Visualization of Impact Damage in Ceramics Using the Edge-On Impact Technique

Projectile impact generates severe fragmentation in ceramics which propagates at high velocities and precedes the penetration of the projectile. The high-speed photographic technique of the Edge-On Impact (EOI) has been developed at the Ernst-Mach-Institute (EMI) in order to visualize dynamic fracture in brittle materials. In a typical EOI test the projectile hits one edge of a specimen and fracture propagation is observed during the first 20 us after impact by means of a Cranz-Schardin highspeed camera. EOI tests allow a characterization of different ceramics by the macroscopic fracture patterns, single crack velocities, and crack front velocities (damage velocities). The phenomenology of damage propagation in several ceramics and a ceramic-metal composite is discussed. The EOI technique is useful for the evaluation of damage models for brittle materials because it enables a direct comparison of model predictions to experimental data obtained during the impact process.     

Effect of interlaminar toughness on the low‐velocity impact damage in composite laminates

Based on the continuum damage mechanics (CDM) and the cohesive zone model (CZM), a numerical analysis method for the evaluation of damage in composite laminates under low‐velocity impact is proposed. The intraply damage including matrix crack and fiber fracture is represented by the CDM which takes into account the progressive failure behavior in the ply, using the damage variable to describe the intraply damage state. The delamination is characterized by a special contact law including the CZM which takes into account the normal crack and the tangential slip. The effect of the interlaminar toughness on the impact damage is investigated, which is as yet seldom discussed in detail. The results reveal that as the interlaminar fracture toughness enhances, the delamination area and the dissipated energy caused by delamination decrease. The contribution of normal crack and tangential slip to delamination is evaluated numerically, and the later one is the dominant delamination type during the impact process. Meanwhile, the numerical prediction has a good agreement with the experimental results. The study is helpful for the optimal design and application of composite laminates, especially for the design of interlaminar toughness according to certain requirements. POLYM. COMPOS. 37:1085–1092, 2016. © 2014 Society of Plastics Engineers     

Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints

The objective of this work is to discuss the adequacy of cohesive and continuum damage models for the prediction of the mechanical behaviour of bonded joints. A cohesive mixed-mode damage model appropriate for ductile adhesives is presented. The double cantilever beam and the end-notched flexure tests are proposed in order to evaluate the cohesive properties of the adhesive as a thin layer under mode I and mode II, respectively. A new data reduction scheme based on the crack equivalent concept is also proposed to overcome crack-monitoring difficulties during propagation in these fracture characterization tests. An inverse method to determine the cohesive parameters of the trapezoidal softening law is discussed. A continuum mixed-mode damage model is developed in order to better simulate the cases where adhesive thickness plays an important role. The model is applied to evaluate the effect of adhesive thickness on fracture characterization of adhesive joints. Some important conclusions about the advantages and drawbacks of cohesive and continuum damage models are reported.     

Modelling Damage and Failure in Adhesive Joints Using A Combined XFEM-Cohesive Element Methodology

In recent years, cohesive elements based on the cohesive zone model (CZM) have been increasingly used within finite element analyses of adhesively bonded joints to predict failure. The cohesive element approach has advantages over fracture mechanics methods in that an initial crack does not have to be incorporated within the model. It is also capable of modelling crack propagation and representing material damage in a process zone ahead of the crack tip. However, the cohesive element approach requires the placement of special elements along the crack path and is, hence, less suited to situations where the exact crack path is not known a priori. The extended finite element method (XFEM) can be used to represent cracking within a finite element and hence removes the requirement to define crack paths or have an initial crack in the structure. In this article, a hybrid XFEM-cohesive element approach is used to model cracking in the fillet area using XFEM where the crack path is not known and then using cohesive elements to model crack and damage progression along the interface. The approach is applied to the case of an aluminium–epoxy single lap joint and is shown to be highly effective.     

Microstructure-based modelling and experimental investigation of crack propagation in glass–alumina functionally graded materials

The aim of the present work was the determination of the fracture mechanisms in glass–alumina functionally graded materials (FGMs). The investigation was performed by means of a combined approach based on microscale computational simulations, which provided for an accurate modelling of the actual FGM microstructure, and experimental analysis. The numerical results proved that microstructural defects, such as pores, deeply influenced the damage evolution. On the contrary, the minimization of the mismatch in the coefficients of thermal expansion of the ingredient materials allowed to obtain low thermal residual stresses, which did not relevantly affect the crack propagation. In order to support the numerical model, microindentation tests were performed on the cross-section of FGM specimens and the experimentally observed crack paths were compared to the computationally predicted ones.     

The mechanical response characteristics of sapphire under dynamic and quasi-static indentation loading

Sapphire is widely used as optical materials and substrate materials due to its excellent physical and chemical properties. The mechanism of crack propagation and fracture damage evolution has important significance for improving the manufacturing quality and application performance of sapphire parts. In this study, dynamic and quasi-static indentation tests have been performed on the c-plane and a-plane of sapphires by Hopkinson pressure bar tester and continuous indentation tester, respectively. The crack propagation path in sapphire has been captured by High-speed camera and the crack velocity has been calculated. The crack propagation and fracture damage evolution has been analyzed based on the fracture morphology of specimen. It was found that the bearing capacity of sapphire is related to the loading velocity, while the crack propagation is affected by the crystal orientation. Under the indentation loading, the cracks in sapphire first propagate steadily, and then the cracks begin to propagate uncontrollably after reaching the critical conditions, where the crack propagation velocity obviously increases, typically from 204?m/s to 1006?m/s (dynamic indentation) or from 0.0032?m/s to 820?m/s (quasi-static indentation). And the crack propagation velocity depends on the loading speed at stable stage. The r-planes of sapphire are weaker than other crystal planes and are prone to crack propagation.     

Fatigue fracture of short-glass-fiber-reinforced poly(vinyl chloride): A crack layer approach

The fatigue behavior and fracture toughness of injection molded short-glass-fiber-reinforced poly(vinyl chloride) (sgfr-PVC) were investigated using the Crack Layer approach and fractography, Fatigue crack propagation (FCP) experiments in single-edge-notched (SEN) specimens were conducted concurrently with microscopic observations. Fracture was observed to propagate as a main crack surrounded by a layer of damage. The magnitude of damage was controlled by the content of glass fiber, which in turn controlled crack reduced acceleration and fracture toughness. FCP behavior was successfully described by the Crack Layer theory, which accounts for the damage associated with crack propagation. In absence of significant interfacial bonding, mechanical fiber/matrix interlocking provided the main resistance to crack propagation. Fiber-induced matrix deformation and fiber pull-out appeared to be the dominant energy absorbing mechanisms.     

Numerical modeling of the carbonization process in the manufacture of carbon/carbon composites

A method for the numerical simulation of the carbonization process is introduced. A general model for the transient analyses of heat and mass transfer together with stress and displacement predictions is constructed using two-dimensional FEM (finite element method) for arbitrary geometry. The established model is applied to the carbonization of a single-phase, homogeneous, isotropic phenolic foam, and an anisotropic, two-phase composite material. A damage model is introduced to account for the development of shrinkage cracks, and a CDM (continuum damage mechanics) model is implemented for the calculation of mechanical property degradation due to crack evolution. The established model is verified by comparison with experimental results, and is applied to various numerical examples.     

An improved model for adhesively bonded DCB joints

An improved analytical model is proposed for characterizing the fracture behavior of an adhesively bonded double cantilever beam joint under Mode I loading. Novel interfacial normal stress distribution function is used with a key parameter c that is determined using continuum mixture theory. In addition to the mechanical and sectional properties of the adherends, crack length, and overlap area, the model also incorporates the adhesive thickness and material properties as well as the crack tip rotation. Model prediction of the fracture toughness of the joint is entered into finite element analysis to simulate crack propagation under peel loading. The effect of various parameters on the joint fracture properties is discussed. Results show that the proposed model provides better correlation with published experimental data.     

Determination of the fracture behaviour of MgO-refractories using multi-cycle wedge splitting test and digital image correlation

Refractories with reduced brittleness show a pronounced deviation from linear elastic behaviour and an enhanced thermal shock resistance. This paper aims to study the influence of microstructure on the fracture behaviour of magnesia refractories. The wedge splitting test(WST), which enables stable crack propagation for quasi-brittle materials, was used to identify the fracture behaviour and evaluate the energy dissipation. The evaluation of the crack lengths of the magnesia and magnesia spinel materials during the entire cyclic WST is based on the localized strain evaluated using the digital image correlation (DIC). A significant fracture process zone develops in the magnesia spinel material. The relationship between the dissipated energy and the actual crack length, which was used to characterize the crack growth resistance, was determined. The refractory materials that showed reduced brittleness consume a small amount of energy for fracture initiation but a large amount of energy for further crack propagation.     

In situ observation of damage nucleation in graphite and carbon/carbon composites

The flexure strength and the fracture toughness at 300 K and 77 K were measured in two isotropic polycrystalline graphites with very different microstructure and in one carbon/carbon composite. In addition, the micromechanisms of damage initiation at the notch tip were examined in situ during the fracture tests through a long focal distance microscope. It was found that the mechanical response of carbon-based materials was insensitive to the effect of cryogenic temperatures. In graphite with coarse microstructure, cracks appeared at very low stresses in various points of an ample region surrounding the notch tip, and damage progressed by their stable crack growth and link up. On the contrary, damage was localized at the notch root in graphite with a fine microstructure. High stresses were necessary to nucleate a single crack, which grew unstably, leading to immediate specimen failure. Damage in carbon/carbon composites was nucleated in the form of matrix cracks around the notch tip, but fiber yarns impeded the crack propagation until the load had increased significantly. This process was repeated several times, leading to a serrated load-deflection curve and to a marked increase in the overall fracture resistance.     

Modeling creep behavior in ceramic matrix composites

In this work, a three-dimensional viscoplasticity formulation with progressive damage is developed and used to investigate the complex time-dependent constituent load transfer and progressive damage behavior in ceramic matrix composites (CMCs) subjected to creep. The viscoplasticity formulation is based on Hill's orthotropic plastic potential, an associative flow rule, and the Norton-Bailey creep power law with Arrhenius temperature dependence. A fracture mechanics-informed isotropic matrix damage model is used to account for CMC brittle matrix damage initiation and propagation, in which two scalar damage variables capture the effects of matrix porosity as well as matrix property degradation due to matrix crack initiation and propagation. The Curtin progressive fiber damage model is utilized to simulate progressive fiber failure. The creep-damage formulation is subsequently implemented as a constitutive model in the generalized method of cells (GMC) micromechanics formulation to simulate time-dependent deformation and material damage under creep loading conditions. The developed framework is used to simulate creep of single fiber SiC/SiC microcomposites. Simulation results are in excellent agreement with experimental and numerical data available in the literature.     

Calibration of cohesive parameters for a castable refractory using 4D tomographic data and realistic crack path from in-situ wedge splitting test

Crack propagation in an alumina castable refractory with mullite-zirconia aggregates was investigated in-situ using a wedge splitting test performed inside a laboratory tomograph. Four-dimensional (i.e., 3D space and time) data from digital volume correlation were used to investigate the influence of a realistic crack path on the simulation of the fracture process. A cohesive law was chosen, since toughening mechanisms were present, and calibrated via finite element model updating. When a straight crack path was assumed instead of the experimental crack path, a 10% higher fracture energy and a 35% higher cohesive strength were calibrated. Although the force alone could be used in the minimized cost function, the kinematic information gives valuable insight into the trustworthiness of the geometrical hypotheses assumed in the finite element model. Such framework can be applied to study nonlinear fracture processes for different materials with complex toughening mechanisms such as crack deflection or branching.     

Effect of Crystallites on Surface Damage and Fracture Behavior of a Glass-Ceramic

A study was conducted of the effect of crystallization on the fracture toughness, strength, and resistance to surface damage of glass-ceramic materials with a range of microstructures obtained by different heat treatments. The hardness indentation method was used as a quantitative tool to simulate mechanical surface damage. In the uncrystallized glass and in the glass-ceramic heat-treated to result in a uniform fine-grained structure, crack size increased monotonically with indentation load. In contrast, in the glass-ceramics heat-treated to result in a microstructure consisting of larger crystallites (a few micrometers) contained within a fine-grained matrix, a discontinuity in the crack size vs load curve presented evidence for crack-pinning at crack sizes which were a small multiple of the intercrystallite spacing. At the position of crack-pinning, the fracture toughness showed a discontinuous increase with increasing crack size that was attributed to crack deflection. The strength of the glass and fine-grained glass-ceramic measured in biaxial flexure decreased monotonically with indentation load. The strength at low values of indenter load of the glass-ceramic heat-treated to yield the coarser crystallites within the fine-grained matrix was independent of indentation load, indicating stable crack propagation prior to fast fracture. At the higher values of indenter load, the coarse-grained glass-ceramics exhibited a monotonic decrease in strength with increasing indentation load. The results of this study indicate that the strengthening observed on crystallization of a glass can be attributed to a combination of a decrease in flaw size achieved at a given mechanical surface treatment, an increase in fracture toughness, and a modification in the mode of crack propagation.     

Influence of the elastic mismatch on the Hertzian cone crack path in ceramic bilayers

Contact damage is a key aspect in the structural integrity of ceramics, particularly ceramic coatings and multilayers that may have an elastic mismatch. An understanding of the critical load and trajectories of the crack produced by contact loads in such materials is valuable to characterize the damage tolerance and improve their reliability. In this work, the Hertzian cone crack initiation and propagation in brittle bilayers has been studied by FEM and verified by experimental observations. It was concluded that the elastic mismatch affects the crack initiation position and critical load for cone cracking. Critical loads are lower in bilayers than in monolithic materials. Cone crack trajectory and the corresponding fracture energy release rate are also affected by the elastic mismatch, which thus influences the damage tolerance of the system.     

Influence of crystal structure on crack propagation under cyclic electric loading in lead–zirconate–titanate

Crack propagation under cyclic electric loading was studied in two non-commercial compositions of lead–zirconate–titanate and compared to earlier results from a commercial composition. These materials were chosen to provide a well-defined variation in crystal structure, ranging from rhombohedral to tetragonal, including a composition from the morphotropic phase boundary. The results are presented in terms of crack propagation as a function of various electric load amplitudes. While the crack propagation rates were of the same order of magnitude in all three compositions, fracture occurred in an either trans- or intergranular manner with crack extension either in the form of a singular crack, a microcrack zone or with extensive secondary cracking. These differences in crack propagation are discussed in the context of different piezoelectric material properties.     

金属基聚合物复合材料短纤维桥接界面强化机理

针对金属基聚合物复合材料易诱发界面剥离损伤失效的共性问题,研究了通过多层复合组装注射成型,在聚合物复合层与粘接层界面形成短纤维桥接,实现复合界面强化。基于内聚力剥离损伤模型,构建了短纤维桥接强化界面剥离裂纹扩展断裂失效过程的模拟仿真技术,模拟建立了界面剥离裂纹快速失稳扩展断裂损伤失效临界载荷—桥接纤维特性—界面剥离断裂韧性（损伤启裂应力T₀和临界应变能释放率G_c）的协同关联理论,诠释了短纤维桥接界面强化机理,提出了预防短纤维桥接强化界面诱发剥离裂纹快速失稳扩展失效的设计准则。结果表明,当桥接纤维密度为20根/mm²,可使其临界载荷增加55.9 %,临界载荷受控于桥接纤维密度、初始预裂纹面积、损伤启裂应力和临界应变能释放率,且与桥接纤维密度、损伤启裂应力和临界应变能释放率呈正关联关系,而与初始预裂纹面积呈负关联关系。     

Crack propagation analysis in composite bonded joints under mixed-mode (I+II) static and fatigue loading: experimental investigation and phenomenological modelling

This paper illustrates the results of an extensive experimental investigation on composite bonded joints under mixed-mode (I+II) static and cyclic loading conditions oriented to understand the influence of the mode mixity condition on the crack propagation resistance at the bondline. The double cantilever beam (DCB), end notch flexure (ENF) and mixed-mode bending (MMB) tests were conducted on pre-cracked samples and both fracture toughness and crack propagation resistance were seen to increase, both for static and fatigue loading, respectively, as the mode II contribution increases. The crack propagation and damage evolution were carefully investigated and documented, and a strong dependence of the propagation mode on the mode mixity was found. Fatigue data under the different loading conditions are then described by a phenomenological model based on the strain energy release rate contributions, which represents a useful engineering tool for preliminary design. After that a damage-based model, developed on the basis of the actual damage mechanisms, is presented in a companion paper.     

Direct numerical simulations on crack formation in ceramic materials under thermal shock by using a non-local fracture model

In this work, a non-local failure model was proposed and implemented into a finite element code. It was then used to simulate the crack evolution in ceramic materials subjected to thermal shock. By using this numerical model, the initiation and propagation of cracks in water quenched ceramic specimens were simulated. The numerical simulations reproduced faithfully the crack patterns in ceramic specimens underwent quenching tests. The periodical and hierarchical characteristics of the crack patterns were accurately predicted. The numerical simulations allow a direct observation on whole the process of crack initiation and growth, which is quite a difficult task in experimental studies. The failure mechanisms and the fracture procedure are discussed according to the numerical results obtained from the simulations. It is shown that the numerical model is simple, robust, accurate and efficient in simulating crack evolution in real structures under thermal shock.     

Predicting subsurface damage in silicon nitride ceramics subjected to rotary ultrasonic assisted face grinding

Silicon nitride is an advanced ceramic used in high performance applications. One of the main problems in machining of brittle materials such as silicon nitride is subsurface damage (SSD). On the other hand, rotary ultrasonic assisted face grinding (RUAFG) is considered as state of the art machining process for brittle and hard to machining materials such as ceramics and optical glasses. In this research, a new study on SSD generation in RUAFG by establishing both ductile deformation and brittle fracture conducted. To achieve this goal, initially single diamond grit cutting force based on Vickers hardness correlation and indentation fracture mechanics established and placed in crack propagation formulas to anticipate SSD. Verification tests performed and average 8% error detected. Moreover, RUAFG depicted up to 30% SSD reduction in comparing to conventional face grinding (CFG). Besides, scanning electron microscope utilized to investigate cracks morphology.