Crack opening displacements of Vickers indentation cracks

Vickers indentation cracks are an appropriate tool to determine the crack-tip toughness K_I0 and, possibly, the bridging relation of ceramics with an R-curve behaviour from the total crack opening displacements. Two contributions to the total crack opening displacement field are addressed. First, the residual stresses occurring in the uncracked body are considered and then, the contact stresses generated by preventing crack face penetration are computed. The COD solution resulting from the superposition of residual and contact displacements is given and an analytical expression is provided. Near-tip displacements are represented by the first terms of series expansions. As an example of application, an evaluation of the actual stress intensity factor is presented for a window glass 1 h after Vickers indentation.     

Moving cracks in layered composites

The dynamic behavior of layered composites is intimately associated with inherent flaws or cracks that are induced in the material during loading. Often, one of the dominant cracks may reach a critical size and begins to spread. Whether this process of material separation would lead to global instability or not depends on the nonhomogeneous properties of the composite structure. Because of the complexity of the physical phenomenon involving interaction of stress waves with varying material properties, a three-layered composite model is assumed with a crack moving in the center layer. The material properties of the middle layer differ from those of the surrounding material. Both in-plane extensional and out-of-plane shear loading are considered. Making use of the Galilean transformation and Fourier sine and cosine transforms, the dynamic crack tip stress fields are determined analytically while the dynamic stress intensity factors are evaluated numerically from the standard Fredholm integral equations. The intensity of the local dynamic stresses are found to either increase or decrease with the crack length to layer thickness depending on the relative magnitudes of the adjoining layer material properties. The crack speed tends to amplify the effect of material nonhomogeneity. These results are discussed in terms of the dynamic stress intensity factors and displayed graphically.     

The simultaneous process of filament winding and curing for polymer composites

The simultaneous process of filament winding and curing a composite cylindrical shell is considered. From the macrokinetic point of view it is characterized by the small thickness of the relative effective reaction zone. The thermochemical conditions in manufacturing are governed by the following process variables: speed of winding, initial conversion and temperature of the filament bundle wound, and the heating applied. A thermochemical model is developed for simulation of the temperature and conversion distributions during the process. An approximate solution of the thermochemical model in the form of the constant traveling wave is derived for constant values of process variables and a thermally isolated mandrel. A non-uniform cure stress model of the process is developed for the case of using elastic orthotropic constitutive relations for a composite material. It is found that the thickness of the relative effective reaction zone drastically influences the cure stresses. The dependence of the stress level on the process variables is analyzed.     

Local variations of the dynamic elastic modulus around running cracks

The variation of the dynamic elastic modulus in the immediate vicinity of the tip of the running crack was studied through an iterative procedure, based on the theoretical expressions for the stress-field components and the experimental relation between strain rate and elastic modulus. It was found that the elastic modulus varied strongly around the tip of the crack, both in radial and polar sense. Also it was observed that the polar distribution of the elastic modulus presented clear off-axis extrema in directions that were in good agreement with experimentally measured branching angles, thus indicating a possible relation between these two phenomena.     

Estimation of modulus of elasticity of plastics and wood plastic composites using a Taber stiffness tester

This study measured the modulus of elasticity (MOE) of various plastics and composite materials with a Taber stiffness tester as an alternative to conventional universal testing machines. The proposed approach presents an expedited means to assess MOE for a wide range of plastics and wood plastic composites (WPCs) with various shapes. The Taber stiffness units and the geometry of the samples acted as the basis for the calculation of the MOE. The results showed a high correlation between the MOE calculated from Taber units and that obtained on a universal testing machine (Instron). Concurrently, Taber units showed the potential to assess stiffness of samples with irregular shapes, such as in the case of extruded rods, which exhibit this characteristic.     

考虑孔隙和微裂纹缺陷的 C/ C2SiC编织复合材料等效模量计算

通过观察 C/ C2SiC复合材料组元分布的扫描电子显微镜(SEM)照片 , 获得了 C/ C2SiC复合材料化学气相渗透(CVI)制备过程中产生孔隙和微裂纹的几何信息。在此基础上 , 建立了包含孔隙和微裂纹的 C/ C2SiC微结构有限元模型 , 并利用均匀化等效计算方法预测了平纹编织 C/ C2 SiC复合材料的模量。针对 CVI沉积方式制备的 2组不同的 C/ C2SiC复合材料 , 实验测试与等效计算结果表明 : 基于 SEM照片建立的 C/ C2SiC纤维束和复合材料微结构有限元模型 , 能够反映 CVI工艺制备 C/ C2SiC中孔隙和微裂纹的分布状况; 计算结果与实验数据有良好的一致性 , 数值计算可有效预测 C/ C2SiC编织复合材料的模量。     

Through-the-thickness displacements measurement in laminated composites using electronic speckle photography

This paper describes an application of electronic speckle photography to measurement of through-the-thickness displacements in composites. Purpose is to assess the accuracy of this technique in presence of the strong gradients and rotations at the layer interfaces of these materials. The software for data acquisition and processing was in-home developed. Experimental results quantifying the thickness distribution of in-plane and transverse displacements in laminated beams are reported for some kinds of beams with metallic, polymeric and carbon fibre layers, to assess the influence of different constituent materials and optical properties. The experimental results are compared with the predictions of a theoretical model previously developed by the author, substantiated by the exact elasticity solution. In all the examined cases, electronic speckle photography appeared suited to accurately measure displacements with a magnitude of technical interest.     

Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals

A planar double slip crystal plasticity model is applied to the evaluation of crack tip opening (CTOD) and sliding (CTSD) displacements for microstructurally small stationary cracks under monotonic loading for a material with nominal stress-strain behavior that is representative of a relatively high strength helicopter rotor hub material. Two-dimensional plane strain finite element calculations are presented for CTSD and CTOD of microstructurally small transgranular surface cracks in a polycrystal subjected to monotonic loading. The effects of crack length relative to grain size, orientation distribution of nearest neighbor grains, stress state and stress level are considered for nominal stress levels below the macroscopic yield strength. The CTOD and CTSD are computed for stationary crystallographic surface cracks with various realizations of crystallographic orientations of surrounding grains. It is found that (i) the opening displacement is dominant for remote tension even for crystallographic cracks oriented along the maximum shear plane in the first surface grain, (ii) there is a strong dependence of the CTOD on the proximity to grain boundaries, but lesser dependence of the CTSD, and (iii) that the elastic solutions for CTOD and CTSD are valid below about 30% of the 0.2% offset-defined yield strength.     

The effective Young's modulus of carbon nanotubes in composites

A detailed study has been undertaken of the efficiency of reinforcement in nanocomposites consisting of single-walled carbon nanotubes (SWNTs) in poly(vinyl alcohol) (PVA). Nanocomposite fibers have been prepared by electrospinning and their behavior has been compared with nanocomposite films of the same composition. Stress transfer from the polymer matrix to the nanotubes has been followed from stress-induced Raman band shifts, which are shown to be controlled by both geometric factors such as the angles between the nanotube axis, the stressing direction and the direction of laser polarization, and by finite length effects and bundling. A theory has been developed that takes into account all of these factors and enables the behavior of the different forms of nanocomposite, both fibers and films, to be compared in different polarization configurations. The effective modulus of the SWNTs has been found to be in the range 530-700 GPa which, while being impressive, is lower than the generally accepted value of around 1000 GPa as a result of factors such as finite length effects and nanotube bundling. This value of effective modulus has, however, been shown to be consistent with the contribution of nanotubes to the 20% increase in Young's modulus found for the nanocomposite films with a loading of only 0.2% of SWNTs. Hence a self-consistent method has been developed which enables the efficiency of reinforcement by nanotubes, and potentially other high-aspect-ratio nanoparticles, to be evaluated from stress-induced Raman bands shifts in nanocomposites independent of the specimen geometry and laser polarization configuration.     

The influence of interphase regions on local thermal displacements in composites

Although the exact physical and chemical mechanisms are not clearly understood, it is widely believed that an interphase region with properties that differ from those of the plain matrix is developed near fiber surfaces in polymer matrix composites. The current study involves experimental investigation and theoretical modeling of the influence of the interphase on local thermal displacements. Experimental studies have centered on the development of a scanning microinterferometer for in-situ measurements of thermal displacements in the interphase. Thermal displacement measurements have been successfully made for specimens containing a single carbon fiber embedded in an epoxy matrix. A three-phase composite cylinder model is adopted to predict the thermal displacements of the single fiber specimen. Comparison of the theoretical displacement predictions with the experimental profiles measured by the interferometer indicate that the value of the matrix properties near the fiber surface differs from the value in the bulk resin. The data provide evidence of the existence of a lower glass transition temperature in the interphase.     

Determination of displacements on the surface of 3D flat cracks in an unbounded elastic medium

A procedure for the determination of stress intensity factors of 3D flat cracks is proposed, which uses integral identities for displacements and strains on the crack surface. New formulations of boundary problems of the mathematical theory of linear fracture mechanics have been obtained, which are used to develop finite element models. The unknown functions are nodal displacements on the crack surface. The data given are compared with analytical solutions and results obtained by other methods.     

Crack tip opening and advance displacements of blunted cracks under plane stress

The phenomenon of ductile blunting under plane stress conditions in cracked polycarbonate plates was studied. Because this phenomenon is intimately connected with the amount of crack opening displacement (CTOD) and its analogous phenomenon of crack tip advance displacement (CTAD), a study was undertaken of the mechanism of the development of blunting by evaluating the mode of evolution of CTOD and CTAD in the specimens. As study by scanning electron microscopy is limited to a thin layer of the surface of the specimen, this method is most convenient for studying blunting phenomena under plane-stress conditions. Interesting results were derived from these experiments and the characteristic properties of plane-stress blunting were determined.     

Modelling the Young''s modulus of platelet reinforced thermoplastic sheet composites

Particulate reinforced polymers is a mature field and many models are available to predict the Young's modulus of such composites. However, most existing models have a common flaw; they all predict that the composite modulus equals that of the reinforcing agent when the polymer content approaches zero. This implies, in this limit, a monolithic reinforcement whereas, in fact, it is composed of discrete particles with very little interaction. This is a serious drawback and therefore this study focussed on deriving an improved model for the prediction of the Young's modulus. The porosity of the present samples was correlated with the volume fraction binder and the maximum packing density of the pure reinforcement. A theoretical model for Young's modulus was derived along the lines of the Padawer and Beecher modified Cox model. However, it includes the effect of composite porosity on the composite's mechanical properties. In contrast to other available models, it correctly predicts the loss of material stiffness and strength in the limit of zero binder content. Good agreement was found between the predictions of this model and experimental measurements.     

New insights into the Young's modulus of staggered biological composites

This communication presents a simplified “mechanics-of-materials” approach for describing the mechanics of staggered composite architectures, such as those arising in a variety of biological tissues. This analysis calculates the effective modulus of the bio-composite and provides physical insights into its elastic behavior. Simplified expressions for high- and low-mineralized tissues are then proposed and the effects of the mineral thickness ratio and aspect ratio on the modulus are demonstrated.