is based on the thermodynamic formalism developed by Rice (1975) and utilization of the available results for the stress intensity factors (SIFs). Compliance contribution tensors of the rectilinear, circular and penny-shaped interfacial cracks are derived in closed form.     

Numerical implementation of imperfect interfaces

One approach to characterizing interfacial stiffness is to introduce imperfect interfaces that allow displacement discontinuities whose magnitudes depend on interfacial traction and on properties of the interface or interphase region. This work implemented such imperfect interfaces into both finite element analysis and the material point method. The finite element approach defined imperfect interface elements that are compatible with static, linear finite element analysis. The material point method interfaces extended prior contact methods to include interfaces with arbitrary traction-displacement laws. The numerical methods were validated by comparison to new or existing stress transfer models for composites with imperfect interfaces. Some possible experiments for measuring the imperfect interface parameters needed for modeling are discussed.     

超高韧性水泥基复合材料与活性粉末混凝土界面剪切强度试验研究

该研究使用双面剪切试验对500 d长龄期的超高韧性水泥基复合材料(UHTCC)、活性粉末混凝土(RPC)和UHTCC/RPC界面的剪切强度进行了测试,并结合数字图像相关技术对其破坏过程进行了观测。结果表明,UHTCC、RPC和UHTCC/RPC界面均表现出良好的剪切延性,在加载过程中均未发生脆性破坏。此外,改进浇筑工艺和提高粘结界面的粗糙度均能够提高UHTCC/RPC界面剪切强度。将现有的界面剪切强度计算经验公式与试验结果对比发现现有的经验公式无法准确预测UHTCC/RPC的界面剪切强度。该研究建立了UHTCC/RPC界面剪切试验的有限元分析模型,并使用COHESIVE单元模拟界面行为,模拟结果与试验结果吻合较好。     

Simulation of dynamic fracture along solder–pad interfaces using a cohesive zone model

In this paper, dynamic fracture of a single solder joint specimen is numerically simulated using the finite element method. The solder–IMC and IMC–Cu pad interfaces are modeled as cohesive zones. The simulated results show that under pure tensile loading, damage typically starts at the edge of the solder–IMC interface, then moves to IMC–Cu pad interface. Eventual failure is typically a brittle interfacial failure of the IMC–Cu interface.     

Simulation of crack propagation resistance in brittle media of high porosity

Summary The crack propagation resistance through a porous or microstructurally heterogeneous brittle solid with local variability in strength and stiffness has been simulated. Specifically, the simulation probes the behavior of porous brittle materials in the range of porosity less than those of cellular materials and greater than those of microstructures that are in the category of dilute porosity. The simulation plane consists of a triangular network of points interacting with each other through both linear central force springs and bond angle springs, incorporating an appropriate element of a noncentral force contribution. Explicit microstructural details were incorporated into the model and the simulation was first carried out under conditions of uniaxial tensile strain in order to investigate the mechanisms of subcritical damage evolution, leading to quasi-homogeneous fracture. In order to investigate material strength and stiffness variability on the scale of a representative volume element for coherent fracture events in a crack tip stress gradient, the explicit microstructural results were incorporated into a simulation with boundary conditions characteristic of the displacement field of an infinite Mode I crack. To impart some 3D realism to the primarily 2D simulations a special 2D super-element was devised, which incorporated variability information as might be sampled by a crack front in three dimensions. For a given porosity, in general, only small differences were found between nominally diverse microstructures in terms of their tensile toughness, maximum strength and elastic moduli. The strongest dependence of the overall fracture toughness was found to come from the average porosity. The variability in local element strength and stiffness on the scale of the porosity produced highly tortuous crack paths, roughly on the scale of the chosen representative volume element. The tortuosity of the crack was largest where local variability of strength and stiffness was uncorrelated. Examples of microcrack toughening and crack bridging were observed.